¹⁸Note that ${\sigma }_{𝜃}=0.1$ is smaller than the estimate for college graduates estimated in Carroll and Samwick (1997) ($=0.197=\sqrt{0.039}$) which is used by Cagetti (2003). The reason for this choice is that Carroll and Samwick (1997) themselves argue that their estimate of ${\sigma }_{𝜃}$ is almost certainly increased by measurement error.