Versión de HTML Básico
Carlos Gustavo Machicado y Paúl Estrada
Analíti a
k
4
Revista de Análisis Estadístico
Journal of Statistical Analysis
3.2.1 Functional Forms
The generic model presented above points to the fol-
lowing functional form for preferences:
u
(
c
m
,
t
,
c
n
,
t
,
g
t
) =
θ
m
ln
(
c
m
,
t
) +
θ
n
ln
(
c
n
,
t
+
µ
g
t
)
with
θ
m
,
θ
n
>
0 and
θ
m
+
θ
n
=
1. The parameter
µ
mea-
sures how a typical individual values public consumption
relative to private consumption. The specification of the
relationship between private consumption of non-tradable
goods and public consumption follows Aschauer (1985),
Barro (1981) and Christiano and Eichenbaum (1992). We
assume that consumption of public goods can be substi-
tuted (depending on the value of
µ
) with consumption of
non-tradable goods and vice versa.
12
We use the following specification for the production
functions:
f
(
z
i
,
t
,
k
i
,
t
,
k
∗
t
) =
z
i
,
t
k
α
i
i
,
t
(
k
∗
t
)
φ
i
where
α
i
+
φ
i
<
1 because both types of capital are fixed
factors.
The parameter
α
i
is capital remuneration as a share of
output for sector
i
=
xh
,
xm
,
xa
,
m
and
n
, and
φ
i
is a co-
efficient indicating the importance of public capital in the
production functions in each of the five sectors in the econ-
omy.
The productivity shocks,
z
i
, follow standard AR(1) pro-
cesses of the form:
z
i
,
t
+
1
= (
1
−
ρ
i
)
z
+
ρ
i
z
i
,
t
+
v
i
,
t
+
1
,
v
i
,
t
+
1
∼
N
(
0,
σ
2
i
)
.
3.2.2 Calibration
Once the laws of motion are specified, we accurately
calibrate the model to display the main characteristics of
the Bolivian economy. We consider 2006 as our base year
and use quarterly data. We show the model parameters
in Table 2, presumed for the time being to be invariant to
changes in economic policy.
The first column of Table 2 shows the deep parameters
of preferences,
i.e.
parameters that will be invariant to a
particular class of interventions. The subjective discount
factor
β
was set consistent with the 10,66 percent annual
rate that Bolivians can borrow at (˜
r
in our model). The pa-
rameters
θ
m
and
θ
n
are calibrated to reproduce total con-
sumption as a share of GDP in the steady state: we de-
fine total consumption as the sum of consumed importa-
bles and consumed non-tradables times the relative price
of this second type of consumption good. We set
µ
=
0.5
as a benchmark, implying imperfect substitution between
private and public consumption.
Preferences
Prod. Functions
Technology
Shocks
Fiscal Variables Exogenous Prices
β
=
0.975
δ
=
0.028 (yearly)
ρ
xh
=
0.72
g
=
0.18
q
xh
=
0.174
θ
m
=
0.4585
α
xh
=
0.66
ρ
xm
=
0.53
ρ
g
=
−
0.083
q
xm
=
0.14
θ
n
=
0.5415
α
xm
=
0.25
ρ
xa
=
0.45
σ
g
=
0.01
q
xa
=
0.19
µ
=
0.5
α
xa
=
0.19
ρ
m
=
0.4
δ
g
=
2
×
δ
ρ
qxh
=
0.87
α
m
=
0.58
ρ
n
=
0.51
θ
=
0.613
ρ
qxm
=
0.91
α
n
=
0.38
σ
xh
=
0.014
τ
m
=
0.1
ρ
qxa
=
0.86
φ
xh
=
0.25
σ
xm
=
0.009
τ
c
=
0.13
σ
qxh
=
0.017
φ
xm
=
0.14
σ
xa
=
0.011
τ
k
=
0.13
σ
qxm
=
0.01
φ
xa
=
0.12
σ
m
=
0.017
τ
xh
=
0.32
σ
qxa
=
0.11
φ
m
=
0.07
σ
n
=
0.03
ϕ
=
0.248
φ
n
=
0.25
zxh
=
0.53
ρ
r
=
0.6576
zxm
=
0.72
σ
r
=
0.01146
zxa
=
0.57
r
∗
=
0.048
zm
=
0.15
ω
=
1.2
zn
=
0.75
Source: Author’s calculations
Table 2.
Parameters.
12
It is reasonable to suppose that, for example, when individuals want to increase their consumption of health services they will sacrifice consump-
tion of non-tradables such as haircuts.
64
Analítika,
Revista de análisis estadístico
, 2 (2012), Vol. 4(2): 57-79