Versión de HTML Básico
Carlos Gustavo Machicado y Paúl Estrada
Analíti a
k
4
Revista de Análisis Estadístico
Journal of Statistical Analysis
1
=
β
E
t
"
u
′
cm
,
t
+
1
u
′
cm
,
t
(
1
+
˜
r
t
+
1
)
#
(6)
1
=
β
E
t
"
u
′
cn
,
t
+
1
u
′
cm
,
t
(
1
−
τ
k
)
(
1
+
τ
m
)(
1
+
τ
c
)
r
t
+
1
+
1
−
δ
#
(7)
Equation (5) states that the relative price between importa-
bles and non-tradables must equate marginal utilities for
each good. The intertemporal conditions are the standard
Euler equations requiring the marginal rates of substitution
between current and future consumption to be equal to the
price ratio in each of the two periods and for each good,
respectively evaluated at the cost of foreign borrowing and
the rate of return on capital investment.
3.1.2 Firms
This economy is represented by five sectors: importa-
bles (manufacturing), non-tradables (services), hydrocar-
bons, mining and agriculture. Each sector has an equal
number of representative firms which use private capital
k and public capital
k
g
to produce their goods. Firms do
not directly own capital. Instead, they rent a quantity of
capital
k
t
from households in each period at a rate of
r
t
,
the domestic interest rate. Public capital is provided by the
government at no direct cost to the firm. We assume that
labour is sector specific, which means that labour cannot
move between sectors. The importable sector is actually a
domestic sector that produces import substitutes.
9
Public capital is included in each sector’s production
function because the Bolivian economy is small and poor.
Any productive activity thus requires some form of gov-
ernment support. An appropriate way to capture this sit-
uation is to reflect government involvement in productive
activities through public provisions of infrastructure and
capital. The firm’s problem in this context is static, so sec-
toral profits are given by:
pi
m
,
t
= (
1
+
τ
m
)
f
(
z
mt
,
k
m
,
t
,
k
∗
t
)
−
r
t
k
m
,
t
(8)
pi
n
,
t
=
p
n
,
t
f
(
z
nt
,
k
n
,
t
,
k
∗
t
)
−
r
t
k
n
,
t
(9)
pi
xh
,
t
= (
1
+
τ
x
h
)
f
(
z
xht
,
k
xh
,
t
,
k
∗
t
)
−
r
t
k
xh
,
t
(10)
pi
xm
,
t
=
q
xm
,
t
f
(
z
xmt
,
k
xm
,
t
,
k
∗
t
)
−
r
t
k
xm
,
t
(11)
pi
xa
,
t
=
q
xa
,
t
f
(
z
xat
,
k
xa
,
t
,
k
∗
t
)
−
r
t
k
xa
,
t
(12)
Where
π
is the representative firm’s profits in sector
i
,
z
i
is
a productive shock in sector
i
,
k
i
is the quantity of private
capital demanded in sector
i
and
q
i
is the relative price of
good
i
in terms of the importable good. Public capital is the
same for all sectors. The only difference is the intensity of
public capital used in each sector. There is also a tax on the
production of hydrocarbons, denoted by
τ
xh
.
Maximizing the above profit function with respect to
the respective capital stock yields the following first-order
conditions:
(
1
+
τ
m
)
f
′
km
(
z
m
,
t
)
,
k
m
,
t
,
k
∗
t
=
r
t
(13)
p
n
,
t
f
′
kn
(
z
n
,
t
,
d
n
,
t
k
∗
t
) =
r
t
(14)
(
1
−
τ
xh
)
q
xh
,
t
f
′
xh
(
z
xh
,
t
,
k
xh
,
t
,
h
∗
t
) =
r
t
(15)
q
xm
,
t
f
′
xm
(
z
xm
,
t
,
k
xm
,
t
,
k
∗
t
) =
r
t
(16)
q
xa
,
t
f
′
xa
(
z
xa
,
t
,
k
xa
,
t
,
k
∗
t
) =
r
t
(17)
These equations describe the demand for capital services
by firms in each production sector of the economy.
3.1.3 Government
The volume of government infrastructure investment
is
I
, current public consumption expenditures are g and
lump-sum transfers to households are
Γ
. The govern-
ment’s budget constraint is therefore
g
t
+
Γ
t
+
I
t
=
τ
c
(
c
m
,
t
+
p
n
,
t
c
n
,
t
+
i
t
)
+
τ
m
(
1
+
τ
c
)(
c
m
,
t
+
i
t
)
−
τ
m
y
m
,
t
+
τ
k
y
m
,
t
+
τ
k
r
t
k
t
+
τ
xh
q
xh
,
t
y
xh
,
t
(18)
Where
y
m
,
t
is the volume of import substitutes produced
in the importables sector. The tariff rate on imports
(
c
m
,
t
+
i
t
−
y
m
,
t
)
is
m
.
Public capital evolves according to the following dy-
namic:
k
g
,
t
+
1
=
I
t
+ (
1
+
δ
g
)
k
g
,
t
(19)
where 0
≤
k
g
≤
1 is the public capital depreciation rate.
As Rioja (2003) does, we assume that the usefulness of this
capital comes in relation to its effectiveness index, given by
k
∗
t
=
θ
k
g
,
t
(20)
where 0
<
θ
<
1 is an infrastructure effectiveness index.
More efficient deployment of public capital stocks is re-
flected by a positive shift of
θ
towards 1, implying greater
benefits to firms.
As usual, the government does not optimize an ex-
plicit objective function. Rather, current public expendi-
tures evolve according to
g
t
+
1
= (
1
−
ρ
g
)
¯
g
+
ρ
g
g
t
+
v
g
,
t
+
1
(21)
with
v
g
,
t
+
1
∼
N
(
0,
σ
2
g
)
.
3.1.4 The foreign sector
Open economies and closed economies have different
properties. When both capital and goods can be imported,
an economy with an initially low stock of capital would do
better to begin by running a current account deficit, sus-
tain a high level of consumption and pay the rest of the
9
Imports and import substitutes are perfect substitutes, which means that they should be sold at the same price. The domestic price of
y
m
,
t
is thus
equal to
(
1
+
τ
m
)
.
62
Analítika,
Revista de análisis estadístico
, 2 (2012), Vol. 4(2): 57-79