Download Commodity windfalls, macroeconomic management and welfare

Commodity windfalls, macroeconomic management and
welfare∗
Fabrizio Orrego
†
Germán Vega
‡
March 31, 2014
Abstract
We study the implications of the so-called Dutch disease in a small open economy that
receives significant inflows of funds due to an extraordinary increase in the international price
of copper. We consider three sectors, the tradeable sector, the booming sector and the nontradeable sector in an otherwise standard real-business-cycle model which is consistent with a
balanced growth path. We find that the booming sector, that benefits from high international
prices, induces the Dutch disease, that is, the tradeable sector declines, the real exchange
rate appreciates, wages increase and the non-tradeable sector improves. We then introduce
fiscal arrangements that aim to alleviate the consequences of the Dutch disease. We find
that a countercyclical rule that boosts the productivity of firms maximizes the welfare of the
representative household and seems to offset the effects of the Dutch disease.
Keywords: Small open economy, Dutch disease, fiscal policy.
JEL classification codes: F31, F41, E62
∗ We are grateful to Gonzalo Llosa and seminar participants at the Central Bank of Peru and the XXXI BCRP
Research Conference for valuable comments and suggestions. This paper has circulated under the title ”Dutch
disease and fiscal policy”. The usual disclaimer applies.
† Research Department, Central Bank of Peru, Jr.
Miro Quesada 441, Lima 1, Peru; and Department
of Economics, Universidad de Piura, Calle Mártir José Olaya 162, Lima 18, Peru. Email address: [email protected]
‡ Department of Economics, Universidad de Piura, Calle Mártir José Olaya 162, Lima 18, Peru. Email address:
[email protected]
1
1
Introduction
In the last decade, several exporters of minerals have benefited from extraordinarily high international prices. Figure 1 shows the case of four countries that belong to the top 10 exporters
of copper. We observe that exports of copper significantly increased after 2003-2004 and foreign
direct investment in the mining sector picked up shortly after in all countries. Figure 2 shows a
close relationship between the share of copper exports and the ratio of non-tradeable GDP to total
GDP. Furthermore, Figure 3 shows a clear mapping between the ratio of non-tradeable GDP to
total GDP and the real exchange rate. All in all, these figures make us suspect of the existence of
the so-called Dutch disease, which may have been induced by high international copper prices.
(a) Peru
(b) Chile
(c) Canada
(d) Australia
Figure 1: Mining exports and FDI in mining sector. Solid line: Ratio of mining exports
to total exports. Dashed line: Ratio of FDI in mining sector to total FDI. Source: Central Banks
and World Bank.
In this paper, we study how the Dutch disease phenomenon emerges. We use a small open
economy model with three sectors, a tradeable sector, a booming sector (that exports copper) and
a non-tradeable sector, consistent with a balanced growth path. Firms in the first two sectors
produce goods that are traded at world prices. Output in the first two sectors use a factor specific
to each sector and labor, but firms in the non-tradeable sector use only labor. Firms in the booming
sector produce only for export. Suddenly there is an exogenous rise in the price of its product on
the world market.
The main effects on the real sector are the following: Labor and total consumption all increase
on impact. Wages and prices in the non-tradeable sector also increase. Since the price of tradeables
is fixed, the higher price of non-tradeables induces a real appreciation of the exchange rate. This
real appreciation deteriorates the competitiveness of the tradeable sector. Hence, output in the
tradeable sector decreases on impact and the higher consumption of tradeables leads to a deficit
in the balance of trade of tradeable goods. Moreover, there is a reduction of labor demand in
the tradeable sector. However, GDP increases, because both the non-tradeable sector and the
booming sector (mining sector) increase. These ingredients suggest that an international increase
2
in the price of copper fosters the symptoms of a Dutch disease.
Then we introduce an arguably active government that collects taxes from private firms, issues
debt, redistributes resources back to households via transfers and invest in public capital. We ask
to what extent this government may pursue certain policies that might offset the effects of the
Dutch disease and, more importantly, increase the welfare of the representative individual. We
find that a countercyclical fiscal rule that boosts the productivity of firms maximizes the welfare
of the household and seems to lean against the wind.
Our three-sector model follows the spirit of early papers that analyze the Dutch disease, for
instance, Bruno and Sachs (1982), Corden and Neary (1982) and Corden (1984). As in Suescun
(1997), the source of the disease in our model is the booming sector and the extraordinarily high
price of copper. Other papers that blame the massive inflows from abroad are Lartey (2008a),
Lartey (2008b) and Acosta, Lartey and Mendelman (2009b).
We introduce fiscal policies in the spirit of Kumhof and Laxton (2013) in order to cope with the
effects of the so-called Dutch disease. Because our model is of the RBC type, we do not assess the
role of monetary policy. However, recent papers by Lama and Medina (2012) or Hevia, Neumeyer
and Nicolini (2013) do study the role of monetary and exchange rate policies in economies that
suffer from the Dutch disease.
