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Fiscal policy and economic growth: a simulation analysis for Bolivia
Analíti ak
4
Revista de Análisis Estadístico
Journal of Statistical Analysis
world later at a time of current account surplus. This ap-
proach is typically not used, making it more difficult to re-
solve models because the strategy induces multiple equi-
libria for each debt pathway and because the variables are
non-stationary.10
Schmitt-Grohé and Uribe (2003) suggest five modifi-
cations to the standard model of a small open economy
with incomplete asset markets in order to achieve station-
arity. We use their modification of a debt-elastic interest-
rate premium, a strategy that has also been adopted by
Bhandari et al. (1990), Turnovsky (1997), and Osang and
Turnovsky (2000). 11 This approach amounts to assuming
that the country faces an upward-sloping supply schedule
for debt, reflecting the degree of risk associated with lend-
ing to the economy. This is expressed as a borrowing rate
charged on foreign debt, ˜rt+ 1 , which takes the form
˜rt +1 = (1 − ρr )r∗ + (1 − ρ τ) ϕ
bt
yt
ω
+ ρr ˜ rt + vr,t +1, ω ′ > 0, w′′ > 0 (22)
where r∗ is the exogenously given world interest rate and
ϕ(bt / yt )ω is the country-specific risk premium that in-
creases with the stock of debt as a share of output. There
are two key elements to this specification. First, the con-
vexity of the function is a convenient way to place a ceil-
ing on borrowing, as suggested by Eaton and Gersovitz
(1981). Second,the form of AR(1) specification of equation
(22), which incorporates uncertainty, explains the need to
use a stochastic model. A non-stochastic model specifica-
tion would otherwise lead to the shortcoming brought up
by Fernandez de Cordoba and Kehoe (2000).
The relative prices of exportable goods in relation to im-
portables, i.e. the terms of trade, are assumed to follow the
law of motion given by:
qxi,t +1 = (1 − ρ qxi) ¯ qxi + ρqxi qxi,t
+ v qxi,t +1 vqxi,t ∼ N 0, σ2
qxi (23)
where ¯qxi is the unconditional expectation of the terms of
trade and xh , xm and xa are the respective exportable sec-
tors.
3.1.5 Market clearing conditions
We define the general form of the production function
in each sector as:
yi, t = f (z i,t , ki ,t , k ∗
t ) (24)
where i again represents each of the five sectors. Note
that the public capital k∗ is the same in each sector, which
means that infrastructure similarly benefits each sector.
Public capital is therefore a non-rival good.
Equations (25) and (26) represent the market clearing
conditions. The first equation describes the equilibrium
in the importable goods market and indicates that the cur-
rent account (CA) balance must be counterbalanced by the
capital account balance. The second equation is the typ-
ical equilibrium condition in the market for non-tradable
goods. These equations are given as
CA = − (bt+ 1 − bt ) = qxh,t y xh,t + qxm,t y xm,t + qxa,t yxa,t
+ ym,t − c m,t − gt − it − It − ˜ rt bt (25)
and
p n,t yn ,t = pn ,t cn, t . (26)
3.1.6 Competitive Equilibrium
The competitive equilibrium is given by the following
set of allocation rules: cm = Cm (s), cn = Cn ( s), k t +1 =
K(s) , bt +1 = B (s), k ∗
t+ 1 = K∗ (s), k xh,t +1 = Kxh( s), k xm,t +1 =
Kxm( s), k xa,t+ 1 = Kxa (s), k m,t +1 = Km( s), k nt,+1 = Kn (s);
the pricing functions r = R( s) and p n = Pn (s); and a law
of motion for the exogenous state variable s+1 = S( s), such
that:
• Households solve problem (4) taking s and the form
of the functions R( s), Pn (s), and S(s ) as given. The
equilibrium solution to this problem satisfies cm =
Cm (s), cn = Cn (s) , k t+ 1 = K(s), and bt +1 = B( s).
• Firms in the hydrocarbons, mining, agriculture, im-
portable and non-tradable sectors maximize profits
as per (13)-(17), taking s and the form of the func-
tions R(s ), Pn( s), and S(s) as given. The equilibrium
solutions to these problems satisfy k xh,t +1 = Kxh (s),
k xm,t +1 = Kxm (s ), k xa,t +1 = Kxa( s), k m,t+ 1 = Km (s),
kn ,t +1 = Kn (s) and k ∗
t +1 = K∗ (s) .
• The economy-wide resource constraints given in (24)
and (25) hold in each period and the factor market
clears, as shown by:
Kxh (s) + Kxm (s) + Kxa(s ) + Km( s) + Kn (s) = K(s).
3.2 Functional forms and calibration
A model with clearly non-linear features is difficult to
solve analytically. An alternative is to use numerical meth-
ods. We therefore adopt functional forms for the utility and
productions functions and set the model parameters as per
Bolivian macroeconomic parameters in 2006.
10 See Fernandez de Cordoba and Kehoe (2000) for an application to the Spanish economy.
11 Other modifications imply a model that has an endogenous discount factor with convex portfolio adjustment costs and complete asset markets,
and without stationarity-inducing features.
Analítika, Revista de análisis estadístico, 2 (2012), Vol. 4(2): 57-79 63