A tail of labor supply and a tale of monetary policy

Cantore, Cristiano; Mumtaz, Haroon; Ferroni, Filippo; Theophilopoulou, Angeliki Working Paper A tail of labor supply and a tale of monetary policy Quaderni - Working Paper DSE, No. 1210 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Cantore, Cristiano; Mumtaz, Haroon; Ferroni, Filippo; Theophilopoulou, Angeliki (2025) : A tail of labor supply and a tale of monetary policy, Quaderni - Working Paper DSE, No. 1210, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/8501 This Version is available at: https://hdl.handle.net/10419/331369 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ ISSN 2282-6483 A tail of labor supply and a tale of monetary policy Cristiano Cantore Haroon Mumtaz Filippo Ferroni Angeliki Theophilopoulou Quaderni - Working Paper DSE N°1210 A tail of labor supply and a tale of monetary policy∗ Cristiano Cantore Sapienza University of Rome Filippo Ferroni University of Bologna Haroon Mumtaz Queen Mary, University of London Angeliki Theophilopoulou Brunel University London September 2, 2025 Abstract We study the interaction between monetary policy and labor supply decisions at the household level. We uncover evidence of heterogeneous responses and a strong countercyclicality of hours worked in the left tail of the income distribution following a monetary policy shock in the U.S. Specifically, while aggregate hours and labor earnings decline after a monetary tightening, individuals at the bottom of the income distribution increase their hours worked. Moreover, this positive labor supply response is quantitatively significant, substantially dampening the decline in aggregate hours worked. We show that the empirical patterns are consistent with a standard one-asset HANK model featuring endogenous labor supply. The model reveals that strong income effects at the bottom of the distribution can account for the observed countercyclical labor responses, highlighting how labor supply adjustments act as an additional margin through which households smooth consumption. Comparing this specification to a model with a homogeneous labor supply, we find that labor supply heterogeneity reduces the aggregate MPC and attenuates the transmission of monetary policy through aggregate demand. As a result, the output cost of disinflation is lower in economies where poorer households can flexibly adjust their labor effort, easing the trade-off faced by the central bank. Keywords: Monetary policy, Household Survey, FAVARs, HANK. JEL classification: E52, E32, C10 ∗We would like to thank Valerio Pieroni for the lenghty discussions and suggestions about the HANK analysis we also thank Michele Andreolli, Guido Ascari, Saleem Bahaj, Christian Bayer, Gadi Barlevy, Florin O. Bilbiie, Davide Debortoli, Luca Fornaro, Luca Gambetti, Nezih Guner, Chris Huckfeldt, Mathias Klein, Guido Lorenzoni, Leonardo Melosi, Carlo Pizzinelli, Ricardo Reis, Kjetil Storesletten, Dan Sullivan, Paolo Surico, Gianluca Violante, three anonymous referees and participants at numerous conferences and seminars for comments and suggestions. 1 Non Technical Summary The paper asks a simple question with a surprising answer: when the central bank raises interest rates, do people change how much they work, and does that change differ by income? Looking at U.S. survey data after unexpected rate hikes, the authors find that total hours and earnings in the economy fall, as standard stories predict. But among people at the bottom of the income distribution, hours worked actually rise. These workers are also less likely to separate from their jobs and their behavior is more sensitive to interest rate moves than that of middleand higher-income households. Because lowand moderate-income workers account for a meaningful share of total hours, this extra effort partially offsets the overall decline in labor input. Why would those with the least resources work more when the economy cools? The paper points to a straightforward intuition. Monetary tightening lowers real wages and raises the cost of servicing debt. Households with little savings and tight budgets have a harder time smoothing their spending by dipping into assets or borrowing. Instead, they smooth by supplying more labor. In other words, the ”income effect” of feeling poorer dominates the usual ”substitution effect” that would make people work less when wages soften. The authors also argue that this pattern reflects people’s choices rather than firms’ selective hiring or scheduling. The result holds in panel data, remains when focusing on fulltime workers, and is accompanied by falling wages alongside rising hours at the bottom–signs that supply, not demand, is doing most of the work. To test the interpretation, the paper builds a standard macro model that allows households to differ and lets each choose how much to work. Calibrated to match realistic variation in income, assets, and borrowing limits, the model reproduces the data’s key feature: after a contractionary monetary shock, lower-income households increase their labor effort while higher-income households reduce it. In the model, the mechanism comes from strong income effects among constrained families, driven by lower real wages and higher debt payments. These differences matter for the broader story of how monetary policy moves the economy. When poorer households can flex their hours, they rely less on cutting spending to adjust, so the hit to overall demand is smaller than in models that assume everyone behaves the same. The authors show that this cushions the output decline that typically accompanies disinflation. Measured by the sacrifice ratio–the cumulative output loss per percentage point reduction in inflation over the first year–the cost is about one-third lower in the version of the model where labor supply can vary across households (for example, roughly 0.67 rather than 1.02 under a calibration with strong income effects). The upshot is that the ”tail” of the income distribution changes the ”tale” of monetary policy. If central banks ignore how low-income households adjust their work, they risk overstating the growth cost of bringing inflation down and misreading the trade-offs involved in raising rates. 2 1 Introduction Do people adjust how much they want to work when the central bank’s monetary policy stance shifts? More specifically, does an interest rate hike induce individuals to work more or fewer hours? And does this effect differ across households with different levels of income (or earnings)? The vast literature on the heterogeneous effects of monetary policy has focused on the inter-temporal channel that affects the consumption and savings plans of households (Bilbiie (2008), Auclert (2019), Cloyne, Ferreira and Surico (2020), Kaplan, Moll and Violante (2018)). However, changes in consumption plans induced by variation in rates also influence the intratemporal allocation between consumption and leisure; i.e., a household’s desired supply of labor depends on how each individual can substitute consumption with working time and/or compensate with different sources of income. In standard models, the lower wage rates induced by a contractionary monetary policy have two effects on households’ labor supply: a substitution effect that reduces how much households would prefer to work and an income effect that increases it. The majority of the theoretical macro literature, assumes no or negligible income effects on the labor supply.1It is often thought that income effects are small because –being shortlived– monetary policy shocks do not have large effects on lifetime income, which is what matters for an optimizing worker-consumer.2Moreover, monetary policy is traditionally viewed as affecting labor demand through the extensive margin and having little effect on labor supply.3 The scope of this paper is to revisit this channel and study the transmission mechanism of monetary policy to the labor supply decisions at the household level.4First, we offer novel empirical evidence on the effect of monetary policy on hours worked at a more granular, disaggregated level. To do this, we study the effects of unexpected shifts in the monetary policy stance on the amount of hours worked by households with different income levels using survey data for the U.S. We find that individuals at the bottom of the income distribution increase their hours worked following a monetary policy tightening, in contrast with conventional macroeconomic theory. At the same time, aggregate hours and wages across the whole distribution decline. This adjustment occurs through both the intensive 1E.g. Gal´ı, Smets and Wouters (2012); Dyrda and Pedroni (2022); Wolf (2021); Auclert and Rognlie (2020); amongst others. 2However, most of the empirical evidence used to support this assumption focuses on other shocks and not on monetary policy shocks. See the literature review section for more details. 3For example, quoting the Federal Reserve Chairman Jerome Powell on a speech on November 30 2022 ”Policies to support labor supply are not the domain of the Fed: Our tools work principally on demand.” 