(a) Peru
(b) Chile
(c) Canada
(d) Australia
Figure 2: Copper exports and non-tradable production. Solid line: Ratio of copper
exports to total exports. Dashed line: Ratio of non-tradable production to total production.
Source: Central Banks and World Bank.
The plan of this paper is as follows. Section 2 introduces the model. Section 3 presents the
detrended equations of the model. Section 4 shows the optimality conditions. Section 5 defines
the competitive equilibrium. Section 6 presents some results. Section 7 studies welfare. Section 8
concludes.
3
(a) Peru
(b) Chile
(c) Canada
(d) Australia
Figure 3: Non-tradable production and real exchange rate. Solid line: Ratio of nontradable production to total production. Dashed line: Effective real exchange rate. Source:
Central Banks and World Bank.
2
The model
We embed a three-sector model, the booming sector, the tradeable sector and the non-tradeable
sector, into a frictionless standard small open economy which is populated by households, firms
and government, which is consistent with a balanced growth path. Firms in the first two sectors
produce goods that are traded at world prices. Output in the first two sectors use a factor specific
to each sector and labor, but firms in the non-tradeable sector use only labor. Since labor is
perfectly mobile, the market wage is the same in all sectors. All production functions have a
deterministic component that increases at a positive rate.
We further assume, in the spirit of Corden (1984), that firms in the booming sector produce only
for export and there is an exogenous rise in the price of its product on the world market which
induces a Dutch disease. We introduce an arguably active government that collects taxes from
private firms, issues debt, redistributes resources back to households via transfers and invest in
public capital that boosts the productivity of private firms in the economy. We evaluate different
fiscal rules that may maximize the welfare of the household and offset the consequences of the
Dutch disease on the economy.
2.1
Households
A representative household wants to maximize the discounted value of his lifetime utility from
consumption Ct and labor Lt :
Et
∞
X
U (Cs , Ls )
s=t
4
(1)
The instantaneous utility function is:
U (Ct , Lt ) =
Ct1−σ [1 − κLνt ]
1−σ
1−σ
−1
(2)
where 1/σ is the intertemporal elasticity of substitution, κ is a constant introduced for analytical
convenience and ν is related to the curvature of the labor supply curve. The functional form is
consistent with long run growth, that is, is consistent with a balanced growth path in which labor
is stationary and consumption increases over time. This particular functional with time separable
preferences owes to Uhlig (2009) and Jaimovich and Rebelo (2009). It is straightforward to verify
that the utility function in equation (2) is also a special case of King, Plosser and Rebelo (1988).
Moreover, as is standard in open economy models, the aggregate consumption good Ct includes
both tradeable consumption CT,t and non-tradeable consumption CN T,t in the following fashion:
θ
h 1
i θ−1
θ−1
θ−1
1
Ct = γ θ (CT,t ) θ + (1 − γ) θ (CN T,t ) θ
,
(3)
where γ is the share of tradeable consumption in the consumption index and θ is the elasticity
of intertemporal substitution between tradeables and non-tradeables. For later reference, the
consumer price index is:
h
i 1
1−θ 1−θ
,
Pt = γ + (1 − γ) (PN T,t )
(4)
where PN T,t is the price of non-tradeable goods and the price of tradeable goods serves as a
numeraire.
In the financial side, the household is allowed to trade a risk-free one-period bond Bt that pays
the international interest rate r. In order to close the model, we assume that the representative
household must pay some portfolio adjustment costs p(Bt ) whenever Bt deviates from its equilibrium level, in line with Schmitt-Grohe and Uribe (2003). The household may trade as well stocks
in the tradeable sector and the booming sector (xT,t and xB,t , respectively). Thus, the budget
constraint is:
Pt Ct + vT,t xT,t + vB,t xB,t + Bt + p(Bt ) = Wt Lt + (vT,t + dT,t )xT,t−1
+ (vB,t + dB,t )xB,t−1 + (1 + r)Bt−1 + T Rt
(5)
where vT,t and vB,t are the stock prices in the tradeable sector and the booming sector, respectively.
On the other hand, dT,t and dB,t represent the dividends paid by firms in the tradeable sector and
the booming sector, respectively. Finally, Lt is the household’s labor supply, Wt is the nominal
market wage expressed in terms of the domestic tradeable good and T Rt stands for the transfers
made by the government.
2.2
Production sectors
In this section we characterize the behavior of firms in the tradeable sector, the booming sector
and the non-tradeable sector. Labor is perfectly mobile across sectors, but capital in the tradeable
sector and the mining sector is specific. Non-tradeable firms use only labor.
