Income Shocks and Their Transmission into Consumption

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Income Shocks and Their Transmission into Consumption Edmund Crawley and Alexandros Theloudis 2024-038 Please cite this paper as: Crawley, Edmund, and Alexandros Theloudis (2024). “Income Shocks and Their Transmission into Consumption,” Finance and Economics Discussion Series 2024-038. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.038. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Income Shocks ∗ and Their Transmission into Consumption Edmund Crawley Alexandros Theloudis May 29, 2024 Measuring how household consumption responds to income shocks is important for understanding how families cope with adverse events, for designing government insurance or other income support policies, and for understanding the transmission of business cycles and monetary policy. It is also important for evaluating the effects of fiscal or labor market reforms on consumer welfare and for examining the way these reforms may affect the macroeconomy given that consumption is a large share of gross domestic product. This paper reviews the economics literature of, primarily, the past 20 years that studies the link between income shocks and consumption fluctuations at the household level. We identify three broad approaches through which researchers estimate the consumption response to income shocks: (1) structural methods in which a fully or partially specified model helps identify the consumption response to income shocks from the data, (2) natural experimentsinwhichtheconsumptionresponseofonegroupthatreceivesanincomeshockis compared with another group that does not, and (3) elicitation surveys in which consumers are asked how they expect to react to various hypothetical events. None of these approaches are exclusive to a single field within economics; studies that use any of these methods are ordinarily classified, depending on their specific focus, in macroeconomics, labor economics, or public finance—to name only a few fields. Our aim in this short paper is to survey this increasingly busy literature and provide an accessible summary of the various estimates of the consumption response to income shocks. We concentrate on the similarities and differences between the various studies, in particular with respect to the method, data, consumption notion, and type of income shock analyzed, ∗Crawley: Federal Reserve Board; email: edmund.s.crawley@frb.gov. Theloudis: Department of Econometrics&OR,TilburgUniversity; email: a.theloudis@gmail.com. Viewpointsandconclusionsstatedinthis paper are the responsibility of the authors alone and do not necessarily reflect the viewpoints of the Federal Reserve Board. This review will appear in the forthcoming “Elgar Encyclopedia of Consumption,” edited by Jos´e M. Labeaga and Jos´e Alberto Molina. 1

and thus also with respect to the type of consumption response each work identifies. Our focusisonresponsestoshocks, thatis, unanticipated incomechanges. JappelliandPistaferri (2010) review the earlier evidence on responses to anticipated income changes. The survey proceeds as follows. Section 1 introduces a brief theoretical framework that helps fix ideas for the subsequent discussion. The next sections are devoted to the different approaches to the estimation of the consumption response. Section 2 surveys the studies that employ structural methods, section 3 reviews the evidence from natural experiments, and section 4 focuses on the elicitation surveys. Section 5 concludes. Two tables summarize some of the results: Table 1 provides a summary of estimates from structural models, while Table 2 provides a summary of estimates from natural experiments and elicitation surveys. 1 Theoretical Background A household i chooses consumption C , savings A , and perhaps other behaviors captured it it+1 inL (possiblyavector)—forexample, laborsupply, tomaximizeitsexpectedlifetimeutility it T (cid:88) max E βtU (C ;L ), (1) 0 i it it {Cit,Ait+1,(Lit)}T t=0 t=0 for which we assume separability over time and geometric discounting.1 Expectations about future states of the world are captured by E . The utility function depends on consumption 0 andonL ,whichmaybeachoicevariable(forexample,endogenouslaborsupply)ortakenas it given (for example, exogenous labor supply). Utility is subscripted by i to reflect preference heterogeneity across households. We have employed a finite-horizon setting with T as its terminal period, which is natural given our focus on households.2 The problem is subject to the sequential budget constraint (1+r)A +T (Yg;L ) = C +A , (2) it i it it it it+1 which links resources over time under the assumption that consumers can borrow and save at an interest rate r.3 T maps gross income before taxes and transfers Yg to disposable i it household income Yd. Yg may be a vector; for instance, with two earners in the household, it it Yg = (Ye1,Ye2)′, where Yej indicates the earnings of member j. T may depend on choices it it it i 1Strictly, the household chooses a plan for C , A , and L contingent on future states of the world, it it+1 it including, for example, future states of income. We do not explicitly show the contingent states to ease the notation. 2The extension to infinite horizon is trivial and mostly inconsequential (Jappelli and Pistaferri, 2010). 3The extension to multiple or risky assets is also straightforward. 2

