Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation



4.1 The non-stochastic steady state

Our OLG model displays the behavior that is typical for this kind of model. The
wealth-age profile is hump-shaped as displayed in the upper left graph in Figure 1.
Notice that due to the hump-shaped age-productivity profile (not displayed) households
dissave during the first 61 quarters (=15 years). Only at real lifetime age 35 do they
start to build up positive savings. Agents with higher productivity attain higher levels
of capital, money balances, and consumption. In addition, consumption as displayed in
the lower right graph in Figure 1 is increasing over the life-time as the discount rate is
smaller than the interest rate.
10 Notice that the household behavior changes abruptly
as they enter retirement. This kind of behavior is absent from most standard OLG
models. Consumption growth increases at retirement, while there is a downward jump
in the real money stock. The reason is the presence of progressive income taxation
in our model. In the first period of retirement at age 60.25, taxable income falls and
the tax rate on capital income is much smaller than during working life. For this
reason, the after-tax rate of return on real capital income increases. As a consequence,
consumption growth is higher, and the household readjusts its portfolio allocation. The
premium on the return on capital relative to the one on money has increased, and the
real money stock is reduced as can be seen from the upper right picture in Figure
1. Furthermore, labor supply (lower left graph) attains a maximum at around age 30
because the age-specific productivity is rather low at young ages. Labor supply also
attains its maximum prior to the maximum in the hourly wages because older agents
have higher wealth and work fewer hours. Notice that high-productive agents work less
hours than agents with low productivity because the income tax is progressive.
11

In our economy, income and wealth are distributed unequally. The heterogeneity of
income is in good accordance with the one observed empirically. In particular, the
Gini coefficient of total gross income amounts to 0.34 and the Gini coefficient of dis-
posable income equals 0.31. For the US economy, Henle and Ryscavage (1980) estimate
an average US earnings Gini coefficient for men of 0.42 in the period 1958-77, while
Castaneda et al. (1998) report a Gini coefficient equal to 0.351.
12 The distribution of

10 In order to imply a more realistic consumption-age profile, we may have introduced stochastic
survival probabilities; in this case, consumption declines at old age. However, our quantitative results
are not sensitive to this modelling choice and, therefore, we kept the model as simple as possible.

11If we assumed a flat tax rate on income instead, high-productive workers would work more than
their low-productive contemporaries.

12The latter estimate is a little lower and in better accordance with our results because the authors

15



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