Dealing with the Dutch Disease:
Fiscal Rules and Macro-prudential policies
∗
Javier Garcı́a-Cicco
Universidad Católica Argentina and
Banco Central de Chile
Enrique Kawamura
Universidad de San Andrés
October, 2014
Abstract
We evaluate from a welfare perspective three policy alternatives frequently proposed
to deal with Dutch-disease problems originated from cyclical movements in commodity prices. Namely, fiscal rules for government expenditures, capital controls, and
taxes to domestic lending. To this end, we develop a DSGE model of a small open
economy with a sectoral decomposition that features three distinctive characteristics:
financial frictions, a learning-by-doing externality in the industrial sector, and a fraction of households being non-Ricardian (credit constrained). The first two features
induce inefficient relocations after commodity shocks, while the later is relevant to
analyze the role of fiscal rules. We calibrate the model using Chilean data. For each
of the policy tools, we analyze optimal simple rules from a welfare (Ramsey) perspective, describing how different households rank the several policy alternatives, and
studying how each of the models features shape the optimal policy design. A general conclusion of the analysis is that the included Dutch-disease inefficiencies are of
limited quantitatively relevance in analyzing the desirability of these policies from a
welfare perspective.
∗
We thank Carlos Vegh, Juan Pablo Medina and Francisco Ciocchini for valuable comments and discussions.
The views and conclusions presented in this paper are exclusively those of the authors and do not necessarily reflect the position of the Central Bank of Chile or its Board members. Authors’ emails: javier garcia@uca.edu.ar,
kawa@udesa.edu.ar
1
1 Introduction
The problem of the Dutch disease generally refers to a contraction in the industrial or manufacturing tradable sector originated from an increase in the income generated by the export of some
commodity. The basic mechanism is quite simple: The wealth effect generated from commodity
income rises desired consumption for all types goods, in particular non-traded goods. The later
generates a rise in production and in the relative price in this sector, as that market has to clear
domestically. As a result, productive resources moves to the non-traded sector, leading to a contraction in other tradable sectors like manufacturing. From a welfare perspective, however, this
relocation is non desirable (i.e the “disease” is actually a disease) only if there are inefficiencies
associated from expanding one sector relative to the other.
In this paper we analyze three policy alternatives that are frequently discussed, both in academic and in policy circles, to deal with Dutch-Disease problems generated by cyclical movements
in commodity prices. First, we consider the role of the cyclicality of government expenditures. A
widely documented fact for emerging countries is that fiscal policy is pro-cyclical. For example,
Frankel, Vegh and Vuletin (2013) find a positive correlation between cyclical components of real
government expenditures with real GDP between 1960 and 1999. One possible consequence of
this behavior is that pro-cyclical fiscal expenditures may intensify the problem of Dutch disease
in many commodity producers.1 The idea is that, when commodity prices go up, a government
with weak institutional background would easily face political pressures or temptation to increase
spending (especially in non-tradable services) given the rise in available funds from the surge in
international prices. But such increase would exacerbate (instead of compensate for) the higher
the demand for non-tradables coming from the private sector. Given certain conditions, this may
induce to real exchange appreciations and sectoral relocation of resources that are not Pareto efficient. In practice, a number of countries have implemented, or are evaluating, either sovereign
funds or even fiscal rules that prevents the government to spend the cyclical part of income generated from commodities; notably the structural-balance rule in place in Chile since 2001.
A second policy tool that we evaluate is capital controls. Such a tool may help to cope
with the symptoms of the Dutch disease if they move in a prudential fashion to compensate for
improvements in international financial conditions. The idea is that a surge in commodities prices
tend to ameliorate financing constraints with the rest of the world, which further exacerbates the
desired to rise domestic absorption. Thus, a tax on international capital flows that raises when
external financial conditions soften may help to reduce the adverse Dutch-disease-style effects.
The third policy alternative is a tax on domestic lending, which can be viewed as a reduced
form representation of financial controls such as reserve requirements or capital buffers for the
banking sector. One of the channels that propagate a positive shock to commodity income is that
domestic lending to finance investment will likely increase, as part of the extra wealth generated
will be saved. In the presence of financial frictions, this additional lending will tend to exacerbate any sectoral relocations, as the financing conditions for the sectors that improve after the
shock (non-tradables) will be relaxed, while the sector that is negatively affected (other tradables
like manufacturing) will face tighter financing conditions. In this context, a policy that limits the
increase in lending can help to cope with those inefficient movements.
We contribute to the evaluation of these policy alternatives by developing a dynamic and
stochastic general equilibrium model (DSGE) featuring a learning-by-doing externalities in the
1
See, for instance, Frankel (2011), Baunsgaard et al (2012) and Villafuerte et al (2013), among other authors.
2
manufacturing sector and financial frictions, and that also includes a non-Ricardian fiscal framework (with credit-constrained households). The first two characteristics allow for inefficient sectoral reallocation (i.e. the “disease” is indeed a disease). The later (non-Ricardian households) is
of interest because it gives a non-trivial role for government debt, while also introducing household heterogeneity that will allow welfare evaluation from the perspective of different types of
households. We take Chile as our case study, and calibrate the key parameters of the model by
matching the impulse responses generated by a typical cyclical shock to commodities terms of
trade, estimated using a VAR model.
After analyzing equilibrium features of the model, we proceed to perform different policy
exercises. First, we study the optimal degree of procyclicality of government expenditures using
a simple rule. Second, we analyze the virtues of both capital controls and taxes to domestic credit
as previously described. For both exercises, the approach to characterize optimal policy is to study
a constrained Ramsey problem, where the cyclical behavior of these instruments are set according
to simple rules. In the optimal Ramsey approach there are generally two features that may affect
the results. First, as households are assumed to be risk averse, optimal policy will assign some
weight to the reduction in uncertainty in the variables that relevant for welfare (consumption and
hours worked). Second, the optimal policy design will also consider how the particular policy can
tackle the inefficiencies in the model, making the equilibrium as close as possible to a frictionless
model. If the tool evaluated can, at the same time, reduce aggregate volatility and limit the impact
of the inefficiencies present in the model then choice of the optimal policy will be straight forward.
However, it might be the case the policy evaluated may generate a trade off; e.g. if it is able to
reduce aggregate volatility at the expense of exacerbating the inefficiencies. In such a case, the
optimal policy will depend on the specificities of the model an on parameter values. As we will
see, for some of the policies that we evaluate such a trade-off is actually present, and we will try to
characterize what are the relevant channels leading to these results.
Our main findings are as follows. In terms of fiscal pro-cyclicality, we evaluate a structural
balance rule (similar to that implemented in Chile) in which a parameter governs how the difference
between actual and structural (long run) revenues determine government expenditures. We analyze
the optimal value for that parameter, from the perspective of both types of households. We find
that Ricardian agents would rather have a pro-cyclical rule. This is the case because such a rule
will help to smooth their consumption, and therefore its variance, despite the fact that a pro-cyclical
policy exacerbates any inefficiencies coming from either financial frictions or LBD externalities. In
other words, the reduction in the variance of consumption outweighs the benefits of compensating
for the inefficiencies present in the model.
From the perspective of non-Ricardians, however, their optimal degree of fiscal pro-cyclicality
depends on the characteristics of the model. For instance, under LBD externalities, they would
rather have a counter-cyclical expenditure, as the inefficient path of real wages generated by the
combination of the externality and a pro-cyclical policy have a negative impact on their expected
consumption. On the contrary, in the presence of financial frictions the reduction in volatility
they experience with a pro-cyclical rule compensates for the inefficient movement in real wages,
making them choose a pro-cyclical policy.
In addition, the welfare gains for Ricardians to have their preferred degree of pro-cyclicality
are much sizable relative to the benefits that non-Ricardians experience. Moreover, we also find
that these policy choices are also obtained in models were no inefficiencies associated with the
3
Dutch-disease problem are present. Therefore, the benefits of this policy tool are not the results of
agents facing Dutch-disease inefficiencies.
In terms of capital controls, we consider a rule in which a tax on foreign borrowing reacts
to changes in international financing conditions (the country premium). When this alternative is
available we also find a discrepancy between both types of agents. Ricardians prefer a prudential
rule, whereby capital controls are tighter as external financial conditions soften. The opposite is
preferred by Non-Ricardians. Such a policy will smooth out part of the responses generated by
movements in international prices of commodities, reducing the variance in consumption for both
types of agents. However, for Non-Ricardians a prudential capital control reduces is expected
consumption. For the chosen parametrization, this trade-off is solved in favor of average consumption, explaining why these agents prefer a pro-cyclical capital control. In any case, welfare gains
associated with this tool are relatively small.
The other policy tool that we evaluate is a tax on domestic credit that increases as lending
to finance capital accumulation rises. We find that both types of households also disagree on how
these taxes should move with the credit cycle. In particular, Ricardians would rather not have this
tax at all, while non-Ricardians would prefer a tax that fully compensate any change in credit.
However, the welfare gains or loses they experience for different degrees of reaction of this tax
rate to total credit are quite small, particularly compared with the benefits of the other alternatives
we have analyzed.
Finally, we also evaluate the possibility of combining the alternative policy instruments.
The results, however, are mainly driven by the fact that welfare gains from fiscal pro-cyclicality
are the largest. Thus, whenever this tools is available, different choices for the other tools generate
only minor changes in welfare.
Before beginning the analysis we should mention that, while we focus on the effects of
cyclical movements in commodity-related income, there is an alternative perspective to analyze
the Dutch-Disease problem. Namely, how long-term changes in commodity-related income affect
the economy. These could be generated by changes in prices (e.g. by a structural break in the
unconditional mean of the price generated, for instance, by an increase in the world demand for
the commodity), or in quantities (for instance, due to the increase in the endowment of a natural
resource, like the discovery of a new oil field). However, a study of this alternative perspective
would be significantly different than the one we present here, for it would require to analyze how
the economy transitions form one steady state to the other, and how policy should be implemented
during this transition. Moreover, for such an study to be relevant, one should explicitly model the
interaction between commodity income and long term growth. While this is of course a relevant
issue to analyze, in this paper we focus instead on cyclical movements and therefore we will
abstract from long-term considerations. Still, our analysis should be of relevance for countries that
need to deal with the cyclical volatility of commodity prices.
The rest of the paper is organized as follows. Section 2 reviews the literatures related to the
analysis intended here. Section 3 presents the model and its parametrization. Section 4 analyzes the
dynamics and the role of different modeling features under an a-cyclical fiscal expenditures rule.
Section 5 analyzes the cyclicality of government expenditures, Section 6 studies capital controls,
Section 7 evaluates the role of taxes to domestic lending, and Section 8 studies the combination of
these alternative tools. Finally, section 8 concludes.
