Frisch Elasticity Of Labor Supply Research Articles

The Norwegian tax holiday: Salience, labor supply responses, and frictions

AbstractAn emerging consensus is that the Frisch elasticity of labor supply is small. This may reflect a lack of salience, inelastic preferences, or prevalence of frictions. Studying survey data collected during a tax holiday in Norway, when earnings were untaxed during a transition between tax systems, I report three findings. First, 80 per cent of adults were aware of the tax holiday. Second, one fifth of adults responded by working more. Third, frictions in adjusting working hours or nonworking time appear to be the reason for a majority of nonresponses. The findings support the long‐held notion that labor supply choices are constrained.

Should Italy switch to a flat tax? An assessment based on a heterogeneous agents OLG model

We use a heterogeneous agents overlapping generations (OLG) model to quantitatively assess the impact of a reform in which a personal income tax with increasing marginal tax rates is replaced by a flat tax possibly complemented with a deduction. The value of the flat tax rate is set in order to balance the government budget and accordingly it increases with the value of the deduction. The model is calibrated and simulated for Italy. For low values of the deduction, aggregate labor supply increases, though this aggregate effect masks a completely different impact on the intensive and the extensive margin of labor supply: in particular, the activity rate is reduced by the introduction of a flat tax. As to inequality, it rises and this increase can be mitigated by using an higher value of the tax deduction, which however dampens down the positive effect of a flat tax on economic performance. Finally, the effect of a flat tax on social welfare crucially depends on the degree of inequality aversion embedded in the social welfare function and on the Frisch elasticity of labor supply.

Accounting for limited commitment between spouses when estimating labor-supply elasticities

The Frisch elasticity of labor supply can be estimated by regressing hours worked on the hourly wage rate, controlling for consumption of the individual worker. However, most household panel surveys contain consumption information only at the household level. We show that proxying individual consumption by household consumption biases estimated Frisch elasticities downward as limited commitment in the household induces individual consumption to behave differently from household consumption. We develop an improved estimation approach that eliminates this bias by exploiting information on the composition of household consumption to infer its distribution. Using PSID data, we estimate Frisch elasticities of about 0.65 for men and 0.8 for women.

THE ROLE OF THE FRISCH ELASTICITY ON HOUSEHOLDS' BEHAVIOR USING THE ENDOGENOUS DISCOUNT FACTOR MODEL

Decisions made by households and society with regard to the economy are heavily influenced by the role and significance of the variables of discount factor and Frisch elasticity of labor supply, on capital formation and consumption, which are among the most significant sources of interest rate, consumption basket, and household leisure. The existence of the endogenous discount factor and the Frisch elasticity of labor supply, which demonstrate the patience of society with regard to consumption and the choice of the household's work-and-leisure mix, respectively, point to significant changes in the household's decisions that may influence the portfolio of consumption and leisure. In order to develop a DSGE model utilizing data from the Iranian economy for the years 1998 to 2020, this article explores the effects of two variables, the endogenous discount factor and Frisch's elasticity, on macroeconomic variables and household performance. The findings show that in a model with an endogenous discount component and a lower value of Frisch's elasticity, the effect of the technological shock on consumption, output, and household income variables is positive and more significant, but it is negative on the debt variable. Thus, it can be said that in general, given that the household is sensitive to the type of discount factor and the extent of the labor supply's Frisch elasticity and that these two factors are crucial in helping the household decide which purchases and activities to include in its basket of leisure activities in order to change its expected utility, an increase in Frisch's elasticity coefficient along with the endogenous discount factor in the household will change its expected utility. Additionally, this road has evolved into the best one for household decisions, and in the best distribution of resources, households place a higher value on leisure and self-importance.

Impact of oil price uncertainty shocks on China’s macro-economy

This study investigates the impacts of crude oil price uncertainty shocks on China’s macro-economy using empirical and theoretical approaches. The vector auto-regression with stochastic volatility in mean (VAR-SVM) model reveals that increasing oil price uncertainty significantly depresses output and raises inflation. To fully understand the transmission channels of oil price uncertainty shocks, we develop a new Keynesian dynamic stochastic general equilibrium (DSGE) model that incorporates oil demand of household, intermediate sector, and transportation sector. Increasing income uncertainty induced by high oil price volatility leads to enhanced precautionary saving and thus a decrease in consumption, particularly durable consumption, of individual households. The precautionary working mechanism is plausible in the changes of households’ labor supply and firms’ production behaviors when oil price uncertainty increases. Furthermore, with decreasing forward-looking market demand, intermediate firms choose higher prices to avert risk, which results in higher inflation in China. To explore how to mitigate the negative effects of oil price uncertainty, we consider a number of possible factors. The results illustrate that increasing competitiveness among transportation firms, reducing oil intensity of intermediate sector, targeting headline inflation by the central bank, and decreasing the Frisch elasticity of labor supply are effective measures. Our findings also suggest that deregulation of refined oil price in China would not amplify negative effects of oil price uncertainty.

Identifying key aspects of household behavior in a representative agent framework

We study three key aspects of household behavior, i.e. the form of household preferences, the existence of interdependence between consumption and leisure choices, and the Frisch elasticity of labor supply. We find that an appropriate form of household preferences to use in non-recursive utility functions that incorporates the feature of interdependence is of the Cobb-Douglas type. By solving the household maximization problem, we derive a simultaneous system of two equations, a consumption equation and a labor supply equation, and estimate them with non-linear GMM. Regarding our estimates, the weight of consumption in the utility function, which is on the upper side of the relevant estimates in the literature, and the elasticity of intertemporal substitution seem to drive up the Frisch elasticity value. Our work highlights the importance of both the choice of the form of household preferences and the appropriate estimation procedure in the household maximization problem for obtaining reasonable values of the preference parameters, especially the Frisch elasticity. Our results may be useful for researchers working with the calibration of preference parameters in DSGE models.

Оценка межвременной эластичности замещения предложения труда для замужних женщин в России

This paper provides an econometric analysis of the labor supply function of married women in Russia based on data from RLMS HSE and methodology from the work (Heckman, MaCurdy, 1980), in which decisions about entering the labor market and the intensity of work are made within a dynamic optimization problem. It is shown that the husband’s leisure and the number of children living in the household have a negative effect on the woman’s hours worked. The estimate of the Frisch elasticity of labor supply with respect to wages lies near 0.16.

Accounting for Limited Commitment between Spouses When Estimating Labor-Supply Elasticities

The Frisch elasticity of labor supply can be estimated by regressing hours worked on the hourly wage rate, controlling for consumption of the individual worker. However, most household panel surveys contain consumption information only at the household level. We show that proxying individual consumption by household consumption biases estimated Frisch elasticities downward as limited commitment in the household induces individual consumption to behave differently from household consumption. We develop an improved estimation approach that eliminates this bias by exploiting information on the composition of household consumption to infer its distribution. Using PSID data, we estimate Frisch elasticities of about 0.7.

