Abstract: This paper provides a general identification approach for a wide range of nonlinear panel data models, including binary choice, ordered response, and other types of limited dependent variable models. Our approach accommodates dynamic models with any number of lagged dependent variables as well as other types of (potentially contemporary) endogeneity. Our identification strategy relies on a partial stationarity condition, which not only allows for an unknown distribution of errors but also for temporal dependencies in errors. We derive partial identification results under flexible model specifications and provide additional support conditions for point identification. We demonstrate the robust finite-sample performance of our approach using Monte Carlo simulations, and apply the approach to analyze the empirical application of income categories using various ordered choice models.  

Abstract: This paper studies semiparametric identification of substitution and complementarity patterns between two goods using a panel multinomial choice model with bundles. The model allows the two goods to be either substitutes or complements and admits heterogeneous complementarity through observed characteristics. I first provide testable implications for the complementarity relationship between goods. I then characterize the sharp identified set for the model parameters and provide sufficient conditions for point identification. The identification analysis accommodates endogenous covariates through flexible dependence structures between observed characteristics and fixed effects while placing no distributional assumptions on unobserved preference shocks. My method is shown to perform more robustly than the parametric method through Monte Carlo simulations. As an extension, I allow for unobserved heterogeneity in the complementarity, investigate scenarios involving more than two goods, and study a class of nonseparable utility functions.

Abstract: This paper provides partial identification of various binary choice models with misreported dependent variables. We propose two distinct approaches by exploiting different instrumental variables respectively. In the first approach, the instrument is assumed to only affect the true dependent variable but not misreporting probabilities. The second approach uses an instrument that influences misreporting probabilities monotonically while having no effect on the true dependent variable. Moreover, we derive identification results under additional restrictions on misreporting, including bounded/monotone misreporting probabilities. We use simulations to demonstrate the robust performance of our approaches, and apply the method to study educational attainment.

Abstract: We study identification and estimation of endogenous linear and nonlinear regression models without excluded instrumental variables, based on the standard mean independence condition and a nonlinear relevance condition. Based on the identification results, we propose two semiparametric estimators as well as a discretization-based estimator that does not require any nonparametric regressions. We establish their asymptotic normality and demonstrate via simulations their robust finite-sample performances with respect to exclusion restrictions violations and endogeneity. Our approach is applied to study the returns to education, and to test the direct effects of college proximity indicators as well as family background variables on the outcome.

Abstract: This paper characterizes point identification results of the local average treatment effect (LATE) using two imperfect instruments. The classical approach (Imbens and Angrist (1994)) establishes the identification of LATE via an instrument that satisfies exclusion, monotonicity, and independence. However, it may be challenging to find a single instrument that satisfies all these assumptions simultaneously. My paper uses two instruments but imposes weaker assumptions on both instruments. The first instrument is allowed to violate the exclusion restriction and the second instrument does not need to satisfy monotonicity. Therefore, the first instrument can affect the outcome via both direct effects and a shift in the treatment status. The direct effects can be identified via exogenous variation in the second instrument and therefore the local average treatment effect is identified. An estimator is proposed, and using Monte Carlo simulations, it is shown to perform more robustly than the instrumental variable estimand.