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.

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

This paper studies differences-in-differences (DID) models that allow the units to endogenously enter treatment in response to the variation in the time-varying unobservable covariates, which relaxes the standard parallel trend assumption and permits the well-known Ashenfelter's dip phenomenon (Ashenfelter, 1978). I show that, in this model, the average treatment effect on the treated (ATT) is point-identified if there exists a group of exogenously untreated units. I then show that, under additional assumptions, the ATT can be partially identified even without such a group. I propose an estimation and inference procedure for the ATT in both cases, whose finite-sample performance is examined by simulations.

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.