Stagflationary Stock Returns

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Stagflationary Stock Returns Ben Knox, Yannick Timmer 2025-056 Please cite this paper as: Knox, Ben, and Yannick Timmer (2025). “Stagflationary Stock Returns,” Finance and Economics Discussion Series 2025-056. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.056. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

∗ Stagflationary Stock Returns † ‡ Ben Knox Yannick Timmer March 14, 2025 Abstract We study investors’ perceptions of inflation through the lens of a high-frequency event study, documenting they have a stagflationary view of the world. In response to higher-than-expected inflation, investors expect firms’ nominal cash flows to remain stagnant while discount rates increase, resulting in lower stock prices. Both the equity risk premium and nominal risk-free yields rise, but longer-term real yields remain unchanged. Consistent with investors interpreting inflation as a cost shock, investors expect firms with low market power to suffer larger declines in cash flows. Cash flow expectationsofequityinvestorsarealignedwiththoseofprofessionalearningsanalysts. JEL Codes: G12, E31, E44, L11 Keywords: Inflation, Stock Returns, Stagnant Cash Flows, Market Power ∗This version: March 14, 2025. Most recent version: here. We are grateful to our discussants Isha Agrawal,KristleCortes,FrancescoD’Acunto,EleonoraGranziera,PreeteshKantak,LifangLi,andGustavo Suarez,aswellasMarkusBrunnermeier,FernandoDuarte,MarkusIbert,LassePedersen,BrunoPellegrino, AndresSchneider,AnnetteVissing-Jorgensen,MichaelWeber,andconferenceparticipantsattheAFA2024, SFS Calvacade 2024, CEPR New Challenges in Monetary Economics & Macro Finance conference, HEC- McGill Winter Finance Conference, Bank of Canada-University of Toronto Conference on “The Return of High Inflation: Challenges for Monetary Policy”, FRB Macro-Finance Conference, BSE Summer Forum Workshop on Financial Shocks, Channels, and Macro Outcomes, the CEMLA Workshop on “Inflation, Expectations, and Forecasts”, Australasian Finance & Banking Conference, and the 2023 Sydney Banking and Financial Stability Conference for useful comments. We thank Diego Silva and John Schindler for excellentresearchassistance. Theviewsexpressedinthepaperarethoseoftheauthorsanddonotnecessarily represent the views of the Federal Reserve Board or the Federal Reserve System. †Federal Reserve Board. Email: ben.knox@frb.gov ‡Federal Reserve Board. Email: yannick.timmer@frb.gov 1

1 Introduction The recent inflationary episode has renewed interest in understanding how inflation affects firms and the economy more broadly. Households and firms generally dislike inflation (Shiller, 1997; Stantcheva, 2024) and often hold a stagflationary view of the world, associating inflation with low growth (Candia, Coibion and Gorodnichenko, 2023). How do financial market participants— considered to be more sophisticated agents with “skin in the game”—view the macroeconomic implications of inflation? Do they share the perception of households and firms, or do they take a more demand-side-driven view of inflation? Investors’ perspectives are crucial to understand as they determine asset prices, which in turn affect the cost and allocation of capital in the economy, as well as measures of inflation expectations. Moreover, rich data availability across firms and asset classes allows us to answer these questions using a high-frequency approach around inflationary news and shed light on the channel driving those beliefs. We show that investors have a stagflationary view of the world. Following inflationary news, investors expect firms’ nominal cash flows to remain stagnant, while inflation expectations and the equity risk premium increase, resulting in lower stock prices. Nominal yields also increase, albeit modestly, driven by inflation compensation rather than real yields. In fact, real yields at policy-sensitive maturities decline. Investors therefore seem to reject a Taylor rule response to inflationary news, suggesting they may not consider inflation as demand-driven, which would necessitate a tighter monetary policy stance. Indeed, one way to rationalize this stagflationary view is that investors interpret inflationary news as supply shocks that increase marginal costs. Canonical models of imperfect competition predict that firms with low market power suffer larger declines in their cash flows in response to inflationary pressures driven by marginal costs. We provide empirical evidence consistent with this prediction of the cost shock hypothesis: Market power shields firms from stagflationary stock returns, with investors expecting high market power firms to generate a relative increase in their cash flows. We first document that the overall stock market is adversely affected by inflationary news— defined as the difference between the inflation release and the median forecast—and that negative returns persist for multiple days. Under the present value formula of the equity price, unexpected stockreturnsmustbeduetochangesininvestors’expectationsoffuturedividends(cashflownews) or future returns (discount rate news). Nominal interest rates increase with expected inflation (Fisher, 1930), but if stocks’ cash flows are real assets, as conventional wisdom suggests, then nominalexpectedcashflowsshouldalsoincreasewithinflation. Thenegativestockreturnsfollowing inflationary news must therefore stem from a combination of declining expectations of future real cash flows and increases in real discount rates, where the latter can occur via increases in investor expectations of future real risk-free yields or because of an increase in the equity risk premium. To disentangle these three stock return components—cash flow, yield curve, and equity risk premium— we build on Knox and Vissing-Jorgensen (2024), who argue that in modern financial 1

markets, rich information about the risk-free yield curve and the equity risk premium (via equity option prices) is observable. This allows a decomposition of stock returns into components using the price changes of other financial instruments. The benefit of the observables-based stock decomposition approach is that the discount rate inputs are forward-looking and are also available in real-time at a high frequency. These latter properties make the approach particularly well suited for implementation in an event-study setting such as ours, as compared to traditional vector autoregression (VAR)-based return decomposition methodologies (Campbell, 1991). Before turning to the full return decomposition results, we study how observable discount rates and direct measures of investor cash flow expectations each respond to inflationary news. In their own right, these variables shed light on investors’ perception of the economic implications of inflation. Moreover, they qualitatively inform us about the drivers of stock returns, which we will later quantify. Westartbystudyinghowyieldsacrossthetermstructurerespondtoinflationarynews. Wefind, unsurprisingly,thatnominalinterestratesincreaseinresponsetoinflationarynews. However,when decomposingnominalinterestratesintorealinterestratesandinflationcompensation, weattribute the entire rise in nominal yields to inflation compensation rather than to an increase in real interest rates. This result is in stark contrast to monetary policy days, during which real yields instead drivenominalyields(HansonandStein,2015;NakamuraandSteinsson,2018;NagelandXu,2024). In fact, at policy-sensitive maturities such as the two-year, real yields even decline in response to inflationary news. This can be rationalized by investors expecting inflation to be supply-driven and to contract output. In response to a supply-driven increase in inflation, investors may expect the central bank to look through the rise in prices, as it can only control demand. Importantly, these yield curve findings challenge the notion that inflationary news days proxy monetary policy days for financial markets, with asset markets driven solely by the expected response of monetary policy to inflationary news. Instead, we find strong evidence from the yield curve that inflationary news days are distinct from monetary days and that factors beyond just monetary policy drive asset markets. Unchanged long-dated real yields in response to inflationary news also imply that the negative stock returns must come from either (or both) declining real cash flow expectations or an increasing equity risk premium, which immediately reveals a negative interpretation of inflationary news for the marginal equity investor. We next study the equity risk premium around inflationary news directly, using the Martin (2017) equity risk premium that is calculated from S&P 500 option prices at the daily level. With thismeasure,wefindevidencethattheequityriskpremiumstronglyincreasesfollowinginflationary news.1 The effect of inflationary news on the equity risk premium is ambiguous ex-ante, as it 1While the Martin measure of the equity risk premium is theoretically a lower bound, Martin (2017) and Knox and Vissing-Jorgensen (2024) provide empirical evidence that the bound is approximately tight. Knox and Vissing-Jorgensen (2024) also provides theoretical evidence that changes in the observed equity risk premium will likely be a lower bound on changes in the true equity risk premium. To the extent the lower bound is not exact, our approach will understate the already-large risk premium increases observed with inflationary news. 2

depends on the correlation between inflation with economic activity and the asset’s cash flows. If inflation (deflation) is associated with bad states of the world, assets that have low real payouts in inflationary (deflationary) times are relatively undesirable and command higher risk premiums. This intuition is embedded in many asset pricing models that explicitly consider the implications of inflation for time-varying risk premiums, such as those with time-varying disaster risk (Gabaix, 2008), long-run risk (Bansal and Shaliastovich, 2013), or risk aversion (Campbell et al., 2020). Therefore, through the lens of this broad range of models, a rising equity risk premium with inflationary news is indicative of investors’ believing that the real cash flows of equities are lower in inflationary times. Investors do not generally seem to view high inflation as being the result of strong economic activity when real cash flows would be high. Lastly, we aim to study the role of the expected cash flows for stock returns around inflationary news, but data limitations make the cash flow component the most difficult to study. Dividend futuresprovideadirectmeasureofinvestors’risk-neutralexpectationsofcashflowsontheaggregate stock market (Gormsen and Koijen, 2020) but are only available in a short sample that begins in 2016. As an alternative, we also use earnings expectations of professional forecasters (De La O and Myers, 2021; Bordalo et al., 2023), which are available at lower frequencies. With either measure of cash flow expectations, we find no evidence that higher-than-expected inflation is associated with an expectation of higher nominal earnings. Taken at face value, these nonresults imply that real earnings expectations have decreased because of the higher price level and increases in inflation expectations. To address the challenge of obtaining the cash flow component over a longer time series and at a daily frequency, we formally decompose stock returns into a yield curve, an equity risk premium, and a cash flow return component. This also allows us to quantify the impact of each return component specifically. We first compute the yield curve component of stock returns, which is defined as the weighted average of changes in interest rates across yield curve maturities, where the weights are the discounted value of dividend payments on the stock market for each corresponding maturity. Intuitively, later dividend payments have smaller present value weights in the stock market, as they are discounted more heavily than near-term dividend payments, and thus changes in discount rates at these maturities matter less for the stock market valuation. Nevertheless, as stock market cash flows are paid to perpetuity, the stock market is a long-duration asset, and its price is highly sensitive to changes in long-maturity yields (van Binsbergen, 2020). We next compute the equity risk premium and cash flow return component from a two-stage approach. First, we adjust returns for the observed yield curve return, and, second, we regress the yield-adjusted return component on changes in the observed equity risk premium. The regressionfitted value provides our equity risk premium return component. By the definition of the present value formula, once the discount rate component of stock returns is accounted for, the remainder is attributed to the cash flow return component. This component captures stock returns due to changes in investors’ expectations of future cash flows. Those can be nominal or real cash flow 3

expectations, depending on whether we implement the yield curve return component using nominal or real yields. With three stock return components available, we then regress each return component on inflationary news separately. Following a one percentage point inflation surprise, we observe a 2.75 percent five-day negative nominal return on the stock market, of which we attribute negative 2.51 percentage points to an increasing equity risk premium, negative 0.49 percentage points to increasing nominal yields, and a small and insignificant positive 0.25 percentage points to increasing nominal cash flow expectations. Real stock prices decline even more. Adjusting for the higher price level, the stock market declines by 3.75 percent in real terms—we attribute 2.17 percentage points of the decline to an increasing equity risk premium, and 2.20 percent points to declining real cash flow expectations. As real yields decline slightly, they even contribute a positive 0.62 percentage points to stock returns. The results from the return decomposition analysis confirm the key takeaway from the dividend futures and earnings expectations data: Nominal cash flow expectations are unchanged following inflationary news, with real cash flow expectations declining significantly. We perform a variety of validation exercises for our residual cash flow component. First, we show that our cash flow estimates from the decomposition approach are strongly correlated with the more direct data from dividend futures and analysts’ earnings expectations. Second, we analyze the impact of economic activity surprises on our nominal cash flow component. We find that investors revise up their expectations of nominal cash flows when economic activity surprises to the upside, i.e. when more jobs than expected were added to the economy, as economic theory would predict.2 While there is variation in the aggregate stock return response to economic activity across the business cycle due to variation in the expected response from the central bank (Boyd et al., 2005; Elenev et al., 2024; Bauer et al., 2022), our cash flow component explicitly controls for this channel by removing the discount rate component of stock returns, and allows us to document a robust positive response of cash flow expectations to positive economic activity news. Our baseline result that investors hold a stagflationary cash flow view in respect to inflationary news represents an average estimate that could potentially vary significantly over time and with the state of the economy. To test for this possibility, we estimate 5-year rolling windows over our entire sample period and find that in 89% of those windows, investors expect real cash flows to decline with inflationary news. When testing for state-dependence, we do not find evidence that observable states of the economy are systematically correlated with the responsiveness of the stock market to inflationary surprises.3 These results suggest that stock market investors consistently take a stagflationary view when observing inflationary news in our empirical setting. 2We view this exercise as a reverse placebo test. A natural concern with our null finding that nominal cash flows do not increase with inflationary news is that the cash flow component has measurement error and does not change even as investors’ true cash flow expectations do. The idea is therefore to test the cash flow component in an alternative setting where the null is expected to be rejected. 3We use a battery of observable variables to test for state dependence that is designed to proxy for a variety of factors including (but not limited to) if the economy is driven by demand or supply shocks and the perceived responsiveness of monetary policy to inflationary news. 4

Indeed,throughoutthesampleweconsistentlyfindanegativecorrelationbetweentherespective responses of stock prices and nominal yields to inflationary news, a stock–bond correlation that is often associated with supply shock news (Cieslak and Pflueger, 2023).4 At first impression, it may be surprising that we observe this even in times when bond yields generally moved in the same direction as stock prices and economic activity was considered to be demand-driven, i.e. during the post-GFC period. However, it is possible to reconcile these findings through a simple AS-AD framework. In an environment in which the aggregate supply curve is relatively flat, aggregate demand shifts have a large effect on real output but the response in prices is limited, with the latter effect consistent with a flat Phillips curve. In addition, if the aggregate demand curve is steeper than the supply curve, price changes would be driven by aggregate supply shifts.5 This wouldrationalizeaneconomyinwhicheconomicactivityisdemand-drivenwhileinflationissupplydriven. Consistently, inthepost-GFCperiodtheeconomywasbelowpotentialandthusarelatively flat supply curve would be expected. During those times, inflation consistently surprised to the downside,potentiallyduetopositivesupplyshocks,e.g. thosestemmingfromtradeandtechnology. That said, a caveat to leveraging inflation surprises around CPI announcement days to infer investors’ perceptions of inflation is that investors also receive inflation-related information from other macroeconomic shock events, such as oil price shocks, FOMC meetings, or labor market announcements. Thisraiseswhetherinvestorsconsistentlyinterpretinflationasstemmingfromsupply shocks outside CPI announcements, or if they solely consider CPI forecast errors as supply-driven. Addressing this question is challenging due to the endogenous nature of inflation developments, where inflationary news is often intertwined with broader economic updates. Our approach therefore aligns with the literature focusing on monetary policy shocks rather than systematic changes in monetary policy, where disentangling the distinct effects of shocks versus systematic changes poses similar challenges. Focusing on CPI announcement days offers significant advantages, particularly in mitigating endogeneity concerns. By isolating the impact of unanticipated inflation surprises, our event-study framework minimizes biases from the simultaneous occurrence of other macroeconomic shocks. One potential explanation for why the marginal investor adopts a stagflationary view could come from the belief that an inflation surprise is a marginal cost shock. In standard industrial organization models with imperfect competition (Tirole, 1989), we show that increases in marginal costs are associated with a decline in firm profits and, crucially, the key determinant of the changes in firms’ profits depends on firms’ demand elasticity—i.e., their market power. Firms with more market power, and lower demand elasticity, see their profitability decline less in response to an increase in marginal costs. We test this hypothesis from canonical models of imperfect competition by leveraging cross- 4This correlation can also be characterized as suggesting monetary policy news (Cieslak and Schrimpf, 2019; Cieslak and Pang, 2021), but as discussed above inflationary news do not proxy for monetary policy. 5A steep demand curve is consistent with high aggregate market power, which has been documented by Philippon (2019) and De Loecker et al. (2020) among others. 5

sectional variation in stock prices and earnings expectations across the firms’ market power distribution. Market power mitigates the negative cash flow expectations of investors in response to inflationary shocks. This test further isolates the impact through cash flow expectations and sheds light on the channel behind the negative stock returns around inflationary news. Leveraging cross-sectional heterogeneity across firms also allows us to control for various time-varying factors that could be correlated with confounding factors in the time series. Our main measure of market power is based on estimating firms’ markup using a production approach that follows De Loecker and Warzynski (2012) and De Loecker, Eeckhout and Unger (2020). Market power is defined as a firm’s ability to set their product price above marginal costs and, hence, face a less elastic demand curve (Syverson, 2019), as in canonical models of imperfect competition. We estimate these firm-level markups using Compustat data with a production function approach, under which the markup of a firm can be defined as sales over the cost of goods sold multiplied by the output elasticity of inputs. As an alternative market power measure, we use the profit-cost elasticity from a network oligopoly demand system based on Pellegrino (2024). Equippedwithourmeasureofmarketpower,westudytheassetpricingimplicationsinresponse toinflationarynewsacrossthefirmdistribution. Westartbysplittingfirmsintohighvs. lowmarket power firms and inspect their stock price response to inflationary news. Consistent with our simple framework in which inflationary news are seen as a marginal cost shock, firms with low markups see a decline in their stock price of around 3.9 percent in response to a one percentage point higherthan-expected inflation, as firms at the upper quarter of the markup distribution see a statistically insignificant decline of 1.2 percent decline in their stock price in response to a one percentage point higher-than-expected inflation. Wenextestimatethedifferentialresponseoffirmswithmoremarketpower. Weuseanempirical specificationthatallowsustocontrolforobservedandunobservedtime-variantfactorsacrossfirms, including firm balance sheet characteristics, their loadings on Fama and French (1993) risk-factor portfolios, and time-variant industry effects. We first show that firms with a differential degree of market power exhibit statistically indistinguishable stock returns and, hence, no differential pretrendinreturnsbeforetheannouncementofinflation. Oncehigher-than-expectedinflationdataare released, firmswithalargerdegreeofmarketpowerstatisticallyandeconomicallyoutperformthose with higher demand elasticity, as predicted by the model. Economically, a one standard deviation larger degree of market power increases the stock return by 0.2 percentage point in response to a one percentage point inflationary shock. Adding firm-level controls only changes the effect of market power very marginally, suggesting that other observed and unobserved heterogeneity is not driving the effect of market power. The relatively better performance of firms with market power could again be attributed to their differential sensitivities with respect to changes in interest rates or the risk premium. For instance, if interest rates rise in response to higher inflation and firms with market power are less sensitive to increases in interest rates—e.g., because their cash flows are nearer in the future than 6

those with less market power and, hence, are discounted less strongly—their stock response may be weaker. Moreover, firms across the market power (Liu et al., 2022; Kroen et al., 2021), leverage (Ottonello and Winberry, 2020), or tangibility (D¨ottling and Ratnovski, 2023) distribution may exhibit differential sensitivities of cash flows themselves to the interest rate environment other than through a cash flow discounting channel. The differential response of firm returns to inflation surprises may therefore be mediated through an increase in nominal interest rates, potentially due to changes in monetary policy expectations, rather than real cash flow expectations directly related to the effect of inflation and market power. To test which component of stock returns is responsible for the differential response of stock prices around inflationary news, we propose a new firm-level stock return decomposition, in a similar spirit as for aggregate stock returns in Knox and Vissing-Jorgensen (2024). This allows us to extract the cash flow component of variation in the cross-section of stock returns. This time, we interact firm characteristics—such as markups, leverage, and tangibility—with changes in the observable discount rate and extract a residual of firm stock returns that we again interpret as a real cash flow component of stock returns. This approach allows us not only to control for differential sensitivities of firm stock returns to interest rates due to cash flow discounting, but also for many other economic mechanisms through which changes in discount rates impact firms’ cash flows. Hence, we can isolate the direct effect of inflationary news on expected cash flows across the markup distribution. Consistent with a stagflationary view of the world, we find that, after inflationary news, real cash flow expectations decline notably for firms without substantial market power. In sharp contrast, when focusing only on firms at the top quartile of the market power distribution, we do not find that investors expect declining real cash flows for those firms. We corroborate our findings by studying firm-level analyst earnings expectations around inflation announcements. On average, analysts expect nominal earnings to remain stagnant following inflationary news, implying expectations of real declining cash flows with higher-than-expected inflation. One concern is that earnings expectations are slow-moving and may generally not move to economic activity. We therefore conduct a “reverse” placebo test, where we show that surprises to economic activity are associated with upward revisions in earnings expectations, mitigating the concern that our non-results stem from simply slow-moving changes. When differentiating between firms with varying degrees of market power, consistently with the stock price responses, we find that analysts expect firms with more market power to increase their earnings more with inflationary news than their counterparts. The rest of the paper is organized as follows. In section 2 we discuss the related literature. In section 3 we present the data. In section 4 we lay out the methodology for the stock return decomposition. In section 5 we describe the empirical strategy. In section 6 we present the results. In section 7 we conclude. 7