4The consequences of monetary policy actions on the labor market dynamics are not only of interest in academic cycles. Policymakers have expressed considerable interest in labor market outcomes across the whole spectrum of the population and in particular in lowand moderate-income communities. E.g. in a Jackson Hole speech on August 27, 2020, J. Powell said in unveiling the new Fed strategy that “our revised statement emphasizes that maximum employment is a broad-based and inclusive goal. This change reflects our appreciation for the benefits of a strong labor market, particularly for many in lowand moderate-income communities.” 3 and extensive margins of labor supply, but with important heterogeneity across the income distribution. In particular, low-income individuals tend to increase their hours worked and exhibit lower separation rates following a monetary contraction. Moreover, their response is more sensitive to interest rate variations compared with other percentiles of income in the population. As the labor supplied by lowand moderate-income households (the tail of labor supply) represents both a non-negligible share of the volatility and a relevant proportion of hours worked in the aggregate, this response is also quantitatively relevant from a macro perspective. The countercyclicality of hours worked in the left tail of the income distribution observed in the data is an equilibrium outcome resulting from the interaction of households’ labor supply forces and firms’ labor demand factors and consistent with multiple explanations. For example, as the recession induced by a contractionary monetary policy increases the probability of becoming unemployed, households with limited income sources have incentives to work more. Similarly, individuals who are close to their borrowing limits may need to work more hours to meet their debt obligations when interest rates rise. Supply-side explanations suggest that when lacking buffer savings or non-labor income sources, households with lowand moderate-incomes have less room to maneuver during tough economic times, and by varying their labor supply they can smooth consumption along the business cycle. Alternatively, on the demand side, firms may lay off temporary or part-time workers and adjust the labor’s input by utilizing more of their existing labor force inducing selection in the sample. While it is very difficult to isolate the dominant channel responsible for our empirical findings and a combination of these stories is more likely, several pieces of evidence suggest that selection is not the dominant force in this context; i.e. the results carry over when using the panel dimensions of our survey data and or when isolating the response of only full-time employed workers. Finally, the evidence of falling wages alongside rising hours worked at the bottom of the income distribution suggests that labor supply forces-rather than labor demand shifts-play a dominant role in driving this pattern. It is therefore natural to ask whether the labor supply behavior observed among lowincome individuals can be theoretically rationalized. Another way to assess whether the empirical patterns are primarily driven by labor supply rather than labor demand forces is to study them in a structural model. If a standard heterogeneous-agent framework with endogenous labor supply-abstracting from heterogeneity in labor demand-can reproduce the countercyclical responses of hours worked at the bottom of the income distribution, this would provide strong support for a supply-side interpretation of the data. The second contribution of the paper is thus to explore these mechanisms in theory and assess their implications for the transmission (the tale) of monetary policy. We start by providing a simple intuition of the mechanism at work. Borrowing constraints and limited consumption smoothing (Athreya, Owens and Schwartzman (2017)) are likely to drive stronger income effects on labor supply decisions for households with low income 4 and limited assets. In particular, constrained or hand-to-mouth (HTM) households face a tighter intertemporal budget constraint and a wedge in their Euler equation, making their marginal utility of consumption highly sensitive to income fluctuations. By analyzing how borrowing constraints and the curvature of the utility function with respect to consumption affect the optimal choices of consumption and leisure, we show that monetary policy shocks can generate an increase in labor supply among constrained households, driven by income effects. This mechanism directly links the intertemporal and intratemporal choices of households, highlighting the importance of heterogeneity in borrowing constraints and marginal propensities to work. We then turn to a quantitative analysis using a standard one-asset heterogeneous-agent New Keynesian (HANK) model with endogenous labor supply and nominal price rigidities. We show that this ”off-the-shelf” HANK model, calibrated to match plausible features of household heterogeneity, is able to reproduce the key labor supply patterns we uncover in the data: following a contractionary monetary policy shock, households in the lower part of the income distribution increase labor supply, while labor supply declines among higherincome households. With this model, we can also decompose the labor supply response into its underlying channels. This reveals that the countercyclical labor supply at the bottom of the income distribution is primarily driven by income effects-specifically, the decline in real wages and the increase in debt repayment burdens following a monetary tightening. We then systematically study how the strength of these heterogeneous labor supply responses varies across different model calibrations by altering the elasticity of intertemporal substitution (EIS) and the borrowing limit. To further quantify the macroeconomic implications of heterogeneous labor supply, we compare this baseline model to a similar HANK economy where labor supply is homogeneous across households, as in Auclert, Rognlie and Straub (2024). To ensure comparability, we calibrate both models to match the labor supply response of the median agent type, and examine differences in the steady state and in the responses to monetary policy shocks. We find that allowing for heterogeneous labor supply has quantitatively significant implications for monetary transmission. In particular, the steady-state aggregate marginal propensity to consume (MPC) is systematically lower in models with endogenous, heterogeneous labor supply than in comparable models where labor supply is homogeneous. This difference is especially pronounced at low values of the elasticity of intertemporal substitution, where income effects are stronger and constrained households rely more on labor effort to buffer shocks. This additional adjustment margin dampens the aggregate consumption response to monetary policy and, crucially, reduces the real cost of disinflation for the monetary authority. We quantify this effect by computing the sacrifice ratio, defined as the cumulative percentage output loss per cumulative percentage point reduction in inflation over the first year following a contractionary monetary shock. Across different calibrations of the EIS, we find that the sacrifice ratio is systematically lower in the model with het5 erogeneous labor supply. For instance, under a low EIS (high income effect), the sacrifice ratio falls from 1.02 in the homogeneous labor supply model to 0.67 in the heterogeneous labor supply one model, a 35% reduction in the output cost of disinflation. This result arises because low-income households increase labor effort in response to the shock, partially offsetting the decline in consumption and mitigating the contraction in aggregate demand. From a policy perspective, this implies that failing to account for heterogeneity in labor supply may lead central banks to overestimate the output costs of achieving disinflation and misjudge the trade-offs involved in monetary tightening. The paper is organized as follows: the next subsection discusses the existing literature. Section 2describes the data and the empirical strategy and presents our empirical evidence. Section 3presents a structural model that accounts for this evidence and investigates the implication for the transmission of monetary policy. Finally, section 4provides some concluding remarks. 