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



are sticky and adjust as in Calvo (1983). Following an unexpected rise of the money
growth rate, we observe unexpected inflation. Prices and markups adjust endogenously
in our economy. As a consequence, both factor prices and the distribution of income
change. In addition, as mentioned above, income is taxed progressively in our model.
If there is unexpected inflation, the real tax burden of the income-rich agents increases,
the so-called “bracket creep“. We also consider the effect of inflation on pensions. In
particular, unexpected inflation results in a reduction of real pensions as the government
adjusts the pensions for higher-than-average inflation only with a lag. Consequently,
following an expansionary monetary policy with an unexpected rise of inflation, the
non-interest income distribution becomes more equal, while the effect on the total
income distribution depends on the distribution of interest income (and, hence, the
distribution of wealth).

The paper is organized as follows. In section 2, we describe the OLG model. The model
is calibrated in section 3, where we also present the algorithm for our computation in
brief. The results are presented in section 4. We compare the heterogeneous-agent with
the corresponding representative-agent economy and make the interesting observation
that the business cycle dynamics in these two models are not completely identical. We
also present the effect of both a productivity and a monetary shock on the distribution
of income and wealth. Section 5 concludes. The Appendix describes the stochastic
OLG and Ramsey model and the solution method in more detail.

2 The Model

The model is based on the stochastic Overlapping Generations (OLG) model with
elastic labor supply and aggregate productivity risk, augmented by a government sector
and the monetary authority. The model is an extension of Rιos-Rull (1996).

Four different sectors are depicted: households, firms, the government, and the mone-
tary authority. Households maximize discounted life-time utility with regard to their
intertemporal consumption, capital and money demand, and labor supply. Firms in the
production sector are competitive, while firms in the retail sector are monopolistically
competitive and set prices in a staggered way a la Calvo (1983). The intermediate good
firms produce using labor input and capital. The government taxes income progres-
sively and spends the revenues on government pensions and transfers. Both aggregate
productivity and monetary policy are stochastic.



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