For the United States, the mean real growth rates of income during the life cycle
before retirement (until age 64) are taken from Cocco, Gomes, and Maenhout (2005).
The profiles are age and education (low, middle, high), but not gender specific. For
Germany, we use profiles based on Fitzenberger and Wunderlich (2002) and Behr et
al. (2003). These profiles are age, education (low, middle, high) and gender specific.
In both, the United States and Germany, real income profiles are in general hump-
shaped in age; in nominal terms (applying the inflation rate defined above), they can
be monotonically increasing in age. During retirement, labor income is exogenously
replaced by (government) pension income by multiplying the income at age 64 with
a replacement factor. For this we use “prospective” replacement factors, reflecting
expected future replacement ratios. For the United States, we use a value of 35% (see
Reno and Lavery, 2007), for Germany we use a value of 40% (see Borsch-Supan and
Wilke, 2004).
To reflect the fact that labor income is risky, we model each period’s labor income to
be lognormally distributed and subject to transitory shocks.10 The mean of Lt is given
by the current income at t = -1 with the growth rates and inflation described above.
Until age 64, the standard deviation for U.S. individuals is set to 0.19 ∙ E(Lt ) (see
Carroll and Samwick, 1997). For German individuals, we do not have empirical
estimates and use 0.05 ∙ E(Lt), which should reflect that in the German welfare state,
income risks are comparatively lower than in the United States. From age 65—that
is, during retirement—we assume no labor income uncertainty.
For our calculations we finally assume no taxes.
Table 1 summarizes the calibration of the model parameters.
10 The literature contains much controversy about whether shocks to labor income are
permanent or transitory. Newer empirical evidence gives mixed results (see, e.g.,
Guvenen, 2007). Because using transitory shocks makes the computational solution of the
optimization problem much faster, we implemented only transitory shocks.
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