1.1 Related Literature This paper contributes to the literature on monetary policy and household heterogeneity. While most empirical work has focused on balance sheet composition and the heterogeneity in MPCs following monetary shocks (Cloyne et al. (2020), Auclert (2019)), we instead study how such shocks affect labor supply decisions across households. By examining heterogeneous labor supply responses in HANK models, we also highlight their implications for aggregate MPCs. Kehoe, Lopez, Pastorino and Salgado (2020) and Amir-Ahmadi, Matthes and Wang (2021) document heterogeneity in the responses of hours worked and unemployment across U.S. demographic groups. The former finds that labor supply is less cyclical for older and college-educated workers, while the latter shows large variation in unemployment responses. We complement these studies by sorting households by income bins rather than demographic traits and focusing on the intensive margin of labor supply. Graves, Huckfeldt and Swanson (2023) study the effect of monetary policy on the labor market flows and find that a monetary policy tightening induces an increase in the fraction of labor force non-participants reporting that they want a job and an increase in the number of distinct job search methods by unemployed individuals. Both these margins of adjustments are consistent with an increase in the labor supply of non-employed individuals. These results are in line and complementary with our findings on the increase of hours worked of workers with low or moderate income (both currently employed or coming from non-employment) following a monetary policy tightening. Del Canto, Grigsby, Qian and Walsh (2025) also study the distributional effects of the US monetary shocks using monthly VARs and data from the CPS, but their focus is normative rather than positive. Several papers use administrative data to study the heterogeneous effects of monetary 6 policy on labor market outcomes. For Scandinavian countries Amberg, Jansson, Klein and Rogantini-Picco (2022), Andersen, Johannesen, Jørgensen and Peydr´o (2021) and Holm, Paul and Tischbirek (2021)) focus on labor income and capture combined effects on both the extensive and intensive margins. Coglianese, Olsson and Patterson (2025) analyze administrative data from Sweden and show that unemployment responses to monetary shocks vary across the earnings distribution, focusing on labor market transitions. Hubert and Savignac (2024) find that in France, most of the variation in labor income for the bottom half of the distribution stems from the extensive margin, while Broer, Kramer and Mitman (2022) document heterogeneous unemployment risk in Germany, with low-income workers facing more pro-cyclical separation rates. However, none of these studies can disentangle hours worked from wages, as we do here. Our contribution is to identify a distinct transmission channel: the heterogeneous response of hours worked to a monetary policy shock. Moreover, unlike most of these studies (except Broer et al. (2022)), we use data at monthly frequency, which allows us to exploit a longer time-series dimension to identify the transmission of monetary policy shocks. Motivated by our empirical findings for the U.S., Das, Hambur, Hellwig and Spray (2025) study the effects of monetary policy on hours worked using administrative data from Australia. Leveraging high-frequency identification and individual-level income and hours data, they find that labor supply responses are stronger among low-income and low-liquidity individuals. Their results confirm that income effects play a key role in shaping labor supply reactions to interest rate shocks. As discussed in the introduction, macroeconomic models often assume negligible income effects on labor supply. However, the empirical evidence supporting this view rarely focuses on business cycle shocks. Most estimates come from idiosyncratic income shocks, such as lottery winnings. For example, Cesarini, Lindqvist, Notowidigdo and ¨ Ostling (2017) use Swedish administrative data and find modest income effects, while Golosov, Graber, Mogstad and Novgorodsky (2023), using U.S. data, argue that labor supply responses to lottery winnings are sizable and not negligible. From a theoretical perspective, we contribute to the literature on micro-level heterogeneity in New Keynesian models. Most existing work focuses on the consumption channel of monetary policy while abstracting from labor supply heterogeneity (e.g., Auclert (2019), Auclert et al. (2024), Bayer, Born and Luetticke (2024), Bilbiie (2024)). A notable exception is Athreya et al. (2017), who emphasize the role of labor supply decisions and marginal propensities to work in shaping the effects of fiscal transfers. To our knowledge, we are the first to study this channel in the context of monetary policy. Similarly, Guerrieri and Lorenzoni (2017) explore how different utility calibrations affect labor supply responses to credit shocks in a heterogeneous-agent model with incomplete markets. Importantly, while our empirical and theoretical results highlight the relevance of heterogeneous labor supply, incorporating this feature into HANK models presents challenges7 Figure 3: Impulse responses to a monetary policy shock. 0 20 40 -0.5 0 0.5 1 1.5 0 20 40 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 20 40 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Notes: This figure depicts the impulse responses to a monetary policy tightening shock. The left panel reports the responses of hours worked for the first quintile of the earning distribution, the cental panel the aggregate measure of hours worked using the CPS data, and right panel the alternative aggregate measure of hours worked which excludes first quintile of the earning distribution. Dark (light) red areas 68 (90)% confidence sets. The extent to which this milder contraction in labor supply translates into less amplification of other variables (especially inflation) is less clear. For answering the latter we need to construct an hypothetical counterfactual economy without the left tail of labor supply. The empirical model does not allow to run such counterfactuals. The structural model presented in section 3can shed some light on this point. Composition Effects A potential concern about the empirical evidence presented earlier is that the observed increase in hours worked among low-income individuals following a monetary tightening may reflect composition effects. For instance, if part-time or low-hour workers are more likely to exit employment during downturns, average hours could rise mechanically even if individual labor supply remains unchanged. To address this concern, we first restrict the sample of our analysis to full-time workers.11 Figure 4displays the response of hours worked for different income levels. Removing part-time workers does not invalidate our main findings and hours increase at the left tail of the earnings distribution after a monetary contraction. Up to now our empirical analysis is constructed using a repeated cross-section which even controlling for partand full-time workers might still be prone to composition effects. To rule those out, we leverage the panel dimension of the CPS constructed by the Kansas City 11For this exercise we use the Kansas Fed extract of the CPS by setting the variable lfdetail76 equal to either 1 or 2. 14 Figure 4: Responses of hours for full-time employees 6 mths 2 years Notes: This figure depicts the impulse responses to a monetary policy tightening shock. Dark (light) red areas 68 (90)% confidence sets. Fed (https://cps.kansascityfed.org/) and track changes in hours worked at the individual level. Specifically, we compute the change in hours between month tand t+ 12 and use its average within income groups as the dependent variable in a FAVAR framework. This approach mitigates composition concerns inherent in cross-sectional averages. The top panel of Figure 5shows the growth in hours worked six months (red) and two years (blue) post-shock, across the income distribution. Despite wider confidence intervals, the results support our main finding: low-income individuals increase their hours worked in response to contractionary policy. The bottom panel of Figure 5reports employment outflows12 over the same horizon. While outflows rise for middleand high-income groups, they decline for low-income individuals, indicating stronger job attachment in the lower tail of the distribution. These findings confirm that both intensive and extensive labor supply margins respond to monetary shocks, but in income-dependent ways. In the next sections, 12See footnote 8and Appendix A.1 for details. 15 Figure 5: Distribution of responses of the growth rate of hours worked and of employment after monetary policy tightening. 6 mths 2 years Notes: The top panel depicts response of the growth rate of hours worked growth six months (red) and two (blue) years after the shock using the panel version of the CPS. The bottom panel depicts response of the outflows from employment six months (red) and two (blue) years after the shock using the panel version of the CPS. Shaded areas (solid lines) 68 (90)% confidence sets. we interpret these patterns through the lens of theory. Supply and demand factors The countercyclical increase in labor supply among lowincome workers reflects the interplay between household labor supply and firm-level labor demand. For middleand high-income individuals, both real wages and hours worked decline 16 following a monetary tightening, consistent with a leftward shift in labor demand. In contrast, among low-income workers, we observe rising hours despite falling real wages-indicating that income effects on labor supply dominate in this group. This pattern of negative comovement between wages and hours is suggestive of supply-side forces at play, as discussed in Katz and Murphy (1992), where such comovement typically reflects movements along a downward-sloping labor demand curve in response to shifts in labor supply. The responses of real wages at different income percentiles are reported in the Appendix D.3 figure D.8. Sectors and education We further explore the heterogeneity behind this pattern by disaggregating responses by industry and education.13 Low-wage workers are largely employed in sectors such as wholesale and retail trade, leisure and hospitality, and education and health services (Appendix Figure D.3). Within these sectors, we observe clear positive responses of hours worked after a monetary contraction, especially at the bottom of the wage distribution (Appendix Figure D.4). Educational attainment also plays a role. Low-income, non-college-educated individuals exhibit a larger increase in labor supply after monetary tightening than their college-educated peers suggesting that education moderates the strength of income effects (Appendix Figure D.7). 