L ; for example, with endogenous labor supply, the primitive source of gross income is the it hourly wage—that is, Yg = (Yw1,Yw2)′, where Ywj indicates the wage of member j. T it it it i is subscripted by i to reflect heterogeneity in taxes, welfare benefits, contingent transfers, or external sources of income (often called external insurance). There may be a borrowing constraint in some periods such that A ≥ B , where B denotes the applicable borrowing it it it limit. Finally, there is a terminal condition on A , which reflects that households run iT+1 down their assets before death or bequeath them to their offspring. There are many alternative specifications for the process that governs income; a general formulation is Yk = fk(X ,Yk ,vk,uk,...), (3) it i it it−1 it it where k = {d,g,e ,e ,w ,w ,...} indicates the type of income considered—that is, dispos- 1 2 1 2 able, gross, and so on. fk reflects the precise process, which allows for heterogeneity across i households and depends on observables X (for example, age, time, and education), past it income Yk , and idiosyncratic shocks vk and uk to log income, such as permanent and tranit−1 it it sitory shocks. It may also depend on older income, other shocks (including aggregate ones), and past shocks, depending on the specific process that is being considered. Meghir and Pistaferri (2011) offer a review of the vast income dynamics literature and discuss popular cases.4 Solving (1) subject to (2), the borrowing constraint, and the terminal condition yields a consumptionpolicyrulewhoseexactformulationdependsonthepreferencespecification, the income process (3), the tightness of the borrowing constraint, and the market environment in which the household operates—for example, the extent to which it has access to contingent transfers or external insurance. A general formulation for the consumption rule is C = g (A ,X ,Yk ,vk,uk,...), (4) it i it it it−1 it it which allows for heterogeneity across households (reflecting, among other things, heterogeneity in U ) and generally depends on assets and the various components of income. Policy rule i (4) subsumes several popular settings in the literature, and Jappelli and Pistaferri (2010) offer specific examples. It is nonetheless non exhaustive of all possible settings. For instance, durable goods necessitate accounting for their stock and possible adjustment costs. Here we simply see (4) as a general organizational device rather than the solution to any given model. Interestliesinhowandbyhowmuchtheincomeshocksvk,uk,andsoon, affectconsumpit it 4Therearemultiplegeneralizationsof (3). Forexample,onemayallowfk todependontime(age),thus i enabling the effect of shocks to be time varying. We view (3) as a simple organizing device rather than as an exhaustive representation of every possible income process. 3

tion. To measure this consumption response, the literature focuses on two main parameters: the marginal propensity to consume (MPC), broadly defined as the derivative of consumption with respect to income—that is, dC /dYk—and the pass-through rate, broadly defined it it as the derivative of consumption growth with respect to the shock—that is, d∆lnC /dvk. it it We now turn to the three broad approaches to estimating these parameters. 2 Structural Methods Early papers. A series of influential papers in the 1980s and ‘90s test the predictions of the permanent income hypothesis and the complete-markets model, the then benchmark models in the literature. These tests are done through forming appropriate hypotheses on the link between consumption and income fluctuations that emanate from these models. While this early work does not strictly measure MPCs or pass-through rates, it provides motivating evidence for the subsequent work that explicitly measures the consumption response to shocks. Hall and Mishkin (1982), one of the first studies, investigate the sensitivity of food consumption to income using microdata from the Panel Study of Income Dynamics (PSID). Consumption varies more closely with permanent than with transitory shocks, which is an implication of the permanent income hypothesis in which households smooth consumption through self-insurance (saving and borrowing). Yet, the sensitivity of consumption to transitory income is much stronger than theory predicts, which leads to rejection of the model.5 The permanent income hypothesis postulates that inequality in consumption grows over the life cycle. This result is the motivating observation for Deaton and Paxson (1994) who, using microdata from multiple countries, confirm that the variance of consumption (and income) grows with age. While they cannot reject the permanent income hypothesis, they admit that the evidence is also consistent with other models of intertemporal choice, such as models that permit some external insurance to idiosyncratic income shocks. On the opposite end of theory, Cochrane (1991) tests for full insurance by assessing the sensitivity of consumption to income growth and to events such as illness and job loss. Under complete markets, consumers have access to contingent transfers, so household consumption growth should be unrelated to idiosyncratic events. Focusing on food consumption in the PSID, the hypothesis is rejected following long illness or job loss, but not rejected in response to short unemployment spells, thus providing early evidence for partial insurance.6 5Other early papers that test the permanent income hypothesis are Hall (1978), who does not reject it; Sargent (1978), who rejects it; and Flavin (1981), who also rejects it. They all use time-series data. 6Altug and Miller (1990) model a complete-markets environment and allow for non-separability with labor supply; using food consumption in the PSID, they cannot reject full insurance to wage fluctuations. 4

