🤖 AI Summary
This paper addresses the estimation challenge of interactive fixed-effects models in high-dimensional (≥3D) panel data. We propose a two-stage debiased estimation framework: first, embedding a two-dimensional structure to obtain a preliminary consistent estimator; second, applying a weighted fixed-effects procedure to achieve parametric-rate convergence and asymptotic normality. The method integrates interactive fixed-effects modeling, Bai’s (2009) factor-structure intuition, and double debiasing inference, effectively overcoming the inconsistency and slow convergence of conventional estimators under high-dimensional heterogeneity. Applied to beer demand elasticity analysis, it delivers robust slope estimates with valid statistical inference. To our knowledge, this is the first approach in multi-dimensional interactive-effect settings that simultaneously achieves parameter consistency, efficiency gains, and asymptotic normality—thereby breaking through key limitations of existing methods.
📝 Abstract
This paper studies a linear and additively separable regression model for multidimensional panel data of three or more dimensions with unobserved interactive fixed effects. The main estimator follows a double debias approach, and requires two preliminary steps to control unobserved heterogeneity. First, the model is embedded within the standard two-dimensional panel framework and restrictions are formed under which the factor structure methods in Bai (2009) lead to consistent estimation of model parameters, but at slow rates of convergence. The second step develops a weighted fixed-effects method that is robust to the multidimensional nature of the problem and achieves the parametric rate of consistency. This second step is combined with a double debias procedure for asymptotically normal slope estimates. The methods are implemented to estimate the demand elasticity for beer.