Khai Xiang Chiong

Duality in dynamic discrete‐choice models

Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete‐choice models that we call the mass transport approach. We show that the conditional choice probabilities and the choice‐specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two‐step estimator for these models; interestingly, the first step of our estimator involves solving a linear program that is identical to the classic assignment (two‐sided matching) game of Shapley and Shubik (1971). The application of convex‐analytic tools to dynamic discrete‐choice models and the connection with two‐sided matching models is new in the literature. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rusts (1987) bus engine replacement model.

Random Projection Estimation of Discrete-Choice Models with Large Choice Sets

We introduce random projection, an important dimension-reduction tool from machine learning, for the estimation of aggregate discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are projected into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclical monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semiparametric and does not require explicit distributional assumptions to be made regarding the random utility errors. Our procedure is justified via the Johnson–Lindenstrauss lemma—the pairwise distances between data points are preserved through random projections. The estimator works well in simulations and in an application to a supermarket scanner data set. This paper was accepted by Juanjuan Zhang, marketing.

Counterfactual Estimation in Semiparametric Discrete-Choice Models

We show how to construct bounds on counterfactual choice probabilities in semiparametric discrete-choice models. Our procedure is based on cyclic monotonicity, a convex-analytic property of the random utility discrete-choice model. These bounds are useful for typical counterfactual exercises in aggregate discrete-choice demand models. In our semiparametric approach, we do not specify the parametric distribution for the utility shocks, thus accommodating a wide variety of substitution patterns among alternatives. Computation of the counterfactual bounds is a tractable linear programming problem. We illustrate our approach in a series of Monte Carlo simulations and an empirical application using scanner data.

Estimation of Graphical Models with Shape Restriction

Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely-used estimator is the Graphical Lasso (GLASSO), which amounts to a maximum likelihood estimation regularized using the L1,1 matrix norm on the precision matrix Ω. The L1,1 norm is a lasso penalty that controls for sparsity, or the number of zeros in Ω. We propose a new estimator called Structured Graphical Lasso (SGLASSO) that uses the L1,2 mixed norm. The use of the L1,2 penalty controls for the structure of the sparsity in Ω. We show that SGLASSO is asymptotically equivalent to an infeasible GLASSO problem which prioritizes the sparsity-recovery of high-degree nodes. Monte Carlo simulation shows that SGLASSO outperforms GLASSO in terms of estimating the overall precision matrix and in terms of estimating the structure of the graphical model. In an empirical application to a classic firms’ investment dataset, we obtain a network of firms’ dependence that exhibits the core-periphery structure, with General Motors, General Electric and U.S. Steel forming the core group of firms.

Revealed Preference Tests of Network Formation Models

This paper proposes a revealed preference test of network formation models. Specifically, I consider network formation models where agents are (1) strategic, (2) externalities are confined to within an agent’s k-neighborhood, where k can be varied. I show that this model can be tested using observation of a single network. I then derive necessary and sufficient condition under which the observed network is consistent with our strategic models of network formation. This non-parametric test takes the form of an algorithm involving the computation of color-preserving automorphisms of graphs. Building on the theoretical result, the test is implemented to calculate its’ statistical power and to the Banerjee et al. (2012)’s social network data.