arXiv subjects

Hiroaki Kaido

Publications and source records attributed to Hiroaki Kaido.

14 recordsLinked to original sources

arXiv2026

Robust Likelihood Ratio Tests for Incomplete Economic Models

Economic models with multiple equilibria, self-selection, or weak behavioral restrictions often make set-valued predictions and therefore do not imply a unique likelihood. This paper develops robust likelihood-ratio tests for structural hypotheses in such incomplete models. We evaluate tests by their power guarantee, defined as the smallest rejection probability over all selection mechanisms compatible with the alternative, while requiring uniform size control over all null selections. Using the Huber--Strassen theory of least favorable pairs, we construct finite-sample minimax likelihood-ratio tests. The main result shows that, in repeated experiments, the least favorable pair is the product of the single-experiment least favorable pairs whenever the latent variables are independent across experiments. This product structure holds even though unrestricted selection may induce arbitrary heterogeneity and dependence in the observed outcomes. It reduces a high-dimensional robust testing problem to single-experiment calculations and yields exact finite-sample critical values and Gaussian approximations. For directed one-sided alternatives, we provide conditions under which conditioning on a selection-invariant statistic delivers exact conditional uniformly most powerful (UMP) tests with respect to the power guarantee. In the examples, these optimal tests are simple and interpretable, using selection-invariant features of the data that are directly tied to the hypothesis of interest. Monte Carlo experiments in entry-game and Roy-model designs illustrate size control, power, and the role of robust testability.

econ.EM↗

arXiv2026

Set-Valued Control Functions

The control function approach allows the researcher to identify various causal effects of interest. While powerful, it requires a strong invertibility assumption in the selection process, which limits its applicability. This paper expands the scope of the nonparametric control function approach by allowing the control function to be set-valued and derive sharp bounds on structural parameters. The proposed generalization accommodates a wide range of selection processes involving discrete endogenous variables, random coefficients, treatment selections with interference, and dynamic treatment selections. The framework also applies to partially observed or identified controls that are directly motivated from economic models.

econ.EM↗

arXiv2026

Information Based Inference in Models with Set-Valued Predictions and Misspecification

This paper proposes an information-based inference method for partially identified parameters in incomplete models that is valid both when the model is correctly specified and when it is misspecified. Key features of the method are: (i) it is based on minimizing a suitably defined Kullback-Leibler information criterion that accounts for incompleteness of the model and delivers a non-empty pseudo-true set; (ii) it is computationally tractable; (iii) its implementation is the same for both correctly and incorrectly specified models; (iv) it exploits all information provided by variation in discrete and continuous covariates; (v) it relies on Rao's score statistic, which is shown to be asymptotically pivotal.

econ.EM↗

arXiv2026

Testing Information Ordering for Strategic Agents

Specifying the information structure in strategic environments is difficult for empirical researchers. We develop a test of information ordering that examines whether the true information structure is at least as informative as a proposed baseline. Using Bayes Correlated Equilibrium (BCE), we translate the ordering of information structures into testable moment inequalities and establish uniform asymptotic validity for our testing procedure. In an application to U.S. airline markets, we test whether hub airlines have informational advantages beyond cost and demand benefits. We reject the privileged information hypothesis, with rejections concentrated in large, competitive markets.

econ.EM↗

arXiv2025

Testing Exclusion and Shape Restrictions in Potential Outcomes Models

Exclusion and shape restrictions play a central role in defining causal effects and interpreting estimates in potential outcomes models. To date, the testable implications of such restrictions have been studied on a case-by-case basis in a limited set of models. In this paper, we develop a general framework for characterizing sharp testable implications of general support restrictions on the potential response functions, based on a novel graph-based representation of the model. The framework provides a unified and constructive method for deriving all observable implications of the modeling assumptions. We illustrate the approach in several popular settings, including instrumental variables, treatment selection, mediation, and interference. As an empirical application, we revisit the US Lung Health Study and test for the presence of spillovers between spouses, specification of exposure maps, and persistence of treatment effects over time.

econ.EM↗

arXiv2025

Universal Inference for Incomplete Discrete Choice Models

A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference framework by Wasserman et al. (2020) and avoids using moment selection tuning parameters, resampling, or simulations. The method is designed for constructing confidence intervals for counterfactual objects and other functionals of the underlying parameter. It can be used in applications that involve model incompleteness, discrete and continuous covariates, and parameters containing nuisance components.

econ.EM↗

arXiv2023

Robust Tests of Model Incompleteness in the Presence of Nuisance Parameters

Economic models may exhibit incompleteness depending on whether or not they admit certain policy-relevant features such as strategic interaction, self-selection, or state dependence. We develop a novel test of model incompleteness and analyze its asymptotic properties. A key observation is that one can identify the least-favorable parametric model that represents the most challenging scenario for detecting local alternatives without knowledge of the selection mechanism. We build a robust test of incompleteness on a score function constructed from such a model. The proposed procedure remains computationally tractable even with nuisance parameters because it suffices to estimate them only under the null hypothesis of model completeness. We illustrate the test by applying it to a market entry model and a triangular model with a set-valued control function.

econ.EM↗

arXiv2022

Nonparametric Identification of Random Coefficients in Endogenous and Heterogeneous Aggregate Demand Models

This paper studies nonparametric identification in market level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as welfare measures, is identified. A key finding is that two leading models, the BLP-model (Berry, Levinsohn, and Pakes, 1995) and the pure characteristics model (Berry and Pakes, 2007), require considerably different conditions on the support of the product characteristics.

econ.EM↗

arXiv2021

Constraint Qualifications in Partial Identification

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian-Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

econ.EM↗

arXiv2020

Decentralization Estimators for Instrumental Variable Quantile Regression Models

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and non-convexity of the IVQR GMM objective function. 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 reformulation leads to new identification results and to fast, easy to implement, and tuning-free estimators that do not require the availability of high-level "black box" optimization routines.

econ.EM↗

arXiv2019

Confidence Intervals for Projections of Partially Identified Parameters

We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of theta, not theta itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.

math.ST↗

arXiv2018

Moment Inequalities in the Context of Simulated and Predicted Variables

This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (first-order) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.

econ.EM↗

arXiv2017

Calibrated Projection in MATLAB: Users' Manual

We present the calibrated-projection MATLAB package implementing the method to construct confidence intervals proposed by Kaido, Molinari and Stoye (2017). This manual provides details on how to use the package for inference on projections of partially identified parameters. It also explains how to use the MATLAB functions we developed to compute confidence intervals on solutions of nonlinear optimization problems with estimated constraints.

econ.EM↗

arXiv2013

Asymptotically Efficient Estimation of Weighted Average Derivatives with an Interval Censored Variable

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any parametric assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. We illustrate efficient estimation by constructing an efficient estimator of the support function for the case of mean regression with an interval censored outcome.

math.ST↗