5
2.2.1
Tradeable sector
We assume a Cobb-Douglas technology with constant returns to scale in capital and labor:
αG
α
YT,t = AT,t XT,t KT,t−1
LT,t 1−α ψKG,t−1
(6)
where YT,t is the tradeable output, AT,t is the total factor productivity that follows a stationary
process and XT,t is a deterministic growth component. As usual, KT,t−1 and LT,t are the capital
and labor inputs in the production function and α measures the intensity of capital in the production function. Public capital KG,t−1 may be an additional input in the production function if αG
is positive (of course, ψ is a positive constant). In order to verify that the production function in
equation (6) is consistent with a balanced growth path, it is enough to have the technical change
written in the labor augmenting form:
1−α
α
YT,t = ÃT,t KT,t−1
X̃T,t LT,t
1
αG
1−α
where ÃT,t ≡ ψAT,t KG,t−1
and X̃T,t = XT,t
. On the other hand, capital in the tradeable sector
follows a standard law of motion:
KT,t = IT,t + (1 − δT )KT,t−1 ,
(7)
where δT is the depreciation rate and IT,t stands for investment in the tradeable sector. In this
model, firms need to pay capital adjustment costs whenever IT,t 6= KT,t−1 . These costs are
summarized by a convex cost function Θ(IT,t , KT,t−1 ).
Finally, assume that output in the tradeable sector is taxed at a rate τ and let ΛT,t be the
stochastic discount factor. Then the firm’s problem is to maximize the discounted value of dividends
ds , that is, revenue minus expenditure:
max
KT ,s ,IT ,s ,LT ,s
Et
∞
X
ΛT,s [(1 − τ )YT,s − IT,s − Θ(IT,s , KT,s−1 ) − Ws LT,s ]
s=t
subject to equations (6) and (7).
2.2.2
Mining sector
Firms in the booming sector first use an investment unit to decide upon the optimal composition of
local investment and foreign investment. This modeling device is in line with Figure 1, in which we
observe that the mining sector receives capital from abroad in the form of foreign direct investment.
Investment unit.- The investment unit produces one unit of investment using local investment
IH,t and foreign investment IF,t . Firms in the tradeable sector supply local investment and foreign
investment comes from abroad. Investment in the booming sector IB,t aggregates the two types of
investment via a CES function:
ρ
i ρ−1
h 1
ρ−1
ρ−1
1
,
IB,t = µ ρ (IH,t ) ρ + (1 − µ) ρ (IF,t ) ρ
(8)
where µ is the share of local investment in the mining sector and ρ is the elasticity of substitution
between the two types of investment. If the price of local investment serve as a numeraire and
6
PF I,t stands for the price of foreign investment, the cost minimization problem of the investment
unit is the following:
min IH,t + PF I,t IF,t
IH,t ,IF,t
subject to equation (8). In an interior solution, we obtain demands for each type of investment:
IH,t = µ(PI,t )ρ IB,t
ρ
PI,t
IB,t
IF,t = (1 − µ)
PF I,t
(9)
(10)
Production unit.- Firms in the booming sector produce only for export. Because firms want
to maximize the discounted value of dividends, they had better establish an optimal demand for
capital, given the external demand and export prices. Moreover, firms inelastically demand labor
in each period, given the capital stock and factor productivity, regardless of the market wage or
the tax system. The production function and the law of motion of capital are:
αG
α
YB,t = AB,t XB,t KB,t−1
L1−α
ψK
B,t
G,t−1
(11)
KB,t = IB,t + (1 − δB )KB,t−1
(12)
where YB,t is the output in the booming sector, AB,t is the total factor productivity that follows
a stationary process and XB,t is a deterministic growth component. Also, KB,t and LB,t are the
capital and labor inputs in the production function and α measures the intensity of capital in
the production function. Again, ψ is a positive constant. Public capital KG,t−1 may serve as
an additional input in the production function whenever αG is positive. On the other hand, IB,t
stands for investment in the booming sector. As in the tradeable sector, firms in the booming
sector face convex adjustment costs given by Θ(IB,t , KB,t−1 ).
If the price of investment in the mining sector PI,t is given by:
h
i 1
1−ρ 1−ρ
PI,t = µ + (1 − µ) (PF I,t )
(13)
then the firm’s problem in the booming sector is to maximize the discounted value of dividends
dB,s , that is, revenue minus expenditure. Assume that output in the booming sector is taxed at a
rate τ and let ΛB,t be the stochastic discount factor:
max
KB,s ,IB,s ,LB,s
Et
∞
X
ΛB,s [(1 − τ )PB,s YB,s − PI,s (IB,s + Θ(IB,s , KB,s−1 )) − Ws LB,s ]
s=t
subject to equations (11) and (12).
2.2.3
Non-tradeable sector
The production function in the non-tradeable sector is linear in labor:
7
αG
YN T,t = Zt XN T,t LN T,t ψKG,t−1
(14)
where Zt is the labor productivity, XN T,t is a deterministic component in the non-tradeable sector
and LN T,t is the demand of labor in the non-tradeable sector. As in the other sectors, assume that
output in the non-tradeable sector is taxed at a rate τ . Hence the problem of the firm is:
max (1 − τ )PN T,t YN T,t − Wt LN T,t
LN T ,t
subject to equation (14).
