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Abstract:
In recent years, much attention has been directed at the ongoing increase in body weight, and what might be done about it. We use data from the National Health Interview Survey (NHIS) for the period 1982-1996 to estimate models relating measures of body weight (BMI, a dummy indicating that a person is overweight or obese, and a dummy indicating that a person is obese) to two food price indexes constructed using regional BLS price data as well as the official BLS food price index. The most aggressive use of our results suggests that variation in year-to-year food prices is unlikely to explain much of the increase in body weight over our sample period. This conclusion holds true regardless of the food price measure we consider.

BMI, fat, diet, health, wild cluster bootstrap, fat tax

Abstract:
We first discuss the role of single-firm event studies in law and finance scholarship and in securities litigation. We discuss the (previously known) invalidity of the standard, t-statistic-based approach to inference in single-firm event studies. We then use a broad cross-section of CRSP data for the 2000-2007 period to investigate the standard approach’s performance using real-world data. Our results show that the standard approach is plagued by systematic, downward bias in asymptotic Type I error rates relative to desired significance levels. We then offer a very simple but statistically sound alternative, called the SQ test. We show analytically that the SQ test’s asymptotic Type I error rate always equals the desired significance level. Using our CRSP data, we offer Monte Carlo evidence that in event studies with 99 pre-event observations, the SQ test performs very well at conventional significance levels. We then analyze the asymptotic power of the SQ test and the standard approach. The SQ test and the standard approach have the same size-corrected asymptotic power, which means that even when the standard approach is appropriate, there is no loss to using the SQ test. More relevant as an empirical matter, we show that the standard approach’s downward bias in asymptotic Type I error rates brings along severe power loss. As an empirical matter, then, use of the standard approach can be expected to lead to substantial anti-plaintiff bias in securities litigation, though either pro- or anti-plaintiff bias is possible as an analytical matter. By contrast, the SQ test has considerable asymptotic power, even against moderately sized fixed alternatives. We also show how to extend our methods to cases with multiple firms, and multiple events. Finally, we show that our SQ test is asymptotically equivalent to bootstrap procedures, including those evaluated in recent finance scholarship.

event study, abnormal return, bootstrap, non-parametric, securities litigation

Abstract:
Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can over-reject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited di¤erences-in-di¤erences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0:05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a Wild cluster bootstrap performs better.

clustered errors, random effects, cluster robust

Abstract:
Economists have long recognized the ability of employers to construct benefits packages to induce workers to sort themselves. For instance, to encourage applications from individuals with a highly valued but largely unobservable characteristic, such as patience, employers might offer benefits that patient individuals are likely to value more than other individuals. By offering a compensation package with highly valued benefits but a relatively low wage, employers will attract workers with the favored characteristic and discourage other individuals from applying for or accepting the job. While economic theory generally views this kind of self-selection in value neutral terms, prejudiced employers could exploit this mechanism design framework to systematically discriminate against individuals on the basis of observable characteristics that the law prohibits employers from considering in their hiring decisions. As long as groups systematically differ in their preferences for various employment terms and conditions, employers can generate sorting in the application and employment acceptance stages, leading to the desired segregated outcome in a way that regulators will find difficult to prevent without dictating uniformity in benefits packages.

We develop a formal model as well as an intuitive discussion of the phenomenon. We provide a number of representative illustrations of how a prejudiced employer could exploit preference heterogeneity for discriminatory ends.These mechanisms include wage and benefit packages such as (1) high pension, low wages, (2) commission-based salaries, (3) Sundays off policies, and (4) free school tuition. We also note that some employers might end up with a segregated workforce even when they have no intention to sort workers or when they intend to sort for a non-discriminatory characteristic.

Finally, we conclude that current federal antidiscrimination law inadequately addresses either intentional or unintentional passive discrimination. Neither disparate treatment nor disparate impact frameworks are well suited to grappling with this form of structural discrimination. Passive discrimination facilitates rather than impedes employee choice and thus, might not be viewed as discrimination per se, even if it results in workplace segregation or means that individuals with protected characteristics who fail to self sort are least likely to value the form of compensation and fringe benefits they receive. We discuss some possible judicial and legislative approaches that may ameliorate passive discrimination, though many raise serious questions of their own.

