Papers by Debopam Bhattacharya
We consider the problem of detecting socially sub-optimal allocation of a binary treatment made b... more We consider the problem of detecting socially sub-optimal allocation of a binary treatment made by decision-makers, such as doctors referring patients to surgery or loan o¢ cers approving credit applications. Such misallocation can arise from a va- riety of mechanisms, including taste-based, implicit or inadvertent discrimination. Our detection method is based on combining the observational dataset with an experimental dataset where the treatment was randomly assigned. The combined data can be used to test an implication of economically e¢ cient treatment assignment under the assumption that the decision-maker can form correct expectations. The methodology centers on a partial identi…cation approach which continues to work when the decision-maker observes more covariates than us and/or when individuals agreeing to be randomized are system- atically worse/better in terms of potential outcomes. Our methods can also be used to (partially) infer those unobserved risk-preferences of the ...
An important goal of empirical demand analysis is choice and welfare prediction on counterfactual... more An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy-interventions. Such predictions are more credible when made without arbitrary functional-form/distributional assumptions, and instead based solely on economic rationality, i.e. that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality 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-Richter's 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 param...
This paper concerns the problem of optimally allocating scarce indivisible re-sources among a tar... more This paper concerns the problem of optimally allocating scarce indivisible re-sources among a target group of individuals based on experimental data for a sam-ple drawn from the same population. For a wide class of social welfare functions, the problem can be set up as a mathematical program with estimated components. The paper develops asymptotic statistical inference on the estimated value function which depends on uniqueness of the population solution. This work complements the "set identification " literature in econometrics by conducting inference on the optimized value of the criterion function and the "treatment choice " literature by allowing aggregate resource constraints. A key methodological contribution is to show that applicability of these techniques extends beyond linear maximands like the mean to other important policy objectives like outcome quantiles which, though nonlinear, are proved to be quasi-convex in the allocation probabilities. I apply ...
Regular use of e¤ective health-products such as insecticide-treated mosquito nets (ITN) by a hous... more Regular use of e¤ective health-products such as insecticide-treated mosquito nets (ITN) by a household bene
ts its neighbors by (a) reducing chances of infection and (b) raising aware-ness about product-e¤ectiveness, thereby increasing product-use. Due to their potential social bene ts and high purchase price, causing free-riding and sub-optimal private procurement, such products may be subsidized in developing countries through means-testing. Owing to associated spillover e¤ects, cost-bene
t analysis of such subsidies requires modelling behavioral responses of both the subsidized household and its neighbors. Using experimental data from Kenya where subsidies were randomized, coupled with GPS-based location information, we show how to es-timate aggregate ITN use resulting from means-tested subsidies in the presence of such spatial spillovers. Accounting for spillovers introduces in
nite-dimensional estimated regressors cor-responding to continuously distributed location coordinates ...
This paper concerns the problem of optimally allocating scarce indivisible resources among a targ... more This paper concerns the problem of optimally allocating scarce indivisible resources among a target population based on experimental data for a sample drawn from this population. For a wide class of social welfare functions, the problem can be set up as a mathematical program with estimated components. The paper develops asymptotic statistical inference on the estimated solutions and values which depends on the degree of uniqueness of the population solution. Subsampling based inference is shown to be invalid when near-uniqueness is allowed but conservative inference is possible. This work complements the "set identi
cation" literature by conducting inference on the optimized value of the criterion function and the "treatment choice" literature by allowing aggregate resource constraints. Applicability of these techniques extends beyond linear maximands like the mean to other important policy objectives like outcome quantiles which, though nonlinear, are shown to ...
