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



(35)

For generations s = 2, . . . , T the log-linearized budget equations (5) are:

ks+1 ,j^ts+11,j + θms+1 ,jmt+1,j - (1 - δ) ksj fcs,j - ms,jmssj + (τ0ysj + msj )πt

= (1 — τ0 ) ys,j y s,j + trtrt + ΩΩ t — cs,j c st,j,

j = 1, . . . , ne, s = 2, . . . ,T.                                                                          (36)

For generations s = T + 1, . . . , T + T R - 1 they are:

ks+1 ,jk S .ll ,j + πms+1,j m t+1,j (1 — δ ) ks,jk s,j — ms,j m S,j + ( τ 0ys,j + ms,j + pens ) π t
= (1 — τ0 ) ys,j y s,j + trtrt + ΩΩ t — cs,j ^ s,j,

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

(37)

The Euler equations (7) and (8) yield:

^s+1,j     ^s,j    β λ + ,j / 0      00 s+1 ,j

λt +1 λt βr λs,j τ + τ y     πt +1

λs+1,j                         λs+1,j

= β''λsj τ 00ys+1 ,jy t+ ,j βl' λs,j(1 τ 0 )r t+1,                                       (38)

β λs+1,j                               β λs+1,j

∏-λt+'1 j λsj I1 + (1 β-P — Y)(1 — σ) ɪ]j πt+1

+ [(1 — γ)(1 — σ) 1] (1 — βλ+j) rmS÷11'j
βλs +1j   s+u

= Y <1 σ ψ ∏-C+^j

j = 1, . . . , ne, s = 1, . . . ,T + TR 1.                                                     (39)

Note that in the equations for s = T + TR 1 we must replace ΛT+T ,j by the right
hand side of (27) for
t + 1 and s = T + TR. The remaining two equations are given by
the New Keynesian Phillips curve equation (17),

,ɔʌ ʌ I (1 φ )(1 βφ )

βπ t+1 π t +         g-------g t = 0,                                              (40)

φ

and the log-linearized definition of the aggregate beginning-of-period real stock of
money
mt := Mt/Pt-1. Together with equation (18) this definition implies:

m t+1 — m t + t = θ t.                                                         (41)

30



More intriguing information

1. The changing face of Chicago: demographic trends in the 1990s
2. The name is absent
3. Innovation Policy and the Economy, Volume 11
4. EXECUTIVE SUMMARY
5. Dynamiques des Entreprises Agroalimentaires (EAA) du Languedoc-Roussillon : évolutions 1998-2003. Programme de recherche PSDR 2001-2006 financé par l'Inra et la Région Languedoc-Roussillon
6. A parametric approach to the estimation of cointegration vectors in panel data
7. Parent child interaction in Nigerian families: conversation analysis, context and culture
8. Midwest prospects and the new economy
9. The name is absent
10. Economie de l’entrepreneur faits et théories (The economics of entrepreneur facts and theories)