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2428Treatment Effects in Bunching Designs: The Impact of Mandatory Overtime Pay on Hours
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A major theme throughout microeconometrics is to separate causal relationships of interest from additional sources of individual heterogeneity in the outcomes observed. When that outcome represents a choice those individuals make---for example when estimating an elasticity of labor supply---a key challenge is to confront the endogeneity introduced by heterogeneity in preferences that may be correlated with prices. Familiar methods for identification leverage random variation (e.g. instrumental variables) or changes over time (e.g. policy reforms), yet many important environments lack opportunities to credibly use such tools. In these settings, new approaches to inferring the responsiveness of agents to incentives are highly valuable.
When a population of decision-makers faces choice sets that exhibit a kink at a common threshold, the popular “bunching design” method uses the cross-sectional distribution of those agents' choices to identify their responsiveness to the incentives that change at that threshold. A generic prediction of optimizing behavior is that the distribution of agents' choices will feature bunching where there are convex kinks in their costs as a function of a second choice variable. saez_taxpayers_2010 observed that under suitable assumptions, the magnitude of this bunching can be informative about how elastic their choices are to the switch in incentives that occurs at a kink. The bunching design has since become a popular research design in a variety of settings, growing from its initial focus on measuring the elasticity of labor supply using the kink in tax liability between tax brackets.\footnote{kleven_behavioural_2012 pioneered a similar approach to “notches” where the level (rather than the slope) of tax liability jumps discretely at a threshold. See kleven_bunching_2016 and guide_to_practice for reviews of related methods.}
However, the literature has recently emphasized some concerning limits to non-parametric identification in the bunching design. The bunching design approach couples two essential ingredients for identification: i) a choice model; and ii) assumptions about the distribution of heterogeneity in agents' preferences. While i) describes how a given agent's choices would be made given alternative choice sets, ii) captures how different agents would choose differently even if confronted with the same choice set. blomquist_bunching_2019 and bertanha_better_2018 show that even if one assumes the restrictive “isoelastic” choice model typical in applications of the bunching design, identification from bunching requires assumptions on the distribution of heterogeneity that cannot be verified directly in the data.
In this paper I find that the upside of confronting this challenge to identification is quite high. In particular, I show that the bunching design remains applicable under weak structural assumptions about choice when the design is used for questions of reduced-form policy evaluation. I do this by recasting the necessary extra assumptions for identification as extrapolation assumptions about two appropriately-defined counterfactual choices, in the context of a general non-parametric choice model. This establishes that the essential identifying power of the bunching design does not depend on the isoelastic model from the tax literature that is typically used to motivate the approach.
Using the language of potential outcomes, I generalize the parameter of interest beyond the isoelastic model to a local average treatment effect parameter, the “buncher ATE”, which captures the mean difference between the two counterfactual choices among observational units that are bunched at the kink. These potential outcomes are directly observed in the data, though not across the full support of their distributions. I propose a new non-parametric assumption to extrapolate from the observed distribution of agents' choices and partially identify the buncher ATE. In particular, I impose a relatively weak shape constraint---bi-log-concavity---on the distribution of each potential outcome. Bi-log-concavity nests many previously proposed distributional assumptions for bunching analyses and is testable within the region in which each potential outcome is observed.
My results supplement other partial identification approaches recently proposed for the bunching design. Notably, the bounds I derive for the buncher ATE are substantially narrowed relative to existing approaches by making extrapolation assumptions separately for each of the two counterfactuals. By contrast, existing approaches constrain the distribution of a single scalar heterogeneity parameter, a simplification that is afforded by the isoelastic choice model. In the context of that model, bertanha_better_2018 and blomquist_bunching_2019 obtain bounds on the elasticity when the researcher is willing to put an explicit limit on how sharply the density of heterogeneous choices can rise or fall. My approach based on bi-log-concavity avoids the need to choose any such tuning parameters, and is applicable in the general choice model. However, I show how an explicit bounding approach can be utilized there as well, which in my empirical application yields similar estimates of the identified set. In the general choice model, I impose assumptions on quantile functions rather than on densities, and the “distance” one is required to extrapolate is equal to the bunching probability, a (dimensionless) quantity known from the data.
I apply the above approach to evaluate a major labor market policy that has proven difficult to assess via other research designs: the “time-and-a-half” overtime pay rule introduced by the U.S. Fair Labor Standards Act (FLSA) of 1938. The time-and-a-half requires a pay premium for long work hours: firms must pay a worker one and a half times their normal hourly wage for any hours worked in excess of 40 within a single week. Although many salaried workers are exempt from it, the time-and-a-half rule applies to a majority of the U.S. workforce, including nearly all of its over 80 million hourly workers. Workers in many industries average multiple overtime hours per week, making overtime the largest form of supplemental pay in the U.S. hart_economics_2004-1,bishow_look_2009-1.
