Endogenous variables and weak instruments in cross-sectional nutrient demand and health information analysis: a comparison of solutions

Abstract

In recent years, increasing attention has turned toward the effect of health information or health knowledge on nutrient intake. In determining the effect of health information on nutrient demand, researchers face the estimation problem of dealing with the endogeneity of health information knowledge. The standard approach for dealing with this problem is an instrumental variables (IV) procedure. Unfortunately, recent research has demonstrated that the IV procedure may not be reliable in the types of data sets that contain health information and nutrient intakes because the instruments are not sufficiently correlated with the endogenous variables (i.e., instruments are weak). This thesis compares the reliability of the IV procedure (and the Hausman test) with a relatively new procedure, directed graphs, given weak instruments. The goal is to determine if the method of directed graphs performs better in identifying an endogenous variable and also relevant instruments. The performance of the Hausman test and directed graphs are first assessed through conducting a Monte-Carlo sampling experiment containing weak instruments. Because the structure of the model is known in the Monte-Carlo experiment, these results are used as a guideline to determine which procedure would be more reliable in a real world setting. The procedures are then applied to a real-world cross-sectional dataset on nutrient intake. This thesis provides empirical evidence that neither the IV estimator (and Hausman test) or the directed graphs are reliable when instruments are weak, as in a cross-sectional dataset.