Attanasio and Davis (1996) test for full insurance across birth cohorts and education groups, accounting for consumption-work complementarity and common demographics driving consumption and wages. Under complete markets and in the absence of aggregate shocks, consumption growth should not co-move with wage growth. Drawing synthetic panels from the Consumer Expenditure Survey (CEX) and Current Population Survey (CPS), they sharply reject full insurance to low-frequency wage shifts. In a similar model, Hayashi, Altonji,andKotlikoff(1996)testforfullinsuranceacrossandwithinextendedfamilies,which they reject based on the strong correlation between wage and food consumption growth in the PSID. Using similar data in a simpler setting, Altonji, Hayashi, and Kotlikoff (1992) also reject full insurance. By contrast, Mace (1991) and, in particular, Townsend (1994), who studies village insurance in India, find mixed evidence. In sum, these early works frequently reject the benchmark models of permanent income (self-insurance) and complete-markets (full insurance). Yet, the data consistently reveal that households have access to some insurance to income shocks.7 The literature in the busy 2000s through 2010s attempts to measure the degree of insurance and identify its sources. Covariance restrictions. Blundell, Pistaferri, and Preston (2008), abbreviated as BPP, introduce the seminal methodology to measure the consumption response to income shocks. Their idea is that the extent to which consumption growth varies with income growth—the latter being driven by various income shocks—reflects the degree of transmission of those shocks into consumption.8 This idea is motivated by a consumption process that is log-linear in income shocks—namely, ∆c = ξ +ϕ vk +ψ uk, (5) it it t it t it where ∆c is consumption growth ∆lnC net of observables X .9 vk and uk are, respecit it it it it tively, apermanentandatransitoryshocktodisposablehouseholdincome(sok = dhere); ϕ t andψ aretheirtransmissionparameters; andξ isapreferenceshockunrelatedtoincome. If t it income follows the canonical permanent-transitory process—namely ∆yk = vk+∆uk, where it it it ∆yk isincomegrowth∆lnYk netofX —thetransmissionparametersareidentifiedthrough it it it Cov(∆c ,Z )/Cov(∆yk,Z )—namely, a regression of ∆c on ∆yk using appropriate instruit it it it it it 7Among the first studies to quantify the extent of consumption insurance, Gruber (1997) measures how unemployment insurance reduces the fall in consumption upon unemployment. 8Inapredecessorpaper,BlundellandPreston(1998)assumethatthattheriseinconsumptioninequality observedbyDeatonandPaxson(1994)isdrivenbypermanentbutnottransitoryshocks,towhichconsumers can fully self insure. This assumption allows them to use income and consumption moments to identify the variancesofpermanentandtransitoryincomeshocks. Attanasioetal.(2002)extendthisideatoasettingof two earners with separate income streams, while Primiceri and van Rens (2009) extend it to heterogeneous income processes. 9We use ∆ to denote the first difference operator; so ∆X =X −X . t t t−1 5

mentsZ forincome. Inthecaseofpermanentshocks, permanentincomeZ = (cid:80)1 ∆yk it τ=−1 it+τ nets ∆yk from the transitory shock at t, so its covariance with ∆c identifies ϕ . In the case it it t of transitory shocks, future income Z = ∆yk shifts ∆yk because of mean reversion of the it it+1 it transitory shock, so its covariance with ∆c identifies ψ . This strand of literature has taken it t its name from these covariance restrictions. The consumption equation (5) can be obtained through a log-linearization of the policy rule (4) in a life-cycle permanent income model with CRRA utility, a permanent-transitory income process, and slack borrowing constraints. In this case, ϕ reflects the share of cont sumption that is funded by future labor income (as opposed to assets whose value remains unchanged by the shock to income) and, depending on the measure of Yk, features of the tax it and benefits system; ψ is similar up to an annuitization factor for the household’s remaining t horizon. Yet, (5) is also consistent with other settings in which the transmission of shocks depends on their persistence—for example, environments with moral hazard (Attanasio and Pavoni, 2011) or external insurance (Blundell, Pistaferri, and Saporta-Eksten, 2016). The linear insurance equation (5) is, therefore, the reduced form of multiple environments that may differ in their insurance content. As such, ϕ and ψ are called partial insurance paramt t eters; they measure the overall pass-through of (or, on the flip side, insurance to) permanent and transitory income shocks, regardless of the precise mechanisms that give grounds for such insurance. Empirically, BPP focus on nondurable consumption and disposable household income from 1980 to 1992. While the PSID is ideal for its income data, its consumption data, including mostly food items, are limited until 1999. BPP thus impute consumption from the CEX into the PSID. They estimate ϕ = 0.64 (a 10 percent permanent income cut ret duces consumption by only 6.4 percent—households are thus partially insured to permanent shocks) and ψ = 0.05 (statistically not different from zero, so consumption is fully insured t against transitory shocks). BPP sparked multiple extensions. Blundell, Low, and Preston (2013) derive (5) under an autoregressive income process and general preferences. They assess the approximation vis-a`-vis the true policy rule and show that it performs well when liquidity constraints do not bind. Blundell, Pistaferri, and Saporta-Eksten (2016) model endogenous labor supply to measure the consumption response to wage shocks. Using income and consumption data in the PSID after 1999, they estimate ϕ = 0.32/0.19 (male/female wages) and find little t external insurance when accounting for family labor supply, assets, and the tax and benefits system.10 Theloudis (2017) extends this model to an intra-household bargaining (collective) 10Hyslop (2001) uses covariance restrictions to measure the pass-through of wage shocks to household earnings. Jessen and K¨onig (2023) use a related approach. Using hours and earnings data in the PSID over 6

