3The empirical literature estimates variance of income shock using annual data. We back out the corresponding quarterly values as follows. For the variance of permanent shocks, σ2
 ψ  , aggregating equation (2) to the annual frequency implies:                                                      ∑4         ∑4           ∑4           ∑4
(pt+4 + pt+3 + pt+2 + pt+1)∕4 = (pt + pt-1 + pt-2 + pt- 3)∕4 +( i=1ψt+i + i=1ψt-1+i + i=1 ψt-2+i + i=1 ψt- 3+i)∕4  . Consequently, the variance of the shocks on the right-hand side is: var((ψt+4 + 2ψt+3 + 3ψt+2 + 4ψt+1 + 3ψt + 2ψt-1 + ψt- 2)∕4) = var(ψ)(1 + 4+ 9+ 16 + 9+ 4+ 1)∕16 = 11∕4× var(ψ)  . For transitory shocks, going from the quarterly frequency to annual implies dividing by 4 as we average over the four quarters.