Disturbing the fiscal theory of the price level: Can it fit the eu-15?



where ct is consumption in real terms in period t, mt = Mt/Pt, and M is the nominal stock
of money.7

The budget constraint for the households, in nominal terms, may be written as

P,(y - txl ) = P,c, + M,,1 - M, + B^- - Bt               (9)

1 + it

where y is the output, assumed constant, ,x, are the lump-sum taxes paid in ,, B, stands
for one period government debt securities, outstanding in period ,, and i is the nominal

interest rate.

The previous constraint may also be presented in real terms as

M 1P1 M B 1P1 1 B

(10)


y - txt = ct + —t+1 —--- + —t+1t+1----t-

t tP P P PP 1 + i P

t t+1    1 t t t 1I+1 11 ɪ + zt 1 t

Defining bt = Bt/Pt and multiplying both members of the last equation by (Pt/Pt+1), the
utility optimization problem of the households is then given by

Max U(ct, mt ) = (1 - σ ) 1A1 ct 1σ + (1 - η ) 1A 2 mt 1η

Pt     Pt              Pt         1          Pt    ,   (11)

s. a    (y-txt) — = —ct + mt+1 - — mt +1—г bt+1 - — bt

Pt+1    Pt+1               Pt+1        1 + it        Pt+1

with the following first order condition for the optimum solution, assuming that

Pe = P
1 t+1     1 t+1

P 1 + i. ,

Uc ( Ct, mt ) = -P- -r-t+1 Uc ( Ct+1, mt+1 ),                    (12)

Pt+1 1 + r

which is the usual Euler equation, now depicting addionally the use of money in the
households utility function.

7 The utility function used here (inspired in McCallum (1999a)) is basically a parametric version of
the general formulations used by Leeper (1991) and Woodford (1995).



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