2 Literature Ourpaperrelatestotheliteratureonhowdifferenteconomicagentsviewtheeconomicimplications ofinflation. Alargeliteraturestudieshowinflationexpectationsaffecthouseholdchoices(D’Acunto et al., 2023; Bachmann et al., 2015; Andre et al., 2022; Coibion et al., 2022, 2023, 2024), their trading behavior (Schnorpfeil, Weber and Hackethal, 2024), and firm decisions (Coibion et al., 2018, 2020) and suggests that both households and firms often associate higher inflation with worse economic outcomes (Candia et al., 2023).6 While understanding households and firms is of first order importance as these agents ultimately make real decisions in the economy, in this paper we instead infer investors’ perceptions of inflationary news. Studying their views is also of crucial importance and has several advantages. First, unlike survey participants, investors’ actions have monetary incentives, i.e., they have “skin in the game”, potentially providing more accurate and informed reflections of expectations. Second, their views are available in high frequency, which we leverageforidentificationpurposes, andforthecrosssectionoffirms, whichweexploittoshedlight on the channel. Third, investors determine asset prices, which in turn affect the cost and allocation of capital in the economy, as well as measures of inflation expectations. A related strand of literature studies the consequences of higher inflation for the real economy. Brunnermeier et al. (2023) show that the German hyperinflation of 1919 to 1923 led to a large reductioninrealdebtburdensandbankruptcies. AgarwalandBaron(2024)rationalizestagflationary effects through a disintermediation channel by showing that banks, which were more exposed to inflation, reduced lending more during the 1977 inflation shock.7 Drechsler et al. (2022) argue that stagflationary episodes can be partly attributed to negative credit supply shocks. In comparison, we show that the marginal stock market investor has a stagflationary view, as they see inflation as a supply-driven cost shock that reduces firms’ profits. Instead of exploring the heterogeneity across firms in terms of their debt (as in Brunnermeier et al. (2023) and Bhamra et al. (2023)), we explore firms’ outcomes across the market power distribution to directly test the supply-driven cost channel of inflation. To do so, we exploit asset price movements around inflation data releases, which relates our paper to a broader literature studying macroeconomic announcements more broadly (Beechey and Wright,2009;Gu¨rkaynaketal.,2010a;Bauer,2015;Gilbertetal.,2017;Lawetal.,2018;Gurkaynak et al., 2020; Boehm and Kroner, 2023; Kroner, 2023). In contrast to this literature, we focus on inflation surprises and study responses across asset classes—equities, nominal and inflationprotected Treasuries, inflation swaps, equity options, and dividend futures—as well as firms. A long literature studies the negative correlation between inflation and equity prices (Fama and Schwert, 1977; Firth, 1979; Fama, 1981; Sharpe, 2002; Gourio and Ngo, 2020; Katz et al., 2017; Fang et al., 2022; De la O and Myers, 2024). One leading explanation of the negative correlation 6See Weber et al. (2022) (page 177–180) for a review of the literature. 7Corhay and Tong (2021) study the asset pricing effects of inflation and the role of the financial intermediation sector. 8

is money illusion (Modigliani and Cohn, 1979; Summers, 1980) under which investors incorrectly discountrealcashflowswithnominaldiscountrates(Cohenetal.,2005;CampbellandVuolteenaho, 2004).8 Our explanation, in contrast, does not require a behavioral explanation and instead can be rationalized in a simple model in which firms face a marginal cost shock. Moreover, money illusion would not predict differential returns across the market power distribution which a cost shock explanation unequivocally does. Finally, we find that the rise in nominal yields in response to inflationary news is relatively muted and cannot quantitatively explain the size of stock market decline, which would be the prediction of a money illusion explanation. In terms of cross-sectional asset pricing, several papers study the role of inflation in the cross section of equity returns (Bhamra et al., 2023; Weber, 2015; Rubio Cruz et al., 2023). We focus on the asset pricing implications of market power, as a canonical model would predict that firms with higher market power are shielded from stagflationary stock returns. Relatedly, Corhay et al. (2020) and Corhay et al. (2022) study the implications of market power and markup shocks for stock prices.9 However, to the best of our knowledge, we are the first to study the interaction between inflation, market power, and asset prices. A more recent literature has linked the stock-bond correlation to that of inflation and real growth. In particular, since the late 1990s as inflation and growth became positively correlated, stock and bond returns started to exhibit a negative correlation, suggesting inflation is demand driven, and thus associated with good times (Campbell et al., 2017; Boons et al., 2020; Campbell et al., 2020; Cieslak and Pflueger, 2023; Pflueger, 2023). We study high-frequency asset price movements around inflationary news, allowing us to isolate the direct effect of inflationary news. Interestingly, we find a positive stock-bond return correlation in response to inflationary news, even post-1999 when the unconditional correlation was negative. We discuss these results further in subsubsection 6.2.3. 3 Data 3.1 Inflationary News Our inflation analysis is based on Consumer Price Index (CPI) releases, which are published by the Bureau of Labor Statistics. We focus on month-on-month headline CPI. Releases are usually published in the second week of the month for the CPI values of the previous month. We construct a measure of inflationary news with each inflation release by subtracting inflation expectations for 8The “Fed model” also postulates that higher inflation is associated with higher bond yields and lower equityprices(BekaertandEngstrom,2010),asinvestorssetstockmarketprice-toearnings-ratiosincorrectly based on nominal interest rates, confusing real and nominal (Asness, 2003). 9Choetal.(2023)distinguishbetweenrealizedandexpectedmarkupstostudylong-termtrendsinstock prices. 9

the release from the actual inflation release data: Inflationary News = π −E [π |I ], (1) t t t′ t t′ where π is the first release value of the headline month-on-month CPI and E [.|I ] is the condit t′ t′ tional expectation just prior to the release based on available information I at t′ < t. To measure t′ conditional expectations, we use Bloomberg median forecasts for each inflation release, which are available from 1997, and supplement this with the median from Haver Analytics’ Money Market Services survey, which extends the sample back to 1977. Figure A2 plots the inflationary news in red. The surprise series does not exhibit a particular trend, which is reassuring from a statistical perspective, and suggests that the data are stationary. However, there are periods when the surprises were larger in absolute value. For instance, in the early1990s,inflationfirstsurprisedtotheupsideandlatertothedownside. Duringandshortlyafter the Global Financial Crisis, the inflationary news was also larger, potentially because the Global Financial Crisis and the accompanying monetary policy actions increased uncertainty about the effectsofinflation. SincetheCOVID-19pandemic, asiswellknown, inflationsurprisedpersistently to the upside. Table A.IV provides summary statistics.10 3.2 Asset Prices Stock Prices. We obtain U.S. firm-level stock returns from Center for Research in Security Prices (CRSP). We follow standard procedures and use ordinary shares traded on the NYSE, AMEX, and NASDAQ exchanges. We also adjust returns for splits, mergers, or other corporate actions and trim at the top and bottom 0.5 percent to mitigate the effects of outliers on our results. Discount rates. For the risk-free rate component of the discount rates, we obtain real Treasury yields from the Federal Reserve website, which provides real yields for the 2-year maturity up through the 20-year maturity that are estimated from Treasury Inflation-Protected Securities (TIPS) yields (Gu¨rkaynak et al., 2010b).11 The data also provides nominal interest rates and implied breakeven inflation, which is the difference between real yields and nominal yields for a given maturity, as well as instantaneous forward rates. The sample begins in 1999, two years after the first TIPS was issued by the U.S. Treasury. We supplement the TIPS yields data with the real yields computed from fixed interest rate swaps and inflation swaps for robustness. This data is taken from Bloomberg and begins in July 2004. For the equity risk premium data, we use the 10Unexpected innovations to inflation are traditionally not considered primitive exogenous forces in macroeconomic models, unlike technology, monetary policy, and fiscal policy shocks (Ramey, 2016). One canthinkofaninflationsurpriseinthespiritofGomesetal.(2016)andCorhayandTong(2021)asviewing it as an exogenous unexpected increase in the rate of inflation that permanently increases the price level in an unanticipated manner. Alternatively, in a standard New Keynesian model an inflation surprise can be supply or demand driven. In our baseline empirical specification, we consider all inflationary news and test how investors perceive this general inflation surprise. 11https://www.federalreserve.gov/data/tips-yield-curve-and-inflation-compensation.htm 10

Martin (2017) lower bound for the one-year equity risk premium. The equity risk premium is calculated from option prices obtained from OptionMetrics, whose sample begins in 1996. Dividend futures. We obtain data on dividend futures, which are claims to dividends on the aggregate stock market in a particular year, from Bloomberg. S&P 500 dividend futures for claims on dividends 10 calendar years ahead begin in 2016. Each year on the third Thursday of December, a new dividend futures is issued that is a claim on dividends in the calendar year 10 years from that year so that the maximum maturity is always approximately 10 years. As is standard in the literature, we linearly interpolate across calendar-year futures prices to generate time series of constant-maturity dividend futures prices.12 Weusedividendfuturesfortwoapplications. First, theyareusedtocomputethedividendstrip weightsrequiredfortheimplementationofthestockreturndecomposition(seeEquation6). Second, dividend futures prices provide a direct measure of investors’ risk-neutral expectations of dividends payments. WeadjustforriskpremiumfollowingIbert, KnoxandVazquez-Grande(2022)andKnox and Vissing-Jorgensen (2024) to compute estimates of investors’ real-world dividend expectations on the stock market. In some specifications, we also adjust for expected inflation - using inflation swapratesofthesamematurityasthedividendfutures-tomovefromnominal expecteddividends to real expected dividends. 3.3 Market Power In microeconomic textbooks, product market power is defined as a firm’s ability to influence the price at which they sell their products and their use of this ability to hold prices over marginal cost, as they do not face perfectly elastic residual demand curves (Pindyck and Rubinfeld, 2014; Goolsbee et al., 2012). The price-marginal cost gap at the firm’s profit-maximizing output level is typically called the markup (Syverson, 2019). Weestimatemarkupsusingtheso-calledproductionapproach,whichwasinventedwithindustrylevel data by Hall (1988, 2018) and advanced with firm-level data by De Loecker and Warzynski (2012) and De Loecker et al. (2020). Under an assumption of cost minimization, the firms’ markup is defined as the product of the revenue to expenditure share of a given variable input times the output elasticity of that variable input. From the cost-minimization problem: θν = 1 P i V ,t V i,t , (2) i,t λ Q i,t i,t where θν is the output elasticity of input V , λ the Lagrange multiplier from the cost minii,t i,t mization, which measures the marginal costs, PV is the price of the variable input, and Q is the i,t i,t 12Dividend strip values can also be inferred from option data in the absence of arbitrage opportunities using the put–call parity relationship (van Binsbergen (2020)). We extend our sample of one-year dividend strips back to 1996 using this method and OptionMetrics equity option data. 11

output. The markup can be defined as: P i,t µ = , (3) i,t λ i,t where P is the output price. Hence, the markup is equal to the output elasticity times the i,t inverse of the variable input’s revenue share: (P Q ) i,t i,t µ = θ . (4) i,t i,t (PVV ) i,t i,t Following De Loecker et al. (2021) we calculate markups using firm-level data from Compustat North American fundamentals, a data set of firm-level financial statements for North American publiclytradedcompanies. Thedataallowsustoimplementtheproductionapproachforestimating markups. We use the cost of goods sold (COGS) as our measure for variable inputs, (PVV ) and i,t i,t sales for revenues P Q . This leaves us with estimating a measure of output elasticities. As in i,t i,t De Loecker et al. (2021), output elasticities are estimated on the (two-digit) sector level using a parametric production function estimation, with a variable input bundle and capital as inputs. There is a large discussion around the validity of estimating markups using the production approach (Raval, 2020; Bond et al., 2021; Basu, 2019; Berry et al., 2019; Syverson, 2019; Doraszelski and Jaumandreu, 2021). For instance, De Ridder et al. (2021) use firm-level administrative production and pricing data and show that the level of markup estimates from revenue data is biased in the time series, but estimates do correlate highly with true markups in the cross section. Bond et al. (2021) show that De Loecker et al. (2020) which relies on production function estimation and proxying physical output using deflated revenues leads to an identification issue that can bias markups downwards towards one. The production function estimation is, to the best of our knowledge, the most appropriate and feasible way to study the consequences of markups across firms in an asset pricing setting, as we do not attempt to either contribute to the markup estimation literature or evaluate the level of markups in the economy. However,asanalternative,weuseameasureofmarketpowerbasedonaatractableandscalable demandsystemfromPellegrino(2024).13 ThisGeneralizedHedonic-Linear(GHL)modelgenerates markups that correlate closely –both in the cross section and over time– with De Loecker et al. (2020), but as it does not rely on time-series production function estimation or proxying output with deflated revenues, Bond et al. (2021)’s criticism cannot apply to this markup estimation. 3.4 Other Firm-Level Financial Data We obtain firm-level financial data from Compustat for controls in the analysis. We use firm size (log of total assets (AT)), the book equity (CEQ) to market equity (PRCC*CSHO/1000) ratio, 13We are grateful for Bruno Pellegrino for this suggestion and sharing the data with us. 12

tangibility (the ratio of tangible assets (PPENT) to total assets) and leverage (the ratio of current debt (DLC) and the long-term debt (DLTT) to total assets).14 Motivated by the cross-sectional asset pricing literature, we control for firm-level exposures to factor portfolio returns. We use the Fama and French (1993) three-factor portfolios, the Fama and French (2015) five-factor portfolios, and the Carhart (1997) momentum factor. We obtain these asset pricing factors from Kenneth French’s website. We implement factor controls using a Fama-Macbeth approach. In the first step, we compute rolling 5-year betas of each stock in the sample with respect to the factor portfolios. We then include the estimated rolling betas—lagged one period—as control variables in the main regression specifications. 3.5 IBES Earnings Expectations To complement our analysis of cash flow expectations derived from dividend futures, we obtain earnings expectations from the Thomson Reuters IBES Estimates Database (as in Bordalo et al. (2023), De La O and Myers (2021), and De la O and Myers (2024) among others).15 IBES is a comprehensive forecast database containing analyst earnings per share estimates since 1976. ThomsonReuterscompilesitsforecastsfromalargenumberofbrokerageandindependentanalysts dedicated to tracking companies as part of their investment research efforts. Each forecast comes with the identifier of the respective analyst or brokerage firm. Given that these forecasts are not anonymous, analysts are incentivized to provide accurate reports of their expectations. We obtain individual company earnings forecasts for S&P 500 firms at the analyst level by multiplying the earnings per share by the shares outstanding. For every earnings forecast of an individual company, we have a date (d) on which the forecast is reported by each analyst (a). We match earnings forecasts to the closest CPI release date (t) with the date the forecasts were reported (d) by the analyst and compute the distance between the forecast date and the CPI release date (d−t). Hence, Earnings is the earnings forecast made by analyst a for company i at i,a,d,t date d for the closest CPI release t. If the forecast is made before the closest CPI release, d−t is negative. We drop observations in which the forecast is not made within 15 days before or after the CPI announcement, |d−t|>15. We then average earnings forecasts across analysts before and after the CPI release date as follows: Earnings Expectationpre = 1 (cid:80) Earnings Expectation ∀d−t < 0 i,t Ni,t d,a i,a,t,d Earnings Expectationpost = 1 (cid:80) Earnings Expectation ∀d−t ≥ 0, i,t Ni,t d,a i,a,t,d 14The market equity is obtained from CRSP variables. We merge year-end values with the Compustat book equity. 15We follow the literature and select only S&P 500 firms because analysts forecasts for these larger firms are likely more robust with more analysts tracking these firms. 13

where N is the number of analysts for CPI date t. i,t Usingtheaveragepreandpost-earningsexpectationsvariables,wethencomputethepercentage change in the forecast around each CPI release dateby taking the log difference between earnings expectations as follows: ∆EarningsExpectation = Log(Earnings Expectationpost)−Log(Earnings Expectationpre). (5) i,t i,t i,t Given that we have firm-level estimates of earnings expectations, we can also merge our measure of market power with the earnings expectations dataset, and we can estimate whether not only average earnings expectations are affected by inflationary surprises but also whether earnings expectationsareaffecteddifferentlyacrossthemarketpowerdistribution.16 Toobtainatime-series measure of earnings expectations, we take the asset-weighted average of the firm-level change in earnings expectations to obtain ∆EarningsExpectation . t 4 Stock Return Decomposition In this section, we propose a stock return decomposition around inflationary news based on the methodology developed by Knox and Vissing-Jorgensen (2024). We first lay out how, in theory, realized stock returns can be decomposed into a yield curve, equity risk premium and cash flow component. We then describe how to use observable data on interest rates and the equity risk premium to obtain the realized stock return components. 4.1 Background Underthepresentvalueformulaofthestockmarket,whichstatesthatthepriceofthestockmarket isthediscountedsumofallfutureexpectedcashflows,anunexpectedreturnontheaggregatestock market must result from changes in expected future real (nominal) cash flows or changes in future real(nominal)requiredreturns(discountrates)orboth. Changesindiscountratescanthenbesplit into changes in the risk-free rate component of the discount rate and changes in the excess return component of the discount rate—i.e., the equity risk premium component. Knox and Vissing- Jorgensen (2024) formalize this present value intuition with a decomposition of realized stock market capital gains into a yield curve return component, risk premium return component, and a cash flow return component, which reflect changes in investors’ expectations of those components. Knox and Vissing-Jorgensen (2024) show that a one-period capital gain on the stock market can be estimated as follows: 16Summary statistics are provided in Table A.V. On average, around three analysts cover the average firm both before and after the CPI release. Across all firms, there are on average between 587 (before) and 711 (after) analysts for a given CPI release. 14

(cid:34) ∞ (cid:35) (cid:34) ∞ (cid:35) (cid:34) ∞ (cid:35) P t+1 (cid:88) (n) D,(n) (cid:88) (n) 1 (cid:88) (n) 1 ≈ 1+ w G −1 + w −1 + w −1 , (6) P t t+1 t YC,(n) t EP,(n) t G G n=1 n=1 t+1 n=1 t+1 (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Cashflowfactort+1 Yieldcurvefactort+1 Equityriskpremiumfactor t+1 (n) where P is the price of the stock market index at time t, w is the price of the expected dividend t t payment on the aggregate stock market in n period’s time as a fraction of the overall price of the stockmarketindex, (i.e. theweight, inpresentvalueterms, thatacashflowinperiodncontributes to the stock market), and GX for X = {D,YC,EP} is the cash flow, risk-free rate, and equity n,t+1 risk premium growth factors for n = 1,2,... G D,(n) = E t+1 [D t+n+1 ] G YC,(n) = (cid:16) 1+y t ( + n) 1 (cid:17)n G EP,(n) = Et (cid:16) + 1 1 + (R y t t ( + + n) 1 1 , (cid:17) n n +1) (7) t+1 E t [D t+n ] t+1 (cid:16) 1+y t (n) (cid:17)n t+1 (cid:16) E 1+ t( y R (n t, ) n (cid:17) ) n t (n) where D is the dividend in n period’s time, y is the n-year government bond yield at time t, t+n t and R is the cumulative hold to maturity return on the n-year dividend strip from time t to n.17 t,n ThedecompositioninEquation6showshowgrowthindividendexpectationsgeneratespositive stock market returns through GD > 1, while growth in risk-free rates and equity risk premium n,t+1 generate negative returns through 1 < 1 or, 1 < 1 respectively. The decomposition also GF GRP n,t+1 n,t+1 (n) highlights the importance of dividend strip weights, w , determine the relative importance in t growth rates of dividends and discount rates of various n maturities. Intuitively, the more a future expected dividend contributes to the stock market in present value terms, the more changes in expectations of that divided, or its discount rate, matter for the overall price level of the market. A key insight of Knox and Vissing-Jorgensen (2024) is that a lot of information about the aggregate stock market discount rates and, to some extent, cash flow expectations, are available in modern financial markets. Furthermore, dividend strip prices (and thus dividend strip weights) can be calculated from dividend futures prices. This observable data means that one can go a long way to decomposing aggregate stock returns as set out in Equation 6 using the prices of other asset prices. These asset prices are available at a daily frequency and are therefore well suited for implementation in a daily return event study setting. We describe the specific data for the return decomposition used in this paper’s implementation in subsection 3.2 and set out details on the implementation in the subsection below. 17At the daily frequency, which is our frequency of interest, the stock market capital gain and the stock marketreturnareapproximatelyequalandthereforeweusethesewordsinterchangeablythroughthepaper. 15