4
2 Related literature
Our paper links two brands of literature. The first one is the literature on fiscal pro-cyclicality. Part
of the literature has shown that, in small open economy models with Ricardian households and
incomplete assets markets, optimal fiscal policy is generally pro-cyclical (e.g. Gavin et al, 1996;
Gavin and Perotti, 1997; Riascos and Vegh, 2003; Caballero and Krishnamurthy, 2004, Cuadra et
al, 2010). A second strand studies fiscal rules in economies with non-ricardian households, embedded in the more general literature on the discussion about procyclical versus anticyclical fiscal
policies. The seminal paper of this brand of literature is Gali et al (2007), based on the modelling
device by Gali et al (2004). That paper surveys a set of empirical findings suggesting that private
consumption increases after a rise in public spending. To explain such a fact that paper builds
a New Keynesian DSGE model with a particular type of consumers, called non-ricardian.2 The
latter are individuals who cannot smooth consumption neither over time nor across future contingencies. The only choices left to them are the intra-periodic ones. The main result is that with
unionized labor markets and at least 25% of non-ricardian consumers (in terms of total population) the impulse-response from the model after a positive public spending shock includes a rise in
aggregate private sector consumption. The latter paper gave room for a stream of extensions, especially to small open economies. Among them, Garcı́a and Restrepo (2007a, 2007b) and Garcı́a,
Restrepo and Tanner (2010 and 2011) build models along the lines of Gali et al (2007) for small
open economies to study the effect of distortionary taxation (2007a), the role of countercyclical
policies (2007b) and the role of a commodity sector (2010). Of particular interest is Garcı́a, Restrepo and Tanner (2011), since the latter consider the welfare consequences of fiscal rules in this
type of models (including a commodity producing sector). Their main result is that fiscal rules that
reduce public spending volatility benefit non-ricardian households but may hurt other households
with access to financial markets.3 More recently, Céspedes et al (2013) present a model based on
the Gali et al (2007) framework calibrated and estimated to Chilean data, which includes a fiscal
rule sufficiently flexible to include a balanced-budget rule and another one similar to that implemented in that country. Their main result is that, under a balanced-budget-fiscal rule, positive
shocks to public transfers to the private sector have positive effects in consumption, but not the
positive shocks to public spending (although the latter do increase output).4 Finally, Gonzalez et
al (2013) also find that, for a model whose parameters were calibrated to the Colombian economy,
a fiscal rule similar to that in Chile would yield higher benefits than a balanced budget rule or
countercyclical ones.
The second literature related to this paper is the one dealing with the generation of the
so-called Dutch disease and the types of policies to deal with it. The literature on Dutch disease
has been developed for several decades, as some surveys state (see, for example, Magud and Sosa,
2013). The early contributions on the theoretical side stress the importance of several frictions or
externalities (such as labor market imperfections or learning-by-doing in the tradables sector) to
ensure that positive shocks to capital inflows would not only imply real appreciation but also an
inefficiency (i.e., that the Dutch disease is really a disease). However, only recently there have been
some development of papers dealing with policy responses to such inflows or positive commodity
2
Gali et al (2007) call them “rule-of-thumb” consumers. Others refer to them as “hand-to-mouth” or “creditconstrained” households.
3 A similar analysis but in a much more complex model is carried by Kumhof and Laxton (2009, 2010).
4 Another application for the Chilean economy focusing on Copper prices is Medina and Soto (2007).
5
price shocks (relevant for commodity exporters). Caballero and Lorenzoni (2009) develop a twosector model (one tradable, the other non-tradable) with financially constrained exporters. They
consider preference shocks as a reduced-form modeling device for more explicit international price
shocks. They analyze tax policies on the consumption of each good that can be applied ex-ante
or ex-post. The Pareto-optimality of applying an ex-ante versus ex-post tax change depends on
how financially constrained exporters are. Lama and Medina (2012) construct a DSGE model
with an explicit commodity exporting sector and learning-by-doing in the non-commodity export
sectors to analyze the macroeconomic and welfare effects of explicit exchange-rate stabilization
policies, suggesting that the latter are dominated by others allowing for real exchange appreciations
after a positive commodity shock. More recently, Schmitt-Grohé and Uribe (2012) also construct
a two-sector model with labor market imperfections and pegged exchange rate regimes to study
the optimal level of capital controls. Given their calibration they find that it is optimal to tax
capital inflows in good times and subsidize external borrowing in bad times, not only in terms of
welfare but also in terms of unemployment drop.5 Benigno et al (2009) construct a two-sector
model with financial frictions, where the latter come under the form of a collateralized borrowing
constraint similar to those in the pecuniary externality literature6 . That paper considers three policy
interventions: capital controls (tax-subsidies on foreign net asset accumulation), taxes on nontradable consumption and taxes on tradables consumption. Their main result is that either of these
two taxes can always implement the first-best allocation, while capital controls cannot. Although
the last paper was originally designed to study problems of sudden stops rather than Dutch disease,
the design may also suggest the same results for positive tradable income shocks. However, none
of those papers put any role on fiscal spending in increasing welfare when Dutch disease is a real
threat for the economy.
Perhaps, the closest reference to this proposed model is Hevia et al (2013). That paper
assumes a New Keynesian DSGE model with a commodity sector and a government consuming
the same varieties of goods as households (and using the same CES aggregator). They consider
both exchange rates (monetary) policies as well as tax policies. Taxes are imposed on labor income,
capital flows, and also subsidies in the non-commodity exporters demand for labor and on profits.
They obtain results of the optimal mix of tax and monetary policies. However, in their model there
is no condition that makes public spending relevant to smooth consumption against Dutch disease,
since all consumers have access to complete financial markets. They do not consider explicit fiscal
rules where the dynamics of public spending is a key ingredient of the discussion7. Thus, the
proposed model can be seen more as a complement of Hevia et al (2013) since their emphasis is
in variables that complementary to those considered in this paper in the first place.
3 The model
We present a multi-sector model of a small open economy in the lines of the seminal work by
Mendoza (1995) and, more recently for instance, by Medina and Naudon (2011) and Garcı́a-Cicco
et al (2013). The backbone of the model is as follows. There are four types of goods: an exportable
(X), an importable (M), a non-tradable (N) and a commodity (Co). Since our economy is small
5 A complementary study is that of Farhi and Werning (2012), who analytically (in a simplified framework) characterize optimal capital controls under other rigidities.
6 For this literature see Bianchi (2011) and a survey by Korinek (2011).
7 Incidentally, as it will be clear below, our proposed model assumes incomplete financial markets, unlike Hevia et al
(2013) who concentrate in the complete markets case.
6
and open, exportable, importable and commodity goods are internationally traded and their prices
are taken as exogenous (we choose M to be the numeraire). The production of commodities is
an endowment that is completely exported abroad. Households consume exportables, importables
and non-tradables. Regarding production location, we assume that the importable good is produced
abroad only, while the other three goods are locally produced. Exportable and non-tradable goods
are produced using capital and labor. In each of these two sectors, there is a representative firm
that rents capital and hire workers. In addition, another set of firms produce investment goods
combining importable and non-tradable goods, and capital accumulation in both sectors is subject
to adjustment costs. All sectors are assumed to be competitive. The only driving force that we
consider is the commodities terms of trade.
The ingredients of the model that are of special interest for our goals are the following.
First, we consider two types of households: a Ricardian group that have access to non-state contingent international bonds, and a non-Ricardian group that can only consume its after-tax labor
income in each period. Second, we assume that the production of exportables (X) is subject to
a learning-by-doing externality. Third, there are two sets of entrepreneurs (on in each sector X
and N) that are the managers of capital and decide how much of it to accumulate overtime. They
need to borrow to finance capital accumulation and they are subject to a costly-state-verification
problem similar to that of Bernanke et al (1999). These last two features open the door to inefficient outcomes in response to real-exchange-rate movements. Finally, there is a fiscal authority
that levies income taxes, consume non-traded goods, decide on its international asset holdings, and
it may use additional fiscal instruments.
3.1 Households
3.1.1 Ricardian
There is a continuum of infinitely-lived Ricardian households whose mass is 1 − κ. Each of them
has a lifetime utility given by,
(∞
)
X
R
E0
β t U(cR
t , ht ) ,
t=0
where β is the intertemporal discount factor, hR represents total hours worked and cR is consumption of final goods.
Each of these households can work in either the exportable sector or the non- tradable
sector and they are indifferent between the two options, i.e.
R,X
hR
+ hR,N
,
t
t = ht
where hR,X
and hR,N
are hours worked in the exportable sector and the non tradable sector respect
t
tively. Notice that this implies that labor is perfectly mobile between sectors.
Individually, each Ricardian household’s faces in period t the following resource constraint,
Co,R
Co Co Co s
R
R
L
R
R
R∗
∗
R∗
y
+(1−τ
)p
+
Ω
)
−
p
l
(1
+
r
+
p
l
=
(1−τ
)
w
h
)−d
(1+r
+d
p t cR
,
t t
t t−1
t t
t
t
t
t−1
t
t−1
t−1
t
(1 − κ)
7
R
where pt is the price of the final consumption bundle,8 dR∗
t is the stock of international debt, lt are
loans to entrepreneurs (denominated in domestic-consumption units), wt denotes real wages, rt∗ is
the world interest rate, rtL is the interest rates on loans, and ΩR
t are profits coming from the ownership of different firms. Additionally, we assume that there is an exogenous stochastic endowment
of commodities ytCo which is fully exported at an international relative price of pCo
t . The fraction
Co,R
s
denotes the share of commodity production that is owned by Ricardian households. Finally,
these households pay two types of taxes: a tax τ proportional to all the domestic non-commodity
sources of income, and a proportional tax to the revenue generated by commodities τ Co .
The world interest rate is assumed to be equal to
∗ ¯∗
dt − d
∗
w
rt = rt + exp φd
− 1,
(1)
d¯∗
where d∗t is the economy-wide foreign debt position, d¯∗ and φd are positive parameters, and rtw is
an exogenous process. This country’s premium (cpt ≡ rt∗ − rtw ) serves as a closing device as in
Schmitt-Grohé and Uribe (2003).
3.1.2 Non-Ricardian
There is also a continuum of non-Ricardian households, with mass κ. Their lifetime utility is the
same as that of Ricardian households, i.e.
(∞
)
X
R
NR
E0
β t U(cN
t , ht ) ,
t=0
R,X
R,N
R
with hN
= hN
+hN
. However, these households do not have access to any type of financial
t
t
t
market, nor they receive income from profits. Thus, every period each of them face the constraint,
R
R
p t cN
= (1 − τ )wt hN
t
t ,
where τ denotes a proportional income tax. As a consequence of the constraints they face, these
households just solve an intra-temporal allocation problem.
3.2 Production
3.2.1 Aggregate consumption
The aggregate consumption good is produced by combining tradables, cTt and non-tradables, cN
t ,
h
i ǫ
1/ǫ
1/ǫ
N 1−1/ǫ
T 1−1/ǫ ǫ−1
ct = ϕ
ct
ct
+ (1 − ϕ)
,
where ǫ is the elasticity of substitution and 0 < ϕ < 1 is a parameter governing the share of
each type of goods in consumption expenditures. Tradable consumption is in turn a Cobb-Douglas
M
aggregation of exportable, cX
t , and importable, ct , goods:
cTt
8
=
cX
t
χ
χ
Notice that 1/pt is the real exchange rate in this model.
8
cM
t
1−χ
1−χ
,
with χ determining the share of exportables in total tradables’ expenditure. The relative prices of
N
tradables, exportables and non-tradables are denoted by, respectively, pTt , pX
t and pt .
3.2.2 Exportables
The technology for exportables goods presents a learning-by-doing feature. Borrowing from Lama
and Medina (2012), producing ytT units of per capita tradable goods involve using the following
production function,
ψ
X αX
X 1−αX −ψ
ytX = aX
(kt−1
)
t (zt ) (ht )
where zt denotes “organizational capital” following the law of motion,
µ
X
zt = zt−1
ȳt−1
1−µ
.
X
aX
t is an exogenous productivity shock and ȳt is the aggregate production of exportables (i.e.
X
X
in equilibrium, ȳt = yt ). This type of technological externality is one of the most traditional
channels generating inefficient Dutch disease effects, as stressed in Magud and Sosa (2013), among
others. Finally, the rental rate of capital in this sector is uX
t .
3.2.3 Non-Tradables
The technology for non-tradable goods is given by
N αN
N 1−αN
ytN = aN
(kt−1
)
t (ht )
In particular, notice that we assume that there is no learning-by-doing technology in this sector.9
The rental rate of capital in this sector is uN
t .