This paper explores the problem of empirical welfare-analysis in multinomial choice settings, all... more This paper explores the problem of empirical welfare-analysis in multinomial choice settings, allowing for completely general consumer-heterogeneity and income-e¤ects. We present results on welfare-analysis under three practically important scenarios, viz., (i) simultaneous pricechange of multiple options, (ii) introduction/elimination of a choice-alternative, and (iii) choice among non-exclusive goods. Our results do not follow from Bhattacharya (Econometrica, 2015). In program-evaluation contexts, these results would enable estimation of compensated programe¤ects, i.e., how much the subjects themselves value the program, and the resulting deadweight loss. Welfare-analysis under income-endogeneity is also briey discussed. The methods are illustrated with hypothetical policy experiments using survey data from India on teenagers who make the choice between school, work and home-stay.
This paper analyzes nonparametric identification of optimal allocations in input matching problem... more This paper analyzes nonparametric identification of optimal allocations in input matching problems and derives asymptotic distribution of resulting estimates under both point and set-identified situations. The key tools in the analysis are (i) the fundamental theorem of linear programming which makes the relevant parameter space discrete and (ii) Cramer’s theorem for large deviations which implies that sampling error in the estimation of optimal solutions does not affect asymptotic distribution of the optimized value. This latter distribution is zero-mean normal when the solution is point-identified but both asymptotically biased and non-normal when the solution is set-identified. The ∗Address for correspondence: 327, Rockefeller Hall, Dartmouth College, Hanover, NH 03755. e-mail: [email protected]. †This research was motivated by the work of Graham, Imbens and Ridder (2005) on alternative matching procedures presented at the econometrics workshop at Harvard-MIT in ...
In this note, we present some theoretical results useful for inference on a population Lorenz cur... more In this note, we present some theoretical results useful for inference on a population Lorenz curve for income and expenditure distributions, when the population density of the distribution is not (uniformly) bounded away from zero, and potentially has thick tails. Our approach is to define Hadamard differentiability in a slightly nonstandard way, and using it to establish a functional delta method for the Lorenz map. Our differentiability concept is nonstandard in that the perturbation functions, which are used to compute the functional derivative, are assumed to satisfy certain limit conditions. These perturbation functions correspond to a (nonparametric) distribution function estimator. Therefore, as long as the employed estimator satis.es the same limit conditions, which we verify in this paper, the delta method and corresponding asymptotic distribution results can be established.
This paper concerns the problem of dividing a set of individuals from a target population into pe... more This paper concerns the problem of dividing a set of individuals from a target population into peer-groups based on observed discrete-valued covariates so as to maximize the expected outcome of the entire set, e.g. allocation of freshmen to dorm rooms to maximize mean GPA. The decision is based on the outcome of random grouping of a pilot sample drawn from the target population. Computationally, the allocation problem reduces to a standard linear program whose objective function involves a first-step nonparametric estimate of the production function. I show that either the population problem has a unique solution or all feasible allocations are optimal which can be tested using a pivotal statistic. Under uniqueness, asymptotic distributions can be established using Cramer’s theorem for large deviations. Under nonuniqueness the estimated maximum value has an asymptotically biased non-normal distribution. This bias can be analytically corrected to produce pretest confidence intervals ...
This paper develops a method that accounts for non-ignorable sample attrition in the presence of ... more This paper develops a method that accounts for non-ignorable sample attrition in the presence of population attrition for use with a non-representative panel sample. When there is population attrition, refreshment samples are not representative of the
rst period population. Therefore, the existing sample attrition-correcting method developed by Hirano, Imbens, Ridder, and Rubin (2001) and Bhattacharya (2008) cannot be applied. This paper shows that the problem can be resolved by generating a counterfactual, but representative cross-section prior to applying their procedure. The proposed method is used to obtain attrition-correcting weights for the native and immigrant panel samples in the Current Population Survey. Keywords: Immigration, Population Attrition, Sample Attrition JEL Classi
cation Codes: C23, C81, J61 0I am grateful to my advisors, Joseph Altonji, Yuichi Kitamura, Fabian Lange, and Mark Rosenzweig. I have also bene
ted from helpful comments made by Donald Andrews, Debo...
