Own-wage labor supply elasticities: variation across time and estimation methods

The principal object of examination in this study is the size of wage and income elasticities stemming from static labor supply models. Responsiveness to financial incentives in these models has been identified in various ways. There is no generally agreed-upon standard estimation approach, and we provide here a brief critical review. A more technical and comprehensive presentation of these methods and their identification strategies are provided in Blundell and MaCurdy (1999) and Blundell et al. (2007).

Traditional estimation techniques rely on some functional specification of a labor supply function and the underlying consumption-leisure preferences. Estimation is then made through local linearization of the budget constraint, accounting for the fact that after-tax wages depend on the labor supply choice (Hall 1973) or using more comprehensive techniques (Hausman 1981, 1985a, b). The approach relies on cross-sectional variation in working hours and in the two main covariates, i.e., the after-tax wage and the virtual income (i.e., the intercept of the linearized budget constraint). As a result, the main identification issue is the endogeneity of wages and unearned income, which can be seen as an omitted variable problem. Indeed, wages may be endogenous because unobservables affecting preferences for work, e.g., being a hardworking person, may well be correlated with unobservables affecting productivity and hence wages. Unearned income may be endogenous for similar reasons, i.e., individuals who work harder because of unobserved preferences for work are also likely to have accumulated more assets; if unearned income also represents income from the spouse, positive assortative mating could imply that hardworking individuals will tend to marry similar persons, another reason for the endogeneity issue. Hence, estimates obtained from cross-sectional variation in wages and non-labor income across individuals are potentially biased.

Instrumental variables methods have been suggested, and the validity of the Hausman approach hinges on whether the exclusion assumptions of the economic model hold. Also, estimates are potentially contaminated by measurement errors from the division bias (cf. Ziliak and Kniesner 1999). In addition, a series of practical difficulties limit the application of the Hausman method. First, relying on tangency conditions, the Hausman model is mainly restricted to the case of piecewise linear and convex budget sets, i.e., a partial representation of the effect of tax-benefit policies on household budget constraints. This limitation applies equally to generalizations of the technique to non-parametric estimations (Blomquist and Newey 2002). To account for non-convexities, as in Hausman (1985b) and Hausman and Ruud (1984), labor supply must be specified parametrically together with the corresponding direct utility function, which implies rather restrictive forms for preferences (see the discussion in van Soest and Das 2001).⁵ Second, quasi-concavity of the utility function is implicitly imposed a priori. As discussed by MaCurdy et al. (1990) and MaCurdy (1992), the Hausman method thus requires global satisfaction of the Slutsky condition by the labor supply function for internal consistency of the model, an unnecessary behavioral restriction that may bias estimates (see a modern statement in Heim and Meyer 2003 and Meghir and Phillips 2008).⁶ Third, the Hausman model makes it difficult to handle joint labor supply decisions within a couple or participation decisions. Instead of non-participation following simply from the corner solution of the model, fixed costs of work can be introduced, yet this additional source of non-convexity has to be dealt with and results seem to be very sensitive to the model specification (see the discussion in Bourguignon and Magnac 1990).

Instead of estimating a labor supply function, the discrete-choice approach is based on the concept of random utility maximization (see Aaberge et al. 1995, 1999; van Soest 1995; or Hoynes 1996, among others). Thus, it requires the explicit parameterization of consumption-leisure preferences, for utility to be evaluated at each discrete alternative. Tangency conditions need not be imposed, and the model is in principle very general. Labor supply decisions are reduced to choosing among a discrete set of possibilities, e.g., inactivity, part-time, and full-time. This solves several problems encountered with the Hausman method. In particular, modeling includes non-participation as one of the options so that both extensive and intensive margins are directly estimated. The complete effect of the tax-benefit system is easily accounted for, even in the presence of non-convexities in budget sets. Work costs, which also create non-convexities, are dealt with relatively easily. Estimated as model parameters as in Callan et al. (2009) or Blundell et al. (2000), they usually improve the fit of these models as they account for the fact that very few observations exist with a small positive number of worked hours. Very few restrictions on preferences need to be imposed in discrete-choice models, notably because fixed costs of work cannot be disentangled from preference parameters, so that it makes no sense to impose the convexity of preferences (see van Soest et al. 2002; Heim and Meyer 2003; Bargain 2009). The only restriction to the model is the imposition of increasing monotonicity in consumption, which seems a minimum requirement for meaningful interpretation and policy analysis. Joint labor supply decision for couples is a straightforward extension of the basic model in the discrete-choice setting. Yet, many applications still treat husbands’ working hours fixed at observed levels and focus on the labor supply of women, i.e., a male chauvinist model (e.g., Bargain 2009; such treatment is typical in Hausman models, e.g., Killingsworth and Heckman 1986). The implication of such separable treatment of spouses’ labor supply choices is relatively unknown.

