In this dissertation, I provide solutions to problems sometimes encountered by researchers when employing an instrumental variable methodology. I explore the instrumental variable problem in a nonparametric framework and in a situation where there exists a large set of instruments that are weakly correlated with the endogenous variable of interest. The latter case is referred to as the many weak instrument problem and is characterized by the fact that it yields inconsistent estimators with nonstandard asymptotic distributions. I also explore the model selection advantages of the least absolute shrinkage and selection operator (LASSO) as an instrument selection procedure in this context.