Monetary Policy without Moving Interest Rates: The Fed Non-Yield Shock

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1392 July 2024 Monetary Policy without Moving Interest Rates: The Fed Non-Yield Shock Christoph E. Boehm and T. Niklas Kroner Please cite this paper as: Boehm, Christoph E, and T. Niklas Kroner (2024). “Monetary Policy without Moving Interest Rates: The Fed Non-Yield Shock,” International Finance Discussion Papers 1392. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2024.1392. NOTE: International Finance Discussion Papers (IFDPs) 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 International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Monetary Policy without Moving Interest Rates: * The Fed Non-Yield Shock Christoph E. Boehm T. Niklas Kroner UT Austin and NBER Federal Reserve Board This draft: June 24, 2024 First draft: March 25, 2021 Abstract Existing high-frequency monetary policy shocks explain surprisingly little variation in stock prices and exchange rates around FOMC announcements. Further, both of these asset classes display heightened volatility relative to nonannouncement times. We use a heteroskedasticity-based procedure to estimate a “Fed non-yield shock”, which is orthogonal to yield changes and is identified from excess volatility in the S&P 500 and various dollar exchange rates. A positive non-yield shock raises stock prices in the U.S. and around the globe, and depreciates the dollar against all major currencies. The non-yield shock is essentially uncorrelated with previous monetary policy shocks and its effects are large in comparison. Its strong effects on the VIX and other risk-related measures point towards a dominant risk premium channel. We show that the non-yield shock can be related to Fed communications and that its existence has implications for the identification of structural monetary policy shocks. JEL Codes: E43, E44, E52, E58, F31, G10 Keywords: Federal Reserve, Monetary Policy, Stock Market, Exchange Rates, Asset Prices, Risk Premia, Information Effects, High-frequency Identification *We thank Borag˘an Aruoba, Anna Cieslak, Pierre De Leo, Thomas Drechsel, Refet Gu¨rkaynak, Tarek Hassan, Sebnem Kalemli-Ozcan, Benjamin Knox, Moritz Lenel (discussant), Matteo Maggiori, Tyler Muir, Adi Sunderam, Eric Swanson, as well as seminar and conference participants at AFA 2024 and Maryland for helpful comments. We thankShailyAcharyaforexcellentresearchassistance,aswellasAnnaCieslak,ThomasDrechsel,MarekJarocin´ski, Benjamin Knox, Lee Smith, and Eric Swanson for generously sharing their data with us. A previous version of this paper was circulated under the title “Beyond the Yield Curve: Understanding the Effect of FOMC Announcements ontheStockMarket”. TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheFederal Reserve Board or the Federal Reserve System. Email: chris.e.boehm@gmail.com and t.niklas.kroner@gmail.com.

1 Introduction No matter how we measure [monetary policy] surprises or how much delay we allow for the response, we can only explain up to about 10 percent of the daily variation in risk appetite. While some of the variation in risk appetite on days with FOMC announcements is certainly driven by news unrelated to monetary policy, it is hard to argue that all, or even most, of the remaining 90 percent of the daily variation in risk appetite is unrelated to monetary policy. — Bauer, Bernanke, and Milstein (2023) High-frequency monetary policy shocks a` la Kuttner (2001) and Gu¨rkaynak, Sack, and Swanson(2005)havepuzzlinglylowexplanatory power forpricesof equities andcurrencies— two asset classes that are crucial for understanding the monetary transmission mechanism. These high-frequency shocks are constructed from unexpected interest rate changes over narrow windows around FOMC announcements and have become the workhorse shocks for empirical research in monetary economics. Although, by construction, they account for most ofthevariationintheyieldcurveovertheeventwindow, theirexplanatorypowerforchanges in stock prices and exchange rates is surprisingly low. Figure 1 illustrates this point by plotting the R-squared of various high-frequency shocks for the S&P 500 and the Euro-Dollar exchange rate. The horizontal axis measures the length of the event window around FOMC announcements. As the figure shows, Nakamura and Steinsson’s (2018) single shock (blue line) and Swanson’s (2021) three shocks (red line) explain less than 30 percent of the variation at all horizons up to 13 hours after the shock. Adding more yield-based shocks does not substantially raise this explanatory power. Specifically, regressing changes in the stock market or the exchange rate on nine yield surprises covering the entire yield curve up to 30 years adds little explanatory power. This is the case regardless of whether we construct the yield changes over 30-minute windows (grey line) or whether we increase the window length to match the window of the dependent variable (black line). One potential avenue to rationalize such low explanatory power is to introduce what the literature has termed “information effects” (Romer and Romer, 2000). If central bank communication reveals private information on economic fundamentals, the observed behavior of stock markets or exchange rates is also needed to identify monetary policy shocks (Jarocin´ski and Karadi, 2020; Gu¨rkaynak, Kara, Kısacıkog˘lu, and Lee, 2021).1 Besides the 1Othernamesforinformationeffectsintheliteratureareinformationshocks,signalingeffectsorDelphicforward 1

Figure 1: Explanatory Power of Yield Curve around FOMC Announcements 100 80 60 40 20 0 1/31 2 4 6 8 10 12 Window (-10 minutes to +X hours) tnecreP S&P 500 100 Nakamura & Steinsson (2018) 30-min. Window Jarocinski & Karadi (2020) Swanson (2021) 80 9 Yields (30-min.) 9 Yields 60 40 20 0 1/31 2 4 6 8 10 12 Window (-10 minutes to +X hours) tnecreP Euro/Dollar 30-min. Window Notes: This figure shows the R2 of regressing the log-return of the front-month S&P E-mini futures contracts (left panel) and the Euro-Dollar exchange rate (right panel) around FOMC announcements on various different highfrequency shocks. The window over which returns are constructed is expanding as indicated on the horizontal axis. The full sample ranges from January 1996 to April 2023. See text for details on the shocks. fact that some research has challenged the importance of information effects (e.g., Bauer and Swanson, 2023), Figure 1 shows that they do not resolve the explanatory power puzzle. Specifically, the explanatory power of Jarocin´ski and Karadi’s (2020) shocks (green line), which are constructed from 30-minute changes in yields and stock prices, falls sharply when considering longer windows. Further, these shocks have very low explanatory power for exchange rates throughout. This point echoes findings by Gu¨rkaynak et al. (2021, p.1) who conclude that “even after conditioning on possible information effects driving longer term interest rates, there appear to be other drivers of exchange rates.” Since both stocks and exchange rates are substantially more volatile than bond yields, the unexplained variation could simply reflect news unrelated to monetary policy. Indeed, (Swanson, 2021, p.13) attributes the low explanatory power of yield curve changes for the stockmarkettothe“largeridiosyncraticvolatilityofstocks(...) relativetoTreasuries”. This contrasts with Bauer, Bernanke, and Milstein (2023) who question such an interpretation. The data suggests that the unexplained variation is not just noise. Specifically, Figure 2 shows that both stock prices and exchange rates exhibit much greater variance on announcement days than at similar times on non-announcement days—even after residualizing with guidance. 2

Figure 2: Distribution of Returns for 6-Hour Window around FOMC Announcements S&P 500 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -4 -2 0 2 4 Return (%) )%( ytisneD Euro/Dollar 4.0 FOMC (residualized with Yields) FOMC (raw) 3.5 Non-FOMC 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -1.5 -1 -0.5 0 0.5 1 1.5 Return (%) )%( ytisneD Notes: Thisfigureshowsthedistributionoflog-returnsofthefront-monthS&PE-minifuturescontracts(leftpanel) andtheEuro-Dollarexchangerate(rightpanel). ThedashedgreylinewithlegendentryFOMC(raw)representsthe distribution of log-returns around FOMC announcements. The full red line represents the same distribution around FOMC announcements after residualizing the returns with nine yield changes (see below for details). The full blue line represents the distribution around similar times on non-FOMC announcement days. The window over which returnsareconstructedbegins10minutespriortothereferencetimeandendssixhoursafter. Thefullsampleranges from January 1996 to April 2023. Appendix Figure C2 displays the distributions of returns for more window sizes. See text for details on the shocks. respect to yield changes. This “excess variance” also points to an omitted dimension of monetary policy. In this paper, we show that the unexplained variation in equities and exchange rates reflects a dimension of monetary policy that is not spanned by changes in the yield curve. We begin our analysis by laying out the estimation framework. Different from the standard event study framework, which assumes that yields capture all changes in monetary policy over the event window, we allow for a latent shock to affect stock prices and exchange rates. The defining feature of this shock is that it is orthogonal to yield changes—giving it its name, the non-yield shock. We estimate its effect on U.S. stock prices and various U.S. dollar exchange rates using a heteroskedasticity-based identification procedure (Rigobon, 2003) and the non-yield shock itself using the Kalman filter (Gu¨rkaynak, Kısacıkog˘lu, and Wright, 2020). Identification tests show that the non-yield shock is strongly identified. Importantly, we find that a single non-yield shock explains a large chunk of the variation in both stock prices and exchange rates unexplained by yields. A positive non-yield shock raises U.S. and foreign stock prices and depreciates the dollar. 3

We show that the non-yield shock has large and significant effects on international financial markets. In a sample of 40 countries, a one standard deviation non-yield shock moves international stock prices by around 45 basis points, on average, in a two-day window around the announcement. The dollar responds by over 30 basis points relative to foreign currencies. These effects of the non-yield shock are greater in magnitude when compared to the effects of commonly used high-frequency monetary policy shocks from the literature (Nakamura and Steinsson, 2018; Swanson, 2021; Jarocin´ski and Karadi, 2020). We present a simple model that helps clarify the nature of the non-yield shock and what its presence implies for the identification of structural monetary policy shocks. The model makes clear that the non-yield shock is, in general, a reduced form monetary policy shock. That is, it is a linear combination of the structural monetary policy shocks. The non-yield shock admits a structural interpretation only as a special case. We present an equivalence result that characterizes whether the non-yield shock is structural. It implies that there are two possible interpretations of our non-yield shock. Under the first interpretation, there exists a structural monetary policy shock that does not affect the yield curve. The non-yield shock then equals this structural monetary policy shock (up to a sign flip). The equivalence result also shows that the non-yield shock is structural if and only if the remaining structural shocks are identifiable from the yield curve alone. Commonly used identification schemes such as those in Kuttner (2001), Gu¨rkaynak, Sack, and Swanson (2005), and the literature that followed may then remain valid despite presence of the non-yield shock. Under this interpretation, the non-yield shock is simply an additional dimension of monetary policy that has large effects on global equity prices and exchange rates. One would expect that it should be possible to relate large realizations of the non-yield shock to concrete policy actions if the non-yield shock is indeed structural. Under the second interpretation, the non-yield shock is not structural and may therefore lack a clear link to policy actions. In this case, structural monetary policy shocks are not identifiable from the yield curve alone. Intuitively, the yield curve alone does not contain enough information to recover the true structural disturbances. Identification requires the use of additional information, such as other asset prices or the non-yield shock itself. An example of this case is a world with information effects as in Jarocin´ski and Karadi (2020). The non-yield shock arises in the presence of information effects since the two structural shocks, a “pure” monetary policy shock and an “information” shock, are not spanned by the yield curve. The yield shock is largely unexplained by existing monetary policy shocks from the liter- 4

ature. This finding is expected for identification schemes, which exclusively focus on interest rates (e.g., Romer and Romer, 2004; Kuttner, 2001; Gu¨rkaynak, Sack, and Swanson, 2005, and the literature that followed). However, we further show that shocks that are identified usingvariationfromadditionalassetprices—suchasthosebyJarocin´skiandKaradi(2020)— also explain only small shares of the variation in the non-yield shock. Hence, we conclude that the dimension(s) of monetary policy captured by the non-yield shock are largely new. The remainder of the paper tries to better understand the origins and effects of the non-yield shock. To do so, we look for clues on what the non-yield shock captures and whether we can tie it to concrete policy actions. We show that the non-yield shock has strong and significant effects on a variety of risk-related measures, such as implied volatility measures of stocks (e.g., the VIX) and exchange rates, as well as various measures of risk premia used in the literature. Theevidencethereforepointstowardadominantriskpremiumchannel. Thenonyield shock is also associated with changes in implied interest rate volatility. This suggests that changes in monetary policy uncertainty may generate the non-yield shock—at least in part. Lastly, we show that the non-yield shock can be statistically linked to Fed communications. Specifically, our results indicate that more communication, for instance through press conferences, is associated with greater shock magnitudes. Further, discussion of risk-related or global economic topics appears to generate variation in the non-yield shock. While these results provide some guidance for the interpretation of the non-yield shock, we acknowledge that more research is needed to fully understand how to best interpret and model the non-yield shock in a structural framework. Related literature Our paper relates to a long literature in monetary economics, which aims to identify exogenous variation in monetary policy, i.e., “monetary policy shocks”, to study the monetary transmission mechanism. Early work constructed shocks from historical narratives (e.g., Friedman and Schwartz, 1963; Romer and Romer, 2004) or vector autoregressions (VARs) (e.g., Christiano, Eichenbaum, and Evans, 1999; Uhlig, 2005). More recent work predominantly measures shocks from high-frequency financial market data following the seminal work by Kuttner (2001) and Gu¨rkaynak, Sack, and Swanson (2005). These shocks have been used, extended, and adapted in a variety of high-frequency applications (e.g., Nakamura and Steinsson, 2018; Swanson, 2021; Lunsford, 2020; Lewis, 2023) or in combination with lower-frequency times series methods (e.g., Gertler and Karadi, 2015; Caldara and Herbst, 2019; Paul, 2020; Miranda-Agrippino and Ricco, 2021). We contribute to this 5

literature by proposing a method that extracts shocks that are informative about a novel and under-researched dimension of monetary policy not spanned by the yield curve. The most closely related papers are Cieslak and Schrimpf (2019), Jarocin´ski and Karadi (2020),andKroencke,Schmeling,andSchrimpf(2021). BuildingonpriorworkbyRomerand Romer (2000), Cieslak and Schrimpf (2019) and Jarocin´ski and Karadi (2020) rationalize the unexplained stock market variation around FOMC announcements with information effects. While the mapping between Cieslak and Schrimpf’s (2019) shocks and our non-yield shock is not straightforward, we show below that our shock is orthogonal to those by Jarocin´ski and Karadi (2020). Kroencke, Schmeling, and Schrimpf (2021) also construct a monetary policy shock that is orthogonal to yield changes based on risky asset prices and interpret this shock as a “risk shift”. While our non-yield shock is conceptually similar to the risk shift, several differences in methodology and implementation ultimately imply that the risk shift explains less than a quarter of the variation of our non-yield shock. We provide a more detailed comparison below. We also contribute to a fast-growing literature studying the effects of monetary policy on risk perceptions and risk appetite, which are often referred to as the risk-taking channel of monetary policy. On the empirical side much work has documented that monetary policy affects risk premia (e.g., Bernanke and Kuttner, 2005; Hanson and Stein, 2015; Gertler and Karadi, 2015). Subsequent work has begun to incorporate these mechanisms into theoretical frameworks (e.g., Alvarez, Atkeson, and Kehoe, 2009; Drechsler, Savov, and Schnabl, 2018; KekreandLenel,2022).2 Weaddtothisliteraturebyshowingthatmonetarypolicyhasmore powerful effects on risk perceptions and risk appetite than previously thought. Our findings further help understand the exchange rate channel of monetary policy (e.g., Eichenbaum and Evans, 1995; Faust and Rogers, 2003; Gu¨rkaynak et al., 2021). Specifically, we show that risk premia are not only important for unconditional exchange fluctuations (e.g., Lustig and Verdelhan, 2007; Lustig, Roussanov, and Verdelhan, 2011; Hassan and Mano, 2019), but also for the monetary policy transmission to exchange rates. In the context of the risk-taking channel, it is important to emphasize that our results differ from those in the literature as our non-yield shock leaves interest rates by construction unaffected on impact. More recently, Bauer, Lakdawala, and Mueller (2022) show that FOMC announcements can affect risk premia through policy uncertainty and Cieslak and McMahon (2023) document a link between the Fed’s policy deliberations and risk premia. While their analyses and focus are distinct from ours, their results also emphasize the effects 2See Bauer, Bernanke, and Milstein (2023) for a comprehensive review of this literature. 6

of “non-traditional” monetary policy on risk premia. Lastly, ourpapercontributestoabodyofworkininternationaleconomicsstudyingflightto-safety or flight-to-quality episodes—or more broadly the link between safe assets, the U.S. dollar, and risk premia. Recent work in this literature includes Maggiori (2017), Caballero and Farhi (2018), Baele, Bekaert, Inghelbrecht, and Wei (2020), Kekre and Lenel (2021), Jiang, Krishnamurthy, and Lustig (2021), and Engel and Wu (2023). We contribute to this literature by showing that monetary policy can potentially generate such flight-to-safety behavior in international markets. Roadmap The remainder of the paper is structured as follows. The next section presents our empirical framework and estimates the non-yield shock. Section 3 documents the importance of the non-yield shock for global asset prices. In Section 4 we discuss how the non-yield shock can arise and what its presence implies for the identification of structural monetary policy shocks. Section 5 provides evidence on the dominant channels through which the non-yield shock affects asset prices and links it to Fed communications. Lastly, Section 6 concludes. 2 The Fed Non-yield Shock In this section, we introduce the Fed non-yield shock. We begin with laying out the estimation framework and discuss the underlying identification assumptions. We then present the data and specification choices before conducting tests on the strength of the identifying variation. We conclude this section with presenting the estimated shock series. 2.1 Framework In conventional high-frequency event-study designs, the estimating equation is ∆p = β sy +ε , for t ∈ F. (1) i,t i t i,t In this specification ∆p is the high-frequency return on asset i around the time-t FOMC i,t announcement and F denotes the set of dates/times of FOMC announcements.3 Further, sy is a vector of k monetary policy shocks that pass through the yield curve (henceforth, t “yield shocks”), and β is the corresponding vector of coefficients. Following Kuttner (2001) i 3Thesetupalsodependsonthelengthoftheeventwindowwhichweomitforeaseofnotation. Wereturntothis point below. 7

and Gu¨rkaynak, Sack, and Swanson (2005), a large literature constructs sy using changes in t interest rate futures around announcements. The coefficient vector β can be consistently i estimated by Ordinary Least Squares (OLS) if the surprise sy is uncorrelated with the error t ε . i,t The economic interpretation of β depends on why yields sy change during the event i t window. Under the common assumption that monetary policy exclusively affects current and future interest rates, β captures the causal effect of these structural monetary policy i shocks on the asset price of interest (Kuttner, 2001; Gu¨rkaynak, Sack, and Swanson, 2005; Swanson, 2021). More generally, β captures the causal effects of reduced-form monetary i policy shocks. For instance, in Jarocin´ski and Karadi’s (2020) framework, in which the structural monetary policy shocks are a “pure” and an “information” shock, β captures the i effect of a linear combination of these two shocks on the return of asset i. As noted in the introduction, both the low explanatory power of yield shocks and the elevated volatility of asset prices around announcements are puzzling and potentially indicative of an unobserved dimension of monetary policy. Thus, instead of (1), we consider the following specification in our analysis ∆p = β sy +γ sny +ε , for t ∈ F, (2) i,t i t i t i,t where sny denotes the latent non-yield shock, which is assumed to be orthogonal to sy t t (Cov[sy,sny] = 0). Hence, this specification allows for the possibility that information t t released during FOMC announcements affects stocks and exchange rates but is not fully captured by interest rates. At this point, we do not take a stance on how the non-yield shock can arise in the data, but focus on its existence. We return to the interpretation of the non-yield shock in Section 4. To estimate γ , we apply a heteroskedasiticty-based approach (Rigobon, 2003). In the i context of this application, the underlying idea is that on trading days, on which there is no announcement, asset returns at similar times as FOMC announcements should neither include sy nor sny, but be otherwise comparable. Formally, t t ∆p = ε , for t ∈ NF, (3) i,t i,t where NF denotes the set of non-announcement dates/times. We will also make use of the fact that we can directly measure sy from interest rate futures following the previous t literature. Under the assumption that sy and sny are orthogonal, we can then identify γ t t i 8

from heightened stock market and exchange rate volatility relative to non-announcement days. We recover sny using the Kalman filter via maximum likelihood estimation following t Gu¨rkaynak, Kısacıkog˘lu, and Wright (2020). The observation equation for asset i combines equations (2) and (3) and is given by ∆p = β sy +γ d sny +ε . i,t i t i t t i,t Here, d = 1(t ∈ F) is an announcement indicator, and sny is independently and identically t t normally distributed with zero mean and unit variance. The variance is normalized to one since γ is otherwise only identified up to scale. We assume that both sy and sny are i t t uncorrelated with the error ε (Cov[sy,ε ] = Cov[sny,ε ] = 0), which is standard in the i,t t i,t t i,t literature and plausible if the event windows are sufficiently narrow to prevent simultaneity and omitted variable bias in the estimation.4 In principle, we could recover our non-yield shock from a single asset. However, our motivating facts in the introduction are consistent with a common non-yield shock affecting different assets and even different asset classes. Further, employing a broader set of assets increases the estimation precision of the non-yield shock. In the case of multiple assets, the observation equation is ∆p = βsy +γd sny +ε , (4) t t t t t where p , β, γ, and ε denote the appropriately dimensioned matrices capturing p , β , t t i,t i γ , and ε . In our baseline estimation we assume that ε is independently and identically i i,t t normally distributed with a diagonal variance-covariance matrix.5 Details on the estimation framework are available in Appendix A. Note that our baseline specification (4) assumes that the changes in stock prices and exchange rates linearly depend on the yield shocks sy as captured by coefficient vector β. t The presence of substantial non-linearities in yield shocks could lead to a misspecification problem.6 We will therefore present various robustness checks in Section 2.3 that alleviate such concerns. 4NotethatourbaselinemodelhasnointerceptfollowingGu¨rkaynak,Kısacıkog˘lu,andWright(2020)asweassume that our employed high-frequency changes are mean-zero in population which is true in our sample. In Appendix Table A1, we check this assumption by estimating our non-yield shock with demeaned data. The results are almost identical. 5We present a robustness check with an unrestricted variance-covariance matrix in Appendix Table A1, which shows very similar results. 6WewillshowinSection4thattimevariationinthecompositionofstructuralshocks,asforinstanceinJarocin´ski and Karadi (2020), can be captured with our framework and does therefore not lead to a misspecification problem. 9