In the discrete-choice approach, identification is mainly provided by non-linearities, non-convexities, and discontinuities in the budget constraint due to tax-benefit rules (see the discussion in Blundell et al. 2007 and Bargain et al. 2014). Precisely, individuals with the same gross wage usually receive different net wages. Indeed, as they are characterized by different circumstances (different marital status, age, family compositions, home-ownership status, disability status) or levels of non-labor income, their effective tax schedules are different, i.e., different actual marginal tax rates or benefit withdrawal rates. Arguably, some of the conditioning characteristics (age, children) are also included as preference variables in the model so that identification is essentially parametric. In practice, some exclusion restrictions come naturally. Indeed, tax-benefit rules depend on characteristics which are much more detailed than usual taste shifters (e.g., benefit rules depending on detailed geographical information while preferences are assumed to depend only on urban versus rural areas or on whether the household lives in the capital city). Additionally, more convincing sources of exogenous variation are also used in some studies. Closer to the natural experiment method, these consist in time or regional variation in tax-benefit rules. For instance, in the USA, variation in income tax rules or in the parameters of the Earned Income Tax Credit (EITC) across states is used in Eissa and Hoynes (2004) or Hoynes (1996). Time variation in tax-benefit rules also provides a better identification when policy reforms occur over the period under consideration, as discussed, e.g., in Bargain et al. (2014).

A third approach consists in using policy reforms explicitly in order to identify labor supply responses, without attempting to estimate a structural model (e.g., Eissa and Liebman 1996). Natural experiments based on important tax-benefit reforms in the USA and the UK have been extensively used to identify behavioral parameters (see the survey of Hotz and Scholz 2003, for the USA). For example, Eissa and Liebman (1996) use a difference-in-difference approach to identify the impact of the EITC reforms on the labor supply of single mothers. They find compelling evidence that single mothers joined the labor market in response to increased financial incentives to work. Regarding identification, the definition of control groups might be an issue in difference-in-difference approaches. For instance, responses to EITC expansions affecting single mothers were evaluated using childless women as control group, which may not be ideal given different long-term trends in labor supply in the two groups (see Hotz and Scholz 2003).⁷ Regression discontinuity (RD) is deemed better in this respect since the nature of individuals on both sides of the discontinuity is “as good as random” (cf. Lemieux and Milligan 2008). Overall, much of the evidence is concentrated in studies from the USA, Canada, and the UK. There is less evidence for other countries and notably for continental Europe maybe because large reforms, creating exogenous variation in tax-benefit rules, were less available. Partly for this reason, structural models described above have been very much in use.⁸ The timing of response to policy reforms or policy discontinuity is unclear. Nonetheless, the implicit model that analysts have in mind when discussing the “next-morning” effect of the policy impact is often a static one (cf. Lemieux and Milligan 2008 or Bargain and Doorley 2011). Reduced-form approaches, based on policy reforms or discontinuities, are increasingly used because natural experiments probably offer one of the most credible sources of identification, despite the limitations outlined above. In this way, it is important to compare estimates from these studies with those stemming from structural model estimations. Unfortunately, these studies do not systematically report wage elasticities. They rather report labor supply elasticities to benefit or tax rate changes. Thus, for comparability purposes, we could include only a few of them in the present survey. Also, the fact that actual reforms—notably welfare reforms in the USA and the UK—typically affect couples or single women with children makes that very little evidence is available for other demographic groups, in particular for childless single individuals.