3.2.4 Entrepreneurs
For each sector j = X, N there are two groups of entrepreneurs who are the managers of the stock
j
j
. They rent
and outstanding loans lt−1
of capital. The start every period with a stock of capital kt−1
j
the stock of capital to the firms in each sector (at a rate ut ) and, after depreciation (whose rate is
denoted by δ), they sell the remaining stock to capital producers (described below) at a price qtj ,
and repay the loans. Afterwards, they buy new capital from these capital-goods producers at price
qtj .
We assume that in order to finance the purchase of new capital, entrepreneurs use both
loans from households and their own net worth (njt ). That is,
qtj ktj = njt + pt ltj .
for j = X, N.
We include a financial friction in the spirit of Bernanke et al (1999). In their setup, there
is a costly-state-verification problem that limits the entrepreneur’s ability to freely borrow from
households. As a result, the optimal (incentive-compatible) debt contract specifies that there is a
wedge between the expected return on purchasing one new unit of capital and the rate at which
households are willing to lend (i.e. their opportunity cost, rtL ). Moreover, as shown by Bernanke
et al (1999), this wedge (known as the external finance premium) will be an increasing function of
qj kj
entrepreneurs’ leverage (given by nt j t ).
t
9
For instance, Begnino and Fornaro (2013) describe evidence supporting this assumption.
9
We borrow these insights from Bernanke et al (1999) and specify the following relationship
between rtL and the expected return on purchasing one new unit of capital,
(
)
j
ujt+1 + (1 − δ)qt+1
Et
= (1 + rtL )rpjt
(2)
j
qt
where
rpjt ≡ rp
qtj ktj 1
njt lev
!ξj
,
for j = X, N. The parameter lev is the steady state leverage, while rp is the steady-state risk
premium, both assumed to be equal across sectors.10 Thus, ξj > 0 captures the elasticity of the
premium with respect to leverage in each sector.
Finally, net worth evolves as following. After repaying loans, a fraction 1 − ϑ of entrepreneurs exit the market and transfer the remaining profits to Ricardian households. The same
fraction enters the market every period, each of them receiving a startup capital injection from
ιj
Ricardian households given by 1−ϑ
. Thus, the law of motion of aggregate net worth in each sector
is given by,
j
j
L
njt = ϑ [ujt + (1 − δ)qtj ]kt−1
− pt lt−1
(1 + rt−1
) + ιj .
3.2.5 Capital and Investment Goods
In each sector, there is a group of firms that buy old capital and combine it with investment goods
to produce new capital using the technology
"
!#
j
i
j
ktj = (1 − δ)kt−1
+ 1 − Sj j t
ijt .
it−1
for j = X, N. The function Sj (·) captures convex adjustment costs in investments. In turn, investment goods are produced by another set of firms operating a technology that combines imported
and non-traded goods to produce. In particular, we assume,
it =
xN
t
γ
γ
xM
t
1−γ
1−γ
,
X
i
where it = iN
t + it . The relative price of investment goods is given by pt .
3.3 Fiscal Policy
In the baseline setup, we assume that fiscal policy levies the taxes previously described, has access
11
to international debt markets (dg∗
t ), and purchases non-traded goods (gt ). Its resource constraint
is given by
g∗
∗
pnt gt + dg∗
t−1 (1 + rt−1 ) = revt + dt .
10
11
Unfortunately, we do not have data that allow us to discriminated these averages across sectors.
To simplify the analysis, we do not consider the case of domestic government debt.
10
where revt denotes total revenues, which is equal to the sum of tax collection and revenues from
ownership of commodity production. In particular, it can be shown that in equilibrium the collection of proportional taxes equals
Co Co,R
X
N N
Co
revt = τ pX
+ pCo
τ (s
+ sCo,∗ ) + sCo,g
t y t + pt y t
t yt
where sCo,∗ and sCo,g are the shares of commodity production owned by, respectively, foreigners
and the government (with sCo,R + sCo,∗ + sCo,g = 1).
Given τ and τ Co , there are two other policy variables to be decided (gt and dg∗
t ) but only
one of them can be chosen by the government, as the other will be determined by its resource
constraint. We specify a rule for expenditures in the spirit of the structural balance rule in place in
Chile:
∗
(3)
pnt gt + dg∗
t−1 (rt−1 + ηr ) = η0 + rev + ηrev (revt − rev),
where rev is the long-run (steady-state) level of revenues.12 The rule is characterized by three
parameters: ηrev ∈ [−1, 1] governs the degree of pro-cyclicality, η0 determines the cyclicallyadjusted structural deficit, and ηr ∈ (0, r W ) is an adjustment factor. The latter is required for a
13
Finally, notice that η0
technical reason: without it, government debt dg∗
t may display a unit root.
g∗
is linked to the long run level of government debt: in steady state d = η0 /ηr .
Our calibration strategy for the fiscal side of the model is as follows. First, we calibrate
g to match the share of government expenditures over GDP observed in the data. Second, we
impose dg∗ = 0. We make this choice because we want to focus on the cyclical properties of
different policy alternatives.14 We also set the adjustment factor ηrev to a small value, and calibrate
η0 = dg∗ ηr . Finally we calibrate τ Co and sCo,g according to the data and let τ to be determined
endogenously in steady state to satisfy the government budget constraint.15
12
Throughout, we use the notational convention that variables without time subscript denote their respective steadystate values.
13 To see this, combine the fiscal rule with the government resource constraint to obtain
g∗
dg∗
t−1 (1 − ηr ) = −η0 + (1 − ηrev )(revt − rev) + dt .
W
Thus, if revt is a stationary ηr = 0 will imply that dg∗
t contains a unit root. Thus we impose ηr ∈ (0, r ) is a
necessary condition that ensures the existence of stationary equilibrium. This is however not a sufficient condition for
equilibrium existence, as the rule can interact in a non-trivial way with other features of the model that may generate
a non-existence result.
14 This and some others assumptions we have already described allow us to isolate the issues regarding the optimal
cyclical properties of fiscal policy, without entering in the discussion about the optimal long-run setup for fiscal policy.
These other issues are of course relevant as well, but we want to narrow the scope of this paper to the cyclical analysis.
15 In the calibration for Chile, we obtain τ = 0.054.
11
3.4 Aggregation and Market Clearing
The following are market clearing conditions in different markets:
Labor:
Consumption:
Foreign debt:
Loans:
Investment:
Non-tradables:
NR
N
(1 − κ)hR
= hX
t + κht
t + ht .
NR
(1 − κ)cR
= ct .
t + κct
g∗
R∗
(1 − κ)dt + dt = d∗t .
(1 − κ)ltR = ltX + ltN .
M
it = iN
t + it .
N
N
yt = ct + xN
t + gt .
In addition, we define the trade balance as follows:
M
impt ≡ cM
t + xt .
Co Co
X
X
expt ≡ pX
t (yt − ct ) + pt yt .
tbt ≡ expt − impt .
With this, the net-foreign lending position evolves as follows,16
∗
Co Co,∗
d∗t−1 (1 + rt−1
) = d∗t + tbt − pCo
(1 − τ Co ).
t yt s
Finally, we define GDP in consumption units as,
X
N N
Co Co
pt gdpt ≡ pX
t y t + pt y t + pt y t .
In equilibrium, the definition of GDP can also be expressed in terms of expenditures as pt gdpt =
pt ct + pit it + pN
t gt + tbt .
3.5 Driving Forces and functional forms
While the model includes a number of exogenous driving forces, we focus the attention on the
dynamics originated by commodities terms of trade (pCo
t ). Accordingly, for all the other driving
X
N Co W
X
forces (at , at ,yt ,rt and pt ) we assume they remain fixed at a constant value, while we assume
that the logarithm of pCo
t follows an AR(1) processes with Gaussian innovations.
We specify the following functional form for the instantaneous utility,
h
i1−θ
(hit )1+υ
cit − ζ 1+υ
−1
1−θ
, for i = R, NR.
This GHH specification is widely used in the literature analyzing business cycles fluctuations in
emerging countries. In particular, in our model it implies that the supply of labor of both types of
agents will be the same in equilibrium. Finally, for investment adjustment costs we assume,
φI
2
ijt
ijt−1
−1
!2
, for j = X, N.
16
This can be derived by combining the households and the government resource constraints with several market
clearing conditions.
12
This completes the description of the model. The appendix contains the set of equilibrium conditions, as well as the computation of the steady state.
3.6 Parametrization
We now describe how we choose the different parameter values. First, we draw from the related
literature to calibrate some preference (θ, ω, χ), technology (αX , αN , δ), and commodity-related
shares parameters (τ Co , sCo,g , sCo,∗ ) as shown in Table 2. The parameters β, d¯∗ , y Co , g, ζ, aX ,
ϕ are set in steady state to match the following averages form Chilean data: the shares of trade
balance, mining production, government expenditures, and non-trade production to GDP; hours
worked, the relative price of non-tradables and the world interest rate. We also pick a small value
for the elasticity of the country premium φd . The share of non-Ricardian households is set to 0.5,
following the evidence presented in Céspedes et al (2013).
In addition, we calibrate the average leverage of entrepreneurs to be 2.05, in line with the
average leverage for non-financial firms in Chile form 1999 to 2014, and we set a risk premium
in steady state equal to 1.23% (quarterly), which is the average lending-deposit spread for 90-days
commercial loans from 1996 to 2014. We also set the survival rate of entrepreneurs to 0.97, a usual
value in the related literature. These determine the values for ιX , ιN in steady state.
The other parameters in the model are ǫ (the elasticity of substitution between cN and
cT ), φI (the capital adjustment cost), ψ (the share of organizational capital z in y X ), µ (the persistence of the learning by doing technology), ξX and ξN (the elasticities of the external finance
premium), ρpCo and σpCo (the persistence and standard error variance for commodities terms of
trade). To calibrate these, we follow an impulse response matching approach, similar to that
proposed by Christiano et al (2010). In particular, we first estimate a VAR model for the following variables using Chilean quarterly data from 1996.Q1 to 2014.Q2: mining terms of trade
(pCo ), the shares of tradable and non-trades production in non-commodity output (respectively,
X
N
pX
pN
t yt
t yt
N
sX
≡
and
s
),17 the real exchange rate (rert = 1/pct ), the ratio
≡
t
t
N N
N N
X
X X
y
y
+
p
+
p
y
y
pX
p
t t
t t
t t
t t
pC
t ct
of consumption to non-commodity GDP (sC
), and the average risk premium
≡
t
X X
N
pt y t + pN
t yt
lX rpX +lN rpN
across sector (rpt = t t lt t t ), proxied by the lending-deposit spread.18 We use shares of aggregate variables instead of levels or some detrended version of these because, as our model does
no feature long term growth, it will be inconsistent to use any of these alternatives to match the
empirical and the theoretical model. Instead, matching the shares and assuming they are stationary
it is consistent with the assumptions in the model.
In addition, there is another non-stationarity issue that we have to deal with to make the
VAR model consistent the theoretical model. Namely, that the mining-terms-of-trade series for
Chile (driven mainly by the price of copper) display a structural break around 2005. Indeed using
both Andrews-QLR structural-break test and the Bai-Perron methodology to detect break dates,
we found a break in the unconditional mean of minning terms of trade in 2005.Q1. Given that
our focus is on cyclical movements of commodity prices, it is relevant to control for this structural
break. If not, the persistence of the estimated process for the pCo will be highly influenced by the
17
The X sector corresponds to manufacturing GDP, while the N sector includes Construction, Retail, restaurants and
hotels, Transportation, Communication, Financial Services, Home services, Personal services, and Public administration.
