We construct the large sample distributions of the OLS and GLS R-squareds of the second pass regression of the Fama-MacBeth (1973) two pass procedure when the observed proxy factors are minorly correlated with the true unobserved factors. The small correlation implies a sizeable unexplained factor structure in the first pass residuals and, consequently, a sizeable estimation error in the estimated beta’s which is spanned by the beta’s of the unexplained true factors. The average portfolio returns and the estimation error of the estimated beta’s are then both linear in the beta’s of the unobserved true factors which leads to possibly large values of the OLS R-squared of the second pass regression. These large values of the OLS R-squareds are not indicative of the strength of the relationship between the expected portfolio returns and the (macro-) economic factors. We propose an easy manner for diagnosing it using a statistic that reflects the unexplained factor structure in the first pass residuals. Similar arguments apply to the second pass t-statistic which are resolved using the identification robust factor statistics of Kleibergen (2009). Our results put into question many of the empirical findings that concern the relationship between expected portfolio returns and (macro-) economic factors. We discuss some prominent ones in passing. (joint work with Zhaoguo Zhan)

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