Are Micro and Macro Labor Supply Elasticities Consistent? a Review of Evidence on the Intensive and Extensive Margins

Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins

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Citation Chetty, Raj, Adam Guren, Day Manoli, and Andrea Weber. 2011. Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review 101(3): 471–475.

Published Version doi:10.1257/aer.101.3.471

Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11878970

Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins

By Raj Chetty, Adam Guren, Day Manoli, and Andrea Weber∗

Macroeconomic models of fluctuations in gin elasticities, the extensive margin elas- hours of work over the business cycle or ticity is often treated as a free parameter across countries imply much larger labor that is calibrated purely to match macro- supply elasticities than microeconometric es- economic moments. But micro estimates timates of hours elasticities. Understanding are equally useful in calibrating extensive this divergence is critical for questions rang- margin responses: the marginal density of ing from the sources of business cycles to the the reservation wage distribution that deter- impacts of tax policy. Since the discrep- mines the impacts of macroeconomic varia- ancy between micro and macro elasticities tion on employment also determines the im- was recognized in the 1980s, economists have pacts of quasi-experiments such as tax policy made significant advances in understanding changes on employment rates. labor supply. For instance, macroecono- We find that micro estimates are consis- mists have developed models of indivisible tent with macro estimates of the steady- labor in which extensive-margin responses state (Hicksian) elasticities relevant for make aggregate-hours elasticities larger than cross-country comparisons on both the ex- intensive-margin elasticities (Richard Roger- tensive and intensive margins. However, mi- son 1988, Gary D. Hansen 1985, Lars cro estimates of intertemporal substitution Ljungqvist and Thomas J. Sargent 2006). (Frisch) elasticities are an order of magni- Meanwhile, microeconomists have amassed tude smaller than the values needed to ex- a large body of evidence on intensive (hours plain business cycle fluctuationsin aggregate conditional on employment) and extensive hours by preferences. Quasi-experimental (participation) labor supply elasticities. estimates of extensive margin intertempo- The goal of this paper is to evaluate ral substitution elasticities are around 0.25, whether state-of-the-art macro models fea- whereas leading pure equilibrium macro turing indivisible labor are consistent with models imply intertemporal substitution ex- modern quasi-experimental micro evidence. tensive margin elasticities around 2. Hence, To do so, we consider evidence on both the key puzzle to be resolved is why employ- the intensive and extensive margins. Al- ment rates fluctuate so much over the busi- though macro models are now calibrated ness cycle relative to what one would pre- to match micro estimates of intensive mar- dict based on the impacts of tax changes on employment rates — that is, why micro and macro estimates of the Frisch extensive mar- ∗ Chetty: Harvard University Department of Eco- nomics and NBER, 1805 Cambridge St., Cam- gin elasticity are so different. bridge, MA 02138 (email: [email protected]). Guren: Harvard University Department of Economics, I. Terminology 1805 Cambridge St., Cambridge, MA 02138 (email: [email protected]). Manoli: UCLA Department of Economics, RAND, and NBER, 8283 Bunche Hall It is helpful to establish conventions about Box 951477, Los Angeles, CA 90095 (email: dsman- terminology given the various elasticity con- [email protected]). Weber: University of Mannheim Department of Economics, L7, 3-5, 68131, Mannheim, cepts used in the micro and macro litera- Germany (email: [email protected]). Thanks tures. We distinguish between elasticities to Peter Ganong and Jessica Laird for outstanding re- based on the margin of response (extensive search assistance and Richard Blundell, Greg Bruich, vs. intensive) and the timing of response (in- David Card, John Friedman, Bob Hall, Greg Mankiw, Richard Rogerson, Robert Shimer, and Danny Yagan tertemporal substitution vs. steady state). for helpful comments. There are four elasticities of interest: steady- 1 2 PAPERSANDPROCEEDINGS MAY2011

Table 1– Micro vs. Macro Labor Supply Elasticities Intensive Margin Extensive Margin Aggregate Hours Steady State micro 0.30 0.26 0.56 (Hicksian) macro 0.38 0.14 0.51 Intertemporal micro 0.54 0.28 0.82 Substitution (Frisch) macro [0.54] [2.30] 2.84

