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

2.3 Monetary authority

The nominal stock of money held by generations s = 2 through s = T + T^R, M_t , grows
at the exogenous rate θ:

Mt+1 = θ..
Mt

The seignorage is transferred lump-sum to the government:

ne

S^eignt = Mt+1 — Mt + X J'/iR Mt j ■

T +T^R

j=1

The growth rate θ_t follows the process:

ʌ ʌ

θt ⁼ ρθθt-1 + ^εθt^,
where ε_θt is assumed to be i.i.d., ε_θt ~ N(0, σ2).

2.4 Government

Nominal government expenditures consists of pensions Pen_t, and government lump-
sum transfers P_tTr_t to households. Government expenditures are financed by an income
tax Taxt and seignorage:

P_tTr_t + Pen_t = Tax_t + Seign_t.                                             (21)

The income tax structure is chosen to match the current income tax structure in the US
most closely. Gouveira and Strauss (1994) have characterized the US effective income
tax function in the year 1989 with the following function:

τ⁽ У ) = a о ( У ^— ( У-a¹ + a 2) - a¹ ´ ^{,                                                     (22)}

and estimate the parameters with a₀ = 0■ 258, a ₁ = 0■ 768 and a2 = 0■ 031. We use the
same functional form for our benchmark tax schedule. The average nominal income in
1989 amounts to approximately $50,000.⁵

⁵We follow Castaneda et al. (2004).

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