Reconciling Jaimovich–Rebello preferences, habit in consumption and labor supply

This note studies a form of a utility function of consumption with habit and leisure that (a) is compatible with long-run balanced growth, (b) hits a steady state observed target for hours worked and (c) is consistent with micro-econometric evidence for the inter-temporal elasticity of substitution and the Frisch elasticity of labor supply. Employing Jaimovich–Rebello preferences our results highlight a constraint on the preference parameter needed to target the steady-state Frisch elasticity. This leads to a lower bound for the latter that cannot be reconciled empirically with external habit, but the introduction of a labor wedge solves the problem. We also propose a dynamic Frisch inverse elasticity measure and examine its business cycle properties.

Land-price dynamics and macroeconomic fluctuations with nonseparable preferences

In this paper, we introduce a complementary relationship between consumption and labor hours by revising the household’s period utility function in Liu et al. (2013). The revision concomitantly allows for a finite Frisch elasticity of labor supply and a stronger consumption smoothing motive. We find that, in general, the estimation of Liu et al. (2013) is quite robust. In addition, the propagation mechanism of the credit constraint triggered by a housing demand shock still persists. However, the amplification effect of the credit constraint triggered by the housing demand shock on key macroeconomic variables is greatly muted. We also find that, except for land price fluctuations, the housing demand shock cannot act as the primary force to drive the fluctuations in other macroeconomic variables.

Labor Market Volatility in the RBC Search Model: A Look at Hagedorn and Manovskii’s Calibration

The standard Diamond–Mortensen–Pissarides (DMP) labor search model generates low volatility in labor market variables relative to average labor productivity, the so-called Shimer puzzle. Hagedorn and Manovskii (Am Econ Rev 98(4):1692–1706, 2008) demonstrate that recalibrating the standard DMP model to be consistent with the small vacancy posting cost and wage elasticity observed in the data can resolve the Shimer puzzle. They close by stating that their calibration strategy would also resolve the Shimer puzzle in the real business cycle (RBC) search framework. In this paper, we examine their claim and find that their strategy resolves the Shimer puzzle in the RBC search model for linear preferences (with risk neutrality and infinite Frisch elasticity of labor supply), but falls significantly short for more standard assumptions on the degree of relative risk aversion (of 1–2) and Frisch elasticity (of 2–3), in line with empirical estimates. While our conclusions are based on highly accurate solutions using the Generalized Stochastic Simulation Algorithm, we also assess the accuracy of a frequently used linearization method and its implications for the assessment of labor market volatility.

Optimal Taxation with Private Insurance

We derive a fully nonlinear optimal income tax schedule in the presence of a private insurance market. The optimal tax formula is expressed in terms of sufficient statistics?such as the Frisch elasticity of labor supply, social preferences, and hazard rates of the income distributions?as in the standard Mirrleesian taxation without private insurance (e.g., Saez (2001)). However, in the presence of a private market, the standard sufficient statistics are no longer sufficient. The optimal tax rate also depends on how private savings interact with public insurance? through substitution and crowding in/out. Based on our formula, we compute the optimal tax schedule using a quantitative general equilibrium model calibrated to reproduce the U.S. income distribution.

Estimates of the Frisch Elasticity of Labor Supply: A Review

This article assesses the literature on the responsiveness of the supply of labor in the case of a temporary change in after-tax compensation. In particular, it reviews the literature on the Frisch elasticity — the sum of the substitution elasticity and a measure of people’s willingness to trade work for consumption over time. The authors find that the estimates of the Frisch elasticity most relevant for fiscal policy analysis range from 0.27 to 0.53 (with a central estimate of 0.40). Using that range, they illustrate how different Frisch elasticities affect the responsiveness of labor supply to changes in fiscal policies. The illustration shows that estimation of the Frisch elasticity can have a significant influence on analyses of the economic effects of such policy changes.

Are taxes a good predictor of time use patterns? Examining the role of some key elasticities

A home-production model is used to explain the allocation of time between leisure, work and home production. We show that differences in taxes alone explain to a great extent the time use patterns in a set of OECD countries once several key elasticities — the elasticity of substitution between market- and home-produced goods, the Frisch elasticity of labor supply, and the relative risk aversion — are set according to empirical evidence. We also show that a realistic calibration of these key elasticities results to be more important than introducing government expenditures substitutive for home-produced goods in order to bring the model's time use predictions in line with data. This is true even for Scandinavian countries, which had posed a challenge in previous studies.

Externalities, endogenous productivity, and poverty traps

We present a version of the neoclassical model with an endogenous industry structure. We construct a distribution of firms׳ productivity that implies multiple steady-state equilibria even with an arbitrarily small degree of increasing returns to scale. While the most productive firms operate across all the steady states, in a poverty trap less productive firms operate as well. This results in lower average firm productivity and total factor productivity. The distributions of employment by firm size across steady states are consistent with the empirical observation that poor countries have a higher fraction of employment in small firms than rich countries. Differences in output and total factor productivity across steady states are increasing in the degree of returns to scale, the capital share, and the Frisch elasticity of labor supply.

Technical Note on "Assessing Bayesian Model Comparison in Small Samples"

