Debopam Bhattacharya

A Nonparametric Analysis of Black-White Differences in Intergenerational Income Mobility in the United States

This paper concerns the problem of inferring the effects of covariates on intergenerational income mobility, i.e. on the relationship between the incomes of parents and future earnings of their children. We focus on two different measures of mobility - (i) traditional transition probability of movement across income quantiles over generations and (ii) a new direct measure of upward mobility, viz. the probability that an adult childs relative position exceeds that of the parents. We estimate the effect of possibly continuously distributed covariates from data using nonparametric regression and average derivatives and derive the distribution theory for these measures. The analytical novelty in the derivation is that the dependent variables involve nonsmooth functions of estimated components - marginal quantiles for transition probabilities and relative ranks for upward mobility - thus necessitating nontrivial modifications of standard nonparametric regression theory. We use these methods on US data from the National Longitudinal Survey of Youth to study black-white differences in intergenerational mobility, a topic which has received scant attention in the literature. We document that whites experience greater intergenerational mobility than blacks. Estimates of conditional mobility using nonparametric regression reveal that most of the interracial mobility gap can be accounted for by differences in cognitive skills during adolescence. The methods developed here have wider applicability to estimation of nonparametric regression and average derivatives where the dependent variable either involves a preliminary finite-dimensional estimate in a nonsmooth way or is a nonsmooth functional of ranks of one or more random variables.

Inferring welfare maximizing treatment assignment under budget constraints

This paper concerns the problem of allocating a binary treatment among a target population based on observed covariates. The goal is to (i) maximize the mean social welfare arising from an eventual outcome distribution, when a budget constraint limits what fraction of the population can be treated and (ii) to infer the dual value, i.e. the minimum resources needed to attain a specific level of mean welfare via efficient treatment assignment. We consider a treatment allocation procedure based on sample data from randomized treatment assignment and derive asymptotic frequentist confidence interval for the welfare generated from it. We propose choosing the conditioning covariates through cross-validation. The methodology is applied to the efficient provision of anti-malaria bed net subsidies, using data from a randomized experiment conducted in Western Kenya. We find that subsidy allocation based on wealth, presence of children and possession of bank account can lead to a rise in subsidy use by about 9% points compared to allocation based on wealth only, and by 17% points compared to a purely random allocation.

Are University Admissions Academically Fair

High-profile universities often face public criticism for undermining academic merit and promoting social elitism through their admissions-process. In this paper, we develop an empirical test for whether access to selective universities is meritocratic. If so, then the academic potential of marginal candidates -- the admission-threshold -- would be equated across demographic groups. But these thresholds are difficult to identify when admission-decisions are based on more characteristics than observed by the analyst. We assume that applicants who are better-qualified on standard observable indicators should on average, but not necessarily with certainty, appear academically stronger to admission-tutors based on characteristics observable to them but not us. This assumption can be used to reveal information about the sign and magnitude of differences in admission thresholds across demographic groups which are robust to omitted characteristics, thus enabling one to test whether different demographic groups face different academic standards for admission. An application to admissions-data at a highly selective British university shows that males and private school applicants face significantly higher admission-thresholds, although application success-rates are equal across gender and school-type. Our methods are potentially useful for testing outcomebased fairness of other binary treatment decisions, where eventual outcomes are observed for those who were treated.

Consistent Nonparametric Tests for Lorenz Dominance

This article proposes consistent nonparametric methods for testing the null hypothesis of Lorenz dominance. The methods are based on a class of statistical functionals defined over the difference between the Lorenz curves for two samples of welfare-related variables. We present two specific test statistics belonging to the general class and derive their asymptotic properties. As the limiting distributions of the test statistics are nonstandard, we propose and justify bootstrap methods of inference. We provide methods appropriate for case where the two samples are independent as well as the case where the two samples represent different measures of welfare for one set of individuals. The small sample performance of the two tests is examined and compared in the context of a Monte Carlo study and an empirical analysis of income and consumption inequality.

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent/compensating variation resulting from price-change of a discrete good using individual-level data, when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV/CV can be expressed as simple closed-form functionals of conditional choice-probabilities under essentially unrestricted preference-distributions. These results hold even when the distribution/dimension of unobserved heterogeneity are neither known nor identified and utilities are neither quasi-linear nor parametrically specified. The welfare distributions take simple forms which are easy to compute in applications. In particular, average EV for a price-rise equals the change in average Marshallian consumer-surplus and is smaller than average CV for a normal good. These nonparametric point-identification results fail for ordered choice if the unit-price is identical for all alternatives, thereby providing a connection to Hausman-Neweys (2014) partial identification results for the limiting case of continuous choice.

Evaluating Treatment Protocols Using Data Combination

In real life, individuals are often assigned to binary treatments according to existing treatment protocols. Such protocols, when designed with “taste-based” motives, would be productively inefficient in that the expected returns to treatment for a marginal treatment recipient would vary across covariates and be larger for discriminated groups. This cannot be directly tested if assignment is based on more covariates than the researcher observes, because then the marginal treatment recipient is not identified. We present (i) a partial identification approach to detecting such inefficiency which is robust to selection on unobservables and (ii) a novel way of point-identifying the necessary counterfactual distributions by combining observational datasets with experimental estimates. These methods can also be used to (partially) infer risk-preferences which may rationalize the observed treatment allocations. Specifically, existing healthcare datasets can be analyzed with the proposed tools to test the allocational efficiency of medical treatments. Using our methodology on data from the Coronary Artery Surgery Study in the US, which combined experimental and observational components, we find that after controlling for age, smokers in the observational dataset had to overcome a higher threshold of expected survival relative to nonsmokers in order to qualify for surgery.

The Empirical Content of Discrete Choice Models

Empirical demand models used for counterfactual predictions and welfare analysis must be rationalizable, i.e. theoretically consistent with utility maximization by heterogeneous consumers. We show that for binary choice under general unobserved heterogeneity, rationalizability is equivalent to a pair of Slutsky-like shape-restrictions on choice-probability functions. The forms of these restrictions differ from Slutsky-inequalities for continuous goods. Unlike McFadden-Richters stochastic revealed preference, our shape-restrictions (a) are global, i.e. their forms do not depend on which and how many budget-sets are observed, (b) are closed-form, hence easy to impose on parametric/semi/non-parametric models in practical applications, and (c) provide computationally simple, theory-consistent bounds on demand and welfare predictions on counterfactual budget-sets.

Empirical Welfare Analysis for Discrete Choice: Some General Results

This paper develops nonparametric methods for welfare-analysis of economic changes in the common setting of multinomial choice. The results cover (a) simultaneous price-change of multiple alternatives, (b) introduction/elimination of an option, (c) changes in choice-characteristics, and (d) choice among non-exclusive alternatives. In these cases, Marshallian consumer surplus becomes path-dependent, but Hicksian welfare remains well-defined. We demonstrate that under completely unrestricted preference-heterogeneity and income-effects, the distributions of Hicksian welfare are point-identified from structural choice-probabilities in scenarios (a), (b), and only set-identified in (c), (d). Weak-separability restores point-identification in (c). In program-evaluation contexts, our results enable the calculation of compensated-effects, i.e. the programs cash-equivalent and resulting deadweight-loss. They also facilitate theoretically justified cost- benefit comparison of interventions targeting different outcomes, e.g. a tuition-subsidy and a health-product subsidy. Welfare-analyses under endogeneity is briefly discussed. An application to data on choice of fishing-mode illustrates the methods.