3 Labor supply and heterogeneity We now turn to a theoretical model to rationalize our empirical findings and assess their implications for the monetary policy transmission mechanism. We start from a general and stylized framework that clarifies the novel link between heterogeneous labor supply and monetary policy. Specifically, constrained agents facing tighter financial conditions tend to sacrifice leisure and increase labor supply to sustain their consumption in response to a decline in income. Our empirical evidence, demonstrating that hours worked increase among households in the lower part of the income distribution after a monetary policy tightening, aligns with several potential theories. While the observed equilibrium outcome reflects both supplyand demand-side factors, the inverse movement of wages and hours worked–wages falling while hours increase–points predominantly toward a labor supply response driven by income effects. For this reason, in this section we focus the theoretical analysis on labor supply heterogeneity while assuming a standard labor demand side, modeled through a representative firm with homogeneous labor demand. 3.1 Income effects We begin by analyzing the household’s problem in partial equilibrium, taking labor income as given, to highlight how the strength of the income effect on individual labor supply is 13For more details see appendix D.2. 17 shaped by two key forces: the curvature of the utility function and the tightness of the borrowing constraint.14 A key feature in macroeconomic models determining household labor supply is the intratemporal optimality condition governing the trade-off between consumption and leisure. Let Htdenote hours worked at time t,Ctconsumption, and U(Ct, Ht) the household’s utility function. With wtas the real wage rate, this optimality condition is: −Uh(Ct, Ht) Uc(Ct, Ht)=wt,(4) where Uhand Ucare partial derivatives with respect to hours and consumption, respectively. Households also face an intertemporal consumption decision summarized by the Euler equation (abstracting from uncertainty for now): Uc(Ct, Ht) Uc(Ct+1, Ht+1)=β(1 + rt)(1 + ωt),(5) where rtis the real interest rate, affected directly by monetary policy, and ωtrepresents a wedge arising from borrowing constraints or other financial frictions. Typically, constrained households face a positive wedge (ωt>0), reflecting a higher marginal utility of current consumption. Following a contractionary monetary policy shock that raises rt, the household’s intratemporal optimality condition determines how hours worked adjust in response to changes in income and wages. The strength of this labor supply adjustment crucially depends on the curvature of the utility function over consumption. We assume preferences of the form: U(Ct, Ht) = C1−1/σ t 1−1/σ −φH1+ν t 1 + ν, where σdenotes the elasticity of intertemporal substitution and νthe inverse of the Frisch elasticity of labor supply. A lower σ(corresponding to a more concave utility in consumption) implies that marginal utility reacts more strongly to income changes, amplifying the labor supply response when consumption declines. Households facing a negative income shock will then supply more labor to stabilize their utility. Conversely, a higher σflattens the utility curve, making households less sensitive to fluctuations in income, and thus dampening the adjustment of hours worked.15 Borrowing constraints (via ωtin the Euler equation) further magnify this effect by forcing some households to adjust labor supply more aggressively in response to changes in current income and interest rates. The borrowing limit directly affects the strength of this labor supply channel. A tighter borrowing constraint (or higher equilibrium debt levels) amplifies the sensitivity of labor supply to monetary policy shocks: when the real interest 14We thank an anonymous referee for suggesting how to structure this section. 15See Bilbiie (2008), who shows, in a two-agent NK model, how σaffects the sign of the response of the labor supply of hand-to-mouth agents. 18 rate rises, higher debt repayments reduce disposable income, strengthening the income effect. Constrained households, unable to smooth consumption through borrowing, respond by increasing their labor supply to offset the higher financial burden. In Appendix F, we illustrate how these forces interact in a simple two-agent (borrowersaver) economy where borrowers face tighter borrowing limits and higher impatience relative to savers. We show analytically how borrowers’ labor supply response after an interest rate increase depends directly on the EIS (decreasing in σ) and their borrowing limit (increasing in the net debt position). Thus, both the EIS and borrowing constraints crucially shape the extent to which the labor supply of constrained households becomes countercyclical following monetary policy shocks, offering a clear theoretical interpretation in terms of labor supply of our empirical findings. In the next section, we move to a general equilibrium analysis and consider a standard one-asset heterogeneous agents New Keynesian model with staggered price setting. 3.2 Heterogeneous Labor Supply in HANK The purpose of this section is to demonstrate that our empirical evidence aligns with the implications for heterogeneous labor supply responses in a standard HANK model. To do so, we use the one-asset HANK model with endogenous labor supply, as in Auclert, Bard´oczy, Rognlie and Straub (2021).16 The goal is to examine how different calibrations of the model affect the behavior of labor supply across the income and wealth distribution, and to compare the aggregate implications for the monetary transmission mechanism with and without heterogeneous labor supply responses in the model. The main results are as follows: (i) An off-the-shelf HANK model with heterogeneous labor supply and homogeneous labor demand can replicate our empirical findings on the labor supply response across the income distribution. (ii) The main driver of the response at the lower end of the distribution is an income effect, stemming from falling wages and rising debt repayments. Moreover, the strength of this response is amplified by the curvature of the utility function in consumption and the tightness of the borrowing limit, further highlighting the importance of income effects. (iii) The presence of labor supply heterogeneity lowers the real cost of disinflation, making it easier for the central bank to achieve its inflation target. 3.2.1 One-asset HANK The model features a heterogeneous agents sector similar to McKay, Nakamura and Steinsson (2016), coupled with a standard New Keynesian supply-side block. Households. There is a unit mass of ex-ante identical households who differ ex-post by their labor productivity e(“skill”) and asset holdings a. For notational simplicity, we use 16The only difference with Auclert et al. (2021) is that we abstract from government spending, given the focus on monetary policy here. Results are not affected by this choice. 