2.3
Government
In this section we basically borrow from Kumhof and Laxton (2013). We study the effects of
several fiscal rules on consumption, capital accumulation, labor, wages and the like in the presence
of the commodity windfall. These rules are supposed to help households cope with the transitory
increase in commodity prices. In principle, if there were complete markets, these rules would not
make much sense since households would be able to insure themselves against all possible states of
nature. Nevertheless, in this model households are not allowed to trade a complete set of contingent
claims and therefore cannot deal with all possible shocks (AT,t , AB,t , Zt ) in the Cartesian product
∆T × ∆B × ∆, not to mention the impact of copper prices and foreign investment PB,t and PF I,t ,
respectively.
Of course, these fiscal rules are not optimal in the sense of the new dynamic public finance
(recent papers by Lama and Medina (2012) and Hevia et al. (2013) do include exercises on Ramsey
taxation). Basically, the rules are either procyclical or countercyclical. First we will explain the
main ingredients of the government budget constraint and then we will disclose the main features
of the fiscal rules.
2.3.1
Government budget constraint
The government budget constraint in this economy is:
τ Yt + Dt = Gt + (1 + r)Dt−1 + T Rt
where τ Yt is the government revenue, Dt is the public debt issued abroad, Gt is the total government
expenditure (includes both investment and consumption), r is the international interest rate and
T Rt are the gross transfers made to households.
Since Gt includes two types of expenditures, it will be useful to explain the nature of each
component:
Investment.- Investment expenditures help build the stock of public capital KG that depreciates
itself at a rate δG . These expenditures mainly take the form of infrastructure projects such as
railroads, bridges and homeland security. The corresponding law of capital accumulation is:
KG,t = IG,t + (1 − δG )KG,t−1
Public investment KG behaves like a positive externality since it raises the total factor productivity of all sectors in the economy.
8
Consumption.- For the case of consumption expenditures, the government may buy goods from
either the tradeable sector or the non-tradeable sector. We assume that the share of expenditures
in each sector mimics that of the consumption basket of the households:
CGT,t = γCG,t
CGN T,t = (1 − γ)
CG,t
PN T
Hence public purchases may be written as:
CG,t = CGT,t + PN T,t CGN T,t
Transfers.- For the case of public transfers to households, we assume for simplicity that T Rt =
τT R Yt , that is, transfers are highly procyclical.
2.3.2
Fiscal rules
Now we study some alternative rules that stem from the following equation:
sYt = τ Yt
Yt
Ȳ
ς
− Gt − rDt−1
where s is a constant that stands for the economic deficit (if negative) or superavit (if positive)
of the public sector, Ȳ is the stationary level of GDP and, more importantly, ς is the elasticity of
fiscal expenditures to fiscal revenues. We evaluate three different scenarios, each associated to a
particular value of ς:
1. Rule I: Procyclical behavior when ς = 0.5.
2. Rule II: Neutral behavior when ς = 0.
3. Rule III: Countercyclical behavior when ς = −0.5.
In each scenario, we also assess the impact of public capital on the productivity of private firms,
that is, we consider two possibilities:
1. Rule A: Public capital is neutral when αG = 0.
2. Rule B: Public capital is a positive externality when αG = 0.2.
All in all, we present six cases, the combinations of rules I, II and III, with rules A and B.
3
Detrending
For analytical convenience, we will assume that XT,t = XB,t = Xt , that is, both the tradeable
sector and the mining sector share the same growth trend. However, since the non-tradeable sector
9
1−αG
1−α−αG
only uses labor, we further assume that XN T,t = Xt
is X
1
1−α−αG
. In this model, the detrending factor
and detrended variables are written as:
Mt
M̂t =
X
1
1−α−αG
As is standard in this class of models, we assume that the growth rate is equal to gX as follows:
1
1−α−αG
Xt
1
1−α−αG
1
= (1 + gX ) 1−α−αG
Xt−1
1
For later use, we let (1 + g) = (1 + gX ) 1−α−αG . As in King et al. (1988), we work with the
transformed economy with detrended variables.
Households.- In the case of households, we need to detrend the objective function and the budget
constraint:
Ĉt1−σ [1 − κLνt ]
1−σ
1−σ
−1
1−σ
and the new discount factor is β̂ = β(1 + g) 1−α−αG . Furthermore the detrended budget constraint
is:
ι
Pt Ĉt + v̂T,t xT,t + v̂B,t xB,t + B̂t + (B̂t − B̄)2 = Ŵt Lt + (v̂T,t + dˆT,t )xT,t−1
2
+ (v̂B,t + dˆB,t )xB,t−1 + (1 + r)B̂t−1 + TˆRt
(15)
where ι is a positive constant.