18 All variables are in logs. The source of the data is the Central Bank of Chile.
13
Table 1. Calibration
Parameter
θ
ω
χ
αX
αN
δ
γ
φd
κ
τ Co
sCo,g
sCo,∗
ηr
ϑ
stb
sCo
sg
sN
lev
rp
rW
pCo
pX
aN
pN
h
Description
Value
Structural parameters
Risk Aversion
2
Frish elasticity
1
X
T
Share of c in c
0.5145
Share of hX in y X
0.36
N
N
Share of h in y
0.65
Depreciation rate
0.015
Share of xN in i
0.4
Elasticity of country premium
0.001
Share of Non-Ricardian households
0.5
Tax rate on copper income
0.35
Government participation in Com. Production
0.4
Foreigners participation in Com. Production
0.6
Adj. Factor in fiscal rule
0.001
Entrepreneurs survival rate
0.97
Steady state targets
Share of tb in gdp
0.04
Share of y Co in gdp
0.1
Share of g in gdp
0.11
Share of y N in gdp
0.5
Entrepreneurs leverage
2.05
External finance premium
1.23%
World interest rate
1.48%
Commodities T.o.T
1
Non-Commodities T.o.T
1
Productivity in the N sector
1
Relative price of N goods
1
Total hours worked
0.3
Source
Garcia-Cicco et al (2010)
Garcia-Cicco et al (2010)
Medina and Naudon (2011)
Medina and Naudon (2011)
Medina and Naudon (2011)
Medina and Soto(2007)
Medina and Naudon (2011)
Calibrated
Céspedes et al (2013)
Medina and Soto (2007)
Medina and Soto (2007)
Medina and Soto (2007)
Normalization
Bernank et al (1999)
Average in Chilean data
Average in Chilean data
Average in Chilean data
Average in Chilean data
Average in Chilean data
Average in Chilean data
Average in Chilean data
Normalization
Normalization
Normalization
Normalization
Normalization
Note: The parameters β, d¯∗ , y Co , g, ζ, aX , ϕ, ιX , ιN are determined endogenously in steady
state to match the targeted values.
14
break, which will then have non-trivial consequences for the welfare analysis below. Thus, to be
consistent with the goal fo the paper, the estimated VAR model includes a dummy variable that
takes a value of one after the detected break date.
Figure 1. VAR and model based responses to a commodity price shock.
Note: The solid-blue lines are VAR responses, the gray areas are 95% confidence bands for
the VAR responses, and dashed-dotted-red lines are the responses generated by the model.
Responses are in percentage.
The commodity-price shock is the identified by a Cholesky decomposition on the shortrun relationship matrix, assuming that mining term of trade is ordered first and that it is strictly
exogenous with respect to domestic variables.19 Figure 1 display in solid-blue lines the responses
from the VAR, while the gray areas represent 95% confidence bands for those responses. As
can be seen, the typical commodity terms-of-trade shock induces Dutch-disease stile responses.
In particular, the other manufacturing sector shrinks, the non-traded sector expands and the real
19
The VAR model contains only one lag, which was chosen according to both BIC and HQ information criteria. In
addition, as previously discussed, the model contains also a constant and a dummy for the break period. Confidence
bands were computed by bootstrap, drawing with replacement 1000 samples from the reduced form residuals. We also
estimated an alternative model that controls also for the EMBI for Chile (in a sample from 1999 to 2014), but results
are quite similar between both samples.
15
exchange rate appreciates. The share of consumptions seems to experience a minor drop at the
moment of the shock, but it increases afterwards. Finally, the average lending-deposit spread
significantly falls after the shocks.
Table 2 shows the combination of parameters that better match the VAR responses.20 The
value for ǫ is similar to previous estimated values for this parameter (see, for instance, the survey by
Akinci, 2011). The parameters for the learning-by-doing technology are somehow different from
those used by Lamma and Medina (2012) for the case of Canada. In particular, they use ψ = 0.25
and µ = 0.63, while in our case the model seems to require a larger fraction of organizational
capital in the production of tradables. The persistence of the learning accumulation process is
somehow smaller in our case.
Table 2. Impulse-response based Calibration
Parameter
ǫ
ψ
µ
ξX
ξN
φI
ρpCo
σpCo
Description
Elasticity of substitution between cN and cT
Share of z in y X
Persistence of learning technology
Elasticity of the risk premium in the X sector
Elasticity of the risk premium in the N sector
Capital adj. cost
Autocorrelation of pCo
t
Co
Standard deviation of ǫpt
Value
0.9813
0.3416
0.5921
0.0169
0.115
5.4315
0.8399
0.1113
In terms of financial frictions, the model requires a larger elasticity for the N sector than
for the X sector. This is the case because, as we will analyze below, after a commodity shock the
premium in the N sector should falls relatively more than in the X sector, as the former is favored
by the shock while the latter is worse off. Thus, the make the average premium fall as in the data,
the model requires the premium in the N sector to be more sensitive the improvements in financial
conditions.
The dynamics generated by this combination of parameters are displayed in the dasheddotted red lines in figure 1. As can be seen, the responses of the model generally lie withing the
VAR error bands. The model does a good job in matching the behavior of the share of non-tradables
and of the average risk premium. The negative response of sX is somehow milder in the model
than in the VAR, although it lies within the VAR confidence bands. The initial real appreciation
implied by the model it is not as large as in the VAR, although it generates a persistent change in
this variable as in the empirical model. Finally, the initial drop in the share of consumption cannot
be replicated by the model, but the behavior of this share after the first quarters is consistent with
the VAR model once uncertainty is taken into account. Overall, the model does a fairly good job
in matching these responses.
20
For this exercise, we assume an a-cyclical fiscal rule (ηrev = 0). The compute the impulse responses, the model
is solved using a log-linear approximation around the non-stochastic steady state. The impulse-response matching
procedures seeks to minimize the distance between the first 16 VAR responses for all the variables with those generated
by the model. Given that there are more moments to match than parameters, we weighted each of the response by the
inverse of its variance in the VAR, computed with the Bootstrap procedure previously described.
16
4 Dynamics Under an A-cyclical Rule
Before analyzing the role of different policy alternatives, we begin by describing the role of several
of the modeling features in propagating the shock to commodity prices (pCo
t ), under the assumption
that the fiscal rule is a-cyclical (i.e. ηrev = 0). This exercise will shed light on how the different
model features affect the dynamics trigged by the commodity shock. To this end, we consider
several alternative versions of the model. The version labeled as “Base” is the model that just
features Ricardian households and that excludes both financial frictions and the learning-by-doing
externality. If a model name includes “NR” it means that Non-Ricardian households are considered, if it includes “FF” the model assumes the presence of financial frictions, and if it includes
“LBD” the setup features the learning-by-doing externality. In the rest of the section we show
impulse-response functions obtained under different versions of the model in response to a shock
21
to commodities terms of trade (pCo
The impulse is a shock that increases pCo
t by 11% and it has
t ).
a half-life of around 5 quarters.
We begin by describing the dynamics in the Base model, depicted in the solid-bule lines in
Figure 2. The shock induces a positive wealth effect that rises desired consumption in all goods,
generating in particular a rise in the relative price of non-tradables (a real appreciation) and a
relocation of resources from the X sector to the N sector. In addition, investment increases for
three reasons. First, the demand for capital in the N sector rises, although it is reduced in the
X sector. Second, given that a large part of investment goods are imported, the real appreciation
drops the relative price of investment goods. Third, the improvement in the trade balance reduces
the aggregate net-foreign-debt position, generating a drop in the country premium which lowers
the domestic interest rate. Thus, in equilibrium, regardless of the contraction in production of X
goods, investment in that sector rises due to the second and third effects, and therefore aggregate
investment rises. In equilibrium, investment in the X sector rises as well, so the first effect that we
mentioned is compensated by the other two.
Notice also that the fiscal rule under the assumption of ηrev = 0 implies that government
expenditures decreases somehow in the first periods, while it persistently rises afterwards. The
former is due to the real appreciation: in the first period, the value of government purchases in
terms of the imported good has to remain fixed; thus, expenditures in non-tradable units need to
drop on impact. The latter effect is due to the accumulation of foreign assets by the government
that the rule generates: given the rule, the government can spend the interest income originated
from asset accumulation. As the shock is quite persistent, the increase in government assets is
quite large and therefore g rises for several periods.
In the same figure the responses in a model that adds the learning-by-doing externality are
also displayed. We can see that this feature intensifies the drop in y X due to the drop in productivity
induced by the learning technology. At the same time, this expected drop in productivity negatively
affects investment in that sector. In equilibrium, the real exchange rate appreciation is milder that
in the Base model. The other relevant difference is the behavior of consumption, which increases
by less in the model that includes the externality. This happens because the real wage increases by
less and the return on capital is reduced in the X sector.22
21
For these exercises, the model is solved with a first-order perturbation approximation around the non-stochastic
steady state. Impulse responses computed using s second-order of approximation yield similar results.
22 In the responses it seems that, although investment increase by less in the LBD model, aggregate investment
increases by more. This happens because, in the steady state of the LBD share of investment in the N relative to total
17
Figure 2. Responses to a commodity price shock, Base vs. Base + LBD, ηrev = 0.
pCo ⇒ c
pCo ⇒ gdp
1.5
1
0.5
0
5
Co
p
10
15
⇒ rer
20
pCo ⇒ i
0.25
1
0.2
0.8
0.15
0.6
0.1
0.4
0.05
5
Co
p
10
⇒y
15
N
0.2
20
0.25
0.2
−0.05
0.2
0.1
−0.1
0.15
0
−0.15
0.1
−0.1
−0.2
5
Co
p
10
⇒i
15
N
20
1.5
1
0.5
0
5
Co
p
10
15
N
⇒ rp
20
0.05
10
⇒i
15
X
20
⇒y
15
X
20
−0.5
5
Co
p
10
⇒c
15
R
20
0.1
0.15
0
0.1
−0.5
p
10
15
X
⇒ rp
20
5
Co
p
10
15
⇒ cp
20
0
5
10
15
20
−1
5
10
15
20
10
15
20
pCo ⇒ g
0.6
0.4
−0.01
0.2
−0.02
−0.5
−1
0.05
20
pCo ⇒ cN R
0.2
Co
15
0.15
0.3
5
10
pCo ⇒ w
0.2
0.5
0.1
5
0.25
0.2
0
20
−0.2
10
0.4
0
15
Co
1
0.5
10
5
0.25
0.5
5
0
0.5
1
−1
Co
p
1
−0.5
5
0.5
p
0
pCo ⇒ stb
1
5
10
15
20
−0.03
0
5
10
15
20
−0.2
5
Note: The solid-blue lines are the responses from the Base model while the dashed-red lines
are from the Base+LBD model. The variables depicted are GDP, consumption, investment,
the trade-balance-to-gdp ratio, the real exchange rate, production of non-tradables and that
of exportables, real wage, investment in non-tradables and that in exportables, consumption
of Ricardian and non-Ricardian households, the external finance premium for non-tradables
and for exportables, the country premium, and government expenditures. All responses are
in percentage deviations with respect to the steady state, except for stb that is expressed in
percentage-points deviations. The time units in the horizontal axes are quarters. The size of
by 5.6% and it has a half-life of 90 quarters.
the shock increases pCo∗
t
18
Figure 3. Responses to a commodity price shock, Base vs. Base + FF, ηrev = 0.
pCo ⇒ gdp
pCo ⇒ c
1.5
pCo ⇒ stb
pCo ⇒ i
0.2
1
0.1
0.5
1
1
0.5
0.5
0
0
5
10
15
20
0
pCo ⇒ rer
5
Co
p
10
15
⇒y
N
0
20
5
Co
p
0
0.4
0.2
−0.1
0.2
0
10
15
⇒y
X
20
−0.5
5
10
Co
15
10
15
p
20
⇒w
0.25
0.2
0.15
−0.2
5
10
15
20
0
pCo ⇒ i N
5
10
15
20
−0.2
pCo ⇒ i X
5
10
15
20
0.1
2
1
0.2
1
1
0.5
0.1
0
0
5
10
Co
p
15
20
0
N
⇒ rp
5
10
Co
x 10 p
−3
0.1
15
0
20
5
X
10
Co
⇒ rp
p
1
0
0
−0.01
−1
−0.02
15
20
−1
5
10
Co
15
10
15
p
⇒ cp
20
20
⇒g
0.5
0
−0.1
5
pCo ⇒ cN R
pCo ⇒ cR
0
5
10
15
20
−2
5
10
15
20
−0.03
5
10
15
20
−0.5
5
Note: The solid-blue lines are the responses from the Base model while the dashed-red lines
are from the Base+FF model. See Figure 2 for variables and unit of measure.