19 the subscript ito denote household-level outcomes, instead of writing them explicitly as functions of state variables. Skill efollows a time-invariant discrete Markov chain with nestates, E={e1, e2, . . . , ene}, and exogenous transition probabilities P(e′, e). This introduces cyclical income risk in the model. The stationary distribution of Pis denoted by πe. Average labor productivity R1 0ei,t di is invariant and normalized to 1. We assume that P(e′, e) discretizes a log AR(1) process: log eit =ρelog eit−1+σeϵit, with normal innovations ϵit ∼ N(0,1), and we use the Rouwenhorst method for discretization. Households can freely choose the number of hours hthey work, subject to an additively separable utility cost of working. Consumption, savings, and labor choices c,a, and hare the solution to the household’s utility maximization problem, characterized by the following Bellman equation: Vt(eit, ait−1) = max cit,hit,ait (c1−σ−1 it 1−σ−1−φh1+ν it 1 + ν+βEtVt+1 (eit+1, ait)) s.t. cit +ait = (1 + rt)ait−1+wteithit −τt¯τ(eit) + dt¯ d(eit) ait ≥a. Households receive an hourly wage wt, pay taxes, and receive dividends from firm ownership according to incidence rules ¯τ(e) and ¯ d(e).17 Firms. A competitive final goods firm assembles its output using a CES production function Yt=R1 0y 1 µ jtdjµ , giving rise to a standard CES demand system for the continuum of intermediate goods. These intermediates, in turn, are supplied by monopolists who produce using only labor, such that yjt =Zthjt, and are subject to quadratic price adjustment costs a la Rotemberg (1982): ψt(pjt, pjt−1) = µ µ−1 1 2κlog pjt pjt−12 Yt. Here, Ztdenotes aggregate productivity that may be time-varying. In a symmetric equilibrium, gross inflation 1 + πt=Pt Pt−1evolves according to the Phillips curve: log(1 + πt) = κwt Zt −1 µ+1 1 + rt+1 Yt+1 Yt log(1 + πt+1), and dividends equal output net of labor and price adjustment costs: dt=Yt−wtHt−ψt. Policy. Monetary policy sets the nominal rate on bonds according to a standard Taylor rule: it=r∗+ϕπt+ϵt, 17This implies that skill edetermines not only a household’s income per hour worked, but also the amount of lump-sum taxes she must pay and the dividends she receives, both of which are distributed proportionally to e. 20 where r∗ tis the economy’s long-run “natural rate” and ϵtthe monetary policy shock. The real interest rate in period tis determined by the previously set nominal rate and inflation so that: 1 + rt=1 + it−1 1 + πt . The fiscal authority, in turn, issues a constant amount of government bonds Beach period and collects the lump-sum taxes τtalready mentioned above. Since there are no other spending items (abstracting from government spending), it chooses the tax rate to cover its interest rate payments every period: τt=rtB. Market Clearing. In an equilibrium, the following market clearing conditions must hold: •Asset market: B=Z1 0 ait di, •Labor market: Yt=Ht=Z1 0 eithit di, •Goods market: Yt=Z1 0 cit di −ψt. These in turn imply that aggregate household savings equal government-provided liquidity, labor demand equals supply in efficiency units, and the final good is used for consumption and price adjustment costs.18 Calibration The model is solved using the sequence-space Jacobians approach pioneered by Auclert et al. (2021).19 For technical details, we refer the reader to their paper. The calibration is also mostly taken from Auclert et al. (2021) and summarised in Table 1. The main difference from their calibration is that here we also choose Bto target a percentage of HTM agents in steady state of 20%. This is to ensure a comparison across different models and/or calibrations keeping fixed the steady state proportion of constrained agents. The other difference is that, in the baseline calibration, we allow for some borrowing in equilibrium (a=−0.5).20 This calibration implies an income-weighted aggregate MPC in steady state equal to 12.5%. 18As is well known, price adjustment costs don’t matter in linearized models. 19See Bayer and Luetticke (2020) for an alternative solution method. 20The implied βand φare almost identical to theirs, while our calibration requires a lower amount of liquidity compared to their model, where they set B= 5.6 and obtain MPC = 11% and HTM = 17%. All the results presented in this section do not change substantially if we use their original calibration. 21 Parameter Value Target Households βDiscount factor 0.98 r= 0.005 φDisutility of labor 0.78 H= 1 σEIS .5 νInverse Frisch 2 aBorrowing constraint -0.5 ρeAutocorrelation of earnings 0.966 σeCross-sectional std of log earnings 0.5 Firms µSteady-state markup 1.2 κSlope of Phillips curve 0.1 Policy BBond supply 3.84 HTM = 0.2 ϕTaylor rule coefficient on inflation 1.5 Monetary Policy Shock ρϵPersistence 0.61 σϵStandard Deviation 0.0025 Discretization nePoints in Markov chain for e7 naPoints on asset grid 500 ¯aUpper limit on asset grid 150 Untargeted Steady State MPC % aggregate Marginal Propensity to Consume 12.5% Table 1: One-asset HANK calibration Rationalizing the empirical evidence Mapping the discrete income states to their positions in the steady-state distribution reveals that both consumption and labor supply, on average, increase with income–consistent with empirical evidence. However, poorer households near the borrowing constraint tend to work more than richer ones due to stronger income effects and tighter liquidity.21 Figure 6shows the impulse responses to a monetary policy tightening, assuming that ϵt follows an AR(1) process with persistence ρϵ= 0.61 and standard deviation σϵ= 0.0025. The upper panels display the dynamics of the interest rate shock, inflation, and aggregate output. The lower panels highlight heterogeneous labor supply and consumption responses across income groups. Poorer households (e.g., P0 2, P2 11, and P11 34) increase labor supply following the shock, consistent with a dominant income effect driven by tight borrowing constraints. In contrast, higher-income households reduce labor supply, reflecting standard substitution effects. Consumption falls across all groups but declines more sharply for lowerincome households, as expected. These results demonstrate that an off-the-shelf HANK 21See appendix G.1 for details. 22 Figure 6: Impulse responses to a 25 basis points Monetary Policy Shock 23 hours worked, while wealthier households reduce them. Importantly, the model allows us to decompose the labor supply responses into underlying channels, and we find that the countercyclical behavior at the bottom of the income distribution is primarily driven by income effects. We systematically study how these heterogeneous labor supply responses vary across different calibrations, changing the elasticity of intertemporal substitution and the borrowing limit, and compare them to a HANK model with homogeneous labor supply. Our quantitative analysis shows that heterogeneity in labor supply behavior alters the aggregate MPC implied by the model. In particular, stronger countercyclical labor supply responses at the bottom of the distribution imply a lower MPC relative to the HANK model where everybody supplies the same amount of hours, highlighting how labor supply act as an additional margin through which households can smooth consumption. This additional adjustment margin also has substantial effects on the dynamics of the model. Importantly it reduces the sacrifice ratio-the cumulative output loss per point of inflation reductionfaced by the monetary authority. Across model calibrations, we find that incorporating heterogeneous labor supply leads to a systematically lower sacrifice ratio, with reductions of up to 35%, implying that disinflationary policies may entail smaller output costs than previously estimated if this margin is accounted for. Therefore, ignoring labor supply heterogeneity risks overstating households’ vulnerability to monetary policy shocks and mischaracterizing both the distributional and aggregate effects of policy interventions. 30 References Amberg, N., Jansson, T., Klein, M. and Rogantini-Picco, A.: 2022, Five Facts about the Distributional Income Effects of Monetary Policy Shocks, American Economic Review: Insights . Amir-Ahmadi, P., Matthes, C. and Wang, M.-C.: 2021, What Does Monetary Policy Do To Different People?, Mimeo. Andersen, A. L., Johannesen, N., Jørgensen, M. and Peydr´o, J.-L.: 2021, Monetary policy and inequality, Economics Working Papers 1761, Department of Economics and Business, Universitat Pompeu Fabra. Athreya, K., Owens, A. and Schwartzman, F.: 2017, Does redistribution increase output? the centrality of labor supply, Quantitative Economics 8(3), 761–808. Auclert, A.: 2019, Monetary Policy and the Redistribution Channel, American Economic Review 109(6), 2333–2367. Auclert, A., Bard´oczy, B., Rognlie, M. and Straub, L.: 2021, Using the sequence-space jacobian to solve and estimate heterogeneous-agent models, Econometrica 89(5), 2375– 2408. URL: https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA17434 Auclert, A. and Rognlie, M.: 2020, Inequality and Aggregate Demand, Mimeo. Auclert, A., Rognlie, M. and Straub, L.: 2024, The intertemporal keynesian cross, Journal of Political Economy 132(12), 4068–4121. URL: https://doi.org/10.1086/732531 Bai, J. and Ng, S.: 2002, Determining the Number of Factors in Approximate Factor Models, Econometrica 70(1), 191–221. Banbura, M., Giannone, D. and Reichlin, L.: 2007, Bayesian vars with large panels, CEPR Discussion Papers 6326. Barigozzi, M., Lippi, M. and Luciani, M.: 2021, Large-dimensional Dynamic Factor Models: Estimation of Impulse-Response Functions with I(1) cointegrated factors, Journal of Econometrics 221(2), 455–482. Bauer, M. D. and Swanson, E. T.: 2023, A Reassessment of Monetary Policy Surprises and High-Frequency Identification, NBER Macroeconomics Annual 37(1), 87–155. URL: https://ideas.repec.org/a/ucp/macann/doi10.1086-723574.html 31 Bayer, C., Born, B. and Luetticke, R.: 2024, Shocks, frictions, and inequality in us business cycles, American Economic Review 114(5), 1211ˆa47. URL: https://www.aeaweb.org/articles?id=10.1257/aer.20201875 Bayer, C. and Luetticke, R.: 2020, Solving heterogeneous agent models in discrete time with many idiosyncratic states by perturbation methods, Quantitative Economics 11, 1253– 1288. Bilbiie, F.: 2008, Limited asset markets