This paper studies dynamic linear panel data models that allow multiplicative as well as additive heterogeneity in a short panel context, by allowing both the coefficients and intercept of linear models to be individual-specific. I show that the model is not point-identified and yet partially identified, and I characterize sharp identified sets of the mean, variance, and CDF of the partial effect distribution. The characterization applies to both discrete and continuous data. A computationally feasible estimation and inference procedure is proposed, based on a fast and exact 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. Results suggest that there are large heterogeneity in earnings persistence and that the households experience weaker earnings persistence than what is reported in the literature on earnings dynamics.

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.