Jonah B. Gelbach

Robust Inference with Multi-way Clustering

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. 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, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.

Bootstrap-Based Improvements for Inference with Clustered Errors

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.

The Impact of Welfare Reform on Marriage and Divorce

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 programs 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 and Children's Living Arrangements.

Little is known about welfare reforms effects on family structure and childrens living arrangements, an important focus for reformers. Using March CPS data, we find that state welfare waivers are associated with children being less likely to live with unmarried parents, more likely to live with married parents, and more likely to live with neither parent. Children living with neither parent are living with grandparents or other relatives, or rarely, in foster care. The estimates vary somewhat by childrens race and ethnicity. Due to the limited variation in TANFs implementation timing across states, we focus on the waiver results.

Migration, the life cycle, and state benefits: How low is the bottom?

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.

Cheap Donuts and Expensive Broccoli: The Effect of Relative Prices on Obesity

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.

Indicator targeting in a political economy: Leakier can be better

In LDCs, policymakers sometimes cannot observe income among the poor. One oft-proposed approach to redistribution is indicator targeting: targeting transfers on corrrelations between income and “indicators” like geography, gender, or occupation. We build a simple model in which maximizing poverty reduction from a fixed budget requires indicator targeting. Because insurance motives drive political support for redistribution, the budget depends on the degree of targeting. When middle income agents receive targeted transfers sufficiently rarely, introducing targeting reduces poor agents’ welfare. The converse holds when middle income agents receive targeted transfers sufficiently rarely, i.e. if the redis-tributive bucket is sufficiently leaky.

Valid Inference in Single-Firm, Single-Event Studies

Single-firm event studies play an important role in both scholarship and litigation despite the general invalidity of standard inference. We use a broad cross-section of 2000--2007 CRSP data and find that the standard approach performs poorly in terms of both Type I and Type II error rates. We discuss a simple-to-use alternative, the SQ test, based on sample quantiles of the empirical distribution of pre-event fitted excess returns, which has correct asymptotic Type I error rate. Results suggest that the test will be useful in studying the impact of firm-specific events such as regulation, anti-trust rulings, and corporate or securities litigation. Copyright 2013, Oxford University Press.

Some Evidence on Race, Welfare Reform, and Household Income

In 1996, federal welfare-reform legislation eliminated Aid to Families with Dependent Children (AFDC) and replaced it with Temporary Assistance for Needy Families (TANF). Numerous studies have estimated impacts of reform on welfare caseloads, employment, earnings, family structure, income, and poverty. Two principal challenges to identifying TANF’s impact have been discussed in the literature. First, factors other than welfare reform should have increased household income. It is well known that reform occurred during a period of strong economic performance. While the unemployment rate for blacks fell to the lowest level ever recorded, wages for low-skill groups rose for the first time since the 1970’s. Further, other policy changes in the second half of the 1990’s focused on improving the economic status of the disadvantaged. Examples include expansions in the Earned Income Tax Credit (EITC), minimum wages, and public health insurance (Medicaid and the Children’s Health Insurance Program). Second, TANF was implemented in all states over just 16 months (between September 1996 and January 1998), leaving only limited scope for identifying impacts of TANF through timing across states. While these challenges are well known, their implications for interpreting estimated TANF impacts in nonexperimental studies are not. In this paper, we do four things. First, we discuss the identification of TANF effects in a prototypical nonexperimental model. We show that if TANF effects are the same in every year, then the lack of time variation in TANF implementation is not problematic. However, if TANF and trend effects are allowed to vary over time in an unrestricted fashion, then TANF effects for later years are unidentified. Second, we propose a method for bounding impacts in light of this identification problem. Third, we apply this method to analyze the impact of TANF on household income for a sample of children in the Current Population Survey (CPS) covering calendar years 1988–1999. Fourth, we document significant heterogeneity in the association between household income and both TANF and residual factors across white, Hispanic, and black children.

Can Variation in Subgroups' Average Treatment Effects Explain Treatment Effect Heterogeneity? Evidence from a Social Experiment

We assess whether welfare reform affects earnings only through mean impacts that are constant within but vary across subgroups. This is important because researchers interested in treatment effect heterogeneity typically focus on estimating mean impacts that only vary across subgroups. Using a novel approach to simulating treatment group earnings under the constant mean impacts within subgroup model, we find this model does a poor job of capturing treatment effect heterogeneity for Connecticuts Jobs First welfare reform experiment. Notably, ignoring within-group heterogeneitywould lead one to miss evidence that treatment effects are consistent with basic labor supply theory.