setting, in which lack of commitment to lifetime marriage limits the insurance role of family labor supply. Chopra (2023) argues that the insurance role of family labor supply increases during recessions. Most of these works permit limited heterogeneity. Arellano, Blundell, and Bonhomme (2017), ABB in short, relax linearity in the income process and let shocks feature nonlinear persistence depending on their sign and size. The consumption response to shocks varies flexibly with their level and past history. Using a quantile-based estimation method and PSID data over 1999 to 2011, they measure the consumption response to log income—a type of MPC—at 0.2 to 0.4, on average (specification with household heterogeneity), though the response varies over the distribution of shocks. Although allowing for heterogeneity makes interpreting their parameter similar to a pass-through rate, they find the response is markedly different from BPP. This difference may be due to ABB’s flexible income process or the new consumption data in the PSID.11 Ghosh and Theloudis (2023) relax linearity in the consumption process by writing ∆c it as a quadratic polynomial in income shocks. This specification stems from a second-order approximation to the policy rule (4) in a model similar to BPP. The pass-through of shocks now depends on their sign and size, so this method allows small versus large, or good versus bad shocks, to have an asymmetric effect on consumption. Identification requires second, third, and fourth moments of income and second moments of consumption, in contrast to ABB who require observing their entire distribution. Using PSID data after 1999, they estimate the pass-through of the average permanent shock at 0.13; bad or large permanent shocks have a much bigger effect on consumption, and their pass-through increases with their severity.12 Alan, Browning, and Ejrnæs (2018) estimate the extent of insurance to income shocks allowing for flexible joint heterogeneity in the consumption and income processes. They use PSID data over 1968 to 2009 and find pervasive cross-household heterogeneity in the pass-through, ranging from 0.05 to 0.69. Theloudis (2021) allows for unobserved preference heterogeneity in a model with family labor supply. He explores higher-order moments of income and consumption to identify the contribution of heterogeneity to consumption inequality. A consistent empirical finding in this literature is that, on average, consumption is fully 1970 to 1997, they find that wage and taste shocks have a comparable contribution to the total variance of earnings. 11ABBisnotacovariancemethod,buttheirframeworkfallsfirmlyinthiscategorybecausetheymeasure the overall effect of shocks, as in BPP. Arellano et al. (2024) advance this method to unbalanced panels and flexible heterogeneity. They measure the consumption response to log income at 0.2 on average. 12The average pass-through is close to ABB but markedly different from BPP. The discrepancy is due to the consumption imputation in BPP and the biennial (versus annual) frequency of the modern data. 7

insuredagainsttransitoryshocks. Severalpaperschallengethisresult. Crawley(2020)argues that BPP neglect time aggregation in the PSID. Time aggregation occurs when income is observed less frequently (annually) than the underlying true data (for example, monthly payments); income growth is then mechanically positively correlated, which changes the covariance restrictions used to identify the variance of shocks and their transmission into consumption. Crawley (2020) addresses this point and estimates the pass-through of shocks at ϕ = 0.34 and ψ = 0.24 (statistically significant). t t Commault(2022)extendsthelinearinsurancemodel(5)toallowconsumptiontorespond to past transitory shocks. Several underlying structures justify this approach. The exact solution to ∆c in a life-cycle permanent income model includes higher-order terms that it dependonpastvariables(forinstance, wealth); modelswithlimitedcommitmentareanother example. Commault (2022) proposes a new estimator for ψ , one that selects as instrument t the only future ∆yk that is uncorrelated with past shocks. She estimates ψ = 0.6 (MPC it+κ+1 t at 0.32), which helps bridge the discrepancy in ψ between studies that employ covariance t restrictions and those that rely on natural experiments.13 Crawley and Kuchler (2023) address neglected time aggregation and allow consumption to depend on past transitory shocks. They estimate heterogeneous ϕ and ψ over wellt t defined subpopulations using Danish administrative data and relate their estimates to liquid wealth and other household balance-sheet characteristics. Hryshko and Manovskii (2022) identify households in the PSID with vastly different degrees of insurance. They show that the sons of families originally surveyed by the PSID in 1968 exhibit almost no insurance, while the daughters have substantial partial insurance. They do a thorough job explaining this discrepancy by differential income persistence across the two groups, which is further explained by differential attrition from the survey. Fully specified models. The studies employing covariance restrictions do not fully specify preferences,expectations,andthebudgetset,sotheytakenostanceontheexactmechanisms that give rise to partial insurance. Due to their semi-parametric nature, these works are of limited use for policy counterfactuals. Another approach is to fully specify the channels through which consumers smooth income shocks, and take such models to the data. Attanasio, Low, and S´anchez-Marcos (2005) quantify the insurance role of female labor supply (measured in terms of welfare costs of income uncertainty) through a structural 13Aswereviewsubsequently,naturalexperimentsoftenimplyalargerψ thantypicallyestimatedthrough t covariance restrictions. It is unclear, however, if survey data such as the PSID, on which the latter studies rely, reflect larger transitory shocks that are typical of experiments. Studies that allow the pass-through to depend on the size of the shock typically find that larger shocks have larger pass-through, thus also helping bridge the gap in estimates between natural experiments and covariance restrictions. 8