Finally, a few studies rely on long-term changes in wages as well as on observation grouping in order to address endogeneity and the problem of measurement error in hourly wages discussed above (Devereux 2003, 2004). Blundell et al. (1998) also use tax-benefit policy variation over a long period to identify labor supply responses in the UK using a grouping IV estimator. Long-term variation may pose the problem of assuming that preferences remain stable in the long run, an issue which is rarely discussed. We include most of these studies, at least those for which estimates can be compared with other studies, in our survey.

In Tables 1, 2, and 3 and Figs. 1 and 2, we have observed much variation across studies in the size of wage elasticities, especially for married women and single mothers. Studies that rule out differences in estimation methods and data years show that little of this is due to genuine variation in preferences across countries (Bargain et al. 2014). We investigate here the relative roles of time variation and estimation methods in explaining the diversity of elasticity estimates.

4.1 Graphical analysis

We begin our investigation of the respective contributions of time change versus estimation methods by relying on simple visual inspections. We focus our meta-analysis on married women and single mothers.

Time trends

In Fig. 3 (left quadrant), we plot estimates by year of data collection as specified in surveyed studies (Tables 1, 2, and 3). A very clear declining trend emerges, showing in particular a concentration of low elasticities since the end of the 1990s, high elasticities in the 1970s, and more variation in between. This pattern can be observed for both married women and single mothers. Given the small number of US studies reporting estimates for the latter group, we focus on married women in the right quadrant of Fig. 3 where we distinguish between EU and US estimates. The trend is similar in both regions, with a strong negative correlation between the period of observation and the elasticity level.¹⁴ These findings tend to corroborate the result of Heim (2007) and Blau and Kahn (2007), who show that the labor supply elasticity of married women has strongly declined over time in the USA. They suggest a change in work preferences of women as possible explanation, but other explanations are possible (change in childcare policies, in domestic technology, etc.). Our results reveal that a similar trend exist for EU countries. Yet, estimates in Heim (2007) and Blau and Kahn (2007) rely on a uniform approach for the different periods while our meta-analysis possibly mixes time effects and changes in modeling and estimation methods over time.

Estimation methods

To investigate this point further, let us go back to survey Tables 1, 2, and 3. A first observation is that early evidence using the Hausman technique points to relatively large own-wage elasticities for married women, sometimes close to 1, or even larger, for instance, in early studies for France, Germany, Italy, or the UK. In contrast, recent evidence based on discrete-choice models shows more modest elasticities for this demographic group, in a range between.1 and.5, with some exceptions. In Table 3, we observe a similar pattern for the USA, with very large estimates in early studies, including Hausman (1981), and more modest and comparable elasticities in the recent studies (total hour-wage elasticities ranging between.2 and.4, for instance, in Eissa and Hoynes 2004 or Heim 2007, 2009). Hence, we can conjecture that the estimation method explains time differences.

What are the possible underlying mechanisms? With the Hausman approach, the combination of restrictive functional forms (linear labor supply) and estimation methods that impose theoretical consistency of the labor supply model everywhere in the sample (global satisfaction of Slutsky conditions) can lead to biased estimates and possibly an overstatement of work incentives, as discussed above. In addition, this approach is more sensitive to the model specification which may explain the large variance in estimates from the 1970s and 1980s. Mroz (1987) shows how the wage effects of married women’s labor supply varies dramatically depending on whether and how one controls for non-random selection into work as well as to alternative exclusion restrictions in the instrument set for wages. Bourguignon and Magnac (1990) discuss the sensitivity of their results to the model specification and show that the Hausman approach can lead to implausibly high elasticity values, as they find in some of their specifications. Drawn from our tables, we can see for instance that married women’s wage elasticity obtained with the Hausman approach vary from.28 (Triest 1990) to.97 (Hausman 1981) in the USA, even when similar periods are considered (1983 and 1975 in these two studies, respectively). For France, estimates for married women are also very high with the basic Hausman model but almost zero when introducing fixed costs (cf. Bourguignon and Magnac 1990). Estimates obtained with discrete-choice models are somewhat more comparable from one study to the next. Yet, there are still differences, which are more likely driven by selection criteria (for France, high elasticities are found for families with children in Choné et al. 2003) and alternative specifications of discrete-choice models (for instance, the degree of flexibility of the model, see Bargain 2009).