2.2 Specification and Data The estimation of the non-yield shock requires, among other things, a choice of the window length as well as a selection of informative asset prices. While previous high-frequency, intraday studies typically use windows of 20, 30, or 60 minutes around announcements, we also consider longer windows. Given the amount of information contained in the FOMC announcements as well as in the subsequent press conferences, we expect that stock and currency markets might need more time to fully incorporate all information. In order to find the optimal window length, we therefore attempt to balance the trade-off between capturing more information and introducing too much noise. A tighter windowisknowntoavoidsimultaneitybiasandomittedvariablebiasarisingfromothernews released during the event window (Gu¨rkaynak, Sack, and Swanson, 2005). Tighter windows further strengthen the identification with heteroskedasticity-based approaches (Lewis, 2022). A wider window, on the other hand, includes the subsequent press conference, which other papers find to be important for asset prices (e.g., Gorodnichenko, Pham, and Talavera, 2023), and allows the market to fully process the information released in both the FOMC announcements and the press conferences. A similar trade-off applies to the selection of asset prices. If an asset price strongly responds to the non-yield shock, including it in the estimation will generally provide information on the shock and thereby improve estimation precision. On the other hand, asset prices that respond to the non-yield shock only weakly, or not at all, will largely add noise to the estimation. Asset prices with poor data coverage are also unlikely to benefit the estimation. We therefore proceed in two steps. In a first step, we consider a range of window lengths and multiple asset prices that we view as appropriate a priori. Good data coverage plays an important role for the selection of asset prices in this step. We subsequently perform pre-tests on the strength of the identifying variation by asset price and window length to finalize our baseline specification. Sample Period Our sample period ranges from January 1996 to April 2023. We obtain dates and times of FOMC announcements from Bloomberg and cross-check them with information from the Federal Reserve website, and data from prior papers. The announcement sample F includes a total of 220 observations over this period. With very few exceptions, the FOMC announcements are released at 2:15 pm EST (Eastern Standard Time) until January 2013 and at 2:00 pm EST thereafter. The non-announcement sample NF comprises 10

Figure 3: Overview of Event Study Windows FOMC Stock Market Macro Data Stock Market Statement Close Releases Open FOMC Press Time in Conference EST/EDT 2pm 4pm 8am 9:30am … 1:50pm +20 min +1 hour Different +2 hours Event Windows +3 hours … +18 hours Notes: This figure presents a timeline of events on a typical FOMC day together with the different event study windows we consider. 5085 observations on regular trading days for which we use a timestamp of 2:15 pm EST. Appendix B.1 provides more details on the sample construction. Event Windows All event windows we consider begin 10 minutes prior to the release. Such a short time period before the announcement is important to circumvent simultaneity problems which would arise, for instance, if the Fed responded to asset price movements within the event window. Further, such a short time span before the announcement avoids omitted variable bias, which could arise if asset prices and the impending policy decision both responded to news. The shortest window we consider ends 20 minutes after the FOMC release and hence matches the typical 30-minute window used in the literature. After that, we consider a window ending 60 minutes after the FOMC release and then proceed in one hourincrements. Throughoutthepaper, weuseℓ-hour window torefertothewindowending ℓ hours after the release and write ℓ-hour return to describe the return over that window. (cid:8) (cid:9) Overall, we consider 19 event windows, i.e., ℓ ∈ 1,1,2,...,18 . The 18-hour window is the 3 widest and ends at 8 am EST on the next day so that U.S. macroeconomic data releases, which often occur 8:30 am, are not included for any window length. Figure 3 provides a visualization of this argument. Yield Shocks Our estimation procedure of sny partials out all variation arising from yield t shocks sy. As shown by Gu¨rkaynak, Sack, and Swanson (2005) and Swanson (2021), among t others, FOMC announcements potentially affect the yield curve through different channels 11

leading to complex and multidimensional effects. To capture these effects, we construct for a given event window length ℓ the vector sy(ℓ) from the following nine surprises across different t yields, (cid:104) sy(ℓ) = MP1(ℓ) MP2(ℓ) ED2(ℓ) ED3(ℓ) ED4(ℓ) T2Y(ℓ) ... t t t t t t t (cid:105)′ (5) T5Y(ℓ) T10(ℓ) T30(ℓ) . t t t InthisexpressionMP1(ℓ) andMP2(ℓ) aresurprisesintheexpectedfederalfundsrateafterthe t t current and subsequent FOMC meeting. Both are constructed from federal funds futures contracts. Further, ED2(ℓ), ED3(ℓ), and ED4(ℓ) are surprises in the implied rates from t t t Eurodollar futures capturing revisions of the expected 3-month US Dollar LIBOR from two to four quarters out. All five measures (MP1(ℓ), MP2(ℓ), ED2(ℓ), ED3(ℓ), and ED4(ℓ)) are t t t t t standard in the literature (Gu¨rkaynak, Sack, and Swanson, 2005; Nakamura and Steinsson, 2018), and cover surprises in the yield curve of maturities up to 14 months. For longer horizons, we use implied rates from Treasury futures of horizons two (T2(ℓ)), five (T5(ℓ)), ten t t (T10(ℓ)), and thirty years (T30(ℓ)) (Gu¨rkaynak, Kısacıkog˘lu, and Wright, 2020). All hight t frequency data is obtained from the Thomson Reuters Tick History database. In Appendix B.2, we provide details on the construction and show that all our surprises closely match those of previous studies. Note that we could alternatively allow for noise in each of the nine surprises by first estimating a factor model via principal components as done in previous work (Gu¨rkaynak, Sack, and Swanson, 2005; Nakamura and Steinsson, 2018; Swanson, 2021). However, we prefer to use all raw surprises as our baseline. The main reason is that this approach is more conservative in the context of our application since it makes sure that the non-yield shock does not pick up any information captured in the yield curve over the estimation window. An added benefit is that we do not need to take a stance on how many shocks adequately capture the effects of monetary policy shocks on the yield curve. It turns out, however, that the non-yield shock is almost identical if we replace the nine yield changes with their first three principal components (see robustness section in Appendix A.4). This is consistent with the findings by Swanson (2021). Equities and Exchange Rates We focus on equities and exchange rates as our outcome variables for the following two reasons: First, both asset classes are, aside from yields, the most studied ones in the empirical monetary policy literature. They also feature prominently in many models. Second, to conduct our analysis with varying window lengths, we require securities that are sufficiently liquid outside of regular trading hours. Currencies typically 12

trade around the clock on regular trading days. Further, stock index futures are traded outside of regular trading hours for a handful of countries, including the U.S. As before, all high-frequency data comes from the Thomson Reuters Tick History database. With regard to stock index futures, we have access to contracts for the U.S. and several other advanced economies (see Boehm and Kroner (2023) for a list of considered futures contracts). However, only the E-mini S&P 500 futures contracts have sufficient data quality to construct returns over the different window sizes of interest to us. This is mostly because trading hours of many international futures contracts extend beyond the trading hours of the underlying stock market only by several of hours. The same issue arises for VIX futures, which only recently extended their trading hours. We therefore use the first and second closest E-mini S&P 500 futures contracts to represent stock markets in our analysis. While this may appear limiting, the results in Boehm and Kroner (2023) suggest that international and U.S. stock markets respond very similarly to U.S. news. We will confirm this interpretation below in Section 3.1 where we study a broader range of stock indexes. Motivated by the need for sufficiently liquid assets, we consider in the forex market the U.S. Dollar exchange rates against the 20 currencies with the highest turnover of over-thecounter (OTC) foreign exchange instruments according to the 2022 Bank of International Settlements (BIS) Triennial Central Bank Survey.7 We drop the Chinese Yuan and Indian Rupee due to the poor quality of the intraday data, leaving us with 18 U.S. Dollar exchange rates. Figure 2 provides an overview of the 20 asset prices we consider for our baseline specification. Note that all these asset prices will be expressed in log-differences throughout our analysis. Appendix B.3 provides details on how these returns are constructed. Baseline Specification We next turn to the second specification step, in which we select the event window and the final set of asset prices. This step is based on pre-tests on the strength of the identifying variation for a given asset price i and event window length ℓ. Specifically, we use Lewis’s (2022) test for weak identification, which recasts the estimation as an instrumental variable problem and produces a first-stage F-statistic that can be used to assess the strength of the identifying variation. We provide details on this tests in Appendix A.3. Table 2 reports the F-statistics for each asset price i and event window ℓ. A green background indicates that we can reject the null hypothesis that the maximum asymptotic bias from a weak instrument exceeds 5 percent, while a red background indicates that we cannot reject it. The robust critical value of the hypothesis test is 37.42 and is taken from 7https://stats.bis.org/statx/srs/table/d11.3 (accessed on September 10, 2023). 13

Table 1: Asset Prices for Consideration as Dependent Variables Name Abbreviation Ticker Sample Observations FOMC Non-FOMC Stock Index Futures E-mini S&P 500 front month ES1 ESc1 1997–2023 208 4779 E-mini S&P 500 second month ES2 ESc2 1997–2023 198 4578 U.S. Dollar Exchange Rates Euro EUR EUR= 1998–2023 197 4577 Japanese Yen JPY JPY= 1996–2023 220 5084 British Pound GBP GBP= 1996–2023 219 5084 Australian Dollar AUD AUD= 1996–2023 219 5084 Canadian Dollar CAD CAD= 1996–2023 218 5085 Swiss Franc CHF CHF= 1996–2023 219 5084 Hong Kong Dollar HKD HKD= 1996–2023 205 4604 Singapore Dollar SGD SGD= 1996–2023 212 4814 Swedish Krona SEK SEK= 1996–2023 214 4994 Korean Won KRW KRW= 1996–2023 123 2632 Norwegian Krone NOK NOK= 1996–2023 219 5048 New Zealand Dollar NZD NZD= 1996–2023 220 5064 Mexican Peso MXN MXN= 1996–2023 220 5078 Taiwan Dollar TWD TWD= 1996–2023 115 2435 South African Rand ZAR ZAR= 1996–2023 215 4837 Brazilian Real BRL BRL= 1996–2023 207 4739 Danish Krone DKK DKK= 1996–2023 217 5048 Polish Zloty PLN PLN= 1996–2023 188 4333 Notes: Thistableshowstheassetpricesconsideredasdependentvariablesinouranalysis. ThedataisfromThomson ReutersTick History. Forallseries,thesampleperiodendsinApril2023. TheU.S.Dollarexchangesratesarelisted indescendingorderintermsofturnoveroftheforeigncurrencybasedontheBISTriennialCentralBankSurvey(see footnote 7). Abbreviation refers to the abbreviation used in this paper, and Ticker refers to the Reuters Instrument Code (RIC). Montiel Olea and Pflueger (2013). Note that this test is conservative for at least two reasons: First,itusesthemaximum asymptoticbias. Second,therobustcriticalvaluebyMontielOlea and Pflueger (2013) is the highest critical value for a given bias level, while the critical value is decreasing in the number of effective degrees of freedom. Table 2 shows that for short windows the identifying variation is excellent across almost all assets, while for longer windows we cannot reject a weak-instrument bias for most assets. Based on these results, we now jointly select a set of assets and a window length ℓ for our baseline specification. Since we expect that a larger event window and more assets improve the estimation of the non-yield shock, our objective is—loosely—to jointly maximize the event window ℓ and the number of assets n while passing the weak instrument test for each 14

Table 2: First-stage F-statistics from Weak Instrument Test Window ES1 ES2 EUR JPY GBP AUD CAD CHF HKD SGD SEK KRW NOK NZD MXN TWD ZAR BRL DKK PLN 20min. 162 107 1508 509 627 1401 888 826 11 1262 983 968 783 959 310 693 542 165 1633 1066 1hour 114 73 1114 322 751 815 669 535 12 683 881 622 585 718 193 181 321 79 931 767 2hours 159 95 621 249 405 481 455 521 11 421 386 164 329 404 107 253 428 88 853 514 3hours 143 96 561 157 375 432 360 425 3 221 257 554 208 251 132 56 249 41 669 377 4hours 133 87 533 81 369 377 282 403 5 417 237 117 253 234 106 18 229 24 566 444 5hours 164 122 582 68 330 321 368 403 6 200 281 51 274 226 115 16 208 15 551 384 6hours 142 109 403 36 275 201 361 232 9 134 174 48 221 154 163 25 222 10 349 263 7hours 132 107 383 26 256 177 307 271 12 102 216 43 274 148 75 6 179 2 333 249 8hours 126 92 326 16 264 152 338 211 17 91 204 53 281 140 85 3 117 0 341 218 9hours 118 89 389 10 207 136 307 242 6 66 180 18 244 120 64 1 195 6 391 241 10hours 84 75 285 15 156 108 359 194 10 62 160 28 217 80 119 8 144 8 277 224 11hours 90 75 244 10 122 102 329 177 8 53 181 9 179 91 163 3 119 0 213 310 12hours 106 87 164 3 98 81 219 108 4 48 132 8 137 71 133 1 66 4 161 144 13hours 117 107 113 6 70 87 241 75 5 49 65 17 83 68 133 4 42 3 119 75 14hours 84 90 67 2 55 61 167 46 6 37 16 17 27 58 73 9 30 3 65 40 15hours 56 50 64 0 24 34 115 34 1 15 16 18 26 31 52 18 17 5 56 40 16hours 48 39 42 0 22 28 111 35 1 6 9 6 14 26 58 26 12 34 40 19 17hours 43 24 33 0 25 29 79 29 1 9 8 6 13 51 67 24 10 3 29 21 18hours 44 33 36 3 25 21 56 26 3 5 7 12 15 39 48 28 12 8 26 19 Notes: Thistableshowstheresultsofthefirst-stageF-tests. Foragiveneventwindow(row)andassetprice(column), the table shows the F-statistic as constructed in equation (A4). The event windows are explained in the text and the asset price abbreviations in Table 1. A green background indicates that we can reject the null hypothesis that themaximumasymptoticbiasfromaweakinstrumentexceeds5percent,andred indicatesthatwecannotrejectit. The robust critical value of the hypothesis test is 37.42 and is taken from Montiel Olea and Pflueger (2013). The highlighted 13-hour window is chosen for our baseline specification where we include the 15 asset prices which pass the weak identification test. asset i = 1,...,n. Based on this criterion, we select the 13-hour window for our estimation and the 15 asset prices in Table 2 that pass the weak instrument test for this window length. That is, we estimate sny based on equation (4) for ∆p = ∆p(13) and sy = sy(13). Here, the yield shocks t t t t t sy(13) are given by equation (5) for ℓ = 13, and the left-hand side vector of asset prices is t (cid:104) ∆p(13) = ∆ES1(13) ∆ES2(13) ∆EUR(13) ∆GBP(13) ∆AUD(13) ∆CAD(13) ... t t t t t t t ∆CHF(13) ∆SGD(13) ∆SEK(13) ∆NOK(13) ∆NZD(13) ... t t t t t (cid:105)′ ∆MXN(13) ∆ZAR(13) ∆DKK(13) ∆PLN(13) . t t t t (6) Note that we have some missing data for the asset prices in vector ∆p(13). This leads t samples sizes to differ not only across assets (as shown in Table 1) but also across event windows. Relative to the total number of observations reported above, we loose 22 observations in our baseline sample. More specifically, we are left with 5064 non-FOMC days (instead of 5085), and 219 FOMC days (instead of 220). 15

Table 3: Estimation Results Return (bp) ES1 ES2 EUR GBP AUD CAD CHF SGD Fed non-yield shock 61.73*** 65.57*** 38.68*** 33.39*** 61.03*** 36.04*** 31.86*** 22.60*** (3.69) (3.73) (1.30) (1.32) (2.14) (1.32) (1.18) (0.97) R2 without shock 0.21 0.19 0.45 0.30 0.25 0.25 0.43 0.28 R2 with shock 0.52 0.59 0.91 0.84 0.86 0.82 0.80 0.67 Return (bp) SEK NOK NZD MXN ZAR DKK PLN Fed non-yield Shock 45.47*** 47.29*** 59.87*** 35.22*** 56.19*** 38.59*** 52.42*** (1.44) (1.52) (2.25) (1.88) (2.09) (1.30) (1.86) R2 without shock 0.41 0.41 0.28 0.30 0.36 0.44 0.33 R2 with shock 0.90 0.91 0.76 0.65 0.79 0.90 0.88 Notes: Thistableshowstheresultsofourbaselineestimation(specification(4)),∆p =βsy+γd sny+ε . Thefirst t t t t t rowdisplayscoefficientvectorγ,i.e.,theeffectofFednon-yieldshocksny oneachofthe15seriesin∆p . Coefficients t t are in basis points per standard deviation shock. Exchange rates are expressed in U.S. dollars per foreign currency so that an increase reflects a depreciation of the U.S. dollar. The R2 are obtained from event study regressions of the respective dependent variable on (i) yield shocks sy, and (ii) yield shocks sy and the non-yield shock sny. t t t Heteroskedasticity-robust standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. Abbreviations of asset prices are explained in Table 1. 2.3 Results We now turn to the results of our baseline estimation, which are shown in Table 3. Two findings stand out. First, as conjectured, the estimates imply that there is indeed a common factor. For each of the 15 asset prices, our non-yield shock more than doubles the explained variation. For some exchange rates it more than triples the R-squared, explaining almost the entire variation in the 13-hour window. Hence, a single factor can account for a large part of the unexplained variation in these asset prices. However, it also worth noting that for the majority of assets a non-negligible share of the variation remains unexplained. This suggests that assuming that the entirety of asset returns around FOMC announcements is driven by monetary policy, as done by some previous work, might be not innocuous.8 Second, the estimated effects of the Fed non-yield shock, i.e., the γˆ , are all highly stai tistical significant at the one percent level.9 They are also quite sizable. A one-standard deviation non-yield shock leads to a 62 basis points increase in the E-mini S&P 500 front month futures contract (ES1) as well as a 39 and 60 basis points depreciation of the U.S. 8Note that the explanatory power of our nine yield shocks for exchange rates, i.e., the R2 without the Fed nonyield shock, is somewhat greater than in previous high-frequency event studies despite using a wider window. This suggests that our non-yield shock is conservatively estimated in the sense that we likely take out too much rather than too little variation attributable to yield changes. We return to this point in the robustness section, where we re-estimate our non-yield shocks with the first three principal components of the nine surprises used here. 9Heteroskedasticity-robust standard errors are obtained from the likelihood estimation. Details are provided in Appendix A. 16

