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

1 + i_t

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

y - tx_t = c_t + —^t+1 —--- + —^t+1—^t+1----^t-

^{t t}P P P PP 1 ₊ i P

t t+1    ¹ t t t ¹I+1 ¹1 ɪ ^{+ z}t 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(c_t, m_t ) = (1 - σ ) ¹A₁ c_t ^1σ + (1 - η ) ¹A 2 m_t ^1η

P_t     P_t              P_t         1          P_t    ,   (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

P^e = P
¹ t+1     ¹ t+1

P 1 + i. ,

Uc ( Ct, m_t ) = -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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