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Marriott Marquis, La Costa
Hosted By:
Econometric Society
Testing in Incomplete and Complete Models
Paper Session
Sunday, Jan. 5, 2020 8:00 AM - 10:00 AM (PDT)
- Chair: Hiroaki Kaido, Boston University
A Simple Uniformly Valid Test for Inequalities
Abstract
We propose a new test for inequalities that is simple and uniformly valid. The test compares the likelihood ratio statistic to a chi-squared critical value, where the degrees of freedom is the rank of the active inequalities. This test requires no tuning parameters or simulations, and therefore is computationally fast, even with many inequalities. Further, it does not require an estimate of the number of binding or close-to-binding inequalities. To show the size property of our test, we establish a new bound on the probability of translations of cones under the multivariate normal distribution that may be of independent interest. The leading application of our test is inference in moment inequality models. We also consider testing affine inequalities in the multivariate normal model and testing nonlinear inequalities in general asymptotically normal models.Adaptive Testing in Instrumental Variable Models
Abstract
This paper is concerned with adaptive inference on a structural function in the semiparametric or nonparametric instrumental variables (NPIV) model. We propose a direct test statistic for hypothesis testing based on a leave-one-out, sieve NPIV estimator. Our test is applicable to identified and partially identified models. We analyze a class of alternative models which are separated from the null hypothesis by a rate of testing which is sensitive to the form of identification. This rate of testing is shown to be minimax: The first type error and the second type error of our test, uniformly over the class of alternative models, cannot be improved by any other test. We also propose an adaptive test statistic that provides a data driven choice of tuning parameters and attains the minimax optimal rate of testing within a loglogn term. This paper concludes with a finite sample analysis of the testing procedure and empirical illustrations.Salvaging Falsified Instrumental Variable Models
Abstract
What should researchers do when their baseline model is refuted? We provide four constructive answers. First, researchers can measure the extent of falsification. To do this, we consider continuous relaxations of the baseline assumptions of concern. We then define the falsification frontier: the boundary between the set of assumptions which falsify the model and those which do not. This frontier provides a quantitative measure of the extent of falsification. Second, researchers can present the identified set for the parameter of interest under the assumption that the true model lies somewhere on this frontier. We call this the emph{falsification adaptive set}. This set generalizes the standard baseline estimand to account for possible falsification. Third, researchers can present the identified set for a specific point on this frontier. Finally, as a sensitivity analysis, researchers can present identified sets for points beyond the frontier. To illustrate these four ways of salvaging falsified models, we study overidentifying restrictions in two instrumental variable models: a homogeneous effects linear model, and heterogeneous effect models with either binary or continuous outcomes. In the linear model, we consider the classical overidentifying restrictions implied when multiple instruments are observed. We generalize these conditions by considering continuous relaxations of the classical exclusion restrictions. By sufficiently weakening the assumptions, a falsified baseline model becomes non-falsified. We obtain analogous results in the heterogeneous effects models, where we derive identified sets for marginal distributions of potential outcomes, falsification frontiers, and falsification adaptive sets under continuous relaxations of the instrument exogeneity assumptions.Inference in High-Dimensional Set-Identified Affine Models
Abstract
This paper proposes both point-wise and uniform confidence sets (CS) for an element θ1 of a parameter vector θ ∈ Rd that is partially identified by affine moment equality and inequality conditions. The method is based on an estimator of a regu- larized support function of the identified set. This estimator is half-median unbiased and has an asymptotic linear representation which provides closed form standard errors and enables optimization-free multiplier bootstrap. The proposed CS can be computed as a solution to a finite number of linear and convex quadratic programs, which leads to a substantial decrease in computation time and guarantee of global optimum. As a result, the method provides uniformly valid inference in applications with the dimension of the parameter space, d, and the number of inequalities, k, that were previously computationally unfeasible (d, k > 100). The proposed approach is then extended to construct polygon-shaped joint CS for multiple components of θ. Inference for coefficients in the linear IV regression model with interval outcome is used as an illustrative example.Robust Likelihood-Ratio Tests for Incomplete Economic Models
Abstract
This paper develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood. The model structure, however, allows to construct tests based on least favorable pairs (LFPs) of likelihoods using the theory of Huber and Strassen (1973). Building on this, we develop tests that are robust to the model incompleteness and possess certain optimality properties. We also show that the sharp identifying restrictions play a role in constructing such tests in a computationally tractable manner. Combining our results with Le Cam's limits of experiments, we further provide a framework for analyzing the asymptotic power of tests against properly defined local alternatives. Examples of hypotheses we consider include those on the presence of strategic interaction effects in discrete games of complete information. Monte Carlo experiments demonstrate robust performance of the proposed tests.JEL Classifications
- C1 - Econometric and Statistical Methods and Methodology: General