In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regime models with normal mean-variance mixture errors and in the semi-parametric switching regime models of Heckman (1990). Our results for parametric switching regime models with normal mean-variance mixture errors extend some existing results for the Gaussian switching regime model and our results for semi-parametric switching regime models supplement the point identification results of Heckman (1990). Compared with the corresponding sharp bounds when selection is random, we observe that self-selection tightens the bounds on the joint distribution of the potential outcomes and the distribution of treatment effects. These bounds depend on the identified model parameters only and can be easily estimated once the identified model parameters are estimated. The important issue of inference is briefly discussed.

ABSTRACT This paper studies whether and how firms’ enhanced public disclosures of patent filings can spill over to the managerial labor market. Consistent with these disclosures crowding out the demand for directors and senior managers’ (DSMs) private information, I find that their external employment opportunities deteriorate when firms disclose patent information more timely. This effect is more pronounced when the strategic value of the disclosed information is higher and when DSMs face fewer barriers to sharing information. Additionally, the decline in their human capital value is reflected in a diminished role in transferring timely information about technological innovations. Collectively, these results shed light on how public disclosures can shape the managerial labor market by substituting private information flows between firms through DSM ties. Data Availability: The data used in this study are available from the sources indicated herein. JEL Classifications: D23; G38; M12; M41.

Instrumental variables (IVs) and control variables are frequently used to assist researchers in investigating endogenous treatment effects. When used together, their identities are typically assumed to be known. However, in many practical situations, one is faced with a large and mixed set of covariates, some of which can serve as excluded IVs, some can serve as control variables, whereas others should be discarded from the model. It is often not possible to classify them based on economic theory alone. This paper proposes a data-driven method to classify a large (increasing with sample size) set of covariates into excluded IVs, controls, and noise to be discarded. The resulting IV estimator is shown to have the oracle property (to have the same first-order asymptotic distribution as the IV estimator, assuming the true classification is known).