Three essays on directed graphs and model selection

In this work we demonstrate that directed graphs shed new light on old problems of model specification in applied econometrics. Directed graphs are applied to the study of proxy variables, causal structures from health data and instrumental variables selection with simultaneous models. Using Monte Carlo simulation methods we show that a proxy variable could end up doing more harm than good in the estimation of another coefficient. A simple rule is suggested: "Include the proxy variable if it is d-separated from the observed relevant variable. Do not include the proxy variable if it is not d-separated from the observed relevant variable."; Directed graphs are applied to the study of the causal relationships between label use and a consumer's intake of fat, cholesterol, sodium and fiber. Three alternative models are considered: an endogenous switching regression, a directed graphs model, and an endogenous switching regression model modified using the variable selection capabilities of the directed graphs. The three models suggest similar results for three variables (total fat, saturated fat and cholesterol): label use decreases consumer intake of calories from total and saturated fat, and decreases consumer intake of cholesterol. In the case of fiber, the endogenous switching regression model and the combined model suggest that label use increases fiber intake, while the directed graphs approach suggests that there is no causal relationship between label use and fiber intake. Out-of-sample prediction performance of these three models shows that there is no superior predictor for the case of total fat and saturated fat. In the case of cholesterol the directed graphs and the combined model are better predictors relative to the endogenous switching regression model.; Heretofore directed graphs have received the bulk of their use in recursive models. We investigate their use in a well-know case of simultaneity, Klein's Model I. Using updated data for this model we compared the out-of-sample prediction from Klein's model and directed graphs using instrumental variables. Directed graphs perform poorly in the prediction when considering the data in levels. However, when we consider the stationarity of the data, directed graphs offer a better predictor.