Abstract:
The goal of the 1996 Personal Responsibility and Work Opportunity Reconciliation Act (PRWORA) was to end the dependency of needy parents on government benefits, in part by promoting marriage; the pre-reform welfare system was widely believed to discourage marriage because it primarily provided benefits to single mothers. However, welfare reform may have actually decreased the incentives to be married by giving women greater financial independence via the program's new emphasis on work. This paper uses Vital Statistics data on marriages and divorces during 1989-2000 to examine the role of welfare reform and other state-level variables on marriage and divorce rates. The results indicate that implementation of TANF is negatively associated with marriage and divorce rates, as are pre-TANF waivers from the AFDC program in some specifications.

welfare reform, marriage, divorce

Abstract:
In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

Abstract:
Labor supply theory predicts systematic heterogeneity in the impact of recent welfare reforms on earnings, transfers, and income. Yet most welfare reform research focuses on mean impacts. We investigate the importance of heterogeneity using random-assignment data from Connecticut's Jobs First waiver, which features key elements of post-1996 welfare programs. Estimated quantile treatment effects exhibit the substantial heterogeneity predicted by labor supply theory. Thus mean impacts miss a great deal. Looking separately at samples of dropouts and other women does not improve the performance of mean impacts. We conclude that welfare reform's effects are likely both more varied and more extensive than has been recognized.

treatment effect heterogeneity, welfare reform, distributional effects

Abstract:
Labor supply theory predicts systematic heterogeneity in the impact of recent welfare reforms on earnings, transfers, and income. Yet most welfare reform research focuses on mean impacts. We investigate the importance of heterogeneity using random-assignment data from Connecticut's Jobs First waiver features key elements of post-1996 welfare programs. Estimated quantile treatment effects exhibit the substantial heterogeneity predicted by labor supply theory. Thus mean impacts miss a great deal. Looking separately at dropouts and other women does not improve the performance of mean impacts. Evaluating Jobs First relative to AFDC using a class of social welfare functions, we find that Jobs First's performance depends on the degree of inequality aversion, the relative valuation of earnings and transfers, and whether one accounts for Jobs First's greater costs. We conclude that welfare reform's effects are likely both more varied and more extensive than has been recognized.

Abstract:
Dura Pharmaceuticals v. Broudo has been heralded as the most important securities case of the past decade. Many have suggested that its requirement that plaintiffs provide evidence of a significant stock price decline associated with a corrective disclosure will make it significantly harder to bring securities fraud cases. We use event study techniques to examine how hard it would have been to meet this requirement in a comprehensive dataset of 10b-5 cases in the two decades before Dura was decided. If those cases are representative of what cases might be brought post-Dura, our findings suggest that Dura will not have much of an effect.

event study, statistical evidence, securities fraud, 10b-5, Dura, loss causation

Abstract:
Many authors add variables sequentially to their covariate sets when using linear estimators to investigate the effect of a variable of interest X1, on some outcome y. One justification for this practice involves robustness: if estimates of the coefficient on X1 are stable across specifications, then researchers conclude that their findings are robust. A second justification involves accounting: by measuring the difference in X1's estimated coefficient as they add sets of covariates to the specification, researchers sometimes claim to have measured the effects of covariate variation on this coefficient. In this paper, I show that sequential covariate addition can be very misleading. The relationship between X1 and a given covariate set may be sensitive to the order in which other covariates have been added. This sensitivity is especially problematic for accounting exercises, as I show using the canonical example of the black-white wage gap. The paper's main contribution is to show how to use the population and sample omitted variables bias formulas to define an economically and econometrically meaningful conditional decomposition that explains how much various covariates account for sensitivity in the estimated coefficient on X1. I illustrate the conditional decomposition using NLSY data on the black-white wage gap, with interesting empirical results. I also discuss a number of extensions, including: instrumental variables estimators; the fact that my decomposition nests the Oaxaca-Blinder decomposition; and using the properties of the omitted variables bias formula to construct a Hausman test for cross-specification differences in coefficient estimates under the null that X1 and X2 are uncorrelated. I also provide asymptotic variance formulas in an appendix, as well as a link to Stata code that implements my estimators.

decompositions, black-white wage gap, omitted variables

Abstract:
We investigate the relationship between welfare reform and health insurance, health care utilization, and self-reported measures of health status for women aged 20-45, using nationally representative data from the Behavioral Risk Factor Surveillance System. We present estimates from both difference-in-difference models (applied to single women and single women with children) and difference-in-difference-in-difference models (using married women and single women without children as comparison groups). We find that welfare reform is associated with reductions in health insurance coverage and specific measures of health care utilization, as well as an increase in the likelihood of needing care but finding it unaffordable. We find no statistically significant effects of reform on health status. Overall, effects are somewhat larger for Hispanics compared to blacks and low educated women.