Production sectors.- In the case of productive firms, we need to detrend the production functions:
αG
α
ŶT,t = AT,t K̂T,t−1
L1−α
ψ
K̂
T,t
G,t−1
αG
1−α
α
ŶB,t = AB,t K̂B,t−1 LB,t ψ K̂G,t−1
b αG
ŶN T,t = Zt LB,t ψ K
G,t−1
(16)
(17)
(18)
And we also need to care of the laws of capital accumulation:
(1 + g)K̂T,t = IˆT,t + (1 − δT )K̂T,t−1
(19)
= IˆB,t + (1 − δB )K̂B,t−1
(20)
(1 + g)K̂B,t
(21)
b M,t , KM,t−1 ) =
Furthermore, the detrended convex cost function is Θ(I
for M that belongs to {T, B}.
φ
2
IˆM,t
K̂M,t−1
− g − δM
2
Government.- In the case of the public sector, we need to detrend the budget constraint, the
10
fiscal rule and the law of capital accumulation:
τ Ŷt = Ĝt + (1 + r)D̂t−1 − D̂t + TˆRt
!ς
ˆ
YT,t
− Ĝt − rD̂t−1
sŶt = τ Ŷt
Yˆ
(1 + g)K̂G,t = IˆG,t + (1 − δG )K̂G,t−1
(22)
(23)
(24)
We also detrend the other relationships:
Ĝt = ĈG,t + IˆG,t
4
(25)
ĈG,t = τC Ĝt
(26)
ĈG,t = ĈGT,t + PN T,t ĈGN T,t
(27)
ĈGT,t = γ ĈG,t
(28)
TˆRt = τT R Ŷt
(29)
Optimality conditions
In the transformed model, the optimality conditions for an interior solution are characterized by
the following first order conditions:
Households.- The necessary conditions for an optimum are:
λĈ,t [1 + g + ι(B̂t − B̄)] = β̂Et λĈ,t+1 (1 + r)Pt /Pt+1
(30)
(1 + g)v̂T,t λĈ,t = β̂Et λĈ,t+1 (v̂T,t+1 + dˆT,t+1 )Pt /Pt+1
(31)
(1 + g)v̂B,t λĈ,t = β̂Et λĈ,t+1 (v̂B,t+1 + ρdˆB,t+1 )Pt /Pt+1
(32)
−
λL,t
Ŵt
=
λĈ,t
Pt
(33)
θ
ĈT,t = γ (Pt ) Ĉt
θ
Pt
Ĉt
ĈN T,t = (1 − γ)
PN T,t
(34)
(35)
where λĈ,t = Ĉt−σ [1 − κLνt ]1−σ is the marginal utility of consumption and λL,t = −κν Ĉt1−σ [1 −
κLνt ]−σ Lν−1
is the disutility of labor. Notice that equation (30) is a standard Euler equation.
t
Equations (31) and (32) reflect optimality conditions related to financial purchases. In these cases,
the marginal utility of forgoing one unit of stock must be equal to the (discounted) expected utility
of the real return of the stock. Equation (33) determines labor supply. On the other hand, consumption in the tradeable sector and non-tradeable sector are given by (34) and (35), respectively.
Production sectors.- In an interior solution, the optimal decisions of the firm in the tradeable
sector give rise to the following conditions:
11
(
α(1 − τ )
(1 + g)QT,t = Et ΛT,t+1

+
IˆT,t+1
φ
2
K̂T,t
ŶT,t+1
K̂T,t
!2
− δT − g
−φ
IˆT,t+1
K̂T,t
!
− δT − g

ˆ
It+1 
K̂t
+ Qt+1 (1 − δT )



(36)
QT,t = 1 + φ
!
IˆT,t
K̂T,t−1
Ŵt = (1 − α)(1 − τ )
− δT − g
(37)
ŶT,t
LT,t
(38)
where QT,t is the shadow price of capital in the tradeable sector and equation (36) is a standard
investment Euler equation. Moreover, equation (37) determines the current value of QT,t and
equation (38) shows the labor demand in the tradeable sector.
In the booming sector, the optimality conditions give rise to the following equations:
(
(1 + g)QB,t = Et ΛB,t+1
α(1 − τ )PB,t+1

φ
+ PI,t+1 
2
IˆB,t+1
K̂B,t
ŶB,t+1
K̂B,t
!2
− δB − g
−φ
IˆB,t+1
K̂B,t
!
− δB − g

IˆB,t+1 
K̂B,t
+ QB,t+1 (1 − δB )

(39)
"
QB,t = PI,t 1 + φ
IˆB,t
K̂B,t−1
!#
− δB − g
(40)
where QB,t is the shadow price of capital in the booming sector. Notice that there are three
differences with the problem of the firm in the tradeable sector, namely the price of copper PB,t
and the price of investment, PI,t . Furthermore, the demand for labor is completely inelastic.