4.2 Implementation 4.2.1 Yield Curve Return Component When estimating the return components of the aggregate stock market return, we start with the yield curve return component and utilize the availability of a rich-term structure of both nominal and real government bond yields out to a 20-year maturity (Gu¨rkaynak et al., 2010b) to compute using the definitions in Equation 6 and Equation 7: ∞ Returnk,YC = (cid:88) w (n) 1 −1. (8) t t YC,(n) G n=1 t+k AsGu¨rkaynaketal.(2010b)yieldsareavailableoutto20years,weneedtomakeanassumption about the changes in forward yields beyond the maximum observed maturity. We follow Knox and Vissing-Jorgensen (2024) and set G YC,(n) = GYC for n > 20 which is the same as assuming n,t+1 (20),t+1 forward rates don’t move beyond the maximum maturity. Economically, the assumption is that monetary policy 20 years out is unaffected by a CPI release today. To the extent that forward risk-free rates beyond the 20-year maturity move in response to inflationary news, our results will understatetheroleoftheyieldcurvereturncomponentinaggregatereturns. However,aswediscuss later, wefindforwardratesbeyondthe10-yearmaturityareunchangedfollowinginflationarynews. 4.2.2 Equity Risk Premium Return Component Aswiththeyieldcurvecomponent, onecanutilizeobservablediscountratedataandthedefinitions in Equation 6 and Equation 7 to compute the risk premium return component: ∞ Returnk,EP = (cid:88) w (n) 1 −1. (9) t t EP,(n) G n=1 t+k Using the Martin (2017) lower bound of the equity risk premium as our measure of observable risk premium, we do not observe the equity risk premium beyond n = 2 years.18 The observable term structure of the equity premium is therefore less rich as compared to the observable term structure of government bond yields. Aswewillseelater,equitypremiumchangesfollowinginflationarynewsarelarge,andtheequity premium component is an important factor in stock returns around inflationary news. To capture potential movements in equity premium beyond the observed maturities, we therefore implement a two-stepregressionapproachtoestimatethetotalriskpremiumreturncomponentofstockreturns. First, we compute the k-day aggregate return that is not due to the observed yield curve return 18Equityriskpremium iscomputedfromthe pricesofS&P500equity options, where the maturityofthe equity risk premium estimate is the same as the maturity of the option’s expiration date. Since 2022, equity options have been available up to five years ahead, but for the majority of our sample equity options have been available up to two years ahead. 16

component on each CPI date, Returnk,Adj = Returnk −Returnk,YC, t t t and, second, estimate the following regression for all k ∈ [−5,10] across CPI dates: (cid:16) (cid:17)′ Returnk,Adj = G EP,(n) Θk +ϵk,Adj, (10) t t+k t EP,(n) where G is a vector of k-day growth rates in the observed equity risk premium of various t+k n maturities. From these estimations, we then define the risk premium component of the k-day aggregate return as the predicted component of the estimation: Returnk,EP = (cid:0) GEP (cid:1)′ Θˆk. (11) t n,t+k This regression approach assigns all yield curve–adjusted stock returns that are correlated with the equity risk premium at observable maturities to the risk premium return component. To the extent that changes in the unobserved longer-dated equity risk premiums are correlated with changes in observed shorter-dated equity risk premiums, the method captures movements in stock prices that are due to changes in unobserved the equity risk premiums. This is a useful feature of the approach given that long-dated maturities of the equity risk premiums are unobserved in daily data. Moreover, Knox and Vissing-Jorgensen (2024) show that changes in the wedge between true riskpremiumandtheobservedMartin(2017)lowerboundofriskpremiumarepositivelycorrelated with changes in the lower bound itself. The regression approach therefore also captures changes in risk premium due to the unobserved changes in the wedge that are correlated with the observed risk premium changes. 4.2.3 Cash Flow Component The final return component of the return decomposition is the cash flow return component, which is due to changes in investors’ expectations of future dividend payments. In our baseline results, we define the cash flow component of the k-day aggregate return as the residual component of the estimation of Equation 10: Returnk,CF = ϵk,Adj (12) t t as this part of the stock returns has removed all variation that is due to observable changes in discount rates. It should be noted that one potential confounding factor in the estimation of Equation 10 are changes in investors’ expectations of cash flows themselves. Or, put differently, our method will attribute stock returns due to changes in investors’ cash flow expectations that are correlated with equity risk premium to the equity risk premium return component. Given the cash flow return 17

component and equity risk premium return component are likely positively correlated, this means we are understating the role of the cash flow return component. As we discuss later, given the changes in stock prices and discount rates around inflationary news that we observe in practice, this means the main finding that real cash flows decline would only be stronger if the confounding factor was controlled for. Instead, the main identifying assumption of the analysis is that the discount rate variables used in Equation 10 capture all discount rate changes that impact aggregate stock returns in our event-window estimations. The assumption is analogous to a variance decomposition of stock returns (Campbell, 1991), where the choice of variables included in the VAR determines how the model apportions returns between the discount rate and cash flow news (Campbell, Polk and Vuolteenaho, 2010; Engsted, Pedersen and Tanggaard, 2012). However,the predictor variables typically used in variance decomposition of stock returns are not commonly available on a highfrequency basis. Our approach, by utilizing observed changes in discount rates that are available contemporaneously, therefore allows us to maintain the identification benefits of an event-study estimation while decomposing the drivers of stock returns. 5 Empirical Strategy Our empirical strategy relies on an event-study approach that examines the financial market variables around the announcement of a CPI release. Studying unexpected realizations of inflation relative to expectations is crucial in causally isolating the effect of inflation. Higher inflation and expectationsthereofcanbecorrelatedwithpositivemacroeconomicenvironments,whichcouldbias a time-series regression of financial market outcomes on realized inflation. Instead, while inflationary news can be interpreted through different lenses (e.g., supply or demand), they are unlikely to be correlated with other non-inflationary news. 5.1 Time-Series Analysis Thetime-seriesanalysisusesevent-studylocalprojections(Jord`a,2005)andestimatesthefollowing sequence of regressions for all k ∈ [−5,10] across CPI dates: yk = αk +βkInflationary News +ϵk, (13) t t t where the yk change in an asset price from the close of business the day before the date t inflation t release to k business days after the inflation release and βk is the effect of inflationary news on the k-day change in the y asset price. We estimate Equation 13 through the sequence of k days separately using a variety of different asset types for y. To start, y is defined as the cumulative stock return between the day before t the announcement and k days after the announcement, Returnk, where we use the equal-weighted t 18

average. We then study changes in the observable discount rate around inflationary news, where yk = y −y is the k-day change in the equity risk premium, nominal risk-free rates or real t t+k t−1 risk-free rates of various maturities.19 Finally, we compute the yield curve return component, equity premium return component, and cash flow return component of aggregate stock market returns as defined in Equation 8, Equation 11 and Equation 12 respectively. We then define y as a cumulative stock return component t between the day before the announcement and k days after the announcement, Returnk,c for t c = {YC,EP,CF}, and study how each of these return components responds to inflationary news. 5.2 Cross-Sectional Analysis TheestimationsinEquation13ignorecross-sectionaldimensionsofreturnsacrossfirms. Totestfor the cross-sectional heterogeneity across firms with different degrees of market power, we estimate the following regressions for all k ∈ [−5,10] across CPI dates: Returnk = αk +βkInflationary News ∗Markup +αk +αk +X′ γk +ϵk , (14) i,t 1 t i,y(t)−1 i t i,t i,t where Returnk is the firm-level stock return of firm i. We interact the inflationary news with our i,t measure of markups, as defined in section 3, over the year y(t) before the inflation release, y(t)−1, to reassure that investors have access to the data. The interaction coefficient indicates whether, following inflationary news, firms with higher (one-year lagged) markups respond differentially compared to their counterparts. A positive coefficient is associated with an over performance of firms with higher markups in response to inflationary news. The specification in which we exploit cross-sectional heterogeneity across firms allows us to include time fixed effects in our regression equation. Time fixed effects (denoted by αk) control for all unobserved and observed heterogeneity t at a given point in time, such as changes in the monetary policy stance, volatility, economic news, or other factors such as sentiment, which are econometrically harder to observe. If these factors were to be correlated with the interaction term Inflationary News ∗Markup , the exclusion t i,y(t)−1 of time fixed effects could bias the coefficient of interest βk of equation Equation 14. Moreover, 1 we include firm fixed effects in the regression specification (αk), which control for time-invariant i characteristics of the firm. We also include a vector of various other characteristics X as a set of control variables. One i,t potentialthreatforidentificationisiffirmcharacteristicsarecorrelatedwithmarkupsandalsoreact differentially with respect to inflationary news. For instance, smaller-sized firms are less responsive to inflationary news than large firms, and firm size is correlated with markups, our coefficient of interest could be biased. To control for the differential impact of various firm-level characteristics on inflationary news, we interact various firm-level characteristics, such as log assets, tangibility, 19The result is robust to using the S&P instead of the equal-weighted average across all firms in our sample. 19

leverage, and market-to-book value with inflationary news. Given our dependent variable is stock returns,wecanalsocontrolforfirmcharacteristicsbycapturingthefirmstockreturn’sriskexposure to asset pricing factor models.20 Using a Fama–Macbeth approach, we first compute rolling five yearstockbetatotheportfoliofactorsandthenincludetheestimatedfirm-levelbetasinthecontrol vectors and, as with firm characteristics, interact them with the inflationary news variable. Onelimitationoftheinteractedfirm-controlapproachisthatunobservabletime-varyingfactors cannotbecontrolledfor. Iffirm×timefixedeffectsweretobeincludedintheregressionequation, they would be collinear with the markup×inflationary news term. However, we can make some progress toward controlling for a certain degree of time-variant variation that differs across firms to compare firms within each industry by including industry×time fixed effects. A further benefit of estimating a regression equation with industry×time fixed effects is that it alleviates a potential concern with the markup estimation by De Loecker et al. (2020). The estimation of industry-level output elasticities can produce inconsistent estimates of the output elasticity and the disturbance and can therefore generate biased markups (Doraszelski and Jaumandreu, 2021). By controlling for industry∗time fixed effects, we partially out the sector-specific output elasticities and solely compare firms with differential markups within an industry. Note that in contrast to standard local projections (LP), we also consider k < 0 in the spirit of an LP-difference-in-differences (DID) proposed by Dube et al. (2023). One difference between the LP-DID and the standard DID is that a sequence of regressions is estimated for each k. This has the advantage of βk not being affected by the choice of the number of lags and leads included. Moreover, the LP-DID avoids several other problems compared to estimating a DID specification withtwo-wayfixedeffects, seee.g. CallawayandSant’Anna(2021);Goodman-Bacon(2021)among many others. FortheDIDestimatortobeunbiased, werequiretheparalleltrendassumptiontobesatisfied— that is, absent a shock, treated and control firms would have evolved the same way. While it is not possible to test this assumption, as the counterfactual post-CPI release behavior without the shock is unobservable, we can test for whether there are differential pre-trends before the shock. Estimating βk for k < 0 allows us to test whether there is a violation of the parallel trend assumption. Recent literature has argued that DID designs are likely to be biased in the presence of a staggered DID approach, as already treated units can act as effective comparison units (Baker et al., 2022). Note that this is not a concern in our setting, as we set k =∈ [−5,10], covering only a window of 15 days, which prevents overlapping observations and staggered treatment, as CPI releases only occur once a month. The concern would be that firms with higher markups are treated for one CPI release but not for the next and are still being treated as comparison units for the next one. 20In the baseline we use the Fama and French (1993) three factor asset pricing model, but the results are also robust to using Fama and French (1993) plus Carhart (1997) or to using Fama and French (2015) five factor model. 20

6 Results 6.1 Aggregate Stock Returns Figure I plots the regression coefficient βk of Equation 13 from k = −5 to k = 10. The coefficient fork = 0representstheeffectofinflationarynewsontheone-dayreturnoftheaveragestockonthe day of the CPI announcement, whereas the one-day return is defined as the difference between the close price of the day of the announcement and the close price of the day before the announcement. Note that the CPI is usually released at 8:30 a.m., when the market is still closed. For robustness, we also test for the difference between close and open prices, and all results are unchanged. The negative coefficient, represented by the square at day=0, of 0.8, shows that in response to a one percentage point inflationary news, stock prices fall by around 0.8%. The shaded area in blue reflects the 95% confidence interval around the point estimate, which ranges from around 0.1% to 1.6%, indicating statistical significance at conventional levels. Moving to the next day (k = 1), we see that the negative effect of inflationary news on the stock market increases. The coefficient indicates that stock prices fall by around 0.9% between the day before the announcement of the CPI release and two days after. The effect after the second day remains persistent and, if anything, strengthens over a period of 10 days. Importantly, before the announcement of inflationary news, stock returns do not exhibit a trend, as shown by the statistically insignificant coefficient for k = −2 to k = −5. This absence of a pre-trend suggests that the parallel trend assumption is likely to hold, which refers to the idea that in a DID analysis the trend in stock prices would have been the same in the absence of inflationary news. Figure A2 plots the one-day stock return of the average firm on the days of inflation announcements together with the inflationary news. Similar to the inflationary news, the one-day stock returns do not exhibit a particular pattern, and while a negative correlation between the two series is not immediately obvious, a simple univariate regression of the average stock return on the inflationary news returns a coefficient of -1.04 and a standard error of 0.31, rendering the relationship between inflationary news and stock returns statistically significant at conventional levels. Figure A3 also confirms the relationship in a binscatterplot. The results for the (absence of a) pre-trend, the contemporaneous effect, and the lagged effect are also summarized in the binscatter plots of Figure A3 in which the x-axis is the inflationary news. The left panel shows a binscatterplot where the y-axis is the contemporaneous (one-day) stock return, the middle panel shows the return over a period of five days, and the right panel shows the one-day return the day before the inflation announcement. The left and middle panels both show a strong negative relationship between the inflation surprise and the return over one and five days, respectively. Consistent with the results above, the relationship becomes stronger (more negative) over five days compared to when only one day’s return is considered. The right panel can be seen as a placebo test. If the inflationary news was expected, one would potentially already see 21

negative stock returns before the announcement. However, the absence of a relationship between inflationary news and stock returns the day before suggests that what we call inflationary news is indeed news and is not yet expected by the market. Inastandardmacromodel,anegativesupplyshockreducesoutputandincreasesprices,whilea positivedemandshockincreasesoutputandprices,potentiallyinducingsignificantstatedependence inourresults. InAppendixA, usingseveralmeasuresofsupply-driveninflation, includingtheoften cited stock–bond correlation, we do not find evidence that our results are dependent on times when inflation is measured to be more supply-driven; even during demand-driven times, such as the post-Global Financial Crisis era, inflationary shocks are associated with declining stock returns, an increasing risk premium, and unchanging real yields. We discuss those results in more detail in subsubsection 6.2.3. 6.2 Discount Rates In this subsection, we first present results showing how yields and the equity risk premium respond to inflationary news. We then discuss the economic implications of the main findings. 6.2.1 The Yield Curve Figure II presents results for the nominal Treasury yield, the breakeven inflation rate, and the real Treasury yield by reporting the regression coefficients βk of Equation 13 from k = −5 to k = 10. The estimation period is 1999-2022, reflecting the sample period for which inflation-linked Treasury yields are available (Gu¨rkaynak et al., 2010b). The first column shows results for the two-year maturity, and the second column shows results for the 10-year maturity. In terms of the stock return decomposition, longer-maturity discount rates are more pertinent for understanding the impact of yields on stock market returns, given the duration of the stock market is very long (van Binsbergen, 2020; Knox and Vissing-Jorgensen, 2024). However, the shorter-maturity yields provide additional information and are particularly interesting, as they are more sensitive to the near-term economic outlook and expected path of monetary policy than longer-dated yields. The first row of Figure II presents nominal yield responses to inflationary news. Yields at shorter maturities that are sensitive to the policy rate are expected to increase with higher-thanexpected inflation. Indeed, and, unsurprisingly, the positive coefficient of 0.11 for two-year nominal Treasuries shows that, in response to a one percentage point inflationary news, the two-year yields rise by 11 basis points. In the second column, we see spillovers from policy-sensitive maturities to longer maturities of the yield curve. The 10-year nominal Treasury yield rises by around 8 basis points following a one percentage point inflationary news. The middle row of Figure II presents the breakeven inflation response to inflationary news. The coefficient of 0.35 at day zero for 2-year breakeven inflation shows that, in response to a one percentage point inflationary news, the 2-year inflation expectations rise by 35 basis points on that 22

day. The notable response of inflation compensation to CPI news is consistent with prior evidence in Bauer (2015) as well as the response of household expectations and professional forecasters (Skaperdas, 2023). As with nominal yields, longer-maturity inflation expectations increase with their shorter-maturity counterparts. At the 10-year maturity, the breakeven inflation rises 7 basis points following a one percentage point inflationary news. The bottom row of Figure II presents the response of real yields to inflationary news. By definition, real yield changes are the difference between the previously described nominal yield changes and breakeven inflation changes. At the 2-year maturity, we see the real yield decline as the dramatic increase in short-term inflation expectations outweighs the relatively modest increase in nominal yields. In particular, the negative coefficient of 0.24 shows that the 2-year real Treasury yieldsdecline24basispointsinresponsetoaonepercentagepointinflationarynews. Atthe10-year maturity, the change in nominal Treasuries and breakeven inflation are approximately the same, each rising 7 basis points following a one percent point inflationary news; thus, longer-dated real yields are unchanged. Table A.VI presents analogous results using interest rate and inflation swaps to compute and decomposerealyields. TIPSarelessliquidthanTreasuries(Fleckensteinetal.,2014),and,thus,one concerncouldbethattimevariationintheTIPSliquiditypremiumaroundinflationannouncements is driving the results. However, we do not find support for this channel, with the results consistent across estimations using swap prices rather than bond prices.21 6.2.2 Equity Risk Premium We now consider the equity risk premium response to inflationary news. Figure III plots the full set of regression coefficients β of Equation 13 from k = −5 through k = 10 using the Martin k (2017) lower bound of the one-year equity risk premium. Equity risk premium is estimated to increase by 30 basis points in response to a 100 basis point inflation surprise the day after the shock, with the response increasing to statistically significant 70 basis points by day five. The positive coefficients illustrate an increasing equity risk premium in response to inflationary news (Bekaert and Engstrom, 2010) and therefore provide evidence that the equity risk premium news at least partially contributes to the equity price declines observed after inflationary news. 6.2.3 Discussion of Discount Rate Findings The movements in discount rates around inflationary news, and their co-movement with stock returns, shed light on investors’ perceptions of the economic implications of inflation. Below, we 21One further concern about interpreting the above findings is that illiquidity issues in either market might bias the results. The period when the inflation-linked market was first developing (1999-2003) and alsotheGlobalFinancialCrisis(2008-2009)arebothknowntobeperiodsofhighilliquidityinthesemarkets. However,inunreportedresults,wefindconsistentresultswhenweremovethesetwoperiods. Ingeneral,the negative response of real yields to inflationary news is robust throughout the subsamples of our full sample period (1999-2022). 23

discuss five key observations from our findings. Policy-sensitive yields and the implied Taylor rule. The Taylor principle states that the nominalinterestrateshouldberaisedmorethanpointforpointwheninflationrisessothatthereal interest rate increases (Taylor, 1993, 1999). By studying policy-sensitive two-year yields, we can estimateinvestorperceptionsoftheTaylorruleinresponsetochangesininflationexpectationsover time.22 Under a Taylor rule, the response of monetary policy—and therefore short-dated nominal interest rates—should exceed the change in inflation expectations. However, in the data, we find that real yields at policy-sensitive maturities decline, as the increase in breakeven inflation is larger than that of nominal Treasury yields, which is inconsistent with the Taylor rule hypothesis. This canberationalizedbyinvestorsexpectinginflationtobesupplydriven, contractingoutputwithout requiring a strong increase in the nominal monetary policy rate. Inflation compensation–driven long-maturity nominal yields. Atlongermaturities,wefind that real yields are unresponsive to inflationary news. This result is in stark contrast to the large andpositiveresponseoflong-datedrealyieldstomonetarypolicyshocks(NakamuraandSteinsson, 2018; Hanson and Stein, 2015). In Appendix B, we explore these distinctive effects of monetary policy news and inflationary news on the long end of the real yield curve using the Hanson and Stein (2015) empirical setting. We first replicate the Hanson and Stein (2015) result, which is that, in response to monetary policy news on FOMC days, nominal and real yield long-dated forwards move in lockstep. However, once we zero into CPI days, the large response of long-dated nominal forward rates to policy-sensitive nominal rates is driven mostly by the breakeven inflation. The inflationary news results are consistent with a model in which long-run inflation expectations are not well anchored and revised in light of incoming inflationary news (Gu¨rkaynak et al., 2005). Importantly, for the context of our analysis, the unresponsiveness of real yields to higher nominalyieldsoninflationarynewsopposesthenotionthatinflationarynewsdaysaresimplyproxy monetarypolicydays, withassetmarketsdrivensolelybytheexpectedresponseofmonetarypolicy to inflationary news. Instead, we find very clear evidence that inflationary news days are distinct, with other factors, beyond monetary policy, driving asset markets. Increasing equity risk premium with inflationary news. Ex-ante, the effect of inflationary news on the equity risk premium is ambiguous. The correlation between inflation and economic activity and the asset’s cash flows should be fundamental to the determination of the risk premium and inflationary news. If inflation (deflation) is associated with bad states of the world, assets that have low real payouts in high inflation (deflationary) times are relatively undesirable and command higher risk premiums. This intuition is embedded in many asset pricing models that explicitly consider the implications of inflation for time-varying risk premiums, such as those with 22Theexerciseisthereforesimilarinspirittorecentworkthatstudiesprofessionalforecasters’perceptions of the Taylor rule from surveys (Bauer et al., 2022). 24

