Inference on factor structures in heterogeneous panels

Abstract

This paper develops an estimation and testing framework for a stationary large panel model with observable regressors and unobservable common factors. We allow for slope heterogeneity and for correlation between the common factors and the regressors. We propose a two stage estimation procedure for the unobservable common factors and their loadings, based on Common Correlated Effects estimator and the Principal Component estimator. We also develop two tests for the null of no factor structure: one for the null that loadings are cross sectionally homogeneous, and one for the null that common factors are homogeneous over time. Our tests are based on using extremes of the estimated loadings and common factors. The test statistics have an asymptotic Gumbel distribution under the null, and have power versus alternatives where only one loading or common factor differs from the others. Monte Carlo evidence shows that the tests have the correct size and good power.JEL codes: C12, C33.

A two-stage estimator for heterogeneous panel models with common factors

“…Assumptions 1-4 are the same set of assumptions as in Castagnetti, Rossi, and Trapani (2012); basically, they are needed in order to prove the consistency of the estimated common factors and loadings. Assumption 4 is specific to the CCE estimator, employed in Step 1.…”

“…This section contains some preliminary Lemmas to prove Theorem 1. Lemmas 1-4 have been derived in Castagnetti, Rossi and Trapani (2012), and we refer to that paper for the proofs; Lemmas 5 and 6 are new, and the proofs are reported here. Their proofs are based on very similar arguments as in Castagnetti, Rossi, and Trapani (2012), and we only report the main passages when possible for the sake of a concise discussion.…”

“…as inputs for diffusion index forecasting (see Stock and Watson, 2005) and as regressors in factor augmented VARs (see Bernanke, Boivin, and Eliasz, 2005). Castagnetti, Rossi, and Trapani (2012) develop an inferential theory for the unobserved common factors and loadings.…”

Interactive Effects Panel Data Models with General Factors and Regressors

“…The (implicit) assumption of a common slope coefficient β 0 is standard in the literature (see, for example, Bai, 2009, andMoon andWeidner, 2015). We speculate that our results can be extended to accommodate heterogeneous slope coefficients as in, for example, Castagnetti et al (2015), Castagnetti et al (2019), Li et al (2020), and Huang et al (2021).…”

Detecting Common Longevity Trends by a Multiple Population Approach

“…This would mean that the model becomes a nonstationary panel regression with one time effect; however, verifying the validity of such a restriction is in general not easy (see e.g. Castagnetti et al, 2013, for the case of stationary data). We, therefore, choose to leave the model unrestricted, pointing out that whilst long-term forecasts may have the implausible property that predictions for the same age x diverge across individual populations, this is not an issue for short term forecasting .…”