3. New Open Economy Macroeconomic Model
Moreover, the following shall hold for the various parameters: χ, γ > 0, 0 < ρ, ε < 1, and ξ < 0.4
Since (1) is a function in real money balances, the model is a variant of the Sidrauski (1967) and Brock
(1974) money-in-the-utility-function (MIU) models, in which putting real money balances into the utility
function is justified by assuming that the use of money facilitates transactions. This modeling shortcut
guarantees the usage of money even though holding money per se does not yield a positive real return.5
The utility function of the representative foreign household is the same as (1), except that C * may differ
from C, as well as M * from M, P * from P, χ* from χ, γ* from γ, and L* from L .6
Moreover, the total domestic consumption index C from above is defined as a population-weighted per-
capita Cobb-Douglas composite of domestic and foreign commodity bundles, which implicitly assumes
that all consumption goods are tradable and that there are no trading costs:7
Ct :=
n 1-n
Ct,H Ct,F
nn (1 - n)1 -n '
(2)
The commodity bundles CH and CF are CES composites of differentiated final goods produced at home
(CH) and abroad (CF) as in Dixit/Stiglitz (1977):8
Ct,H
Ct,F
μ n )1' ∕o n-∙∙-1ψ1
( 1-n ) ’ I,.C‘ (z) - dz
(3)
(4)
The preference for differentiated goods expresses a love of variety on part of the households. As one
can see from (2), the elasticity of substitution between domestic and foreign commodity bundles σCH,CF
equals 1 (Cobb-Douglas specification). One gets from (3) and (4) that the elasticity of substitution across
4 Therefore, we obtain the subsequent first and second partial derivatives of the utility function (1) with respect to the
single variables:
∂U
∂C
∂U
∂(M)
∂U
∂ (-L )
c-ρ > 0> = (-P)C-ρ- 1 < 0,
∂C2
« μM)- > o, ⅝=(-^ μM) -∙-1 < ».
γL-ξ > 0, "U = ξγL-ξ- 1 < 0∙
∂(-L)2
1 minus each of these parameters represents the elasticity of the partial utility function in one of the three arguments,
denoted by the respective subscript, with respect to this very argument:
eUc ,C
eU M , M
P P
eU(-L) ,(-L)
∂U C
∂CUc
C-ρ
∂U (-L)
∂(-L) U(-L)
C
C1 -ρ
1 -ρ
= 1 - ρ,
= γL-ξ
1 -ε
M∖
p)
L
γ. l 1-ξ
= 1 - ε,
= 1 - ξ.
5 Note, however, that some New Open Economy Macroeconomic models abstract from explicitly modeling liquidity services
provided by the use of money (see, e.g., Clarida et al. 2002, p. 882). Note further that domestic households are assumed
to derive utility from holding domestic money only, whereas foreign households are assumed to derive utility from using
foreign money only.
6 As one can see here, real foreign variables are denoted by a superscript asterisk. The same holds for nominal foreign
variables in foreign currency, except for nominal internationally traded bonds, which will be discussed in more detail
below.
7 Hence, there is no source for the Harrod-Balassa-Samuelson effect as described in Obstfeld/Rogoff (1996, pp. 210-216).
Furthermore, the total domestic consumption index (2) is population-weighted for the CPI (5) below to have the usual
form rather than a form such as, e.g., in Clarida et al. (2002, p. 882).
8 Alternatively, one could treat imported goods as production factors rather than consumption goods as in McCal-
lum/Nelson (2001). This formulation shall not be adopted, however.