time-varying disaster risk (Gabaix, 2008), long-run risk (Bansal and Shaliastovich, 2013), or risk aversion(Campbelletal.,2020). Indeed, theriskpremiumistypicallyanamplificationoftheeffect of inflation on the assets’ cash flows. Therefore, through the lens of a broad range of models, a rising equity risk premium with inflationary news is indicative of investors believing that the real cash flows of equities are lower in inflationary times. Positive stock–bond return correlation. In response to inflationary news, we find a positive stock–bond return correlation as stock prices decline and nominal yields rise. In a New Keynesian model, a positive stock–bond correlation is indicative of the economy being hit by supply shocks, and a negative stock–bond correlation suggests the economy being hit by demand shocks (Cieslak andPflueger,2023). Undersimilarintuition,apositive(negative)stock–bondreturncorrelationcan also be interpreted as monetary (growth) news (Cieslak and Pang, 2021). Taken at face value, the correlation we observe on inflationary news suggests investors interpret inflation as supply shocks or monetary news. However, the positive correlation between nominal yields and inflation expectations is inconsistent with a monetary policy interpretation, and therefore the evidence points to supply shock news. In fact, this correlation even occurs in periods where the stock–bond return correlation on other days is negative (see Appendix A). These results raise the question of why the stock–bond return correlation has, on average, been negative since the 2000s—if it is not driven by inflationary news. However, even in an economy where economic activity is demand-driven, it is is possible for inflation to be supply driven. For instance, a flat Phillips curve would imply that changes in economic activity have small effects on inflation; and supply shocks, even if smaller in magnitude, drive inflationary dynamics. In the case of a flat Phillips curve, investors may not take much signal from inflationary news about the strength of the economy, and could attribute them to supply.23 Negative correlation between inflation expectations and stock returns. We find a strong negative correlation between stock returns and inflation expectations in their respective responses to inflationary news. This result holds even in a sample period where the daily correlation between inflation compensation and stock returns has been positive, with with this positive correlation even holding on days with CPI releases specifically (Chaudhary and Marrow, 2024). However, in Table A.VII, we show that once changes in inflation expectations are instrumented with inflationary news, the effect of inflation expectations on stock returns is negative on CPI days. This highlights the importance of studying unexpected realizations of inflation in an event-study setting instead of studying broader correlations that will be confounded with other factors. For example, both demand shocks and monetary policy shocks lead to a positive correlation between stock returns 23Another possible explanation is that the shift in the general stock–bond correlation is not related to relative importance of demand shocks and is instead driven by other factors such as precautionary saving motives (Laarits, 2022) or changes in the persistence of consumption shocks hitting the economy (Chernov et al., 2023). 25

and inflation expectations. Importantly, our two stage estimation in Table A.VII shows that the positive correlation between stock returns and inflation expectations is not driven by inflationary news itself. In fact, the negative effect of inflationary news driven inflation expectations on stock prices provides more evidence that investors interpret news about inflation as a cost-push supply shock. The results presented above show that inflationary news increases investors’ inflation expectations and yet is bad news for stock prices, with several findings suggesting that investors have a stagflationary view of the world.24 The most direct, but also challenging, test of this hypothesis is to measure how investors’ cash flow expectations change with inflationary news. The stagflationary view should lead to stagnant (unchanged) nominal cash flow expectations and thus declining real cash flow expectations. We tackle this question in the next subsection. 6.3 Cash Flow Expectations To study investors’ cash flow expectations, we implement the stock return decomposition methodology described in section 4. This method allows us to quantify the impact of changing discount rates on the overall stock market return, and extract a residual, which, by definition, is due to changes in investors’ expectations of future cash flows. Whether these are real or nominal cash flow expectations depends on whether we quantify the impact of real risk-free rates or nominal risk-free rates when calculating the yield curve return component of the aggregate stock return. Either way, realized returns of the stock market are the sum of the yield curve return component, the equity risk premium return component, and the cash flow return component. This means that the beta of the k-day stock market return on inflationary news, βk, is by definition equal to the sum of the r beta of k-day return components on inflationary news (cid:88) βk = βk, (15) r c c where βk and the βk’s are all estimated from the regression specification in Equation 13, but r c whereeachestimationusesadifferentdependentvariables. Thereturndecompositionmethodology thereforeallowsustoquantifytherelativeimportanceofthevariousreturncomponentstoaggregate stock market returns in response to inflationary news. 6.3.1 Nominal Cash Flows and Stock Return Decomposition Panel A of Table I presents a decomposition of realized nominal stock returns that is broken down into return components around inflationary news. The first four columns show the stock return components on the day of the CPI release. Columns (5)–(8) show the components five days after 24These results are robust to using core inflation surprises instead of headline, as shown in Table A.VIII. 26

the release. The first column shows that in response to a one percent inflation surprise, stock prices overall decline by 1.42%.25 The next three columns decompose this number into the three return components in Equation 6. Focusing first on the contribution of the nominal yield curve return component, we see that the increases in nominal risk-free rates documented in Figure II unsurprisingly lead to a negative yield curve return component. This shows that, following inflationary news, investors revise up nominal interest rate expectations, and thus the stock market’s future cash flows are discounted by more and the present value falls. However, quantitatively, the yield curve return component is only 0.61 percentage points on the first day and a cumulative negative 0.49 percentage points over five days, so the yield curve return component can not explain the full decline in the stock market following inflationary news.26 We next turn to the equity risk premium return component of the aggregate stock return. Consistent with the large increase in the equity risk premium following inflationary news documented inFigureII, weestimatethatanincreasingequityriskpremiumcontributesasignificantfractionof thenegativestockreturns. Fortheone-dayreturn,equityriskpremiumcontributes1.05percentage points to the negative 1.42 percent points return of the stock market, and over a five-day period equity risk premium contributes 2.51 percentage points to the 2.75 percentage points cumulative negative return on the stock market. The equity risk premium therefore accounts for 70 to 80 percent of the negative stock returns following inflationary news. Finally, we look at the contribution of investors’ expectations of future nominal cash flows. After accounting for the increases in discount rates following inflationary news, we find that the residual impact assigned to changing investor expectations of cash flows is small and insignificant. After 1 day the contribution is positive 0.24 percentage points and after five days the cumulative contribution is 0.25 percentage points, but neither of these coefficients are statistically significant. Toshowinmoredetail,thetoppanelofFigureIVplotstheregressioncoefficientβk ofEquation13 CF for all days from k = −5 to k = 10 with the cumulative nominal cash flow return component used as the dependent variable. For all days, the nominal cash flow component is statistically indistinguishable from zero, and is consistent with investors’ having stagnant nominal cash flow expectations following inflationary news. Inflation expectations increase following higher than expected inflation, yet nominal cash flow expectations are unchanged. We conclude this subsection by discussing the implications of the regression approach for estimating the equity risk premium and cash flow return components. The advantage of the approach 25The aggregate stock return is more negative than shown in Figure I because in this post-1999 sample (where discount rate data is available) the stock returns are more negative in response to inflationary news. For example, the 1-day return for k = 0 is -0.8% in the full sample and the cumulative return for k = 5 is -1.8%. 26Asdiscussedinsection4,ourmethodologywillunderstatetheroleofyieldcurvenewsifforwardnominal yields move beyond the maximum observed maturity of 20 years. However, in Figure A4 we see that we can empirically reject this, with observed forward yields not moving beyond the 10-year horizon. This tells us that the changes in long-term nominal yields observed in response to inflationary news are predominately drivenbychangesinforwardyieldsatshort-termmaturities. NagelandXu(2024)observesimilardynamics of long-term forward rates in response to monetary policy news. 27

is that the coefficient on the 1-year equity risk premium in Equation 10 not only captures the impact of changes in the observed 1-year equity risk premium on the stock market price but also the changes in the unobserved longer maturity equity risk premium changes (providing that the longer maturity equity risk premiums are correlated with the 1-year equity risk premium). Indeed, for k = 0 we estimate a regression coefficient of -2.4 on the 1-year equity risk premium in Equation 10. If the unobserved forward equity risk premium beyond the 1-year maturity were unchanged followinginflationary news, thecoefficientwould onlybenegativeone; thus, theregression coefficientless than minus one shows that our estimation captures a significant contribution from implied changes in the unobserved equity risk premium beyond the 1-year maturity. However, as discussed in section 4, the drawback of the regression approach is that it has a confounding bias. The impact of changes in cash flow expectations on the stock price that are correlated with risk premium will be incorrectly assigned to the risk premium return component rather than the cash flow return component. That said, the equity risk premium and cash flow return components are likely positively correlated. In this case, the key conclusion that nominal cash flows are stagnant is not invalidated by the confounding factor and, in fact, would be even more striking than we document here. 6.3.2 Real Cash Flows and Stock Return Decomposition We next turn to a decomposition of real stock returns and the extracting of investor expectations of future real cash flows following inflationary news. Before presenting the results, we make two observations. First,evenwithoutimplementingtherealreturndecomposition,theobservedchanges in real yields that we find are already a powerful result consistent with the stagflationary view hypothesis. The fact that real yields do not rise following inflation surprises means that real yield curve news is not the driver of negative stock returns in response to inflationary news. Instead, the negative stock returns must thus be due to one or both of the following: (a) increases in the equity risk premium or (b) declines (stagnant) expectations of future real (nominal) cash flows. As discussed in subsection 6.2, it is unlikely to get an increase in equity risk premium with inflationary news without investors associating inflation with a lower real cash flow expectations, and, thus, while our decomposition quantifies the relative importance of each factor, with real yields alone we caninferthatinflationisconsideredstagflationary. Inthislight, theincreasingequityriskpremium we observe is a complementary finding to the unchanged real yields with declining stock prices. Second, we note that inflationary news (see Equation 1) results in an instantaneous increase in the level of the consumer price index. This instantaneous increase becomes a permanent increase if the price index is not expected to decrease following the news. As shown in Figure II, inflation expectations are increasing (not decreasing) with inflationary news, and, therefore, inflationary news is expected to be associated with a permanent increase in the consumer price index. This increaseinthepricelevelmeansthenominalstockreturnsshowninFigureIareevenmorenegative when considered on a real basis. For instance, if inflation is 1 percentage point higher than was 28

expected, this can be thought of as an instantaneous increase in the price level of 1 percent and implies that the real stock price is lower by the same amount at the time of the inflation release. We therefore calculate real returns around inflationary news by simply subtracting the inflationary shock from the nominal stock return, R (cid:94) eturn k = Returnk −Inflationary news , i,t i,t t for all days since the inflationary news (i.e., for all k ≥ 0). If investors viewed the stock market as a real asset, in the sense that the cash flows generated by the asset increase with the price level in the economy, then nominal expectations of all future cash flows should increase with the instantaneous level shift in the consumer price index that is associated with the inflationary news. Thus, even holding fixed investors’ discount rates and investors’ expectations for future cash flow growth, this price-level adjustment to expected nominal cash flows means an inflation surprise would lead to a nominal stock market return equal to the size of the inflationary news itself following inflationary news. Subtracting the realized inflationary news from the nominal stock returns thus removes this potential impact of changes in perceptions of the price level on expected nominal cash flows. Panel B of Table I now presents a decomposition of realized real stock returns into return components around inflationary news. The first four columns show the stock return components onthedayoftheCPIrelease. Columns(5)-(8)showthecomponentsfivedaysaftertherelease. The first column shows that in response to a one percent inflation surprise, stock prices overall decline in real terms by 2.42%. The next three columns decompose this number into three components. Focusing first on the real yield curve return component, we see that the small changes in real risk-free rate documented in Figure II unsurprisingly lead to a small contribution from risk-free rates on aggregate stock returns. The real yield contributions are less negative relative to the nominal yield contributions because the rise in inflation expectations offsets the rise in nominal yields. In fact, on net, real yields slightly decrease, and this means we observe a positive impact from the real yield curve component on stock returns following inflationary news. For k = 0, decreases in real yields mean that the real yield curve return component contributes positive 0.15 percentage point to the -2.42 percentage points negative stock return, and for k = 5 the positive contribution is 0.62 percentage points. Turing next to the equity risk premium contribution, we estimate that, consistent with the nominal return decomposition, the increasing equity risk premium contributes 0.75 percentage point to one-day equity declines and around 2.17 percentage points to cumulative 5-day stock returns. In total, the equity risk premium accounts for 30 percent of the negative stock return on the day of an inflation announcement and up to 58 percent of the cumulative return through k = 5. Finally,welookatthecontributionofinvestors’expectationsoffuturerealcashflowstonegative stock returns following inflationary news. Even after accounting for the large move in the equity risk premium around inflationary news, and the smaller moves in real risk-free rates, we find there is a large contribution of the real cash flow return component. In particular, the decline in 29

investor expectations of real cash flows contribute -1.82 percentage points to the -2.42 percentage point return on day k = 0 and contribute -2.20 percentage points to the -3.75 percentage point cumulative return on day k = 5. We therefore estimate that changes in investors’ expectations of future real cash flows account for 75 percent of the negative stock return on the day of an inflation announcement and 59 percent of the cumulative return through k = 5. The bottom panel of Figure IV plots the regression coefficient βk of Equation 13 for all days fromk = −5tok = 10, withthecumulativerealcashflowreturncomponentusedasthedependent variable. We see that for most days the real cash flow return component is statistically negative, with the negative coefficient on cumulative returns showing a persistence level of just below -2 percentage points. Figure V presents a decomposition of realized real stock returns into return components around inflationary news. The figure presents stack bars of the return contribution of real cash flows, real risk-free rates, and the equity risk premium on the aggregate stock return, as well as presenting the aggregaterealstockreturnitselfwiththeblackline. Formally,thebarsplotthefullsetofestimated regression coefficients βk,c of Equation 13 from k = −5 through k = 10 and for c = {C(cid:103)F,EP,Y(cid:103)C}, where the coefficients for each k are stacked across c. The return components are the returns generated from changes in real cash flow expectations, C(cid:103)F, changes in the equity risk premium, EP, and changes in real risk-free rates, Y(cid:103)C. Because k-day return components sum to the k-day aggregate return, the sum of the regression coefficients of return components on inflationary news equals the regression coefficient of aggregate stock returns on inflationary news by definition (see Equation 15). 6.3.3 Validation of Cash Flow Component Assigning the residual of the stock return decomposition to the cash flow component of stock returns may raise the concern that the cash flow component does not actually measure what it is intended to. Instead it could reflect unobserved or mismeasured discount rate movements. In this subsection, wethereforeprovidevalidationsofourstockreturndecompositioncashflowcomponent to show it indeed measures news about cash flows. Validation 1: Correlation of cash flow component with analysts’ earnings forecasts. We first compare the cash flow component to other measures of cash flows that are more directly observable. As described in subsection 3.5, we can use data on analysts earnings expectations to understand how analysts’ view about companies earnings change around CPI announcements and compare those earnings expectations to our estimated cash flow component. While earnings expectations are not confounded with market-based components, such as liquidity and risk premium, that could bias the measure, analysts only update their estimates infrequently, which prevents us from using earnings expectations at the high frequency. Instead, we aggregate changes in earnings expectations in the 2 weeks before and after the CPI release to obtain a lower-frequency estimate 30

of how earnings are expected to change. We aggregate the change in earnings expectations across all firms for a given CPI date, as defined in Equation 5, by using an (asset-) weighted average. We then compare our estimated nominal cash flow component to the change in earnings expectations of analysts. The upper-left panel of Figure VI shows a strong correlation between the same-day change in the estimated cash flow component of the stock return and the change in earnings expectations. The lower-left panel confirms this strong correlation for the 5-day change in the estimated cash flow component and the same earnings expectations. Validation 2: Correlation of cash flow component with dividend futures prices. An alternative approach to confirming the validity of the estimated cash flow component is to compare it to dividend futures price changes. Dividend futures prices carry important information about the expectations of investors about cash flows across different horizons, providing a more direct measure of investors’ expectations of cash flows on the aggregate stock market. For example, Gormsen and Koijen (2020) show how dividend futures prices fell significantly during the onset of the COVID-19 crisis as investors revised down their growth expectations. There are, however, some caveats when using dividend futures. First, dividend futures are only available from 2016 in Bloomberg, with this data limitation preventing us from studying a longer times series. Second, although volume has increased over time, the liquidity is not as rich as for other financial markets. Third, dividend futures prices contain a risk premium. That said, we do adjust dividend futures prices for the observed Martin (2017) equity risk premium of the same maturity as the dividend futures, following Ibert et al. (2022) and Knox and Vissing-Jorgensen (2024). For the sample period in which dividend futures are available, we construct the percentage change in dividend futures prices around CPI print releases and compare them to our stock return cash flow component. The middle column of Figure VI shows the same cash flow component of stock returns as in the left panel but plots it against the same k-period change in 2-year dividend futures prices adjusted for risk premium.27 As for analyst earnings expectations, the correlation between the two different measures of expected cash flows by market participants is very strong. In the right panel of Figure VI, we move from nominal cash flows to real cash flows based on both our decomposition approach and the dividend futures. For dividend futures, we adjust the dividend futurespricebytheinflationsurpriseandalsodeflatebyexpectedinflationasmeasuredbyinflation swaps of the same maturity as the dividend maturity. These adjustments change dividend futures from nominal to real quantities. As for the nominal cash flow component and nominal dividend futures prices, the real parts of the cash flow component and the dividend futures are also strongly related to each other. Appendix C provides further analysis of dividend futures price changes in response to inflationary news, with the finding supporting the conclusion that investors’ nominal (real) cash flow expectations are stagnant (declining) when inflation if higher-than-expected. 27As most dividends are expected to be paid out in later periods, we use the longest maturity dividend where we have equity risk premium estimates such that we can do the risk-premium adjustment. 31

Validation 3: Cash flow measures response to economic activity news. In a further validation exercise, we analyze the impact of economic activity surprises, rather than the inflation surprises used in the main analysis, on our nominal cash flow component. A natural concern with our null finding that nominal cash flows do not increase with inflationary news is that the cash flow component is mismeasured and does not change even as investors’ true cash flow expectations do. The idea is therefore to test the cash flow component in an alternative setting where economic theory predicts that the null hypothesis is expected to be rejected. We estimate Equation 13 for all days from k = −5 to k = 10 with the cumulative nominal cash flow return component used as the dependent variable, but with inflationary news replaced by nonfarm payroll (NFP) news for the independent variable. NFP news is defined as the difference between the published monthly rise in total nonfarm payroll employment and the median expectation of forecasts ahead of the announcement (in 100k). The results are presented in the top left panel of Figure VII. We find that investors revise up their expectations of nominal cash flows when economic activity surprises to the upside, i.e. when more jobs than expected were added to the economy. We view this exercise as a reverse placebo test. In response to a shock that is more likely to be interpreted as a demand shock, we show that our methodology does indeed identify an increase in investors’ cash flow expectations.28 The top right further illustrates the result, presenting a binscatterplot of the k = 1 1-day nominal cash flow component of stock returns against the NFP news. In the bottom row of Figure VII we provide further validation, this time of analyst’s earning expectations, showing the null result that nominal cash flow expectations to do not increase with inflationary news (left figure), but importantly cash flow expectations do increase with NFP news (right figure). Overall, theresultspresentedinthissubsectionsuggestthattheestimatedcashflowcomponent fromourstockreturndecompositioncarriesimportantinformationonhowmarketparticipantsand analysts view the cash flow outlook and verifies the validity of our approach. 6.4 Market Power Onepotentialreasonforwhythemarginalinvestorhasastagflationaryviewoftheworld—expecting nominal growth and dividends to remain stagnant for the average firm—could be that the inflation surprise is interpreted by investors to be a shock to marginal costs. To understand the implications of such a view, we consider a canonical model of imperfect competition, where firms set prices that are the product of the markup and marginal cost (Tirole, 1989). The prediction about how a marginal cost shock affects firm profitability follows from this model simple setup (all proofs in 28Boyd et al. (2005) and Elenev et al. (2024) show that the response of the stock market to economic activity surprises varies over the business cycle due variation in the expected response of the central bank to economic news (Bauer et al., 2022), which in turn impacts on the discounting channel of stock returns. Our nominal cash flow component by construction explicitly controls for this variation by removing the discounting component of stock returns. 32