Finally, the static optimization problem of the firm yields the following equilibrium condition:
(1 − τ )
ŶN T,t
Ŵt
=
,
LN T,t
PN T,t
(41)
Government.- The detrended equations of the government were already included in the previous
section.
5
Market clearing conditions, competitive equilibrium and
calibration
5.1
Market clearing conditions
In this section, we state the market-clearing conditions of the model. For simplicity, we assume
that adjustment costs in the tradeable and booming sectors are expressed in terms of tradeable
goods. The market clearing conditions in the goods market and the labor market are:
12


Ybt = YbT,t + PN T,t YbN T,t + PB,t YbB,t
(42)
bT,t + C
bGT,t + IbT,t + IbG,t + IbH,t + BC
d T,t
YbT,t = C
!2
φ
IbB,t
b B,t−1 + φ
+ PI,t
− δ − gy K
b B,t−1
2 K
2
IbT,t
− δ − gy
b T,t−1
K
!2
b T,t−1
K
bN T,t + C
bGN T,t
YbN T,t = C
(43)
(44)
Lt = LT,t + LB,t + LN T,t
(45)
The demand for local tradeable goods does not necessarily match the local supply and the
difference is captured in the balance of trade without minerals or BoTT,t . We also need to define
some variables such as exports of minerals (XB,t ), external demand for exports (YRoW,t ), real
exchange rate (RERt ), balance of trade (BoTt ) and current account (CAt ). Since firms in the
booming sector produce only for export, it must be the case that XB,t = YB,t in equilibrium.
$
X̂B,t = γB PB,t
ŶRoW,t
1
RERt =
Pt
[ t = BoT
[ T,t + PB,t X̂B,t
BoT
d t = rB̂t−1 − ι (B̂t − B̄)2 + BoT
[ t − PF I,t IˆF,t − rD̂t−1
CA
2
(46)
(47)
(48)
(49)
Equation (46) shows that nominal exports of minerals depend on both the international price
and the demand of the rest of world. Moreover, equation (47) suggests that an increase of RERt
implies a real depreciation. On the other hand, equation (48) shows all transactions with international partners. Finally, equation (49) shows the current account of the small open economy.
5.2
Equilibrium
We solve the model up to a first-order approximation around the non-stochastic steady state. We
use the Dynare toolbox in Matlab. The equations we need are:
• Given prices, wages, tranfers, interest rates and dividends, households choose consumption,
labor supply and bond holdings according to equations (15), (30), (33), (34) and (35).
• Given wages, the total factor productivity and the stochastic discount factor, firms in the
tradeable sector chooses labor, capital, the shadow price of capital and determines the level
of output according to equations (16), (19), (36), (37) and (38).
• Given the foreign demand for copper, the foreign price of investment, the stochastic discount
factor and the total factor productivity, firms in the booming sector chooses investment,
capital, the shadow price of capital and labor according to equations (9), (10), (46), (20),
(39) and (40).
• Given prices, total factor productivity and stochastic discount factor, firms in the nontradeable sector chooses labor and determines the level of output according to equations
(14) and (41).
13
• Total output in the economy is determined according to equation (42).
• Fiscal revenue and fiscal rules obey equations (22), (24), (23), (25), (26), (27), (28) and (29).
• Relative prices and wages obey equations (4), (13),(44) and (45).
• The gap between domestic demand and supply of tradeable goods determine the balance of
trade according to equation (43).
• Foreign demand for copper, real exchange rate, total balance of trade and current account
obey equations (46), (47),(48) and (49).
• All six exogenous variables follow stationary processes that are mutually uncorrelated. There
are two types of exogenous variables in this model. On the one hand, there are internal
exogenous variables such as total factor productivity of the tradeable sector (AT,t ), the
booming sector (AB,t ) and the non-tradeable sector (Zt ). On the other hand, we have
exogenous variables that are determined in international markets such as the price of the
booming sector (PB,t ), the price of international investment (PF I,t ) and the stance of the
world economy (YRoW,t ). In particular, PB,t follows a stationary AR(2) process.
5.3
Calibration
Table 1 depicts the baseline calibration in this paper. Few parameters are fairly standard in the
literature, such as α, ν and δ. We also assume that σ =2 to ensure certain curvature of the utility
function. The international interest rate is 0.028, which means that the discount factor is 0.99
in any stationary equilibrium. We follow Devereux, Lane and Xu (2006) and set the share of
tradeable consumption equal to 0.45. As in Acosta et al. (2009b), the elasticity of substitution θ
between tradeables and non-tradeables is 0.4. Since it turns out that this parameter is important,
we perform robustness checks with alternative values of 0.2 and 0.8 (available upon request).
Furthermore, the elasticity of substitution between domestic investment and foreign investment,
ρ, is equal to 1.5. We calibrate κ and γB so as to match the ratios of balance of trade to GDP and
exports of copper to GDP. Finally, we assume that capital adjustment costs are equal to 3.