This paper concerns the problem of inferring the effects of covariates on intergenerational incom... more 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 child's 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 me...
McFadden's random-utility model of multinomial choice has long been the workhorse of applied ... more McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with nonparametric unobserved heterogeneity and general income-effects. When combined with an additional restriction, the above conditions are equivalent to the canonical Additive Random Utility Model. The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments. A corollary shows that Slutsky-symmetry, a key condition for previous rationalizability results, is equivalent to absence of income-effects. Our results imply theory-consistent nonparametric bounds for choice-probabilities on counterfactual budget-sets. They also apply to widely used random-coefficient models, upon conditioning on observable choice characteristics. The theory of pa...
This paper concerns empirical measurement of Hicksian consumer welfare under intervalreported inc... more This paper concerns empirical measurement of Hicksian consumer welfare under intervalreported income. Bhattacharya (2015) has shown that for discrete choice, welfare distributions resulting from a hypothetical price-change can be expressed as closed-form transformations of choice probabilities. However, when income is interval-reported, as is the case in many surveys, the choice probabilities, and hence welfare distributions are not point-identified. We derive bounds on average welfare in such scenarios under the assumption of a normal good. A finding of independent interest is a set of Slutsky-like shape restrictions which are linear in average demand, unlike those for continuous choice. A parametric specification of choice probabilities facilitates imposition of these Slutsky conditions, and leads to computationally simple inference for the partially identified features of welfare. In particular, the estimand is shown to be directionally differentiable, so that recently developed ...
Econometrica
An important goal of empirical demand analysis is choice and welfare prediction on counterfactual... more An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional‐form/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality 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–Richter's stochastic revealed preference, our shape restrictions (a) are global, that is, their forms do not depend on which and how many budget sets are observed, (b) are closed form, hence easy to impose ...
Quantitative Economics
This paper develops nonparametric methods for welfare-analysis of economic changes in the common ... more 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 nonexclusive alternatives. In these cases, Marshallian consumer surplus becomes pathdependent, 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 choiceprobabilities in scenarios (a), (b), and only set-identified in (c), (d). In programevaluation contexts, our results enable the calculation of compensated-effects, that is, the program's cash-equivalent and resulting deadweight-loss. They also facilitate a theoretically justified cost-benefit comparison of interventions targeting different outcomes, for example, 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.
Many real-life settings of consumer-choice involve social interactions, causing targeted policies... more Many real-life settings of consumer-choice involve social interactions, causing targeted policies to have spillover-effects. This paper develops novel empirical tools for analyzing demand and welfare-effects of policy-interventions in binary choice settings with social interactions. Examples include subsidies for healthproduct adoption and vouchers for attending a high-achieving school. We establish the connection between econometrics of large games and Brock-Durlauf-type interaction models, under both I.I.D. and spatially correlated unobservables. We develop new convergence results for associated beliefs and estimates of preference-parameters under increasing-domain spatial asymptotics. Next, we show that even with fully parametric specifications and unique equilibrium, choice data, that are sufficient for counterfactual demandprediction under interactions, are insufficient for welfare-calculations. This is because distinct underlying mechanisms producing the same interaction coefficient can imply different welfare-effects and deadweightloss from a policy-intervention. Standard index-restrictions imply distribution-free bounds on welfare. We illustrate our results using experimental data on mosquito-net adoption in rural Kenya.
SSRN Electronic Journal
In multinomial choice settings, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closedf... more In multinomial choice settings, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closedform conditions, under which choice probability functions can be rationalized via random utility models. A key condition is Slutsky symmetry. We first show that in the multinomial context, Daly-Zachary's Slutsky symmetry is equivalent to absence of income-effects. Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be sufficient for rationalizability. Finally, we outline nonparametric identification of preference distributions using these results. The theory of linear partial differential equations plays a key role in our analysis.
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Papers by Debopam Bhattacharya