Appendix D). Hypothesis 1 (firm profitability and marginal costs) In simple models of imperfect competition, firm profitability declines following an increase in marginal costs. Consistent with the empirical evidence presented thus far on aggregate asset prices, the costshock hypothesis does indeed predict that investors should expect firm profitability to decline with inflation. Crucially, we also show that in the textbook model of imperfect competition, the key parameter for how much firm profits decline with marginal costs is a firm’s market power. Hypothesis 2 (market power, firm profitability, and marginal costs) The extent to which firm profitability declines with marginal costs is determined by a firm’s market power. In particular, firms with more market power see a smaller decline in profitability following an increase in marginal costs. This second hypothesis motivates the studying of the cross section of firms to help with understanding the economic drivers of stagflationary stock returns. In particular, we can exploit crosssectional heterogeneity in firms’ market power to ask whether firms with higher market power are expected to suffer smaller profitability declines following inflationary news, as the theory predicts. Cross-sectional empirical analysis will also allow us to estimate specifications that control for unobserved and observed time-varying factors affecting average stock returns and also to further narrow down the cash flow channel of stock returns. In the results below, we first study the cross section of stock returns in response to inflationary news, before we then turn to investors’ cash flow expectations. We initially extract cash flow expectations from observable discount rates and the return decomposition methodology. We then look at earnings expectations directly. 6.4.1 Stock Returns We start with stock returns. For each CPI announcement, we split the sample of firms into those that have high and low markups. High markup firms are those that had markups above the 75th percentile of the markup distribution in the previous year, while those with low markups are those with markups below the 25th percentile of the distribution in the previous year. We estimate the following equation: Returnk =α+β Inflationary News ∗Low Markup i,t 1 t i,y(t)−1 (16) +β Inflationary News ∗High Markup +β Low Markup +ϵ 2 t i,y(t)−1 3 i,y(t)−1 i,t Figure VIII plots β andβ for different k′s. In the upper panel, which plots β , the effect of 1 2 1 inflationary news for low markup firms resembles qualitatively Figure I, but the magnitudes are larger in absolute values. In particular, firms with low markups see their stock prices decline by 33

around 3.8% in five days after a one percentage point inflationary news shock (compared to 1.9 for the average firm), with the 95% confidence interval ranging between 1.2 and 5.8. In contrast, firms with high markups see their stock prices declining only modestly in response to inflationary news. Five days after the inflationary news shock, stock prices are down only 0.9% with the 95% confidence interval touching zero. For firms with high markups, we can therefore reject the null hypothesis that inflationary news leads to declines in stock prices after five days. We test more formally the difference between firms with differential degrees of market power by estimating Equation 14. Figure IX plots the interaction coefficient between the inflationary news shock and markups. The interaction coefficient tests whether firms with higher markups exhibit differential stock returns around the announcement of inflationary news. The results for k <= 0 help shed light on whether there is a pre-trend in the data. If firms with higher markups already before the CPI announcement had rising stock prices relative to those with lower markups, this would likely lead to a violation of the parallel trend assumption which implies that both types of firms would have experienced the same return dynamic around the event, had the announcement not been an inflationary news shock. The close-to-zero and statistically insignificant coefficient that does not exhibit a trend before the CPI announcement, suggests that there is no pre-trend in the data. If there was a preexisting trend, it could be more difficult to determine whether the trend in the returns for the high markup group would have been the same as the trend in the returns for the firms with low markup in the absence of inflationary news, which could lead to biased estimates of the treatment effect. A positive coefficient on the interaction for k >= 0 indicates that firms with higher markups earn higher returns after inflationary news. Since markups are standardized with a mean of zero and a standard deviation of one, the coefficient can be interpreted as the differential impact of inflationary news on firms with a one standard deviation higher markup. The coefficient rises from around 0.08 to 0.28 from the day of the event to five days after the event. Hence, a firm with a one standard deviation higher markup has a 0.28 percentage point higher stock price compared to anotherfirmfivedaysaftertheeventinresponsetoaonepercentagepointinflationarynewsshock. Note that the average firm suffers a decline of around 1.5% in response to a one percentage point inflationary news shock so that the interaction coefficient is around 19% of the base coefficient. A firm that has one standard deviation higher markup suffers a decline in the stock price of 1.22% (1.50-0.28) in response to a one percentage point inflationary news shock, a difference of 16% (1- 1.59/1.9). The result is also illustrated in Table II for k = 5. Column (1) displays the regression result without time fixed effects, which allows us to estimate the coefficient for the inflationary news on its own. Similarly to Figure I, the inflation surprise coefficient is -1.501 and the main coefficient of interest, the interaction between markups and the inflation surprise is 0.260. Column (2) introduces time fixed effect in the regression equation. The inclusion of time fixed effects introduces collinearity with the inflation surprise so that the effect of inflationary news cannot be interpreted 34

anymore. However, the advantage of the inclusion of time fixed effects is that through its inclusion we control for all unobservable and observable time-variant factors that could bias the result that firms with higher markups earn higher returns than their counterparts in response to inflationary news. Through the inclusion of time fixed effects we control for the average effect of being in a particular time period, and it allows us to make a within-time period comparison. For instance, we can control for any underlying trends in monetary policy, and uncertainty and instead isolate the effect of inflationary news on firms with differential degrees of market power. The coefficient on the interaction between market power and inflationary news remains virtually the same, indicating that time-variant factors that are correlated with the interaction of inflationary news and markup are not driving the results. Column (3) introduces industry*time fixed effects to not only control for unit-invariant time specific factors, but also for industry-specific time-variation that is both observable and unobservable. While the coefficient shrinks slightly in absolute terms, it is still statistically significant. Columns(4)and(5)introduceinteractedfirm-levelcontrolstocontrolforpotentialconfounding firm-level characteristics. In column (4) we first rely on balance sheet characteristics from Compustat, Tobin’s Q, log assets, leverage, and tangibility, and in column (5) we use firms’ conditional beta to the three Fama French factors that are estimated using lagged rolling 5-year regressions.29 Through the inclusion of the interacted firm-level characteristics, we control for the heterogeneous impact of inflation across the leverage distribution (Bhamra et al., 2023). Given the increasing equity risk premium is a driver of negative stock returns in the aggregate, the Fama French risk-factor betas are important to rule out a potential explanation of the results that is that firms with lower markups are riskier and therefore load more on increasing the equity risk premium in response to inflationary news. However, the coefficient on the interaction between inflationary news and markup remains stable with these additional controls, indicating neither alternate firm characteristics nor firm’s risk exposures are confounding factors. Forrobustness, weuseanalternativemeasureofmarketpowermeasureisdefinedasthechange in economic profits of the focal firm following a 1% rise in all firms’ marginal costs based on the Pellegrino (2024) GHL approach, discussed in subsection 3.3. Table A.IX replicates Table II but replaces De Loecker et al. (2020) markups with the Pellegrino (2024) cost elasticity. The results are qualitatively the same. The negative effects of inflation on stock prices are mitigated by market power. In sum, we find strong evidence that inflationary news reduces stock prices for a firm that has a limited degree of market power, but firms with market power are less severely hit and those that have a substantial degree do not suffer from inflationary news. The stark difference suggests that stock market investors see the impact of inflation on future discounted cash flows of high market power firms more benignly than that of firms that do not have market power. These findings can be rationalized in a model in which inflation is seen as a marginal cost shock rather than a demand 29There are less observations in specifications which include the Fama French factors due to the requirement of 5 years of firm-level data before the betas are first observed. 35

shock, as shown in Appendix D. 6.4.2 Real Cash Flows Component In subsubsection 6.3.2 we have shown that declining real cash flow news around inflationary news areanimportantdriverofthedeclineinstockprices. Inthissection,wetestwhetherrealcashflows expectations are also the driver behind the differences in stock returns across firms with differential degree of market power in response to inflationary news. Given that changes in discount rate affect the present value of discounted cash flows, differences in the cash flow duration of firms across the market power distribution would mechanically lead to heterogeneous returns in response to discount rate changes that occur with inflationary news. This variation in realized returns, which is purely due to discounting, would occur even if there was no change in expected cash flows across firms in the market power distribution. Toextractthecashflowcomponentofvariationinthecrosssectionofstockreturns,wetherefore follow a similar two-stage strategy as in subsubsection 6.3.2. In the first stage, we estimate the following series of regressions for all k ∈ [−5,10] across CPI dates: R (cid:94) eturn k = αk +(∆ D (cid:94) CR ′ ×Markup )Θk +Γ Ψk +ϵ(cid:102)k , (17) i,t i k t i,y(t)−1 i,t i,t (cid:94) k whereReturn istherealstockreturnaroundtheCPIreleaseandfirm-levelmarkups,Markup , i,t i,y(t)−1 (cid:104) (cid:105) (cid:94) are interacted with a vector of discount rates, DCR t = R(cid:103)F t ,ERP t , that includes real risk-free rates yields across various maturities, R(cid:103)F t , and the Martin (2017) equity risk premium, ERP t . The regression also includes a control vector, Γ , that includes firm-level markups, Markup , the i,t i,t (cid:94) discount rate vector, DCR , other firm-level characteristics, X : log assets, tangibility, leverage, t i,t market-to-book value, rolling betas to Fama and French (1993) asset pricing factors market beta, size, and value. The control vector Γ additionally includes interactions between discount rates i,t and firm-level characteristics. Asdiscussedinsection4forthetimeseries, byabsorbingvariationinreturnsrelatedtochanges indiscountrates,wecanthendefinetherealcashflowcomponentoffirm-levelstockreturnsaround CPI releases as: (cid:92) k,C(cid:103)F ϵ(cid:102)k = Return i,t i,t and, because Equation 17 does not include the inflation surprise itself in the equation, we can now test how this real cash flow component of stock returns respond differentially to inflationary news depending on the degree of market power firms have. To do to so, we estimate in a second stage the following sequence of regressions for all k ∈ [−5,10] across CPI dates: (cid:92) k,C(cid:103)F Return =α+β Inflationary News ∗Low Markup i,t 1 t i,y(t)−1 (18) +β Inflationary News ∗High Markup +β Low Markup +ϵ , 2 t i,y(t)−1 3 i,y(t)−1 i,t 36

(cid:92) k,C(cid:103)F where Return is the predicted real cash flow component of the k-day stocks returns. High i,t markupfirmsarethosefirmsthathaveatanygivenpointintimemarkupsabovethe75thpercentile of the markup distribution while those with low markups are those with markups below the 25th percentile of the distribution. Notethatfirmsacrosstheleverage(OttonelloandWinberry,2020), markup(Duvaletal.,2021; Liu et al., 2022; Duval et al., 2023), or tangibility (D¨ottling and Ratnovski, 2023) distribution may exhibit differential sensitivity with respect to changes in the interest rate relative to their counterparts. The differential response of firm returns to inflation surprises may therefore be mediated through an increase in nominal interest rates (see Figure II), potentially due to changes in monetary policy expectations, rather than real cash flow expectations directly related to the effect of inflation. It is therefore important that the interaction of firm-level markups (and other firm characteristics) with discount rates in Equation 17 controls not only for the differential impact of changes in discount rates on firm returns through a cash flow discounting channel, but also controls for the potentially differential impact of changes in discount rates on firm returns due to different sensitivities of firm cash flows themselves to the interest rate environment. The response (cid:92) k,C(cid:103)F of Return to inflationary news estimated in Equation 18 should therefore be interpreted as the i,t component of stock returns that is due to changing investor expectations of future real cash flows that, importantly, are not changes in cash flow expectations that are due to changes in the interest rate environment that come with inflationary news. FigureXplotsβ andβ fordifferentk′s. Theleftpanelplotsβ —theeffectofinflationarynews 1 2 1 on the predicted real cash flow component of stock returns for high-markup firms. The coefficient is negative but not statistically significant for most of the horizon, indicating that investors do not expect real flows to decline with inflationary news for firms that do have market power. This result is consistent with the main model prediction that investors expect firms with market power to see nominal revenue decline less with inflation for firms with high market power if the inflation surprise is considered a cost shock. In contrast, for firms with a small degree of market power, investors expect real cash flows to decline significantly (right panel). With higher inflation, firms without market power see a stronger decline in profits. These results confirm the hypothesis that the differential stock price response for firms across themarketpowerdistributionistoalargepartdrivenbycashflowexpectationsdirectlyinresponse to higher inflation, rather than through differential effects of changes in discount rates, as predicted in Appendix D. 6.4.3 Earnings Expectations Given that we find a real cash flow channel for the response of equity prices to inflationary news, a naturalquestioniswhetherweobserveachangeininvestor’sexpectationsofcompanyearnings. To tacklethisquestion,weobtainchangesinfirm-levelearningsexpectations(∆EarningsExpectation ) i,t around CPI news, as described in subsection 3.5. This variable allows us to test whether higher 37

inflationary news are associated with different changes in earnings expectations across firms. To do so, we estimate the following empirical specification that is equivalent to Equation 14 but replaces the firm-level return with the change in the firm-level earnings expectations on the left-hand side: ∆EarningsExpectation = α+β Inflationary News ∗Markup +α +α +X′γ+ϵ , (19) i,t 1 t i,y(t)−1 i t i,t where, as previously, Inflationary News is the difference between the published month-on-month t CPIinflationandthethemedianexpectationofforecastsaheadoftheannouncement. Markup i,y(t)−1 is the estimated markup from De Loecker et al. (2020) and standardized to have mean zero and a standard deviation of one. α is a firm fixed effect. α is a date fixed effect. X are controls and i t fixed effects, depending on the specification. Table III show the results. In column (1) the coefficient on inflationary news shows the effect of the average firm, as markups are demeaned and standardized. Contrary to the idea that nominal earnings should increase with higher-than-expected inflation, we do not find evidence for the hypothesis that nominal earnings move higher with inflation. Instead, if anything, nominal earnings are expected to fall instead of increase after inflationary news; see also ??. This result also suggests that earnings analysts do not see the inflationary surprise as a shock to demand, but rather as one to supply, which reduces earnings. The interaction coefficient between inflationary news and market power is positive and statistically significant, indicating that firms with market power are expected to lose less earnings than their counterparts. This result is consistent with the previous evidence that firms with market power earn higher stock returns because of higher expected earnings by the marginal stock market investor. Columns (2)–(4) confirm the result when time fixed effects and other firm-level controls are included in the regression specification. Despite a substantial increase in the R-squared value, the coefficient estimate remains relatively stable, suggesting that market power, and not other firm characteristics that are in the control vector, is responsible for the differential response in earnings expectations around inflationary surprises. Figure XI further illustrates the cross-sectional results. We split firms into those that have marketpower—definedasadummybeingoneifthefirmisinthe75thpercentileofthedistribution of markups and zero otherwise—and we estimate the relationship between inflationary news and the change in earnings expectations separately for the two samples of firms. For firms without market power, higher inflationary news, as shown on the x-axis, are associated with lower earnings expectations,whileforfirmswithmarketpower,higherinflationarynewsareassociatedwithhigher earnings expectations. 7 Conclusion Inthispaper,wehavestudiedinvestors’perceptionsofinflationthroughthelensofahigh-frequency event study. We have shown that inflation is expected to decrease firms’ real cash flows, which is 38

consistentwithinterpretinginflationasstagflationary. Thesefindingscanberationalizedinamodel in which inflation is seen as a shock to marginal costs, instead of one to demand. Another main prediction from this model is that market power shields firms’ earnings declines. When exploiting heterogeneity across firms, we have indeed found consistent evidence that stock prices, driven by differential earnings expectations, decline less for firms with more market power. Overall, these results indicate that investors consider inflation bad news for the economy. Assuming investors are rational, and the lower real cash flows for firms are accurate, one may want to conclude that surprise inflation does not only lead to stagflationary stock returns but also to stagflation in the macroeconomy. However, drawing implications from the movement in cash flow expectations for the actual implications of inflation should be done with caution. While stock returns may have real effects themselves (Bond et al., 2012), investors’ expectations may contain systematic errors, and their expectations are not in line with realized future economic outcomes (Bordalo et al., 2023). Hence, our results raise important further questions, which we leave for future research. Is investors’ perception that inflationary news are stagflationary accurate? Or does Wall Street have a biased “stagflationary” view of the world, as it incorrectly interprets inflationary news as supply shocks that drive up marginal costs? Does higher inflation lead to an increasing market share of firms with already high market power, potentially leading to higher prices in aggregate? What are the implications for monetary policy if an initial increase in inflation leads to more inflation because of an aggregate increase in market power? 39

References Agarwal, Isha and Matthew Baron (2024) “Inflation and disintermediation”, Journal of Financial Economics (forthcoming). Andre, Peter, Carlo Pizzinelli, Christopher Roth, and Johannes Wohlfart (2022) “Subjective models of the macroeconomy: Evidence from experts and representative samples”, The Review of Economic Studies, 89 (6), pp. 2958–2991. Asness, Clifford S(2003)“Fightthefedmodel”,The Journal of Portfolio Management,30(1),pp.11–24. Bachmann, Ru¨diger, Tim O Berg, and Eric R Sims (2015) “Inflation expectations and readiness to spend: Cross-sectional evidence”, American Economic Journal: Economic Policy, 7 (1), pp. 1–35. Baker, Andrew C, David F Larcker, and Charles CY Wang (2022) “How much should we trust staggered difference-in-differences estimates?”, Journal of Financial Economics, 144 (2), pp. 370–395. Bansal, Ravi and Ivan Shaliastovich (2013) “A long-run risks explanation of predictability puzzles in bond and currency markets”, Review of Financial Studies, 26. Basu, Susanto (2019) “Are price-cost markups rising in the united states? a discussion of the evidence”, Journal of Economic Perspectives, 33 (3), pp. 3–22. Bauer,MichaelD.(2015)“Inflationexpectationsandthenews”,InternationalJournalofCentralBanking, 11. Bauer, Michael D, Carolin Pflueger, and Adi Sunderam (2022) “Perceptions about monetary policy”,Technical report, National Bureau of Economic Research. Beechey, Meredith J. and Jonathan H. Wright (2009) “The high-frequency impact of news on longterm yields and forward rates: Is it real?”, Journal of Monetary Economics, 56. Bekaert, Geert and Eric Engstrom (2010) “Inflation and the stock market: Understanding the “fed model””, Journal of Monetary Economics, 57 (3), pp. 278–294. Berry, Steven, Martin Gaynor, and Fiona Scott Morton (2019) “Do increasing markups matter? lessons from empirical industrial organization”, Journal of Economic Perspectives, 33 (3), pp. 44–68. Bhamra, Harjoat S, Christian Dorion, Alexandre Jeanneret, and Michael Weber (2023) “High inflation: Lowdefaultriskandlowequityvaluations”, The Review of Financial Studies, 36(3), pp.1192– 1252. van Binsbergen, Jules H.(2020)“Duration-basedstockvaluation: Reassessingstockmarketperformance and volatility”, SSRN Electronic Journal. Boehm, Christoph E. and T. Niklas Kroner (2023) “The us, economic news, and the global financial cycle”, International Finance Discussion Paper. Bond, Philip, Alex Edmans, and Itay Goldstein (2012) “The real effects of financial markets”, Annu. Rev. Financ. Econ., 4 (1), pp. 339–360. Bond, Steve, Arshia Hashemi, Greg Kaplan, and Piotr Zoch (2021) “Some unpleasant markup arithmetic: Production function elasticities and their estimation from production data”, Journal of Monetary Economics, 121, pp. 1–14. Boons, Martijn, Fernando Duarte, Frans De Roon, and Marta Szymanowska (2020) “Timevarying inflation risk and stock returns”, Journal of Financial Economics, 136 (2), pp. 444–470. 40

Bordalo, Pedro, NicolaGennaioli, RafaelLaPorta, andAndreiShleifer(2023)“Beliefoverreaction and stock market puzzles”, Journal of Political Economy (forthcoming). Boyd, John H, Jian Hu, and Ravi Jagannathan(2005)“Thestockmarket’sreactiontounemployment news: Why bad news is usually good for stocks”, The Journal of Finance, 60 (2), pp. 649–672. Brunnermeier, Markus K, Sergio A Correia, Stephan Luck, Emil Verner, and Tom Zimmermann(2023)“Thedebt-inflationchannelofthegermanhyperinflation”,Technicalreport,NationalBureau of Economic Research. Callaway, Brantly and Pedro HC Sant’Anna (2021) “Difference-in-differences with multiple time periods”, Journal of Econometrics, 225 (2), pp. 200–230. Campbell, John Y. (1991) “A variance decomposition for stock returns”, The Economic Journal, 101. Campbell, John Y., Carolin Pflueger, and Luis M. Viceira (2020) “Macroeconomic drivers of bond and equity risks”, Journal of Political Economy, 128. Campbell, John Y., Christopher Polk, and Tuomo Vuolteenaho (2010) “Growth or glamour? fundamentals and systematic risk in stock returns”, Review of Financial Studies, 23. Campbell, John Y., Adi Sunderam, and Luis M. Viceira (2017) “Inflation bets or deflation hedges? the changing risks of nominal bonds”, Critical Finance Review, 6. Campbell, John Y and Tuomo Vuolteenaho (2004) “Inflation illusion and stock prices”, American Economic Review, 94 (2), pp. 19–23. Candia, Bernardo, Olivier Coibion, and Yuriy Gorodnichenko (2023) “The macroeconomic expectations of firms”, Handbook of Economic Expectations, Elsevier, pp. 321–353. Carhart, Mark M (1997) “On persistence in mutual fund performance”, The Journal of finance, 52 (1), pp. 57–82. Chaudhary, Manav and Benjamin Marrow (2024) “Inflation expectations and stock returns”. Chernov, Mikhail, Lars A. Lochstoer, and Dongho Song(2023)“Therealchannelfornominalbondstock puzzles”. Cho, Thummim, Marco Grotteria, Lukas Kremens, and Howard Kung (2023) “The present value of future market power”, Available at SSRN 3921171. Cieslak, Anna and Hao Pang (2021) “Common shocks in stocks and bonds”, Journal of Financial Economics, 142. Cieslak, Anna and Carolin Pflueger (2023) “Inflation and asset returns”, Available at SSRN. Cieslak, Anna and Andreas Schrimpf (2019) “Non-monetary news in central bank communication”, Journal of International Economics, 118. Cohen, RandolphB,ChristopherPolk, andTuomoVuolteenaho(2005)“Moneyillusioninthestock market: The modigliani-cohn hypothesis”, The Quarterly journal of economics, 120 (2), pp. 639–668. Coibion, Olivier, Dimitris Georgarakos, Yuriy Gorodnichenko, Geoff Kenny, and Michael Weber (2024) “The effect of macroeconomic uncertainty on household spending”, American Economic Review, 114 (3), pp. 645–677. 41