19
20
Figure 3 compares the responses in the Base model with and specification that includes
financial frictions. After this expansionary shock, and given the sectoral relocation, the increase
in the value of capital and in the return from capital in the N sector induces an improvement in
net worth in this sector, decreasing the leverage and reducing the external finance premium. On
the contrary, the spread in the X sector improves only marginally in the short run and it increases
persistently after some quarters. Indeed, the drop in the premium for this sector is much short lived
than in the N sector. As a consequence, iX increases by less in the FF model relative to the Base,
while iN increases by more than in the base model. The real exchange rate present a slightly larger
appreciation in the first periods, while afterwards it experiences a milder appreciation relative to
the Base case. In addition, we can see that the path for consumption moves upwards relative to that
in the Base case. In other words, as investment is less attractive in the presence of financial friction,
agents choose to devote a relatively larger fraction of the extra income generated for consumption.
Finally, Figure 4 plots the responses of the Base model and the Base+NR alternative. As
can be seen, the consumption of Non-Ricardian households increases after the shocks, lead by
the increase in real wages. At the same time, the rise in consumption for Ricardian consumers
is milder than in the Base model, which can be explained as follows. Ceteris paribus, the rise
in consumption by Non-Ricardians is expansionary, for it increases the demand for all goods.
Everything else equal, this translates in a larger increase in income for Ricardians who, instead
of consuming it, increase saving. Thus the overall response of aggregate consumption can be
larger or smaller than in the Base model depending on parameter values. In this case, aggregate
consumption rises by less than in the Base model. In turn, this additional saving is devoted in part
to invest, hence investment increases by more in the Base+NR model.
5 Fiscal Pro-cyclicality
We now turn to the analysis of the optimal degree of pro-cyclicality. First, we use impulse
response analysis to describe how different values for ηrev in the rule (3) affect the dynamics
originated by a shock to commodity prices. Figure 5 compares the responses in the full model
(Base+NR+FF+LBD) for three alternative values for ηrev : 0, 0.5 and -0.5. When ηrev is positive,
the path of government expenditures moves upwards relative to the case of ηrev . For Ricardian consumers, this ameliorates the expansion in their consumption, while for non-Ricardians consumption rises by more. Overall, as the change for Ricardians dominates and aggregate consumption
increases.
In terms of production, the rise in G increases the demand of N goods, increasing production in this sector and generating a larger appreciation. This effect is partially compensated by the
relative reduction in consumption, but it is not fully offset as the consumption bundle includes both
types of goods. Thus, fiscal pro-cyclicality clearly exacerbates the relocation effects. In addition,
we can also see that investment is negatively affected under a pro-cyclical policy. When ηrev is
negative, the opposite happens.
For the welfare analysis that we implement below a relevant observation is in order. While
a negative value for ηrev allows Ricardian households to enjoy more consumption,23 the path of
consumption is more volatile in such a case. Moreover, the change in volatility of consumption for
invetsment is larger than in the X sector, and therefore the weighted sum in the log linear approximation generates a
larger percentage change in total investment with the Base+LBD model.
23 The equilibrium path of aggregate labor (not shown) does not vary significantly with different values of η
rev ; a
result driven by the GHH preferences that we have assumed.
20
Figure 4. Responses to a commodity price shock, Base vs. Base + NR, ηrev = 0.
1
0.5
0
5
Co
p
10
15
⇒ rer
pCo ⇒ i
pCo ⇒ c
pCo ⇒ gdp
1.5
20
0.16
1
0.14
0.8
0.12
0.6
0.1
0.4
0.08
5
Co
p
10
⇒y
15
N
0.2
20
pCo ⇒ stb
1
0.5
0
5
Co
p
10
⇒y
15
X
20
−0.5
0
0.2
0.05
0.25
−0.05
0.15
0
0.2
−0.1
0.1
−0.05
0.15
−0.15
0.05
−0.1
0.1
−0.2
5
Co
p
10
⇒i
15
N
20
1.5
0.5
5
Co
p
Co
p
10
⇒i
15
X
20
10
15
N
⇒ rp
20
20
0.05
0.15
0.1
0.2
0.1
0.05
0
5
Co
p
10
15
X
⇒ rp
20
5
Co
p
10
15
⇒ cp
20
0
15
20
10
15
20
0
5
10
15
20
10
15
20
pCo ⇒ g
0.6
0.4
−0.01
0.2
−0.02
−0.5
−1
0.05
5
10
pCo ⇒ w
pCo ⇒ cN R
0.2
0
20
⇒c
15
R
0.15
0
15
p
10
0.4
0.5
10
Co
0.6
0.5
5
5
0.2
1
−0.5
−0.15
0.25
1
−1
5
0.8
1
0
0
5
5
10
15
20
−0.03
0
5
10
15
20
−0.2
5
Note: The solid-blue lines are the responses from the Base model while the dashed-red lines
are from the Base+NR model. See Figure 2 for variables and unit of measure.
21
Figure 5. Responses to a commodities price shock, Base+NR+FF+LBD model, different values for ηrev .
pCo ⇒ gdp
pCo ⇒ c
1.5
2
0.3
1
pCo ⇒ stb
pCo ⇒ i
0.4
1.5
1
1
0.2
0.5
0
0.1
5
Co
p
10
15
⇒ rer
20
0.5
0
−0.5
5
Co
p
10
⇒i
15
N
20
3
2
1
0
0.5
0
5
10
15
pCo ⇒ rpN
20
0
5
Co
p
10
⇒y
15
N
−1
20
0.4
0.4
0.2
0.2
0
0
−0.2
5
Co
p
10
⇒i
15
X
20
5
Co
p
0.6
−0.2
0
−0.4
10
⇒y
15
X
20
−0.5
5
Co
p
10
⇒c
15
R
20
−0.5
0.3
0.4
0
0.2
0.2
−1
0.1
0
15
0
20
5
10
15
pCo ⇒ cp
20
−0.2
0.05
0.02
0
4
0
0.01
−0.01
2
−0.05
0
−0.02
0
−0.1
−0.01
−0.03
−2
−0.15
5
10
15
20
−0.02
5
10
15
20
−0.04
5
10
15
20
5
10
15
20
10
15
20
10
15
20
pCo ⇒ cN R
1
10
20
0
0.6
pCo ⇒ rpX
15
0.5
0.4
5
10
pCo ⇒ w
1
2
−2
5
−4
5
5
pCo ⇒ g
Note: The solid-blue, the dashed-red and the dashed-dotted-black lines correspond, respectively, to the models with ηrev = {0, 0.5, −0.5}. See Figure 2 for variables and unit of measure.
22
different values of ηrev is likely to be large, given the response of consumption is highly persistent.
Thus, it is not clear what the optimal policy would recommend, as a tension between mean and
variance will likely influence the welfare analyze based on a second order of approximation.24 For
non-Ricardians the responses are less clear. While it seem that either positive or negative values
for ηrev induce a larger variance in consumption, a negative value for ηrev seems to increase the net
present value of consumption relative to the case with ηrev = 0,25
We next turn to the welfare evaluation of the optimal value for ηrev . In particular we choose
the value of ηrev the maximizes
(∞
)
X
E0
β t U[cit (ηrev ), hit (ηrev )] .
t=0
for agent i = R, NR. In addition, in some cases we also compute the policy that maximizes a
weighted average of both welfare criteria. We approximate the value of this expected utility using
a second-order Taylor approximation around the non-stochastic steady state, following SchmittGrohe and Uribe (2007a,b). We also compute the consumption equivalent that would make the
household indifferent between the equilibrium with the optimal ηrev and that obtained with the
a-cyclical rule (ηrev = 0). In other words, we define λi such that,
(∞
)
(∞
)
X
X
opt
opt
E
U[cit (ηrev
), hit (ηrev
)] = E
U[(1 − λi )cit (ηrev = 0), hit (ηrev = 0)] .
t=0
t=0
for agent i = R, NR. We compute a second order approximation to λi around the non-stochastic
steady state.26 We also compute the ratio of the standard deviation and of both consumption and
opt
hours worked obtained with ηrev
relative to the case with ηrev = 0, as well as the percentage
opt
increase in these two variables ηrev
relative to the case with ηrev = 0.27 This set of statistics will
be useful to understand the welfare ranking of different policy alternatives.
The results are displayed in Table 3, were we have performed the welfare evaluation for
different versions of the model. Panel A show the results when policy is chosen to maximize Riopt
cardian welfare. We can see that in all the specifications they prefer full pro-cyclicality (ηrev
= 1).
As we previously described, a counter-cyclical policy allows them enjoy a larger consumption after a positive shock and, in the presence of inefficiencies, a counter-cyclical policy reduces the
adverse effect generated by the relocation across sectors. However, the reduction in volatility in
consumption and, to a less extent, in hours generates an increase in the average value fo consumption up-to-second order, which is also translated in a larger value for expected utility. This is the
case because, as we already mentioned, an evaluation based on a second-order-of approximation
will in part depend on the impact of volatility in the endogenous variables due to precautionary
opt
savings motives. In other words, as consumption is less volatile ηrev
= 1, precautionary savings
24
Recall that up to second order the variance affects the unconditional mean of the endogenous variables.
While in the short run C N R fall with ηrev < 0, it later rises persistently above the response with ηrev = 0.
26 Schmitt-Grohe and Uribe (2007a,b) show how to implement this approximation for the case in which the utility
function is such that U [(1 − λ)ct , ht ] = (1 − λ)U (ct , ht ). However, our GHH specification does not satisfy this
condition. Thus, in the appendix we show how the method proposed by Schmitt-Grohe and Uribe can extended for
the general case.
27 These moments are computed using a second-order approximation to the solution.
25
23
Table 3. Welfare evaluation: fiscal pro-cyclicality.
Model
opt
ηrev
100λR
Base+NR
Base+NR+FF
Base+NR+LBD
Base+NR+LBD+FF
1
1
1
1
-4.04
-3.17
-3.79
-3.22
Base+NR
Base+NR+FF
Base+NR+LBD
Base+NR+LBD+FF
-1
1
-1
-1
6.23
-3.17
4.62
2.91
Base+NR+LBD+FF
1
-3.22
Comparision relative to ηrev = 0
Ricardians
Non-Ricardians
St.Dev.