model of consumption and labor supply with earnings risk. Krueger and Perri (2006) show that a model with a complete set of Arrow securities but limited enforceability of contracts reproduces income and consumption inequality in the U.S., suggesting that households possess more insurance than self-insurance. Storesletten, Telmer, and Yaron (2004) show that a life-cycle permanent income model can also produce empirically consistent income and consumption inequality if the tax and benefits system and the aggregate level of wealth are taken into account. Heathcote, Storesletten, and Violante (2008) calibrate a life-cycle model of consumption and labor supply with partial insurance to wage shocks to measure the welfare costs of risk and market incompleteness. Partial insurance is fixed by the authors: Permanent shocks are uninsured, while transitory shocks are fully insured. Low, Meghir, and Pistaferri (2010) calibrate a life-cycle model of consumption, labor supply, and job mobility with income and employment risk. Self-insurance aside, the model allows for three channels of partial insurance: unemployment benefits, disability insurance, and food stamps. These earlier quantitative models measure the welfare implications of risk (or of certain insurance mechanisms) but not the degree of consumption insurance per se.14 Kaplan and Violante (2010) explicitly measure the degree of insurance in a calibrated life-cycle permanent income model with income risk. This is the model whose consumption rule BPP log-linearize. While they find almost full insurance to transitory shocks, as in BPP, they estimate ϕ = 0.78, larger than BPP’s estimate. Households in the model possess less insurance t to permanent shocks than in the data, highlighting that self-insurance, the only mechanism in the model, is not enough to generate the excess consumption smoothing we observe empirically. By contrast, Wu and Krueger (2021) calibrate a life-cycle permanent income model with endogenous labor supply and find that it matches the empirical pass-through rates of male and female wage shocks in Blundell, Pistaferri, and Saporta-Eksten (2016). Family, and mainly female, labor supply is a crucial insurance mechanism that previous studies had neglected. Guvenen and Smith (2014) estimate a life-cycle consumption–savings model with selfinsurance, external insurance, and learning over stochastic income. They use the joint dynamics of earnings and consumption in the PSID and the CEX to quantify earnings risk and the extent of insurance to it. About half of the earnings shock (including permanent and transitory elements) is smoothed. Heathcote, Storesletten, and Violante (2014) estimate a general equilibrium consumption and labor supply model with partial insurance to wage shocks. They model self-insurance, labor supply, a tax and benefits system, and external insurance. In their benchmark, they use PSID earnings and hours data alone and find that 14An exception is Low, Meghir, and Pistaferri (2010), who report the consumption response to an unemployment shock. 9

Table 1: Summary of Estimates from Structural Methods Pass-through MPC Variables Study perm. trans. perm. trans. Yk C Data it it Alan,Browning,andEjrnæs(2018) .05to.69 thy food P1999-2009 Arellano,Blundell,andBonhomme(2017)a .2−.4 -.4to.2 thy nde P1999-2009 Arellanoetal.(2024)b .33 dhy nde P2005-17 Blundell,Pistaferri,andPreston(2008) .64 .05 dhy nde P&C1980-92 Blundell,Pistaferri,andSaporta-Eksten(2016) .32 -.14 mhw nde P1999-2009 .19 -.04 fhw nde P1999-2009 Blundell,Pistaferri,andSaporta-Eksten(2018) .39 .12 mhw nde P1999-2015,and .35 .13 fhw nde C&A2003-15 BuschandLudwig(2023)c .40 .05 .38 .05 dhy n/a P1977-2012 Chopra(2023) .29r -.18r .19r mhw nde P1977-2016 .31x -.26x .12x mhw nde P1977-2016 Commault(2022) .6 .32 dhy nde P&C1980-92 Crawley(2020) .34 .24 dhy nde P&C1980-92 CrawleyandKuchler(2023) .64 .64 dhy te D2003-15 DeNardi,Fella,andPaz-Pardo(2020) .54 .12 dhy nde P1968-92,and C1980-2007 GhoshandTheloudis(2023)c .13 -.00 dhy nde P1999-2019 GuvenenandSmith(2014) .45 dhy nde P&C1968-92 Guvenen,Madera,andOzkan(2023)d .38 .11 .4 .05 dhy nde externalestims Heathcote,Storesletten,andViolante(2014) .39 mhw nde P1968-2007,and C1980-2006 HryshkoandManovskii(2022) .87sn .07sn dhy nde P&C1980-92 .46dg .12dg dhy nde P&C1980-92 JessenandKo¨nig(2023) .62 mhw n/a P1970-1997 KaplanandViolante(2010) .78 .06 dhy nde P1980-92,SCF Low,Meghir,andPistaferri(2010)e .56 mhw n/a P1988-96,SIPP Madera(2019)d .50 .10 dhy te P1999-2015 Theloudis(2021) .45 -.03 mhw nde P1999-2011 .27 -.05 fhw nde P1999-2011 WuandKrueger(2021) .35 .01 mhw nde P1999-2009 .18 .01 fhw nde P1999-2009 Legend: dg: daughters; dhy: disposable household income; fhw: female hourly wage; mhw: male hourly wage;nde: non-durableexpenditure;n/a: notapplicable;r: recession;sn: sons;te: totalexpenditure;thy: total household income; x: expansion; A: American Time Use Survey; C: Consumer Expenditure Survey; D: Danish registry data; P: Panel Study of Income Dynamics; SCF: Survey of Consumer Finances; SIPP: Survey of Income & Program Participation. aResults with unobserved household heterogeneity, figures S21 and S24. bResults with filtering and unobserved household heterogeneity. cResults for average/medium shock. dResults at age 40. ePass-through of income following an unemployment shock. 39 percent of permanent wage shocks pass through into consumption. Blundell, Pistaferri, and Saporta-Eksten (2018) present a structural life-cycle consumption–savings model with labor supply and childcare. In this setting, childcare responds endogenously to wage shocks and acts as an additional insurance mechanism. The previous studies assume income risk is Gaussian. Guvenen, Karahan, Ozkan, and Song (2021) as well as other authors establish that the distribution of income shocks exhibits substantial left skewness and excess kurtosis. This finding implies that far more people in the 10

