Robust Inference for Consumption-Based Asset Pricing

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-RossShanken 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.