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

3 Calibration and computation

The OLG model is calibrated with regard to the characteristics of the US postwar
economy. We use standard values for the parameters of the model. Periods correspond
to quarters. The first T = 160 periods, agents are working, the remaining T ^R = 80
periods they are retired.

3.1 Preferences

β is set equal to 0.9909 implying a non-stochastic steady state annual real rate of
return equal to r(1 - τ⁰) - δ = 4.5% and an annualized capital-output ratio equal to
K/Y = 2.1. The relative risk aversion coefficient σ is set equal to 2.0. η0 = 0.26 is set
so that the average labor supply is approximately equal to 1/3, n ≈ 1 /3. Furthermore,
we choose η = 7.0 which implies a conservative value of 0.3 for the Frisch labor supply
elasticity.⁶ γ is chosen so that the (annualized) average velocity of money PY/M is
equal to the velocity of M1 during 1960-2002, which is equal to approximately 6.0. This
requires γ = 0.981.

3.2 Government

Pensions are constant. We choose a non-stochastic replacement ratio of pensions rel-
ative to average net wage earnings ζ equal to 30%, ζ = (₁ -peWt_nt, where n_t and τ
are the average labor supply and the income tax rate of the average income in the
non-stochastic steady state of the economy, respectively. The calibration of the tax
schedule follows Goveira and Strauss (1994). We adjust the parameter a2 in (22) so
that the average (and also the marginal) tax rate on annual average US-income equals
the quarterly tax rate on average income in the model.

⁶The estimates of the Frisch intertemporal labor supply elasticity ηn,w implied by microeconometric
studies and the implied values of γ vary considerably. MaCurdy (1981) and Altonji (1986) both use
PSID data in order to estimate values of 0.23 and 0.28, respectively, while Killingsworth (1983) finds
an US labor supply elasticity equal to ηn,w = 0.4. Domeij and Floden (2006), however, argue that
these estimates are biased downward due to the omission of borrowing constraints.

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