Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

By H. R. Moon, Martin P. Weidner. 2015

281 citations recorded by the source corpus.

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed e ffects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data we establish the limiting distribution of the LS estimator for the regression coefficients, as the number of time periods and the number of crosssectional units jointly go to infi nity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed eff ects consistently. Supplementary material for this paper is available here.

Subfields: Economics and Econometrics

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Citations in the corpus

Common correlated effects estimation of heterogeneous dynamic panel quantile regression models (2020, unknown): “Recent papers have focused on the estimation of models with a fixed number of unobserved factors (see e.g. Pesaran (2006), Bai (2009), Pesaran and Chudik (2014), Moon and Weidner (2015, 2017), Chudik and Pesaran (2015)).”
Knowing factors or factor loadings, or neither? Evaluating estimators of large covariance matrices with noisy and asynchronous data (2019, unknown): “Factormodels based on stock characteristics date back to Rosenberg (1974), who suggestsmodeling factor betas of stocks as linear functions of observable security characteristics. Connor and Linton (2007) and Connor et al.”
On Time-Varying Factor Models: Estimation and Testing ∗ (2017, background): “For example, Moon and Weidner (2015) demonstrate that A.4(i) can be satisfied for various processes; Su et al. (2015) verify similar conditions to those in A.4(ii)-(v) under some mixing conditions.”
Grouped Patterns of Heterogeneity in Panel Data (2015, methodology): “A similar intuition applies to interactive fixed-effects models: Moon and Weidner (2010b) show that the asymptotic distribution of the interactive FE estimator with G ≥ G0 factors is identical to that of the estimator based on the correct number of factors.”
A diagnostic criterion for approximate factor structure (2016, background): “Finally, due the unbalanced property, we observe that the selection criteria by Onatski (2010) and Bai and Ng (2002) tend to overestimate the number of factors.”
Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Data Models with Weakly Exogenous Regressors (2015, unknown): “The case of strictly exogenous regressors, covered in Pesaran (2006), refers to the special case when αi = 0 k×1 .”
Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls (2016, methodology): “It might be useful to implement tests regarding the number of factors (Bai & Ng, 2002; Moon & Weidner, 2015), but these tests are fragile (Onatski, Moreira, & Hallin, 2013).”
Two-Stage Instrumental Variable Estimation of Linear Panel Data Models with Interactive Effects (2020, methodology): “The representative method is the Iterative Principal Components (IPC) estimator of Bai (2009a), further developed by Moon and Weidner (2015, 2017), among many others.”
Instrumental Variable Estimation of Dynamic Linear Panel Data Models with Defactored Regressors and a Multifactor Error Structure (2019, unknown): “Under somewhat weaker assumptions, Moon and Weidner (2015) show that the estimator of Bai (2009) is interpretable as a quasi maximum likelihood estimator (QMLE), the consistency of which is maintained even when the number of factors is not specified correctly, so long as it is larger than or equal…”
Synthetic controls with imperfect pretreatment fit (2016, result): “This is also consistent with the literature on linear factor models, which shows that these models can be consistently estimated in large panels (e.g., Bai (2003), Bai and Ng (2002), Bai (2009), and Moon, Roger, and Weidner (2015)).”
DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS (2017, methodology): “According to the results in Moon and Weidner (2013) we expect the limiting distribution of the correctly specified (R = 1) and incorrectly specified (R = 2) FLS estimator to be identical when N and T grow at the same rate.”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, unknown): “…Bonhomme and Manresa (2015), Moon and Weidner (2015), Moon and Weidner (2016), Kock (2016b), Manresa (2016), Lu and Su (2016), Su et al. (2016), Moon et al. (2018), Kock and Tang (2019), Bonhomme et al. (2019a), Bonhomme et al. (2019b), Gao and Li (2019), Chen et al. (2020), Lu and Su (2020))…”