Paper by Frank Kleibergen in the Journal of Finance
The reliability of traditional asset pricing tests depends on: (i) the correlations between asset returns and factors; (ii) the time series sample size T compared to the number of assets N . For macro‐risk factors, like consumption growth, (i) and (ii) are often such that traditional tests cannot be trusted. We extend the Gibbons‐Ross‐Shanken statistic to test identification of risk premia and construct their 95% confidence sets. These sets are wide or unbounded when T and N are close, but show that average returns are not fully spanned by betas when T exceeds N considerably. Our findings indicate when meaningful empirical inference is feasible.