A New Kind of Two-Stage Least Squares Based on Shapley Value Regression

The Two-Stage Least squares method for obtaining the estimated structural coefficients of a simultaneous linear equations model is a celebrated method that uses OLS at the first stage for estimating the reduced form coefficients and obtaining the expected values in the arrays of current exogenous variables. At the second stage it uses OLS, equation by equation, in which the explanatory expected current endogenous variables are used as instruments representing their observed counterpart. It has been pointed out that since the explanatory expected current endogenous variables are linear functions of the predetermined variables in the model, inclusion of such expected current endogenous variables together with a subset of predetermined variables as regressors make the estimation procedure susceptible to the deleterious effects of collinearity, which may render some of the estimated structural coefficients with inflated variance as well as wrong sign. As a remedy to this problem, the use of Shapley value regression at the second stage has been proposed. For illustration a model has been constructed in which the measures of the different aspects of globalization are the endogenous variables while the measures of the different aspects of democracy are the predetermined variables. It has been found that the conventional (OLS-based) Two-Stage Least Squares (2-SLS) gives some of the estimated structural coefficients with an unexpected sign. In contrast, all structural coefficients estimated with the proposed 2-SLS (in which Shapley value regression has been used at the second stage) have an expected sign. These empirical findings suggest that the measures of globalization are conformal among themselves as well as they are positively affected by democratic regimes.