Coibion, Olivier, Dimitris Georgarakos, Yuriy Gorodnichenko, and Maarten Van Rooij (2023) “Howdoesconsumptionrespondtonewsaboutinflation? fieldevidencefromarandomizedcontroltrial”, American Economic Journal: Macroeconomics, 15 (3), pp. 109–152. Coibion, Olivier, Yuriy Gorodnichenko, and Saten Kumar (2018) “How do firms form their expectations? new survey evidence”, American Economic Review, 108 (9), pp. 2671–2713. Coibion, Olivier, Yuriy Gorodnichenko, and Tiziano Ropele(2020)“Inflationexpectationsandfirm decisions: New causal evidence”, The Quarterly Journal of Economics, 135 (1), pp. 165–219. Coibion, Olivier, Yuriy Gorodnichenko, and Michael Weber (2022) “Monetary policy communications and their effects on household inflation expectations”, Journal of Political Economy, 130 (6), pp. 1537–1584. Corhay, Alexandre, Howard Kung, and Lukas Schmid (2020) “Competition, markups, and predictable returns”, The Review of Financial Studies, 33 (12), pp. 5906–5939. Corhay, Alexandre, Jun E Li, and Jincheng Tong (2022)“Markupshocksandassetprices”,Available at SSRN 4060403. Corhay, Alexandre and Jincheng Tong (2021) “Inflation risk and the finance-growth nexus”, Rotman School of Management Working Paper (3795679). De La O, Ricardo and Sean Myers (2021) “Subjective cash flow and discount rate expectations”, The Journal of Finance, 76 (3), pp. 1339–1387. De Loecker, Jan, Jan Eeckhout, and Simon Mongey (2021)“Quantifyingmarketpowerandbusiness dynamism in the macroeconomy”, (28761). De Loecker, Jan, Jan Eeckhout, and Gabriel Unger (2020) “The rise of market power and the macroeconomic implications”, The Quarterly Journal of Economics, 135 (2), pp. 561–644. De Loecker, Jan and Frederic Warzynski (2012) “Markups and firm-level export status”, American economic review, 102 (6), pp. 2437–2471. De Ridder, Maarten, Basile Grassi, and Giovanni Morzenti (2021) “The hitchhiker’s guide to markup estimation”,Technical report. Doraszelski, Ulrich and Jordi Jaumandreu (2021) “Reexamining the de loecker & warzynski (2012) method for estimating markups”. D¨ottling, Robin and Lev Ratnovski (2023) “Monetary policy and intangible investment”, Journal of Monetary Economics, 134, pp. 53–72. Drechsler, Itamar, Alexi Savov, and Philipp Schnabl (2022) “Credit crunches and the great stagflation”. Dube, Arindrajit, Daniele Girardi, Oscar Jorda, and Alan M Taylor (2023) “A local projections approach to difference-in-differences event studies”,Technical report, National Bureau of Economic Research. Duval, Mr Romain A, Davide Furceri, Raphael Lee, and Marina M Tavares(2021)Market power and monetary policy transmission, International Monetary Fund. Duval, Romain, DavideFurceri, RaphaelLee, andMarinaMTavares(2023)“Marketpower,financial constraints, and monetary transmission”, AEA Papers and Proceedings, 113, pp. 99–104, American Economic Association 2014 Broadway, Suite 305, Nashville, TN 37203. 42

D’Acunto, Francesco, Daniel Hoang, Maritta Paloviita, and Michael Weber (2023) “Iq, expectations, and choice”, Review of Economic Studies (forthcoming). d’Amico, Stefania, Don H Kim, and Min Wei (2018) “Tips from tips: the informational content of treasury inflation-protected security prices”, Journal of Financial and Quantitative Analysis, 53 (1), pp. 395–436. Elenev, Vadim, Tzuo-Hann Law, Dongho Song, and Amir Yaron (2024) “Fearing the fed: How wall street reads main street”, Journal of Financial Economics, 153, p. 103790. Engsted, Tom, Thomas Q. Pedersen, and Carsten Tanggaard (2012) “Pitfalls in var based return decompositions: A clarification”, Journal of Banking and Finance, 36. Fama, Eugene F (1981) “Stock returns, real activity, inflation, and money”, The American Economic Review, 71 (4), pp. 545–565. Fama, Eugene F. and Kenneth R. French (1993) “Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics, 33. Fama, Eugene F. and Kenneth R. French (2015) “A five-factor asset pricing model”, Journal of Financial Economics, 116. Fama, Eugene F and G William Schwert (1977) “Asset returns and inflation”, Journal of financial economics, 5 (2), pp. 115–146. Fang, Xiang, Yang Liu, and Nikolai Roussanov (2022) “Getting to the core: Inflation risks within and across asset classes”,Technical report, National Bureau of Economic Research. Firth, Michael(1979)“Therelationshipbetweenstockmarketreturnsandratesofinflation”,The Journal of Finance, 34 (3), pp. 743–749. Fischer, Stanley (1993) “The role of macroeconomic factors in growth”, Journal of monetary economics, 32 (3), pp. 485–512. Fisher, Irving (1930) The Theory of Interest, New York: McMillan. Fleckenstein, Matthias, Francis A. Longstaff, and Hanno Lustig (2014) “The tips-treasury bond puzzle”, Journal of Finance, 69. Gabaix, Xavier (2008) “Variable rare disasters: A tractable theory of ten puzzles in macro-finance”, American Economic Review, 98 (2), pp. 64–67. Gilbert, Thomas, Chiara Scotti, Georg Strasser, and Clara Vega (2017) “Is the intrinsic value of a macroeconomic news announcement related to its asset price impact?”, Journal of Monetary Economics, 92, pp. 78–95. Gomes, Joao, Urban Jermann, and Lukas Schmid (2016) “Sticky leverage”, American Economic Review, 106 (12), pp. 3800–3828. Goodman-Bacon, Andrew (2021)“Difference-in-differenceswithvariationintreatmenttiming”, Journal of Econometrics, 225 (2), pp. 254–277. Goolsbee, Austan, Steven Levitt, and Chad Syverson (2012) Microeconomics, Macmillan Higher Education. Gormsen, Niels Joachim and Ralph S.J. Koijen (2020) “Coronavirus: Impact on stock prices and growth expectations”, Review of Asset Pricing Studies, 10. 43

Gourio, Franc¸ois and Phuong Ngo (2020) “Risk premia at the zlb: a macroeconomic interpretation”. Gurkaynak, Refet S, Bur¸cin Kisaciko˘glu, and Jonathan H Wright (2020) “Missing events in event studies: Identifying the effects of partially measured news surprises”, American Economic Review, 110 (12), pp. 3871–3912. Gu¨rkaynak,RefetS.,AndrewLevin,andEricSwanson(2010a)“Doesinflationtargetinganchorlongrun inflation expectations? evidence from the u.s., uk, and sweden”, Journal of the European Economic Association, 8. Gu¨rkaynak, Refet S., Brian Sack, and Eric Swanson (2005) “The sensitivity of long-term interest rates to economic news: Evidence and implications for macroeconomic models”, American Economic Review, 95. Gu¨rkaynak, Refet S., Brian Sack, and Jonathan H. Wright (2010b) “The tips yield curve and inflation compensation”, American Economic Journal: Macroeconomics, 2. Hall, Robert (1988) “The relation between price and marginal cost in u.s. industry”, Journal of Political Economy. Hall, Robert(2018)“Newevidenceonthemarkupofpricesovermarginalcostsandtheroleofmoega-firms in the us economy”, NBER Working Papers. Hanson, Samuel G., David O. Lucca, and Jonathan H. Wright (2021) “Rate-amplifying demand and the excess sensitivity of long-term rates”, Quarterly Journal of Economics, 136. Hanson, Samuel G. and Jeremy C. Stein (2015) “Monetary policy and long-term real rates”, Journal of Financial Economics, 115. Hoek, Jasper, Steve Kamin, and Emre Yoldas (2022) “Are higher u.s. interest rates always bad news for emerging markets?”, Journal of International Economics, 137. Ibert, Markus, Ben Knox, and Francisco Vazquez-Grande (2022) “Are stocks pricing in recession risks? evidence from dividend futures”. Jarocin´ski, Marek and Peter Karadi (2020) “Deconstructing monetary policy surprises-the role of information shocks”, American Economic Journal: Macroeconomics, 12. Jord`a, O (2005) “Estimation and inference of impulse responses by local projections”, American Economic Review, 95 (1), pp. 161–182. Katz, Michael, Hanno Lustig, and Lars Nielsen (2017) “Are stocks real assets? sticky discount rates in stock markets”, Review of Financial Studies, 30. Knox, Benjamin and Annette Vissing-Jorgensen (2024) “A stock returndecomposition using observables”. Kroen, Thomas, Ernest Liu, Atif R Mian, and Amir Sufi (2021) “Falling rates and rising superstars”,Technical report, National Bureau of Economic Research. Kroner, Niklas (2023) ““inflation and attention: evidence from the market reaction to macro announcements”, Available at SSRN. Laarits, Toomas (2022) “Precautionary savings and the stock-bond covariance”. Law, Tzuo Hann, Dongho Song, and Amir Yaron (2018) “Fearing the fed: How wall street reads main street”, Available at SSRN 3092629. 44

Liu, Ernest, Atif Mian, and Amir Sufi (2022) “Low interest rates, market power, and productivity growth”, Econometrica, 90 (1), pp. 193–221. Martin, Ian (2017) “What is the expected return on the market?”, The Quarterly Journal of Economics, 132 (1), pp. 367–433. Modigliani, Franco and Richard A Cohn(1979)“Inflation,rationalvaluationandthemarket”, Financial Analysts Journal, 35 (2), pp. 24–44. Nagel, Stefan and Zhengyang Xu (2024) “Movements in yields, not the equity premium: Bernankekuttner redux”. Nakamura, Emi and Jon Steinsson (2018) “High-frequency identification of monetary non-neutrality: The information effect”, 133, p. 1283–1330. De la O, Ricardo and Sean Myers (2024) “Which subjective expectations explain asset prices?”, The Review of Financial Studies, 37 (6), pp. 1929–1978. Ottonello, Pablo and Thomas Winberry (2020) “Financial heterogeneity and the investment channel of monetary policy”, Econometrica, 88 (6), pp. 2473–2502. Pellegrino, Bruno (2024) “Product differentiation and oligopoly: A network approach”, American Economic Review (forthcoming). Pflueger, Carolin (2023) “Back to the 1980s or not? the drivers of inflation and real risks in treasury bonds”, NBER Working Paper. Philippon, Thomas (2019) The great reversal: How America gave up on free markets, Harvard University Press. Pindyck, Robert S and Daniel L Rubinfeld (2014) Microeconomics, Pearson Education. Ramey, Valerie A. (2016) “Macroeconomic shocks and their propagation”, Handbook of Macroeconomics, 2, pp. 71–162. Raval, Devesh (2020) “Testing the production approach to markup estimation”, Available at SSRN 3324849. Gil de Rubio Cruz, Antonio, Emilio Osambela, Berardino Palazzo, Francisco Palomino, and Gustavo Suarez (2023) “Inflation surprises in the cross-section of equity returns”, Available at SSRN. Schnorpfeil, Philip, Michael Weber, and Andreas Hackethal (2024) “Inflation and trading”. Shapiro, Adam (2022) “How much do supply and demand drive inflation?”, FRBSF Economic Letter, 15. Sharpe, Steven A (2002) “Reexamining stock valuation and inflation: The implications of analysts’ earnings forecasts”, Review of Economics and Statistics, 84 (4), pp. 632–648. Shiller, Robert J (1997) “Why do people dislike inflation?”, NBER Chapters, pp. 13–70. Skaperdas, Arsenios(2023)“Inflationexpectationsandthepersistenceofunanticipatedinflation”, Available at SSRN 4618109. Stantcheva, Stefanie(2024)“Whydowedislikeinflation?”,Technicalreport,NationalBureauofEconomic Research. Summers,LawrenceH(1980)“Inflation,thestockmarket,andowner-occupiedhousing”,Technicalreport, National Bureau of Economic Research. 45

Syverson, Chad (2019) “Macroeconomics and market power: Context, implications, and open questions”, Journal of Economic Perspectives, 33 (3), pp. 23–43. Taylor, John B (1993) “Discretion versus policy rules in practice”, Carnegie-Rochester conference series on public policy, 39, pp. 195–214, Elsevier. Taylor, John B (1999) “A historical analysis of monetary policy rules”, Monetary policy rules, University of Chicago Press, pp. 319–348. Tirole, Jean (1989) The Theory of Industrial Organization, The MIT Press. Weber, Michael (2015) “Nominal rigidities and asset pricing”, Available at SSRN 2478500. Weber, Michael, Francesco D’Acunto, Yuriy Gorodnichenko, and Olivier Coibion (2022) “The subjectiveinflationexpectationsofhouseholdsandfirms: Measurement,determinants,andimplications”, Journal of Economic Perspectives, 36 (3), pp. 157–184. 46

Figures and Tables Figure I: Stock returns around inflationary news 2 0 -2 -4 % -5 0 5 10 Days This figure plots the estimated coefficient of Equation 13: yk =αk+βkInflationary News +ϵk, t t t whereyk isthecumulativereturnbetweenthedaybeforetheCPIannouncementondatetandk daysafter. t Inflationary News is the difference between the published month-on-month CPI inflation and the median t expectation of forecasts ahead of the announcement. The sample period is 1977–2022. The shaded area reflects the 90% confidence interval. 47

Figure II: The yield curve around inflationary news 20 10 0 -10 -20 stnioP sisaB 2-year Nominal Treasury Yield 30 20 10 0 -10 -20 -5 0 5 10 Days stnioP sisaB 10-year Nominal Treasury Yield -5 0 5 10 Days 60 40 20 0 -20 stnioP sisaB 2-year Breakeven Inflation 30 20 10 0 -10 -20 -5 0 5 10 Days stnioP sisaB 10-year Breakeven Inflation -5 0 5 10 Days 20 0 -20 -40 -60 stnioP sisaB 2-year Real Treasury Yield 30 20 10 0 -10 -20 -5 0 5 10 Days stnioP sisaB 10-year Real Treasury Yield -5 0 5 10 Days This figure plots the estimated coefficient of Equation 13: yk =αk+βkInflationary News +ϵk, t t t where yk is the change in nominal yields, real yields, and breakeven inflation from the day before the CPI t announcement on date t to k days after the announcement. Inflationary News is the difference between the t publishedmonth-on-monthCPIinflationandthemedianexpectationofforecastsaheadoftheannouncement. The left column shows changes in the 2-year nominal Treasury yield, the 2-year breakeven inflation rate, and the 2-year real Treasury yield in rows 1 through 3, respectively. The right column shows changes in the 10-year nominal Treasury yield, the 10-year breakeven inflation rate, and the 10-year real Treasury yield in rows 1 through 3, respectively. Data for the real yield curve is taken from Gu¨rkaynak et al. (2010b). All figures are based on the sample period 1999–2022. The shaded area reflects the 90% confidence interval. 48

Figure III: Equity risk premium around inflationary news 150 100 50 0 -50 stnioP sisaB -5 0 5 10 Days This figure plots the estimated coefficient of Equation 13: yk =αk+βkInflationary News +ϵk, t t t whereyk =EP −EP isthechangeintheMartin(2017)lowerboundofthe1-yearequityriskpremium t t+k t−1 fromthedaybeforetheCPIannouncementondatettokdaysaftertheannouncement. Inflationary News is t thedifferencebetweenthepublishedmonth-on-monthCPIinflationandthemedianexpectationofforecasts ahead of the announcement. The sample period is 1999–2022. The shaded area reflects the 90% confidence interval. 49

Figure IV: Cash flow component of stock returns around inflationary news 4 2 0 -2 -4 -6 % Nominal Cashflow Return Component -5 0 5 10 Days 4 2 0 -2 -4 -6 % Real Cashflow Return Component -5 0 5 10 Days These figure plots the estimated coefficient of Equation 13: yk =αk+βkInflationary News +ϵk, t t t where yk is the nominal and real cash flow return components, as defined in section 4, from the day before t the CPI announcement on date t to k days after the announcement. Inflationary News is the difference t between the published month-on-month CPI inflation and the median expectation of forecasts ahead of the announcement. The sample period is 1999–2022. The shaded area reflects the 90% confidence interval. 50

Figure V: Decomposition of real stock returns around inflationary news 1 0 -1 -2 -3 -4 % -5 0 5 10 Days Realized Real Return Real Cash Flow Component Equity Risk Premium Component Real Yield Curve Component This figure stacks the estimated coefficient of Equation 13: yk,c =αk,c+βk,cInflationary News +ϵk,c, t t t where yk,c is the predicted c = {C(cid:103)F,EP,Y(cid:103)C} component of the cumulative real return between the day t before the CPI announcement on date t and k days after. The return components are the returns generated from changes in real cash flow expectations, C(cid:103)F, changes in equity risk premium, EP, and changes in real governmentbondyields,Y(cid:103)C. Theblacklineinthefigureplotsthecoefficientsofrealrealizedreturnregressed on inflation news for k = −5 through k = 10, which is by definition the sum of the stacked coefficients on the return components. Inflationary News is the difference between the published month-on-month CPI t inflation and the median expectation of forecasts ahead of the announcement. The sample period is 1999– 2022. 51

Figure VI: Cash flow component validation: correlation with direct cash flow measures .01 .005 0 -.005 -.01 yaD 1 tnenopmoC wolF hsaC lanimoN .005 0 -.005 -.01 -.015 -10 -5 0 5 10 D Earnings Expectations yaD 1 tnenopmoC wolF hsaC lanimoN .005 0 -.005 -.01 -.015 -.02 -1 -.5 0 .5 D Nominal Dividend Futures 1 Day yaD 1 tnenopmoC wolF hsaC laeR -1 -.5 0 .5 1 D Real Dividend Futures 1 Day .02 .01 0 -.01 -.02 yaD 5 tnenopmoC wolF hsaC lanimoN .04 .02 0 -.02 -.04 -10 -5 0 5 10 D Earnings Expectations yaD 5 tnenopmoC wolF hsaC lanimoN .04 .02 0 -.02 -.04 -2 -1 0 1 2 D Nominal Dividend Futures 5 Day yaD 5 tnenopmoC wolF hsaC laeR -3 -2 -1 0 1 D Real Dividend Futures 5 Day This figure combines binscatterplots between the 1- (5-) day extracted cash flow component of stock returns, as defined in section 4, on the y-axis on the upper (lower) panels against alternative measures of cash flow expectations. In the left panels we plot nominal extracted earnings expectations against ∆Earnings Expectation and ∆ ln(Div.Futures2) (middle panel) on the x-axis. The right panels plot the t k t real cash flow component of stock returns and real dividend futures on the x-axis. ∆Earnings Expectation t is the (asset-) weighted average change in earnings expectations around CPI dates, as described in subsection 3.5. ∆ ln(Div.Futures2) are risk premium-adjusted log changes in the 2-year-ahead dividend future k t price over period k, as described in subsection 3.2. 52

Figure VII: Cash flow component validation: cash flow expectations around economic activity news YzS9 YzS Yzz9 z AYzz9 X GA0 whNRLCN Ih, c@8IRsha3jnaNh,RLURN3Nj : l z Al A: A9 z 9 Sz / wc XhjN3NRULR+hsRI8@c +hI NCLRM SA0 whNRLCN Ih, c@8IRsha3jnaNh,RLURN3Nj Al AS z S l M7ThM3schVCNhSzzGW SY9 S Y9 z cNRCj j,3Uu2hc<NCNa 2hD D h2 aNCN<ch2uU3,j jCRNc S Y9 z AY9 AS AYl AYS z YS Yl Yk BN8I jCRN awhM3sc cNRCj j,3Uu2hc<NCNa 2hD D h2 aNCN<ch2uU3,j jCRNc Al AS z S l M7ThM3schVCNhSzzGW The top left figure plots the estimated coefficient of the equation: yk =αk+βkNFP News +ϵk, t t t whereyk isthenominalcashflowreturncomponentsfromthestockreturndecompositionfromthedaybefore t thenonfarmpayrollannouncementondatettok daysaftertheannouncement. NFP News isthedifference t between the published monthly rise in total nonfarm payroll employment and the median expectation of forecasts ahead of the announcement (in 100k). The shaded area reflects the 90% confidence interval. The top right figure presents a binscatterplot between the 1-day nominal cash flow return component, y1, on the t y-axis against the NFP News on the x-axis. The sample period of the top row is 1999–2022. The bottom t row presents binscatterplots between ∆Earnings Expectation on the y-axis and Inflationary News (left i,t t figure) and NFP News (right figure) on the x-axis’ respectively. ∆Earnings Expectation is the log change t i,t in earnings expectations between 15 days after and before the CPI release. The black line plots the linear fit across all releases. 53

Figure VIII: Stock returns around inflationary news by market power 2 0 -2 -4 -6 % High Markup Firms 2 0 -2 -4 -6 -5 0 5 10 Days b2 Inflationary News * High Markup % Low Markup Firms -5 0 5 10 Days b1 Inflationary News * Low Markup This figure plots the estimated coefficient of Equation 16: Returnk =α+β Inflationary News ∗Low Markup i,t 1 t i,y(t)−1 +β Inflationary News ∗High Markup +β Low Markup +ϵ 2 t i,y(t)−1 3 i,y(t)−1 i,t whereReturnk isthecumulativereturnbetweenthedaybeforetheCPIannouncementondatetandkdays i,t after for stock i. Inflationary News is the difference between the published month-on-month CPI inflation t and the median expectation of forecasts ahead of the announcement. High Markup is a dummy i,y(t)−1 that is equal to 1 if the firm has a markup above the 75th percentile of the distribution and 0 otherwise. Low Markup is a dummy that is equal to 1 if the firm has a markup below the 25th percentile of i,y(t)−1 the distribution and 0 otherwise. Markup is defined as the estimated markup from De Loecker et al. (2020). Standarderrorsaredoubleclusteredatthefirmanddatelevel. Theshadedareareflectsthe90%confidence interval. The sample period is 1977–2022. 54

Figure IX: The role of market power for stock returns around inflationary news .6 .4 .2 0 -.2 stnioP egatnecreP -5 0 5 10 Days b Inflationary News * Markup 1 This figure plots the estimated coefficient of Equation 14: Returnk =α+β Inflationary News ∗Markup +α +α +X′γ+ϵ i,t 1 t i,y(t)−1 i t i,t whereReturnk isthecumulativereturnbetweenthedaybeforetheCPIannouncementondatetandkdays i,t after for stock i. Inflationary News is the difference between the published month-on-month CPI inflation t andthemedianexpectationofforecastsaheadoftheannouncement. Markup istheestimatedmarkup i,y(t)−1 from De Loecker et al. (2020) and standardized to have mean 0 and a standard deviation of 1. α is a firm i fixed effect. α is a date fixed effect. X are controls. Low Markup is a dummy that is equal to 1 if t i,y(t)−1 the firm has a markup below the 25th% percentile of the distribution and 0 otherwise. Standard errors are double clustered at the firm and date level. The shaded area reflects the 90% confidence interval. 55