Figure 4: Time Series of Fed Non-yield Shock 4 3 2 1 0 -1 -2 -3 -4 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 snoitaiveD dradnatS Notes: This figure displays the time series of the Fed non-yield shock over the sample period. Grey bars indicate NBER recession periods. Dollar against the Euro (EUR) and New Zealand Dollar (NZD), respectively. We provide a comparison of the effect sizes to those of other monetary policy shocks in the next section. Figure4showsthetimeseriesoftheestimatednon-yieldshock. Asisclearfromthefigure, the series displays substantial variation throughout our sample period. There are no extreme outliers. All observations are within four standard deviations. Further, we have roughly an equal number of positive (106) and negative (113) observations. The autocorrelation of the non-yield shock series is -0.07 (p > 0.2). Robustness We briefly summarize several robustness checks. Appendix Table A1 shows that the baseline estimates of the non-yield shock are robust across a variety of alternative specifications choices. Specifically, we show that our shock is very similar when (i) allowing for a generalized covariance matrix in the estimation, (ii) allowing yield shocks to be present on non-FOMC days, (iii) using three yield curve factors as in Swanson (2021), as well as (iv) including intercepts in the estimation specification. The baseline specification (4) assumes that the effects of yield shocks on stock prices and exchange rates are linear. Substantial nonlinearities could drive the low explanatory power of yield shocks illustrated in Figure 1 and therefore potentially the existence of the non-yield shock. We check this concern by regressing our baseline non-yield shock on yields while 17

allowing for non-linear effects. Appendix Table A2 shows that the non-yield shock cannot be explained by (i) squares and interactions of yield shocks, (ii) yield shocks whose effect may vary with their signs, as well as interactions of the yield shocks with (iii) the VIX, (iv) the unemployment rate, or (v) a zero lower bound (ZLB) indicator. 3 The Response of Financial Markets around the World In this section, we study the high-frequency effects of the Fed non-yield shock on a broad range of asset prices around the world. We focus on international stock markets, currencies, and government bond yields. We estimate two types of specifications. First, we estimate a cross-country pooled effect from the event study regression ∆dx = α +δsny +η for t ∈ F, (7) c,t c t c,t where ∆dx is a generic dependent variable. In the case of stock indexes and currencies, c,t the dependent variable is the 2-day log-difference in the stock index or currency of country c around the FOMC announcement at time t. When studying government bond yields, the dependent variable is the 2-day change in the yield. Throughout this section we consider 2-day changes, which are constructed from the closing price of the day before the FOMC announcement and the closing price of the day after the announcement. We study 2-day changes to ensure that all information captured by the non-yield shock becomes available between the beginning and end-point of this window. If not otherwise noted, the data comes from Bloomberg. Appendix B.4 provides details on this data. Note that we do not exclude any data during periods of financial market stress. However, some of our daily series display extremely large changes in episodes of high market volatility, which are unrelated to the FOMC releases. To mitigate the influence of such extreme values, we winsorize the 2-day returns at the top and bottom 1 percent. The pooled effect δ, estimated from specification (7), is informative about the average effect on international stock markets. It masks, however, potential heterogeneity in the responses across countries. We therefore also estimate the specification ∆dx = α +δ sny +η for t ∈ F, (8) c,t c c t c,t where the coefficients of interest, δ , are now country-specific. c 18

Figure 5: Effects of Fed Non-yield Shock on Stock Markets by Country 120 90 60 30 0 stnioP sisaB Americas Europe Africa Asia Oceania TUR ARG HKG MEX BRA COL RUS ZAF IDN All USA* CAN CHL GBR FRA ITA ESP NLD POLSWE BEL NOR CZE JPN IND TWN SGP AUS DEU CHE KOR THA DNK ISR EGY CHN MAR NZL NGA TUN SAU Notes: This figure shows the response of international stock indexes to a one standard deviation positive Fed nonyield shock. The dependent variable is the 2-day return on the stock index of country c, expressed in basis points. The leftmost, grey bar shows the pooled effect, i.e., the estimate of common coefficient δ from equation (7), while theremainingbarsshowthecountry-specificeffects,i.e.,theestimatesofcoefficientsδ fromequation(8). Theblack c error bands depict 95 percent confidence intervals, where standard errors are two-way clustered by announcement andbycountry. Wewinsorizeeachcountry-levelreturnseriesatthetopandbottom1percent. ∗ denotesassetprices which have been used in the shock estimation. Abbreviations of asset prices are explained in Appendix Table B3. 3.1 Stock Markets We begin with estimating the effects of the Fed non-yield shock on international stock markets. Much research has documented the effects of yield-based monetary policy shocks on domestic and international stock markets (see, e.g., Bernanke and Kuttner, 2005; Miranda- Agrippino and Rey, 2020). Since our shock is orthogonal to yield shocks, however, these prior estimates are unlikely to be informative about the effects of the non-yield shock. Figure 5 illustrates the estimates of equations (7) and (8) with the 2-day log-difference of countries’ stock indexes as the dependent variable. The pooled estimate, depicted by the leftmost grey bar, shows that a one standard deviation positive non-yield shock raises international stock markets by 44 basis points, on average. This effect is highly significant. Further, the non-yield shock generates co-movement in stock prices – making it a driver of the global financial cycle (Rey, 2013; Miranda-Agrippino and Rey, 2020; Boehm and Kroner, 2023). Almost all stock indices increase after a positive non-yield shock. This is the case even though foreign stock market data is not used in the estimation of the non-yield shock. There is some heterogeneity in effect sizes across regions. Countries in North America, South America, and Europe respond most consistently to the non-yield shock. This contrasts with 19

Figure 6: Effects of Fed Non-yield Shock on U.S. Dollar Exchange Rates 90 75 60 45 30 15 0 stnioP sisaB Americas Europe Dollar Depreciation Africa Asia Oceania NZL* ZAF* AUS* POL* NOR* SWE* CZE CAN* COL EUR* GBR* CHE* DNK* KOR TUR BRAMEX* All CHL RUS MARTUN IDN ISRSGP* THA IND TWN CHNJPN ARG EGY NGA SAU HKG Notes: This figure shows the response of U.S. dollar exchange rates to the Fed non-yield shock. The dependent variable is the 2-day return of the exchange rate, expressed in basis points. Exchange rates are in U.S. dollars per unit of foreign currency so that an increase reflects a depreciation of the U.S. dollar. The leftmost, grey bar shows the pooled effect, i.e., the estimate of the common coefficient δ from equation (7), while the remaining bars show the country-specific effects, i.e., the estimates of coefficients δ from equation (8). The black error bands depict 95 c percent confidence intervals, where standard errors are two-way clustered by announcement and by country. We winsorize each currency return series at the top and bottom 1 percent. ∗ denotes asset prices which have been used in the shock estimation. Abbreviations of asset prices are explained in Appendix Table B3. countries in Africa, Asia, and Oceania, which display more heterogeneity in the estimated effect sizes. 3.2 Exchange Rates We next turn to the effects of the non-yield shock on exchange rates.10 Specifically, we estimatepooledandcountry-specificeffectsbasedonequations(7)and(8), wherethedependent variables are now 2-day log-changes of various exchange rates. Figure 6 shows the estimates. All exchange rates are expressed in U.S. dollars per unit of foreign currency so that an increase reflects a depreciation of the U.S. dollar. As the figure shows, a one standard deviation positive Fed non-yield shock leads the U.S. dollar to depreciate against other currencies by 32 basis points, on average. While the U.S. dollar depreciates against all currencies considered here, there is large heterogeneity in effect sizes. For instance, the U.S. dollar depreciates by more than 60 basis points vis-a`-vis the South African Rand, the New Zealand dollar, and the Australian dollar. In comparison, there is essentially no change in the value of the U.S. dollar relative to the Saudi Riyal or the 10For prior work on monetary policy and exchange rates see, e.g., Eichenbaum and Evans (1995). 20

Hong Kong Dollar. Note that all exchange rates, which are included in the estimation of the non-yield shock, are marked with asterisks in Figure 6. The fact that the U.S. dollar also depreciates against currencies such as the Czech Koruna and the Turkish Lira, which are not included in the shock estimation, indicates that the effects of the non-yield shock are quite broad. 3.3 Bond Markets Figure 7: Effects of Fed Non-yield Shock on Bond Yields 2-Year 5 ISR 4 3 CHL 2 0 1 CAN ARGCOL FRA RUS NLD BEL DNK NGA MAR TUN CHN KORIDNSAU TWN AUS -1 AllUSA BRA DEU GBR ITAESP CHE SWE NOR CZE JPN IND THA SGP NZL -2 POL HKG EGYZAF -3 MEX -4 TUR (-7.4) -5 stnioP sisaB Americas Europe Africa Asia Oceania 10-Year 5 4 3 2 ISR 1 0 ARG CHL SWE NOR DNK TUN KOR SAU AUS NZL -1 All USACAN BRA DEU GBR FRA RUSITA ESP NLDCHE POL BEL CZE NGA MAR CHN JPN IND TWN THA SGP HKG -2 EGY ZAF -3 COL MEX TUR -4 IDN -5 stnioP sisaB Notes: This figure shows the response of international government bond yields to the Fed non-yield shock. The dependent variable is the 2-day change in local-currency government bond yields, expressed in basis points. The leftmost,greybarshowsthepooledeffect,i.e.,theestimateofthecommoncoefficientδ fromequation(7),whilethe remaining bars show the country-specific effects, i.e., the estimates of coefficients δ from equation (8). The black c error bands depict 95 percent confidence intervals, where standard errors are two-way clustered by announcement and by country. We winsorize each country’s series at the top and bottom 1 percent. Abbreviations of asset prices are explained in Appendix Table B3. Lastly, we study the effects of the non-yield shock on bond markets. Since the Fed non- 21

yield shock is by construction orthogonal to surprise changes in the U.S. yield curve within a 13-hour window around FOMC announcements, we expect no or only small effects on U.S. bond markets within a 2-day window as well.11 A priori less clear, however, are the reactions of international bond yields to the non-yield shock. Figure 7 shows the effects on the yields of 2-year and 10-year local-currency denominated government bonds. These estimates are obtained from specifications (7) and (8) with the 2-day changes in yields on the left-hand side. As the figure shows, the pooled effects are economically small and statistically insignificant. Since the standard errors are small, this amounts to a “tight zero”. Only for a handful of countries are the effects different from zero. Government bond yields in Mexico and Turkey, for instance, fall significantly after a positive non-yield shock. Yields in Israel, by contrast, increase. In summary, a positive non-yield shock raises international stock prices, it depreciates the U.S. dollar against a large number of foreign currencies, and it leaves most government bond yields approximately unchanged. We document large effects of the non-yield shock on commodities in Appendix C.2. 3.4 Comparison with Previous Monetary Policy Shocks To assess the importance of our non-yield shock, we next compare its effects with the effects of other commonly used monetary policy shocks in the literature. To so do, we re-estimate the pooled specification (7) replacing the non-yield shock with other monetary policy shocks. As in the introduction, we consider shocks from Nakamura and Steinsson (2018), Jarocin´ski and Karadi (2020), and Swanson (2021). Figure 8 shows the estimates. For comparison, the figure also plots the pooled effects of the non-yield shock from Figures 5–7. Two points stand out. First, the non-yield shock has the largest effects on international stock markets and exchange rates among all shocks. For example, a one standard deviation federal funds rate shock by Swanson (2021), which is essentially the Kuttner (2001) shock and the target rate shock by Gu¨rkaynak, Sack, and Swanson (2005), leads to an 18 basis points change in international stock prices, while the Fed non-yield has an effect of 44 basis points. Second, our non-yield shock has no significant effect on yields while most previous shocks strongly affect yields. These results underscore both the economic significance and the particular nature of our non-yield shock. 11We show in Appendix Table C1 that the Fed non-yield shock has no discernible effects on the U.S. yield curve in a 2-day window using both data from Bloomberg as well as Gu¨rkaynak, Sack, and Wright (2007). 22

Figure 8: Effects of Fed Non-yield Shock and Other Monetary Policy Shocks on Asset Prices Stock Markets 60 45 NY 30 PN MP FFR FG 15 0 LSAP -15 CBI stnioP sisaB U.S. Dollar Exchange Rates 40 NY Dollar Depreciation 30 20 FG PN MP FFR 10 LSAP 0 CBI -10 stnioP sisaB 2-Year Yield 0.5 CBI 0 -0.5 NY LSAP -1.0 -1.5 FFR PN -2.0 FG MP -2.5 -3.0 stnioP sisaB 10-Year Yield 0.5 0 CBI -0.5 NY -1.0 FFR -1.5 LSAP MP -2.0 PN -2.5 FG -3.0 stnioP sisaB Non-yield Shock Swanson (2021) Nakamura & Steinsson (2018) Jarocinski & Karadi (2020) Notes: This figure compares the response of international asset prices to our Fed non-yield shock with the responses to other monetary policy shocks. Each panel displays the pooled effects for a given asset class and each bar denotes thepooledeffect,i.e.,theestimateofthecommoncoefficientδ fromequation(7),foragivenmonetarypolicyshock of interest. The dependent variable is always the 2-day change in the asset price of interest, expressed in basis points. All shocks have been standardized and signed to have a negative effect on the 10-year yield. The black error bands depict 95 percent confidence intervals, where standard errors are two-way clustered by announcement and by country. We winsorize each country’s series at the top and bottom 1 percent. Shock Abbreviations: NY—Fed nonyield; FFR—Federal Funds Rate; FG—Forward Guidance; LSAP—Large-scale Asset Purchase; PN—Policy News; MP—Monetary Policy; CBI—Central Bank Information. 4 Implications for the Identification of Monetary Policy Shocks Thissectiondiscusseswhatthepresenceofthenon-yieldshockimpliesfortheidentificationof structural monetary policy shocks. To do so, we introduce a framework that clarifies how the non-yield shock can arise in the data and how it relates to the underlying structural shocks. Weshowthatthenon-yieldshockisingeneralareducedformmonetarypolicyshockbutcan have a structural interpretation under specific assumptions. We also compare the non-yield shock to previously identified shocks in the literature. It turns out that a substantial amount of information associated with FOMC announcements has not been captured by previous shocks. Details on this section and proofs are relegated to Appendix D. 23

4.1 Framework Suppose that the data over narrow event windows is generated by the model (cid:32) (cid:33) (cid:32) (cid:33) (cid:32) (cid:33) sy A 0 t = y z + . (9) t ∆p A ε t p t Here, sy is a k×1 vector of yield shocks, ∆p is a n×1 vector of stock price and exchange rate t t changes, z is a r×1 vector of structural monetary policy shocks which satisfy Cov[z ] = I t t r and are zero on non-event days, ε is a n×1 vector of non-monetary drivers of stock prices t and currencies over the window in question, and A and A are matrices capturing how yield y p changes, stock price changes, and exchange rate changes depend on the structural monetary policy shocks. This model is quite general. The main restrictions we impose on this data generating process is that the endogenous variables linearly depend on the shocks z and t that yield changes are not affected by non-monetary drivers within narrow windows. In line with our implementation we also assume that n ≥ r ≥ k, that A is of full row rank (k) and y A of full column rank (r) for some of the results below. A useful way of thinking about the p yield shocks sy is that they represent the first k principal components of observed changes in t the yield curve over the narrow event window. For instance, we could have k = 3 principal components as in Swanson (2021). Wenowapplyourestimationproceduretothisdatageneratingprocessinthepopulation— ormore precisely, aslightlymore general procedurethat allows formultiplenon-yield shocks. The estimating equation is ∆p = βsy +Γsny +ε , (10) t t t t for t ∈ F. Estimating β in the population yields β = A A′ (cid:0) A A′ (cid:1)−1 , (11) p y y y provided that A is of rank k ≤ r. In words, β is the matrix of projection coefficients y obtained by projecting ∆p on sy on announcement dates/times. Further, for a coefficient t t matrix Γ that is pinned down by the estimation procedure, the non-yield shock is implicitly defined as satisfying equation (cid:16) (cid:17) Γsny = A I −A′ (cid:0) A A′ (cid:1)−1 A z . (12) t p r y y y y t The orthogonality assumption between sy and sny is reflected in the annihilator matrix t t 24

I −A′ (cid:0) A A′ (cid:1)−1 A , which residualizes with respect to the yield curve. r y y y y It follows from equation (12) that the non-yield shocks are in general reduced form monetary policy shocks. Non-yield shocks are reduced form shocks, because they are linear combinations of the structural monetary policy shocks z . (This is most clearly seen for the t case in which Γ is invertible.) While reduced form shocks are generally difficult to interpret, equation (12) also makes clear that the non-yield shock is only a function of the structural monetary policy shocks z . Since the non-yield shocks do not depend on the non-monetary t disturbances ε , they are reduced form monetary policy shocks. t 4.2 Dimensions of Monetary Policy Pluggingexpressions(11)and(12)intoequation(10)andusingthatsy = A z fromequation t y t (9) gives (cid:16) (cid:17) ∆p = A A′ (cid:0) A A′ (cid:1)−1 A z +A I −A′ (cid:0) A A′ (cid:1)−1 A z +ε . (13) t p y y y y t p r y y y y t t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Effectpassingthroughyields Effectorthogonaltoyieldchanges This expression shows that our estimation procedure decomposes the effects of the structural monetary policy shocks z on ∆p into a part that passes through the yield curve and a part t t that does not pass through the yield curve (the orthogonal complement). The properties of projections then imply the following result. Proposition 1. Suppose n ≥ r ≥ k, A is of full row rank, and A is of full column rank. y p Then the number of non-yield shocks equals the number of structural monetary policy shocks r minus the number of yield shocks k. Hence, if there are k yield shocks and we detect r−k non-yield shocks in the data, then there must be r structural monetary policy shocks. Note that the framework allows for the possibility that no non-yield shock exists (if r = k). 4.3 Two Interpretations of the Non-yield Shock In the case of one non-yield shock (r = k + 1), as in our empirical analysis, the following equivalence result holds: Proposition 2. Suppose that r = k + 1, A is of full row rank, and A is of full column y p rank. Then the following statements are equivalent: 25

1. There exists a structural shock that does not affect the yield curve. 2. k structural monetary policy shocks are identifiable from the yield curve alone. 3. There is one non-yield shock and it has a structural interpretation. The intuition of the equivalence of points 1. and 2. is as follows. If all r structural monetary policy shocks in z affect the yield curve, then the k = r − 1 yield shocks do t not contain sufficient information to recover z . This is because we have k = r − 1 linear t equations, but r unknowns. Identifiability is only given if one of the structural monetary policy shocks does not affect the yield curve. In this case, the system of k = r−1 equations only contains k = r−1 unknowns and it has a unique solution if matrix A has rank k. Note y that the proposition makes a statement about identifiability. The actual identification of shocks typically requires additional assumptions about the matrix A (see, e.g., Gu¨rkaynak, y Sack, and Swanson, 2005; Swanson, 2021). The equivalence of points 1. and 3. follows from the fact that the non-yield shock is constructed to be orthogonal to the yield shocks. Proposition 2 implies that there are two possible interpretations of the non-yield shock. Under to the first interpretation, the non-yield shock is structural. This implies that the vector of structural monetary policy shocks z can be partitioned into a k×1 vector z1 and t t a scalar z2, which—and this is the key assumption for this interpretation—does not affect t (cid:16) (cid:17) yields. Partitioning A = A 0 , where A is a k ×k matrix of full rank, it follows that y (i) z1 = A−1sy, that is, k structural monetary policy shocks z1 are identifiable from the yield t t t curve alone, and (ii) the non-yield shock is structural, sny = ±z2. Hence, while the non-yield t t shock is in general a reduced form monetary policy shock, it is structural in this special case. If the non-yield shock is structural, identification schemes that construct the remaining k structural monetary policy shocks from yields alone can principally remain valid despite the presence of the non-yield shock. Such identification schemes include, among many others, Kuttner (2001); Gu¨rkaynak, Sack, and Swanson (2005) and Swanson (2021). In addition, if the non-yield shock is structural, it should be possible to tie large realizations to concrete policy actions, which cause the observed asset price responses documented in Sections 2.3 and 3 above as well as Section 5.1 below. The second interpretation is that the non-yield shock is a reduced form shock. In this case, identification schemes based on yields alone cannot recover the remaining k structural monetary policy shocks and any attempt to do so would only recover linear combinations of structural shocks. Further, if the non-yield shock is a reduced-form shock, it can serve as an input for identification schemes to recover structural shocks—together with yield shocks. 26

We illustrate both of these point with an example. Consider the case of Jarocin´ski and Karadi (2020). In their framework, there are two (cid:16) (cid:17)′ structural monetary policy shocks z = zpure zinfo , where zpure is the pure monetary t t t t policy shock and zinfo is the information shock. These two shocks are identified from the t co-movement of one interest rate, k = 1, and the S&P 500, n = 1. The key assumptions are that a pure monetary policy shock has opposite effects on interest rates and stock prices while the information shock moves interest rates and stock prices in the same direction. (cid:16) (cid:17) (cid:16) (cid:17) Formally, these restrictions are captured as A = a b and A = −c d for strictly y p positive (but unknown) constants a,b,c,d. Equation (9) then implies that sy = azpure +bzinfo. (14) t t t Further, straightforward algebra shows that in this case one non-yield shock exists and takes the form 1 sny = ±√ (cid:0) −bzpure +azinfo (cid:1) . (15) t t t a2 +b2 Hence, the yield shock and the non-yield shock are both linear combinations of the pure and the information shock. Clearly, a single yield shock sy is not sufficient to identify the two t structural monetary policy shocks zpure and zinfo, even if a and b were known. In addition t t to the yield shock, the non-yield shock sny, and hence the S&P 500, is required—as well t as knowledge of the constants a and b. Interestingly, knowledge of c and d is not directly required for identification although the derivation necessitates that they are not both zero. Relative to directly using a small number of asset prices, such as a single stock price change (Jarocin´ski and Karadi, 2020), the non-yield shock has the advantage that it is purified of the noise ε (partially so in finite samples). t Note that equation (15) has a testable prediction. If the true data generating process follows the identification assumptions of Jarocin´ski and Karadi (2020), and we implement our estimation procedure on the resulting data, then the non-yield shock should be a linear combination of the pure and the information shock. A regression of the non-yield shock on the pure and the information shock should deliver a high R-squared. Of course, such a relationship holds more generally. As equation (12) shows, the non-yield shock is generally a linear function of the structural shocks. We proceed in the next section with relating our non-yield shock to prior monetary policy shocks from the literature. 27