This technical note is developed as a companion to the paper ‘Assessing Bayesian Model Comparison in Small Samples’ (Globalization and Monetary Policy Institute working paper no. 189). Taking the workhorse open-economy model of Martinez-Garcia and Wynne (2010) with nominal rigidities under monopolistic competition as our Data-Generating Process, we investigate with simulated data how Bayesian model comparison based on posterior odds performs when the model becomes arbitrarily close to a closed-economy and/or an economy with flexible prices and perfect competition. This technical note elaborates on three key technical points relevant for Martinez-Garcia and Wynne (2014). First, we explain the building blocks of the open-economy model of Martinez-Garcia and Wynne (2010). We also derive the equilibrium conditions (and the steady state) under producer-currency pricing. Second, we discuss the log-linearization of the equilibrium conditions around the deterministic steady state and our benchmark parameterization. The linear rational expectations model that results from the log-linearization is used to simulate the data under our benchmark parameterization. These simulated data is used in Martinez-Garcia and Wynne (2014) to conduct their Bayesian model comparison exercises. Third, we describe the Bayesian estimation and model comparison techniques with special emphasis on the questions of: (a) how we elicit priors on the models themselves and the parameters of a given model, and (b) how we compute posterior model probabilities. Simultaneously, commentary is provided whenever appropriate to clarify the economic significance of the assumptions embedded in our workhorse open-economy model. JEL codes: C11, C13, F41 * Enrique Martinez-Garcia, Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201. 214-922-5262. enrique.martinez-garcia@dal.frb.org. Mark A. Wynne, Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201. 214-922-5159. Mark.A.Wynne@dal.frgb.org. We would like to thank Nathan Balke, Maria Teresa Martinez-Garcia and Valentin Martinez Mira for helpful suggestions. Diego Vilan was a co-author in a related project and contributed to the early stages of development of this paper. We gratefully acknowledge the outstanding research assistance provided by Valerie Grossman, the help of Kuhu Parasrampuria, and the Federal Reserve Bank of Dallas support. The views in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System. 1 New Open Economy Macro (NOEM) Model The NOEM model that we use in Martinez-Garcia and Wynne (2014) is a variant of the workhorse model of Clarida et al. (2002) introduced in Martinez-Garcia and Wynne (2010). This is a symmetric two-country model with a continuum of unit mass of households and consumption varieties, equally divided between the Home country and the Foreign country. We employ this framework because it integrates an open-economy New Keynesian Phillips curve that ‡eshes out the content of the global slack hypothesis into a stylized dynamic stochastic general equilibrium model, but also because it nests model speci…cations without nominal rigidities (monetary neutrality) and/or under autarky (closed-economies) as limiting cases. We abstract from a number of relevant modelling features like capital and investment (see, e.g., Chari et al. (2002), and Martinez-Garcia and Sondergaard (2008)), durable goods (see, e.g., Engel and Wang (2011)), and monopolistically competitive suppliers of labor (see, e.g., Clarida et al. (2002)) in order to assess Bayesian model comparison solely in the presence of e¤ects from increased trade openness and monetary non-neutrality induced by nominal rigidities. Households. The lifetime utility for the representative household in the Home country is additively separable in consumption, Ct, and labor, Lt, i.e., X+1 =0 Et ln (Ct+ ) 1 1 + ' (Lt+ ) 1+' ; (1) and similarly the lifetime utility for the representative household in the Foreign country is additively separable in consumption, C t , and labor, L t , i.e., X+1 =0 Et ln C t+ 1 1 + ' L t+ 1+' ; (2) where 0 0 is the inverse of the Frisch elasticity of labor supply. The inverse of the intertemporal elasticity of substitution is equal to 1 under the assumption of log-utility on consumption. The Home household maximizes its lifetime utility subject to the sequence of budget constraints,