Figure X: Real estimated cash flows around inflationary news by market power 1 -1 -3 -5 -7 % High Markup Firms 1 -1 -3 -5 -7 -5 0 5 10 Days b2 Inflationary News * High Markup % Low Markup Firms -5 0 5 10 Days b1 Inflationary News * Low Markup This figure plots the estimated coefficient of Equation 18: (cid:92) k,C(cid:103)F Return =α+β Inflationary News ∗Low Markup i,t 1 t i,y(t)−1 +β Inflationary News ∗High Markup +β Low Markup +ϵ , 2 t i,y(t)−1 3 i,y(t)−1 i,t (cid:92) k,C(cid:103)F where Return is the estimated real cash flow component of stock returns between the day before the i,t CPI announcement on date t and k days after for stock i. Inflationary News is the difference between the t publishedmonth-on-monthCPIinflationandthemedianexpectationofforecastsaheadoftheannouncement. High Markup isadummythatisequalto1ifthefirmhasamarkupabovethe75thpercentileofthe i,y(t)−1 distribution and 0 otherwise. Low Markup is a dummy that is equal to 1 if the firm has a markup i,y(t)−1 below the 25th percentile of the distribution and 0 otherwise. Markup is defined as the estimated markup from De Loecker et al. (2020). Standard errors are double clustered at the firm and date level. The shaded area reflects the 90% confidence interval. The sample period is 1977–2022. 56

Figure XI: Inflationary News, Earnings Expectations, and Market Power 2 1 0 -1 snoitatcepxE sgninraE D -.2 -.1 0 .1 .2 .3 Inflationary News Low Market Power High Market Power This figure is a binscatterplot between ∆Earnings Expectation on the y-axis and the Inflationary News i,t t on the x-axis. ∆Earnings Expectation is the log change in earnings expectations between 15 days after i,t and before the CPI release. The blue line plots the linear fit for firms at the top 25th percentile of markups. The red line plots the linear fit for firms below the top 25th percentile of markups. Inflationary News is t thedifferencebetweenthepublishedmonth-on-monthCPIinflationandthemedianexpectationofforecasts ahead of the announcement. 57

Table I: Stock return decomposition around inflationary news Panel A: Nominal return decomposition 1-day Decomposition 5-day Decomposition Return Yield Curve Equity Premium Cash Flow Return Yield Curve Equity Premium Cash Flow Inflationary News -1.42∗∗ -0.61 -1.05∗ 0.24 -2.75∗ -0.49 -2.51∗∗ 0.25 (0.58) (0.40) (0.55) (0.52) (1.42) (0.91) (1.00) (1.40) R-squared 0.021 0.008 0.013 0.001 0.013 0.001 0.022 0.000 N 283 283 283 283 283 283 283 283 Panel B: Real return decomposition 1-day Decomposition 5-day Decomposition Return Yield Curve Equity Premium Cash Flow Return Yield Curve Equity Premium Cash Flow Inflationary News -2.42∗∗∗ 0.15 -0.75∗ -1.82∗∗∗ -3.75∗∗∗ 0.62 -2.17∗∗ -2.20∗ (0.58) (0.37) (0.41) (0.50) (1.42) (0.80) (0.87) (1.21) R-squared 0.059 0.001 0.012 0.045 0.024 0.002 0.022 0.012 N 283 283 283 283 283 283 283 283 The table presents the coefficients from the following equation: Returnk =αk+βkInflationary News +ϵk. t t t It also presents the coefficients across c={yield curve, equity risk premium, cash flow}: Returnk,c =αk,c+βk,cInflationary News +ϵk,c, t t t where Returnk = (cid:80)3 Returnk,c is the k-day cumulative return on the stock market and is the sum of three return components: the k-day t c=1 t cumulative yield curve return component, the k-day cumulative equity risk premium return component, and the k-day cumulative cash flow return component. Panel A decomposes nominal realized returns into a nominal yield curve return component, an equity risk premium component, and a nominal cash flow return component. Panel B decomposes real realized returns into a real yield curve return component, an equity risk premium component, and a real cash flow return component. Each panel shows coefficient estimates on k = 1 and k = 5 cumulative returns. Inflationary News is the difference between the published month-on-month CPI inflation and the median expectation t of forecasts ahead of the announcement. Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. The sample period is 1999–2022. 58

Table II: Inflationary news, market power, and stock returns Dependent Variable: Returns5 i,t (1) (2) (3) (4) (5) (6) Inflationary News -1.501∗ (0.798) Markup 0.0129 0.0105 -0.000807 0.00674 -0.00147 0.00545 (0.0147) (0.0150) (0.00925) (0.00938) (0.0101) (0.0103) Inflationary News × Markup 0.260∗∗ 0.271∗∗ 0.165∗∗ 0.174∗∗ 0.185∗∗ 0.177∗∗ (0.115) (0.121) (0.0805) (0.0755) (0.0838) (0.0804) R-squared 0.014 0.128 0.155 0.156 0.165 0.165 N 2,283,661 2,283,661 2,283,628 2,227,067 1,651,423 1,628,093 Firm FE ✓ ✓ ✓ ✓ ✓ ✓ Time FE ✓ - - - - Industry-Time FE ✓ ✓ ✓ ✓ Int. Firm Controls ✓ ✓ Int. Factor Controls ✓ ✓ This table shows results from the following equation Equation 14: Return5 =α+β Inflationary News ∗Markup +α +α +X′γ+ϵ , i,t 1 t i,y(t)−1 i t i,t where Return5 is the cumulative stock returns calculated from day t-1, before CPI release, to day i,t t+5,aftertheCPIrelease. Inflationary News isthedifferencebetweenthepublishedmonth-on-month t CPI inflation and the median expectation of forecasts ahead of the announcement. Markup i,y(t)−1 is the estimated markup from De Loecker et al. (2020) and is standardized to have mean 0 and a standard deviation of 1. α is a firm fixed effect. α is a date fixed effect. X are controls. Int. i t Firm Controls includes firm characteristics controls—log assets, tangibility, leverage, and market-tobook value—interacted with Inflationary News. Int. Factor Controls includes firm-level rolling-betas to the Fama and French (1993) asset pricing factors—market beta, size, and value, each interacted with Inflationary News. The sample period is 1977–2022. Standard errors (in parentheses) are double clustered at the firm and date level. *** p<0.01, ** p<0.05, * p<0.1. 59

Table III: Inflationary news, market power, and earnings expectations Dependent Variable: ∆EarningsExpectation i,t (1) (2) (3) (4) Inflationary News -0.313 -0.330 (0.828) (0.834) Markup 0.019 -0.108 -0.075 -0.054 (0.052) (0.096) (0.096) (0.099) Inflationary News × Markup 0.842∗ 0.910∗ 1.140∗∗ 1.182∗∗ (0.471) (0.475) (0.480) (0.489) R-squared 0.000 0.026 0.054 0.054 N 44,627 44,603 44,602 42,898 Firm FE ✓ ✓ ✓ Time FE ✓ ✓ Int. Firm Controls ✓ This table shows results from Equation 19: ∆EarningsExpectation =α+β Inflationary News ∗Markup +α +α +X′γ+ϵ , i,t 1 t i,y(t)−1 i t i,t where∆EarningsExpectation isthelogdifferenceinearningsexpectationsforfirmsbetweenthe15 i,t daysafterandthe15daysbeforetheCPIannouncementatdatet. Inflationary News isthedifference t between the published month-on-month CPI inflation and the median expectation of forecasts ahead of the announcement. Markup is the estimated markup from De Loecker et al. (2020) and i,y(t)−1 standardized to have mean 0 and a standard deviation of 1. α is a firm fixed effect. α is a date i t fixed effect. X are controls. Int. Firm Controls includes firm characteristics controls—log assets, tangibility, leverage, and market-to- book value—interacted with Inflationary News. Standard errors (in parentheses) are double clustered at the firm and date level. *** p<0.01, ** p<0.05, * p<0.1. 60

Internet Appendix to “Stagflationary Stock Returns” This Appendix provides additional descriptive and empirical evidence to supplement the analyses provided in the main text. It also provides a simple model that motivates the cross-sectional empirical analysis. Below, we list the content. 1. Appendix A studies how the response of the stock market to inflation news depends on the state of the economy. 2. Appendix B studies the interaction of long-dated interest rates with short-dated nominal rates around inflationary news using the empirical setting of Hanson and Stein (2015). 3. Appendix C reports the response of dividend futures to inflation news. 4. Appendix D presents a simple model with imperfect competition and studies the impact of changing marginal costs for firm profitability in this setting. 5. Table A.IV reports summary statistics of the variables used in the main empirical analysis. 6. Table A.V reports summary statistics for earnings expectations. 7. Table A.VI reports the response of interest rate swaps and inflation swaps to inflation news. 8. Table A.VII demonstrates how changes in inflation expectations around CPI releases affect stock returns. 9. Table A.VIII studies the role of core inflation shocks. 10. Table A.IX studies the interaction between inflationary news, cost elasticity, and stock returns. 11. Figure A2 reports the time series of measured inflationary news and daily stock returns. 12. Figure A3 presented binscatterplots of stock returns with inflation news. 13. Figure A4 reports the response of forward nominal yields to inflation news. 61

A Time Series and State Dependence In the baseline analysis, we have not allowed the coefficients of interest to vary over time or across statesoftheeconomy. Thissectionthereforeexplorestheextenttowhichourmainfindingsdepend on the estimation sample period or on various conditioning variables that proxy for the state of the economy. Time series dependence. To test for time series variation in our coefficient estimations, we reestimate Equation 13 using 5-year rolling estimation windows. First, we run the rolling regressions withtherealreturnontheaggregatestockmarketasthedependentvariable,beforecyclingthrough with each of the real yield curve, the real cash flow, and the equity premium return component as the dependent variable. The exercise is thus similar to that in Figure V, but based on rolling regression estimates. Figure A1 presents the rolling decomposition results for 1-day real returns in response to inflationary news. It shows that in 97 percent of the 222 estimation windows, the stock market is estimated to have declined with inflationary news, highlighting that the fact that higher-thanexpected(lower-than-expected)inflationleadstonegative(positive)stockreturnsisahighlyrobust feature of the data. That said, the coefficient is not consistent over time, with the stock market being particularly sensitive to inflationary news in the 5-year sample windows ending in 2004-2006, 2013-2016 and 2021-2022. The estimated coefficient is less than -2 percent in each of these sample windows. Figure A1 also documents interesting variation in the component drivers of the stock market’s negative response to inflationary news. The real cashflow component is negative in 89 percent of the estimation window periods, and thus is nearly always a negative contributor, while the real yield curve is only a negative contributor in 15 percent of the window periods. This negative contribution of the real yield curve all occurred at the end of our sample, as the expected monetary response to inflationary news in the above target inflationary regime of the post COVID-era likely ledinvestorstoincreasetheirexpectationsoffuturerealyields. Fortheequitypremiumcomponent of the stock return, the time series variation in the estimated coefficient is much more pronounced, with a negative coefficient estimated in 57 percent of the sample windows. For the windows ending in 2015-2016, equity premium particularly weighed on the stock market response to inflationary news, with the most negative equity premium return component estimates in these periods. State dependence. To test for state dependence, we adjust Equation 13 with an additional interaction term between inflationary news and the state of the economy: Returnk = α+β Inflationary News +β State +β Inflationary News ×State +ϵ . (20) t 1 t 2 t 3 t t i,t Our coefficient of interest is β , which captures the marginal stock market effect of being in a 3 particular state of the economy with respect to an inflationary shock. We use several variables to define the state of the economy, as described below, and present results from Equation 20 across all measures of State in Table A.I. In summary, we do not find evidence of state dependence. t Ina standardmacromodela negativesupplyshock reducesoutputandincreases prices, whilea positive demand shock increases output and prices. Our first set of conditioning variables therefore 62

focus on whether the current economic situation is dominated by supply- or demand-driven shocks. First, we compute the correlation between stock and bond daily returns using an exponentially weighted moving average with 75% of the weight distributed over the most recent 22 days. When inflation is demand driven, interest rates rise, lowering bond prices just as the output gap and stock prices rise, inducing a negative correlation between bond and stock returns (Pflueger, 2023). Instead, supply-driven inflation induces a positive correlation between bond returns and stock returns, as the negative supply shock reduces the output gap and stock returns, but at the same lowers bond prices because of higher interest rates and/or inflation expectations. The interaction coefficient β tests whether the effect of inflationary news on negative stock returns is stronger 3 when the stock-bond correlation is 1 standard deviation above its mean, i.e. inflation may be more supply-driven. Theinteractionbetweeninflationarynewsandthestockbondcorrelation, presented in column (2) of Table A.I, is statistically insignificant and economically small, suggesting that in times of a higher stock-bond correlation, the effect of inflationary news on the stock market is not different than in times when the stock and bond market go in opposite direction. Next, we use the inflation risk premium derived from a no-arbitrage term structure model of (d’Amico et al., 2018) to measure the premium investors require for the possibility that inflation may rise or fall more than they expect over the period in which they hold a bond. A positive inflation risk premium indicates that investors require compensation for taking inflation risk, as their utility is negative correlated with inflation. Instead, a negative inflation risk premium implies that a pickup in inflation and the resulting losses to nominal bondholders are likely to coincide with a higher a marginal utility of wealth, as good states of the world are positively correlated with inflation. For instance, the 1970s and early 1980s inflation was countercyclical and generally characterized by supply-driven inflation shocks, which generated a positive inflation risk premium (d’Amico et al., 2018). Conversely, the period since the global financial crisis was characterized by a persistently low inflation environment that was often associated with insufficient demand and an inflation risk premium that was very low or even negative. Using the inflation risk premium as a proxy for more supply-driven inflation, one could expect that a higher inflation risk premium corresponds with periods where stock returns response with respect to inflationary news in even more negative. Empirically, however, a positive inflation risk premium, if anything, dampens the effect of inflationary news on negative stock returns, with the β coefficient positive (see column 3 (3) of Table A.I). Finally, we use a measure that separates inflation by its supply and demand factors from the San Francisco Federal Reserve Bank. Proposed by Shapiro (2022), this measure seeks to separate the impact of supply and demand factors on monthly inflation. To do this, inflation rates are classifiedbyspendingcategory, thendividethesecategoriesintosupplyanddemand-drivengroups. Demand-driven categories take place when surprising price changes happen in the same direction as the unexpected change in quantity. Supply-driven categories take place when surprising price changes move in the opposite direction as the quantity changes.30 When exploiting heterogeneity in the response of stock returns to inflation surprises as a function of the share of inflation that is supply-driven in the previous month, we do not find that more supply-driven inflation is associated with a stronger impact of inflation shocks on the stock market (see column (4) of Table A.I). 30The measure is only available for a shorter time series which reduces the number of observations in our regression. 63

We now shift focus away from whether the economy is demand or supply driven and consider other ways in which the economy could be state dependent. First, the effects of inflation on the economy may not be linear (Fischer, 1993). When inflation is very low, higher inflation may be associated with better economic outcomes, e.g. in a secular stagnation environment, but when inflation exceeds a certain threshold the cost of inflation can become very large, as price dispersion increases rapidly with inflation. To test for the non-linear effects of inflationary news on the stock market we interact the inflation shock with the 3-month moving average inflation print in column (5). As for the previous tests for state dependence, we do not find evidence that a higher inflation rate is associated with a stronger decline in the stock market to a surprise inflation shock than in a lower inflation environment. Second, we test for the asymmetric effects of inflation. While more recently inflation has surprised to the upside, in the post-GFC period inflation has often surprised to the downside. To test for whether higher-than-expected inflation leads to stock market losses or lower-than-expected inflation leads to stock market gains, we define a dummy that is 1 for an inflationary shock and 0 for a disinflationary shock, i.e. is 1 if the shock is positive and 0 if it is negative. The result is presented in column (6) of Table A.I. The estimated interaction coefficient between the upward surprise dummy and the inflation surprise is negative, indicating that the effect of inflationary shocks is stronger than the effect of disinflationary shocks, i.e. the losses of upward surprise are larger than the gains from downward surprises. However, even for downward surprises the sign is negative, confirming that lower than expected inflation is associated with an increase in the stock market. In column (7) we test for whether variation in the state of the business cycle, measured by the unemployment gap, can explain time-varying effects of inflation on the stock market, but also here, we do not find evidence. Finally, we test whether perceptions about monetary policy responsiveness is driving the sensitivity of the stock market to inflation news, as suggested in Rubio Cruz et al. (2023) for the most recent period, and evidence shown in (Boyd et al., 2005; Elenev et al., 2024) for other macro news. To test this hypothesis, our variable takes the value of the change in the 2 year nominal and real bond yield in columns (8) and (9), respectively. When the nominal or real interest rate increases strongly in response to inflationary news, indicating monetary policy is very responsive to higher inflation, the negative effect on the stock market may be exacerbated. Indeed, the interactions between those variables and the inflationary news variable are negative. However, the negative coefficientsareneitherstatisticallynoreconomicallysignificant. Economically, a1standarddeviation larger increase in the nominal (real) 2 year yield increases the negative stock market response by less than 10%. The coefficient on inflationary news itself, however, remains statistically significant, indicating once again, that independent of the perceived monetary policy response, stock market investors see the inflationary news as stagflationary. Overall, the results in this section show that the effect of inflationary news on stock returns does not seem to be dependent on the state of the economy.31 Instead, the results suggest that the marginal stock market investor unconditionally sees inflationary news as reducing real earnings. 31In unreported robustness tests we use test for the state dependence of the yield curve and the equity premium to inflationary news, and find little evidence. The results are available upon request and are not reported for brevity. 64

Figure A1: Rolling decomposition of 1-day real stock returns around inflationary news : l z Al A: Af X zSE Nlzz: zSEnIlzz4 zSE NlzSk zSEnIlzSe zSE Nlzll `3 ICy30h`3 Ih`3jnaN `3 Ih+ c@h7IRsh+RLURN3Nj 2\nCjwh`CcGhTa3LCnLh+RLURN3Nj `3 IhvC3I0h+naq3h+RLURN3Nj This figure stacks the rolling time series of the estimated beta coefficient from Equation 13: yc =αc+βcInflationary News +ϵc, t t t where yc is the predicted c = {C(cid:103)F,ERP,Y(cid:103)C} component of the 1-day real return on the day of the CPI t announcementondatet,andtherollingestimationwindowis5-yearperiods. Thereturncomponentsarethe returns generated from changes in real cash flow expectations, C(cid:103)F, changes in equity risk premium, ERP, and changes in real risk-free rates, Y(cid:103)C. The black line in the figure plots the rolling coefficients of 1-day realrealizedreturnsregressedoninflationarynews, whichisbydefinitionthesumofthestackedcoefficients on the return components. Inflationary News is the difference between the published month-on-month CPI t inflation and the median expectation of forecasts ahead of the announcement. The overall sample period is 1999–2022, which means the first 5-year window period in 2004. 65

Table A.I: State Dependence Dependent Variable: Return0 t (1) (2) (3) (4) (5) (6) (7) (8) (9) Inflationary News -0.928∗∗∗ -0.983∗∗∗ -1.012∗∗∗ -1.368∗∗ -0.913∗∗∗ -0.614 -0.896∗∗∗ -1.371∗∗ -0.909∗∗∗ (0.307) (0.333) (0.379) (0.590) (0.323) (0.576) (0.310) (0.610) (0.311) State 0.0309 0.0815∗ -0.0413 -0.0340 0.180 -0.0333 -0.0502 -0.0139 (0.0442) (0.0488) (0.0763) (0.0431) (0.165) (0.0428) (0.0856) (0.0438) Inflationary News × State 0.0994 0.809∗∗ 0.876 0.00310 -1.439 0.348 -0.260 -0.165 (0.245) (0.400) (0.715) (0.247) (1.008) (0.339) (0.746) (0.282) R-squared 0.017 0.018 0.029 0.024 0.018 0.021 0.017 0.018 0.018 N 529 504 467 279 528 529 528 279 529 State Stock-Bond Inflation RP Supply Inflation Positive U-gap ∆ 2yr ∆ 2yn 0 0 This table shows the coefficient estimates from regression Equation 20: Return =α+β Inflationary News +β State +β Inflationary News ×State +ϵ , i,t 1 t 2 t 3 t t i,t where Returnk is the cumulative average stock return between the day before the CPI announcement on date t and k days after for stock i. t Inflationary News is the difference between the published month-on-month CPI inflation and the median expectation of forecasts ahead of the t announcement. β captures the marginal stock market effect of being in a particular state of the economy with respect to an inflationary shock. 3 Robust standard errors in parenthesis. Stock-Bond is the standardized correlation between stock and bond returns. Inflation RP is a measure of the inflation risk premium from d’Amico et al. (2018). Supply is the standardized share of inflation that is supply-driven from Shapiro (2022). Inflation is the last inflation print. Positive is a dummy if the inflation surprise is positive. U-gap is the unemployment gap. ∆ 2yr and ∆ 2yr are the same 0 0 day change in the 2 year real and nominal bond yield, respectively. Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 66