Table 4: Explanatory Power of Previous Monetary Policy Shocks for Fed Non-yield Shock Specification: sny =βshocksx+ε t t t Yields Yields + other Assets shocksx RR 2004 NS 2018 Sw 2021 BRW 2021 AD 2022 JK 2020 KSS 2021 Le 2023 t No. of Shocks 1 1 3 1 1 2 3 4 R2 0.02 0.00 0.01 0.02 0.01 0.00 0.23 0.17 Observations 91 104 187 185 91 167 112 191 Notes: This table shows the explanatory power of different sets of monetary policy shocks for our non-yield shock. Each column displays the results for a different set of shocks. Yields refers to papers which identify shocks purely fromchangesininterestrates. Yields+otherAssets referstopaperswhichidentifyshocksfromchangesinyieldsand otherassetprices. Abbreviations: AD2022—AruobaandDrechsel(2022); BRW2021—Bu,Rogers,andWu(2021); JK 2020—Jarocin´ski and Karadi (2020); KSS 2021—Kroencke, Schmeling, and Schrimpf (2021); Le 2023—Lewis (2023);NS2018—NakamuraandSteinsson(2018);RR2004—RomerandRomer(2004);Sw2021—Swanson(2021). 4.4 Common Variation with Previous Monetary Policy Shocks To do so we regress the non-yield shock on monetary policy shocks constructed in previous work. Table 4 displays the findings of this exercise. First, shocks constructed from yields (Nakamura and Steinsson (2018) (NS 2018), Swanson (2021) (Sw 2021), Bu, Rogers, and Wu (2021) (BRW 2021)) or otherwise centered on interest rates (Romer and Romer (2004) (RR 2004), Aruoba and Drechsel (2022) (AD 2022)) are indeed orthogonal to our non-yield shock. This property is, of course, in large part the result of constructing the non-yield shock as orthogonal to yields. Since our sample, window length, etc., differ from these studies, and Romer and Romer (2004) and Aruoba and Drechsel (2022) use no high-frequency data at all, however, the lack of explanatory power shown in Table 4 is not ex-ante guaranteed. Second, the shocks by Jarocin´ski and Karadi (2020), who also use the S&P 500 in their estimation, are orthogonal to our shock, while the shocks by Kroencke, Schmeling, and Schrimpf(2021)andLewis(2023)haveexplanatorypowersofonly23and17percent, respectively, despite the fact that they directly use stocks and exchange rates in the construction of their shocks. We conclude from this exercise that the large majority of variation that is captured by the non-yield shock has not been directly explored in the prior literature. 5 Understanding the Non-yield Shock In this section we present evidence on the origins of the non-yield shock as well as the dominant channels through which it affects asset prices. 28

5.1 Evidence from Asset Prices Having documented the importance of the Fed non-yield shock for international financial markets in Section 3, we now seek to understand why these asset prices respond. To do so, wecombinebasicassetpricingtheorywithdataonavarietyofindicatorsthatareinformative about the underlying channels. 5.1.1 Framework First, as shown by Boyd, Hu, and Jagannathan (2005), stock prices decompose into its three fundamentalcomponents: arisk-freeinterestrate,ariskpremium,andagrowthexpectations component: (cid:16) (cid:17) ∆p ≈ pd ∆g − ∆ep − ∆rf (16) c,t c c,t c,t c,t (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124)(cid:123)(cid:122)(cid:125) growthexpectations equitypremium risk-freerate In this decomposition ∆p is the observed change in the stock price index of country c, c,t ∆g is the change in the weighted average of expected future growth rates of cash flows, c,t ∆ep is the change of the equity (risk) premium, ∆rf is the change in the interest rate on c,t c,t long-term risk-free claims, and pd is a positive constant (the average price-dividend ratio). c ¨ Second, following Jiang, Krishnamurthy, and Lustig (2021), Kalemli-Ozcan and Varela (2021), and Obstfeld and Zhou (2022), we decompose the nominal exchange rate as follows: (cid:16) (cid:17) ∆e = − ∆ rf −rf − ∆(λ −λ ) − ∆rp . (17) c,t US,t c,t US,t c,t c,t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) convenienceyielddifferential riskpremium interestratedifferential In this expression, e is the log of the exchange rate, which is measured in U.S. dollars per c,t unit of foreign currency of country c. As before, ∆ denotes the difference over the window (cid:16) (cid:17) length of the event study. Turning to the right-hand side, ∆ rf −rf is the change US,t c,t in the interest differential between U.S. and foreign long-term risk-free claims. Further, ∆(λ −λ ) is the change in the convenience yield of the U.S. dollar bond relative to the US,t c,t foreign bond. Lastly, ∆rp denotes the change in the excess return of an investor borrowing c,t in dollars and purchasing a foreign-currency denominated bond.12 Increases in (i) U.S. riskfree rates relative to foreign risk-free rates, (ii) the U.S. convenience yield relative to the foreign convenience yield, and (iii) the risk premium all appreciate the dollar. This framework helps interpret the Fed non-yield shock. By construction, the shock is 12This decomposition assumes that the expectation of the exchange rate is constant in the limit, so that ∆E [lim e ]=0. t T→∞ c,t+T 29

orthogonal to changes in the U.S. interest rates. We verify below that the non-yield shock also leaves risk-free rates unchanged, so that ∆rf = 0 in equation (17). Further, as shown US,t in Section 3.3, foreign bond yields display no systematic response pattern to the non-yield shock. Instead, the pooled effect is close to zero and precisely estimated. We interpret this lack of response as implying that for most countries ∆rf ≈ 0 in equations (16) and c,t (17). This implies that the observed stock price changes in response to the Fed non-yield shock must follow from a change in growth expectations and/or the equity risk premium. Further, the exchange rate responses must arise from a change in the relative convenience yield and/or the currency risk premium. We next explore the changes in these components in greater detail. 5.1.2 Interest Rates As noted above, neither U.S. nor foreign yields are affected by the non-yield shock. In Appendix C.1, we provide more evidence on the effects of the Fed non-yield shock on interest rates. First, we show that not only yields but also forward rates are unaffected by the shock. Further, we investigate the response of inflation compensations and real yields. For the U.S., we find some evidence that our a positive non-yield shock leads to increases in inflation compensation. However, the effects are small and the economic interpretation is not straightforward, as TIPS liquidity premia seem to be driving the results rather than inflation expectations. Internationally, inflation compensations do not respond to our shock. Based on this evidence, we conclude that neither real nor nominal interest rates are much affected by the Fed non-yield shock and hence are not of first-order importance for the interpretation of the non-yield shock. 5.1.3 Risk Premia We begin with investigating the role of risk and uncertainty as well as risk appetite for explaining the effects of the Fed non-yield shock on foreign stock markets and currencies. Note that we use the terms “risk” and “uncertainty” interchangeably to describe actual or perceived changes in the second moments of the underlying fundamentals. We use “risk appetite” (or “risk aversion” as the flipside) to describe changes in investors’ preference to bear risk. Appendix Table B4 provides the sources of the underlying data in this section. We first study the effects on option-implied stock market volatility indexes, such as the VIX, which measure risk aversion and uncertainty. To do so, we estimate a pooled effect as 30

Figure 9: Effects of Fed Non-yield Shock on Implied Volatilities 1 0 -1 -2 -3 -4 tnecreP Stock Indexes Americas 1 Europe Africa Asia Oceania 0 JPN FRA -1 CHE All DEU HKG EUR GBR AUS -2 USA (VIX) -3 tnecreP U.S. Dollar Exchange Rates CAN CHE SWE EUR All GBR NOR JPN NZL AUS Notes: This figure shows the response of option-implied volatilities for stocks (left panel) and exchange rates (right panel) to the Fed non-yield shock. The dependent variables are constructed as 2-day log-returns, expressed in basis points. Theleftmost,greybarshowsthepooledeffect,i.e.,theestimateofcommoncoefficientδofequation(7),while the other bars show the country-specific effects, i.e., the estimates of coefficients δ of equation (8). The black error c bands depict 95 percent confidence intervals, where standard errors are clustered by announcement. We winsorize each country-level series at the top and bottom 1 percent. Abbreviations of asset prices are explained in Appendix Table B4. well as country-specific effects using versions of equations (7) and (8), with changes in the VIX and other countries’ implied volatility indexes as dependent variables. The left panel of Figure 9 displays the estimates. As the figure shows, the Fed non-yield shock leads to a decline in implied volatility indexes by 1.6 percent, on average. Except for France and Japan, all country-specific effects are significant at the 5 percent level. The effect on the VIX is the largest. These estimates imply that either uncertainty declines, investors’ willingness to take risk rises, or both. Uncertainty and risk-bearing capacity are also important for exchange rates (e.g., Lustig and Verdelhan, 2007). Due to the lack of high-frequency measures of expected excess returns onexchangerates, alsoreferredtoasuncoveredinterestrate(UIP)deviations, weuseoptionimplied volatility to proxy for currency risk premia.13 The right panel of Figure 9 shows the estimates of the pooled and county-specific effects. Similar to implied stock volatilities, the option-implied volatilities of U.S. dollar exchange rates fall following a positive non-yield shock. These responses suggest that currency risk premia explain part of the U.S. dollar movements observed after non-yield shocks. 13Lyons (1988) shows that option-implied volatilities are predictive of realized UIP deviations. 31

To better understand these channels, we next turn to a variety of additional indicators for risk, risk appetite, interest rate volatility, and term premia. Specifically, we estimate the specification ∆dx = α+δsny +η , for t ∈ F, (18) t t t with the different indicators as the dependent variables. Table 5 provides the estimates of this exercise. The first measure we consider is Martin’s (2017) SVIX, a proxy for the equity premium at the 1-year horizon. While we observe a decline in the SVIX, it is relatively noisy. Asemphasizedabove, theeffectsontheVIXcaneithercomefromchangesinthepriceofrisk (risk aversion) or the amount of risk (uncertainty). Bekaert and Hoerova (2014) provide a decomposition of the VIX into measures of risk aversion and uncertainty. We further study the effects on Bekaert, Engstrom, and Xu’s (2022) measures, which are constructed from equities and corporate bonds. As our estimates show, a positive non-yield shock leads to a decline in risk aversion as well as uncertainty. We next study the effects on term premia. Using measures from Adrian, Crump, and Moench (2013) and Kim and Wright (2005), the middle panel of Table 5 shows that the nonyield shock has no discernible effects on term premia. Note that the absence of an effect here is not implied by the identification assumption. While our estimation procedure implies that the non-yield shock is orthogonal to yield changes at all maturities, it does not imply that the non-yield shock is orthogonal to both expected future short-term rates and term premia. Nonetheless, the results in Table 5 indicate that term premia are largely unresponsive to the non-yield shock. Together with the orthogonalization with respect to yield changes, this implies that the non-yield shock leaves expected future short-term rates unchanged as well (see also Appendix C.1). Theevidencethisfarindicatesthatpremiaofriskierassetssuchstocksandexchangerates decrease following our non-yield shock, while premia of U.S. bonds are mostly unaffected. Hence, the results suggest that our non-yield shock either leads to higher risk-tolerance of investors or incorporates risk-related information, which is not captured in the yield changes. One potential explanation might be that our non-yield shock captures monetary policy uncertainty—an aspect of monetary policy, which has recently received increased attention (e.g., Husted, Rogers, and Sun, 2020; De Pooter, Favara, Modugno, and Wu, 2021; Bauer, Lakdawala, and Mueller, 2022; Bundick, Herriford, and Smith, 2024). To investigate this hypothesis, we employ uncertainty measures based on option-implied interest rate volatility. We start with implied volatility from Eurodollar options, which are based on the LIBOR, a benchmark short-term interest rate, and thus capture short-rate 32

Table 5: Effects of Fed Non-Yield Shock on Indicators of Risk Premia Return (%) VIX SVIX Risk Aversion Uncertainty BH 2014 BEX 2022 BH 2014 BEX 2022 Fed non-yield shock -2.64*** -0.56* -3.25** -1.68*** -2.14** -0.64** (0.73) (0.28) (1.55) (0.64) (0.89) (0.25) R2 0.07 0.03 0.02 0.06 0.05 0.03 Observations 219 216 208 217 210 217 Return (bp) Term Premia—ACM 2013 Term Premia—KW 2005 1-Year 2-Year 10-Year 1-Year 2-Year 10-Year Fed non-yield shock 0.42 0.35 1.03 -0.05 -0.08 -0.01 (0.28) (0.47) (0.98) (0.15) (0.25) (0.49) R2 0.02 0.00 0.01 0.00 0.00 0.00 Observations 219 219 219 219 219 219 Return (%) Implied Interest Rate Volatility EDX1 SRU MOVE TYVIX Fed non-yield shock -2.38*** -0.91*** -1.22*** -1.49*** (0.62) (0.33) (0.44) (0.55) R2 0.02 0.04 0.03 0.04 Observations 193 199 219 141 Notes: This table presents estimates of δ from specification (18), where the dependent variables are now 2-day logchanges of risk and uncertainty indicators, or 2-day changes in term premium measures. See the text for details on theemployedvariables. KW2005,ACM2013,BH2014,andBEX2022refertothecorrespondingmeasuresbyKim and Wright (2005), Bekaert and Hoerova (2014), Adrian, Crump, and Moench (2013), and Bekaert, Engstrom, and Xu (2022), respectively. Heteroskedasticity-consistent standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. We winsorize each dependent variable at the top and bottom 1 percent. uncertainty over the near term. In particular, we use the measure by Bundick, Herriford, and Smith (2024) (EDX1), which proxies uncertainty over the next half year, as well as the measure by Bauer, Lakdawala, and Mueller (2022) (SRU), which captures uncertainty over the next year. To capture longer-term uncertainty, we also use the Merrill Lynch Option Volatility Estimate (MOVE) index, which measures the 1-month ahead option-implied yield volatility of 2-year, 5-year, 10-year, and 30-year Treasuries, as well as the CBOE/CBOT 10-year U.S. Treasury Note Volatility (TYVIX) Index, which measures the 1-month ahead option-implied volatility of 10-year Treasury futures. ThebottompanelofTable5showstheestimatesforallfourimpliedinterestratevolatility indexes. In all cases, the Fed non-yield shock leads to a significant decline in implied interest 33

rate volatility, with the strongest effects on the EDX1 measure, i.e., policy-rate uncertainty over the very near term. These estimates imply that the non-yield shock either directly captures changes in interest-rate volatility or affects various asset prices through a change in interest rate volatility. That being said, the implied interest rate volatility measures only explainasmallamountofvariationofournon-yieldshock, indicatingthatourshockcaptures information beyond these measures. These results also imply that information on interest rate uncertainty is not fully captured in the yield curve, echoing findings of prior work in the literature. 5.1.4 Convenience Yields To measure convenience yields we use the “U.S. Treasury premium” series from Du, Im, and Schreger (2018). The Treasury premium measures the convenience yields of U.S. Treasuries relative to other countries’ convenience yields on government bonds, i.e., λ − λ in US,t c,t equation (17). For example, an increase implies that the convenience yield of the U.S. Treasury increases relative to the convenience yield of country c’s government bond. Following Du, Im, and Schreger (2018), we focus on 10 currencies of advanced economies forwhichconvenienceyieldscanbeconstructedinarelativecleanmanner. Figure10displays the effects of the Fed non-yield shock on convenience yields for various maturities.14 The results show that the non-yield shock typically leads to a decrease of the Treasury premium. The effects are broadly similar across maturities. Drawing on decomposition (17), these results suggest that the dollar depreciation documented in Figure 6 is partly driven by a reduction in the relative convenience yield of treasuries. 5.2 The Role of Fed Communication We next seek to understand whether the Federal Reserve’s communication on FOMC days is linked to our Fed non-yield shock. Relating asset price movements to specific aspects of the FOMC statement or the press conference is a challenging task and an active literature works on this very question (e.g., Gorodnichenko, Pham, and Talavera, 2023). In the following analysis, we study several dimensions through which Fed communication may cause the Fed non-yield shock. We begin with a visualization. Figure 11 plots the time series of the non-yield shock and complements each observation with additional information on the Fed chair at the time of 14We do not consider the 3-month maturity as it is constructed differently compared to the rest and much more volatile during the Great Recession. 34

Figure 10: Effects of Fed Non-yield Shock on Convenience Yields 0 -1 -2 stnioP sisaB All Maturities 0 All CAN EUR GBR CHE SWE NOR JPN AUS NZL -1 Americas Europe Asia -2 Oceania stnioP sisaB 1-Year CAN CHE GBR AUS NZL All JPN SWE NOR EUR 0 -1 -2 stnioP sisaB 2-Year 0 CAN NOR AUS GBR All EUR SWE CHE JPN NZL -1 -2 stnioP sisaB 10-Year NZL All CAN EUR GBR CHE SWE NOR JPN AUS Notes: This figure shows the response of U.S. convenience yields relative to foreign countries’ convenience yields to the Fed non-yield shock. The top-left panel shows effects pooled across maturities, for maturities starting at 1-year, i.e.,1-,2-,3-,5-,7-,and10-year. Thetop-rightpaneldisplayscoefficientsforthe1-yearmaturity,whereasthebottomleft and bottom-right panels for the 2-year and 10-year maturities, respectively. The dependent variables are 2-day log-returns,expressedinbasispoints. Theleftmost,greybarsshoweffectspooledacrosscountries,i.e., theestimate of common coefficient δ of equation (7), while the other bars show the country-specific effects, i.e., the estimates of coefficientsδ ofequation(8). Theblackerrorbandsdepict95percentconfidenceintervals,wherestandarderrorsare c clustered by announcement. We winsorize each country-level series at the top and bottom 1 percent. Abbreviations of asset prices are explained in Appendix Table B4. the shock as well as whether the announcement was accompanied by a statement and a press conference. Several points stand out. First, some of the largest observation occurred under the chairmanship of Ben Bernanke. In contrast, the magnitudes of the shock appear smallest under Alan Greenspan. Further, during the tenures of Yellen and Powell observations with press conference appear somewhat larger in magnitude. Since there are few announcement days without conference, however, it is difficult to draw firm conclusions from the figure alone.15 15Ofour219announcements,23comewithoutastatement. ExceptfortwoduringtheGreatRecession,allofthem arebeforeMay1999whenstatementswerenotaregularpartofFOMCannouncements. Wehave63announcements with press conferences. They were introduced in 2012 and are part of every scheduled meeting since 2019. 35

Figure 11: Fed Non-yield Shock across Fed Chairs and Types of FOMC Announcements 4 2 0 -2 Greenspan Bernanke -4 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 snoitaiveD dradnatS 4 2 0 -2 -4 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 snoitaiveD dradnatS None Statement Statement & Conference Yellen Powell Notes: This figure displays the time series of the Fed non-yield shock over the sample period. The color coding indicates the chairmanship at the time and the shading whether the announcement was accompanied by a FOMC statement and press conference. We therefore proceed with a more formal analysis. Specifically, we regress the absolute value of our non-yield shock on a variety of communication-related variables using the specification |sny| = α+βx +η for t ∈ F, (19) t t t where x is a generic vector of independent variables. We use the absolute value of the nont yield shock as the dependent variable since we hypothesize that the independent variables in x raise the magnitude of the shocks while they have no prediction for the sign. Note that t throughout the analysis we include a recession indicator as a control to mitigate concerns that the results are driven by recession-specific factors. We begin with regressing the absolute value of the non-yield shock on two indicator variables. The first indicator equals one on announcement days, which are accompanied by a statement, while the other equals one if the announcement is accompanied by a press 36

conference. The first column of Table 6 shows that both statement and press conference are associated with greater shock magnitudes. For example, announcements with statements have shocks that are 0.26 standard deviations greater than on announcement days without statements. Column two of Table 6 shows that shock magnitudes were greater under the three most recent chairs when compared to the period under chairman Greenspan (omitted base group). This is consistent with the view that the Federal Reserve’s communication greatly expanded when Bernanke became chairman. When considering all indicators jointly as shown in column three, only the coefficients on the chairmen remain significant, with Bernanke’s one standing out as the largest and most significant. We next investigate whether specific topics are linked to the magnitude of the non-yield shock. Based on our results this far, we focus on the following three topics: financial, risk-related, and international. To construct each of these topics, we use the term frequencyinverse document frequency (tf-idf) measure of relevant words in the FOMC statement and the press conference. The tf-idf is a widely used statistic in text analysis and measures the importance of a word or group of words in a given document. It takes into account both the frequency of the words in the document as well as the rarity of the words across documents. Details on the construction of the tf-idf measures are available in Appendix B.6. To measure discussions related to financial markets, we construct td-idfs for words associated with the word stem “financ”. Column four of Table 6 displays the estimates of equation (19) with these measures on the right-hand side. We find for FOMC statements that more discussionoffinancialconditionsisindeedlinkedtovariationofournon-yieldshock. Column five shows the estimates using td-idfs for words with stems “uncertain” or “risk” and column six presents similarly the estimates for words with stems “international” or “glob”. For both topics, we find evidence that they are associated with more variation in our non-yield shock. Overall, the results are consistent with our non-yield shock being caused by new information in the context of financial, risk-related, and/or international developments. Lastly, we consider equation (19) with all measures included in the same specification. Column seven of Table 6 displays the estimates of this exercise. Clearly, multiple coefficients become insignificant in the joint specification although none of the individually significant effects change signs. The three regressors whose effects remain significant are the press conference indicator, the chairman Bernanke indicator, and the tf-idf measure of international discussions in the FOMC statement. The potential importance of the press conference for financial markets is consistent with prior papers (e.g., Gorodnichenko, Pham, and Talavera, 37

