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.

Physiogenomic Analysis of Weight Loss Induced by Dietary Carbohydrate Restriction

ABSTRACT : BACKGROUND : Diets that restrict carbohydrate (CHO) have proven to be a successful dietary treatment of obesity for many people, but the degree of weight loss varies across individuals. The extent to which genetic factors associate with the magnitude of weight loss induced by CHO restriction is unknown. We examined associations among polymorphisms in candidate genes and weight loss in order to understand the physiological factors influencing body weight responses to CHO restriction. METHODS : We screened for genetic associations with weight loss in 86 healthy adults who were instructed to restrict CHO to a level that induced a small level of ketosis (CHO ~10% of total energy). A total of 27 single nucleotide polymorphisms (SNPs) were selected from 15 candidate genes involved in fat digestion/metabolism, intracellular glucose metabolism, lipoprotein remodeling, and appetite regulation. Multiple linear regression was used to rank the SNPs according to probability of association, and the most significant associations were analyzed in greater detail. RESULTS : Mean weight loss was 6.4 kg. SNPs in the gastric lipase (LIPF), hepatic glycogen synthase (GYS2), cholesteryl ester transfer protein (CETP) and galanin (GAL) genes were significantly associated with weight loss. CONCLUSION : A strong association between weight loss induced by dietary CHO restriction and variability in genes regulating fat digestion, hepatic glucose metabolism, intravascular lipoprotein remodeling, and appetite were detected. These discoveries could provide clues to important physiologic adaptations underlying the body mass response to CHO restriction.