CCE estimation of factor‐augmented regression models with more factors than observables

Abstract

This paper considers estimation of factor-augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006Econometrica, , 74, 967-1012Econometrica, , 2006. For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross-section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross-section combinations. Asymptotic properties of the resulting combination-augmented CCE (C 3 E) estimator are provided and tested in small samples using both simulated and real data. which can be estimated consistently using least squares (LS). If, however, x i is correlated with F, then consistency will be Our very good friend and co-author Jean-Pierre Urbain passed away shortly after the submission of the first version of this paper. 268 SUPPORTING INFORMATIONAdditional supporting information may be found online in the Supporting Information section at the end of the article.How to cite this article: Karabiyik H, Urbain J-P, Westerlund J. CCE estimation of factor-augmented regression models with more factors than observables. J Appl Econ. 2019;34:268-284. https://doi.

A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors

“…Example 1. Suppose that L = 1, such that the factor component in Equation 2reduces to f (1) λ (1) i , but v i is driven by two factors, that is, F e = (f (1) , f (2) ) and w i is a [2 × 1] vector. Then,…”

“…There are several potential choices for w i . Consider initially the case L e = L = 1 and suppose that the factor component in Equation 11reduces to f (1) γ (1) i . One simple choice is to set the value of the weight across all individuals equal to a fixed constant, that is, w i = 1.…”

“…However, the above formulation does not imply that each column in V i must be driven by the full set of columns in F e . For instance, let L = L e = 2, F = F e = (f (1) , f (2)…”

“…Assumption 3.1. Factor proxies are asymptotically linear such (1) and Assumption 3.1 is fairly intuitive. In particular, Assumptions 3.1.1 and Assumption 3.1.2 are employed so as to enable the application of a standard central limit theorem.…”

Robust Nearly-Efficient Estimation of Large Panels With Factor Structures

“…Pesaran & Tosetti (2011) and Chudik & Pesaran (2015) confirm the same asymptotic results of Pesaran (2006) when spatial-dependence in the idiosyncratic component of the innovation's factor structure as well as dynamic panel, respectively, are allowed for. Karabiyik et al (2015) show that Pesaran's estimator retains its asymptotic properties under weaker conditions, allowing for either correlated loadings or for the number of latent factor m to be larger than the number of observables, whereas discuss some limitations. Song (2013) extends Bai (2009) to the case of non-constant regression coefficients establishing √ T -asymptotics when T /N 2 → 0.…”