Mean
St.Dev. Mean
NR
c
h
c
h
100λ
c
c
A. Maximization of Ricardian Welfare
0.08 0.44 4.25 0.03
0.01
0.47
0.02
0.10 0.50 3.30 0.09
-0.05
0.53
0.14
0.08 0.59 3.98 0.05
0.00
0.62
0.05
0.17 0.76 3.36 0.06
-0.01
0.78
0.08
B. Maximization of Non-Ricardian Welfare
2.64 2.76 -5.71 0.37
-0.33
2.75
0.79
0.10 0.50 3.30 0.09
-0.05
0.53
0.14
2.28 2.52 -4.37 0.29
-0.28
2.51
0.63
2.24 2.49 -2.72 0.07
-0.07
2.47
0.17
C. Welfare weight 50%
0.17 0.78 3.36 0.06
0.00
0.08
0.06
Note: The second column display the welfare maximizing ηrev , the third to seventh columns
compare the optimal relative to the case of ηrev = 0 in the given model. These columns display: 100 ∗ λi is the welfare equivalent consumption in percentage terms, “St.Dev. c” is the
opt
ratio of the standard deviation of consumption with ηrev
relative to the case with ηrev = 0,
“St.Dev. h” is the analogous with hours worked, “Mean c” is the percentage increase in the
opt
mean of consumption with ηrev
relative to the case with ηrev = 0, and “Mean h” is the analogous with hours worked. All these have been computed using a second-order approximation.
We do not report results for hours worked for non-Ricardians because this variable is the same
for both types of agents
24
drop allowing them to enjoy a larger consumption on average. Moreover, we can see that the
reduction in the variance is quite large. This is not surprising because, as it was evident in the
impulse-response analysis, the process for consumption is highly persistence. Thus, even a small
downward shift in the path of consumption will imply a large reduction in its variance. Overall,
they are willing to give up around 4% of the consumption stream obtained under an a-cyclical rule.
In panel B of Table 3 we ask Non-Ricardians which value of ηrev they prefer, and we can see
that the answer depends on the details fo the model. In models with no financial frictions (Base+NR
and Base+NR+LBD), they would rather have a fully counter-cyclical policy (ηrev = −1). In both
setups, we can see that the counter-cyclical policy actually rises the variance of non-Ricardian consumption but at the same time it increases average consumption. For this agents the precautionary
savings channel is not present, for they do not have access to financial markets. Thus, a larger
variance does not necessarily imply a reduction in average consumption. Therefore, in welfare
terms a trade-off may arise for them between a reduction in volatility, which they would like to
have due to risk aversion, and an increase in average consumption. Given the parameters values,
in these two models they prefer to have a larger average consumption, despite being exposed to a
much larger variance. Still, the gains in terms of equivalent consumption are quite small.
In the model that includes financial frictions (Base+NR+FF) the result is different, for it
seems that here a pro-cyclical policy can reduce the variance of consumption for non-Ricardians
while it increases its average value at the same time. So in this cases there is no trade-off present.
But as can be seen the welfare gain is small, even smaller that in the other two models. Thus, in the
full model (Base+NR+FF+LBD), the results obtained without financial frictions seem to dominate
and non-Ricardians still prefer a counter-cyclical policy.
Finally, in panel C of Table 3 we use as a welfare criteria the equally-weighted average
of both agents’ individual expected utility. As we can see, the preference of Ricardians dominate
and the optimal policy is full pro-cyclicality. This is not surprising given that the welfare gains
obtained by non-Ricardians when they chose optimally were relatively small.
Overall, the results in this section are in line with the literature previously discussed that
finds that fiscal policy ought to be pro-cyclical in model with incomplete markets, particularly
for Ricardian agents. Our analysis contribute to this literature by showing that the presence of
inefficiencies that may generate social cost as in the Dutch Disease literature, that could in principle
call for a countercyclical fiscal policy, do not change this general result. We have also shown
that for non-Ricardians this choice is less trivial, although the their welfare does not seems to be
significantly altered by different degrees of pro-cyclicality.
6 Capital Controls
As we discussed in the introduction, another tool that is frequently proposed to cope with the Dutch
disease is capital controls. We model this as a tax rate τtcc charged to Ricardian household for every
unit of foreign debt d∗R
t . Moreover, we assume that the government rebates in a lump-sum fashion
the proceeding from this taxes to Ricardian, so the presence of capital controls do not interact with
the fiscal rule. Additionally, we assume for these exercises that ηrev = 0. In equilibrium, the only
condition that changes in the presence of such a tax is the intertemporal condition for holdings of
foreign debt by Ricardian households, that now reads
λt
(1 + rt∗ )
λt+1
,
=β
Et
pt
(1 − τtcc )
pt+1
25
In an economy with only Ricardian households and no other inefficiencies, a Ramsey planer would
like n
to use
tax
to offset changes in the country premium, which according to (1) is rt∗ − rtW =
this
o
∗
∗
d −d¯
exp φd t d¯∗
− 1. Thus, we consider a simple rule for τtcc of the form,28
τtcc = φτ cc (rt∗ − rtW ),
for φτ cc ∈ (−1, 1). Notice that because the country premium is proportional to foreign debt, a positive value for φτ cc implies that controls are tighter as the country receives more net capital inflows
and external financial conditions are tighter. As we motivated in the introduction, the reduction in
the country premium generated after a positive commodity shock exacerbates the increase in domestic absorption that triggers the relocation effects, which further motivates considering a policy
tool that tackles that change in the country premium.
Figure 6 shows the responses in the Base+NR+FF+LBD model obtained under three alternative values for φτ cc : 0, 0.5 and -0.5. We can see that a negative value for φτ cc contributes
to smooth the fluctuations generated by the rise in commodity prices, while the opposite happens
with a positive value. In this sense, we can refer to a negative φτ cc as prudential. Moreover, the
changes in the responses are not symmetrical. In particular, when φτ cc = 0.5 it generates a milder
absolute change in the variables (relative to φτ cc = 0) that what happens when φτ cc = 0.5.
Looking at the path of consumption for both types of agents, we can see that a prudential
capital control generates a downward shift in the whole consumption schedule relative to the case
of φτ cc = 0. Therefore, prudential capital controls will tend to reduce the variance of consumption
for both types of agents.
In addition, we can see that with prudential capital controls, the relocation between sector
is reduced: y N increases by lees and the reduction in y X is milder. This is also reflected in a smaller
real appreciation.
In table 4 the results of the welfare evaluation are displayed. In this case, Ricardian households prefer highly prudential capital controls (i.e. φopt
τ cc is close to -1) in all models. In line with
the analysis based on impulse responses, a prudential capital control reduces the variance of consumption and hours worked for these agents, rising also the average value of consumption and
reducing that of labor. It should be noticed, however, that the welfare gains of having the optimal
policy instead of no capital controls are relatively small; less than one percent of the consumption
obtained in a word without this policy tools.
On the contrary, non-Ricardians would rather have the opositive policy: capital controls
being pro-cyclical. This results seems to reflect, as analyzed also in the previous section, that these
agents value relatively more the increase in average consumption than a reduction on its variance.
In any case, the welfare gains are even smaller than those computed for Ricardians so the presence
of this policy tools does not seem to be that relevant for these agents. We have also computed the
policy that maximizes the equally-weighted average welfare, finding that the taste of Ricardians
seems to also dominate in this case.
Finally, we should notice that the desirability of prudential capital controls appears also
in the versions of the model that does not include Dutch-Disease related inefficiencies.29 In fact,
examining the welfare equivalent consumption, we can see that, for Ricardians, the gains for hav28
29
Given our calibration, the premium is zero in steady state. Thus, capital controls are also zero in steady state.
Actually, although not shown, the same result holds in the Base model with only Ricardian households.
26
Figure 6. Responses to a commodities price shock, Base+NR+FF+LBD model, different values for φτ cc .
pCo ⇒ gdp
pCo ⇒ i
pCo ⇒ c
1.5
0.2
pCo ⇒ stb
1.5
1
1
0.5
0.5
0
1
0.1
0.5
0
5
10
Co
p
15
20
0
5
10
Co
⇒ rer
p
⇒y
15
N
0
20
5
10
Co
p
⇒y
15
X
20
−0.5
0.4
0
0.2
−0.1
0.2
−0.1
0.1
5
10
Co
p
⇒i
15
N
20
0
5
10
Co
p
⇒i
15
X
20
−0.2
5
10
Co
p
⇒c
15
R
20
0
0.5
0.4
0.2
1
0
0.2
0.1
5
10
15
N
20
−0.5
pCo ⇒ rp
5
10
15
X
0
20
5
Co
⇒ rp
x 10 p
−3
0.1
10
15
20
0
pCo ⇒ cp
1
15
10
15
NR
20
15
20
5
Co
2
0
10
Co
p
0
−0.2
5
20
⇒w
p
⇒c
5
10
pCo ⇒ τcc
0
0.02
−0.02
0
0
0
−1
−0.1
5
10
15
20
−2
5
10
15
20
−0.04
5
10
15
20
−0.02
5
10
15
Note: The solid-blue, the dashed-red and the dashed-dotted-black lines correspond, respectively, to teh models with φτ cc = {0, 0.5, −0.5}. See Figure 2 for variables and unit of measure.
27
20
Table 4. Welfare evaluation: capital controls
Model
φopt
τ cc
100λR
Base+NR
Base+NR+FF
Base+NR+LBD
Base+NR+LBD+FF
-0.93
-0.88
-0.92
-0.88
-0.33
-0.16
-0.18
-0.10
Base+NR
Base+NR+FF
Base+NR+LBD
Base+NR+LBD+FF
1
1
1
1
0.13
0.06
0.08
0.04
Base+NR+LBD+FF
-0.90
-0.10
Comparision relative to φτ cc = 0
Ricardians
Non-Ricardians
St.Dev.
Mean
St.Dev. Mean
NR
c
h
c
h
100λ
c
c
A. Maximization of Ricardian Welfare
0.86 0.70 0.30 -0.05
0.04
0.70
-0.10
0.85 0.60 0.14 -0.01
0.00
0.60
-0.02
0.88 0.60 0.16 -0.03
0.03
0.60
-0.07
0.89 0.54 0.09 -0.01
0.01
0.54
-0.02
B. Maximization of Non-Ricardian Welfare
1.01 1.01 -0.11 0.04
-0.04
1.01
0.08
1.02 1.07 -0.05 0.01
-0.01
1.07
0.03
1.01 1.03 -0.07 0.03
-0.03
1.03
0.05
1.02 1.10 -0.03 0.01
-0.01
1.10
0.02
C. Welfare weight 50%
0.87 0.49 0.09 -0.01
0.01
0.49
-0.02
Note: See Table 3 for a description. Recall that hours worked are the same for both types of
agents.
ing prudential capital controls is larger in a model that does not feature either learning-by-doing
externalities or financial frictions. Therefore, the recommendation from our analysis in favor of
prudential capital controls is not due in particular to the presence of Dutch-disease concerns.
7 Tax on Domestic Lending
The final policy tool that we analyze is a tax on domestic credit. As we argued in the introduction,
given that part of the extra income from commodities will be saved, it is likely that the positive
shock will increase lending to finance capital accumulation. This additional credit will be devoted
relatively more to the N sector, as the return on capital in that sector will be relatively higher due to
the sectoral relocation. In the absence of financial frictions, there are no inefficiencies associated
with that relative distribution of credit. However, under financial frictions the relocation will be
larger, as the external finance premium in th N sector will decrease while it will rise in the X
sector.30 Therefore, to prevent this inefficiency to arise, one can consider taxing domestic credit to
compensate this effect.31
30
Given the relevance of financial frictions for this argument, we will only consider the versions of the model that
feature this characteristic.
