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.

Liquidity Constraint and Child Labor In India: Is Market Really Incapable Of Eradicating It From Wage-Labor Households?

One way to measure the lower steady state equilibrium outcome in human capital development is the incidence of child labor in most of the developing countries. With the help of Indian household level data in an overlapping generation framework, we show that production loans under credit rationing are not optimally extended towards firms because of issues with adverse selection. More stringent rationing in the credit market creates a distortion in the labor market by increasing adult wage rate and the demand for child labor. Lower availability of funds under stringent rationing coupled with increased demand for loans induces the high risk firms to replace adult labor by child labor. A switch of regime from credit rationing to revelation regime can clear such imperfections in the labor market. The equilibrium higher wage rate elevates the household consumption to a significantly higher level than the subsistence under credit rationing and therefore higher level of human capital development is assured leading to no supply of child labor.