| 简介： | The triangular model is a very popular way to allow for causal inference in the presence of endogeneity. In this model, an outcome is determined by an endogenous regressor, which in turn is first caused by an instrument. In this paper, we study the triangular model with random coefficients and exogenous regressors in both equations. We establish nonidentification of the joint distribution of the random coefficients, implying that counterfactual outcomes are also not identified. This result continues to hold, if we confine ourselves to the joint distribution of coefficients in the outcome equation or any marginal, except the one on the endogenous regressor. Identification continues to fail, even if we focus on means of random coefficients (implying that IV is generally biased), or let the instrument enter the first stage in a monotonic fashion. Based on this insight, we derive bounds on the joint distribution of random parameters, and suggest an additional restriction that allows to point identify the distribution of random coefficients in the outcome equation. We extend this framework to cover the case where the regressors and instruments have limited support, and analyze semi- and nonparametric sample counterpart estimators in finite and large samples. Finally, we provide an application of the framework to consumer demand. |