participation, monetary policy and (inverted) aggregate demand logic, Journal of Economic Theory 140(1), 162–196. Bilbiie, F.: 2020, The new keynesian cross, Journal of Monetary Economics 114, 90–108. Bilbiie, F. O.: 2024, Monetary policy and heterogeneity: An analytical framework*, The Review of Economic Studies p. rdae066. URL: https://doi.org/10.1093/restud/rdae066 Bilbiie, F. O., Monacelli, T. and Perotti, R.: 2013, Public debt and redistribution with borrowing constraints, The Economic Journal 123(566), F64–F98. Broer, T., Kramer, J. and Mitman, K.: 2022, The Curious Incidence of Monetary Policy Shocks Across the Income Distribution, Working Paper Series 416, Sveriges Riksbank (Central Bank of Sweden). Canova, F. and Ferroni, F.: 2022, Mind the gap! Stylized dynamic facts and structural models, American Economic Journal: Macroeconomics forthcoming. Cesarini, D., Lindqvist, E., Notowidigdo, M. J. and ¨ Ostling, R.: 2017, The effect of wealth on individual and household labor supply: Evidence from swedish lotteries, American Economic Review 107(12), 3917–46. Cloyne, Ferreira, C. and Surico, P.: 2020, Monetary Policy when Households have Debt: New Evidence on the Transmission Mechanism, Review of Economic Studies 87(1), 102–129. Coglianese, J., Olsson, M. and Patterson, C.: 2025, Monetary policy and the labor market: A quasi-experiment in sweden, American Economic Review . Das, M., Hambur, J., Hellwig, K. and Spray, J.: 2025, Labor supply effects of monetary policy: Evidence from australian mortgage holders, mimeo. De Giorgi, G. and Gambetti, L.: 2017, Business cycle fluctuations and the distribution of consumption, Review of Economic Dynamics 23, 19 – 41. Del Canto, F., Grigsby, J., Qian, E. and Walsh, C.: 2025, Are inflationary shocks regressive? a feasible set approach, The Quarterly Journal of Economics . 32 Dyrda, S. and Pedroni, M.: 2022, Optimal fiscal policy in a model with uninsurable idiosyncratic shocks, Review of Economic Studies . Forni, M. and Gambetti, L.: 2014, Sufficient information in structural VARs, Journal of Monetary Economics 66(C), 124–136. Gal´ı, J., Smets, F. and Wouters, R.: 2012, Unemployment in an estimated new keynesian model, NBER Macroeconomics Annual 26, 329–360. Gerke, R., Giesen, S., Lozej, M. and Rottger, J.: 2024, On household labour supply in sticky-wage HANK models, Technical report. Gertler, M. and Karadi, P.: 2015, Monetary policy surprises, credit costs, and economic activity, American Economic Journal: Macroeconomics 7(1), 44–76. Golosov, M., Graber, M., Mogstad, M. and Novgorodsky, D.: 2023, How americans respond to idiosyncratic and exogenous changes in household wealth and unearned income*, The Quarterly Journal of Economics 139(2), 1321–1395. URL: https://doi.org/10.1093/qje/qjad053 Graves, S., Huckfeldt, C. and Swanson, E. T.: 2023, The labor demand and labor supply channels of monetary policy, mimeo. Guerrieri, V. and Lorenzoni, G.: 2017, Credit Crises, Precautionary Savings, and the Liquidity Trap, The Quarterly Journal of Economics 132(3), 1427–1467. Holm, M. B., Paul, P. and Tischbirek, A.: 2021, The transmission of monetary policy under the microscope, Journal of Political Economy 129(10), 2861–2904. Hubert, P. and Savignac, F.: 2024, The heterogeneous effects of monetary policy on labor income: Disentangling the extensive and intensive margins, Journal of Political Economy Macroeconomics 2(4), 687–719. URL: https://doi.org/10.1086/732469 Kaplan, G., Moll, B. and Violante, G. L.: 2018, Monetary policy according to hank, American Economic Review 108(3), 697–743. Katz, L. F. and Murphy, K. M.: 1992, Changes in relative wages, 1963ˆa1987: Supply and demand factors, The Quarterly Journal of Economics 107(1), 35–78. Kehoe, P. J., Lopez, P., Pastorino, E. and Salgado, S.: 2020, On the Dynamic Effects of Monetary Policy With Heterogeneous Agents, Mimeo. McKay, A., Nakamura, E. and Steinsson, J.: 2016, The power of forward guidance revisited, American Economic Review 106(10), 3133–58. 33 Mertens, K. and Ravn, M. O.: 2013, The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States, American Economic Review 103(4), 1212–47. Miranda-Agrippino, S. and Ricco, G.: 2021, The transmission of monetary policy shocks, American Economic Journal: Macroeconomics 13(3), 74–107. Pijoan-Mas, J.: 2006, Precautionary savings or working longer hours?, Review of Economic Dynamics 9(2), 326–352. Rotemberg, J. J.: 1982, Sticky prices in the united states, Journal of Political Economy 90(6), 1187–1211. Stock, J. H. and Watson, M. W.: 2008, What’s new in econometrics - time series, Lecture 7, National Bureau of Economic Research, Inc. Wolf, C.: 2021, The Missing Intercept: A Demand Equivalence Approach, National Bureau of Economic Research WP29558. 34 Online Appendix A Household level data A.1 US: CPS Survey For the US, individual level data is obtained from the current population survey (CPS) for each month from 1985 to 2019. In the benchmark case we use the uniform CPS outgoing rotation group extracts created by CEPR data. Our benchmark measure of hours is the variable hourslw (Hours last week, all jobs). We use the variable rw as our measure of real hourly wage. This is the recommended consistent real wage variable across the sample we employ. For details see the CEPR FAQ. Figure A.1: Characteristics along the wage distribution. Average across the sample. Hours <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 20 40 College <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 0.2 0.4 0.6 0.8 Male <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 0.2 0.4 0.6 White <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 0.2 0.4 0.6 0.8 Age <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 20 40 35 Figure A.2: Proportion of individuals in different industries. Industry by wage <20 >20 and <=40 >40 and <=60 >60 and <=80 >80 wage distribution 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 agr min con man trade trans info fin prof health fun other public Notes: The proportions are averaged over the sample. agr is Agriculture, forestry, fishing and hunting. min is mining, con is construction, man is manufacturing, trade is wholesale and retail trade, trans is transport and utilities, info is information, fin is financial activities, prof is professional and business services, health is education and health services, fun is leisure and hospitality, other is other services and public denotes public administration. Figure A.1 provides information regarding the characteristics of the earnings distribution. Respondents in the right tail of the distribution tend to be older, better educated, are likely to work longer hours and be white and Male. Figure A.2 shows industry of employment across the wage distribution. At the left tail, industries such as wholesale and retail trade, health, leisure and manufacturing are important. As discussed above, we also employ the longitudinally matched version of CPS provided by the Kansas Fed. We employ the variable wageperhrclean82 as our measure of hourly earnings. This series is deflated by CPI. The change in hours is constructed as the difference in the log of hours82 and hours82 tm12 where the former denotes a consistent series constructed 36 using actual or usual hours and the latter is the 12 month lag of this variable. We construct the rate of transition from employment using the labour market status variable mlr76 and the 12 month lag of this variable mlr76 tm12. As discussed in the text, we impute earnings for individuals that are not employed or do not report earnings data. To do this we regress earnings on experience and individual characteristics including gender, occupation, industry of employment, geographical characteristics (US state, metropolitan indicator) and race. The fitted values from this regression are used to obtain imputed earnings.The coefficients of the regression are shocked and used to produce predicted values. These are assigned to individuals with missing earnings data using predicted mean matching. We produce 5 replicates, with the final imputed data taken to be the mean across these replications. A.2 Comparison with aggregate data The top panel of Figure A.3 compares aggregate actual hours from the CPS to a measure of monthly hours from the Bureau of Labour statistics (average weekly hours of production and non-supervisory employees). The CPS data captures the main movements in the aggregate data fairly well. Figure A.3: Comparison of survey based total hours (blue) with aggregate (orange). 