Table 6: Predictive Power of Fed Communication for Fed Non-Yield Shock Dependent variable: |sny| (1) (2) (3) (4) (5) (6) (7) t 1(Statement) 0.26** 0.07 0.13 (0.12) (0.12) (0.14) 1(Press Conference) 0.22** 0.06 0.53** (0.08) (0.15) (0.26) 1(Bernanke) 0.46*** 0.44*** 0.32*** (0.10) (0.11) (0.12) 1(Yellen) 0.36*** 0.31** 0.10 (0.11) (0.13) (0.16) 1(Powell) 0.46*** 0.38** 0.09 (0.09) (0.17) (0.20) Discussion of Financial Issues Statement 4.27*** 1.33 (1.13) (1.29) Press Conference—Statement -0.09 -4.03 (2.90) (3.06) Press Conference—Q&A 1.41 -4.00 (2.32) (3.35) Discussion of Risk-related Issues Statement -1.81 -1.73 (1.16) (1.35) Press Conference—Statement 3.57** 2.17 (1.78) (2.25) Press Conference—Q&A -0.04 -3.95 (1.99) (3.06) Discussion of Global Issues Statement 5.67*** 3.81** (1.36) (1.86) Press Conference—Statement -0.33 -1.87 (4.31) (4.34) Press Conference—Q&A -2.65 -1.60 (3.81) (4.71) Recession Dummy Yes Yes Yes Yes Yes Yes Yes R2 0.07 0.15 0.15 0.10 0.05 0.09 0.20 Observations 219 219 219 219 219 219 219 Notes: Thetablepresentsestimatesofdifferentspecificationsofequation(19). Thedependentvariableisalwaysthe absolute value of the Fed non-yield shock, whereas the set of independent variables varies as indicated in the table. See text and Appendix B.6 for details on the construction of the independent variables. Heteroskedasticity-robust standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. 38

2023),16 and the strong effects of the Bernanke indicator is consistent with the expansion of Fed communication under his chairmanship (Yellen, 2012). Since discussions of international conditionsarelessfrequenttheymaybemoresurprising, whichcouldexplainthesignificance of this topic. 6 Conclusion In this paper we argue that U.S. monetary policy affects asset prices through channels that are not captured by interest rates. Motivated by the facts that (i) yield-based monetary policy shocks have little explanatory power for stocks and currencies around FOMC announcements and (ii) that stocks and currencies display elevated variances around these announcements, we use a heteroskedasticity-based procedure to estimate a Fed non-yield shock. Econometric tests show that this shock is strongly identified. A positive non-yield shock raises global stock prices and depreciates the dollar. Relative to other commonly used monetary policy its effects on these asset classes are large. We further show that the non-yield shock has a structural interpretation if there exists a structural monetary policy shock that does not affect yields. In this case the presence of the non-yield shock has no immediate implications for the identification of structural monetary policy shock except that it adds an additional dimension that has large effects on certain asset classes. In general, however, the non-yield shock is not structural and its existence implies that structural monetary policy shocks cannot be identified from the yield curve alone because the yield curve lacks sufficient information. The non-yield shock triggers substantial movements in measures of risk aversion and uncertainty, suggesting that the main channel through which the non-yield shock affects asset prices is through risk premia. One possibility consistent with our findings is that Fed actions affect interest rate uncertainty. Further, information effects can principally generate thenon-yieldshock. However, wealsoshowedthatJarocin´skiandKaradi’s(2020)serieshave noexplanatorypowerforthenon-yieldshock. Therefore, explainingthenon-yieldshockwith information effects would require a modification of the information effects framework. While we demonstrate that the non-yield shock can be related to Fed communications, more work is needed to fully understand its origins. 16Note that since we only have 23 announcements without a statement over our sample period, the statement indicator cannot be as precisely estimated as the one for the press conference. 39

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For online publication 45

A Estimation Appendix This appendix provides details on the estimation of our “non-yield shock”. Our estimation and code is adapted from Gu¨rkaynak, Kısacıko˘glu, and Wright (2020). A.1 Setup Our estimation framework can be written as a state-space model. The estimation equation (4) for the n asset case, restated here for convenience, is the measurement equation ∆p = βsy +γd sny +ε , (A1) t t t t t wherep = [ p ... p ]′,β = [ β′ ... β′ ]′,γ = [ γ ... γ ]′,andε = [ ε ... ε ]′. t 1,t n,t 1 n 1 n t 1,t n,t Further, β = [ β ... β ], and the yield shocks sy = [ sy ... sy ]′ as well as the ani 1,i k,i t 1,t k,t nouncement indicator d = 1(t ∈ F) are exogenous. The announcement indicator d gives rise t t to time-varying coefficients γd . We assume that ε is independently and identically normally dist t tributedwithzeromeanandadiagonalvariance-covariancematrixΣ . The(degenerate)transition ε equation is given by sny ∼ i.i.d. N (0,1). (A2) t The variance is normalized to one since γ is otherwise only identified up to scale. The parameters (cid:104) (cid:105) of the system are summarized by the parameter vector θ = β γ Σ . The goal is to estimate ε theunobservedfactorsny, givenasetofparametersθˆ, whichareestimatedbymaximumlikelihood. t A.2 Estimation Algorithm We estimate sny by using the Kalman filter to obtain the log-likelihood function of the model, t T (cid:26) L(θ) = − 1 2 (cid:88) 1(d t = 1) (cid:104) (∆p t −βsy t ) ′(cid:0) Σ ε +γγ′(cid:1)−1 (∆p t −βsy t )+log (cid:0)(cid:12) (cid:12)Σ ε +γγ′(cid:12) (cid:12) (cid:1) (cid:105) t=1 (A3) (cid:27) +1(d = 0) (cid:2) ∆p′Σ−1∆p +log(|Σ |) (cid:3) t t ε t ε and then maximize it via the following EM algorithm: 1. Start with initial guess for the parameters θ(0), where β(0) = βOLS = (cid:0) sy′sy(cid:1)−1 sy′∆p t t t t (cid:18) (cid:20) (cid:21)(cid:19) (cid:16) (cid:17)2 Σ(0) = diag E ∆p −β(0)sy ε t t t γ(0) = [0.01 ... 0.01]. (cid:124) (cid:123)(cid:122) (cid:125) ntimes 46

2. Run Kalman filter: The updating equations are given by s ny(j) = γ(j−1)′F−1v d , t|t t t t q (j) = 1−γ(j−1)′F−1γ(j−1)d , t|t t t where (cid:16) (cid:17) F = γγ′d +Σ(j−1) , t t ε v = ∆p −β(j−1)sy, t t t (cid:20) (cid:21) (cid:16) (cid:17)(cid:16) (cid:17)′ andq (j) istheMSEofs ny(j) , i.e. q (j) = E sny −s ny(j) sny −s ny(j) . Thelog-likelihood t|t t|t t|t t t|t t t|t (A3) can then be written as T (cid:88) L(θ)(j) = L (θ)(j) t t=1 T (cid:18) (cid:19) = (cid:88) − 1 (cid:2) log(2π)+log|F |+v′F−1v (cid:3) 2 t t t t t=1 T T T 1 (cid:88) 1 (cid:88) = − log(2π)− log|F |− v′F−1v . 2 2 t 2 t t t t=1 t=1 3. Run Kalman smoother: Due to the non-degenerate form of the transition equation, the smoothed estimates are equal to the filtered ones: ny(j) ny(j) s = s , t|T t|t (j) (j) q = q . t|T t|t (cid:104) (cid:105) 4. Calculate θ(1): Let us define ω = β γ such that the measurement equation (A1) can be (cid:104) (cid:105)′ (cid:16) (cid:17) written as ∆p = ωx +ε . Further, let x (j) = sy′ s ny(j) and Q (j) = diag 0 q (j) , t t t t|T t t|T t|T t|T then θ(1) is given by (cid:32) T (cid:33)−1 T ω(j) = (cid:88)(cid:0) E (cid:0) x x′(cid:1)(cid:1) (cid:88) E (cid:0) x′∆p (cid:1) T t t T t t t=1 t=1 (cid:32) T (cid:33)−1 T = (cid:88)(cid:16) x x′ +Q (j) (cid:17) (cid:88) x′ ∆p , t|T t|T t|T t|T t t=1 t=1 47

and (cid:32) T (cid:33) 1 (cid:88) (cid:16) (cid:17)2 Σ(j) = diag E ∆p −ω(j)x ε T T t t t=1 (cid:32) T T (cid:33) = diag 1 (cid:88)(cid:16) ∆p −ω(j)x (cid:17)2 +ω(j)′ (cid:88) Q (j) ω(j) . T t t|T t|T t=1 t=1 5. Repeat step 2-4 until the improvement in the log-likelihood is below a certain threshold. Let j∗ denote the final iteration of the algorithm. Then the final parameter estimates are given by θˆ= θ(j∗) with γˆ = γ(j∗) being reported in Table 3. The non-yield shock series is given by sˆny = s ny(j∗) . t t|T 6. Construction of heteroskedasticity-robust standard errors of θˆ: The formula for the variancecovariance matrix of the parameters is given by Cov(θˆ) = (cid:0) HG−1H (cid:1)−1 , where (cid:88) T ∂2L t (θˆ) H = − ∂θˆ∂θˆ′ t=1 and (cid:88) T ∂L t (θˆ) (cid:32) ∂L t (θˆ) (cid:33)′ G = . ∂θˆ ∂θˆ t=1 The matrices H and G are computed by plugging in small deviations from θˆ, i.e., ∂θˆ, into the Kalman filter. Remarks (cid:136) Gu¨rkaynak, Kısacıko˘glu, and Wright (2020) show that the parameter vector θ is identified. To achieve that, we need to assume that non-yield shock has a variance of one since it is only identified up to scale. Further, we normalize the first element of γ to be positive since it is only identified up to signing convention. (cid:136) We have missing observations in ∆p which the code can handle since the updating equations t of Kalman filter can be adequately adjusted depending on the available data for period t. If there are no missing values, we have βˆ= βOLS and sy and sny are fully orthogonal. t t A.3 Test for Weak Identification The pre-tests use the equivalence between the one-step Kalman filter estimation of (4) and a twostep procedure (Gu¨rkaynak, Kısacıko˘glu, and Wright, 2020), which applies the Rigobon (2003) 48

heteroskedasticity estimator to the residual ϕ , where ϕ is given by i,t i,t ϕ ≡ ∆p −β sy = γ sny +ε for t ∈ F, i,t i,t i t i t i,t after estimating β by OLS, and i ϕ ≡ ∆p = ε for t ∈ NF.17 i,t i,t i,t With this alternative formulation, we can use Lewis’s (2022) test for weak identification, which isbasedontheideathataheteroskedasticityestimatorcanberewrittenasaninstrumentalvariable (ℓ) problem(RigobonandSack,2004). Withsomeabuseofnotation, let∆p betheℓ-hourlog-return i,t (ℓ) of an asset price i in Table 1, and let ϕ be the corresponding residual constructed based on yield i,t y(ℓ) shocks s as defined in (5). We can then construct for each asset price i and event window ℓ, the t following F-statistic (cid:16) (cid:17)2 (cid:18) (cid:16) (cid:17)2 (cid:19)2 Πˆ(ℓ) (cid:80)T z (ℓ) i t=1 i,t (ℓ) F = , (A4) i (cid:16) (cid:17)2(cid:16) (cid:17)2 (cid:80)T z (ℓ) νˆ (ℓ) t=1 i,t i,t where Πˆ(ℓ) and νˆ (ℓ) are OLS estimates from the first stage i i,t (ℓ) (ℓ) (ℓ) (ℓ) ϕ = Π z +ν , i,t i i,t i,t (ℓ) with the instrumental variable z , satisfying i,t (cid:34) (cid:35) (cid:16) (cid:17) T(ℓ) (cid:16) (cid:17) T(ℓ) z (ℓ) = 1 t ∈ F(ℓ) × −1 t ∈ NF(ℓ) × ϕ (ℓ) . i,t (ℓ) (ℓ) i,t T T F NF Here, T(ℓ) is the total number of observations, T (ℓ) is the number of observations in the announce- F ment sample F(ℓ), and T (ℓ) is the number of observations in the non-announcement sample NF(ℓ). NF A.4 Robustness A.4.1 Re-estimation under Alternative Assumptions In this section, we analyze the robustness of our baseline series of the Fed non-yield shock by estimating alternate specifications of equation (4). In the following, we discuss each robustness exercise in detail. Table A1 summarizes the results. Note that the left-hand side variables are always the same 15 asset prices as in the baseline version. Generalized Covariance Following Gu¨rkaynak, Kısacıko˘glu, and Wright (2020), we also estimate a version with an unrestricted variance-covariance matrix of ε in (4) instead of the diagonal t 17AsshownbyGu¨rkaynak,Kısacıkog˘lu,andWright(2020),bothapproachesleadtoslightlydifferentresultswhen more than one series is included in ∆p . The reason for that is that the Kalman filter takes the covariance of the t assets in ∆p into account while the two-step procedure can only be implemented for a single asset at a time. t 49

Table A1: Robustness of Fed Non-Yield Shock Baseline Generalized Non-FOMC 3 Yield Curve Intercept Intercept for Covariance Days Purified Factors each Regime Correlation with Baseline Shock 1.00 0.94 1.00 0.94 1.00 1.00 Average R2 without shock 0.33 0.33 0.33 0.26 0.33 0.33 with shock 0.79 0.74 0.79 0.77 0.79 0.79 Observations 219 219 219 219 219 219 Notes: This table shows the results of our robustness analyzes. We re-estimate alternate versions of baseline specification (4), ∆p =βsy+γd sny+ε , using the Kalman filter. The left-hand side variables are always the same 15 t t t t t variables used in the baseline analysis. The R2 values are constructed as the average R2 values from announcement day regressionsofeachofthe 15assetprices on(i)yieldshocks sy, and(ii) yieldshockssy andnon-yield shocksny. t t t Further, we report the correlation of our re-estimated series with our baseline one. matrix under the baseline. This specification allows for the possibility of ever-present factors, i.e., drivers which lead to systematic movements on announcement and non-announcement days. As column two of Table A1 illustrates, the shock is very close to the baseline one indicating our estimation is robust to allowing for other unobserved factors which are not related to the FOMC announcement. Non-FOMC Days Purified We also do a robustness check in which we allow monetary policy shocks, sy, to be present during times non-announcement days. That is, instead of equation (3), t we now have for each asset price i ∆p = β˜sy +ε , for t ∈ NF, (A5) i,t i t i,t while the other equations are unchanged. Note that we allow sy to have a difference effect on t FOMC days and non-FOMC days. However, the nine surprises in sy are constructed the same way t on announcement and non-announcement days. We implement this specification by estimating (A5) by OLS and then run the Kalman filter based on the purified changes, i.e., the residuals of regression(A5). ColumnthreeofofTableA1displaystheresults. Thenon-yieldshockisessentially unchanged which is consistent with the, on average, low explanatory power of yields for exchange rates and stock prices on non-announcement days. In other words, the exploited variation is very similar to the baseline estimation. 3 Yield Curve Factors We also change the data series used for sy in our estimation. While t we use nine interest rate surprises in the baseline version, we now employ three yield curve factors instead. These factors are extracted from the nine series via principal components analysis as in Swanson (2021). The three factors explain 90 percent of the variation in the nine series. With the yield curve factors at hand, we can estimate the model. The fourth column of Table A1 shows the results of this exercise. The estimated shock his very highly correlated with the baseline 50

series. One thing worth point out is that the average explanatory power of the three factors for the asset returns drops to 26 percent, while the explanatory power including the non-yield shock is 77 percent—almost as much as in the baseline estimation. This may indicate that the Fed non-yield shock in this alternative specification is contaminated with changes in the yield curve that are not captured accurately by the three principal components. The high correlation also suggests that our baseline version is robust to allowing for noise in the yield curve surprises by using the first three principal components instead. Intercepts As our baseline specification (4) includes no intercept, we also estimate the baseline specification including intercepts, ∆p = α+βsy+γd sny+ε , and intercepts for each regime, i.e., t t t t t announcement and non-announcement days, ∆p = α +d α +βsy+γd sny+ε . Note that α, α , t 0 t 1 t t t t 0 and α are n-dimensional vectors. Both models are implemented by demeaning each series prior 1 to estimation, where in the first case the mean over both announcement and non-announcement days is taken, and in the second model a separate mean is calculated for announcement and nonannouncement days. After the both models can be estimated estimated via the Kalman filter. Columns five and six of Table A1 display the results. In essence, the intercepts do not affect our results consistent with the employed returns in stocks and exchange rates having a mean close to zero over our sample period. A.4.2 The Role of Nonlinearities We now analyze to what extent our non-yield shock captures nonlinearities with respect to the yield curve shocks. To do so, we regress our non-yield shock on various variables, which capture important nonlinearities, to see how much variation of the non-yield shock can be explained by nonlinearities. We start by re-estimating Swanson’s (2021) three shocks over our sample period and based on the 13-hour changes. With the three yield shocks at hand, we can capture different nonlinearities in a parsimonious way. Specifically, we consider five separate specifications. First, we consider second-order terms of the three yield shocks, i.e., squared shocks and interactions across shocks. Second, we allow for the shocks to have different effects for positive and negative observations. Third, fourth, and fifth, we allow the effects of the shocks to depend on the level of the VIX, the unemployment rate, and the zero lower bound, respectively. As Table A2 illustrates, none of the nonlinearities considered can explain more the 6 percent of our non-yield shock. 51

Table A2: Robustness of Fed Non-Yield Shock to Nonlinearities Dependent variable: sny Second-order Positive VIX Unemployment ZLB t Shocks Shocks Rate R2 0.01 0.03 0.05 0.04 0.06 FFR shock -0.11 0.10 0.00 -0.19** 0.02 FG shock -0.03 0.13 -0.05 0.08 0.03 LSAP shock -0.01 0.13 0.04 0.07 -0.10 FFR shock2 -0.04 FG shock2 -0.04 LSAP shock2 0.01 FFR shock × FG shock -0.04 FFR shock × LSAP shock -0.03 FG shock × LSAP shock 0.01 1(FFRshock>0) -0.40** 1(FGshock>0) -0.13 1(LSAPshock>0) -0.12 FFR shock × 1(FFRshock>0) -0.09 FG shock × 1(FGshock>0) -0.19 LSAP shock × 1(LSAPshock>0) -0.11 log(VIX) -0.05 FFR shock × log(VIX) -0.04 FG shock × log(VIX) 0.14 LSAP shock × log(VIX) -0.10 Fu -0.01 t FFR shock × Fu -0.24*** t FG shock × Fu 0.12 t LSAP shock × Fu 0.00 t 1(ZLB) 0.12 FFR shock × 1(ZLB) -1.81** FG shock × 1(ZLB) 0.10 LSAP shock × 1(ZLB) 0.37** Constant 0.03 0.52** -0.01 0.00 0.02 Observations 219 219 219 219 219 Notes: ThetableshowsestimatesofregressingtheFednon-yieldshockonvariousvariableswhichcapture different nonlinearities. Each column shows the estimates of a separate regression. For brevity, the standard errors of the coefficients are omitted. ***, **, and * indicate significance at the 1, 5, and 10 percent level. See text for more details on the specifications. 52

