revise and resubmit at Review of Economic Studies

I study panel data linear models with predetermined regressors (e.g. lagged dependent variables) that allow the coefficients as well as the intercept to be individual-specific, permitting unobserved heterogeneity in the effects of regressors on the dependent variable. I show that the model is not point-identified in a short panel context but rather partially identified, and I characterize sharp identified sets of the mean, variance, and CDF of the coefficient distributions. The characterization is general, allowing discrete, continuous, and unbounded data. A computationally efficient estimation and inference procedure is proposed, based on a fast and precise global polynomial optimization algorithm. The method is applied to study lifecycle earnings dynamics in U.S. households in the Panel Study of Income Dynamics (PSID) dataset. The results suggest substantial unobserved heterogeneity in earnings persistence, which implies that households face different levels of earnings risk that lead to heterogeneity in their consumption and savings behaviors.

(with Mario Fiorini and Gregor Pfeifer)

We establish identifying assumptions and estimation procedures for the ATT in a Difference-in-Differences model with staggered treatment adoption in the presence of spillovers. We show that the ATT can be estimated by a simple TWFE regression that extends the approach of Wooldridge (2022)'s fully interacted regression. Moreover, we broaden our framework to nonlinear cases, offering estimation of the ATT by Poisson, Probit, and Logit regressions. We apply our method to revisit a corresponding application from the crime literature. Monte Carlo simulations suggest that our estimator performs competitively.

This paper studies difference-in-differences models where units make treatment decisions as dynamic choices based on the information available at each time period, allowing units to make treatment decisions in response to the unexpected shocks to their outcomes. This behavior leads to selection on unobservables and causes treatment and control groups to exhibit different time trends, invalidating the standard parallel trend assumption.

Statistical Inference for Stochastic Processes, 2017, 20 (2):237–252.

We consider estimation of the drift function of a stationary diffusion process when we observe high-frequency data with microstructure noise over a long time interval. We propose to estimate the drift function at a point by a Nadaraya–Watson estimator that uses observations that have been pre-averaged to reduce the noise. We give conditions under which our estimator is consistent and asympotically normal. Its rate and asymptotic bias and variance are the same as those without microstructure noise. To use our method in data analysis, we propose a data-based cross-validation method to determine the bandwidth in the Nadaraya–Watson estimator. Via simulation, we study several methods of bandwidth choices, and compare our estimator to several existing estimators. In terms of mean squared error, our new estimator outperforms existing estimators.