B Movements in the Yield Curve following Inflationary and Monetary News The unresponsiveness of long-dated real yields to inflation news contrasts with large and positive response of long-dated real yields to monetary policy shocks (Hanson and Stein, 2015). To further explore these distinctive effects of monetary policy news and inflation news on the long end of the real yield curve, we estimate the Hanson and Stein (2015) main regression specification: ∆ f10,r = α +β ∆ y2+∆ ϵr, (21) 1 t r r 1 t 1 t where f10,r is the 10-year r = {nominal,real,breakeven inflation} instantaneous forward rate, y2 is t t 2-year nominal Treasury yield, and ∆ x = x −y is the 2-day change in variable x around an 1 t t+1 t−1 inflation release on the morning of day t. Changes in 2-year nominal yields are used as a measure of monetary policy news that captures surprise changes in both the current federal funds rate and the expected path of the federal funds rate over the next several quarters. Panel A of Table A.II presents the results from Equation 21, where columns 1-3 shows the estimation on FOMC days. Consistent with Hanson and Stein (2015), but on an extended sample through to 2022, we find a large impact of monetary policy news on long-dated nominal instantaneous forward rates, with this sensitivity driven by the real rate component of the nominal forward rates.32 Columns4-6thenshowsestimationresultsonCPIreleasedays. AswithFOMCdays,there is a large response in long-dated nominal instantaneous forward rates but, in contrast to FOMC days, this sensitivity is driven mostly by the breakeven inflation component of nominal forward rates. For a 100 basis point increase in the 2-year nominal Treasury yield in the 2-days following a CPI release, the nominal instantaneous forward rate increases by 56 basis points, with 40 basis points driven by breakeven inflation, and nominal forward rates only increasing 17 basis points. The dependent variable on CPI days can be interpreted as capturing the expected monetary policy responsetoinflationnewsonthatday, andthustheresultspointtofundamentaldifferencebetween news on CPI release days relative to monetary policy days. In particular, the results indicate that yield moves on CPI release days should not be considered just a monetary policy phenomena, i.e. nominal yields increase only because of the expected monetary policy response to higher inflation, and instead there are other forces at play driving changes in yields. To further explore yield curve dynamics in response to various economic shocks, Table A.II Panel B first estimates Equation 21 on all other days in our sample, i.e. excluding FOMC and CPI release days, and shows that, consistent with Hanson et al. (2021), long-dated nominal instantaneous forward rates are typically highly responsive to moves in short-dated nominal rates, with the majority of the sensitivity driven by the real rate component of the nominal rate, but also a role for breakeven inflation component. More importantly, Columns 4-9 of Panel B Table A.II next shows the results splitting other days into monetary policy news days and growth news days.33 32Using different shocks for monetary policy, Nakamura and Steinsson (2018) do not find an impact of monetary policy shocks on 10-year real forward rates, but do find monetary policy effects 5-year forward rates and other shorter maturities of the real yield curve. 33We split days into two groups conditional on the correlation of yields and stock returns on that day: days when stock returns and yields are positively correlated are labeled monetary policy news days, and days when stock returns and yields are negatively correlated are labeled growth dates. This split follows a recent literature (Cieslak and Schrimpf, 2019; Jarocin´ski and Karadi, 2020; Cieslak and Pang, 2021; Hoek 67

Strikingly, yield curve dynamics on monetary policy (but non-FOMC) days exhibit very similar behavior as on FOMC days themselves, with nominal forward rates purely driven by real rates. On growth news days, nominal forward rates are mostly driven by real rates, but there is a role for breakeven inflation too. Nevertheless, CPI releases standout, even relative to growth days, as days when the long-end of the nominal yield curve is particularly driven by inflation compensation changes. The results therefore indicate that particular economic channels are at play on CPI days and are consistent, for example, with a model in which long-run inflation expectations are not well anchored and revise in light of incoming inflationary news (Gu¨rkaynak, Sack and Swanson, 2005). et al., 2022) that uses the intuition that days with a positive correlation between yields and stock returns must contain positive growth news. Increasing yields increase the discounting of expected cash flows and thus, for stock returns to be positive, there must also be positive news about expected cash flows. 68

Table A.II: Forward yields around monetary and inflationary news Panel A: FOMC and CPI release days FOMC CPI releases Nominal Real Inflation Nominal Real Inflation 2-year treasury 0.49∗∗∗ 0.50∗∗∗ -0.01 0.56∗∗∗ 0.17∗∗ 0.40∗∗∗ (0.15) (0.12) (0.09) (0.10) (0.08) (0.09) R-squared 0.068 0.104 0.000 0.131 0.019 0.090 N 146 146 146 218 218 218 Panel B: All other days All other days Monetary news days Growth news days Nominal Real Inflation Nominal Real Inflation Nominal Real Inflation 2-year treasury 0.58∗∗∗ 0.45∗∗∗ 0.14∗∗∗ 0.46∗∗∗ 0.46∗∗∗ 0.01 0.63∗∗∗ 0.44∗∗∗ 0.19∗∗∗ (0.02) (0.02) (0.02) (0.04) (0.03) (0.03) (0.02) (0.02) (0.02) R-squared 0.159 0.118 0.018 0.085 0.099 0.000 0.202 0.129 0.041 N 4,226 4,226 4,226 1,662 1,662 1,662 2,564 2,564 2,564 This table shows results from Equation 21: ∆ f10,r =α +β ∆ y2+ϵr, 1 t r r 1 t t where f10,r is the 10-year r = {nominal, real, breakeven inflation} instantaneous forward rate, y2 is 2-year nominal Treasury yield, and t t ∆ x =x −x is the 2-day change in variable x . The regressions are estimated over the sample period 2004–2022 and robust standard 1 t t+1 t−1 t errors are in parentheses. Panel A shows estimation results on FOMC days and CPI release days separately. Panel B shows results on all other non-FOMC and non-CPI release days, before splitting all days into ’monetary news’ days and ’growth news’ days, where days are assigned conditional on the correlation between stock returns and nominal yields. *** p<0.01, ** p<0.05, * p<0.1. 69

C Dividend Future Prices around Inflationary News In this section we consider how dividend futures respond to inflationary news in the later sample where we observe dividend future prices (2016–2022). Panel A of Table A.III presents log changes intheconstant-maturity1-yearand2-yeardividendfuturespricearoundinflationnews. Itpresents 1-day changes and 5-days following inflation announcements and for each window presents both nominal and real changes. For real changes, dividend future prices are discounted by expected inflationofthesamematurity(asmeasuredfrombreakeveninflationrates)sothattheyareadjusted from nominal to real quantities, and changes are adjusted for the inflationary news that reflects an immediate change in the economy price level. Panel A of Table A.III shows that nominal dividend futures are close to unchanged following inflationary news, while real cash flows exhibit statistically significant declines. For example, following a 1 percentage point inflationary surprise, the 1-year dividend future declines by 162 basis points that day on a real basis. The results from dividend futures are consistent with the previous analysis extracting cash flow news from the decomposition approach. As dividend futures are risk neutral-expectations of stock market dividend payments their price declines following inflationary news could partially reflect increases in risk premium. Following Knox and Vissing-Jorgensen (2024), we therefore adjust dividend futures prices for the Martin (2017) lower bound of equity risk premium at the same maturity, which generates a lower bound of expected dividends. The results of regressing these adjusted dividend futures prices on inflationary news are presented in Table A.III of Panel B, with the key takeaways being broadly the same as in Panel A: Nominal cash flow expectations are unchanged following inflationary news, while real dividend expectations decline significantly. 70

Table A.III: Dividend futures, expected dividends, and inflationary news Panel A: Dividend Futures 1-day log change 5-day log change 1-yr nom 2-yr nom 1-yr real 2-yr real 1-yr nom 2-yr nom 1-yr real 2-yr real Inflationary News -0.09 -0.17 -1.62∗∗∗ -1.85∗∗∗ -0.70 -1.72 -2.09∗ -3.10 (0.14) (0.32) (0.15) (0.31) (1.17) (2.44) (1.11) (2.35) R-squared 0.003 0.004 0.511 0.312 0.002 0.002 0.016 0.008 N 77 77 77 75 76 76 75 74 Panel B: Lower Bound of Expected Dividend 1-day log change 5-day log change 1-yr nom 2-yr nom 1-yr real 2-yr real 1-yr nom 2-yr nom 1-yr real 2-yr real Inflationary News 0.15 0.06 -1.38∗∗∗ -1.62∗∗∗ 0.15 -0.83 -1.26∗ -2.21 (0.17) (0.21) (0.20) (0.25) (0.77) (1.94) (0.74) (1.86) R-squared 0.010 0.001 0.441 0.354 0.000 0.001 0.015 0.007 N 77 77 77 75 76 76 75 74 This table shows estimation coefficients from the regression: ∆ ln(xn)=α +β Inflationary News +ϵk, k t k k t t where the dependent variable xn is the n={1,2}-year dividend futures price (Panel A) or lower bound of the expected dividend (Panel B). t Theexpecteddividendisthedividendfuturespricesadjustedforriskpremium(asmeasuredbytheMartin(2017)lowerboundoftheequity risk premium). Panel A and Panel B both present log changes in nominal and in real terms. The real versions adjusts nominal changes for changes in expected inflation (measured by inflation swap rates) and the surprise component of realized inflation over the change period ∆ . k The regressions are estimated over the sample period 2016–2022 and robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 71

D A Simple Model of a Firm Facing a Cost Shock In standard industrial organization models (Tirole, 1989), firm profit is Π(p) = (p−c)Q(p) (22) wherepistheproductprice,cisthemarginalcostofproduction,andQ(p)isthequantityproduced. First order conditions with respect to the firm’s pricing decision imply that the equilibrium price is ϵ p = c, (23) ϵ−1 ∂lnQ(p) where ϵ = − > 1 is the elasticity of demand facing the firm. ∂lnp Defining the markup m = ϵ > 1 and substituting the equilibrium price Equation 23 into ϵ−1 Equation 22, we find that firm profit in equilibrium is thus Π∗ = (m−1)cq, (24) where q = Q(p∗) is the equilibrium quantity produced. We now consider the impact of a change in marginal costs on firm profits. The first derivative of equilibrium firm profits with respect to the marginal cost is the following: ∂Π∗ (cid:18) ∂q (cid:19) = (m−1) q+ c ∂c ∂c (cid:18) (cid:19) ∂q∂p = (m−1) q+ c ∂p∂c (cid:18) (cid:19) q = (m−1) q−ϵ mc p = (m−1)(1−ϵ)q, where the second line uses the chain rule and the third line uses that ϵ = − p ∂Q(p) =⇒ ∂Q(p) = Q(p) ∂p ∂p −ϵ Q(p) and that p = mc =⇒ ∂p = m. The fourth line simplifies. p ∂c Fromthis equation, multiplybothsides throughby c toderivethe firstkey testableprediction: Π ∂Π∗/Π∗ = 1−ϵ < 0 (25) ∂c/c which shows that, given ϵ > 1, firm profits decline following an increase in marginal costs. The second key testable prediction is then to show that a firm’s sensitivity to cost shocks is directly related to the firm’s market power by taking the second derivative with respect to the elasticity of demand: ∂2Π∗/Π∗ = −1. (26) (∂c/c)(∂ϵ) We therefore see that firms with higher elasticity of demand—i.e., less market power—suffer more negative declines in profitability in response to marginal cost shocks as compared to firms 72

with lower elasticity of demand. 73

Table A.IV: Summary statistics Panel A: Cross section variables N Mean SD p10 p25 p50 p75 p90 1-day stock return (perc.) 2,320,391 0.05 4.69 -3.57 -1.37 0.00 1.28 3.57 5-day stock return (perc.) 2,320,248 0.36 9.61 -8.12 -3.33 0.05 3.54 8.68 Markup 2,320,527 1.73 1.74 0.93 1.07 1.29 1.76 2.75 Size: ln(assets) 2,320,422 5.51 2.37 2.47 3.77 5.42 7.15 8.62 Book-to-market ratio 2,288,857 0.69 2.97 0.14 0.30 0.56 0.93 1.45 Leverage 2,310,867 0.23 0.24 0.00 0.04 0.18 0.35 0.51 Asset tangibility 2,303,175 0.26 0.24 0.02 0.06 0.18 0.39 0.66 Stock market beta 1,673,444 0.99 0.71 0.24 0.57 0.94 1.34 1.80 SMB risk factor beta 1,673,444 0.80 1.14 -0.25 0.15 0.66 1.29 2.05 HML risk factor beta 1,673,444 0.15 1.13 -1.06 -0.38 0.20 0.72 1.27 Panel B: Time-series variables (percentages) N Mean SD p10 p25 p50 p75 p90 Inflationary news 536 -0.00 0.14 -0.20 -0.10 0.00 0.10 0.20 1-day return (CRSP equal-weighted portfolio) 536 0.05 1.14 -1.10 -0.44 0.11 0.57 1.15 1-year equity risk premium (lower bound) 438 4.03 2.06 2.14 2.66 3.58 4.87 6.17 2-year nominal Treasury yield 536 4.91 3.72 0.40 1.51 4.72 7.47 10.04 10-year nominal Treasury yield 536 5.98 3.22 2.03 3.09 5.58 8.25 10.70 2-year real Treasury yield 283 0.34 1.68 -1.49 -0.83 0.08 1.26 3.03 10-year real Treasury yield 283 1.36 1.40 -0.55 0.40 1.14 2.30 3.46 2-year Treasury breakeven inflation 283 1.78 0.97 0.92 1.41 1.79 2.35 2.76 10-year Treasury breakeven inflation 283 2.13 0.42 1.57 1.85 2.20 2.44 2.60 This table presents summary statistics of the variables used in the empirical analysis. Panel A shows panel variables that are available in the cross section of firms, and Panel B shows time-series variables. HML is high minus low. SMB is small minus big. The full sample extends from 1977 through 2022 with 12 observations per calendar year that correspond to the monthly CPI releases, as published by theBureauofLaborStatistics. Inflationarynewsaremeasuredasthedifferencebetweenthepublished month-on-month CPI inflation and the median expectation of forecasts ahead of the announcement. For full information on data sources and variable construction, refer to section 3. Table A.V: Summary statistics—earnings expectations N Mean SD p10 p25 p50 p75 p90 Analysis for firm before news 381 3.4 1.8 1.6 2 3 4 6.1 Analysis for firm after news 381 3.5 2.6 1.5 1.9 2.4 4 8.1 Analysis total after news 381 711 861 100 190 344 668 2177 Analysis total after news 381 587 486 113 234 417 849 1337 ∆AverageEarningsExpectation 381 .31 4.4 -4.1 -1.8 .13 2.6 4.8 This table presents summary statistics for the earnings expectations analysis. 74

Table A.VI: The yield curve and inflationary News—evidence from swap rates 2-year maturity 10-year maturity Nominal Inflation Real Nominal Inflation Real Inflationary News 0.13∗∗∗ 0.27∗∗∗ -0.14∗∗ 0.10∗∗ 0.09∗∗∗ 0.01 (0.04) (0.05) (0.07) (0.04) (0.03) (0.05) R-squared 0.071 0.176 0.040 0.039 0.074 0.000 N 220 220 220 220 220 220 This table shows coefficient estimates from regression Equation 13: ∆y =α+βInflationary News +ϵ , t t t where ∆y =y −y is the 1-day change in the 2-year or 10-year yield from the day before the CPI t t t−1 announcement on date t. Inflationary News is the difference between the published month-on-month t CPI inflation and the median expectation of forecasts ahead of the announcement. The table shows results for 2-year and 10-year yields on interest rate swaps (nominal), inflation swap rates (inflation), andtheswap-impliedrealyield(theinterestrateswapyieldminustheinflationswapyield). Swapdata is taken from Bloomberg, and the sample period extends from 2004 through 2022. Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 75

Table A.VII: Stock returns, inflation expectations and inflationary news (1) (2) (3) (4) Inflation Expectations Return Return Return Inflation News 0.074∗∗∗ -0.014∗ (0.025) (0.008) Inflation Expectations 0.070∗∗ (0.029) Inflation Expectations (Predicted) -0.193 (0.150) Constant -0.000 -0.000 -0.000 -0.000 (0.003) (0.001) (0.001) (0.001) R-squared 0.041 0.017 0.058 . First-stage F-statistic 8.653 N 285 285 285 285 InflationaryNewsisthedifferencebetweenthepublishedmonth-on-monthCPIinflationandthemedian expectation of forecasts ahead of the announcement. Inflation Expectations are the 1-day change in 10-yearinflationexpectations. Returnisthe1-dayS&P500return. InflationExpectations(Predicted) are the change in inflation expectations instrumented with inflationary news. Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Table A.VIII: Core inflation surprises 2-year maturity 10-year maturity Return ∆ ERP Nominal Inflation Real Nominal Inflation Real Core News -1.24∗∗ 0.27∗ 0.15∗∗∗ 0.30∗∗∗ -0.20∗∗ 0.12∗∗∗ 0.13∗∗∗ -0.03 (0.49) (0.14) (0.03) (0.10) (0.10) (0.03) (0.02) (0.03) R-squared 0.016 0.010 0.079 0.033 0.014 0.041 0.087 0.004 N 387 387 387 278 278 387 278 278 Core News is the difference between the published month-on-month core CPI inflation and the median expectation of forecasts ahead of the announcement. Return is the S&P 500 return, ∆ERP is the changeintheequityriskpremium. Nominal isthechangeinnominalyields. Inflation isthechangein inflation expectations. Real is the change real yields. Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. 76

Table A.IX: Inflationary news, cost elasticity, and stock returns Dependent Variable: Returns5 i,t (1) (2) (3) (4) (5) (6) Inflationary News -1.138 (1.249) Cost Elasticity 0.00560∗∗∗ 0.00650∗∗∗ 0.00675∗∗∗ 0.00721∗∗∗ 0.00876∗∗∗ 0.00916∗∗∗ (0.000317) (0.000294) (0.000473) (0.000743) (0.000907) (0.00127) Inflationary News × Cost Elasticity 0.0665∗∗∗ 0.0712∗∗∗ 0.0671∗∗∗ 0.0666∗∗∗ 0.0699∗∗∗ 0.0698∗∗∗ (0.00348) (0.000491) (0.00105) (0.00335) (0.00273) (0.00473) R-squared 0.014 0.142 0.176 0.176 0.185 0.185 N 935,259 935,259 933,018 918,065 765,095 754,113 Firm FE ✓ ✓ ✓ ✓ ✓ ✓ Time FE ✓ - - - - Industry-Time FE ✓ ✓ ✓ ✓ Int. Firm Controls ✓ ✓ Int. Factor Controls ✓ ✓ This table shows results from Equation 14: Return5 =α+β Inflationary News ∗Cost Elasticity +α +α +X′γ+ϵ , i,t 1 t i,y(t)−1 i t i,t whereReturn5 isthecumulativestockreturnscalculatedfromdayt-1,beforeCPIrelease,todayt+5, i,t after the CPI release. Inflationary News is the difference between the published month-on-month CPI t inflation and the median expectation of forecasts ahead of the announcement. Cost Elasticity is i,y(t)−1 thethepercentchangeineconomicprofitsofthefirmfollowinga1%riseinallfirmsmarginalcostsand standardized to have mean 0 and a standard deviation of 1. α is a firm fixed effect. α is a date fixed i t effect. Xarecontrols. Int. Firm Controls includesfirmcharacteristicscontrols—logassets,tangibility, leverage, andmarket-to-bookvalue—interactedwithInflationaryNews. Int. Factor Controls includes firm-level rolling-betas to the Fama and French (1993) asset pricing factors—market beta, size, and value—each interacted with Inflationary News. Standard errors (in parentheses) are double clustered at the firm and date level. *** p<0.01, ** p<0.05, * p<0.1. 77

Figure A2: Inflationary news and stock returns 5 0 -5 -10 1980 1990 2000 2010 2020 Year Stock Return Inflation Surprise b =-1.04 standard error=.31 This figure plots the inflationary news as defined section 3 in solid red and the stock return on the day of the CPI announcement in dashed blue. β is the coefficient of the univariate regression of the stock returns on the inflation surprise, and standard error reports the standard error of the coefficient. 78

Figure A3: Inflationary news for different return horizons 2 1 0 -1 -2 -3 % nruteR kcotS yaD-1 2 1 0 -1 -2 -3 -.5 0 .5 Inflationary News % nruteR kcotS yaD-5 2 1 0 -1 -2 -3 -.5 0 .5 Inflationary News % nruteR kcotS yaD suoiverP -.5 0 .5 Inflationary News This figure combines binscatterplot between Return0 (left panel), Return5 (middle panel), and Return−1 i,t i,t i,t (right panel) on the y-axis and the Inflationary News on the x-axis. Returnk is the cumulative return t i,t between the day before the CPI announcement on date t and k days after for stock i. Inflationary News is t thedifferencebetweenthepublishedmonth-on-monthCPIinflationandthemedianexpectationofforecasts ahead of the announcement. 79

Figure A4: Forward nominal yields around inflationary news 20 15 10 5 0 -5 stnioP sisaB 0 5 10 15 20 Forward Maturity This figure plots the estimated coefficient of the regression specification: ∆f(j) =αj +βjInflation News +ϵj, t t t where ∆f(j) =f(j)−f(j) is the 1-day change in the j-year forward 1-year nominal yield. The x-axis label t t t−1 denotes the number of years ahead the 1-year forward rate refers to. For j = 0, we use the raw 1-year nominal yield, while for all other j >0 we use the 1-year yield in j years’ time. The figures is based on the sample period extends from 1999 through 2022, and the shaded area reflects the 90% confidence interval. 80