B Data Appendix B.1 Sample Construction FOMC days Our sample of FOMC announcements ranges from January 1996 until April 2023. We obtain dates and times of the FOMC press releases from Bloomberg, which we cross-check with information the Federal Reserve website, and data from Gu¨rkaynak, Sack, and Swanson (2005) and Jarocin´ski and Karadi (2020). Based on our sample of scheduled and unscheduled announcements, we remove dates for which the intraday data has large time gaps due to outages from Thomson Reuters Tick History. These outages are more common in the early sample period but otherwise completely random mitigating concerns of sample selection. As a result, we exclude the two scheduled FOMC announcements on July 1, 1998, and August 21, 2001, and the unscheduled meeting on April 18, 2001. We end up with 220 observations. Non-FOMC days Our sample of non-FOMC day ranges from January 1996 until April 2023. We use 2:15 pm EST as the reference time around which we construct our event windows around since most FOMC announcements in our sample are at that time. Our sample construction starts with all U.S. trading days over the period. We exclude all FOMC announcement days (scheduled and unscheduled). Since our window can range into the next business day, we also exclude Fridays. Further, we drop days with shortened trading hours before or around holidays (e.g., July 3 or December 24). We also remove dates for which the intraday data has large time gaps around 2:15 pm EST due to outages from Thomson Reuters Tick History. These outages are more common in the early sample period but otherwise completely random mitigating concerns of sample selection. Lastly, as done by Nakamura and Steinsson (2018), we drop the days of market turmoil following September 11, 2001, i.e., from September 11 till 22, and the days of the Lehman and AIG collapse, i.e., September 15 and 16, 2008, from our sample. We end up with 5085 observations. B.2 Yield Shocks For each FOMC announcement day, we construct nine yield shocks which capture the effects of monetary policy to the yield curve. To construct these, we employ intraday data on interest rate futures from Thomson Reuters Tick History. The sample period ranges from January 1996 and to April 2023. Table 1 provides an overview of the employed data. For each futures contract, we have a minute-by-minute series which we aggregate up to 5-minute intervals. Following previous papers, the first five variables MP1, MP2, ED2, ED3, ED4 cover surprises to maturities up to 14 months and are standard measures in the literature following Gu¨rkaynak, Sack, and Swanson (2005). For longer horizons, we employ Treasury futures following Gu¨rkaynak, Kısacıko˘glu, and Wright (2020). In the following, we detail the construction of the yield shocks from the futures contracts. As discussed in the main text, we consider different event windows which range from 10 minutes prior to the release to ℓ hours after the release, where ℓ ∈ (cid:8)1,1,2,...,18 (cid:9) . Hence, we need to construct 3 for each FOMC announcement and each window length a given yield shock. To ease notion, let τ be the times of FOMC announcements, i.e., for t ∈ F. Further, we define ℓ− and ℓ+ as the window adjacent to the window ℓ in our analysis, respectively. For example for a window of ℓ = 3, we have 53

Table B1: Overview of Intraday Interest Rate Futures Data Variable in Text Underlying Instruments RICs Sample MP1 Federal Funds Rate Futures FFc1–FFc2 1996–2023 MP2 Federal Funds Rate Futures FFc3–FFc4 1996–2023 ED2 2-Quarter Eurodollar/SOFR Futures EDcm2/SRAcm3 1996–2023 ED3 3-Quarter Eurodollar/SOFR Futures EDcm3/SRAcm4 1996–2023 ED4 4-Quarter Eurodollar/SOFR Futures EDcm4/SRAcm5 1996–2023 T2 2-Year Treasury Futures TUc1/TUc2 1996–2023 T5 5-Year Treasury Futures FVc1/FVc2 1996–2023 T10 10-Year Treasury Futures TYc1/TYc2 1996–2023 T30 30-Year Treasury Futures USc1/USc2 1996–2023 Notes: This table provides an overview of the intraday data employed to construct the monetary policy surprises to the yield curve. The data comes from Thomson Reuters Tick History. RIC refers to the Reuters Instrument Code, which uniquely identifies each instrument. Abbreviations: SOFR—Secured Overnight Financing Rate. ℓ− = 2 and ℓ+ = 4. B.2.1 Federal Funds Futures For given expiry month, a federal funds rate futures contract pays out, on the last day of the expiry month,100minustheaverage(effective)federalfundsrateovertheexpirymonth. Precisely,letpffj ζ bethepriceattimeζ ofthe(j −1)monthaheadfederalfundsfuturescontract. Then,theexpected average federal funds rate of the (j −1) month ahead at time ζ is calculated as ffj = 100−pffj . ζ ζ Federal Funds Rate Surprise—Current Meeting We calculate the federal funds rate meet- (ℓ) ing surprise MP1 as τ MP1(ℓ) = m 0 (cid:0) ff1 −ff1 (cid:1) , (B1) τ m −d τ+ℓ τ−10 0 0 whereff1 andff1 arethecurrentmonth’simpliedfederalfundsratesfromthelasttradethat τ−10 τ+ℓ occurred more than 10 minutes before the FOMC announcement and the first trade that occurred more than ℓ hours and less than ℓ+ hours after the FOMC announcement, respectively. Further, m isthetotalnumberofdaysinthemonthofannouncementτ, andd isthedayofannouncement 0 0 τ. See Gu¨rkaynak (2005) for a derivation of (B1). The construction is done in the followings steps: 1. For each available time ζ, calculate the implied federal funds rate, i.e. ff1 = 100−pff1 . ζ ζ 2. Calculate m0 (cid:0) ff1 −ff1 (cid:1) for each FOMC announcement τ and event window ℓ. m0−d0 τ+ℓ τ−10 3. Ifm −d +1 ≤ 7,i.e.,theannouncementoccursinthelastsevendaysofthemonth,weusethe 0 0 change in the price of next month’s fed funds futures contract, i.e. MP1 (ℓ) = ff2 −ff2 . τ τ+ℓ τ−10 54

This avoids multiplying by large m0 . For example, for the FOMC announcement on m0−d0 January 29, 2014, we have d = 29, m = 31, and hence 31−29+1 = 3 < 7. 0 0 Federal Funds Rate Surprise—Next Meeting We calculate the revision in expectations at FOMC meeting τ about the federal funds rate change at FOMC meeting τ +1 as (cid:20) (cid:21) m (cid:16) (cid:17) d MP2(ℓ) = 1 ff j(1) −ff j(1) − 1 MP1(ℓ) , (B2) τ m −d τ+ℓ τ−10 m τ 1 1 1 j(1) j(1) whereff andff aretheimpliedrateofthefederalfundsratefuturescontractforthemonth τ−10 τ+ℓ ofthenextscheduledFOMCmeetingfromthelasttradethatoccurredmorethan10minutesbefore the FOMC announcement and the first trade that occurred more than ℓ hours and less than ℓ+ hours after the FOMC announcement, respectively. Further, m is the total number of days in the 1 month of announcement τ+1, and d is the day of announcement τ+1. Note that we have usually, 0 j(1) = {3,4}. With a little bit of an abuse of notation, τ +1 refers here to the next scheduled FOMC meeting at the time of announcement τ. Hence, ex-post there might be an unscheduled meeting in between those. See Gu¨rkaynak (2005) for a derivation of (B2). The construction is done in the followings steps: 1. For a given FOMC announcement τ, find month of next scheduled FOMC meeting, i.e., j(1). (cid:104)(cid:16) (cid:17) (cid:105) 2. Calculate m1 ff j(1) −ff j(1) − d1 MP1 (ℓ) for each announcement τ and event winm1−d1 τ+ℓ τ−10 m1 τ dow ℓ. 3. If m −d +1 ≤ 7, i.e., the announcement occurs in the last seven days of the month, use 1 1 (ℓ) j(1)+1 the change in the price of next month’s fed funds futures contract, i.e., MP2 = ff − τ τ+ℓ j(1)+1 ff . τ−10 B.2.2 Eurodollar/SOFR Futures Eurodollar futures are quarterly contracts which pay out 100 minus the 3-month U.S. dollar BBA LIBOR interest rate at the time of expiration. The last trading day is the second London bank business day (typically the Monday) before the third Wednesday of the last month of the expiry quarter. With the cessation of the LIBOR, we use the Secured Overnight Financing Rate (SOFR) futures which are the successor futures contracts at the Chicago Mercantile Exchange (CME). We follow Kroner (2023) and use them from April 2022 onwards as this the first month in which the trading volumes of the SOFR futures contracts exceed the ones of the corresponding Eurodollar futures. For simplicity, we describe in the following the construction with respect to the Eurodollar futures contracts. The SOFR futures are handled in the same manner. Let pedj be the price at time ζ of the jth nearest quarterly Eurodollar futures contract (March, ζ June, September, December), then the expiration date of pedj is between j and j −1 quarters in ζ the future at any given point in time. Further, the implied rate is given by edj = 100−pedj. For ζ ζ a given FOMC announcement τ, we calculate the difference in the implied rate EDj(ℓ) = edj −edj , for j ∈ {2,3,4}, (B3) τ τ+ℓ τ−10 55

whereedj andedj aretheimpliedrateofthejthnearestquarterlyEurodollarfuturescontract τ−10 τ+ℓ from the last trade that occurred more than 10 minutes before the FOMC announcement and the first trade that occurred more than ℓ hours and less than ℓ+ hours after the FOMC announcement, respectively. The construction is done in the followings steps: 1. For each ζ, calculate the implied rate, i.e. , edj = 100−pedj. ζ ζ 2. For a given FOMC announcement τ, calculate the difference in the implied rate of contract j, EDj (ℓ) = edj −edj ,. τ τ+ℓ τ−10 B.2.3 Treasury Futures Treasury futures are quarterly contracts which obligate the seller to deliver a Treasury bond within a range of maturities to the buyer at the time of expiration. Let pt2j be the price at time ζ of the ζ jthnearestquarterly2-yearTreasuryfuturescontract. Wethencalculatetheimpliedyieldsurprise around FOMC announcement τ by dividing the price change by the approximate duration of the underlying Treasury bond and flipping the sign of it, i.e., (cid:16) (cid:17) T2(ℓ) = − pt21 −pt21 /2. (B4) τ τ+ℓ τ−10 If the announcement τ is in the month of expiration (March, June, September, December) and (cid:16) (cid:17) prior to the expiration date, we employ the next closest contract, i.e., T2 (ℓ) = − pt22 −pt22 /2, τ τ+ℓ τ−10 due to its higher liquidity. Similarly, we calculate the implied yield changes from 5-year, 10-year, and 30-year futures contracts, i.e., (cid:16) (cid:17) T5(ℓ) = − pt51 −pt51 /4, τ τ+ℓ τ−10 (cid:16) (cid:17) T10(ℓ) = − pt101 −pt101 /7, τ τ+ℓ τ−10 (cid:16) (cid:17) T30(ℓ) = − pt301 −pt301 /15, τ τ+ℓ τ−10 where we use the approximate maturities as in Gu¨rkaynak, Kısacıko˘glu, and Wright (2020). B.2.4 Treatment of Missing Observations For some of the interest rate futures contracts, the trading is sometimes sparse early in our sample. Hence, ifayieldshockismissingforagivenwindowℓ, wetaketheshockofthenextshorterwindow ℓ−. The underlying assumption is that if no price is observed, the futures price did not change between ℓ− and ℓ. We also apply this in the few very cases in which we have extreme values. B.2.5 Validation To validate our data and our construction methodology, we compare our constructed variables with the ones of Nakamura and Steinsson (2018) and Gu¨rkaynak, Kısacıko˘glu, and Wright (2020). Table B2 shows the correlation of each of our variables with the corresponding one by the prior paper. 56

To match the window lengths, we use 30-minute changes in the case of Nakamura and Steinsson (2018), ranging from 10 minutes before to 20 minutes after, and 20-minute changes in the case of Gu¨rkaynak, Kısacıko˘glu, and Wright (2020), ranging from 5 minutes before to 15 minutes after. Note that both papers employ different data sources than us. Table B2: NS 2018 GKW 2020 MP1 MP2 ED2 ED3 ED4 T2 T5 T10 T30 MP1 0.99 MP2 0.93 ED2 0.99 ED3 0.99 ED4 0.99 T2 0.94 T5 0.91 T10 0.95 T30 0.93 Observations 105 105 105 105 105 77 94 93 94 Notes: Thistableshowsthecorrelationofourconstructedinterestratesurpriseswiththeones ofNakamuraandSteinsson(2018)(NS2018)andGu¨rkaynak,Kısacıkog˘lu,andWright(2020) (GKW 2020) for the overlapping FOMC announcements. To match the window lengths, we use 30-minute changes in the case of NS 2018, ranging from 10 minutes before to 20 minutes after, and 20-minute changes in the case of GKW 2020, ranging from 5 minutes before to 15 minutes after. Note that we use 13-hour windows for our shock estimation. B.3 Left-hand-side Asset Prices for Estimation We construct the ℓ-hour log-return of asset price i as (ℓ) ∆p = log(p )−log(p ), (B5) i,t i,τ+ℓ i,τ−10 where p is the last price that occurred more than 10 minutes before the FOMC announcement i,τ+ℓ and p is first price that occurred more than ℓ hours and less than ℓ+ hours after the FOMC i,τ−10 announcement, respectively. If we do not observe any price between ℓ and ℓ+, we set . Note that our Kalman filter algorithm can handle missing observations in ∆p as long as at lease one ∆p is t i,t available for each t. We also inspect the data for extreme values which we set to missing. 57

B.4 Daily Financial Market Data Table B3: Daily Cross-Country Data—Part I U.S.Dollar 2-YearGovt. 10-YearGovt. Countries ISO StockIndex ExchangeRate BondYield BondYield Ticker Sample Ticker Sample Ticker Sample Ticker Sample Americas UnitedStates USA SPXIndex 1996-2023 USGG2YRIndex 1996-2023 USGG10YRIndex 1996-2023 Canada CAN SPTSXIndex 1996-2023 CADCurncy 1996-2023 GTCAD2YGovt 1996-2023 GTCAD10YGovt 1996-2023 Brazil BRA IBOVIndex 1996-2023 BRLCurncy 1996-2023 *BR2YT=RR 2002-2023 *BR10YT=RR 1998-2023 Mexico MEX MEXBOLIndex 1996-2023 MXNCurncy 1996-2023 GTMXN2YGovt 2011-2023 *MX10YT=RR 2002-2023 Argentina ARG MERVALIndex 1996-2023 ARSCurncy 1996-2023 Colombia COL COLCAPIndex 2002-2023 COPCurncy 1996-2023 *CO2YT=RR 2002-2023 *CO10YT=RR 2002-2023 Chile CHL IPSAIndex 1996-2023 CLPCurncy 1996-2023 *CL2YT=RR 2007-2023 *CL10YT=RR 2007-2023 Europe EuroArea EUR EURCurncy 1996-2023 Germany DEU DAXIndex 1996-2023 GTDEM2YGovt 1996-2023 GTDEM10YGovt 1996-2023 UnitedKingdom GBR UKXIndex 1996-2023 GBPCurncy 1996-2023 GTGBP2YGovt 1996-2023 GTGBP10YGovt 1996-2023 France FRA CACIndex 1996-2023 GTFRF2YGovt 1996-2023 GTFRF10YGovt 1996-2023 Russia RUS IMOEXIndex 1997-2023 RUBCurncy 1996-2023 *RU2YT=RR 2001-2023 *RU10YT=RR 2003-2023 Italy ITA FTSEMIBIndex 1998-2023 *IT2YT=RR 1998-2023 *IT10YT=RR 1996-2023 Spain ESP IBEXIndex 1996-2023 *IT2YT=RR 1998-2023 *IT10YT=RR 1996-2023 Netherlands NLD AEXIndex 1996-2023 *NL2YT=RR 1996-2023 *NL10YT=RR 1996-2023 Switzerland CHE SMIIndex 1996-2023 CHFCurncy 1996-2023 *CH2YT=RR 1996-2023 *CH10YT=RR 1996-2023 Poland POL WIG20Index 1996-2023 PLNCurncy 1996-2023 *PO2YT=RR 1998-2023 *PO10YT=RR 1999-2023 Sweden SWE OMXIndex 1996-2023 SEKCurncy 1996-2023 *SE2YT=RR 1996-2023 *SE10YT=RR 1996-2023 Belgium BEL BEL20Index 1996-2023 *BE2YT=RR 1996-2023 *BE10YT=RR 1996-2023 Norway NOR OBXIndex 1996-2023 NOKCurncy 1996-2023 GTNOK2YGovt 2007-2023 *NO10YT=RR 1996-2023 Denmark DNK KFXIndex 1996-2023 DKKCurncy 1996-2023 *DK2YT=RR 1996-2023 *DK10YT=RR 1996-2023 CzechRepublic CZE PXIndex 1996-2023 CZKCurncy 1996-2023 *CZ2YT=RR 1998-2023 *CZ10YT=RR 2000-2023 Africa Nigeria NGA NGXINDXIndex 1998-2023 NGNCurncy 1996-2023 *NG2YT=RR 2008-2023 *NG10YT=RR 2007-2023 Egypt EGY EGX30Index 1998-2023 EGPCurncy 1996-2023 *EG2YT=RR 2016-2023 *EG10YT=RR 2010-2023 SouthAfrica ZAF TOP40Index 1996-2023 ZARCurncy 1996-2023 *ZA2YT=RR 2007-2023 *ZA10YT=RR 1996-2023 Morocco MAR MOSENEWIndex 1996-2023 MADCurncy 1996-2023 *MA2YT=RR 2012-2023 *MA10YT=RR 2012-2023 Tunisia TUN TUSISEIndex 1999-2023 TNDCurncy 1996-2023 Asia China CHN SHCOMPIndex 1996-2023 CNYCurncy 1996-2023 *CN2YT=RR 2000-2023 *CN10YT=RR 2000-2023 Japan JPN NKYIndex 1996-2023 JPYCurncy 1996-2023 GTJPY2YGovt 1996-2023 GTJPY10YGovt 1996-2023 India IND NIFTYIndex 1996-2023 INRCurncy 1996-2023 *IN2YT=RR 1997-2023 *IN10YT=RR 1998-2023 Korea KOR KOSPIIndex 1996-2023 KRWCurncy 1996-2023 GTKRW2YGovt 1999-2023 GTKRW10YGovt 2001-2023 Indonesia IDN JCIIndex 1996-2023 IDRCurncy 1996-2023 *ID10YT=RR 2003-2023 SaudiArabia SAU SASEIDXIndex 1996-2023 SARCurncy 1996-2023 Turkey TUR XU100Index 1996-2023 TRYCurncy 1996-2023 *TR2YT=RR 2005-2023 *TR10YT=RR 2010-2023 Taiwan TWN TWSEIndex 1996-2023 TWDCurncy 1996-2023 *TW2YT=RR 1998-2023 *TW10YT=RR 1998-2023 Thailand THA SETIndex 1996-2023 THBCurncy 1996-2023 *TH2YT=RR 2000-2023 *TH10YT=RR 2001-2023 Israel ISR TA125Index 1996-2023 ILSCurncy 1996-2023 *IS2YT=RR 2006-2023 *IS10YT=RR 2002-2023 Singapore SGP STIIndex 1999-2023 SGDCurncy 1996-2023 *SG2YT=RR 1996-2023 *SG10YT=RR 1998-2023 HongKong HKG HSIIndex 1996-2023 HKDCurncy 1996-2023 *HK2YT=RR 1997-2023 *HK10YT=RR 1996-2023 Oceania Australia AUS AS51Index 1996-2023 AUDCurncy 1996-2023 *AU2YT=RR 1996-2023 *AU10YT=RR 1996-2023 NewZealand NZL NZSE50FGIndex 2001-2023 NZDCurncy 1996-2023 *NZ2YT=RR 1996-2023 *NZ10YT=RR 1996-2023 Notes: This table shows the daily asset prices considered as outcome variables in Section 3 by country. The data is from Bloomberg and Refinitiv. For each series, we report sample period (Sample) and the Bloomberg or Refinitiv identifier(Ticker). ∗ denotesdatafromRefinitiv. Countriesarelistedbycontinentanddescendingorderintermsof their 2022 nominal GDP (in U.S. dollars) taken from IMF World Economic Outlook (WEO) database. 58

