Methods

The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data => decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data => inference => decision]. This paper offers remarks on the use of statistical inference in statistical decisions.

In a model with endogenous regressors, heteroskedastic and autocorrelated (HAC) errors and weak instruments, tests that depend on the data only through the Anderson-Rubin (AR) and Lagrange Multiplier (LM) statistics ignore important information on the regression coefficients. This is in contrast to the homoskedastic case, where these statistics, together with the rank statistic, are one-to-one with the maximal invariant. The information loss with heteroskedastic and/or autocorrelated errors can be so extreme that the LM and conditional quasi-likelihood ratio (CQLR) tests have power close to size when it is trivial to distinguish the null from the alternative hypothesis. The severe loss of power can occur if the Hermitian part of the reduced-form covariance matrix has eigenvalues of opposite signs.

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control.

This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size.

We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions.

Slides and software used to introduce the study of inter-temporal life-cycle models of consumption and savings and support the development of code to solve these type of problems numerically.

This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression sub-problems, which are convex and can be solved efficiently. This allows for reformulating the original estimation problem as the problem of finding the fixed point of a low dimensional map.

Many empirical questions can be cast as inference on a parameter selected through optimization. For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data. Such settings give rise to a winner’s curse, where conventional estimates are biased and conventional confidence intervals are unreliable.

We consider nonlinear moment restriction semiparametric models where both the dimension of the parameter vector and the number of restrictions are divergent with sample size and an unknown smooth function is involved.

e develop a consistent estimator using external information on the true distribution of prices. Examining the demand for gasoline in the U.S., accounting for Berkson errors is found to be quantitatively important for estimating price effects and for welfare calculations. Imposing the Slutsky shape constraint greatly reduces the sensitivity to Berkson errors.

We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much rich patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identification of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the first step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation.

Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. We consider heterogenous coefficients models where the outcome is a linear combination of known functions of treatment and heterogenous coefficients.

We propose a new approach to computation of NPMLEs for binary response models that signicantly increase their computational tractability thereby facilitating greater exibility in applications.

We study social learning in a continuous action space experiment. Subjects, acting in sequence, state their belief about the value of a good, after observing their predecessors' statements and a private signal.

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set-identified models by adopting a multiple-prior (robust) Bayesian approach.

Let Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment control variables.

Many econometric models used in applied work integrate over unobserved heterogeneity. We show that a class of these models that includes many random coefficients demand systems can be approximated by a "small-sigma" expansion that yields a straightforward 2SLS estimator. We study in detail the models of market shares popular in empirical IO ("macro BLP").

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n.

While poverty may impair decision-making, some of the apparently irrational behaviour observed among the poor may have a rational expectation. In particular, estimates of "present-bias" among the poor may be exaggerated if poor individuals are credit-constrained and expect to have greater liquidity in future. I conduct an experiment in rural Pakistan which provides evidence of this effect.