Comment

Previous articleNext article FreeCommentRobert ShimerRobert ShimerUniversity of Chicago and NBER Search for more articles by this author University of Chicago and NBERPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreThis paper provides a meta-analysis of how total hours worked respond to permanent and transitory changes in the tax code. Chetty, Guren, Manoli, and Weber’s thesis is that existing studies provide important information about the Hicksian and Frisch elasticities of labor supply. The labor supply elasticity has been a key parameter in most macroeconomic models since Lucas and Rapping (1969), and so the authors argue that we need systematic evidence to pin down its value. In particular, they conclude that the elasticity of labor supply in response to a transitory shock to after-tax earnings is about 0.25 on the extensive margin and twice as large on the intensive margin. This is far smaller than macroeconomic models need in order to explain the volatility of employment and hours worked over the business cycle.The authors illustrate the discrepancy between microeconomic and macroeconomic elasticities of labor supply by examining three real-world changes in the tax code through the lens of a particular life cycle model with indivisible labor (Rogerson and Wallenius 2009). Iceland cut taxes to zero for one year, in 1987. In response, employment rose, as most theories would predict. However, when they simulate the tax cut in the laboratory of the Rogerson Wallenius model, the model predicts an employment response that is an order of magnitude larger than what happened in reality. Similarly, Canada significantly reduced the taxes of some welfare recipients for three years. In response, many of the workers eligible for the tax break entered the labor force. But once again, when they simulate the tax cut in the Rogerson Wallenius laboratory, the theory predicts an employment response that is an order of magnitude larger than what happened in reality. The third experiment, the permanent introduction of the EITC in the United States, caused a modest increase in employment, in line with what the Rogerson Wallenius model predicts.This is an impressive paper and I have no major qualms with any component of the analysis. Instead, I will concentrate my comments on the interpretation of the results. In particular, how should we reconcile the low elasticity of labor supply in response to temporary tax changes with the large volatility of employment relative to real wages over the business cycle? The authors state that, Any macro model that relies primarily on changes in labor supply to generate business cycle fluctuations must feature a large extensive margin Frisch elasticity. As a result, any such model will overpredict the response to temporary wage changes, such as the tax holiday in Iceland and work subsidies in Canada.They therefore conclude that their analysis points “in favor of recent macro models that feature a cyclical ‘labor wedge’ between the marginal rate of substitution of consumption for leisure and the marginal product of labor” and that their “estimates could be used to calibrate the labor supply component of models that seek to explain aggregate fluctuations with labor wedges.”My discussion explores the validity of this conclusion. I show formally that if workers are not on their labor supply curve—for example, because wages are rigid—then a model can simultaneously generate a small micro elasticity (response to a tax cut) and a large macro elasticity (response to business cycle shock), consistent with the evidence in this paper. Interestingly, however, in a simple example, neither the micro nor the macro elasticity reveal any information about the structural parameter of interest, the elasticity of labor supply. Instead, both reveal something about the nature of the wage rigidity. This significantly changes the interpretation of the results in this paper, an issue I return to at the end of my discussion.I focus on a simple continuous time model with a representative household and a representative firm. The household chooses how much to consume c(t) and how much leisure to enjoy l(t) to maximize its expected utilitysubject to a lifetime budget constraintwhere w(t) is the pretax wage, n(t) is labor supply, τ(t) is the labor income tax rate, q(t) is the price of consumption at date t relative to date 0 (so q(0) = 1), a0 is the present value of wealth and transfer income, and the household has a unit endowment of time to either work or enjoy leisure, n(t) + l(t) = 1. With this specification of preferences, the Frisch elasticity of labor supply is .A firm chooses how much labor to hire to maximize its expected profitssubject to the law of motion for capital k(t) = x(t) − dk(t), where x(t) is investment and δ is the depreciation rate on capital. This notation is deliberately vague about the nature of uncertainty, which might reflect variation in productivity and taxes. Still, to start I will restrict attention to onetime shocks that do not affect the probability distribution over future outcomes.In a competitive economy, household optimization implies that the marginal rate of substitution between consumption and leisure is equal to the after-tax wage, while firm optimization implies that the marginal product of labor is equal to the wage. Eliminating the wage givesA onetime shock to the tax rate or to productivity that does not alter the probability distribution over future outcomes cannot affect the capital stock and does not affect consumption.1 Therefore, their impact on labor supply is closely linked:Two conclusions follow. The first is that if the capital share of income is positive, α > 0, neither experiment uncovers the Frisch labor supply elasticity because of the general equilibrium impact on wages. The second is that this model cannot explain why the real-world response to the two experiments is so different.One possibility is that wages do not adjust to clear the labor market. For expositional purposes, suppose there is a minimum wage w that exceeds the equilibrium wage w(t). At this wage, households are rationed on their labor supply. That is, although households can choose how much to consume, n(t) is pinned down from firms’ labor demand, which equates the marginal product of labor to the binding minimum wage: . We can now redo the tax experiment and the productivity shock experiment:According to the definitions in this paper, the former is a micro elasticity of labor supply (zero) while the latter is a macro elasticity (three, if the capital share of income is one-third). Although these elasticities are very different, neither of them has anything to do with the Frisch elasticity of labor supply −f′(1 − n)/nf′′(1 − n).Of course, the assumption that a minimum wage binds for most workers is untenable, so the relevance of this toy model may seem limited. But the basic insights from this model carry over to a search theoretic environment with wage rigidities (Hall 2005; Shimer 2012a, 2012b). My treatment here follows Shimer (2012b). As before, there is a representative household that has preferences over consumption and leisure and faces a single lifetime budget constraint:In this formulation, I assume that the household is large and so interpret n(t) as the fraction of household members who are employed. Unfortunately, the household cannot control the path of n (t) = 1 − l(t), which instead is determined by firms’ recruiting decisions. It therefore makes its consumption decision taking the path of employment and leisure as given.The representative firm chooses investment x(t) and recruiting v(t) to maximize the present value of its profitssubject to a law of motion for capital k(t) = x(t) − k(t) and a law of motion for employment n(t) = m(q(t))v(t) − sn(t). The firm employs n(t) workers. Of those, n(t) – v(t) are engaged in production with the usual Cobb–Douglas technology, while v(t) are recruiters, attracting workers at rate μ(θ(t), the job-filling rate. The job-filling rate in turn depends on the recruiter–unemployment ratio, θ(t) = v(t)/l(t). The representative firm takes the recruiter–unemployment ratio as given, although of course it is determined in equilibrium. Finally, workers separate for unemployment at rate s.A key feature of this model is that there is a range of wages at which households are willing to supply labor and firms are willing to employ workers. In what follows, I assume that the wage path is unaffected by transitory tax and productivity shocks. One can think of wage rigidities as coming from a self-fulfilling prophecy: on this wage path, every worker strictly prefers employment to unemployment and every firm prefers employing its workers rather than firing them. There is, therefore, no compelling reason for the wage path to adjust following a small shock. This is the essential insight of Hall (2005).Given the setup of the model, it is straightforward to verify that recruiting and investment at time t depend on the endogenous state variables k(t) and n(t), on the exogenous path for future wages w(t′), t′ > t, on the endogenous path for intertemporal prices q(t′), and on future productivity shocks A(t′). Intertermporal prices are in turn pinned down from the household first-order condition and so depend only on consumption growth, . Two conclusions follow immediately. First, household preferences over leisure have absolutely no impact on employment or the response of employment to shocks. In particular, there is no way to recover the Frisch elasticity of labor supply from either micro or macro experiments in this model economy. Second, taxes only affect employment by changing consumption growth and hence the intertemporal price q(t). In contrast, productivity shocks also have a direct effect on employment by altering the marginal product of labor. It therefore will always be the case that sufficiently transitory productivity shocks will have a bigger impact on employment than will equally transitory tax changes, as in the toy model I started with.Of course, this model is still highly stylized and the robustness of some of these conclusions may be suspect. For example, I have imposed for expositional simplicity that households have no control over employment. Shimer (2012a) assumes that households also have a search decision, allocating nonemployed workers between unemployment u(t) and leisure , with employment n (t) = 1 − u(t) − l(t) given. Unemployed workers are more likely to find a job than nonparticipants, but nonparticipants get more leisure. In this case, productivity shocks still directly impact firms’ recruiting decisions, but now taxes affect households’ labor force participation decision. Still, a regression of employment on taxes does not directly reveal the elasticity of labor supply because firms will respond to an increase in workers’ job search by economizing on recruiting so as to stabilize employment near their desired level. Conversely, firms’ desire to recruit in response to a productivity shock is mitigated if households offset any increase in recruiting with a reduction in their search intensity. This suggests that the response of employment to a productivity shock will depend on the elasticity of labor supply even if wages are fixed.The bottom line is that rigid wages models offer a reasonable hope of reconciling the low micro elasticity of labor supply with the high macro elasticity; however, it is as yet unclear whether either source of variation will be useful for identifying the true preference parameter, at least without imposing a full structural model.The final question is why we care what the function ϕ looks like if it does not have much impact on these sorts of outcomes. There are two potential answers. First, the elasticity of labor supply is important for understanding the costs of cyclical fluctuations and of tax rate distortions. The more elastic is labor supply, the less households suffer from their inability to choose employment at each moment. Second, a deeper theory of wage determination might recognize that if households are very dissatisfied with the current level of employment, they will find a mechanism for changing the wage and so changing employment. This suggests that an elastic labor supply is necessary for wages to be rigid in response to large, persistent shocks. These claims are both speculative at this stage, but there is no doubt that Chetty, Guren, Manoli, and Weber have highlighted some important unresolved issues in the literature on labor supply. Notes For acknowledgments, sources of research support, and disclosure of the author’s material financial relationships, if any, please see http://www.nber.org/chapters/c12749.ack.1This last conclusion would not hold exactly if the shock were persistent, which explains why I focus on onetime shocks.ReferencesHall, Robert E. 2005. “Employment Fluctuations with Equilibrium Wage Stickiness.” American Economic Review 95 (1): 50–65.First citation in articleCrossrefGoogle ScholarLucas, Robert E., and Leonard A. Rapping. 1969. “Real Wages, Employment, and Inflation.” Journal of Political Economy 77 (5): 721–54.First citation in articleLinkGoogle ScholarRogerson, Richard, and Johanna Wallenius. 2009. “Micro and Macro Elasticities in a Life Cycle Model with Taxes.” Journal of Economic Theory 144 (6): 2277–92.First citation in articleCrossrefGoogle ScholarShimer, Robert. 2013. “Job Search, Labor Force Participation, and Wage Rigidities.” Forthcoming in Advances in Economics and Econometrics: Theory and Applications, Tenth World Conference, edited by Daron Acemoglu, Manuel Arellano, and Eddie Dekel. Cambridge University Press.First citation in articleGoogle Scholar———. 2012b. “Wage Rigidities and Jobless Recoveries.” Journal of Monetary Economics 59 (S): S65-–S77.First citation in articleGoogle Scholar Previous articleNext article DetailsFiguresReferencesCited by NBER Macroeconomics Annual Volume 272012 Sponsored by the National Bureau of Economic Research (NBER) Article DOIhttps://doi.org/10.1086/669172 Views: 179Total views on this site Citations: 1Citations are reported from Crossref © 2013 by The National Bureau of Economic Research. All rights reserved.PDF download Crossref reports the following articles citing this article:Tian-neng HUANG, Jin-long XU, Ling-ling XIE Research on measurement of industrial structural transformation and upgrading level in resource-exhausted cities and its influencing factors:Based on panel data of 24 prefecture-level cities of China, JOURNAL OF NATURAL RESOURCES 36, no.88 (Jan 2021): 2065.https://doi.org/10.31497/zrzyxb.20210812

