Valid Instrumental Variable Selection Using Lasso under the Control Function Approach

Music City Center 

In recent years, valid instrumental variable selection method has attracted attention across different fields of study, including biostatistics, econometrics, and epidemiology. Under the plurality rule, where valid instruments form the largest group of clusters from taking ratios between coefficients of regressing the outcome variable on candidate instruments as well as the covariates and corresponding coefficients from regressing the endogenous variable(s) again on the same variables, exploration of this method has extended to deal with cases of multiple endogenous variables and heterogenous treatment effect. However, the up-to-date agglomerative hierarchical clustering method that groups instruments for multiple endogenous variables based on their Euclidean distances from each other could be computationally complex and does not provide well-defined explanations for heterogeneous treatment effects by non-categorical variables. In this study, we propose Lasso under the control function approach to deal with multiple endogenous regressors, endogenous variables with non-normal distributions, and heterogeneous treatment effects in interaction and higher-order terms.

Lasso

instrumental variable

the control function approach

multiple endogenous variables

heterogenous treatment effect 

Section on Statistics in Epidemiology