In the presence of fiscal rules, we set the tax rate in order to match the ratio of public expenditures to GDP of Peru in the period 1994-2012, that is, 0.14. The ratio of government expenditures
to GDP is 0.12, consistent with Peruvian data. We further assume that ψ is equal to 1.0169 in
order not to overestimate the effects of the positive externality of public capital. Because we want
to compare among the different fiscal rules, we calibrate κ and γB to ensure that the ratios of
balance of trade to GDP and exports of minerals to GDP are equal to -0.02 and 0.09, respectively,
as in the data.
In order to evaluate the calibration, we plug the parameters in the equations that characterize
the non-stochastic steady state without fiscal expenditures and calculate several ratios with respect
to GDP. Table 2 shows the comparison between the ratios obtained from the model and the real
ratios calculated with Peruvian data from 1994 to 2012 (we use quarterly data that have been
previously seasonally adjusted and detrended). The main differences that arise are the low ratio
of investment and the high ratio of consumption, because the model, by construction, does not
have capital in the non-tradeable sector, which reduces the aggregate amount of investment. The
ratio of non-tradable consumption to total consumption is close to the real ratio and the share
of non-tradable labor is 0.6, which is a stylized fact in small open economies. In any stationary
14
Parameter
σ
β
ν
κ
α
ι
γ
θ
δT
δB
δG
φ
µ
ρ
g
r
ω
γB
τ
τC
αG
ς
ψ
s
Value
2
0.99
1.455
0.465
0.33
0.074x10−2
0.45
0.4
0.05
0.05
0.05
3
0.8
1.5
0.005
0.028
1
0.112
0.14
0.68
0
0
1.0169
-0.004
Parameters of standard model
Description
Source
Elasticity of intertemporal substitution
Lartey (2008a)
Discount factor
Standard in SoE
Inverse of elasticity of labor supply
Mendoza (1991)
Adjusts labor supply
Match BoT of −0.02% in SS
Share of capital in production
Standard in SoE
Portfolio adjustment cost
Schmitt-Grohe and Uribe (2003)
Share of tradeable goods in consumption Devereux et al. (2006)
Elasticity of substitution
Acosta, Lartey and Mandelman (2009a)
Depreciation rate
Standard in SoE
Depreciation rate
Standard in SoE
Depreciation rate
Standard in SoE
Capital adjustment cost
Acosta et al. (2009a)
Share of domestic inv. in booming sector Lartey (2008a)
Elasticity of substitution in investment
Lartey (2008a)
Technology growth
Trend growth of 0.9% quarterly.
Foreign interest rate
Determined by g and β
Elasticity of exports
Acosta et al. (2009a)
Adjustment in foreign demand
Match Exports/GDP
Tax rate
Match G/GDP
Share of government purchases
Match Peruvian data
Intensity of public capital
Baseline scenario
Fiscal rule
Baseline scenario
Intensity of public externality
Imply no productivity gain
Government deficit
Match debt to GDP of 40% in SS
Table 1: Baseline parameterization
Comparison of model with public expenditures and Peruvian data
Variable
Model
Data
Consumption
0.8
0.70
Investment
0.1
0.19
Balance of trade
-0.02
-0.02
Exports of copper
0.09
0.09
Government expenditures
0.12
0.13
Ratio non-tradable labor
0.6
0.6
Table 2: We compare the ratios from the model with the real ratios obtained with Peruvian
data between 1994 and 2012. Here we consider the baseline model.
equilibrium, the current account is zero, and the balance of trade and exports of copper roughly
match the data.
6
Results
Baseline model.- We perturb the model with a 10% (transitory) increase in PB,t . Figure 4 depicts
the responses of the relevant endogenous variables in the economy when government is absent (that
is, when αG = ς = 0). Labor and total consumption all increase on impact. Wages and prices in
the non-tradeable sector also increase. Since the price of tradeables is fixed, the higher price of
non-tradeables induces a real appreciation of the exchange rate. This real appreciation deteriorates
the competitiveness of the tradeable sector.
Hence, output in the tradeable sector decreases on impact and the higher consumption of tradeables leads to a deficit in the balance of trade of tradeable goods. Moreover, we observe a reduction
of labor demand in the tradeable sector. However, GDP increases, because both the non-tradeable
sector and the booming sector (mining sector) increase. These ingredients suggest that an inter-
15
national increase in the price of copper fosters the symptoms of a Dutch disease.
Fiscal rules.- Figure 5 depicts the IRFs associated with the case in which public capital does
not foster the productivity of private firms (that is, Rule A when αG = 0). We observe Rules I,
II and III in action though. The IRFs suggest that in the countercyclical case, the government
accumulates foreign assets and output and employment in the non-tradeable sector do not increase
vigorously on impact. On the contrary, in the procyclical case, the government spends more,
accumulates more debt and fosters employment and production in the non-tradeable sector. In
this case, the government worsens the balance of trade, since the tradeable sector deteriorates on
impact.