Time trends versus estimation methods

To further investigate whether elasticities truly decline over time or whether this pattern is due to changes in estimation methods, we compare the trends in elasticities obtained with the two main methods.¹⁵ That is, Fig. 4 plots against data years the estimates obtained with continuous models (which rely mainly on the Hausman approach) and those from discrete-choice models (as recently used in many policy papers). Graphs in the upper panels show that the former was mainly used before 1990 while the latter approach took over in the 1990s and 2000s.

For continuous models, there are nonetheless some observations in the more recent years so that we can suggest tentative interpretations. For our group of interest, and whether single mothers are included (upper panel, right) or not (left), the time shrinking elasticity hypothesis is verified over all estimates relying on the Hausman approach. The linear correlation between time and elasticity size is around −.55 for married women with or without single mothers. When differentiating between regions and focusing on married women, in the lower panels of Fig. 4, this meta-analysis corroborates the findings in Heim (2007) and Blau and Kahn (2007) for the USA (both studies relying on a Hausman-type approach) and also finds a similar pattern for EU countries. Yet, it is noticeable that there are very few estimates based on the Hausman model for the period after 1990 in the EU, so the result is more fragile than for the USA.

If we turn to estimates from discrete-choice models, the upper graphs show fewer points of observations available before the 1990s. There is nonetheless a negative linear correlation between years and estimates due to the high density of very low estimates in the years 2000s. Over all years, this correlation is −.37 for married women (going down to −.22 if German estimates, which are numerous in this period, are taken out) and −.47 when adding single mothers (−.40 without Germany). If we take out the 2000s, it goes down to −.08 for married women and −.34 when adding single mothers (Germany does not change the picture this time). For a comparison, the correlation between years and Hausman estimates remain at −.47 over this subperiod (with or without single mothers). The lower panel confirms results for the EU while too few estimates based on discrete-choice models exist for the USA to attempt any interpretation.

¹ Bargain et al. (2014) conduct an estimate labor supply elasticities for 17 European countries and the USA, separately by gender and marital status. Measurement differences are netted out by using a harmonized empirical approach and comparable data sources and years. Bargain et al. (2014) find that own-wage elasticities are relatively small and much more uniform across countries than previously thought. Differences exist nonetheless and are found not to arise from different tax-benefit systems or demographic compositions across countries.

² See Chetty (2012) for an interesting discussion about the potential bias in the estimation of labor supply in the presence of optimization frictions. To cope with this problem, Chetty provides bounds on the structural elasticities derived from reduced-form estimates that might suffer from optimization friction bias. The derived bounds imply that frictions affect intensive margin elasticities much more than extensive margin elasticities.

³ Arguably, these other margins partly relate to responses not directly pertaining to productive behavior, like tax evasion and optimization. In this regard, hours of work still constitute an interesting benchmark. Another margin is work effort that may affect wage rates. In the short run, however, hours and participation are the only variables of adjustment for a majority of workers.

⁴ These elasticities are much larger than in microeconomic studies (e.g., Prescott 2004). Several reasons have been suggested for this: the use of representative agents and difficulties around an aggregation theory when heterogeneity matters (see Blanchard 2006), the existence of a social multiplier whereby the utility from not working is increasing in the number of people who do not work (see Alesina et al. 2005), and factors related to the timing and the nature of labor supply adjustments in the presence of frictions (Chetty et al. 2011).

