Haitian Xie (解海天)

Haitian Xie (解海天)

Assistant Professor

Research

Working Papers

  • Nonlinear and Nonseparable Structural Functions in Fuzzy Regression Discontinuity Designs

  • November 2022. Revise and Resubmit, Journal of Econometrics.

  • Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.

  • Efficient and Robust Estimation of the Generalized LATE Model

  • February 2022. Revise and Resubmit, Journal of Business & Economic Statistics.

  • This paper studies the estimation of causal parameters in the generalized local average treatment effect (GLATE) model, a generalization of the classical LATE model encompassing multi-valued treatment and instrument. We derive the efficient influence function (EIF) and the semiparametric efficiency bound (SPEB) for two types of parameters: local average structural function (LASF) and local average structural function for the treated (LASF-T). The moment condition generated by the EIF satisfies two robustness properties: double robustness and Neyman orthogonality. Based on the robust moment condition, we propose the double/debiased machine learning (DML) estimators for LASF and LASF-T. The DML estimator is semiparametric efficient and suitable for high dimensional settings. We also propose null-restricted inference methods that are robust against weak identification issues. As an empirical application, we study the effects across different sources of health insurance by applying the developed methods to the Oregon Health Insurance Experiment.

  • Information-theoretic Limitations of Data-based Price Discrimination

  • This paper studies third-degree price discrimination (3PD) based on a random sample of valuation and covariate data, where the covariate is continuous, and the distribution of the data is unknown to the seller. The main results of this paper are twofold. The first set of results is pricing strategy independent and reveals the fundamental information-theoretic limitation of any data-based pricing strategy in revenue generation for two cases: 3PD and uniform pricing. The second set of results proposes the $K$-markets empirical revenue maximization (ERM) strategy and shows that the $K$-markets ERM and the uniform ERM strategies achieve the optimal rate of convergence in revenue to that generated by their respective true-distribution 3PD and uniform pricing optima. Our theoretical and numerical results suggest that the uniform (i.e., $1$-market) ERM strategy generates a larger revenue than the K-markets ERM strategy when the sample size is small enough, and vice versa.

  • Grenander-type Density Estimation under Myerson Regularity

  • May 2023.

  • This study presents a novel approach to the density estimation of private values from second-price auctions, diverging from the conventional use of smoothing-based estimators. We introduce a Grenander-type estimator, constructed based on a shape restriction in the form of a convexity constraint. This constraint corresponds to the renowned Myerson regularity condition in auction theory, which is equivalent to the concavity of the revenue function for selling the auction item. Our estimator is nonparametric and does not require any tuning parameters. Under mild assumptions, we establish the cube-root consistency and show that the estimator asymptotically follows the scaled Chernoff's distribution. Moreover, we demonstrate that the estimator achieves the minimax optimal convergence rate.

  • Personalized Subsidy Rules

  • Subsidies are commonly used to encourage behaviors that can lead to short- or long-term benefits. Typical examples include subsidized job training programs and provisions of preventive health products, in which both behavioral responses and associated gains can exhibit heterogeneity. This study uses the marginal treatment effect (MTE) framework to study personalized assignments of subsidies based on individual characteristics. First, we derive the optimality condition for a welfare-maximizing subsidy rule by showing that the welfare can be represented as a function of the MTE. Next, we show that subsidies generally result in better welfare than directly mandating the encouraged behavior because subsidy rules implicitly target individuals through unobserved heterogeneity in the behavioral response. When there is positive selection, that is, when individuals with higher returns are more likely to select the encouraged behavior, the optimal subsidy rule achieves the first-best welfare, which is the optimal welfare if a policy-maker can observe individuals' private information. We then provide methods to (partially) identify the optimal subsidy rule when the MTE is identified and unidentified. Particularly, positive selection allows for the point identification of the optimal subsidy rule even when the MTE curve is not identified. As an empirical application, we study the optimal wage subsidy using the experimental data from the Jordan New Opportunities for Women pilot study.

Publications

  • Uniform Convergence Results for the Local Linear Estimation of the Conditional Distribution

  • Accepted, Statistics & Probability Letters.

  • This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both $x$ and $y$ and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. We demonstrate the usefulness of these uniform results with two examples: the stochastic equicontinuity condition in $y$, and the estimation of the integrated conditional distribution function.

  • Strength in Numbers: Robust Mechanisms for Public Goods with Many Agents

  • (with Jin Xi) Accepted, Social Choice and Welfare.

  • This study examines the mechanism design problem for public goods provision in a large economy with $n$ independent agents. We propose a class of dominant-strategy incentive compatible and ex-post individually rational mechanisms, which we call the adjusted mean-thresholding (AMT) mechanisms. We show that when the cost of provision grows slower than the $\sqrt{n}$-rate, the AMT mechanisms are both eventually ex-ante budget balanced and asymptotically efficient. When the cost grows faster than the $\sqrt{n}$-rate, in contrast, we show that any incentive compatible, individually rational, and eventually ex-ante budget balanced mechanism must have provision probability converging to zero and hence cannot be asymptotically efficient. The AMT mechanisms have a simple form and are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of an AMT mechanism depends only on the first moment of the valuation distribution.

  • Global Representation of the Conditional LATE Model: A Separability Result

  • (with Yu-Chang Chen) Oxford Bulletin of Economics and Statistics, 84: 789-798, August 2022.
  • This paper studies the latent index representation of the conditional LATE model, making explicit the role of covariates in treatment selection. We find that if the directions of the monotonicity condition are the same across all values of the conditioning covariate, which is often assumed in the literature, then the treatment choice equation has to satisfy a separability condition between the instrument and the covariate. This global representation result establishes testable restrictions imposed on the way covariates enter the treatment choice equation. We later extend the representation theorem to incorporate multiple ordered levels of treatment.