Aggregation and Labor Supply Elasticities

The aggregate Frisch elasticity of labor supply has played a key role in business cycle analysis. This paper develops a statistical aggregation procedure which allows for worker heterogeneity in observables and unobservables and is applicable to an individual labor supply function with non-employment as a possible outcome. Performing a thought experiment in which all offered or paid wages are subject to an unanticipated temporary change, we can derive an analytical expression for the aggregate Frisch elasticity and illustrate its main components: (i) the intensive and extensive adjustment of hours worked, (ii) the extensive adjustment of wages, and (iii) the aggregate employment rate. We use individual-specific data from the German Socio-Economic Panel (SOEP) for males at working-age in order to quantify each component. This data base provides indirect evidence on non-employed workers' reservation wages. We use this variable in conjunction with a two-step conditional density estimator to retrieve the extensive adjustment of hours worked and wages paid. The intensive hours' adjustment follows from estimating a conventional panel data model of individual hours worked. Our estimated aggregate Frisch elasticity varies between .63 and .70. These results are sensitive to the assumed nature of wage changes.

The Prospect of Higher Taxes and Weak Job Growth During the Recovery from The Great Recession: Macro versus Micro Frisch Elasticities

Labor input growth during the recovery of the U.S. economy from the Great Recession of 2008–2009 has been considerably lower than expected. A number of scholars have attributed this disappointing outcome to the prospect of higher taxes, induced by the fiscal imbalances that will materialize in coming decades under current policies. The paper examines this fiscal sentiment hypothesis from the perspective of a neoclassical growth model, under the assumption that the typical household's preferences can be represented by a utility function that implies a constant intertemporal (Frisch) elasticity of substitution for aggregate hours of work, and for a hypothetical tax regime that incorporates the Congressional Budget Office' s assessment of the U.S. fiscal situation. The paper finds that the empirical relevance of the fiscal sentiment hypothesis depends on whether this Frisch elasticity of labor supply is closer to the relatively large values needed to account for the observed volatility of labor input at business cycle frequencies, than to the lower values estimated by microeconomic and quasi-experimental studies.

Does Indivisible Labor Explain the Difference between Micro and Macro Elasticities? A Meta-Analysis of Extensive Margin Elasticities

