Research

Job Market Paper

• Estimation of BLP Models with High-dimensional Controls
  
  [abstract] [arXiv] [slides]

  This paper develops a framework for estimating demand in differentiated product markets with high-dimensional product characteristics, building on the Berry, Levinsohn, and Pakes (1995) model with market-level data; the number of characteristics may exceed the number of markets. First, we propose a Neyman orthogonal estimator in which high-dimensional nuisance parameters are estimated by machine-learning methods such as LASSO, and show that it is $\sqrt{T}$-asymptotically normal for the parameters of interest, such as the price coefficient and price heterogeneity, even when the nuisance parameters converge at slower rates. Second, under approximate sparsity, we provide LASSO-based nuisance estimators that attain the required rates, although mean utility is recovered from market shares only when the nonlinear parameters are known. Monte Carlo simulations show good finite-sample performance. We illustrate the method with Dominick's Finer Foods data.

Working Papers

• Conditional-Moment Estimation and Inference in the BLP Model
  with Tian Xie.
  [abstract] [arXiv]

  The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound under certain conditions. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.
• Local Polynomial Estimation in Irregular Correlated Random Coefficient Panel Data Models
  with Yelong Chen and Yuxuan Ren.
  [abstract] [arXiv]

  We study estimation of the average partial effect (APE) in an irregular correlated random coefficients panel data model in which the time dimension equals the number of random coefficients, T equals p, and the density function is degenerate. We extend Graham and Powell (2012) in two directions. First, we allow the density of the determinant of the individual regressor matrix to vanish or diverge at the origin at a polynomial rate of order a, with a greater than minus one, and show that the aggregate time effects and the APE remain identified for every such a; extending earlier work studying the case where a equals zero. Second, we propose a three-step estimator: a local polynomial regression of order m over the stayers for the time effects; a local polynomial fit of the conditional mean coefficient just outside the trimming threshold; and an imputation step that extrapolates the latter into the stayer region rather than discarding stayers. We establish joint asymptotic normality in three regimes determined by the sign of a, and obtain a convergence rate approaching n to the power of negative (m+1)/(2m+3) when a equals zero, against the cube root of n rate of Graham and Powell (2012), whose estimator is the special case where m and a are both zero. The results show that smoothness of the underlying conditional expectations can be traded for a faster convergence rate in irregularly identified models. Simulations confirm lower bias and root mean squared error across designs. We redo the over-identification analysis of a markup model in Raval (2023) where we allow for correlated random elasticity.
• Non-Asymptotic Convergence Rates for High-Dimensional Penalized Estimators
  with Dennis Kristensen.
  [abstract]

Selected Work in Progress

High-Dimensional GMM Estimation (with Dennis Kristensen)

Flexible Nonparametric Estimation of Random Coefficients (with Yihan Li and Tian Xie)