arXiv subjects

Vishal Kamat

Publications and source records attributed to Vishal Kamat.

5 recordsLinked to original sources

arXiv2026

Identification in Multiple Treatment Models under Discrete Variation

We develop a marginal treatment effect based method to learn about causal effects in multiple treatment models with discrete instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that permit multidimensional unobserved heterogeneity. An inherent complication is that the primitives characterizing the selection model are not generally point-identified. Allowing these primitives to be point-identified up to a finite-dimensional parameter, we show how a two-step computational program can be used to obtain sharp bounds for a number of treatment effect parameters when the marginal treatment response functions are allowed to satisfy only nonparametric shape restrictions or are additionally parameterized. We demonstrate the benefits of our method by revisiting Kline and Walters' (2016) empirical analysis of the Head Start program. Our approach relaxes their point-identifying assumptions on the selection model and marginal treatment response functions, allowing us to assess the robustness of their conclusions.

econ.EM↗

arXiv2024

Estimating Welfare Effects in a Nonparametric Choice Model: The Case of School Vouchers

We develop new robust discrete choice tools to learn about the average willingness to pay for a price subsidy and its effects on demand given exogenous, discrete variation in prices. Our starting point is a nonparametric, nonseparable model of choice. We exploit the insight that our welfare parameters in this model can be expressed as functions of demand for the different alternatives. However, while the variation in the data reveals the value of demand at the observed prices, the parameters generally depend on its values beyond these prices. We show how to sharply characterize what we can learn when demand is specified to be entirely nonparametric or to be parameterized in a flexible manner, both of which imply that the parameters are not necessarily point identified. We use our tools to analyze the welfare effects of price subsidies provided by school vouchers in the DC Opportunity Scholarship Program. We find that the provision of the status quo voucher and a wide range of counterfactual vouchers of different amounts can have positive and potentially large benefits net of costs. The positive effect can be explained by the popularity of low-tuition schools in the program; removing them from the program can result in a negative net benefit. We also find that various standard logit specifications, in comparison, limit attention to demand functions with low demand for the voucher, which do not capture the large magnitudes of benefits credibly consistent with the data.

econ.GN↗

arXiv2023

Identifying the Effects of a Program Offer with an Application to Head Start

I propose a treatment selection model that introduces unobserved heterogeneity in both choice sets and preferences to evaluate the average effects of a program offer. I show how to exploit the model structure to define parameters capturing these effects and then computationally characterize their identified sets under instrumental variable variation in choice sets. I illustrate these tools by analyzing the effects of providing an offer to the Head Start preschool program using data from the Head Start Impact Study. I find that such a policy affects a large number of children who take up the offer, and that they subsequently have positive effects on test scores. These effects arise from children who do not have any preschool as an outside option. A cost-benefit analysis reveals that the earning benefits associated with the test score gains can be large and outweigh the net costs associated with offer take up.

econ.EM↗

arXiv2019

On the Identifying Content of Instrument Monotonicity

This paper studies the identifying content of the instrument monotonicity assumption of Imbens and Angrist (1994) on the distribution of potential outcomes in a model with a binary outcome, a binary treatment and an exogenous binary instrument. Specifically, I derive necessary and sufficient conditions on the distribution of the data under which the identified set for the distribution of potential outcomes when the instrument monotonicity assumption is imposed can be a strict subset of that when it is not imposed.

econ.EM↗

arXiv2016

On Nonparametric Inference in the Regression Discontinuity Design

This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified value. We first show that, under assumptions used in the majority of the literature, for \emph{any} test the power against any alternative is bounded above by its size. This result implies that, under these assumptions, any test with nontrivial power will exhibit size distortions. We next provide a sufficient strengthening of the standard assumptions under which we show that a novel test in the literature can control limiting size.

stat.ME↗