Table B4: Daily Cross-Country Data—Part II ImpliedVol. ImpliedVol. Dividend InflationSwap Breakeven Countries ISO StockIndex ExchangeRate Futures Rate InflationRate Ticker Sample Ticker Sample Ticker Sample Ticker Sample Ticker Sample Americas USGGBE02/ 2004-2023 UnitedStates USA VIXIndex 1996-2023 USGGBE05/ 2002-2023 USGGBE10Index 1998-2023 USSWIT2/ 2004-2023 USDCADV1M ASD1-ASD8 2015/16- CDGGBE05/ 2016-2023 Canada CAN 1998-2023 USSWIT5/ 2004-2023 Curncy Index 2023 CDGGBE10Index 2008-2023 USSWIT10Curncy 2004-2023 Europe EUSWI2/ 2004-2023 EURUSDV1M DED1-DED8 2008/09- EuroArea EUR V2XIndex 1999-2023 1998-2023 EUSWI5/ 2004-2023 Curncy Index 2023 EUSWI10Curncy 2004-2023 DEGGBE02/ 2011-2023 Germany DEU V1XIndex 1996-2023 DEGGBE05/ 2008-2023 DEGGBE10Index 2009-2023 BPSWIT2/ 2004-2023 UKGGBE02/ 1996-2023 GBPUSDV1M UnitedKingdom GBR IVIUKIndex 2000-2023 1996-2023 BPSWIT5/ 2004-2023 UKGGBE05/ 1996-2023 Curncy BPSWIT10Curncy 2004-2023 UKGGBE10Index 1996-2023 France FRA VCACIndex 2000-2020 USDCHFV1M Switzerland CHE V3XIndex 1999-2023 1996-2023 Curncy SKGGBE02/ 2002-2023 USDSEKV1M Sweden SWE 1998-2023 SKGGBE05/ 2004-2023 Curncy SKGGBE10Index 2004-2023 USDNOKV1M Norway NOR 1999-2023 Curncy Asia JYGGBE02/ 2012-2023 USDJPYV1M INT1-INT8 Japan JPN VXJIndex 1996-2023 1996-2023 2010-2023 JYGGBE05/ 2009-2023 Curncy Index JYGGBE10Index 2004-2023 HongKong HKG VHSIIndex 2001-2020 Oceania ADGGBE02/ 2003-2023 AUDUSDV1M Australia AUS AS51VIXIndex 2008-2020 1996-2023 ADGGBE05/ 2000-2023 Curncy ADGGBE10Index 2000-2023 NZDUSDV1M NewZealand NZL 1997-2023 Curncy Notes: This table shows the daily asset prices considered as outcome variables in Section 3 by country. The data is from Bloomberg. For each series, we report sample period (Sample) and Bloomberg identifier (Ticker). Countries are listed by continent and descending order in terms of their 2022 nominal GDP (in U.S. dollars) taken from IMF World Economic Outlook (WEO) database. 59

Table B5: Daily Commodity Prices and Implied Interest Rate Volatilities Name Ticker Sample Commodity Prices S&P GSCI Total SPGSCI Index 1996-2023 S&P GSCI Energy SPGSEN Index 1996-2023 S&P GSCI Precious Metals SPGSPM Index 1996-2023 S&P GSCI Industrial Metals SPGSIN Index 1996-2023 S&P GSCI Agriculture & Livestock SPGSAL Index 1996-2023 WTI Oil—Front-month Futures Contract CL1 Comdty 1996-2023 Brent Oil—Front-month Futures Contract CO1 Comdty 1996-2023 Gold—Gold/USD Dollar Exchange Rate XAU Curncy 1996-2023 Silver—Silver/USD Dollar Exchange Rate XAG Curncy 1996-2023 Implied Interest Rate Volatility Indexes Merrill Lynch Option Volatility Estimate (MOVE) MOVE Index 1996-2023 CBOE/CBOT 10-year U.S. Treasury Note Volatility (TYVIX) TYVIX Index 2003-2020 Notes: ThistableshowsthedailyassetpricesconsideredasoutcomevariablesinTable5andTableC1. Thedatais from Bloomberg. For each series, we report sample period (Sample) and Bloomberg identifier (Ticker). Table B6: Compositions of Commodity Indexes Energy Industrial Metals Precious Metals Agriculture & Livestock Commodity Weight Commodity Weight Commodity Weight Commodity Weight WTI Crude Oil 20.34% Aluminum 4.18% Gold 5.33% Chicago Wheat 3.64% Heating Oil 3.50% Copper 5.80% Silver 0.64% Kansas Wheat 1.40% RBOB Gasoline 4.34% Nickel 1.00% Corn 6.54% Brent Crude Oil 17.19% Lead 0.66% Soybeans 4.64% Gasoil 4.78% Zinc 1.08% Coffee 0.83% Natural Gas 3.33% Sugar 1.81% Cocoa 0.36% Cotton 1.26% Lean Hogs 2.36% Live Cattle 3.76% Feeder Cattle 1.25% Contribution 53.48% 12.72% 5.97% 27.85% to Total Notes: This table shows the underlying commodity prices and corresponding weights for each of the S&P GS sector commodity indexes, as well as their contributions to the total index. 60

B.5 Data from other Papers (cid:136) Adrian, Crump, and Moench (2013): https://www.newyorkfed.org/research/data_ind icators/term-premia-tabs#/overview (cid:136) Aruoba and Drechsel (2022): privately shared (cid:136) Bauer, Lakdawala, and Mueller (2022): https://www.michaeldbauer.com/files/mpu.csv (cid:136) Bu, Rogers, and Wu (2021): https://ars.els-cdn.com/content/image/1-s2.0-S030439 3220301276-mmc1.csv (cid:136) Bundick, Herriford, and Smith (2024): privately shared (cid:136) Du, Im, and Schreger (2018): https://sites.google.com/view/jschreger/CIP?authus er=0 (cid:136) d’Amico, Kim, and Wei (2018): https://www.federalreserve.gov/econres/notes/fed s-notes/DKW_updates.csv (cid:136) Gu¨rkaynak, Kısacıko˘glu, and Wright (2020): https://www.openicpsr.org/openicpsr/pr oject/119697/version/V1/view (cid:136) Gu¨rkaynak, Sack, and Wright (2007): https://www.federalreserve.gov/pubs/feds/200 6/200628/200628abs.html (cid:136) Gu¨rkaynak, Sack, and Wright (2010): https://www.federalreserve.gov/data/tips-yie ld-curve-and-inflation-compensation.htm (cid:136) Jarocin´ski and Karadi (2020): https://www.aeaweb.org/journals/dataset?id=10.1257 /mac.20180090 (cid:136) Kroencke, Schmeling, and Schrimpf (2021): https://ars.els-cdn.com/content/image/1 -s2.0-S0304393221000258-mmc2.xls (cid:136) Lewis (2023): https://docs.google.com/spreadsheets/d/1l21TwrQpTY5cuqWH92oG-OQH QKpQt9Lm/edit#gid=227445324 (cid:136) Martin (2017): Updated data from Knox and Vissing-Jorgensen (2022) (privately shared) (cid:136) Nakamura and Steinsson (2018): https://dataverse.harvard.edu/dataset.xhtml?pers istentId=doi:10.7910/DVN/HZOXKN (cid:136) Romer and Romer’s (2004): Updated data from Aruoba and Drechsel (2022) (privately shared) (cid:136) Swanson (2021): https://sites.socsci.uci.edu/~swanson2/papers/pre-and-post-ZLB -factors-extended.xlsx 61

B.6 Textual Analysis We download the texts of the FOMC statements and press conferences directly from the Federal Reserve website.18 We do a standard cleaning of the documents, where we remove headers, footers, and page numbers. For the press conference, we eliminate sentences that convey no relevant information such as the chair’s initial greeting or its transitioning sentence to the Q&A. We have 219 FOMC announcements in total. 23 of these come without a statement which, except for two during the Great Recession, are all before May 1999 when statements were not a regular part of the FOMC. We have 63 announcements with press conferences. They were introduced in 2012 and became a regular part of each meeting in 2019. Press conferences include both an initial statement and subsequent Q&A which we treat as separate documents. Overall, a given announcement t has between zero and three documents (statement, press conference statement, and press conference Q&A) associated with it. Let q be the set of terms of interest. The term frequency-inverse document frequency (tf-idf) of q in document d is then given by (cid:18) (cid:19) Q (q) 1+D d tf-idf = × log +1 , d,q Q 1+D(q) d (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) termfrequencyofq ind inversedocumentfrequencyofq where Q (q) is the number of times terms in set q appear in document d, Q is the total number d d of terms in document d, D(q) is the number of documents that contain terms in q, and D is the total number of documents in the sample. Based on tf-idf , we can construct the announcement series used in our analysis. Specifically, d,q we have for statements tf-idfs = 1(d ∈ t∩d ∈ D ) tf-idf , t,q s d,q for press conference statements tf-idfps = 1(d ∈ t∩d ∈ D ) tf-idf , t,q ps d,q and for press conference Q&As tf-idfpq = 1(d ∈ t∩d ∈ D ) tf-idf . t,q pq d,q NotethatD ,D ,andD denotethesubsetsofdocumentswhicharestatements,pressconference s ps pq statements, and press conference Q&As, respectively. 18https://www.federalreserve.gov/monetarypolicy/fomccalendars.htm (accessed on March 30, 2024). 62

C Additional Results C.1 Effects on Yields and Inflation Compensation We study the effects of our Fed non-yield shock on various interest rates and inflation compensations. Inparticular,welookattheeffectson2-daychangesaroundFOMCannouncements. Wefirst show in Table C1 that our shock has no discernible effects on nominal yields as well as nominal forward rates. We then move to inflation compensations measured from Treasury Inflation-Protected Securities (TIPS) and inflation swap rates. Table C1: Effects of Fed Non-Yield Shock on U.S. Yields Change (bp) 1Month 3Month 6Month 1Year 2Year 5Year 10Year 20Year 30Year Yield—Bloomberg Fednon-yieldshock -0.48 -0.89 -0.54 -0.09 -0.58 -0.65 0.06 0.44 0.67 (0.66) (0.82) (0.62) (0.53) (0.57) (0.80) (0.86) (1.62) (0.80) R2 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.01 Observations 176 219 219 219 219 219 219 23 219 Yield—GSW 2007 Fednon-yieldshock -0.06 -0.65 -0.67 0.16 0.62 0.79 (0.51) (0.60) (0.79) (0.89) (0.81) (0.70) R2 0.00 0.01 0.00 0.00 0.00 0.01 Observations 219 219 219 219 219 219 Instantaneous Forward Rate—GSW 2007 Fednon-yieldshock -1.31 0.08 1.25 1.08 (0.91) (1.11) (1.12) (0.82) R2 0.01 0.00 0.01 0.01 Observations 219 219 219 219 Notes: This table presents estimates of δ from specification (18), where the left-hand side variables are now 2day changes in U.S. government yields of different maturities. The top panel shows results for yields coming from Bloomberg, while the bottom two panels displays estimates for yields and instantaneous forward rates taken from Gu¨rkaynak, Sack, and Wright (2007). We winsorize the top and bottom 1 percent of each left-hand variable. Heteroskedasticity-consistent standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. In Table C2, we show that these generally increase following our non-yield shock. As nominal yields are unaffected, TIPS yields need to decrease which is also shown in the table. However, it is not clear that the non-yield shock leads necessarily to increases in inflation expectations. As shown by d’Amico, Kim, and Wei (2018), TIPS yield and inflation compensation (IC) can be decomposed as follows TIPS yield = real yield+TIPS liquidity premium TIPS IC = expected inflation+inflation risk premium−TIPS liquidity premium. Basedonano-arbitragetermstructuremodel,d’Amico,Kim,andWei(2018)alsoprovideestimates 63

of each term in the decomposition. Table C2 shows the results for these terms. Based on d’Amico, Kim, and Wei (2018)’s estimates, the non-yield shock affects TIPS inflation compensations mostly through TIPS liquidity premia, rather than through expected inflation or inflation risk premia. However, this liquidity premium should not be able to explain why inflation swap rates are also increasing. Hence, the evidence based on US data is mixed as to whether our non-yield shock is affecting inflation expectations. Table C2: Effects of Fed Non-Yield Shock on U.S. Inflation Compensation & Real Yields Change (bp) 1 Year 2 Year 5 Year 10 Year 20 Year TIPS Inflation Compensation 3.30** 1.73** 1.30** 0.97* (1.44) (0.70) (0.53) (0.52) Expected Inflation -0.03 0.01 (0.21) (0.18) Inflation Risk Premium -0.06 0.01 (0.11) (0.13) Liquidity Premium -1.66** -1.28*** (0.67) (0.49) TIPS Yield -4.11*** -2.68*** -1.47* -0.76 (1.48) (0.95) (0.85) (0.76) Real Yield -0.50 -0.16 (0.48) (0.58) TIPS Instantaneous Forward Rate -3.81** -0.58 -0.45 -0.51 (1.77) (1.27) (0.88) (0.77) Inflation Swap Rate 0.41 2.48*** 2.15*** 1.48** (1.26) (0.95) (0.62) (0.72) Notes: Each estimate in this table comes from a separate version of (18), where only the left-hand side variable varies. Data on TIPS inflation compensations and TIPS yields comes from the updated dataset of Gu¨rkaynak, Sack, and Wright (2010), whereas the inflation swap rates are from Bloomberg. The remaining variables are from the updated dataset of d’Amico, Kim, and Wei (2018). Since we employ 2-daychanges,wewinsorizethetopandbottom1percentofeachleft-handvariable. Heteroskedasticityconsistent standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. Abbreviations: TIPS—Treasury Inflation Protected Security. Hence, to figure out if inflation expectations are indeed a key channel of our non-yield shock, we move to international data on inflation compensations. Table C2 shows the results of this analysis. The estimates indicate that international inflation compensations are generally unaffected by our non-yield shock. Overall, we conclude that while our non-yield shock seems to have some positive effects on inflation compensation, the results indicate that the inflation channel is not an important part in understanding our non-yield shock. 64

Table C3: Effects of Fed Non-Yield Shock on International Inflation Compensations Return (bp) Inflation Swap Rate Breakeven Inflation Rate EUR GBR CAN DEU JPN GBR AUS SWE 2-Year Fed non-yield shock 0.13 -0.37 1.83* 0.23 0.13 0.08 -0.29 (0.60) (0.66) (1.09) (0.38) (0.11) (0.13) (0.31) R2 0.00 0.00 0.05 0.00 0.00 0.00 0.00 Observations 158 157 95 85 216 158 168 5-Year Fed non-yield shock 0.13 0.07 0.62 0.68 0.20 -0.12 0.26 0.21 (0.36) (0.41) (0.51) (0.41) (0.21) (0.52) (0.25) (0.32) R2 0.00 0.00 0.02 0.03 0.01 0.00 0.00 0.00 Observations 155 155 52 115 111 217 187 157 10-Year Fed non-yield shock 0.07 -0.26 0.99** 0.33 0.24 -0.26 -0.10 -0.10 (0.25) (0.42) (0.46) (0.35) (0.34) (0.35) (0.25) (0.36) R2 0.00 0.00 0.05 0.01 0.01 0.00 0.00 0.00 Observations 155 155 120 111 155 219 187 157 Notes: This table presents estimates of δ from specification (18), where the left-hand side variables are now 2-day log-changesininflationswaporinflationbreakevenrates. Heteroskedasticity-consistentstandarderrorsarereported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent level. We winsorize each dependent variable at the top and bottom 1 percent. C.2 Effects on Commodities In this section, we study the effects of the Fed non-yield shock on commodity prices. Similar to stocks and exchange rates, previous papers have documented the response of commodity prices to monetary policy shocks (e.g., Frankel, 2008). To investigate the response to our shock, we estimate specification (18) where ∆dx is the 2-day log-change in the commodity index or price of interest t around the FOMC announcement at time t. In our analysis, we focus on S&P GS commodity indexes to cover the full range of commodities. Appendix Table B6 provides an overview of the commodities underlying each index. We also report separately results for three popular commodity prices: oil, gold, and silver. Figure C1 illustrates the estimation results. First and foremost, the Fed non-yield shock leads to significant increases in commodities prices on average and across all classes. Further, the effects are strongest for energy and metals. 65

Figure C1: Effects of Fed Non-yield Shock on Commodity Prices 180 150 120 90 60 30 0 stnioP sisaB Prec. Metals Brent WTI Energy Ind. Metals Total Agriculture & Livestock S&P GS Commodity Indexes Oil Gold Silver Notes: Thisfigureshowstheresponseofdifferentcommodityindexesandpricestothenon-yieldshock. Commodity price changes are expressed in basis points. Each bars show the effect on a given commodity price or index, i.e., the estimateofcoefficientδ ofequation(18)withthe2-daylog-changeofthecommoditypriceorindexofinterestonthe left-hand side. The black error bands depict 95 percent confidence intervals, where standard errors are clustered by announcement. Wewinsorizeeachdependentvariableatthetopandbottom1percent. Moredetailsoncommodity prices are provided in Appendix Table B5 and B6. 66

C.3 Miscellaneous Figures and Tables Figure C2: Distributions of Asset Returns around FOMC and Non-FOMC Days Raw 2.5 2 1.5 1 0.5 0 1 W 4 indow (ho 7 u 1 rs 0 ) 13 -3 -2 -1 Retur 0 n (%) 1 2 3 005 P&S )%( ytisneD FOMC Days Non-FOMC Days Residualized with Yields Raw 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 1 1 4 4 7 7 10 13 -3 -2 -1 0 1 2 3 10 13 -3 -2 -1 0 1 2 3 Return (%) Return (%) 5 4 3 2 1 0 1 W 4 indow (ho 7 u 1 rs 0 ) 13 -1.5 -1 -0.5 Ret 0 urn (% 0 ) .5 1 1.5 ralloD/oruE )%( ytisneD 5 5 4 4 3 3 2 2 1 1 0 0 1 1 4 4 7 7 10 13 -1.5 -1 -0.5 0 0.5 1 1.5 10 13 -1.5 -1 -0.5 0 0.5 1 1.5 Return (%) Return (%) Notes: This figure shows return distributions around times of FOMC announcements and around comparable times onnon-announcementtradingdays. Eachpaneldisplaysdistributionsfordifferentwindowlengthsoverwhichreturns areconstructed,whereeachwindowbegins10minutespriortothereferencetimeandendsstartingat20minutesup to13hoursafterthereferencetime. Foreachwindowsize,thekerneldensityestimatesintegratetoone. Thesample ranges from January 1996 to April 2023. Panels in the top row present results for the Euro-Dollar exchange rate, while panels in the bottom row for the front-month S&P 500 E-mini futures contracts. Raw refers to the returns, while Residualized with Yields refers to returns which orthogonalized by the entire yield curve. Details are provided in Section 2. 67

D Framework Appendix In this appendix we provide details on the argument in Section 4. We begin with stating the assumptions on the data generating process. We then review the assumptions on the estimation procedure before implementing it on the data from the data generating process assumed here. Note that the estimation in Section 4 and this appendix is implemented in the population, that is, the argument abstracts from sampling error. D.1 Data generating process Suppose the data over narrow event windows is generated by the model (9), where (cid:136) sy is a k×1 vector of yield shocks. t (cid:136) ∆p is a n×1 vector of stock prices and exchange rates. t (cid:136) z is a r×1 vector of structural monetary policy shocks satisfying E[z ] = 0 and V [z ] = I t t t r for t ∈ F, where I is the r×r identity matrix, and z = 0 for t ∈ NF. r t (cid:136) ε is a n × 1 vector of non-monetary drivers of stock prices and exchange rates satisfying t E[ε ] = 0 and E[ε ε′] = Σ for all t. We additionally assume that E[z ε′] = 0 . t t t ε t t k×n (cid:136) A is a k×r matrix capturing the relationship between yield shocks sy and structural shocks y t z . We assume that there are weakly fewer yield shocks than structural monetary policy t shocks k ≤ r, and that the rank of A is k. y (cid:136) A is a n×r matrix capturing how stock price and exchange rate changes in ∆p depend on p t the structural shocks z . For some results below we assume that n ≥ r and that the rank of t A is r, although these two conditions are not generally necessary (the Jarocin´ski and Karadi p (2020) special case below has 1 = n < r = 2). D.2 Assumptions on estimation framework The assumptions on the estimation framework are: (cid:136) The empirical model (10) is correctly specified. (cid:136) No monetary policy shocks exist during non-event windows: sy = 0 and d = 0 for t ∈ NF. t t (cid:136) Orthogonality with non-monetary shocks: E[syε′] = 0 and E[snyε′] = 0. t t t t (cid:104) (cid:105) (cid:136) Orthogonality between yield and non-yield shocks: E sy(sny) ′ = 0. t t (cid:136) Normalization: V [sny] = I . t r−k Relative to the estimation framework described in Section 2, the framework here principally allows for more than one non-yield shock. The effects of the non-yield shock(s) are captured by Γ. 68