Abstract:
Labor market outcomes of welfare reform have been the subject of extensive research by economists, but there has been relatively little work on living arrangements, which was an important focus of reformers. Our research fills that gap by using data from the March CPS to examine the impacts of 1990s welfare waivers and the 1996 Federal welfare reform on living arrangements in samples of both children and women. Our findings suggest three main conclusions. First, welfare reform has had large effects on some important measures of living arrangements, including household size, parental co-residence among children, and marital status among women. Second, those effects are neither entirely aligned with the stated goals of reform nor entirely in spite of these goals. For example, in states that never had waivers, TANF was associated with a reduction of 14 percentage points in the fraction of Black children living in central cities who live with an unmarried parent. However, the fraction of these children living with neither parent rose by 8 percentage points, essentially doubling the baseline level. Third, there is a great deal of treatment heterogeneity both with respect to racial and ethnic groups, and with respect to whether reforms were waivers, TANF in states that had waivers, or TANF in states that did not (e.g., waiver effects on parental co-residence among Black, central-city children was much smaller than were TANF effects). Standard approaches - using only data on adult women, pooling the data across racial and ethnic groups, focusing only on high school dropouts, and/or assuming that TANF effects are the same in waiver and nonwaiver states - would generally not uncover these important changes in living arrangements.

Abstract:
A large literature has been concerned with the impacts of recent welfare reforms on income, earnings, transfers, and labor-force attachment. While one strand of this literature relies on observational studies conducted with large survey-sample data sets, a second makes use of data generated by experimental evaluations of changes to means-tested programs. Much of the overall literature has focused on mean impacts. In this paper, we use random-assignment experimental data from Canada`s Self-Sufficiency Project (SSP) to look at impacts of this unique reform on the distributions of income, earnings, and transfers. SSP offered members of the treatment group a generous subsidy for working full time. Quantile treatment effect (QTE) estimates show there was considerable heterogeneity in the impacts of SSP on the distributions of earnings, transfers, and total income; heterogeneity that would be missed by looking only at average treatment effects. Moreover, these heterogeneous impacts are consistent with the predictions of labor supply theory. During the period when the subsidy is available, the SSP impact on the earnings distribution is zero for the bottom half of the distribution. The SSP earnings distribution is higher for much of the upper third of the distribution except at the very top, where the earnings distribution is the same under either program or possibly lower under SSP. Further, during the period when SSP receipt was possible, the impacts on the distributions of transfer payments (IA plus the subsidy) and total income (earnings plus transfers) are also different at different points of the distribution. In particular, positive impacts on the transfer distribution are concentrated at the lower end of the transfer distribution while positive impacts on the income distribution are concentrated in the upper end of the income distribution. Impacts of SSP on these distributions were essentially zero after the subsidy was no longer available.

Abstract:
I show that among women likely to use welfare, movers move to higher-benefit states. I also find that the probability likely welfare users will move at all is lower in higher-benefit states. This effect is concentrated early in the life cycle, as theory predicts. I construct a theoretical framework to measure the impact of welfare migration on optimal state benefits. Simulation results suggest little impact in higher-benefit states, but possibly a more substantial impact in other states. Finally, evidence suggests little reason for concern (due to welfare migration) in using cross-state variation in welfare generosity to identify incentive effects of the welfare system on other outcome variables.

Abstract:
Welfare eligibility has traditionally required presence of a minor child in the household. Welfare migration incentives should thus be stronger among mothers of young children than among mothers of older children. Moreover, once migration has occurred, it is less likely to occur in the future, so that the population distribution is selected on locational preferences after initial locational decisions are made. Both of these factors suggest that welfare migration should be observed primarily among mothers of relatively young children. Using several welfare migration measures, I present evidence of substantial lifecycle welfare migration among women observed in the 1980 Census, with 1990 Census data suggesting positive but relatively less welfare migration. I argue that this pattern of evidence is to be expected based on theoretical models of the joint determination of locational choice and state benefit determination; intergenerational correlation in income also leads to the prediction of declining welfare migration. My results suggest that previous literature on welfare migration has understated the extent of welfare migration because of failure to address dynamic incentive and selection effects.