31 Ideally, one would like to have a differential treatment in each sector: taxing lending to the N sector and subsidizing
it for X companies. We do not evaluate that alternative because, while in the model it is simple to distinguish both
sectors, it is likely that such a distinction in real life would be harder to specify. For that reason, we just consider a tax
on aggregate credit.
28
In particular, we assume that the equations characterizing the external finance premium (2)
now reads,
(
)
j
ujt+1 + (1 − δ)qt+1
Et
= (1 + rtL )rpjt (1 + τtl ),
qtj
for j = X, N. A possible, reduced-form, way to interpret the tax rate τtl is to think in a model with
banks that are subject to reserve requirements; for they would induce a gap between the rate that
households perceive from banks (1 + rtL in this case) and the opportunity cost that banks face in
lending to entrepreneurs ((1 + rtL )(1 + τtl ) in our notation). Further, we assume (as we did with
capital controls) that the government rebates in a lump-sum fashion the proceeding from this taxes
to Ricardians, so the presence of capital controls do not interact with the fiscal rule. Moreover,
we assume for these exercises that ηrev = 0. Hence, these are the only equilibrium conditions that
change in this case.
Given the motivation for considering this policy tool, we consider a simple rule of the form
lt − l
l
,
τt = φτ l
l
with φτ l ∈ [0, 1],32 and where lt is the sum of the credit to both types of entrepreneurs.33 Thus, the
tax reacts to the difference (in percentage points) of credit relative to its steady state value.
Figure 7 displays the responses in the Base+NR+FF+LBD model obtained for different
values of φτ l (0, 0.3 and 0.6). We can see that when φτ l is greater than zero, the expansion of total
credit (l) is much more limited, offsetting the effects on the premium in both sectors. In terms
of aggregate activity, a positive value for φτ l tend to smooth the expansion in investment. This
happens because, while the premium moves in both sectors, total credit is reduced and the same
will happen with investment.
In terms of consumption, the role of φτ l is different for both types of households. For
Ricardians the fact that credit is limited mildly increases their consumption in the first periods
by more than in the case without these taxes. Non-Ricardians, on the contrary, have a path for
consumption that, while in the first periods is close to the case with φτ l = 0, it lies below after
some periods when φτ l > 0. Thus, while for Ricardians it is not obvious how the variance of
consumption will be affected, for non-Ricardians the volatility of consumption will be reduced
with an active rule for these taxes.
The welfare-based analysis is presented in Table 5. The preference of both agent is quite
different. Ricardians would rather have no taxes on domestic credit,34 while non-Ricardian would
like a tax that completely offsets any increase in credit. And this results holds in both models.
For Ricardians, as shown in the impulse responses, their consumption path is not significantly
altered by a positive value of φτ l . In fact, one can verify numerically that the welfare function
is relatively insensitive to the value of φτ l . For non-Ricardians, it seems that the reduction in the
variance brought about by the positive φτ l improve their welfare. But again, the welfare gains
are relatively relatively small. Therefore, it seems that this policy tool is not that relevant from a
welfare perspective for neither type of households.
32
33
34
A stationary equilibrium ceases to exist if φτ l < 0.
Notice that we are implicitly assuming that this tax is zero in steady state.
This results also holds in models without non-Ricardian households.
29
Figure 7. Responses to a commodities price shock, Base+NR+FF+LBD model, different values for φτ l .
pCo ⇒ gdp
pCo ⇒ i
pCo ⇒ c
1.5
0.2
pCo ⇒ stb
1.5
1
1
0.5
0.5
0
1
0.1
0.5
0
5
10
15
20
0
5
pCo ⇒ rer
10
pCo ⇒ y
15
N
0
20
5
10
pCo ⇒ y
15
X
20
−0.5
0.4
0
0.2
−0.1
0.2
−0.1
0.1
5
10
Co
p
⇒i
15
N
20
0
5
10
Co
p
1.5
0.5
1
0
⇒i
15
X
20
−0.2
5
10
Co
p
⇒c
15
R
10
15
20
pCo ⇒ w
0
−0.2
5
20
0
5
10
Co
p
0.4
⇒c
15
NR
20
15
20
0.2
0.15
0.2
0.5
0
−0.5
5
10
Co
p
15
N
20
0.1
−1
⇒ rp
5
x 10
Co
p
−3
0.1
10
15
X
0
20
5
⇒ rp
10
Co
p
2
15
20
5
10
Co
⇒l
p
0.4
⇒ τL
0.015
0
0.01
0
0.2
−2
−0.1
0.05
5
10
15
20
−4
0.005
5
10
15
20
0
5
10
15
20
0
5
10
15
Note: The solid-blue, the dashed-red and the dashed-dotted-black lines correspond, respectively, to teh models with φτ l = {0, 0.3, 0.6}. See Figure 2 for variables and unit of measure.
30
20
Table 5. Welfare evaluation: tax on domestic lending.
Model
φopt
τL
Base+NR+FF
Base+NR+LBD+FF
0
0
Base+NR+FF
Base+NR+LBD+FF
1
1
Base+NR+LBD+FF
1
Comparision relative to φτ L = 0
Ricardians
Non-Ricardians
St.Dev.
Mean
St.Dev. Mean
100λ
c
h
c
h
100λ
c
c
A. Maximization of Ricardian Welfare
0.00 1.00 1.00 0.00 0.00
0.00
1.00
0.00
0.00 1.00 1.00 0.00 0.00
0.00
1.00
0.00
B. Maximization of Non-Ricardian Welfare
0.33 0.92 0.67 -0.28 0.16
-0.16
0.67
0.32
0.04 0.95 0.62 -0.03 0.03
-0.03
0.62
0.05
5. Welfare weight 50%
0.04 0.95 0.62 -0.03 0.03
-0.03
0.62
0.05
Note: See Table 3 for a description. Recall that hours worked are the same for both types of
agents.
8 Combining Different Policy Tools
Finally, we explore the possibility of combining the different policy instruments. For this exercise,
we continue to assume that the revenues collected for either capital controls or tax on domestic
credit are rebated in a lump-sum fashion to Ricardian households. We think this is a reasonable
assumption, for it is not likely that either of these two tax alternative will generate a large revenue
for the government. The analysis will me presented only for the full model (Base+NR+FF+LBD).
Table 6 show the results. For every possible combination of tools, we computed the optimal values
of the coefficients characterizing the rules according to the three alternative welfare criteria.
When we consider having both the expenditure rule and capital controls, we can see that
the optimal choice resembles what we have find for each instrument individually. In particular,
Ricardians would like to have a pro-cyclical policy and a prudential capital control, while the
opposite is true for No-Ricardians. A difference with the individual analysis is that Ricardians
would like a smaller negative value for the elasticity of capital controls that when we analyze this
tool in isolation.
A non trivial interaction appears for non-Ricardians when they can choose ηrev and φτ l at
the same time. In particular, their choice will be the opposite that they like with each policy in
isolation, for here they would like a pro-cyclical policy and a zero tax on domestic credit in these
cases.
If we allow the to chose only φτ cc and φτ l , both types of agents would also have opposite
preferences. Ricardians prefer prudential capital controls and no taxes on domestic credit, while
Non-Ricardians would rather have a pro-cyclical capital control and a high tax rate on domestic
credit.
Finally, when the three instruments are available, both households would coincide in having
a pro-cyclical expenditure rule and zero tax on domestic credit, but the would disagree on how
capital controls should behave.
31
Table 6. Welfare evaluation: combining different tools.
Welfare
opt
maximized ηrev
R
NR
50%
1
-1
1
R
NR
50%
1
1
1
R
NR
50%
R
NR
50%
φopt
τ cc
-0.44
1
-0.92
-0.88
1
-0.87
1
1
1
φopt
τl
100λ
Comparision relative to ηrev = ητ cc = φτ l = 0
Ricardians
Non-Ricardians
St.Dev.
Mean
St.Dev. Mean
c
h
c
h
100λ
c
c
-3.28 0.18 0.76 3.42
3.23 2.31 2.64 -3.00
-3.27 0.21 0.80 3.41
0.06
0.10
0.07
-0.06
-0.08
-0.07
0.76
2.64
0.80
0.12
0.21
0.14
0
0
0.65
-3.27 0.16 0.75
-3.28 0.16 0.75
-3.27 0.15 0.75
0.06
0.06
0.05
-0.06
-0.06
-0.05
0.75
0.75
0.75
0.11
0.12
0.09
0
0.79
1
-0.10 0.89 0.54 0.09 -0.01
0.06 0.97 0.73 -0.06 0.03
-0.01 0.87 0.34 0.00 0.03
0.01
-0.03
-0.03
0.54
0.73
0.34
-0.02
0.06
0.05
-3.28 0.17 0.75
-3.28 0.16 0.75
-3.27 0.14 0.75
-0.06
-0.06
-0.05
0.75
0.75
0.75
0.12
0.11
0.10
-0.18
0
0.7963 0.00
1
1
Note: See Table 3 for a description.
32
3.41
3.41
3.40
3.42
3.41
3.40
0.06
0.06
0.05
As a general conclusion for this part of the analysis, we can see that the larger effect on
welfare arise by the Ricardians taste for fiscal pro-cyclicality. Non-Ricardians, on the other hand,
seem to have a welfare function that is relatively flat in these policy parameters, so that minor
changes in the model induce different answers in terms of the policies they would prefer. However,
most of these alternative generate only minor welfare gains for them.
9 Conclusions
This paper presents a DSGE model of a small open economy with sectoral distinctions that also included non-Ricardian agents, financial frictions and a learning-by-doing externality. The inclusion
of non-Ricardians agents is relevant both as a way to meaningfully analyze to role of fiscal rules,
and also to have different perspectives in welfare evaluations. The last two model features generate
inefficient sectoral relocations after an increase in commodity income, making the Dutch disease
truly a disease. We use this model to evaluate three policy alternatives to deal with shock to commodity prices: a structural-balanced rule for government expenditures, capital controls that react
to changes in foreign financial conditions, and taxes to domestic credit to ameliorate expansions in
lending after increases in commodity income.
In terms of the expenditure rule we find that, on the one hand, Ricardian agents would rather
have a pro-cyclical rule, for such a rule will help to smooth their consumption. This is so despite
the fact that a pro-cyclical exacerbates any inefficiencies coming from either financial frictions or
LBD externalities (so the reduction of variance is more important for them than compensating for
inefficiencies). On the other hand, non-Ricardians would not necessarily prefer the same thing,
and their optimal degree of fiscal pro-cyclicality depends on the characteristics of the model. For
instance, under LBD externalities, they would rather have a counter-cyclical expenditure, as the
inefficient path of real wages generated by the combination of the externality and a pro-cyclical
policy have a negative impact on their expected consumption. On the contrary, in the presence of
financial frictions the reduction in volatility they experience with a pro-cyclical rule compensates
for the inefficient movement in real wages, making them choose a pro-cyclical policy.
The analysis of capital controls also show such a discrepancy between both types of agents.
Ricardian agents would choose a prudential rule for taxes on foreign borrowing, when these taxes
increase whenever external financial conditions are relaxes; while Non-Ricardians prefer the opposite. A prudential rule for capital controls will smooth out part of the responses generated by
movements in international prices of commodities, but for non-Ricardians it also lowers their average consumption.
Finally, both types of households also disagree on how taxes on domestic credit should
move with the credit cycle. In particular, Ricardians would rather not have this tax at all, while
non-Ricardians would prefer a tax that fully compensate any change in credit. However, the welfare
gains or loses they experience for different degrees of reaction of this tax rate to total credit is quite
small, particularly compared with the benefits of the other alternatives we have analyzed.
