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

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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