1990 1995 2000 2005 2010 2015 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 Annual Growth of hours worked Constructed from CPS AWHNONAG 37 B Priors and estimation of the FAVAR The FAVAR model is defined by the following equations: Xit =ci+biτ+ ΛiFt+ξit (B.1) Yt=c+ P X j=1 βjYt−j+ut(B.2) cov (ut) = Σ = A0A′ 0(B.3) Where Yt=Rt Ft | {z } N×1 ,Rtdenotes the 1 year interest rate, i= 1,2, .., M denotes the cross-sectional dimension of the panel data-set Xit while t= 1,2, .., T is the dimension. As described in Barigozzi et al. (2021), the factors can be consistently estimated using a principal components (PC) estimator. In particular, the factor loadings are estimated via PC analysis of the first differenced data ∆Xit. With these in hand, the factors are estimated as ˆ Ft=1 Mˆ Λ′˜ Xt. Here,Λ is the matrix of factor loadings, ˜ Xtis given by (x1t, x2t, ..., xMt) where xit =Xit −ˆci−ˆ biτNote that Barigozzi et al. (2021) describe a procedure to check if the ith series contains a linear trend and that ˆ biis different from zero. Given the estimated factors, the VAR in equations B.2 is estimated using a Bayesian methods. B.1 Priors Denote the var coefficients as B=vec ([β1, β2, .., βP, c]). We follow Banbura, Giannone and Reichlin (2007) and use a Natural Conjugate prior implemented via dummy observations. The priors are implemented by the dummy observations yDand xDthat are defined as: yD=      diag(γ1s1...γnsn) κ 0N×(P−1)×N diag (s1...sn) .............. 0EX×N       , xD=      JP⊗diag(s1...sn) κ0NP×EX .............. 0N×(NP)+EX .............. 0EX×NP IEX ×1/c       (B.4) where JP=diag(1,2, ..., P), γ1to γndenote the prior mean for the parameters on the first lag obtained by estimating individual AR(1) regressions, s1to snis an estimate of the variance of the endogenous variables obtained individual AR(1) regressions, κmeasures the tightness of the prior on the autoregressive VAR coefficients, and cis the tightness of the prior on the remaining regressors. We set κ= 0.2 and c= 1000. We also implement priors on the sum of coefficients (see Banbura et al. (2007)). The dummy observations for this prior are defined as: ˜yD=diag (γ1µ1...γnµn) τ,˜xD=(11×P)⊗diag(γ1µ1...γnµn) τ0N×EX (B.5) where µiis the sample average of the ith variable. As in Banbura et al. (2007) we set τ= 10κ. The total number of dummy observations is TD. 38 B.2 MCMC algorithm Banbura et al. (2007) show that posterior distribution can be written as: g(Σ|Y)∼iW ¯ Σ, TD+2+T−K(B.6) g(B|Σ, Y )∼N¯ B, Σ⊗X′ ∗X∗−1(B.7) where iW denotes the inverse Wishart distribution, Kdenotes the number of regressors in each equation of the VAR model. Note that Y∗=  Y yD ˜yD and X∗=  X xD ˜xD ,Xcollects the regressors, and ˜ B=X′ ∗X∗−1X′ ∗Y∗ ¯ B=vec ˜ B ¯ Σ = Y∗−X∗˜ B′Y∗−X∗˜ B Posterior draws can be easily generated by drawing Σ from the marginal distribution in B.6 and then bfrom the conditional distribution in equation B.7. We set the number of draws to 21,000 with a burn-in of 1,000. We retain every second draw after the burn-in period. C IV Identification For a given draw of B, Σ and ut, we obtain the first column of A0by using the procedure proposed by Mertens and Ravn (2013). We assume that the instrument is relevant and exogenous: cov (mt, ε1t) = α cov mt, ε− t= 0 where ε1tdenotes the structural shock of interest that is ordered first for convenience, while ε− trepresent all remaining shocks and εt=ε1tε− t. Re-writing the relevance and exogeneity conditions in vector form: E(mtε′ t) = [α0] (C.1) E(mtε′ tA′ 0)=[α0]A′ 0(C.2) E(mtu′ t) = αa0(C.3) where a0is a (1 ×R) vector corresponding to the first row of A′ 0(hence first column of A0). An estimate of E(mtu′ t) =       E(mtu′ 1t) E(mtu′ 2t) . . E(mtu′ Nt)       ′ can be easily obtained by using a linear 39 Figure D.5: Proportion of individuals with education less than high school (LTHS), high school (HS), some college (somecollege), college and advanced degrees (advanced). Education Across the wage distribution <5 <10 <15 <20 <25 <30 <35 <40 <45 <50 <55 <60 <65 <70 <75 <80 <85 <90 <95 wage distribution 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 LTHS HS Somecollege college advanced Notes: The proportions are averaged over the sample. 46 Figure D.6: Employees by level of education in each industry for individuals earning below the 20th percentile of wage. Notes: Proportion of individuals with education less than high school (LTHS), high school (HS), some college (somecollege), college and advanced degrees (advanced). The proportions are averaged over the sample. 47 Figure D.7: IRF of hours at the 6mth horizon to a monetary contraction 48 D.3 Response of real wages Figure D.8 reports the responses of real wages both in the aggregate and across different percentiles of the income distribution. We find that for individuals in the middle and upper parts of the distribution, real wages and hours worked both decline following a monetary tightening. This pattern is consistent with a reduction in labor demand. In contrast, for individuals in the lower end of the distribution, real wages also decline, but hours worked increase. This divergence suggests that, in this group, an increase in labor supply is the dominant force driving the response. The overall picture thus points to heterogeneous labor market adjustment mechanisms across the income distribution, with labor supply playing a more prominent role for lower-income workers. Figure D.8: Responses of real wages after monetary policy tightening. 0 50 -2.5 -2 -1.5 -1 -0.5 0 0 50 -3 -2 -1 0 0 50 -2.5 -2 -1.5 -1 -0.5 0 0 50 -3 -2 -1 0 0 50 -3 -2 -1 0 0 50 -3 -2 -1 0 6 months 2 years Notes: The top panels show the response of the real wages at different quintile of the wage distribution and the aggregate real wages (rightmost panel). The bottom panel displays the distribution of the responses of real wages six months (red) and two (blue) years after the shock. Shaded areas (solid lines) 68 (90)% confidence sets. 49 E Sample of Individuals Employed Continuously for Three Months Figure E.1: IRF of hours for Individuals Employed Continuously for Three Months 6 mths 2 years We restrict the sample to workers employed for three months by setting the variables mlr76,mlr76 tm1, and mlr76 tm2 equal to 1. For this exercise we use the Kansas Fed extract. Figure E.1 shows that Hours for this cohort go up at the left tail of the Wage distribution after a contractionary monetary policy shock. 50 F TANK model with Borrowers and Savers A simple way to characterize the household heterogeneity and retain analytical tractability is to consider a two agents model where one type of agents are net borrower (indexed with B) and the other net saver (indexed with S), as in Bilbiie, Monacelli and Perotti (2013).27 The key features of this class of models are that borrowers are more impatient than savers, have no access to government bonds, and can borrow up to a limit. Following Bilbiie (2020) and McKay et al. (2016) we consider an economy where the monetary authority can effectively choose the real rate which makes the algebra simpler. The key equations of the log-linearized model are reported in table F.1. Log-linearized Conditions 1: Labor Supply S νˆ HS t= ˆwt−σ−1ˆcS t 2: Euler S ˆcS t= ˆcS t+1|t−σˆ Rt−ˆ Πt+1|t 3: Labor Supply B νˆ HB t= ˆwt−σ−1ˆcB t 4: Budget constraint B ˆcB tγ+¯ D(ˆ Rt−1−ˆ Πt) = ˆwt+ˆ HB t 5: Phillips Curve ˆ Πt=βEtˆ Πt+1 +κˆwt 6: Aggregate C ˆct=λγˆcB t+ (1 −λγ)ˆcS t 7: Aggregate B ˆct=ˆ Ht=λˆ HB t+ (1 −λ)ˆ HS t 8: Taylor Rule ˆ Rt=ˆ Πt+1|t+ϵm t Table F.1: Log-linearized Conditions of Savers/Borrowers model This section follows a different notational convention that the one used for the HANK model in the main text. Small case letters represent real variables while capital letters represent nominal variables or hours worked. A ’hat’ on top of the variable denotes percentage deviations from the steady state. The assumption that borrowers discount more future consumption, βB< βS=β, implies that they become net borrower in equilibrium with the borrowing limit ( ¯ D) always binding.28 γis a steady state parameter which captures the consumption inequality between borrowers and savers, i.e. γ=cB/c = 1 + ¯ D(β−1) <1. Notice that when ¯ D= 0 →γ= 1 and the model is identical to the one with Savers and HTM consumers.29 In this model, a fraction of agents are not on the Euler equation and cannot optimize intertemporally. Importantly, and differently from a model with HTM that are not net borrowers, a change in the nominal rate will have an impact not only on the 27See their paper for details on the model derivation. Relative to them we simplify it further by abstracting from government debt, expenditure, and redistribution concerns. We follow Bilbiie (2020) and assume that there is a production subsidy that induces marginal cost pricing which implies that the steady state of marginal costs is 1 which simplifies substantially the steady state and the log-linearized conditions. 28Note that in equation (4) in table F.1 ¯ Dis effectively divided by the steady state of total income/consumption. But this is =1 one in this simple set up. 29In that set up, Bilbiie (2008) showed that σ < 1 is the condition for the hours of hand-to-mouth agents to increase following a decline in their income. 