²⁹Note that $σ𝜃𝜃𝜃 = 0.1$ is smaller than the estimate for college graduates estimated in Carroll and Samwick (1997) ( $√----- = 0.197 = 0.039$ ) which is used by Cagetti (2003). The reason for this choice is that Carroll and Samwick (1997) themselves argue that their estimate of $σ𝜃𝜃𝜃$ is almost certainly increased by measurement error.