Note: Each cell shows a point estimate of the relevant elasticity based on meta analyses of existing micro and macro evidence. Micro estimates are identified from quasi-experimental studies; macro estimates are identified from cross- country variation in tax rates (steady state elasticities) and business cycle fluctuations (intertemporal substitution elasticities). The aggregate hours elasticity is the sum of the extensive and intensive elasticities. Macro studies do not always decompose intertemporal aggregate hours elasticities into extensive and intensive elasticities. Therefore, the estimates in brackets show the values implied by the macro aggregate hours elasticity if the intensive Frisch elasticity is chosen to match the micro estimate of 0.54. Sources are described in the appendix. state extensive, steady-state intensive, in- country differences in aggregate hours imply tertemporal extensive, and intertemporal in- an elasticity of 3 in a representative-agent tensive. We use the terms “micro” and model, whereas Steven J. Davis and Mag- “macro” elasticities to refer to the sources nus Henrekson (2005) estimate an elasticity of variation used to estimate the elasticities. of 0.33 using similar data. The difference The elasticity of aggregate hours —the rele- is almost entirely because Prescott reports a vant parameter for calibrating a representa- Frisch elasticity whereas Davis and Henrek- tive agent model —is the sum of the extensive son report a Hicksian elasticity. and intensive margin elasticities, weighted by hours of work if individuals have hetero- II. Comparing Micro and Macro geneous preferences (Richard Blundell, An- Estimates toine Bozio, and Guy Laroque 2011). We summarize the micro and macro evi- The macro literature uses the term “macro dence on the extensive and intensive margins elasticity” to refer to the Frisch elasticity in Table 1. The rows of consider steady- of aggregate hours and the term “micro state (Hicksian) vs. intertemporal substitu- elasticity” to refer to the intensive-margin tion (Frisch) elasticities, while the columns elasticity of hours conditional on employ- compare intensive margin (hours conditional ment (e.g. Edward Prescott 2004, Roger- on employment) and extensive margin (par- son and Johanna Wallenius 2009). We ticipation) elasticities. Within each of the use different terminology here for two rea- four cells, we report micro and macro esti- sons. First, the intensive-margin is no more mates of the elasticity based on (unweighted) “micro” than the extensive margin; both means of existing studies. We also calculate reflect household-level responses and both aggregate hours elasticities by summing the have been estimated using micro data. Sec- extensive and intensive elasticities.1 ond, although the Frisch elasticity is crit- There are wide confidence intervals asso- ical for understanding business cycle fluc- ciated with each of the point estimates in tuations, it is not relevant for evaluating Table 1, as well as methodological disputes the steady-state impacts of differences in about the validity of some of the studies. taxes across countries. The Frisch (mar- Therefore, the estimates should be used to ginal utility constant) elasticity controls in- gauge orders of magnitude: differences of 0.1 tertemporal substitution responses to tem- between elasticity estimates could be due to porary wage fluctuations,while the Hicksian (wealth constant) elasticity controls steady- 1 This calculation requires that preferences are ho- state responses and the welfare cost of taxa- mogenous. If some groups work few hours and also have higher extensive elasticities, as suggested by existing ev- tion. This distinction is quite important in idence, this will yield an upper bound on the aggregate practice. Prescott (2004) reports that cross- hours elasticity (Blundell, Bozio, and Laroque 2011). VOL. 101 NO. 2 MICRO AND MACRO ELASTICITIES: INTENSIVE AND EXTENSIVE MARGINS 3 noise or choice of specification, while differ- of steady-state aggregate hours elasticities ences of 1 reflect fundamental discrepancies. match once one accounts for extensive mar- Steady-State Elasticities. On the exten- gin responses and the attenuation of intensive margin, Chetty et al. (2011b) conduct sive margin micro elasticities due to opti- a meta-analysis of quasi-experimental stud- mization frictions. ies that span a broad range of countries, de- Intertemporal Substitution Elasticities. mographic groups, time periods, and sources On the extensive margin, our micro estimate of variation. Every extensive margin steady of 0.28 comes from Chetty et al.’s (2011b) state elasticity Chetty et al. consider is be- meta-analysis of studies of intertemporal low 0.45. We use their mean estimate of 0.26 substitution, which examine the impacts for the micro extensive margin steady-state of changes in retirement incentives or elasticity. temporary tax reforms. On the intensive On the intensive margin, Chetty (2009) margin, there is less quasi-experimental presents a meta-analysis of micro estimates evidence on intertemporal substitution of Hicksian elasticities and reports a mean elasticities. Marco Bianchi, Björn R. value of 0.12 (Chetty 2009, Table 1, un- Gudmundsson, and Gylfi Zoega (2001) find weighted mean of Panels A and B). How- an intensive-margin elasticity of 0.37 by ever, Chetty and Chetty et al. (2011a) ar- studying a temporary tax change in Iceland gue that these elasticities are significantly at- (see Chetty (2009) for the elasticity calcu- tenuated by optimization frictions: the small lation). Luigi Pistaferri (2003) reports a tax changes used to identify micro elastici- Frisch intensive