D.3 Estimation and Proofs We now apply our estimation procedure to the data generating process (9). The estimating equation is (10), where sny is unobserved. Letting u := d Γsny +ε , we can t t t t t write ∆p = βsy +u . (D1) t t t Then (cid:104) (cid:105) (cid:104) (cid:105) (cid:104) (cid:105) (cid:104) (cid:105) E u (sy) ′ = E (d Γsny +ε )(sy) ′ = d ΓE sny(sy) ′ +E ε (sy) ′ = 0, t t t t t t t t t t t (cid:104) (cid:105) where the last equality uses the assumptions that E[syε′] = 0 and E sy(sny) ′ = 0 imposed by t t t t (cid:104) (cid:105) the estimation procedure. Note that imposing the assumption E sy(sny) ′ = 0 here implies that t t the non-yield shocks will be constructed to be orthogonal to the yield shocks. Given the orthogonality between u and sy, β can be estimated by OLS from equation (D1) for t t t ∈ F in the population. This gives (cid:104) (cid:105)(cid:16) (cid:104) (cid:105)(cid:17)−1 β = E ∆p (sy) ′ E sy(sy) ′ t t t t = E (cid:2) (A z +ε )(A z )′(cid:3)(cid:0) E (cid:2) A z (A z )′(cid:3)(cid:1)−1 p t t y t y t y t = (cid:0) A E (cid:2) z z′(cid:3) A′ +E (cid:2) ε z′(cid:3) A′(cid:1)(cid:0) A E (cid:2) z z′(cid:3) A′(cid:1)−1 p t t y t t y y t t y = A A′ (cid:0) A A′(cid:1)−1 , p y y y which is equation (11) in the text. Note that the second equality uses equation (9) and the fourth equality uses the facts that V [z ] = I and E[z ε′] = 0. The matrix A A′ is invertible because the t r t t y y rank of A is k. y Now the regression error is u = ∆p −βsy t t t = A z +ε −A A′ (cid:0) A A′(cid:1)−1 A z p t t p y y y y t (cid:16) (cid:17) = A I −A′ (cid:0) A A′(cid:1)−1 A z +ε . p r y y y y t t Hence, to be consistent with equation (10), the non-yield shock must satisfy (cid:16) (cid:17) Γsny := A I −A′ (cid:0) A A′(cid:1)−1 A z . t p r y y y y t (cid:16) (cid:17) This is equation (12) in the text. Note that the annihilator matrix I −A′ (cid:0) A A′(cid:1)−1 A reflects r y y y y the orthogonality between sny and sy. t t We can then rewrite the estimating equation as ∆p = βsy +u t t t (cid:16) (cid:17) = A A′ (cid:0) A A′(cid:1)−1 A z +A I −A′ (cid:0) A A′(cid:1)−1 A z +ε . p y y y y t p r y y y y t t 69

This is equation (13) in the text. This equation shows that the estimation procedure decomposes the effect of the structural shocks z on ∆p into a component that passes through the yield curve, t t (cid:16) (cid:17) A A′ (cid:0) A A′(cid:1)−1 A ,andacomponentthatisorthogonaltotheyieldcurve,A I −A′ (cid:0) A A′(cid:1)−1 A . p y y y y p r y y y y Proposition 1. Suppose n ≥ r ≥ k, A is of full row rank, and A is of full column rank. Then y p the number of non-yield shocks equals the number of structural monetary policy shocks r minus the number of yield shocks k. Proof. The projection matrix A′ (cid:0) A A′(cid:1)−1 A maps any structural shock z ∈ Rr into the space y y y y t spanned by the columns of A′, which is a k-dimensional subspace of Rr. Similarly, the projection y matrix I −A′ (cid:0) A A′(cid:1)−1 A maps any structural shock z ∈ Rr into the orthogonal complement r y y y y t of the space spanned by the columns of A′, which is a (r−k)-dimensional subspace of Rr (see y Davidson and MacKinnon, 2004, p. 61). If n ≥ r and A is of full column rank, then the matrix p (cid:16) (cid:17) A I −A′ (cid:0) A A′(cid:1)−1 A maps the structural shock z ∈ Rr into a (r−k)-dimensional subspace p r y y y y t of Rn. Hence, there must be r−k non-yield shocks. Taking the variance of equation (12) and imposing the normalizations V [sny] = I as well as t r−k V [z ] = I , we obtain t k (cid:16) (cid:17) ΓΓ′ = A I −A′ (cid:0) A A′(cid:1)−1 A A′. p r y y y y p ThisexpressiondefinesΓinthepopulation. Notethatthesolutionisnotunique. Foranyorthogonal matrix U, if Γ solves the above equation, then Γ˜ = ΓU will also solve the above equation. In the case of one non-yield shock, this property implies that Γ and sny are both pinned down up to a t sign flip. In what follows, we will mostly constrain ourselves to instances in which either r = k so that no non-yield shock exists, or to the case where r −k = 1, so that there is one non-yield shock. In the case of one non-yield shock, we normalize the first coefficient of Γ to be positive (as in Gu¨rkaynak, Kısacıko˘glu, and Wright, 2020). It also follows that the rank of Γ must equal r − k. Since for any matrix A, rank(A) = (cid:16) (cid:17) rank(AA′), and Proposition 1 implies that the rank of A I −A′ (cid:0) A A′(cid:1)−1 A is r − k, the p r y y y y (cid:16) (cid:17) rank of A I −A′ (cid:0) A A′(cid:1)−1 A A′ must also be r−k. It follows then that ΓΓ′ must also have p r y y y y p rank r−k and so must Γ. We will use the property that Γ has full column rank below. Asinthedata,Γcanbeestimatedfromtheexcessvarianceonannouncementdays. Specifically, the variance of u on announcement days is t (cid:104) (cid:16) (cid:17) (cid:105) V [u ] = V A I −A′ (cid:0) A A′(cid:1)−1 A z +ε F t p r y y y y t t (cid:16) (cid:17) (cid:16) (cid:17) = A I −A′ (cid:0) A A′(cid:1)−1 A V [z ] I −A′ (cid:0) A A′(cid:1)−1 A A′ +V [ε ] p r y y y y t r y y y y p t (cid:16) (cid:17) = A I −A′ (cid:0) A A′(cid:1)−1 A A′ +V [ε ]. p r y y y y p t On non-announcement days we have V [∆p ] = V [ε ]. NF t t 70

Hence, (cid:16) (cid:17) V [u ]−V [∆p ] = A I −A′ (cid:0) A A′(cid:1)−1 A A′ = ΓΓ′, F t NF t p r y y y y p so Γ can be estimated from the observables u for t ∈ F and ∆p for t ∈ NF. t t Note that Section 4 and this Appendix study the properties of our estimation procedure under theassumptionthattheempiricalmodeliscorrectlyspecified. Thereisnoformofmisspecification. We briefly verify that all assumptions imposed by the estimation procedure hold. Specifically, 1. Given that sy = A z and how β, Γ, and sny are constructed, the empirical model (10) is t y t t correctly specified. 2. There are no monetary policy shocks during the non-event window, since sy = A z = 0 for t y t t ∈ NF and d = 0 for t ∈ NF by assumption. t 3. E[syε′] = 0 follows since t t E (cid:2) syε′(cid:3) = E (cid:2) A z ε′(cid:3) = A E (cid:2) z ε′(cid:3) = 0 . t t y t t y t t k×n Further, E[snyε′] = 0 whenever the non-yield shock exists. To see this, suppose that WLOG t t E[snyε′] = Φ for some matrix Φ ∈ R . Then pre-multiplying by Γ and using equation t t (r−k)×n (12) gives (cid:104) (cid:16) (cid:17) (cid:105) (cid:16) (cid:17) ΓΦ = E A I −A′ (cid:0) A A′(cid:1)−1 A z ε′ = A I −A′ (cid:0) A A′(cid:1)−1 A E (cid:2) z ε′(cid:3) = 0 . p y y y y t t p y y y y t t n×n Now, for each column m = 1,...,n of the matrix Φ we have r−k (cid:88) γ ϕ = 0 , l lm n×1 l=1 where γ is the l’th column of Γ and ϕ is the (l,m)-th element of Φ. Since the columns of l lm Γ are linearly independent (see above), the only solution is ϕ = 0 for all l = 1,...,r−k and lm all m = 1,...,n. Hence, E[snyε′] = 0 . t t (r−k)×n (cid:104) (cid:105) 4. Lastly, the non-yield shock is constructed to satisfy E sy(sny) ′ = 0 and V [sny] = I . t t t r−k Before turning to the proof of Proposition 2, we introduce what we mean by identifiability and prove one lemma. Definition 1 (Identifiability). We say that k structural monetary policy shocks are identifiable from the yield curve alone if there exists a partition (cid:32) (cid:33) z1 z = t t z2 t where z1 is a k ×1 vector shocks and z2is a scalar, and an invertible matrix A satisfying A = t t y 71

(cid:16) (cid:17) A B such that z1 = A−1sy. t t Hence, for the observable yield shocks sy and an invertible matrix A, it is possible to solve for the t k structural shocks in vector z1. t Lemma 1. Consider the partition of the k×(k+1) matrix A into a k×k matrix A and a k×1 y (cid:16) (cid:17) vector B such that A = A B . Then y (cid:32) (cid:33) I −A′ (cid:0) A A′(cid:1)−1 A = 1 A−1BB′(A′)−1 −A−1B . r y y y y 1+B′(AA′)−1B −B′(A′)−1 1 Proof. The proof follows from direct computation: (cid:34) (cid:35)(cid:32) (cid:34) (cid:35)(cid:33)−1 I −A′ (cid:0) A A′(cid:1)−1 A = I − A′ (cid:104) A B (cid:105) A′ (cid:104) A B (cid:105) r y y y y r B′ B′ (cid:34) (cid:35) = I − A′ (cid:0) AA′+BB′(cid:1)−1 (cid:104) A B (cid:105) . r B′ Next apply the Sherman-Morrison formula to obtain (cid:0) AA′+BB′(cid:1)−1 = (cid:0) AA′(cid:1)−1 − 1 (cid:0) AA′(cid:1)−1 BB′(cid:0) AA′(cid:1)−1 . 1+B′(AA′)−1B Then I −A′ (cid:0) A A′(cid:1)−1A r y y y y =I − (cid:32) A′ (cid:33)(cid:18) (cid:0) AA′(cid:1)−1− 1 (cid:0) AA′(cid:1)−1BB′(cid:0) AA′(cid:1)−1 (cid:19)(cid:16) A B (cid:17) r B′ 1+B′(AA′)−1B  (cid:16) (cid:17)  A′ (AA′)−1− 1 (AA′)−1BB′(AA′)−1 (cid:16) (cid:17) =I r − B′ (cid:16) (AA′)−1− 1+B′(A 1 A′)−1B (AA′)−1BB′(AA′)−1 (cid:17)  A B 1+B′(AA′)−1B  (cid:16) (cid:17) (cid:16) (cid:17)  A′ (AA′)−1− 1 (AA′)−1BB′(AA′)−1 A A′ (AA′)−1− 1 (AA′)−1BB′(AA′)−1 B =I r − B′ (cid:16) (AA′)−1− 1+B′(A 1 A′)−1B (AA′)−1BB′(AA′)−1 (cid:17) A B′ (cid:16) (AA′)−1− 1+B′(A 1 A′)−1B (AA′)−1BB′(AA′)−1 (cid:17) B  1+B′(AA′)−1B 1+B′(AA′)−1B  (cid:16) I − 1 A−1BB′(A′)−1 (cid:17) (cid:16) A−1B− 1 A−1BB′(A′)−1A−1B (cid:17)  k 1+B′(AA′)−1B 1+B′(AA′)−1B =I r − (cid:16) B′(A′)−1− 1 B′(A′)−1(A)−1BB′(A′)−1 (cid:17) B′(AA′)−1B  1+B′(AA′)−1B 1+B′(AA′)−1B  1 A−1BB′(A′)−1 − (cid:16) A−1B− 1 A−1BB′(A′)−1A−1B (cid:17)  1+B′(AA′)−1B 1+B′(AA′)−1B = − (cid:16) B′(A′)−1− 1 B′(A′)−1(A)−1BB′(A′)−1 (cid:17) 1− B′(AA′)−1B  1+B′(AA′)−1B 1+B′(AA′)−1B  1 A−1BB′(A′)−1 −A−1B (cid:18) 1− B′(A′)−1A−1B (cid:19)   1+B′(AA′)−1B 1+B′(AA′)−1B  =  − (cid:18) 1− B′(A′)−1(A)−1B (cid:19) B′(A′)−1 (cid:18) 1− B′(AA′)−1B (cid:19)   1+B′(AA′)−1B 1+B′(AA′)−1B 72

(cid:32) (cid:33) 1 A−1BB′(A′)−1 −A−1B = . 1+B′(AA′)−1B −B′(A′)−1 1 Proposition 2. Suppose that r = k +1, A is of full row rank, and A is of full column rank. y p Then the following statements are equivalent: 1. There exists a structural shock that does not affect the yield curve. 2. k structural monetary policy shocks are identifiable from the yield curve alone. 3. There is one non-yield shock and it has a structural interpretation. Proof. We begin with showing that 1. implies 2. Since there exists a structural shock that does not affect the yield curve, there exists a partition of z , t (cid:32) (cid:33) z1 z = t , t z2 t where z1 is k×1 and z2 is is a scalar such that z2 has no effects on the yields. We can then write t t t (cid:16) (cid:17) A = A 0 . y k×1 Since A is of full row rank, the k × k matrix A must be invertible. It follows from the data y generating process (9) that (cid:32) (cid:33) (cid:104) (cid:105) z1 sy = A z = A 0 t = Az1. t y t z2 t t Since A is invertible, the k structural shocks in z1 are identifiable from the yield curve alone: t z1 = A−1sy. t t We next show that 2. implies 1. The data generating process implies that sy = A z . WLOG partition t y t (cid:32) (cid:33) z1 z = t , t z2 t where z1 is a k×1 vector of identifiable shocks and z2is a scalar. Further, partition t t (cid:18) (cid:19) A B A y = (cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125) . k×k k×1 Then (cid:32) (cid:33) (cid:16) (cid:17) z1 sy = A B t = Az1+Bz2. t z2 t t t 73

Since by assumption k shocks are identifiable from the yield curve, we have z1 = A−1sy. Plugging t t this into the above equation gives sy = AA−1sy +Bz2, t t t so that Bz2 = 0 for all z2. Hence, it must be that B = 0. t t We next show that 1. implies 3. Since there exists a structural shock that does not affect the yield curve, there exists a partition of z , t (cid:32) (cid:33) z1 z = t , t z2 t where z1 is k×1 and z2 is is a scalar such that z2 has no effects on the yields. We can then write t t t (cid:16) (cid:17) A = A 0 . y k×1 Since A is of full row rank, the k×k matrix A must be invertible. y Plugging A into equation (12) gives y (cid:16) (cid:17) Γsny = A I −A′ (cid:0) A A′(cid:1)−1 A z t p r y y y y t   (cid:32) (cid:33)(cid:32) (cid:32) (cid:33)(cid:33)−1 A′ (cid:16) (cid:17) A′ (cid:16) (cid:17) = A pI r − A 0 A 0 z t 0 0 (cid:32) (cid:32) (cid:33) (cid:33) = A I − A′ (cid:0) AA′(cid:1)−1 (cid:16) A 0 (cid:17) z p r t 0 (cid:32) (cid:32) (cid:33)(cid:33)(cid:32) (cid:33) A′(AA′)−1A 0 z1 = A I − t p r 0 0 z2 t (cid:32) (cid:32) (cid:33)(cid:33)(cid:32) (cid:33) A′(A′)−1A−1A 0 z1 = A I − t p r 0 0 z2 t (cid:32) (cid:32) (cid:33)(cid:33)(cid:32) (cid:33) I 0 z1 = A I − k t p r 0 0 z2 t (cid:32) (cid:33)(cid:32) (cid:33) 0 0 z1 = A t p 0 1 z2 t (cid:32) (cid:33) 0 = A . p z2 t Further, partitioning A into a n×k matrix C and a n×1 vector D gives p (cid:32) (cid:33) (cid:16) (cid:17) 0 Γsny = C D , t z2 t 74

and hence Γsny = Dz2. t t Taking variances on both sides gives and using the normalizations that V [sny] = 1 and that t V (cid:2) z2(cid:3) = 1, we obtain t ΓΓ′ = DD′. Hence, Γ = ±D and sny = ±z2. t t Lastly, we show that 3. implies 1. WLOG partition the structural shocks z into a k×1 vector z1 and a scalar z2 such that t t t (cid:32) (cid:33) z1 z = t t z2 t and sny = z2. (The case in which sny = −z2 is analogous.) Then equation (12) implies that t t t t (cid:32) (cid:33) Γz2 = A (cid:16) I −A′ (cid:0) A A′(cid:1)−1 A (cid:17) z t 1 . t p r y y y y z2 t Since this condition holds for all z1 and z2, it follows that t t (cid:32) (cid:33) A (cid:16) I −A′ (cid:0) A A′(cid:1)−1 A (cid:17) z t 1 = 0 (D2) p r y y y y 0 n×1 for all z1. t (cid:16) (cid:17) (cid:16) (cid:17) Next, partition A = A B , where A is k×k and B is k×1, and A = C D , where y p C is n×k and D is n×1. Then Lemma 1 implies that (cid:32) (cid:33) A (cid:16) I −A′ (cid:0) A A′(cid:1)−1 A (cid:17) = 1 (cid:16) C D (cid:17) A−1BB′(A′)−1 −A−1B p r y y y y 1+B′(AA′)−1B −B′(A′)−1 1 1 (cid:16) (cid:17) = (cid:0) CA−1B−D (cid:1) B′(A′)−1 −CA−1B+D . 1+B′(AA′)−1B Condition (D2) then becomes 1 (cid:0) CA−1B−D (cid:1) B′(cid:0) A′(cid:1)−1 z1 = 0 . 1+B′(AA′)−1B t n×1 In order for this to hold for all z1, it must be that t (cid:0) CA−1B−D (cid:1) B′(cid:0) A′(cid:1)−1 = 0 . n×k (To see this, choose z1 to be the different unit vectors.) Since A is invertible, it follows that t (cid:0) CA−1B−D (cid:1) B′ = 0 . n×k 75

Let next (cid:16) (cid:17) B′ = b b ... b 1 2 k so that (cid:0) CA−1B−D (cid:1) b = 0 l n×1 for all l = 1,...,k. Now suppose by contradiction that there is an l ∈ {1,...,k} such that b ̸= 0, l then we must have that CA−1B−D = 0 . n×1 But if this was true, then A (cid:16) I −A′ (cid:0) A A′(cid:1)−1 A (cid:17) = 1 (cid:16) (cid:0) CA−1B−D (cid:1) B′(A′)−1 −CA−1B+D (cid:17) p r y y y y 1+B′(AA′)−1B (cid:16) (cid:17) = 0 0 , n×k n×1 which,togetherwithequation(12),impliesthatthereisnonon-yieldshock. Thisisacontradiction. Hence, it must be that B = 0 . k×1 The special case of Jarocin´ski and Karadi (2020) In Jarocin´ski and Karadi’s (2020) framework, there are two structural monetary policy shocks (cid:104) (cid:105)′ z = zpure zinfo , where zpure is the pure monetary policy shock and zinfo is the information t t t t t shock. These two shocks are identified from the co-movement of one interest rate, k = 1, and the S&P 500, n = 1. The key assumptions are that a pure monetary policy shock has opposite effects on interest rates and stock prices while the information shock moves interest rates and (cid:16) (cid:17) stock prices in the same direction. Formally, these restrictions are captured as A = a b and y (cid:16) (cid:17) A = −c d for strictly positive (but unknown) constants a,b,c,d. Then the data generating p process (9) implies that (cid:32) (cid:33) (cid:16) (cid:17) zpure sy = A z = a b t = azpure+bzinfo. t y t zinfo t t t Further, (cid:16) (cid:17) Γsny = A I −A′ (cid:0) A A′(cid:1)−1 A z t p 2 y y y y t   (cid:32) (cid:33)(cid:32) (cid:32) (cid:33)(cid:33)−1 (cid:32) (cid:33) (cid:16) (cid:17) a (cid:16) (cid:17) a (cid:16) (cid:17) zpure = −c d I 2 − b a b b a b  z t info t (cid:32)(cid:32) (cid:33) (cid:32) (cid:33)(cid:33)(cid:32) (cid:33) (cid:16) (cid:17) 1 0 1 a2 ab zpure = −c d − t 0 1 a2+b2 ab b2 zinfo t (cid:32) (cid:33)(cid:32) (cid:33) (cid:16) (cid:17) 1− a2 − ab zpure = −c d a2+b2 a2+b2 t − ab 1− b2 zinfo a2+b2 a2+b2 t 76

(cid:32) (cid:33) (cid:16) (cid:17) b2 zpure− ab zinfo = −c d a2+b2 t a2+b2 t − ab zpure+ a2 zinfo a2+b2 t a2+b2 t (cid:18) b2 ab (cid:19) (cid:18) ab a2 (cid:19) = −c zpure− zinfo +d − zpure+ zinfo a2+b2 t a2+b2 t a2+b2 t a2+b2 t (cid:18) b2 ab (cid:19) (cid:18) ab a2 (cid:19) = − c +d zpure+ c +d zinfo a2+b2 a2+b2 t a2+b2 a2+b2 t cb+da (cid:16) (cid:17) = −bzpure+azinfo . a2+b2 t t Taking the variance on both sides gives (cid:20) (cid:21) cb+da (cid:16) (cid:17) V [Γsny] = V −bzpure+azinfo . t a2+b2 t t Then, using that V [sny] = V [zpure] = V (cid:2) zinfo(cid:3) = 1 and Cov (cid:2) zpure,zinfo(cid:3) = 0, we obtain t t t t t Γ2 = (cid:18) cb+da (cid:19)2 (cid:0) a2+b2(cid:1) , a2+b2 so that cb+ad Γ = ±√ . a2+b2 Note that if c = d = 0, then Γ = 0, which is why we ruled out this case by assumption. Lastly, plugging back in gives 1 (cid:16) (cid:17) sny = ±√ −bzpure+azinfo . t a2+b2 t t 77