Manu Navjeevan

When beliefs are heterogeneous, information provision may induce responses in opposite directions, and standard intent-to-treat estimates may fail to capture the full effect of an information intervention. In this paper, we show how elicited prior beliefs can be used to test for a uniform response to information and bound the share of agents whose decisions change. We demonstrate that testing for a uniform response to information is equivalent to the problem of testing for instrument validity in LATE models, with elicited prior beliefs in place of observed outcomes. Under random assignment, the joint distribution of reported prior beliefs and choices yields sharp lower bounds on flows into and out of each choice. For a binary choice, these lower bounds are exact under a testable behavioral model in which reported priors coincide with underlying beliefs and the information intervention causes agents to update their beliefs towards a common signal. We apply these results to an information RCT in Ibadan, Nigeria, where adolescents chose whether to register for senior high school and which track to pursue. Among students whose earnings priors lie on the same side of every signal provided by the intervention, we reject a uniform response to information at the 10 percent level. In a rebalanced sample, we estimate that at least 14.6 percent of students changed continuation decisions upon receipt of new information — three times the 4.9 percentage-point decline in continuation. Accounting for changes in educational track, we estimate that at least 17 percent of students changed their schooling choice in response to the intervention.

Estimating an instrumental variables (IV) first stage with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary and penalty. Existing rules target first-stage objectives, although these choices affect structural estimation. We derive a feasible approximate mean squared error (AMSE) criterion for full-sample IV-LASSO with one endogenous regressor and homoskedastic Gaussian errors. For a prespecified list of dictionary--penalty pairs, the criterion trades off approximation of the optimal instrument against a complexity cost that depends on the first two moments of the LASSO effective dimension and on the degree of endogeneity. The selected pair attains the smallest candidate-specific AMSE component up to vanishing relative error. In simulations calibrated to Paravisini et al. (2015), the criterion improves substantially on the plug-in rule at low endogeneity and on cross-validation at high endogeneity, with nearly identical results under non-Gaussian errors. A supplementary appendix formally extends analysis to a class of non-Gaussian errors.

We study inference in models where a transformation of parameters exhibits first-order degeneracy — that is, its gradient is zero or close to zero, making the standard delta method invalid. A leading example is causal mediation analysis, where the indirect effect is a product of coefficients and the gradient degenerates near the origin. In these local regions of degeneracy the limiting behaviors of plug-in estimators depend on nuisance parameters that are not consistently estimable. We show that this failure is intrinsic — around points of degeneracy, both regular and quantile-unbiased estimation are impossible. Despite these restrictions, we develop minimum-distance methods that deliver uniformly valid confidence intervals. We establish sufficient conditions under which standard chi-square critical values remain valid, and propose a simple bootstrap procedure when they are not. We demonstrate favorable power in simulations and in an empirical application linking teacher gender attitudes to student outcomes.

Using modifications of Lindeberg's interpolation technique, I propose a new identification-robust test for the structural parameter in a heteroskedastic instrumental variables model. While my analysis allows the number of instruments to be much larger than the sample size, it does not require many instruments, making my test applicable in settings that have not been well studied. Instead, the proposed test statistic has a limiting chi-squared distribution so long as an auxiliary parameter can be consistently estimated. This is possible using machine learning methods even when the number of instruments is much larger than the sample size. To improve power, a simple combination with the sup-score statistic of Belloni et al. (2012) is proposed. I point out that first-stage F-statistics calculated on LASSO selected variables may be misleading indicators of identification strength and demonstrate favorable performance of my proposed methods in both empirical data and simulation study.

We study instrumental variables models characterized by: (i) Unobserved heterogeneity consisting of potential outcomes and response types that describe how the instrument determines treatment choice; (ii) Conditional independence of the instrument and the unobserved heterogeneity; and (iii) Convex restrictions on the distribution of unobserved heterogeneity. We show certain causal parameters are identified in these models if and only if a version of the kappa of Abadie (2003) exists. Our identification results are constructive in yielding estimating moment conditions. Focusing on a leading special case, we develop asymptotically normal estimators based on a doubly robust version of these moment conditions.

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.