In marked contrast to the federal minimum wage (which was also introduced by the 1938 FLSA), only a small literature has studied the effects of the FLSA overtime rule on the labor market. A key reason for this is that the overtime rule has hardly varied: the policy has remained as time-and-a-half after 40 hours in a week, for now more than 80 years. Reforms to overtime policy have been rare and have focused on eligibility, leaving the central parameters of the rule unaffected. This lack of variation has afforded few opportunities to leverage research designs that exploit policy changes to identify causal effects,\footnote{See brown_wages_2019. A few studies that have used difference-in-differences approaches to estimating effects of U.S. overtime policy on hours: hamermesh_demand_2003 consider the expansion of a daily overtime rule in California to men in 1980, while johnson_impact_2003 use a supreme court decision on the eligibility of public-sector workers in 1985. costa_hours_2000 studies the initial phase-in of the FLSA in the years following 1938. See footnotes (ref) and (ref) for a comparison of my results to these papers. quach_labor_2020 looks at very recent reforms to eligibility criteria for exemption from the FLSA, estimating effects of the expansion on employment and the incomes of salaried workers.} and remains as the Department of Labor plans a major expansion to eligibility in 2024 dolschedule.
By leveraging the bunching design, this paper makes use of variation within the overtime rule itself. With wages held constant, the policy introduces a sharp discontinuity in the marginal cost to the firm of a worker-hour---a convex “kink” in firms' costs---which provides firms with an incentive to set workers' hours exactly at 40 in a given week. I take the perspective of firms setting workers' hours in an optimizing way, which yields the implication that the mass of workers working 40 hours in a given week will be larger or smaller depending on how responsive firms are to the wage increase imposed by the time-and-a-half rule. I draw on a novel administrative dataset of the exact hours for which workers are paid in a single week, using the bunching observed at 40 hours among hourly workers in these data to assess how the FLSA has affected the hours of U.S. workers.
In the overtime setting, the potential outcomes considered by the buncher ATE correspond to, respectively: i) the number of hours the firm would choose for the worker this week if the worker's normal wage rate applied to all of this week's hours; and ii) the number that the firm would choose if the worker's overtime rate applied to all of this week's hours. The buncher ATE then reflects a local average wage elasticity of hours demand between workers' standard wage and overtime wage rates. Choice from the kinked choice set can be fully characterized by these counterfactuals: firms choose one or the other of them or they choose the location of the kink. The magnitude of bunching at 40 hours then identifies directly a feature of the joint distribution of the potential outcomes, allowing one to make statements about treatment effects purged of selection bias.\footnote{This echoes klinetartari_bounding_2016's klinetartari_bounding_2016 approach to studying labor supply, but in reverse. They use observed marginal distributions of counterfactual choices to identify features of their joint distribution, assuming optimizing behavior.}
However, as noted above, identification hinges crucially on extrapolation assumptions about the marginal distributions of the two potential outcomes. The bi-log-concavity assumption I rely on can be economically motivated in the case of working hours, in addition to being partially testable in the payroll data I use. The resulting bounds for the buncher ATE turn out to be quite informative. While the buncher ATE represents a local reduced-form quantity, I use it to assess the overall average effect of the FLSA by layering on additional (also non-parametric) assumptions.
I also show that the data in the bunching design are informative about counterfactual policies that change the location or “sharpness” of a kink. To do so, I extend a characterization of bunching from blomquist_individual_2015, and show that when combined with a general continuity equation kasy_who_2017 it yields bounds on the derivative of bunching and mean hours with respect to policy parameters. I use this to evaluate proposed reforms to the FLSA: e.g. lowering the overtime threshold below 40 hours (e.g. the Thirty-Two Hour Workweek Act proposed in the U.S. House of Representatives in 2021), or increasing the premium pay factor from 1.5 to 2.
The empirical setting of overtime pay involves confronting two challenges that are not typical of existing bunching-design analyses. Firstly, 40 hours is not an “arbitrary” point and bunching there could arise in part from factors other than it being the location of the kink. I use two strategies to estimate the amount of bunching that would exist at 40 absent the FLSA, and deliver clean estimates of the rule's effect. My preferred approach exploits the fact that when a worker makes use of paid-time-off hours these do not count towards that week's overtime threshold, shifting the location of the kink week-to-week in a plausibly idiosyncratic way. A second feature of the overtime setting is that work hours may not be set unilaterally by one party: in principle either the firm or the worker could choose a given worker's schedule. I provide evidence that week-to-week variation in hours is mostly driven by firms. Even if bargaining weight between workers and firms varies arbitrarily, I show that bunching at 40 hours is informative about labor demand rather than supply.