Figure 6 depicts the IRFs associated with the case in which public capital acts as a positive
externality in the production functions of private firms (that is, Rule A when αG = 0.2). Again
we observe Rules I, II and III. Now we see more action coming from the IRFs. When public
investment generates a positive externality in all sectors, the impact of higher commodity prices
on output is highly persistent. When the fiscal rule is countercyclical, households do not receive
higher wages, consumption is more stable and the real exchange rate suffers less on impact. On the
other hand, when the fiscal rule is procyclical, the productivity of firms increases in the tradeable
sector, consumption increases and the balance of trade heavily deteriorates on impact.
7
Welfare
Unfortunately, we do not know from the previous section what the best rule is. Some rules perform
really well in some aspects, but not that well in others. Hence, in this section we want to rank the
different rules in terms of the welfare of the representative household. That is, we look for the rule
that minimizes the variance of consumption.
We closely follow Woodford (2002) and Elekdag and Tchakarov (2007) to accomplish this task.
We work with detrended variables (even though we do not write the hats over the variables) and
apply a second order Taylor expansion of the utility function around the non-stochastic steady
state:
E(Ut ) = U + C −σ Υ1−σ E(Ct − C) − κνC 1−σ Υ−σ Lv−1 E(Lt − L)
σ
κν 1−σ v−2 −σ − C −σ−1 Υ1−σ Var(Ct ) −
C
L Υ
(v − 1) + σκνLν Υ−1 Var(Lt )
2
2
(50)
where Υ = [1 − κLνt ]. Then we ask how much the household is willing to pay to smooth consumption, that is, we want to find ξ in the following equation:
U ((1 + ξ)C, 1 − L) =
(C(1 + ξ))1−σ Υ − 1
= E(Ut )
1−σ
16
(51)
In order to pin down ξ we manipulate equation (51) as follows:
(1 − σ)
(1 − σ)κνLν−1
σ
ξ = 1+
E(Ct − C) −
E(Lt − L) − (1 − σ)C −2 Var(Ct )
C
Υ
2
1
1−σ
v−2
ν
κν (1 − σ)L
σκνL
(ν − 1) +
Var(Lt )
−1
−
2
Υ
Υ
(52)
Finally, Table 3 says unambiguously that households would prefer a countercyclical fiscal rule
with productive capital, because it minimizes the variance in consumption.
8
Final remarks
We study a small open economy with three sectors, the tradeable sector, the booming sector and
the non-tradeable sector. We show that after an unanticipated increase in the price of copper,
there is a real appreciation of the exchange rate, a deterioration of the tradeable sector and more
favorable conditions for the non-tradeable sector and the booming sector. Then we evaluate the
usefulness of alternative fiscal rules that aim to minimize the variance of consumption of the
representative household. We find that a countercyclical fiscal rule that boosts the productivity of
firms maximizes the welfare of the household and seems to lean against the wind. In this fashion,
fiscal rules counteract the Dutch disease, as originally suggested in Corden (1984).
However, we are left to pursue several avenues. First, we may want to contrast the effects of
the Dutch disease with other sources of real exchange appreciations, such as the typical BalassaSamuelson effect, and rank the associated welfare gains or losses. We are currently undertaking all
these issues.
References
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economies,” Economic Journal, September 2006, 116 (511), 478–506.
Elekdag, S. and I. Tchakarov, “Balance sheets, exchange rate policy and welfare,” Journal of
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17
Hevia, C., A. Neumeyer, and J. Nicolini, “Optimal monetary and fiscal policy in a New Keynesian model with a Dutch disease: The case of complete markets,” Working Paper, Universidad
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18
Fiscal rules
Countercyclical rule with ς = −0.5
Neutral rule with ς = 0
Procyclical rule with ς = 0.5
Welfare gains
Neutral KG with αG = 0
0.0353%
0.0352%
0.0399%
Productive KG with αG = 0.2
0.0512%
0.0425%
0.0345%
Table 3: We compute welfare gains from eliminating consumption fluctuations.
19
Figure 4: Impulse response functions (in %) after a 10% increase in copper prices in the
baseline scenario with αG = 0 and no government at all. The IRFs are the natural responses of
the economy to the foreign shock.
20
Figure 5: Impulse response functions (in %) after a 10% increase in copper prices with αG = 0.
Solid line is the neutral case (with ς = 0). Dotted line is the countercyclical case ((with ς < 0).
Dashed line is the procyclical case (with ς > 0).
21
Figure 6: Impulse response functions (in %) after a 10% increase in copper prices with αG > 0.
Solid line is the neutral case (with ς = 0). Dotted line is the countercyclical case ((with ς < 0).
Dashed line is the procyclical case (with ς > 0).
22