Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Corruption and Growth Under Weak Identification

The goal of this paper is to revisit the influential work of Mauro [1995] focusing on the strength of his results under weak identification. He finds a negative impact of corruption on investment and economic growth that appears to be robust to endogeneity when using two-stage least squares (2SLS). Since the inception of Mauro [1995], much literature has focused on 2SLS methods revealing the dangers of estimation and thus inference under weak identification. We reproduce the original results of Mauro [1995] with a high level of confidence and show that the instrument used in the original work is in fact 'weak' as defined by Staiger and Stock [1997]. Thus we update the analysis using a test statistic robust to weak instruments. Our results suggest that under Mauro's original model there is a high probability that the parameters of interest are locally almost unidentified in multivariate specifications. To address this problem, we also investigate other instruments commonly used in the corruption literature and obtain similar results.