Previous articleNext article FreeDoes Indivisible Labor Explain the Difference between Micro and Macro Elasticities? A Meta-Analysis of Extensive Margin ElasticitiesRaj Chetty, Adam Guren, Day Manoli, and Andrea WeberRaj ChettyHarvard University and NBER Search for more articles by this author , Adam GurenHarvard University Search for more articles by this author , Day ManoliUniversity of California, Los Angeles, and NBER Search for more articles by this author , and Andrea WeberUniversity of Mannheim Search for more articles by this author Harvard University and NBERHarvard UniversityUniversity of California, Los Angeles, and NBERUniversity of MannheimPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionMacroeconomic models of fluctuations in hours of work over the business cycle or across countries imply much larger labor supply elasticities than microeconometric estimates of hours elasticities. Understanding this divergence is critical for questions ranging from the sources of business cycles to the impacts of tax policy on growth and inequality. Starting with the seminal work of Rogerson (1988) and Hansen (1985), one leading explanation of the divergence is the extensive margin response created by indivisible labor supply. If labor supply is indivisible, changes in tax or wage rates can generate large changes in aggregate hours by inducing extensive margin (participation) responses even if they have little effect on hours conditional on employment. In view of this argument, modern macro models are calibrated to match low micro estimates of intensive margin elasticities. However, the extensive margin elasticity is usually treated as a free parameter that can be calibrated purely to match macroeconomic moments.We argue that the extensive margin elasticity should not be treated as a free parameter. Macro models should be calibrated to match micro estimates of extensive margin elasticities in the same way that they are calibrated to match micro estimates of intensive margin elasticities. The size of the extensive margin responses depends on the density of the distribution of reservation wages around the economy’s equilibrium. The same marginal density that determines the impacts of macroeconomic variation on aggregate employment also determines the impacts of quasi-experiments such as tax policy changes on employment rates. Micro estimates of extensive margin elasticities can therefore be used to calibrate macro models.1In this paper, we assess whether existing calibrations of macro models are consistent with micro evidence on extensive margin responses. In doing so, we find that it is crucial to distinguish between two types of elasticities: Hicksian and Frisch. The Frisch (marginal utility constant) elasticity controls intertemporal substitution responses to temporary wage fluctuations and is therefore the relevant parameter for understanding labor supply fluctuations over the business cycle.2 The Hicksian (wealth constant) elasticity controls steady-state responses to permanent wage changes and is therefore the relevant parameter for understanding differences in labor supply across countries with different tax systems. We use two approaches to comparing macro calibrations with micro evidence: simulations of quasi-experiments and a meta-analysis of micro elasticity estimates. Both approaches show that micro and macro evidence agree about Hicksian (steady state) elasticities but disagree about Frisch (intertemporal substitution) elasticities.We begin by simulating the impacts of policy changes that generate exogenous changes in incentives to work in a standard macro model and comparing the predicted responses with the findings of microeconometric studies. We use Rogerson and Wallenius’s (2009, henceforth, RW) calibrated model of life cycle labor supply as a benchmark model for this exercise. The RW model matches macro evidence by generating an intertemporal substitution elasticity of aggregate hours above 2 even when calibrated to generate a Frisch intensive-margin elasticity below 0.5. We simulate labor supply responses to three policies using this model: (1) a tax-free year in Iceland in 1987 studied by Bianchi, Gudmundsson, and Zoega (2001); (2) a randomized experiment providing temporary subsidies for work to welfare recipients in Canada (Card and Hyslop 2005); and (3) the 1994 expansion of the Earned Income Tax Credit (EITC) for low-income individuals in the United States (Meyer and Rosenbaum 2001). The first two examples are ideal for identifying Frisch elasticities because they induce temporary variation in wage rates. Bianchi, Gudmundsson, and Zoega (2001) find that employment rates in Iceland do indeed rise in 1987, but the increase is only one-fifth as large as that predicted by the RW model. Similarly, the calibrated RW model predicts intertemporal substitution responses to the work subsidies in Canada that are nearly four times larger than what Card and Hyslop observe in their data. The third example—the EITC expansion—generates permanent variation in tax rates and thus is well-suited for identifying steady-state elasticities. The RW model performs better in matching the impacts of the EITC expansion on employment rates because it generates a Hicksian aggregate hours elasticity of approximately 0.7, resulting in steady-state impacts of taxes on labor supply that are closer to micro estimates.While our quantitative results rest on the particular assumptions of the RW model, our qualitative conclusions apply more generally. Any macro model that relies primarily on changes in labor supply to generate business cycle fluctuations must feature a large extensive margin Frisch elasticity. As a result, any such model will overpredict the response to temporary wage changes such as the tax holiday in Iceland and work subsidies in Canada. Intuitively, fluctuations in employment over the business cycle and the employment effects of quasi-experimental wage changes are both fundamentally determined by the same density of the reservation wage distribution at the margin irrespective of model specification. Thus, any labor supply model that fits the quasi-experimental evidence cannot generate large fluctuations in employment over the business cycle.To explore whether the results of the three studies we consider in the simulations are representative of the broader empirical literature, we conduct a meta-analysis of quasi-experimental estimates of extensive margin elasticities. We summarize results from fifteen studies that span a broad range of countries, demographic groups, time periods, and sources of variation. These studies generally analyze changes in incentives for small subgroups of the population, permitting identification of labor supply elasticities that are not confounded by changes in equilibrium wage rates. Despite the great variation in methodologies, there is consensus about extensive margin elasticities. The mean extensive margin elasticity among the studies we consider is 0.28 and every estimate is below 0.43. The intertemporal substitution (Frisch) elasticity estimates for temporary policy changes turn out be quite similar to the steady-state elasticity estimates obtained from permanent policy changes. The small elasticities imply that most individuals are at a corner in their employment choices; that is, the density of individuals at the margin of employment is thin in practice.We conclude our analysis by evaluating whether extensive margin elasticities of around 0.25 as suggested by micro evidence are adequate to reconcile the gap between micro and macro estimates of aggregate hours elasticities. To do so, we summarize micro and macro estimates of Hicksian and Frisch elasticities on both the extensive and intensive margins. We find that micro and macro studies agree about the steady-state impacts of taxes on labor supply. Both micro and macro studies imply Hicksian extensive margin elasticities around 0.2. And both micro and macro evidence are consistent with intensive margin elasticities around 0.3 once one accounts for frictions that may attenuate observed micro estimates (Chetty, Friedman, et al. 2011; Chetty 2012). Prescott’s (2004) widely-cited cross-country data set implies an aggregate hours (extensive plus intensive) Hicksian elasticity of 0.7, only slightly larger than micro estimates.3 These findings indicate that labor supply responses to taxation could indeed explain much of the variation in hours of work across countries with different tax systems.4On the intertemporal substitution margin, the limited existing evidence on intensive margin elasticities suggests that values around 0.5 are consistent with both micro and macro data. However, micro and macro estimates of extensive margin intertemporal substitution elasticities differ by an order of magnitude. Quasi-experimental estimates of extensive margin intertemporal substitution elasticities are around 0.25. In contrast, pure equilibrium macro models, in which employment fluctuations are driven purely by preferences, imply intertemporal substitution extensive margin elasticities in excess of 2. Hence, the puzzle to be resolved is why employment rates fluctuate so much over the business cycle relative to what one would predict based on the impacts of tax changes on employment rates—that is, why micro and macro estimates of the Frisch extensive margin elasticity are so different.5 Even accounting for indivisible labor, micro studies do not support representative-agent macro models that generate Frisch elasticities above 1.There are two potential concerns that one may have with using microeconomic estimates to calibrate macroeconomic models. The first is that heterogeneity in extensive margin responses complicates the mapping from micro estimates to macro elasticities that reflect economy-wide behavior.6 This problem is compounded by the concern that