Modelling cross-sectional profitability and capital intensity using panel corrected significance tests

Abstract

Employing seemingly unrelated regression (SUR) models with panel corrected standard errors (PCSE) this research augments and extends Fama and French's (2000) ‘first stage’ model of expected cross-sectional profitability. Capital intensity, defined as the ratio of depreciation plus interest expense to total assets was found to be significantly inversely related to profitability. In addition, specific market sector and country fixed-effects proved significant in models that simultaneously corrected for cross-sectional heteroscedasticity and cross-equation residual correlation. Both of these corrections addressed the potential bias from least squares standard errors or ‘inference problem’ noted in the previous work by Fama and French. Unrestricted and restricted SUR cross-sectional models with PCSE are used to compute t-statistics based on Fama–MacBeth, Litzenberger–Ramaswamy and standard panel methodologies. The former two methods provided significant results compared to those using the Fama–MacBeth approach.

Acknowledgements

This research was supported by grants from the Ramapo Foundation and the Separately Budgeted Research program at Ramapo College of New Jersey.

Notes

¹All models are estimated as SUR PCSE ‘systems’ with summary performance measures (e.g. adjusted R ², F-statistics, etc.). The difference is that ‘unrestricted’ cross sectional models allow the coefficients to vary by year while the restricted panel model does not. F–M and L–R t-statistics are based on the ‘unrestricted’ models.

²Campbell et al. (1997, pp. 215–7) cogently summarize the Fama–MacBeth approach in the context of the CAPM.

³‘As a simple remedy [to the errors in variables problem] Fama and MacBeth (1973) used portfolios in their cross-sectional regressions instead of individual stocks to decrease the measurement error variance. Since then this method has been commonly used in most investigations. But, forming portfolios results in losing information and does not solve the problem. There are several methods available to tackle the errors in variables problem and to derive consistent estimators within the two-pass methodology (see for example, Litzenberger and Ramaswamy, 1979 …’(Asgharian and Hannson, 1999, p. 215).

⁴This follows F&F's rule to mitigate the effect of influential outliers whose values may be close to zero. They also use a somewhat lower of threshold of $10 million in assets and $5 million in book equity for data from 1964 to 1996.

⁵While F&F correct for residual cross equation correlation, they do not correct for cross-firm heteroscedasticity.