Abstract: In this paper, we develop a unified approach to study partial identification of a finite-dimensional parameter defined by a moment equality model with incomplete data. We establish a novel characterization of the identified set for the true parameter in terms of a continuum of inequalities defined by optimal transport costs. For a special class of moment functions, we show that the identified set is convex, and its support function can be easily computed by solving an optimal transport problem. We demonstrate the generality and effectiveness of our approach through several running examples, including the linear projection model and two algorithmic fairness measures.

Keywords: Algorithmic Fairness, Causal Inference, Convex Analysis, Data Combination, Linear Projection, Partial Optimal Transport, Support Function, Time Complexity

Abstract: The gravity equation, the most popular empirical tool in International Trade, is usually estimated by the OLS or Poisson Pseudo-Maximum Likelihood (PPML), with PPML being robust to the heteroskedasticity of the error term. We find that when the trade elasticity is heterogeneous between country pairs, OLS and PPML estimates have different interpretations: OLS estimates the average elasticity and PPML estimates the elasticity of average. We show that most of the differences between the PPML and OLS estimates are explained by the difference in the interpretation of the coefficients. We also develop a new weighted PPML estimator for the elasticity of average in case of heterogeneous trade shock.

Keywords:  elasticity, heterogeneity, heteroskedasticity, gravity model, misspecification

Abstract: This article introduces an iterative distributed computing estimator for the multinomial logistic regression model with large choice sets. Compared to the maximum likelihood estimator, the proposed iterative distributed estimator achieves significantly faster computation and, when initialized with a consistent estimator, attains asymptotic efficiency under a weak dominance condition. Additionally, we propose a parametric bootstrap inference procedure based on the iterative distributed estimator and establish its consistency. Extensive simulation studies validate the effectiveness of the proposed methods and highlight the computational efficiency of the iterative distributed estimator.

Keywords: Distributed computing, Iterative methods, Maximum likelihood, Multinomial logistic regression.

Keywords: unobserved heterogeneity, matching-types problem, multistep moment selection, time complexity, space complexity

Keywords: extremum estimator, inequality constraint, uniform inference, implicit nuisance parameter, polytope projection, Mincer regression, random coefficients model

Keywords: copula theory, Bernstein copula, sieve estimation, inequality constraint, data combination, selection-on-observables, distributional treatment effects, counterfactual distribution

Keywords: interval data, extreme value theory, point process, uniform inference, inequality constraint, Bonferroni-type correction