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.

Table to accompany Religion/Spirituality and Change in Meaning after Bereavement: Qualitative Evidence for the Meaning Making Model

This table accompanies the manuscript entitled "Religion/Spirituality and Change in Meaning after Bereavement: Qualitative Evidence for the Meaning Making Model" by Wortmann & Park (2009). The table summarizes the sample characteristics for published, qualitative studies that describe the involvement of religion/spirituality in adjustment after bereavement. Fields include author(s)'s last name, publication year, population characteristics and sample size, study design, age of the bereaved, type or cause of death, and time post-loss.

Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

A Qualitative Study of the Assistive Technology Decision-Making Process in Four Pennsylvania School Districts

The purpose of this study was to gain an understanding of the Assistive Technology decision making process at four regional school districts in Pennsylvania. A qualitative case study research method involving the triangulation of data sources was implemented to collect and analyze data. Through an analysis of the data, three major topics emerged that will be addressed in the body of this paper: (a) the procedure for determining assistive technology needs and the dynamics of the decision-making process, b) the cohesiveness of Special Education and General Education programs, and c) major concerns that impact the delivery of assistive technology services.