🤖 AI Summary
In high-dimensional covariate modeling, parameter rank deficiency arising from multicollinearity undermines identification, and conventional sparsity or discrete heterogeneity assumptions often violate economic theory, leading to severe estimation bias. This paper proposes a novel joint estimation framework that sequentially learns high-dimensional parameters and an adaptive projection matrix—marking the first method to map unidentifiable high-dimensional parameters into a low-dimensional space amenable to consistent estimation. The approach preserves original parameter accuracy under rank-deficient conditions and enjoys rigorous consistency and asymptotic normality guarantees. Validated via sequential algorithms, high-dimensional projection learning, and Monte Carlo simulations, the method substantially reduces bias and improves estimation precision. Empirically, it reveals positive R&D spillover effects among firms, though private returns remain dominant.
📝 Abstract
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.