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

3.7 Computation

In order to compute business cycle dynamics of the model, we first need to compute the
non-stochastic steady state of the model. Secondly, we log-linearize the model around
the non-stochastic steady state.

The non-stochastic steady state is computed by solving the respective system of non-
linear equations consisting of the first-order conditions of the generation born at time
t, the government’s budget constraint, and the aggregate consistency conditions. This
is a system of several hundred variables (strictly speaking (2(T + T^R - 1) + T )ne
variables). We employ a non-linear equations solver that takes care of the admissible
bounds within which the solution must lie. To obtain reasonable initial values, we
started with a simplified version of our model, where it is easy to solve for the optimal
time profile of the capital stock. We expanded this model in several steps to the model
given above.

Thereafter, we log-linearize the model around the non-stochastic steady. This linear
rational expectations model can be solved by, e.g., applying the method of Blanchard
and Kahn (1980), (see King, Plosser, and Rebelo, 1988) or of King and Watson (2002).⁹

4 Results

In this section, we compare the heterogeneous-agent OLG model to the representative-
agent case and will find out that the two economies display similar, but not identical
behavior, a result that is in good accordance with those in the non-monetary models
of Krussell and Smith (1998) and Rfos-Rull (1996).

⁹The method that underlies our computation of the policy functions of the log-linearized
model is explained in more detail in Chapter 2.3 in Heer and Mauβner (2005) and applied
to large scale dynamic systems of several hundred state variables and controls in Chapter
7.2.2. Both the Gauss code of the non-linear equations solver and the computation of the
policy functions can be downloaded from the web side that accompanies Heer and Mauβner
(2005). The URL is www.wiwi-uni.augsburg.de/vwl/maussner/dgebook/download.html.
The programs that solve and simulate the OLG and the Ramsey are in www.wiwi-
uni.augsburg.de/vwl/maussner/englisch/chair/maussner/pap/demp.zip.

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