THE COMPOSITION OF GOVERNMENT SPENDING AND THE REAL EXCHANGE RATE
Equations (1) to (12) together with the first-order conditions for private consumption
and private investment and the profits of the non-traded sector form the system.
Our primary interest is in the long-run behavior of the real exchange rate. Accord-
ingly, we focus on the steady-state solution of the model. In order to obtain an analytical
solution, we assume no depreciation.6 We initially solve for a benchmark steady state in
which the levels of net foreign assets and government consumption are zero (in order to
obtain a closed-form solution). Then we log-linearize the system around this benchmark,
in order to examine the sensitivity of the steady-state real exchange rate to shifts in the
steady-state values of the exogenous variables.
In the benchmark steady state, the relative price of non-traded goods is7 8
PN =
ηLN
1-βK
αz βz
Z 1-ακ 1-βκ
(13)
In the next stage, we log-linearize around this steady state and solve the system. The
« ∙ . . Γ ∙ ∙ i . . . I ∙ . ∣1 . . ... . ∙ . « 1 . .1. 1 .. « . тЧ ^r~t ∙ « 1
equation of primary interest is the one governing the real exchange rate, P = γPN, with
the relative price of non-traded goods given by
1 — Л?
-
(14)
P3N = -AN + :j-----AT + μ0(rB + [GN - GT]) + μ1Z
1 - αK
where hatted variables denote percentage deviations from the steady-state values.9 Equa-
tion (14) shows that an improvement in productivity in the nontraded sector generates
real depreciation and a decline in the relative price of nontradables, while an increase in
productivity in the traded sector generates real appreciation and an increase in the rel-
ative price of nontradables, where these forces operate according to the classic Balassa-
Samuelson mechanism.10 The other key coefficients are
αL(1 - βL - βK)(1 - Y)
αL(1 - Y) + βLY
>0
(15)
and
(1-jβκ2αz.--(1.-..ακ}βz.
<=> 0
(16)
6With depreciation the model has to be solved numerically.
7See Appendix A for the set of steady state equations.
8The parameter η is a complex product of the underlying parameters: η =
αK αK βK __βK
αLαK-αK r 1-ακ 1-βκ β-1βκ 1-βK .
9The equations governing sectoral output and consumptiond dynamics are given in Appendix B.
10A symmetric increase in productivity in both sectors generates real appreciation if the nontraded sector
is less capital intensive than the traded sector (βK < αK).