Manu Navjeevan

Working Papers

1. An Identification and Dimensionality Robust Test for Instrumental Variables Models

Abstract

I propose a new identification-robust test for the structural parameter in a heteroskedastic linear instrumental variables model. The proposed test statistic is similar in spirit to, though structurally distinct from, a jackknife version of the K-statistic and the resulting test has correct asymptotic size so long as an auxiliary parameter can be consistently estimated. This is possible under approximate sparsity even when the number of instruments is much larger than the sample size. As the number of instruments is allowed, but not required, to be large, the limiting behavior of the test statistic cannot be examined with traditional central limit theorems. Instead, I directly derive the asymptotic chi-squared distribution of the test statistic using novel modifications of Lindeberg's interpolation technique. To improve power against certain alternatives, I propose a simple combination with the sup-score statistic of Belloni et al. (2012) based on a thresholding rule. I point out that first-stage F-statistics calculated on LASSO selected variables may be misleading indicators of identification strength and apply the new methods to revisit the effect of social spillovers in movie consumption. In a simulation study, the newly proposed methods are additionally shown to have favorable size control and power properties compared to existing tests, particularly when the instruments are highly correlated.

Draft, Slides, ArXiv

2. Identification and Estimation in a Class of Potential Outcomes Models (with Rodrigo Pinto and Andres Santos)

Abstract

This paper develops a class of potential outcomes models characterized by three main features: (i) Unobserved heterogeneity can be represented by a vector of potential outcomes and a “type” describing the manner in which an instrument determines the choice of treatment; (ii) The availability of an instrumental variable that is conditionally independent of unobserved heterogeneity; and (iii) The imposition of convex restrictions on the distribution of unobserved heterogeneity. The proposed class of models encompasses multiple classical and novel research designs, yet possesses a common structure that permits a unifying analysis of identification and estimation. In particular, we establish that these models share a common necessary and sufficient condition for identifying certain causal parameters. Our identification results are constructive in that they yield estimating moment conditions for the parameters of interest. Focusing on a leading special case of our framework, we further show how these estimating moment conditions may be modified to be doubly robust. The corresponding double robust estimators are shown to be asymptotically normally distributed, bootstrap based inference is shown to be asymptotically valid, and the semi-parametric efficiency bound is derived for those parameters that are root-n estimable. We illustrate the usefulness of our results for developing, identifying, and estimating causal models through an empirical evaluation of the role of mental health as a mediating variable in the Moving To Opportunity experiment.

Draft, ArXiv

3. Doubly Robust Inference for Conditional Average Treatment Effects with High-Dimensional Controls (with Adam Baybutt) R&R, Journal of Econometrics

Abstract

Plausible identification of conditional average treatment effects (CATEs) can rely on controlling for a large number of variables to account for confounding factors. In these high-dimensional settings, estimation of the CATE requires estimating first-stage models whose consistency relies on correctly specifying their parametric forms. While doubly-robust estimators of the CATE exist, inference procedures based on the second stage CATE estimator are not doubly robust. Using the popular augmented inverse propensity weighting signal, we propose an estimator for the CATE whose resulting Wald-type confidence intervals are doubly robust. We assume a logistic model for the propensity score and a linear model for the outcome regression, and estimate the parameters of these models using an ℓ1 (Lasso) penalty to address the high dimensional covariates. Our proposed estimator remains consistent at the nonparametric rate and our proposed pointwise and uniform confidence intervals remain asymptotically valid even if one of the logistic propensity score or linear outcome regression models are misspecified.

Draft, Slides, ArXiv