51 time tconsumption and labor supply decision but also on the t+ 1 decisions because the debt repayments at t+ 1 depend on the time tinterest rates. Under mild conditions, borrowers have an incentive to increase their labor supply after an interest rate hike; this is formalized in the following proposition. Proposition 1 Under SADL (λ < 1 1+ν(1+ ¯ Dκ)) and σ < 1+ ¯ Dκ γ, a rate hike at time tinduces an increases in the borrowers labor supply both at time tand t+ 1. The proof is on the next page. At the core of this result, we have that consumption and the labor supply of the borrowers move in opposite directions. This can be appreciated when combining the time t+ 1 optimal response of borrowers in terms of consumption and labor supply after a monetary policy shock which are30 ˆ HB t+1 =¯ D(νλγσ −1 + λ) (νλ −1 + λ)(1 + γνσ)ϵm t, ˆcB t+1 =νσ ¯ D (νλ −1 + λ)(1 + γνσ)ϵm t. Combining the latter two equations we have that ˆcB t+1 =νσ νλγσ −1 + λˆ HB t+1. The numerator is positive. Notice that if the conditions of Proposition 1hold, we have λ < 1 1+ν(1+ ¯ Dκ)<1 1+νσγ , which implies that (1 −λ−νσλγ)>0; hence the denominator is negative. Derivation of Proposition 1Recall that ϵm t+j= 0 for j > 0 and ϵm t= 0. This implies that from t+2 onward the economy is back to steady states and all quantities are zero. This means also that ˆ Rt+j=ˆ Πt+j+1|t+jfor j > 0, which implies that ˆcS t+1 = 0 The saver labor supply becomes νˆ HS t+1 = ˆwt+1 Using the borrowers BC we have ˆcB t+1γ+¯ D(ˆ Rt−ˆ Πt+1) = ˆwt+1 +ˆ HB t+1 ˆcB t+1γ+¯ D(ˆ Πt+1|t+ϵm t−ˆ Πt+1) = (1 + ν)ˆ HB t+1 + 1/σˆcB t+1 1/σˆcB t+1 =1 + ν γσ −1ˆ HB t+1 −¯ D γσ −1ϵm t 30The time toptimal responses are analogous but more involved. To ease the notation we only discuss the time t+ 1 decisions. 52 notice that in absence of shocks in t+ 1 ˆ Πt+1 =ˆ Πt+1|t. Combining the to labor supply conditions we have νˆ HS t+1 +σ−1ˆcS t+1 =νˆ HB t+1 +σ−1ˆcB t+1 νˆ HS t+1 =νˆ HB t+1 +1 + ν γσ −1ˆ HB t+1 −¯ D γσ −1ϵm t νˆ HS t+1 =1 + γνσ γσ −1ˆ HB t+1 −¯ D γσ −1ϵm t Combining the aggregate conditions we have λγˆcB t+1 + (1 −λγ)ˆcS t+1 =λˆ HB t+1 + (1 −λ)ˆ HS t+1 λγσ 1 + ν γσ −1ˆ HB t+1 −¯ D γσ −1ϵm t=λˆ HB t+1 + (1 −λ)1 + γνσ ν(γσ −1) ˆ HB t+1 −¯ D ν(γσ −1)ϵm t ˆ HB t+1 (1 + ν)λγσ γσ −1−λ−(1 −λ)1 + γνσ ν(γσ −1)=¯ Dλγσ γσ −1−(1 −λ)¯ D ν(γσ −1)ϵm t ˆ HB t+1 (1 + ν)νλγσ −λν(γσ −1) −(1 −λ)(1 + γνσ) ν(γσ −1) =νλγσ −(1 −λ) ν(γσ −1) ¯ Dϵm t ˆ HB t+1 νλ(γσ +νγσ −γσ + 1) −(1 −λ)(1 + γνσ) ν(γσ −1) =νλγσ −(1 −λ) ν(γσ −1) ¯ Dϵm t ˆ HB t+1 (νλ −1 + λ)(1 + γνσ) ν(γσ −1) =νλγσ −(1 −λ) ν(γσ −1) ¯ Dϵm t which yield to ˆ HB t+1 =νλγσ −1 + λ (νλ −1 + λ)(1 + γνσ)¯ D ϵm t(F.1) This implies that borrower consumption at time t+ 1 is ˆcB t+1 =σ(1 + ν) γσ −1ˆ HB t+1 −σ¯ D γσ −1ϵm t =σ(1 + ν) γσ −1 νλγσ −1 + λ (νλ −1 + λ)(1 + γνσ)¯ D ϵm t−σ¯ D γσ −1ϵm t =ϵm t σ¯ D γσ −1(1 + ν)(−1 + λ(1 + νγσ)) −(νλ −1 + λ)(1 + γνσ) (νλ −1 + λ)(1 + γνσ) =ϵm t σ¯ D γσ −1−(1 + ν) + (1 + ν)λ(1 + νγσ)−νλ(1 + γνσ) + (1 −λ)(1 + γνσ) (νλ −1 + λ)(1 + γνσ) =ϵm t σ¯ D γσ −1−1−ν+1+γνσ (νλ −1 + λ)(1 + γνσ) =ϵm t νσ ¯ D (νλ −1 + λ)(1 + γνσ) 53 and wages ˆwt+1 =νˆ HB t+1 + 1/σˆcB t+1 =ννλγσ −1 + λ (νλ −1 + λ)(1 + γνσ)¯ D ϵm t+ϵm t ν¯ D (νλ −1 + λ)(1 + γνσ) =ϵm t¯ Dν νλγσ −1 + λ+ 1 (νλ −1 + λ)(1 + γνσ) =ϵm t ¯ Dνλ νλ −1 + λ and inflation ˆ Πt+1 =βˆ Πt+2|t+1 +κˆwt+1 =ϵm t ¯ Dνλκ νλ −1 + λ Now, we are in a position to solve for time t. Solving the Euler equation forward we have ˆcS t=−σϵm t From the NKP we have an expression for today inflation ˆ Πt=βˆ Πt+1|t+κˆwt=ϵm t ¯ Dνλκβ νλ −1 + λ+κˆwt Using the borrowers BC we have γˆcB t+¯ D(ˆ Rt−1−ˆ Πt) = ˆwt+ˆ HB t γˆcB t−ϵm t¯ D¯ Dνλκβ νλ −1 + λ−¯ Dκν ˆ HB t−¯ Dκ/σˆcB t=νˆ HB t+ 1/σˆcB t+ˆ HB t which yields to ˆcB t=σ(1 + ν(1 + ¯ Dκ)) γσ −1−¯ Dκ ˆ HB t+¯ D2σνλκβ e1e0 ϵm t where e1=γσ −1−¯ Dκ and e0=νλ −1 + λ. Combining the labor supply decision we have νˆ HS t+σ−1ˆcS t=νˆ HB t+σ−1ˆcB t νˆ HS t−ϵm t=νˆ HB t+1 + ν+ν¯ Dκ γσ −1−¯ Dκ ˆ HB t+¯ D2νλκβ (γσ −1−¯ Dκ)(νλ −1 + λ)ϵm t which yields to ˆ HS t=1 + νγσ ν(γσ −1−¯ Dκ)ˆ HB t+¯ D2νλκβ +e0e1 νe0e1 ϵm t where e1=γσ −1−¯ Dκ and e0=νλ −1 + λ. Combining the aggregate conditions we have λγˆcB t+1 + (1 −λγ)ˆcS t+1 =λˆ HB t+1 + (1 −λ)ˆ HS t+1 λγ σ(1 + ν(1 + ¯ Dκ)) γσ −1−¯ Dκ ˆ HB t+¯ D2σνλκβ e1e0 ϵm t+ (1 −λγ)[−σϵm t] =λˆ HB t+1 + (1 −λ)1 + νγσ ν(γσ −1−¯ Dκ)ˆ HB t+¯ D2νλκβ +e0e1 νe0e1 ϵm t 54 ˆ HB tλγνσ(1 + ν(1 + ¯ Dκ)) ν(γσ −1−¯ Dκ)−λν(γσ −1−¯ Dκ) ν(γσ −1−¯ Dκ)−(1 −λ)(1 + νγσ) ν(γσ −1−¯ Dκ) =ϵm tσ(1 −λγ)−γλ ¯ D2σνλκβ e1e0 + (1 −λ)¯ D2νλκβ +e0e1 νe0e1 Focusing on terms inside the left hand side square bracket we have ν−1e−1 1νλ(σγ +σγν(1 + ¯ Dκ)) −λν(γσ −1−¯ Dκ)−(1 −λ)(1 + νγσ) =ν−1e−1 1νλ(1 + σγν)(1 + ¯ Dκ)−(1 −λ)(1 + νγσ) =ν−1e−1 1(1 + σγν)(νλ(1 + ¯ Dκ)−1 + λ) Focusing on terms inside the right hand side square bracket we have (νe0e1)−1νσ(1 −λγ)e0e1−νγλ(¯ D2σνλκβ) + (1 −λ)( ¯ D2νλκβ +e0e1) = (νe0e1)−1νσ(1 −λγ)e0e1−νγλ(¯ D2σνλκβ) + (1 −λ)¯ D2νλκβ + (1 −λ)e0e1 = (νe0e1)−1e0e1(νσ(1 −λγ)+1−λ)−νγλσ ¯ D2νλκβ + (1 −λ)¯ D2νλκβ = (νe0e1)−1νσe0e1+e0e1(1 −λ−νσλγ) + ¯ D2νλκβ(1 −λ−νσλγ) = (νe0e1)−1νσe0e1+ (e0e1+¯ D2νλκβ)(1 −λ−νσλγ) Rearranging terms we have ˆ HB t=νσe0e1+ (e0e1+¯ D2νλκβ)(1 −λ−νσλγ) (1 + σγν)(νλ(1 + ¯ Dκ)−1 + λ)(νλ −1 + λ)ϵm t(F.2) where e1=γσ−1−¯ Dκ and e0=νλ−1+λ. While still not very tractable we can derive a set of sufficient conditions such that the latter expression becomes positive. These conditions are 1. λ < 1 1+ν(1+ ¯ Dκ) 2. σ < 1+ ¯ Dκ γ Condition 1 implies that e1= [νλ(1+ ¯ Dκ)−1+λ]<0; this implies also that (νλ−1+λ)<0. Thus, if condition 1 holds, the denominator is positive. Condition 2 implies that e0= (σγ −1−¯ Dκ)<0; this implies also that e0e1>0. Moreover, if condition 2 hold, it is the case that λ < 1 1 + ν(1 + ¯ Dκ)<1 1 + νσγ The latter implies that (1 −λ−νσλγ)>0. Therefore also the numerator is positive. These conditions imply also that the coefficient in (F.1) is positive. 55 Figure G.12: Labor Supply Policy Functions with a= 0 and σ= 0.5 Figure G.13: Consumption policy function with a= 0 and σ= 0.5 62 Figure G.14: Impulse responses to a 25 basis points Monetary Policy Shock with a= 0 and σ= 0.5 Figure G.15: Labor Supply Policy Functions with a= 0 and σ= 0.25 63 Figure G.16: Consumption policy function with a= 0 and σ= 0.25 Figure G.17: Impulse responses to a 25 basis points Monetary Policy Shock with a= 0 and σ= 0.25 64 G.3 IRFs decompositions HANK Figure G.18: Decomposition of consumption Response in HANK. Notes: Note: Percent deviation in aggregate labor hours from steady state, decomposed into marginal channels: interest rate, dividends, taxes, and wages. 65 Figure G.19: Decomposition of consumption Responses by Income Bin — HANK. Notes: Notes: Each panel shows percent deviation in labor hours from steady state, decomposed into marginal channels: interest rate, dividends, taxes, and wages. 66 G.4 HANK vs HANK-HomL Figure G.20: Impact response of labor supply across income states in HANK vs the aggregate impact response in HANK-HomL 67 Figure G.21: Direct vs indirect effects of monetary policy on aggregate consumption in HANK vs HANK-HomL for baseline σ. 68 Table 2in the main text highlights that accounting for heterogeneity in labor supply has quantitatively significant implications, notably lowering the economy’s average MPC. This, in turn, affects the transmission of monetary policy. To illustrate this we compare here the dynamic responses to a contractionary monetary policy shock in the HANK and HANKHomL models. Figure G.22 reports aggregate impulse responses for interest rates, inflation, output, wages, dividends, and the share of hand-to-mouth households. Aggregate price and dividend dynamics are broadly similar across models, as expected given their identical firm and policy structure. However, two notable differences emerge. First, the HTM share rises more and remains elevated longer in HANK, suggesting that flexible labor supply amplifies inequality in downturns.Second, aggregate consumption declines by 16% less on impact in HANK compared to HANK-HomL. This muted response reflects the additional margin of adjustment provided by heterogeneous labor supply, which allows low-income households to buffer shocks through work effort. We explore the distributional responses that drive this result next. Figure G.23 shows that, by construction, labor supply responses are almost identical for the median agent type (34–66%). At the bottom of the distribution, agents increase their labor supply, consistent with our empirical evidence. In contrast, upper-middle and topincome households reduce their labor supply more in the HANK model compared to HANKHomL. This highlights that the left tail of the labor supply distribution is responsible for the muted amplification of monetary policy on aggregate demand. Figure G.24 shows how these labor responses translate into individual consumption dynamics. The consumption decline is most severe at the bottom of the distribution in both models, but the drop is smaller and less persistent in the HANK model. At the top of the distribution, consumption responses are very similar across models. Another way to quantify the role of different households across the income distribution in shaping the aggregate effects of monetary policy is to compute their respective contributions to the overall impact on consumption and labor supply, measured in basis point deviations. Figure G.25 presents the results. 69 Figure G.22: Impulse Responses of Core Macroeconomic Variables: HANK-HomL vs HANK Figure G.23: Labor Supply Responses Across the Income Distribution 70 Figure G.24: Consumption Responses Across the Income Distribution Figure G.25: Contribution of each income bin to the aggregate response. (a) Hours (b) Contribution of each income bin to the aggregate response. (c) Consumption 71