elasticity of 0.7 using micro ties do not generate substantial changes in data on expectations about wages. The hours because the costs of adjusting hours similarity between these estimates and our outweigh the second-order benefits of re- preferred estimate of the intensive Hicksian optimization. Chetty (2009) develops a elasticity of 0.3 is not surprising. Chetty bounding method of recovering the underly- (2009) shows that the Frisch elasticity must ing structural elasticity relevant for evaluat- be less than 0.61 given a Hicksian elasticity ing the steady-state impacts of taxes. Pool- of 0.3 in a model with balanced growth and ing the twenty studies he analyzes, he ob- an elasticity of intertemporal substitution tains a preferred estimate of the structural below 1. Hence, micro evidence suggests intensive margin Hicksian elasticity of 0.3.2 that Frisch and Hicksian elasticities are Macro steady-state estimates are obtained similar in magnitude. from comparisons across countries with dif- Equilibrium macro models —in which fluc- ferent tax regimes. On the extensive mar- tuations in hours are driven by preferences gin, Steven Nickell (2003) and Davis and — identify intertemporal substitution labor Henrekson (2005) find steady-state elastici- supply elasticities from business cycle vari- ties of 0.14 on average by comparing employ- ation. Most macro studies calibrate repre- ment rates across countries. On the inten- sentative agent models and therefore report sive margin, analogous comparisons of work only intertemporal elasticities of aggregate hours across OECD countries by Prescott hours. The intertemporal aggregate hours (2004) and Davis and Henrekson (2005) im- elasticity required to match business cycle ply a mean steady-state elasticity of 0.38. data is between 2.61 and 4 in real business We conclude that micro and macro estimates cycle models (Jang-Ok Cho and Thomas F. Cooley 1994, Table 1; Robert G. King and 2 Our proposed elasticities may appear to contradict Sergio T. Rebelo 1999, p975) and 1.92 in the common view that tax changes have smaller effects menu cost models (Frank Smets and Rafael on the intensive margin than extensive margin. Chetty (2009) shows that frictions attenuate observed extensive Wouters 2007, Table 1A). The mean in- margin elasticities much less than intensive margin elas- tertemporal aggregate hours elasticities im- ticities because the utility gains from reoptimizing are plied by these three models is 2.84. Micro first-order on the extensive margin and second-order on estimates imply a Frisch elasticity of aggre- the intensive margin. Consequently, the structural intensive margin elasticity is larger than the structural gate hours of 0.82, well below this value. extensive margin elasticity. The few available decompositions of macro 4 PAPERSANDPROCEEDINGS MAY2011 aggregate hours elasticities into extensive ment rates fluctuate substantially over the and intensive margins suggest that macro es- business cycle even for this subgroup (Nir timates are roughly in alignment with micro Jaimovich and Henry E. Siu 2009). estimates on the intensive margin. Busi- The importance of reconciling micro and ness cycle fluctuations in hours conditional macro evidence on both the intensive and on employment account for only 1/6 of the extensive margins can be seen by simulat- fluctuations in aggregate hours at an annual ing the impacts of quasi-experiments such as level (James J. Heckman 1984). Given that tax policy changes in macro models. Chetty elasticities of 4 fit the fluctuations in aggre- et al. (2011b) use Rogerson and Wallenius’ gate hours in real business cycle models, we (2009) calibrated life cycle model to simu- infer that intensive Frisch elasticities around late the impacts of tax reforms studied in the 0.66 match macro evidence in RBC models. micro literature on employment rates. The In contrast, macro evidence sharply con- Rogerson and Wallenius model over-predicts tradicts micro estimates of the extensive in- the employment impacts of temporary tax tertemporal elasticity. The fact that em- changes that induce intertemporal substitu- ployment fluctuations account for 5/6 of tion by an order of magnitude, but comes the fluctuation in aggregate hours suggests much closer to matching the steady-state im- that extensive elasticities above 3 would be pacts of permanent tax changes, mirroring needed to match the data in standard RBC the conclusions drawn above. models. If macro models with an extensive margin were calibrated to match an in- III. Conclusion tensive intertemporal elasticity of 0.54, they would require extensive intertemporal elas- Based on our reading of the micro ev- ticities of 2.84-0.54 = 2.30 on average to idence, we recommend calibrating macro match aggregate hours fluctuations. This models to match Hicksian elasticities of 0.3 value is an order of magnitude larger than all on the intensive and 0.25 on the extensive of the micro estimates considered by Chetty margin and Frisch elasticities of 0.5 on the et al. (2011b). Hence, extensive labor sup- intensive and 0.25 on the extensive margin. ply responses are not large enough to explain Hence, it would be reasonable to calibrate the large fluctuationsin employment rates at representative agent macro models to match business cycle frequencies. In the terminol- a Frisch elasticity of aggregate hours of 0.75.3 ogy of Ljungqvist and Sargent (2011), the These elasticities are consistent with the ob- micro data reveal that most individuals are served differences in aggregate hours across at a corner in their employment decisions. countries with different tax systems. They Macro models may not perfectly match