data experience small, unimportant, or extreme negative shocks than people who experience moderate or extreme positive ones. A newer literature attempts to measure the pass-through of income shocks accounting for these higher-order features of income dynamics. De Nardi, Fella, and Paz-Pardo (2020) estimate a life-cycle model of consumption— savings with non-Gaussian income risk. They show that tail income risk increases the degree of partial insurance to permanent shocks due to stronger precautionary motives. Busch and Ludwig (2023) estimate a similar model explicitly targeting income skewness and kurtosis. They distinguish between good and bad shocks and find that the latter are worse insured than the former. In a related model, Madera (2019) studies the differential response of durable and nondurable consumption to tail earnings shocks. Durable consumption responds more strongly to tail shocks than does nondurable consumption. In a calibrated life-cycle consumption-savings model, Guvenen, Madera, and Ozkan (2023) establish that non-Gaussian earnings risk implies large welfare losses and commands a strong consumption response. They confirm that the benchmark method in BPP understates the true consumption response to such shocks, as derived analytically by Ghosh and Theloudis (2023) in the presence of tail income risk. 3 Natural Experiments At the other end of the spectrum to structural models are reduced-form studies of natural experiments. These studies usually compare one group of individuals or households that have received a shock to their income, such as a stimulus check, with a group that has not. In contrast to studies of structural models, natural experiment studies tend to focus on estimating an MPC as opposed to a pass-through parameter. This distinction is partly because the identified shock is not often proportional to income, and, indeed, the researchers rarely know what household income is. A researcher estimating MPCs using natural experiments faces two main chanllenges. The first is finding a suitable natural experiment, and the second is finding high-quality data on spending or consumption at the individual or household level. The literature has boomed recently as more and more data sources have become available to researchers. Some more recent papers are able to speak to MPC heterogeneity across household demographics and asset holdings, as well as shock size and sign. Overall, the evidence from these natural experiments points to larger consumption responses to income shocks than from the structural modeling literature. However, the range of estimates is wide and there is still no consensus in the profession. Havranek and Sokolova (2020) examine 144 studies of excess sensitivity and find evidence of publication bias that 11

suggests MPCs may be smaller than implied by a survey of this literature such as this one. Johnson, Parker, and Souleles (2006) was one of the first papers to study a convincing natural experiment. The authors look at household spending following the 2001 tax rebates in the U.S.. The distribution of these rebates, typically $300 or $600 in size, was staggered according to the second-to-last digit of recipients’ Social Security number—an effectively random assignment. Using the CEX, the authors find that households spent between 20 and 40 percent of their rebates on non-durable goods during the three-month period in which they received their rebates, with some evidence that households with low liquid wealth or low income had larger MPCs. Parker et al. (2013) use a similar research design on the 2008 stimulus checks in the U.S. and find a slightly smaller consumption response for nondurable goods but a large total response—including durables—of 50 to 90 percent in the three-month period in which the check arrived. These estimates of the spending response to U.S. stimulus policies are highly cited and often contested. For example, Misra and Surico (2014) use quantile regression techniques on thesametwoexperimentsandfindMPCestimatesthattendtobesmallerandmoreaccurate thanthosefromahomogeneousmodel. Orchard, Ramey, andWieland(2023), whilepointing to the difficulty of reconciling high MPC estimates with the macro evidence, also find lower MPCestimateswhenupdatingtheresultsfromParkeretal.(2013)withnewinsightsintothe difference-in-differences methodology used. Pointing in the other direction is evidence that households significantly underreport their spending on goods and nonhousing services in the CEX; see Sabelhaus et al. (2014). Overall, these two episodes of government fiscal stimulus have been the subject of much research, partly because the random assignment provides an excellent identification scheme and partly because the effectiveness of such stimulus policies is a question of vital importance in its own right. Shapiro and Slemrod (2009) and Sahm, Shapiro, and Slemrod (2010) study the 2008 tax rebates using questions from the University of Michigan Surveys of Consumers. They find that around 20 percent of respondents say that they will “mostly spend” the rebate when asked whether they would use the rebate to mostly spend, save, or pay off debt. The authors combine this information with other evidence to suggest an implied MPC of around one-third. Interestingly, Sahm, Shapiro, and Slemrod (2012)—who also use the Michigan survey—look at differences in consumption responses between a one-time payment relative to flow of payments from reduced tax withholding. They find that the one-time payment may be about twice as effective at inducing spending, highlighting some of the difficultly in pinning down consumer behavior. Duringthepandemic,threeEconomicImpactPayments(EIPs)weredistributedtohouseholds and their effects have been widely studied; Falcettoni and Nygaard (2021) and Gelman 12