micro studies sometimes exclude important subgroups that could matter for economy-wide extensive margin responses (Dyrda, Kaplan, and Ríos-Rull 2012). In practice, however, heterogeneity across subgroups appears to strengthen our main conclusion about agreement on the Hicksian elasticity but disagreement on the Frisch elasticity. The heterogeneity in micro estimates of extensive-margin Hicksian elasticities mirrors the heterogeneity observed in macro studies of steady-state responses. For instance, both micro and macro studies indicate that extensive-margin elasticities are higher for subgroups that are less attached to the labor force, such as single mothers and individuals near retirement. However, heterogeneity magnifies the discrepancy between micro and macro estimates of intertemporal substitution elasticities. Most notably, employment rates fluctuate substantially over the business cycle even for prime-age males, which stands in sharp contrast with the near-zero micro extensive margin Frisch elasticity estimates for this group.A second potential concern in mapping micro estimates to macro labor supply elasticities is that reduced-form micro studies may not directly identify the structural primitives of the reservation wage distribution that control extensive margin labor supply choices. This is particularly a concern if frictions prevent the labor market from clearing, as our analysis suggests. In a model with frictions, reduced-form micro elasticity estimates represent a convolution of the density of the reservation wage distribution at the margin and other structural parameters, such as the distribution of adjustment costs or search frictions or the degree of liquidity constraints. Importantly, the same reduced-form elasticities would also determine the impact of wage changes on labor supply over the business cycle in such an environment. Hence, micro estimates should continue to provide useful targets for calibrating macro models even though they do not identify the structure of preferences or other primitives necessary for normative analysis.7 However, especially when reduced-form elasticities combine several structural parameters, they may not be stable across settings. Because of this instability, one should not seek to calibrate macro models to match any single estimate of a micro elasticity. Nevertheless, one can gauge the range of plausible magnitudes by pooling evidence from many different studies and settings as we do here. The fact that every quasi-experimental study we review finds elasticities significantly less than 0.5 casts doubt upon macro models calibrated with extensive margin elasticities above 1.The article is organized as follows. The next section briefly reviews the existing literature on indivisible labor. In section III, we establish a terminology for the various elasticity concepts, as these terms are often used in different ways in the existing literature. Section IV reports simulations of the three quasi-experiments in the Rogerson and Wallenius (2009) model. Section V presents the meta-analysis of micro estimates. In section VI, we compare micro and macro evidence on the intensive and extensive margins. Section VII concludes. Details of the simulation methods and meta-analysis are given in the appendix.II. Indivisible Labor: BackgroundEquilibrium macroeconomic models—in which differences in hours of work are driven by preferences—require large labor supply elasticities to explain the variation in hours of work over the business cycle and across countries with different tax regimes. In contrast, quasi-experimental microeconometric studies of the impacts of tax reforms on hours of work and earnings typically obtain elasticities close to zero for most groups except very high income earners.8A large literature has posited that the discrepancy between micro and macro elasticities can be explained by indivisibilities in labor (e.g., Hansen 1985; Rogerson 1988; Cho and Rogerson 1988; Christiano and Eichenbaum 1992; Cho and Cooley 1994; King and Rebelo 1999; Chang and Kim 2006; Ljungqvist and Sargent 2006; Prescott, Rogerson, and Wallenius 2009; Rogerson and Wallenius 2009).9 If individuals cannot freely choose hours of work or face fixed costs of entry, aggregate employment depends upon the distribution of reservation wages in the economy. If this distribution has substantial density at the margin—that is, many individuals are indifferent between working and not working at prevailing wage rates—then a small reduction in wage rates could reduce aggregate hours of work significantly because many individuals will stop working. Yet the same change in wage rates may not affect hours of work conditional on employment very much, implying a small intensive margin labor supply elasticity. As a result, a model with large extensive margin elasticities and small intensive margin elasticities could match both the micro and macro evidence. Motivated by these results, modern macro models are calibrated to match micro estimates of intensive margin elasticities but typically calibrate the extensive margin elasticity purely to match macroeconomic moments (King and Rebelo 1999; Rogerson and Wallenius 2009; Ljungqvist and Sargent 2011).In parallel with the development of macro models of indivisible labor supply, a large microeconometric literature has recognized the importance of the extensive margin in the analysis of labor supply. Ashenfelter (1984) and Heckman (1984) discuss the importance of extensive margin labor supply choices in the analysis of aggregate fluctuations. Heckman and Killingsworth (1986) and Heckman (1993) review the literature on labor supply models that explicitly model participation decisions. More recent research has estimated extensive margin elasticities using quasi-experimental methods.However, macro models have not been calibrated to match micro evidence on extensive margin elasticities. One complication in performing such a calibration is that extensive margin elasticities vary with the wage rate unless the density of the reservation wage distribution happens to be uniform. Hence, any micro estimate of an extensive margin elasticity is necessarily local to the wage variation used for identification. However, this argument does not justify treating the extensive margin elasticity as a free parameter for two reasons. First, if the micro estimates are identified using variation similar to that used in macroeconomic comparisons, one will obtain the appropriate local elasticity relevant for macro calibrations. Second, the same problem arises when calibrating macro models with micro estimates of intensive margin elasticities, insofar as elasticities will only be constant on the intensive margin if utility happens to produce a constant-elasticity labor supply function. We revisit this issue in section VI and show that, if anything, observable heterogeneity in elasticities reinforces the conclusions drawn later.III. TerminologyIt is helpful to establish some conventions about terminology given the various elasticity concepts discussed in this paper. We distinguish between elasticities based on the margin of response (extensive vs. intensive) and the timing of response (intertemporal substitution vs. steady state). There are four elasticities of interest: steady-state extensive, steady-state intensive, intertemporal extensive, and intertemporal intensive. Each of these four elasticities can be estimated using both micro (quasi-experimental) and macroeconomic variation. We use the terms “micro” and “macro” elasticities exclusively to refer to the source of variation used to estimate the elasticity. The elasticity of aggregate hours—the relevant parameter for calibrating a representative agent model—is the sum of the extensive and intensive margin elasticities, weighted by hours of work if individuals have heterogeneous preferences (Blundell, Bozio, and Laroque 2011).The macro literature uses the term “macro elasticity” to refer to the Frisch elasticity of aggregate hours and “micro elasticity” to refer to the intensive-margin elasticity of hours conditional on employment (e.g., Prescott 2004; Rogerson and Wallenius 2009). We use different terminology here for two reasons. First, the intensive-margin is no more “micro” than the extensive margin; both are determined by household-level choices and both have been estimated using micro data. Second, and more importantly, the Frisch elasticity is critical for understanding business cycle fluctuations in models where aggregate hours fluctuations are purely driven by labor supply, but it is not the relevant parameter for evaluating the steady-state impacts of differences in taxes across countries. The Frisch (marginal utility constant) elasticity controls intertemporal substitution responses to temporary wage fluctuations, while the Hicksian (wealth constant) elasticity controls steady-state responses and the welfare consequences of taxation (MaCurdy 1981; Auerbach 1985).10The distinction between Hicksian and Frisch elasticities is quite important in practice. Prescott (2004) reports that cross-country differences in aggregate hours imply an elasticity of 3 in a representative-agent model, whereas Davis and Henrekson (2005) estimate an elasticity of 0.33 using similar data. The difference arises primarily because Prescott reports a Frisch elasticity whereas Davis and Henrekson report a Hicksian elasticity. Regressing log hours on log tax rates in Prescott’s data yields a Hicksian elasticity of 0.7, as shown in figure 2, panel A. Prescott maps this estimate of the Hicksian elasticity into a value for a Frisch elasticity based on parametric assumptions about utility and the wealth-earnings ratio. When utility is time-separable, the Frisch (εF) and Hicksian (εH) elasticities are related by the following identity (Ziliak and Kniesner 1999; Browning 2005):where ρ is the