Clustered Covariate Regression

This paper introduces an estimator for a general class of models under rank deficiency arising from high dimensionality, multicollinearity, or both. Our approach obtains a projection matrix that projects a high-dimensional (potentially growing p >> n) parameter vector into a reduced consistently estimable one. We show consistency and asymptotic normality of the estimator. Recovering the high-dimensional parameter vector using the projection matrix leaves precision unaffected. We employ a sequential estimation algorithm that, at once, obtains parameter estimates and the projection matrix. Our Monte Carlo simulations demonstrate a high approximative ability of high-dimensional parameters, improved precision, and reduced bias even under multicollinearity. In our empirical application, we find that firms on average generate positive R&D spillovers on firm productivity though these are dominated by private returns to R&D