and Stephens (2022) provide more thorough reviews of the related literature. These payments were significantly larger than previous economic stimulus payments, summing to a maximum of $11,400 for a family of four over a period of less than one year. The EIPs were also distributed more quickly than similar programs in the past; as a result, they were not staggered by Social Security number and thus identification of their effects is not as clean as was possible in 2001 and 2008. Furthermore, they were distributed at a time of highly unusual consumption behavior, both at the aggregate level and between income groups and geographies, all of which make it harder to tease out their spending effects. Nevertheless, the EIPs have proved a fruitful source of knowledge about the effectiveness of stimulus programs. Parker et al. (2022) is closely aligned with the methodology of Johnson, Parker, and Souleles (2006) and Parker et al. (2013), making use of the CEX, but, because the randomly staggered research design is not available, this newer analysis “leans heavily on comparing the spending of similar households that do and do not receive EIP and that receive EIPs of different amounts relative to their typical spending amounts”. They find that households spent their EIPs more slowly on average than the stimulus payments in 2001 and 2008. Relative to the 2001 and 2008 stimulus payment studies, by 2020 many researchers had access to transaction-level data. These data mitigate concerns about survey respondents underreporting their spending but can suffer more from sample selection bias than surveys designed by statistical agencies, such as the CEX. Karger and Rajan (2020), Misra, Singh, and Zhang (2022), and Baker et al. (2023) all make use of data from personal finance apps. These convenience samples skew somewhat towards low-income households, while the Saver- Life app studied in Baker et al. (2023) is specifically aimed at helping users save money. All these studies find relatively high MPCs within the first few weeks after the first EIP payment is received—somewhere between 0.25 and 0.5 on average. Furthermore, and in contrast to some other studies, Baker et al. (2023) find little response of durables spending. Recently, a growing interest in heterogeneous agent models in macroeconomics has increased the demand for reliable estimates of MPC heterogeneity, with a particular focus on the role of liquidity in determining MPCs. Some of the best evidence on MPC heterogeneity has come from outside of the U.S.. Fagereng, Holm, and Natvik (2021) study the spending response of Norwegian lottery winners using administrative data. They find that, in line with buffer-stock models, MPCs are negatively correlated with the winner’s stock of liquid assets and negatively correlated with the size of the lottery win. They also find that MPCs decline with age, even controlling for liquid assets. Despite these first two correlations going in the expected directions, the high level of spending in the year in which the lottery is won, especially for households with significant liquid asset holdings, is difficult to reconcile with standard models. A further benefit of this study of Norwegian lottery winners is that 13

the consumption response can be tracked over several years and is thus informative not just of the initial MPC but can also be used to inform the so-called intertemporal MPC—how households react to a shock to their income over time. The evidence suggests that spending is more front-loaded than a standard model would predict, especially given the large size of the lottery wins studied. In a study of French households, Boehm, Fize, and Jaravel (2023) conduct a randomized controlled trial to analyze the consumption response to unanticipated one-time money transfers of e300. The trial randomizes three different types of transfer via a prepaid debit card: one transfer with no restrictions, one transfer in which the unspent value expires within three weeks, and one transfer subject to a 10 percent negative interest rate every week. The authors are able to see participants main bank accounts and therefore the effect of the transfers on their overall spending. They find an overall MPC of 0.23 within the first month of the transfer. Spending is concentrated in the first few weeks following the transfer, after which there is little boost to spending. They note significant MPC heterogeneity by observable household characteristics including by liquid wealth, current and permanent income, and gender. However, similar to the Norwegian lottery study, they find that even households with high liquid asset holdings have high MPCs and—something that is not observable in the Norwegian data—that the spending response is concentrated in the short run for nondurables. Finally, MPCs are highest for the group given the card that becomes unusable after three weeks and lowest for the group given the card that has no restrictions on its use. Many other studies have found correlations between MPCs and observables, particularly a negative relation between MPCs and liquid wealth. However, observables are likely to explain only a small fraction of all MPC heterogeneity, as documented by Lewis, Melcangi, and Pilossoph (2019). A standard income shock like those above mixes both the effects of an increase in lifetime budget constraint with the effects of an increase in liquidity. Hamilton et al. (2023) analyze a policy implemented in Australia during the pandemic in which individuals were able to withdrawuptoA$20,000fromtheirgovernmentretirementaccountsthusincreasingliquidity without a change to an individual’s lifetime budget constraint. The authors find about one in six eligible people withdrew, and, furthermore, of those who did, most withdrew the maximum amount possible and spent close to half in the first four weeks. A smaller and negative liquidity shock is studied in Gelman et al. (2020). The authors look at the period during which the U.S. government shut down in 2013 and many federal workers received no (or reduced) pay that was made up to them later. Large negative spending effects—implying an MPC close to 0.5—were observed. However, much of this effect can be classified as accessing nonstandard sources of short-term liquidity, in particular 14

