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



1,1       T+TR,1         1,ne         T+TR,ne 0

market income yt := [yt, , . . .yt      , , . . . ,yt, , . . . ,yt      , ]0,

the rental rate of capital rt , the real wage wt , the aggregate capital stock Kt ,
effective aggregate labor input
Nt , the beginning-of-period stock of real money
balances
mt, aggregate transfers Trt, and aggregate profits Ωt. Thus, ut is a
vector of
ne[2(T + TR) + T] + 7 elements.

We seek a representation of our model in the form

DEt


x t +1

ʌ

λt+1


+ F


xt

ʌ
λ t


Cu u t = Cχλ

x t

+ Cz

z t

ʌ

ʌ

λ t

θ t


DuEtu t+1 + Fuu t + Dz Et


zt +1

ʌ

θ t +1


+ Fz


zt

ʌ
θ t


(26a)

(26b)


where the hat denotes percentage deviations from the non-stochastic steady state value
of a variable.

We first derive the set of equations (26a). The log-linearized Euler equations (6) are20

ʌ      ∙                                                                        ∙                                                                i-            ∙                 -I

ʌtj = (γ(1 - σ) - 1) cs,j + (1 - γ)(1 - σ) £ms,j - πt] ,

s= 1,...,T+TR, j = 1,...,ne.,

m 1,j = 0 j = 1,..., ne.                                                                 (27)

The log-linearized Euler equations (9) are:

η1


nsj

-----:П

- ns,j


s,j
t


τ00


- τ0


y∙-j ^sj


- wt = λstj


τ 0 + τ 00ysj

1 - τ0


π t,


s = 1,2,... ,T, j = 1,2,... ,ne,                   (28)

where τ0 and τ00 denote the first and second derivative of the tax function evaluated at
ys,j , respectively. The ne(T + TR) definitions of market income yield:

0 = У 1,jУt,j - we(1, j)n 1 ,jn1 ,j - we(1, j)n1 ,jw^t,

j = 1,...,ne,

rks,jkS,j = ys,jyS,j - we(s,j)ns,jns, - we(s,j)ns,jw^t - rks,jrt,

s = 2, . . . , T, j = 1, . . . , ne,

rks,jкS,j = ys,jyS,j - rks,j^t,

s=T+1,...,T+TR,

j = 1, . . . ,ne.                                                                               (29)

20We will use the ne equations for generation T + TR later to eliminate ^T+T ,j, which is a control
rather than a costate variable.

28



More intriguing information

1. LABOR POLICY AND THE OVER-ALL ECONOMY
2. EU enlargement and environmental policy
3. A THEORETICAL FRAMEWORK FOR EVALUATING SOCIAL WELFARE EFFECTS OF NEW AGRICULTURAL TECHNOLOGY
4. Disturbing the fiscal theory of the price level: Can it fit the eu-15?
5. The Integration Order of Vector Autoregressive Processes
6. Moi individuel et moi cosmique Dans la pensee de Romain Rolland
7. Design and investigation of scalable multicast recursive protocols for wired and wireless ad hoc networks
8. The economic doctrines in the wine trade and wine production sectors: the case of Bastiat and the Port wine sector: 1850-1908
9. The name is absent
10. Foreign Direct Investment and Unequal Regional Economic Growth in China
11. The name is absent
12. Empirical Calibration of a Least-Cost Conservation Reserve Program
13. A Note on Costly Sequential Search and Oligopoly Pricing (new title: Truly Costly Sequential Search and Oligopolistic Pricing,)
14. THE WAEA -- WHICH NICHE IN THE PROFESSION?
15. The name is absent
16. Valuing Access to our Public Lands: A Unique Public Good Pricing Experiment
17. Examining the Regional Aspect of Foreign Direct Investment to Developing Countries
18. The name is absent
19. Outsourcing, Complementary Innovations and Growth
20. Globalization, Divergence and Stagnation