⁵ Another approach is the reconvexification of the budget set. For instance, to estimate the labor supply of married women on 1985 French data, Bourguignon and Magnac (1990) use the Hausman technique and eliminate minor non-convexities by replacing the budget set by its convex envelope. This approach is not possible for later years as the implementation of a minimum income scheme in 1988 has introduced high non-convexity in the budget constraint. Similar non-convexities arise in all countries with substantial means-tested transfers.

⁶ See Eklöf and Sacklén (2000) for a critical discussion of the MaCurdy critique.

⁷ This issue is shared with the literature on the elasticity of taxable income, whereby results are sensitive to the type of reforms exploited for identification (Saez et al. 2012). Indeed, control group definition follows from their income level, so that specific preferences are identified and results cannot be extrapolated. For instance, changes in tax rates (tax credits) identify the preferences of high (low)-income groups and may not be generalized to the whole population.

⁸ Things are changing in the recent period. For France, for instance, some studies have recently used tax-benefit changes to evaluate the responsiveness of the labor force, including the introduction of a small tax credit (Stancanelli 2008), time change in income tax schedule (Carbonnier 2008), changes in the possibility to cumulate welfare payment for lone mothers and earnings (González 2008), and age condition on children for a replacement income targeted at low-income mothers who opt for full-time childcare (Piketty 1998). RD estimations using age conditions on the level of social assistance program are also used in Bargain and Doorley (2011), in a similar way as Lemieux and Milligan (2008) for Canada.

⁹ Note that few papers report uncompensated elasticities. One reason for this is that income effects are often very small and, hence, compensated and uncompensated elasticities are almost identical. This is confirmed by the findings in Bargain et al. (2014)—one of the few studies reporting both types of elasticities.

¹⁰ Note that almost all papers report elasticities with respect to the gross wage. Bargain et al. (2014) show that net wage elasticities are—mechanically—slightly larger than gross wage elasticities.

¹¹ Note that a variety of different elasticities is used in different studies. For example, there are compensated and uncompensated wage elasticities, different ways in which the tax system is (or is not) accounted for, elasticities with respect to gross wage rates or net wage rates, etc. Moreover, it also may matter how elasticities are aggregated over the group of interest. Some studies present the elasticity for a benchmark (average) observation, others an elasticity of total hours of work in the whole group for a uniform wage rate increase, some even present an average of the elasticities for all observations. However, most studies report uncompensated elasticities with respect to the gross wage for total hours of work. We have tried to harmonize the definitions as much as possible when choosing the elasticities.

¹² Note that not all papers report elasticities in the same way. It was our task to make sure that we identified the same parameter—namely the uncompensated wage elasticity or the income elasticity—from each paper. We have always chosen the author’s preferred estimate in case they reported several estimates (for example, as robustness checks).

¹³ For instance, Euwals and van Soest (1999) report wage elasticities for childless single individuals in the Netherlands of around.10–.11. For Germany, a series of studies report estimates between.10 and.36 for childless single men and women.

¹⁴ We also find similar patterns when looking separately at hour-wage elasticities (correlation of −.59 with observation years) and participation-wage elasticities (correlation of −.54) for married women.

¹⁵ Further potentially important factors are the treatment of wages in the estimation procedure (Löffler et al. 2014) and the choice of the reference tax system for the benchmark.

¹⁶ Note that—like all meta-regressions—our analysis is not identifying causal effects since one can think of several potentially omitted variables.

¹⁷ Note that we cannot include all possible aspects of model specification in our paper since there are too many dimensions and to few observations. For example, Löffler et al. (2014) investigate the role of the treatment of wages for the size of elasticities. In order to do this, the authors estimate 3500 elasticities using a discrete-choice framework with all possible permutations of model choices. Unfortunately, such a variation is missing in the estimates collected for our study.

¹⁸ We do not report similar estimations for the USA only given the small number of observations in this case.