Estimating panel data fixed and random effects with application to new Fama-French model with GMM robust instruments

Sharpe (1964), Lintner (1965), and Mossin (1966) developed what is known as the capital asset pricing model (CAPM). Jensen (1968) is credited with the development of alpha , which he applied to investigate the performance of mutual funds via the CAPM. There were many attempts to extend the CAPM to a dynamic framework, such as the intertemporal CAPM (Merton, 1973) and the consumption CAPM due to Hansen and Singleton (1982, 1984). Nevertheless, it appears that the most appealing extension of the CAPM is the static Fama and French (FF, 1992, 1993) three-factor asset pricing model that is akin to the arbitrage pricing theory (APT) of Ross (1976).

Our approach employs generalized versions of Durbin (1954) and Pal (1980) higher moment estimators. The principal two features of this approach are it i) is parsimonious in the sense that it requires minimal computational power and ii) essentially minimizes a distance (d) measure. Based on this distance notion, we will refer to this approach as (generalized method of moments) GMM_d.

This article develops an empirical extension of Racicot (2015) that generalizes the GMM_d approach to a fixed and random effects panel data framework. In addition, we allow not only for the Jensen performance measure to vary across individuals (sectors) but also the systematic risk measure to vary. This generalization enables us to i) evaluate the robustness of the new five-factor FF (2015) model and ii) compare this model to a six-factor model that incorporates the Pastor and Stambaugh (PS, 2003) illiquidity risk factor. This empirical framework allows us to provide some new insights on the effects of unobserved heterogeneity in panel data models that may compound measurement errors. Arrenallo (2003) showed that it is only by chance that the method of first-differencing in a panel data framework will diminish measurement errors.

Our results show that using ordinary least squares (OLS) in panel data for fixed or random effects models, most of the new FF portfolio risk factors are significant although the PS portfolio illiquidity is not. However, when we use the GMM_d approach, we obtain a different picture, viz., the only strongly significant risk factor is the market factor and the illiquidity factor is weakly significant for the pooled GMM_d (fixed effects). We also find significant measurement errors for the new FF investment factor and for the PS illiquidity factor using our modified artificial regression Hausman (1978) test (Haus_d).