Description: This figure shows the distribution of GMM estimates of the coefficient of relative risk aversion from the simulated data in Figure 3. Below “strong,” the correlation between consumption growth and the market excess return is imposed to be 0.80. Below “empirical,” the correlation between unfiltered consumption growth and the market excess return is similar to the empirical data (0.45). Below “useless,” the correlation between consumption growth and the market excess return is imposed to be zero.

Interpretation: For the strong and the empirical factors, the distribution becomes more normally distributed and gets narrower when the sample size increases. For the “useless” factor, the distribution is non-standard but centered around zero and gets wider when the sample size is increased (indicating a lack of identification). Bootstrapped standard errors are therefore not applicable. But bootstrapped confidence intervals will account for the non-standard shape of the distribution and they will avoid an over-rejection problem as one does not incorrectly rely on the asymptotic distribution of a “useful” factor.