Temporary help service firms' use of employer tax credits: implications for disadvantaged workers' labor market outcomes.

5. Panel Matching Estimation of the Effects of WOTC/THS Interaction

We use a panel version of the econometric method of matching to address the two key issues of this article: the labor market effects of the WOTC on workers in the THS sector and the labor market effects of THS employment (relative to traditional employment) on workers who are certified for the WOTC. The matching estimator for treatment effects was introduced to the economics literature in a series of papers published in the late 1990s by economists Heckman, Ichimura, Smith, and Todd (Heckman, Ichimura, and Todd 1997; Heckman et al. 1998; Heckman, Ichimura, and Todd 1998). This methodology, which originated in the statistics literature (e.g., Rosenbaum and Rubin 1983), allows estimation of treatment effects in contexts where there is nonrandom selection into treatment. This is a key feature for our purposes since workers select into THS employment and firms select into WOTC participation. Matching also generates estimates with more limited functional-form assumptions than many other estimators since part of the estimation is nonparametric. In addition, matching deals explicitly with the so-called common support problem, in which some treated individuals have no observationally similar counterparts among the untreated and thus cannot be reasonably used in estimation of treatment effects. (26) And, finally, Heckman et al. (1998) emphasize that matching works best when both treatment and comparison groups are from the same local labor markets, which is also a feature of our data.

The matching estimator is consistent for the effect of interest, called the treatment on the treated, which can be expressed as

E([Y.sub.1] - [V.sub.0] | D = 1),

where [Y.sub.1 is the labor market outcome in the presence of treatment, [Y.sub.0] is the outcome in its absence, and D = 1 indicates treatment (WOTC participation or THS employment). (27) The general approach of matching is to estimate counterfactuals for each treated person so that his or her treated outcome (which is observed) can be compared to what would have happened in the absence of treatment (which we estimate using the comparison group).

Although more flexible than linear regression, matching still requires a maintained assumption about the relationship between the treated and untreated. Cross-sectional matching is valid only if, after controlling for observable characteristics X, a person's ultimate treatment status is not related to what his or her outcome would have been in the absence of treatment. In other words, people select into treatment on the basis of observables only. In order to relax this assumption, we use a panel version of the matching estimator that allows a time-invariant (unobserved) difference in outcomes between the treated and the untreated. These estimates use dependent variables defined as the difference between pre--and posttreatment outcomes for each individual. The following mean-independence assumption must hold for the periods t (before treatment) and t' (after treatment):

E([[Y.sub.0t'] - [Y.sub.0t] [absolute value of D = 1,X) = E([Y.sub.0t'] - [Y.sub.0t]] D = 0,X) for X [epsilon] S,

where S is defined as the overlapping support among the treatment and comparison groups. (28) This assumption implies that the outcome trajectories of the treatment and comparison groups must match, but their outcome levels are allowed to differ by an unobserved constant. For example, this assumption can hold even if the people who select into THS employment have lower wage levels in all periods due to something unobservable about them. This panel version of the matching estimator often performs better than its cross-sectional counterpart, perhaps because it allows for this unobserved heterogeneity (see, e.g., Heckman et al. 1998).

The common application of matching we use, called propensity score matching, is a two-step process in which we first estimate the probability of treatment based on the conditioning variables. By generating predicted probabilities of treatment (i.e., propensity scores), we reduce the matching process to the one-dimensional problem of comparing treated and untreated workers with similar propensity scores (rather than requiring matches on all the X variables). (29) On estimation of the propensity score, we perform the matching estimation by comparing the outcome trajectory of each treated person to a weighted average of the outcome trajectories of untreated people with similar propensity scores. To make this weighted average an appropriate counterfactual for a given treated person, the highest weight is placed on those untreated people with propensity scores most similar to the treated individual. We use nonparametric local-linear regression (similar to a kernel estimator) to calculate and apply these weights, which produces an estimated treatment effect for each treated individual without imposing functional-form assumptions on the relationship between the propensity scores and the outcomes. (30) These individual effects are averaged to form the overall treatment-effect estimate.

The Effects of the WOTC on THS Workers

We use the sample of THS workers who were WOTC eligible or WOTC certified (from Table 1) to investigate the effects of the WOTC within the THS industry. (31) As we discovered earlier, there are a number of worker and firm characteristics that are associated with WOTC certification. Many of these factors, such as education, are also likely to influence wages and job tenure. We include these variables in the propensity score estimation reported in Table 4.

The results of the propensity score estimation reflect some of the patterns we observed in our earlier tabulations. Workers who are older, white, or more highly educated are significantly more likely to be WOTC certified than younger, minority, or less educated workers. The effect of the number of children is negative, which is consistent with Table 1. In addition, Milwaukee residents and workers at firms headquartered in Wisconsin are less likely to become WOTC certified. Finally, higher typical earnings at the firm for all their disadvantaged workers (in the past year) are predictive of higher earnings for the THS worker being observed.

Using these propensity scores in the matching estimation, we examine the effects of WOTC certification on the earnings and job tenure of THS workers who are WOTC eligible. Since the panel estimation requires each worker's outcomes to be measured both before and after treatment in order to control for time-invariant unobservables, we must choose broad measures of earnings and tenure that are not specific to the THS job of interest (which, by definition, is not observed in prior periods). We choose to examine total earnings and total quarters employed in all jobs for periods up to two years before and after the start date at the job of interest. (32) This incorporates the outcomes at the job of interest into a broader measure of earnings growth and labor force attachment extending (in many cases) to time periods subsequent to the end of that particular job.

For our application of panel matching, we use local linear regression to create a "counterfactual" change in earnings and tenure for each WOTC-certified worker, predicted by a weighted average of workers with similar propensity scores who were WOTC eligible but not certified. The difference between this counterfactual and the worker's actual change in outcomes is attributed to the effects of the WOTC program. These differences are averaged across workers to generate an estimate of the average effect of treatment on the treated. Table 5 contains these results, which are estimated separately for the first year and the second year after the THS job begins.

We do not find much evidence that being certified for the WOTC brings about improvements in workers' job outcomes during these two years. While Table 5 shows positive point estimates of the effect of the WOTC on earnings, these are imprecisely estimated, so we cannot reject the hypothesis of no effect. Similarly, we do not find evidence of any WOTC effects on labor force attachment as measured by quarters worked per year. In fact, while the sign of any effect cannot be determined, the small coefficients (0.071 and 0.141) combined with their standard errors (0.099 and 0.114, respectively) suggest that any large effect in either direction is quite unlikely. We therefore find no support for the hypothesis that the WOTC provides a "foot in the door" for THS workers to improve future outcomes beyond the WOTC job. This is consistent with the findings in Hamersma (2008) that overall earnings and labor force attachment do not appear to be affected by WOTC certification. The results could reflect the limited scope of the subsidy or a broader general equilibrium effect that equalizes wages over time.

The Effects of THS Employment on WOTC/WtW Workers

We use the sample of WOTC workers (from Table 2B) to investigate the effects of THS employment among WOTC recipients. (33) Since particular demographic characteristics and target group information proved to be associated with selection into THS employment, we include those characteristics in the propensity score estimation shown in Table 6.