also match the relatively small fluctuations micro evidence on the extensive margin be- in hours conditional on employment over the cause extensive margin elasticities vary with business cycle. The challenge is to formulate the distribution of reservation wages at the models that fit the large fluctuations in em- margin. While one may be reluctant to ployment rates over the business cycle when calibrate a macro model to match an ex- calibrated to match an extensive margin la- tensive margin elasticity estimate from any bor supply elasticity of 0.25.4 Even with in- single study, the fact that all fifteen quasi- divisible labor, models that require a Frisch experimental studies reviewed by Chetty et al (2011b) find elasticities less than 0.45 3 We suspect that this estimate is, if anything, biased casts doubt upon macro models calibrated upward for two reasons: (1) the mean extensive margin with extensive margin elasticities above 1. elasticity for the population as a whole is less than 0.25 as noted above and (2) publication bias may drive micro Moreover, observable heterogeneity in elas- studies toward reporting higher elasticity estimates. ticities reinforces the divergence between mi- 4 One approach, pursued e.g. by Hall (2009), is to cro and macro evidence on intertemporal move away from models in which employment fluctu- elasticities. While microeconomic evidence ations are driven purely by worker preferences. Hall shows that a search and matching model can generate suggests that extensive margin elasticities large fluctuations in employment rates over the business are near zero for prime-age men, employ- cycle without large extensive labor supply responses. VOL. 101 NO. 2 MICRO AND MACRO ELASTICITIES: INTENSIVE AND EXTENSIVE MARGINS 5 elasticity of aggregate hours above 1 are in- (2001), as reported in Chetty (2009). The consistent with micro evidence. macro value in brackets is set equal to the micro estimate. APPENDIX: SOURCES OF ESTIMATES Frisch, extensive margin: The micro esti- FOR TABLE 1 mate is the mean of the estimates in Panel This appendix describes how each of the B of Table 1 in Chetty et al. (2011b). The values in Table 1 are calculated. With macro value in brackets is computed by sub- the exception of the Frisch aggregate hours tracting the Frisch micro intensive margin macro elasticity, the aggregate hours elastic- elasticity from the Frisch aggregate hours ities are defined as the sums of the intensive macro elasticity. and extensive margin elasticities. Frisch, aggregate hours macro: The es- Hicksian, extensive margin: The micro estimate is the mean of the aggregate (to- timate is the mean of the estimates in Panel tal hours) elasticities implied by three mod- A of Table 1 in Chetty et al. (2011b). els of business cycles: (1) Cho and Cooley The macro estimate is computed by taking (1994): 2.61 from the sum of the intensive the mean of 0.13 from Davis and Henrekson and extensive margin elasticities implied by (2005) and 0.14 from Nickell (2003). The the parameters in Table 2; (2) King and Re- elasticity from Davis and Henrekson is com- belo (1999): 4 for representative agent RBC puted using the log difference in employment models, from page 975, and (3) Smets and based on the slope coeffi cient in Table 3 (bot- Wouters (2007): 1.92 from Table 1A, Poste- tom panel, Sample C) and the sample means rior Distribution, Mode. of labor force participation and tax rates in Table 1 for the corresponding sample. The REFERENCES elasticity from Nickell is computed using the average point estimate of 2 percent (reported Bianchi, Marco, Björn R. Gudmunds- on page 8) and the sample means of employ- son, and Gylfi Zoega. 2001. “Iceland’s ment rates and tax rates from Tables 1 and Natural Experiment in Supply-Side Eco- 2, respectively. nomics.”American Economic Review, 91(5): Hicksian, intensive margin: The micro es- 1564-79. timate is the preferred estimate of the structural elasticity reported by Chetty (2009). Blundell, Richard, Antoine Bozio, The macro estimate is the mean of the values and Guy Laroque. 2011. “Labour Sup- implied by Davis and Henrekson (2005) and ply and the Extensive Margin”Forthcoming, Prescott (2004). The value from Davis and American Economic Review Papers and Pro- Henrekson (2005) is computed using log dif- ceedings. ferences in annual hours per employed adult Chetty, Raj. 2009. “Bounds on Elastici- based on the slope coeffi cient in Table 3 ties with Optimization Frictions: A Synthe- (middle panel, Sample C) and the sample sis of Micro and Macro Evidence on Labor means of annual hours per employed person Supply.”NBER Working Paper 15616. and tax rates in Table 1 for the correspond- Chetty, Raj, John N. Friedman, Tore ing sample. The value from Prescott (2004) Olsen, and Luigi Pistaferri. 2011a. comes from subtracting the Hicksian macro “Adjustment Costs, Firm Responses, and extensive margin elasticity (0.14) from the Micro vs. Macro Labor Supply Elasticities: aggregate hours elasticity (0.70), which is Evidence from Danish Tax Records.”Quar- estimated using a cross-sectional regression terly Journal of Economics, forthcoming. of log actual hours on log net-of-tax rates (1 τ) based on the pooled data from both Chetty, Raj, Adam Guren, Day periods− reported by Prescott in Table 2. Manoli, and Andrea Weber. 2011b. Frisch, intensive margin elasticities: the “Does Indivisible Labor Explain the Differ- micro estimate is the unweighted mean of ence between Micro and Macro Elasticities? 0.70 in Table 2 from Pistaferri (2003) and A Meta-Analysis of Extensive Margin Elas- 0.37 from Bianchi, Gudmundson, and Zoega ticities.”NBER Working Paper. 6 PAPERSANDPROCEEDINGS MAY2011

