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

3.3 Monetary authority

In accordance with Cooley and Hansen (1995), the quarterly inflation factor is set equal
to π = 1.013. Money growth follows an AR(1)-process. For the postwar US economy,
Cooley and Hansen estimate ρθ = 0.49 and σ_θ² = 0.0089. The initial endowment with
money equals 21 percent of the average disposable income of the first generation. This
is about the amount of money held by the 21 year old US citizens according to the
1994 PSID survey.⁷

3.4 Production

The production elasticity of capital α = 0.36 and the quarterly depreciation rate δ =
0.019 are taken from Prescott (1986) and Cooley and Hansen (1995), respectively. The
annual quarterly fraction of producers that do not adjust their prices in any quarter is
set equal to φ = 0.25. This value is smaller than the value chosen, e.g., in Bernanke
et al. (1999), who use φ = 0.75, yet it introduces sufficient nominal rigidity into our
model. Following empirical evidence presented by Basu and Fernard (1997), we set
the average mark-up at the amount of 1/g = 1.2 implying a constant elasticity of
substitution between any two intermediate goods equal to e = 6.0. The parameters of
the AR(1) for the technology are set equal to ρz = 0.95 and σz = 0.007 as in Cooley
and Hansen (1995).

3.5 Individual productivity

The idiosyncratic productivity level is given by e(s,j) = e^ys^+x, where y^s is the mean
log-normal income of the s-year old and x^j is the idiosyncratic component. The mean
efficiency index y^s of the s-year old is taken from Hansen (1993) and is interpolated to
in-between quarters. As a consequence, the model replicates the cross-section age distri-
bution of earnings of the US economy. The age-productivity profile is hump-shaped and
earnings peak at age 50 corresponding to the model period 121 (not displayed). With
regard to the idiosyncratic component x^j, we follow Huggett (1996) and choose a log-
normal distribution of earnings for the 20-year old with a variance equal to σ_y²1 = 0.38

⁷We use data from the 1994 PSID data and wealth file. We included only households with strictly
positive cash holdings in our sample. Money is defined as money in checking or savings accounts,
money market funds, certificates of deposit, government savings bonds, and treasury bills.

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