Working Papers

Identification of a triangular random coefficient model using a correction function (Accepted at Review of Economics and Statistics)

Previously, identification of triangular random coefficient models required a restriction on the dimension of the first stage heterogeneity or independence assumptions across the different sources of the heterogeneity. This note proposes a new identification strategy that does not rely on either of these restrictions but rather uses conditional linear projections to construct “correction functions” to address endogeneity and gain identification of the average partial effect. This identification strategy allows for both continuous and discrete instruments although the formulation of the correction function differs depending on the setting. Finally, a simple simulation illustrates that the proposed identification strategy is valid in settings where no other existing methods can identify average partial effects.

gtsheckman: Generalized Two Step Heckman Estimator. (Accepted at The Stata Journal)

In this article I introduce the gtsheckman command which estimates a generalized two step Heckman sample selection estimator adjusted for heteroskedasticity. This estimator has been previously proposed in Carlson and Joshi (2022) where the presence of heteroskedasticity was motivated by a panel data setting with random coefficients. The gtsheckman offers several advantages to the heckman, twostep command including robust inference, a more general control function specification and incorporating heteroskedasticity. 

Stata command: gtsheckman.ado

Stata help file: gtsheckman.sthlp

Stata examples:

Stata 2022 Conference Slides 

Heckman sample selection estimators under heteroskedasticity (Under review at The Stata Journal, Joint with Wei Zhao)

This paper studies the properties of two Heckman sample selection estimators, full information maximum likelihood (FIML) and limited information maximum likelihood (LIML), under heteroskedasticity. In this case, FIML is inconsistent while LIML can be consistent in certain settings. For the LIML estimator, we provide robust asymptotic variance formulas, not currently provided with standard Stata commands. Since heteroskedasticity affects these two estimators' performance, this paper also offers guidance on how to properly test for heteroskedasticity. We propose a new demeaned Breusch-Pagan test to detect general heteroskedasticity in sample selection settings as well as a test for when LIML is consistent under heteroskedasticity. The Monte Carlo simulations illustrate that both of the proposed test procedures perform well.

Estimation of a Binary Response Dynamic Panel Data Model with Attrition (Joint with Anastasia Semykina)

We present a general framework for nonlinear dynamic panel data models subject to missing outcomes due to endogenous attrition. We consider two cases of attrition. First, ignorable attrition where the distribution of the outcome does not depend on missingness conditional on unobserved individual heterogeneity. Second, non-ignorable attrition where the conditional distribution of the outcome does depend on attrition. In either case, a major challenge posed by the dynamic specification is the inherent correlation between lagged dependent variable and the unobserved individual heterogeneity. Our key assumption is that the distribution of the unobserved heterogeneity does not depend on selection or the lagged outcome once conditioning on observed covariates and initial condition. The resulting estimator is a joint MLE that accommodates a dynamic specification, correlated unobserved heterogeneity, and endogenous attrition. We discuss the derivation and estimation of the average partial effects within this framework and provide examples for the binary response, ordinal response, and censored response cases. The proposed method is applied to a dynamic health model among older women.

Heterogeneity in State Solar and Wind Deployments: Trade-offs between Technology-neutral and Technology-specific Renewable Energy Policies (Joint with Jian Chen and Hongli Feng)

There are large heterogeneities among U.S. states regarding solar and wind energy development and natural endowment. We examine the roles of renewable portfolio standards (RPS) without or with solar carve-outs (SRPS) in the uneven solar and wind development across states. We first develop a theoretical framework that differentiates between renewables and nonrenewables and between two types of renewables (solar and wind) to evaluate the impacts of technology-neutral or specific renewable energy policies. Our results with state-level data from 2001 to 2019 suggest that adopting a solar carve-out within RPS boosts solar share by 0.15 percentage points but decreases wind share by 0.46 percentage points. Our results also indicate that the decreasing cost of solar and wind electricity during our study period contributed to solar and wind development by 0.65 and 5.42 percentage points, respectively. We also examine the role of credit trading, costs of SRPS, heterogeneous impacts across time periods, operator scales, and treatment timing.

Behavior of Pooled and Joint Estimators in Probit Model with Random Coefficients and Serial Correlation. (Joint with Jeffrey Wooldridge and Ying Zhu, draft coming soon)