Latent instrumental variables, a new approach to solve for endogeneity

This thesis aims at resolving problems surrounding classical independence assumptions in mixed linear models. Those assumptions involve independence of the regressors and the random coefficients and independence of the regressors and the (model) error term. To tackle the dependence between regressors and error terms we develop a general instrumental variable approach, the latent instrumental variable (LIV) method, where the instruments are unobserved and are estimated from the data. This leads to a finite mixture formulation. We prove identifiability and discuss estimation of the model parameters. Furthermore, we propose methodologies to investigate regressor and error dependencies. We present results of various simulation studies and illustrate the LIV method on previously published datasets. Our simulation results show that the LIV method yields consistent estimates for the model parameters without having observable instrumental variables at hand. We reanalyze data of three studies that examine the effect of education on income, where the variable ‘education’ is potentially endogenous due to omitted ‘ability’ or other causes. In all three applications we find an upward bias in the OLS estimates of approximately 7%.