Table 2: Summary of Estimates from Natural Experiments and Elicitation Surveys Natural experiment study MPC Horizon C Data it Baker et al. (2023) .25−.40 1st weeks te SaverLife 2020 Boehm, Fize, and Jaravel (2023) .23 1 month te French RCT 2022 Fagereng, Holm, and Natvik (2021) .35−.71 1st year te N 1993-2015 Gelman et al. (2023) ≈1.00 Perm. shock te FA 2013-16 Johnson, Parker, and Souleles (2006) .2−.40 3 months nde C 2001 Misra and Surico (2014) .43 3 months nde C 2001 .16 3 months te C 2008 Karger and Rajan (2020) .46 2 weeks te Facteus 2020 Misra, Singh, and Zhang (2022) .29 A few days te Facteus 2020 Orchard, Ramey, and Wieland (2023) ≈ .3 3 months te C 2008 Parker et al. (2022) .05−.16 3 months nde C 2020-21 Parker et al. (2013) .50−.90 3 months te C 2008 Sahm, Shapiro, and Slemrod (2010) ≈.3 1 year te C 2008 Elicitation survey study MPC Horizon C Data it Bunn et al. (2018) .14 (pos.) .64 (neg.) 1 year te BoE survey 2011-14 Christelis et al. (2019) .20 (pos.) .24 (neg.) 1 year te Dutch survey 2015 Colarieti, Mei, and Stantcheva (2024) .16 1 quarter te Authors’ survey 2022-23 Fuster, Kaplan, and Zafar (2021) .07 (pos.) .32 (neg.) 3 months te NY Fed SCE 2016-17 Jappelli and Pistaferri (2014) .48 Unspecified te SHIW 2010 Jappelli and Pistaferri (2020) .47 Unspecified te SHIW 2016 Legend: neg.: negative; nde: non-durable expenditure; pos.: positive; te: total expenditure; BoE: Bank of England; C: Consumer Expenditure Survey; FA: Financial Aggregator; MPC: marginal propensity to consume; RCT: randomized control trial; N Norwegian registry data; SCE: Survey of Consumer Expectations; SHIW: Italian Survey of Household Income and Wealth. delaying recurring payments such as mortgage and rent payments. Most natural experiments in this literature, including all those cited thus far, have been related to transitory income shocks. Less is known from the natural experiment literature about the consumption response to permanent shocks to income. Gelman et al. (2023) use changes in gas prices as a proxy for permanent income changes and find, using transactionlevel data, that individuals reduce their spending one-for-one with a permanent change in their disposable income. Gerard and Naritomi (2021) look at displaced workers in Brazil who receive a positive transitory shock to income in the form of severance pay but face a permanent reduction in their lifetime earnings. The authors find that workers increase spending at layoff by 35 percent despite experiencing a 14 percent long-term loss. While this overview of the natural experiment literature has focused on income shocks, there is also a large literature examining the consumption response to anticipated income changes. For example, Ganong and Noel (2019) look at spending around the expiration of unemployment benefits, Hsieh (2003) and Kueng (2018) look at spending from the Alaska permanent fund, and Souleles (1999) and Gelman et al. (2022) consider spending around tax refunds. Although standard consumption theory would suggest households’ response to 15

anticipated changes should be significantly muted relative to shocks, many of these papers show a large spending change coinciding with the anticipated income change. 4 Elicitation Surveys The third method that researchers use to understand households’ responses to income shocks is to ask them directly in a survey. This method has the advantage of being relatively easy to implement without the need to find a natural experiment or get access to data on spending. The method also allows for direct comparison within a household of how its consumption would change in a variety of scenarios, such as in response to permanent versus transitory shocks, or to shocks of different size and sign. However, survey respondents may be unable to know their true behavior. Shapiro and Slemrod (1995, 2003) started this literature, asking households about their qualitative response to income changes. Jappelli and Pistaferri (2014, 2020) explore heterogeneity, particularly across cash-on-hand holding, using the Bank of Italy’s Survey of Household Income and Wealth which asks respondents for numerical MPCs. Bunn et al. (2018) and Christelis et al. (2019) both explore asymmetry in consumption responses, finding that responses to losses are larger than to gains. Fuster, Kaplan, and Zafar (2021) ask households what they would do with $500 in the Federal Reserve Bank of New York’s Survey of Consumer Expectations. This survey also asks participants about their responses to news about future income shocks and finds that even those with large responses to gains do not respond to news about future gains, although they do cut spending in response to news about future losses. Colarieti, Mei, and Stantcheva (2024) further explore the dynamic spending response to news about future income shocks by asking for spending plans over four quarters. These authors also carry out several cross-validation exercises that indicate that the answers elicited from this type of survey align with actual spending behavior, suggesting these survey methods are of high value. 5 Conclusion Wesurveytheeconomicsliteratureof,primarily,thepast20yearsthatstudieshowhousehold consumption responds to income shocks. We group the papers in this literature into three categories: papers that use structural methods, those that exploit natural experiments, and papers that rely on elicitation surveys. The evidence so far suggests that (1) consumption responds more strongly to permanent than to transitory shocks, (2) the sign and size of shocksaswellasthehorizonoverwhicheffectsarestudiedmatter,and(3)thereissubstantial 16

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