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Being More Flexible at the Statistician’s Workplace: Researchers find good approximation of finite sample properties with a bias-corrected least squares estimator
Factor models are widely studied in various economics applications and disciplines such as asset pricing, forecasting, empirical macroeconomics, and empirical labor economics. These models have been used to represent time-varying individual effects or heterogeneous interactions of common shocks known as interactive fixed effects.
Professor Hyungsik Roger Moon, affiliated to Yonsei University and the University of Southern California, along with Martin Weidner, from University College London, recently studied linear panel regression models in which individual fixed effects, or factor loadings, interact with common time-specific effects.
According to Prof. Moon, their proposed model is “significantly more flexible than the conventional individual and time effect model because it allows the factors to affect each individual with a different loading.” Building on the literature of Bai (2009) and Moon and Weidner (2015), the researchers investigate the least squares (LS) estimator for a linear panel regression with interactive fixed effects. The main difference between the researchers’ study and that of Bai is that Moon and Weidner consider predetermined regressors, which allow the feedback of past outcomes to affect future regressors. The researchers also differ from Bai by introducing a model where “low-rank regressors” and “high-rank regressors” are present at the same time.
The researchers employ the LS estimation method because it imposes no restrictions between the observed explanatory variables and the unobserved heterogeneity components.
One of the main findings of this study, as Prof. Moon describes is that “the limit distribution of the LS estimator has two types of biases: one type of bias due to correlated or heteroscedastic errors and the other type of bias due to the predetermined regressors.”
The study also establishes the asymptotic theory of the Wald test, the likelihood ratio test, and the Lagrange multiplier test. For this, the researchers use the quadratic approximation of the profile LS objective function developed by Moon and Weidner (2015) as the key approximation analysis tool.
Through Monte Carlo simulations, the researchers show that the asymptotic results on the distribution of the bias-corrected LS estimator and the bias-corrected test statistics provide a good approximation of their finite sample properties.
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