Empirically, I find that the FLSA overtime rule does in fact reduce hours of work among hourly workers, despite the theoretical possibility that offsetting wage adjustments might eliminate any such effect trejo_effects_1991. My preferred estimate suggests that about one quarter of the bunching observed at 40 among hourly workers is due to the FLSA, and those working at least 40 hours work, on average, about 30 minutes less in a week than they would absent the time-and-a-half rule. Across specifications, I obtain estimates of the local wage elasticity of weekly hours demand near 40 hours in the range $-0.04$ to $-0.19$, indicating that firms are fairly resistant to changing hours to avoid overtime payments.
The structure of the paper is as follows. Section (ref) lays out a motivating conceptual framework for work hours that relates my bunching approach to existing literature on overtime policy. Section (ref) introduces the payroll data I use in the empirical analysis. In Section (ref) I develop the generalized bunching-design approach in the context of the overtime application, with Appendix (ref) expanding on some of the supporting formal results and further generalizations. Section (ref) applies these results to estimate effect of the FLSA overtime rule on work hours, as well as the effects of proposed reforms to the FLSA. Section (ref) discusses the empirical findings from the standpoint of policy objectives, and Section (ref) concludes.
The estimates from the preceding section suggest that FLSA regulation indeed has real effects on hours worked, in line with labor demand theory when wages do not fully adjust to absorb the added cost of overtime hours. When averaged over affected workers and across pay periods, I find that hourly workers in my sample work at least 30 minutes less per week than they would without the overtime rule. This lower bound is broadly comparable to the few causal estimates that exist in the literature, including hamermesh_demand_2003 who assess the effects of expanding California's daily overtime rule to cover men in 1980, and brown_wages_2019 who use the erosion of the salary threshold for exemption of white-collar jobs in real terms over the last several decades.\footnote{ hamermesh_demand_2003 and brown_wages_2019 report estimates of $-0.5$ and $-0.18$ for the elasticity of overtime hours with respect to the overtime rate. My preferred estimate of $-0.04$ for the buncher ATE as an elasticity is the elasticity of total hours, including the first 40. An elasticity of overtime hours can be computed from this using the ratio of mean hours to mean overtime hours in the sample, resulting in an estimate of roughly $-0.45$.} By contrast, my estimates use an identification strategy that does not require focusing on the sub-population affected by a natural experiment, and are based on recent and administrative data.
My estimates speak to the substitutability of hours of labor between workers. The primary justifications for overtime regulation have been to reduce excessive workweeks, while encouraging hours to be distributed over more workers ehrenberg_longer_1982. How well this plays out in practice hinges on how easily an hour of work can be moved from one worker to another or across time, from the perspective of the firm. The results of this paper find hours demand to be relatively inelastic: hours cannot be easily so reallocated between workers or weeks. This suggests that ongoing efforts to expand coverage of the FLSA overtime rule may have limited scope to dramatically affect the hours of U.S. workers.
Nevertheless, the overall impact of the FLSA overtime rule on workers is still notable. The data suggest that at least about $3\%$ and as many as about $12\%$ of workers' hours are adjusted to the threshold introduced by the policy, indicating that it may have distortionary impacts for a significant portion of the labor force. The policy may also have important effects on unemployment. While an assessment of the employment effects of the FLSA overtime rule is beyond the scope of this paper, my estimates of the hours effect can be used to build a back-of-the-envelope calculation, following hamermesh_labor_1996-1. As detailed in Appendix (ref) I assume a value for the rate at which firms substitute labor for capital to obtain a “best-guess” estimate that the FLSA overtime rule creates about 700,000 jobs. To get an overall upper bound on the size of employment effects, one can instead attribute all of the bunching at 40 to the FLSA and assume that the total number of worker-hours is not reduced by the FLSA. By this estimate the FLSA increases employment by at most 3 million jobs, or roughly 3% among covered workers. A reasonable range of parameter values in this simple calculation rules out that the FLSA overtime rule has negative overall employment effects on hourly workers.
This paper has provided a new interpretation of the popular bunching-design method in the language of treatment effects, showing that the basic identifying power of the method is robust to a wide variety of underlying choice models. Across such models, the parameter of interest remains a reduced-form average treatment effect (local to the kink) between two appropriately-defined counterfactual choices, which is partially identified under a natural nonparametric assumption about those counterfactuals' distributions. This provides conditions under which the bunching design can be useful to answer program evaluation questions in a variety of contexts, particularly beyond those in which the researcher is prepared to posit a parametric model of agents' preferences.
By leveraging these insights with a new payroll dataset recording exact weekly hours paid at the individual level, I estimate that U.S. hourly workers subject to the Fair Labor Standard Act work shorter hours due to its overtime provision, which may lead to positive employment effects. Given the large amount of within-worker variation in hours observed, the modest size of the FLSA effects estimated in this paper suggest that firms do face significant incentives to maintain longer working hours, countervailing against the ones introduced by policies intended to reduce them.
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