Cho, Jang-Ok, and Thomas F. Coo- Nickell, Steven. 2003. “Employment and ley. 1994. “Employment and Hours Over Taxes.”CESifo Working Paper 1109. the Business Cycle.” Journal of Economic Pistaferri, Luigi. 2003. “Anticipated and Dynamics and Control, 18(2): 411-32. Unanticipated Wage Changes, Wage Risk, Davis, Steven J., and Magnus Hen- and Intertemporal Labor Supply.” Journal rekson. 2005. “Tax Eﬀects on Work Activ- of Labor Economics, 21(3): 729-54. ity, Industry Mix and Shadow Economy Size: Prescott, Edward. 2004. “Why Do Evidence from Rich-Country Comparisons.” Americans Work So Much More Than Euro- In Labour Supply and Incentives to Work in peans?”Federal Reserve Bank of Minneapo- Europe, ed. Ramón Gómez Salvador, Ana lis Quarterly Review, 28(1): 2—13. Lamo, Barbara Petrongolo, Melanie Ward, Rogerson, Richard. 1988. “Indivisible and Etienne Wasmer, 44-104. Northamp- Labor, Lotteries and Equilibrium.” Journal tion, MA: Edward Elgar Press. of Monetary Economics, 21(1): 3—16. Hall, Robert E. 2009. “Reconciling Rogerson, Richard, and Johanna Wal- Cyclical Movements in the Marginal Value lenius. 2009. “Micro and Macro Elasticities of Time and the Marginal Product of La- in a Life Cycle Model with Taxes.” Journal bor.” Journal of Political Economy, 117(2): of Economic Theory, 144(6): 2277-92. 281-323. Smets, Frank, and Rafael Wouters. Hansen, Gary D. 1985. “Indivisible La- 2007. “Shocks and Frictions in US Business bor and the Business Cycle.” Journal of Cycle: A Bayesian DSGE Approach.”Amer- Monetary Economics. 16(3): 309-327. ican Economic Review. 97(3): 586-606.

Heckman, James J. 1984. “Comments on the Ashenfelter and Kydland Papers.” Carnegie-Rochester Conference Series on Public Policy, 21: 209-24. Jaimovich, Nir, and Henry E. Siu. 2009. “The Young, the Old, and the Restless: Demographics and Business Cy- cle Volatility” American Economic Review, 99(3): 804-26. King, Robert G., and Sergio T. Re- belo. 1999. “Resuscitating Real Business Cycles.” In Handbook of Macroeconomics, ed. John B. Taylor and Michael Woodford, 927-1007. Amsterdam: North-Holland. Ljungqvist, Lars, and Thomas J. Sar- gent. 2006. “Do Taxes Explain European Employment? Indivisible Labor, Human Capital, Lotteries, and Savings.” In NBER Macroeconomics Annual 2006, ed. Daron Acemoglu, Kenneth Rogoﬀ, and Michael Woodford, 181-246. Cambridge, MA: MIT Press. Ljungqvist, Lars, and Thomas J. Sar- gent. 2011. “A Labor Supply Elasticity Accord?”Forthcoming, American Economic Review Papers and Proceedings.