elasticity of intertemporal substitution (EIS), (d[wl])/dA is the marginal propensity to earn out of unearned income, and A/wl is the ratio of assets to earnings. The reason that Prescott obtains a much larger value of εF than εH is that the parametric utility specification he uses produces large values of A/wl and (d[wl])/dA. However, microeconometric evidence shows that income effects on labor supply are much smaller than those produced by the Prescott utility specification (Holtz-Eakin, Joulfaian, and Rosen 1993; Imbens, Rubin, and Sacerdote 2001). Under a utility specification that matches empirical estimates of the mean values of (d[wl])/dA and A/wl, the Frisch elasticity is only slightly larger than the Hicksian elasticity because the difference between the two elasticities is proportional to the income effect squared (d[wl]/dA)2 (Chetty 2012, table III).11IV. Simulations of Quasi-Experiments in the RW ModelWe evaluate whether macro models with indivisible labor are consistent with micro evidence on extensive margin responses by focusing on the Rogerson and Wallenius (2009) model. The RW model is a leading example of recent models of indivisible labor that aggregate over individuals by time-averaging over the life cycle, as in Ljungqvist and Sargent (2006). The model is well-suited for our purposes because it features both an extensive and intensive margin of labor supply. Rogerson and Wallenius calibrate their model to show that small intensive- margin micro elasticities are consistent with a large Frisch elasticity of aggregate hours. We adopt the parameters chosen by RW and simulate the impacts of policy changes analyzed in three prominent microeconometric studies.12Setup. RW analyze an overlapping-generations model in which a unit mass of agents is born at each instant and lives for one unit of time. An individual who supplies h(a) ∈ [0, 1] hours at age a produces efficiency units of labor, whereis a tent-shaped life cycle productivity profile and . Complete asset markets lead to perfect consumption smoothing. With log utility over consumption, each generation solveswhere τ is the tax rate and T is a lump-sum tax rebate that balances the government’s budget. The model can be solved analytically as described in RW and in the technical appendix. Because wages are paid per efficiency unit, individuals have low hourly wage rates at the beginning and end of their lives and find it optimal not to work at those points. This generates an extensive margin of participation over the life cycle. The convex disutility over hours of work generates an intensive margin hours response to changes in wage rates as well. Rogerson and Wallenius normalize the price of output to 1 and assume a constant- returns-to-scale production technology, so changes in tax rates have no impact on pretax wages and prices. Accordingly, the quasi-experiments we simulate also hold pretax wages and prices constant, as the studies on which they are based typically analyze the impacts of differential changes in incentives for relatively small subgroups of the population.Rogerson and Wallenius calibrate the parameters α, e1, and to match empirically observed values for the fraction of life worked (f), the maximum hours worked per week over the life cycle (hmax), and the wage rate at retirement relative to the maximum wage rate over the life cycle (wR/wmax). Following RW, we set hmax = 45% (45 hours per week) and wR/ wmax = 1/2. We set f to match the aggregate employment rate in the period prior to each policy experiment we consider. The parameter controls the Frisch elasticity of labor supply, as in standard life cycle models (Card 1990). We set γ = 2 to obtain an intensive margin Frisch elasticity of εINT = 1/γ = 0.5, consistent with the microeconometric evidence summarized in the following; we show in appendix A that setting εINT = 0.25 yields similar results.13 For each of the three tax policy changes simulated in the following, we choose the model’s remaining parameters {α, e1, } to match the moments {hmax, wR/wmax, f } under the tax system prior to the tax change.14 In all three cases, the calibrated model generates an intertemporal substitution elasticity for aggregate hours above 2 despite having an intensive margin intertemporal substitution elasticity of only 0.5, consistent with RW’s main result.15 As in RW, we assume that each agent lives for sixty years (corresponding to average adult working lives) and simulate each quasi-experiment by changing the tax rate for the number of periods in the model that correspond to the duration of the tax policy change in the data.16To simulate the impacts of unanticipated tax changes, we must specify how the lump sum rebate T changes for each agent. To simplify aggregation, we assume that each generation receives a lump-sum rebate equal to the taxes they pay at each instant in time.17 We ignore heterogeneity in the tax system across individuals and set τ equal to the average tax rate for the subgroup analyzed (which is relevant for extensive margin decisions).Experiment 1: Tax holiday in Iceland. In 1987, Iceland suspended its income tax for one year as it transitioned from a system under which taxes were paid on the previous year’s income to a system where taxes were paid on current earnings. In 1987, individuals paid tax on income earned in 1986; in 1988, individuals were taxed on income earned in 1988, and thus income in 1987 was untaxed. The average tax rate was 14.5 percent in 1986, 0 in 1987, and 8.0 percent in 1988 (Bianchi, Gudmundsson, and Zoega 2001). Although this tax change could also produce a change in labor demand due to a general equilibrium impact on wage rates, the tax holiday had no impact on labor supply for individuals with low initial tax rates (Bianchi, Gudmundsson, and Zoega 2001, figure 9). This implies that the general equilibrium feedback on wage rates was negligible, so the aggregate employment response can be interpreted as a labor supply elasticity.18 We simulate the tax reform in Iceland in the RW model under the assumption that the tax system remains stable prior to 1986 and after 1988. The reform was announced in late 1986, so we model the tax change as an unanticipated change at the start of 1987. The average employment rate in the three-year period prior to the reform is f = 79.2%, which implies that individuals work for 47.5 years in the model. The single-year tax reduction thus comes close to the ideal experiment for identifying a Frisch elasticity of reducing tax rates for an infinitesimal fraction of the working life.Panel A of figure 1 plots annual changes in employment rates (the employment rate in year t minus the employment rate in year t – 1) around the reform, demarcated by the vertical line. The Icelandic administrative records analyzed by Bianchi and colleagues (squares) show a modest but significant increase in employment rates in 1987 followed by a sharp dip in 1988, consistent with intertemporal substitution. The impact predicted by the RW model (circles) is an order of magnitude larger than the observed impact. In the data, employment is 3 percentage points higher in 1987 relative to 1988, but the RW model predicts that it would be 13.5 percentage points higher. The model generates a much larger spike in employment because the fraction of cohorts that are close to being indifferent between working and staying out of the labor force is large. The temporary increase in the wage rates therefore induces a large group of agents to work. Note that it is precisely this mechanism—having a large fraction of individuals near the margin—that allows the RW model to generate a large Frisch elasticity for aggregate hours and thus explain fluctuations in aggregate hours over the business cycle.Fig. 1. Impacts of tax changes on employment rates: Simulations versus dataNotes: Each panel shows the impact of an unanticipated change in incentives to work on employment rates. The dashed series shows the impact predicted by the calibrated Rogerson and Wallenius (2009) model, while the solid series shows the impact observed in the data. Panel A: Iceland suspended its income tax for one year in 1987. Average tax rates in Iceland changed from 14.5 percent in 1986 to 0 percent in 1987 and then 8.0 percent in 1988. Following Bianchi, Gudmunsson, and Zoega (2001), we define the employment rate as the fraction of weeks worked in a given year in the adult population. This panel plots annual changes in employment rates. Panel B: The Canadian SSP demonstration randomly assigned a group of welfare recipients a wage subsidy for thirty-six months in the early 1990s. Individuals in the control group faced an effective average tax rate of 74.3 percent for working full time at the minimum wage, while individuals in the treatment group faced an effective average tax rate of 16.7 percent. Following Card and Hyslop (2005), we plot the difference in monthly employment rates between the treatment and control groups. We add the observed control group mean at the start of the experiment (23.5 percent) to the difference for scaling purposes. Simulated employment rates are the fraction of individuals aged sixteen to forty-six working in a given month, reflecting the age distribution of the SSP treatment group (see appendix A). Panel C: The EITC expansion in the United States in 1994 and 1995 lowered average tax rates net of taxes and transfers for single mothers from 50.8 percent in 1992 to 43.6 percent in 1996. Meyer (2010, figure 2) reports annual employment rates for single women using CPS data. We plot the employment rates of single mothers adjusted for observables and time trends as in Meyer (2010); simulated employment rates are reported for individuals aged sixteen to forty-six.View Large ImageDownload PowerPointExperiment 2: SSP welfare demonstration in Canada. The Iceland analysis focuses on employment ch