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27

APPENDIX

Derivation of initial share of income taxes on total taxes.

Equations (13), (17) and (20) imply that in the initial steady state we have the following equations:

y0 = C0 = l0 = [(

1τ 1+τ I 0 C 0

)(

θ 1 θ

)]

1 ν +1

(A1)

0 P =

θ

θ 1

w0

(A2)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) ( l P w l P l w C P l w N R C C I C I C I τ τ τ τ τ τ + = + = + =

(A3)

We can therefore express the share of initial labor income taxes on total taxes as

u=

) ( 0 0 0 0 0 0 0 0 l P w l w C I I τ τ τ +

=

) ( 0 0 0 0 0 0 P w w C I I τ τ τ +

(A4)

Using the initial nominal wage as a numeraire (w0 = 1) our benchmark parameterization ) 1 ; 1 1 ; 0 8 . 0 ; 2 . 0 ( 0 0 = = = = ν θ τ τ C I a n d e q u a t i o n s ( A 1 ) , ( A 2 ) a n d ( A 3 ) i m p l y t h a t 1 . 1 0 = P .

We can therefore evaluate (A4) numerically as

u=

0.2 0.2 + (0.08)(1.1)

= 0.7

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