Tests of risk premia in linear factor models

We show that inference on risk premia in linear factor models that is based on the Fama-MacBeth and GLS risk premia estimators is misleading when the ß’s are small and/or the number of assets is large. We propose some novel statistics that remain trustworthy in these cases. The inadequacy of Fama-MacBeth and GLS based Wald statistics is highlighted in a power comparison and using daily portfolio returns from Jagannathan and Wang (1996). The power comparison shows that the Fama-MacBeth and GLS Wald statistics can be severely size distorted. The daily portfolio returns from Jagannathan and Wang (1996) reveal a large discrepancy between the 95% confidence sets for the risk premia that result from the different statistics. The Fama-MacBeth and GLS Wald statistics imply small 95% confidence sets for the risk premia on the yield premium and labor income growth while the statistics that remain trustworthy in case of small ß’s imply large and possibly unbounded confidence sets for these risk premia.