Kotlarski's Lemma for Dyadic Models(with Grigory Franguridi)
Abstract: We show how to identify the distributions of the error components in the two-way dyadic model. To this end, we extend the lemma of Kotlarski (1967), mimicking the arguments of Evdokimov and White (2012). We allow the characteristic functions of the error components to have real zeros, as long as they do not overlap with zeros of their first derivatives.
(arXiv)
Robust Estimation of Regression Models with Potentially Endogenous Outliers via a Modern Optimization Lens (with Zhan Gao)
Abstract: This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing L_1-regularized estimation methods, including the Huber estimator and the least absolute deviation (LAD) estimator, exhibit significant bias when outliers are endogenous. Motivated by this finding, we investigate L_0-regularized estimation methods. We propose systematic heuristic algorithms, notably an iterative hard-thresholding algorithm and a local combinatorial search refinement, to solve the combinatorial optimization problem of the L_0-regularized estimation efficiently. Our Monte Carlo simulations yield two key results: (i) The local combinatorial search algorithm substantially improves solution quality compared to the initial projection-based hard-thresholding algorithm while offering greater computational efficiency than directly solving the mixed integer optimization problem. (ii) The L_0-regularized estimator demonstrates superior performance in terms of bias reduction, estimation accuracy, and out-of-sample prediction errors compared to -regularized alternatives. We illustrate the practical value of our method through an empirical application to stock return forecasting.
(arXiv)
Bayesian Estimation of Panel Models Under Potentially Sparse Heterogeneity (with Frank Schorfheide and Boyuan Zhang)
Abstract: We incorporate a version of a spike and slab prior, comprising a pointmass at zero ("spike") and a Normal distribution around zero ("slab") into a dynamic panel data framework to model coefficient heterogeneity. In addition to homogeneity and full heterogeneity, our specification can also capture sparse heterogeneity, that is, there is a core group of units that share common parameters and a set of deviators with idiosyncratic parameters. We fit a model with unobserved components to income data from the Panel Study of Income Dynamics. We find evidence for sparse heterogeneity for balanced panels composed of individuals with long employment histories.
(arXiv)
Optimal Discrete Decisions when Payoffs are Partially Identified (with Timothy Christensen and Frank Schorfheide)
Abstract: We derive optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter θ and the decision maker can use a point-identified parameter P to deduce restrictions on θ. Leading examples include optimal treatment choice under partial identification and optimal pricing with rich unobserved heterogeneity. Our optimal decision rules minimize the maximum risk or regret over the identified set of payoffs conditional on P and use the data efficiently to learn about P. We discuss implementation of optimal decision rules via the bootstrap and Bayesian methods, in both parametric and semiparametric models. We provide detailed applications to treatment choice and optimal pricing. Using a limits of experiments framework, we show that our optimal decision rules can dominate seemingly natural alternatives. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.
(arXiv)
Test of Neglected Heterogeneity in Dyadic Models (with Jinyong Hahn and Luoyao Shi)
Abstract: We develop a Lagrange Multiplier (LM) test of neglected heterogeneity in dyadic models. The test statistic is derived by modifying Breusch and Pagan (1980)’s test. We establish the asymptotic distribution of the test statistic under the null using a novel martingale construction. We also consider the power of the LM test in generic panel models. Even though the test is motivated by random effects, we show that it has a power for detecting fixed effects as well. Finally, we examine how the estimation noise of the maximum likelihood estimator affects the asymptotic distribution of the test under the null, and show that such a noise may be ignored in large samples.
Normal Approximation in Large Network Models (with Michael Leung)
Abstract: We prove a central limit theorem for network moments in a model of network formation with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size diverges. We argue that a modification of "exponential stabilization" conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence, which we use to establish an abstract central limit theorem. We then derive primitive conditions for stabilization using results in branching process theory. We discuss practical inference procedures justified by our results and outline a methodology for deriving primitive conditions that can be applied more broadly to other large network models with strategic interactions.
(arXiv)
Nuclear Norm Regularized Estimation of Panel Regression Models (with Martin Weidner)
Abstract: In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.
(arXiv)