Going back to the motivation of the paper (namely, if these policy tools where appropriate
to deal with Dutch-disease problems originated from cyclical movements in commodity prices) we
have found that most of the results can also be obtained in versions of the model not featuring any
inefficient reallocation effects. Thus, whether one policy alternative is preferred to the other is not
related to Dutch-disease concerns.
The analysis also highlights that welfare evaluations are not trivial in stochastic models with
heterogeneous agents. In particular, in many cases we have found that non-Ricardian agents face
33
a trade-off between higher variance of their outcomes and unconditional means. For Ricardians
such a trade-off is not generally present, because for them a less volatile world increases average
consumption due to the reduction in precautionary savings. However, as non-Ricardians cannot
access any saving vehicle, their choice is generally more complicated.
We have also described that the largest gains in terms of welfare are produce when Ricardians can choose their preferred degree of fiscal pro-cyclicality. All the other alternatives deliver
only minor improvements in terms of welfare.
To conclude, we discuss some limitations of our analysis. As we mentioned in the introduction, one could also study the appropriate way to deal with Dutch-disease situations that arise not
due to cyclical movements in commodity prices but rather due to persistent changes in commodity
income. The latter can occurred due to a sudden increase in the endowment of natural resources, or
to a permanent rise in the price of the commodity. The analysis of such a situation is not trivial, for
it requires to specify how the change in commodity income will impact the long run behavior of
the economy; something that a model like ours cannot account for. Moreover, in such a framework
policies can have two different effects: to smooth the transition to the new steady state or to affect
the long run equilibrium of the economy. And it is not clear whether a trade off will arise between
these two goals, particularly in a world with uncertainty. Still, as this alternative approach is quite
relevant, we consider a promising line of future research to study the welfare consequence’s of
permanent changes in commodity-related income in model with endogenous growth.
Finally, in this paper we have focused on analyzing only simple rules for the policy alternatives that we have consider. While we think that the analysis of simple rule is of practical
relevance, one can alternatively evaluate the optimal Ramsey policy that is not constrained to a
particular simple rule. In fact, as we surveyed in section 2, much of the normative literature on the
Dutch disease has taken this approach. Therefore, given that many of the simple rules that we have
analyzed deliver only minor welfare improvements, a study that is not based on simple rules can
shed some light on how these policy instruments should be set, and what are the potential welfare
gains of using those policies. We left this alternative approach for future research.
34
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37
A
Technical Appendix
A.1 Equilibrium conditions
Ricardian Households (4):
R
λt = Uc,t
,
(E.1)
λt
(1 − τ )wt ,
pt
λt
λt+1
∗
,
= β(1 + rt )Et
pt
pt+1
R
− Uh,t
=
λt = β(1 + rtL )Et {λt+1 } ,
(E.2)
(E.3)
(E.4)
Non-Ricardian Households (2):
−
NR
Uh,t
NR
Uc,t
=
(1 − τ )wt ,
pt
R
R
p t cN
= (1 − τ )wt hN
t
t ,
(E.5)
(E.6)
Aggregate consumption (6)
h
i ǫ
1−1/ǫ
1/ǫ
T 1−1/ǫ ǫ−1
,
ct = ϕ1/ǫ cN
+
(1
−
ϕ)
c
t
t
cTt
Production of tradables (4):
1−χ
cM
t
=
,
1−χ
ǫ
pt
N
ct = ϕ N ct ,
pt
ǫ
pt
T
ct = (1 − ϕ) T ct ,
pt
T
pt
cX
cTt ,
t = χ
pX
t
M
ct = (1 − χ) pTt cTt .
cX
t
χ
χ
ψ
X αX
X 1−αX −ψ
ytX = aX
(kt−1
)
,
t (zt ) (ht )
µ
X
yt−1
zt = zt−1
w t = pX
t αX
1−µ
ytX
,
hX
t
X
uX
t = pt (1 − αX − ψ)
38
,
(E.7)
(E.8)
(E.9)
(E.10)
(E.11)
(E.12)
(E.13)
(E.14)
(E.15)
ytX
,
X
kt−1
(E.16)
Production of non-tradables (3):
N αN
N 1−αN
ytN = aN
(kt−1
)
,
t (ht )
w t = pN
t αN
(E.17)
ytN
,
hN
t
N
uN
t = pt (1 − αN )
(E.18)
ytN
,
N
kt−1
(E.19)
Entrepreneurs (6):
X
qtX ktX = nX
t + p t lt ,
X
X X ξX
X
ut+1 + (1 − δ)qt+1
qt kt
L
Et
,
= (1 + rt )rp
X
qt
nX
t lev
(E.20)
(E.21)
X
X X
X
L
X
nX
t = ϑ [ut + (1 − δ)qt ]kt−1 − pt lt−1 (1 + rt−1 ) + ι ,
(E.22)
N
qtN ktN = nN
t + p t lt ,
N N ξN
N
N
ut+1 + (1 − δ)qt+1
qt kt
L
,
= (1 + rt )rp
Et
N
qt
nN
t lev
(E.23)
(E.24)
N
N N
N
L
N
nN
t = ϑ [ut + (1 − δ)qt ]kt−1 − pt lt−1 (1 + rt−1 ) + ι ,
(E.25)
Capital and Investment (7):
ktX
pIt = qtX 1 − SX
iX
t
X
it−1
′
− SX
ktN
pIt = qtN 1 − SN
iN
t
iN
t−1
= (1 −
iX
t
X
it−1
= (1 −
′
− SN
X
δ)kt−1
iX
t
X
it−1
N
δ)kt−1
iN
t
iN
t−1
X
i
+ 1 − SX Xt
iX
t ,
it−1
+ Et
(
β
λt+1 X ′
q S
λt t+1 X
N
i
+ 1 − SN Nt
iN
t ,
it−1
iX
t+1
iX
t
iX
t+1
iX
t
2 )
,(E.27)
(E.28)
(
N N 2 )
it+1
it+1
iN
λ
t+1 N
t
′
qt+1 SN
+ Et β
,(E.29)
N
N
λt
it−1
it
iN
t
1−γ
xM
t
it =
,
1−γ
I
pt
N
it ,
xt = γ
pN
t
(E.26)
xN
t
γ
γ
39
(E.30)
(E.31)
I
xM
t = (1 − γ) pt it ,
Fiscal Policy (3):
g∗
∗
pnt gt + dg∗
t−1 (1 + rt−1 ) = revt + dt ,
Co Co,R
X
N N
Co
revt = τ pX
+ pCo
τ (s
+ sCo,∗ ) + sCo,g ,
t y t + pt y t
t yt
pnt gt +
∗
dg∗
t−1 (rt−1
+ ηr ) = η0 + rev + ηrev (revt − rev),
(E.32)
(E.33)
(E.34)
(E.35)
Aggregation and market clearing (12):
NR
N
(1 − κ)hR
= hX
t + κht
t + ht ,
(E.36)
NR
(1 − κ)cR
= ct ,
t + κct
(E.37)
g∗
∗
(1 − κ)dR∗
t + dt = dt ,
(E.38)
(1 − κ)ltR = ltX + ltN ,
(E.39)
M
it = iN
t + it ,
(E.40)
N
ytN = cN
t + xt + gt ,
(E.41)
M
impt = cM
t + xt ,
(E.42)
Co Co
X
X
expt = pX
t (yt − ct ) + pt yt ,
(E.43)
tbt = expt − impt ,
(E.44)
X
N N
Co Co
pt gdpt = pX
t y t + pt y t + pt y t ,
(E.45)
rert = 1/pt ,
(E.46)
∗
Co Co,∗
d∗t−1 (1 + rt−1
) = d∗t + tbt − pCo
(1 − τ Co ),
t yt s
∗
dt − d∗
∗
w
− 1,
rt = rt + exp φd
d∗
(E.47)
gdpm
t = pt gdpt .
(E.48)
(E.49)
Endogenous variables (49):
R
R
λ t cR
cN
hR
hN
wt
pt rtL
ct
cN
t
t
t
t
t
cTt cX
cM
pN
pTt
ytX
zt hX
ktX
ytN
t
t
t
t
hN
ktN uX
uN
qtX
qtN nX
nN
ltX
ltN
t
t
t
t
t
iX
iN
pIt
it
xN
xM
gt dg∗
revt dR∗
t
t
t
t
t
t
∗
R
∗
dt lt impt expt tbt gdpt rert rt gdpm
t
Exogenous variables (6):
N
Co
aX
rtW pCo
pX
t at yt
t
t
A.2 Steady state
We show how to compute the steady state for given values of all parameters and steady state values
¯ y Co, β, ζ, ϕ, aX that are determined endogenously to match
of exogenous variables, except for d,
40
the following steady state values: stb =
tb
,
gdpm
sCo =
pCo y Co
,
gdpm
r W , hX , hN , and pN . Also, as the
fiscal rule does not pin down the steady state level of g, we we also calibrate sg =
From (E.3), (E.4) and (E.48),
pN g
.
gdpm
β = (1 + r W )−1 , r ∗ = r W , r L = r ∗ .
From (E.30)-(E.32), (E.10)-(E.12), (E.27) and (E.29),
pI = (pN )γ , pT = (pX )χ , q X = pI , q N = pI .
From (E.21) and (E.23),
uX = q X [(1 + r L )rp − 1 + δ], uN = q N [(1 + r L )rp − 1 + δ].
From (E.17)-(E.19),
uN
k = N
p (1 − αN )aN
N
− α1
N
hN , y N = aN (hN )αN (k N )1−αN , w = pN αN
yN
.
hN
From (E.13)-(E.16),
1−ψ X 1−αX
w
h
w(1 − αX − ψ) X
X
h , a =
,
k =
X
X
u αX
p αX
kX
X
αX
1
αX
y X = (aX ) 1−ψ (hX ) 1−ψ (k X )1− 1−ψ , z = y X .
From (E.26), (E.28), (E.31), (E.32) and (E.40),
X
X
N
N
X
N
N
i = δk , i = δk , i = i + i , x = γ
pI
pN
From (E.45) and (E.49), and shares’ definitions
gdpm =
i, xM = (1 − γ) pI i.
pX y X + pN y N
sCo gdpm
g
m
Co
,
g
=
s
gdp
,
y
=
, tb = stb gdpm.
Co
Co
1−s
p
From (E.41),
cN = y N − xN − g.
From (E.42)-(E.44), (E.8) and (E.11)-(E.12),
c
M
X X
Co Co
= (1 − χ)(p y + p y
M
−x
χ cM
− tb), c =
, cT =
(1 − χ) pX
X
imp = cM + xM , exp = pX (y X − cX ) + pCo y Co.
41
cX
χ
χ
cM
1−χ
1−χ
,
From (E.7) and (E.9)-(E.10),
ϕ= 1+
pT
pN
ǫ
cT
cN
From (E.46)-(E.49),
gdp =
−1
N 1ǫ
i ǫ
h
c
1/ǫ
T 1−1/ǫ ǫ−1
N
1/ǫ
N 1−1/ǫ
c
, c= ϕ
c
+ (1 − ϕ)
, p=p
.
ϕc
gdpm
tb − pCo y Co sCo,∗ (1 − τ Co ) ¯
d∗
, rer = 1/p, d∗ =
,
d
=
.
p
r∗
gdpm
From (E.20)-(E.25),
nX =
qN kN X
q X k X − nX N
q N k N − nN
qX kX
, nN =
, l =
, l =
,
lev
lev
p
p
ιX = nX − ϑ [uX + (1 − δ)q X ]k X − plX (1 + r L ) ,
ιN = nN − ϑ [uN + (1 − δ)q N ]k N − plN (1 + r L ) .
Finally, from (E.1)-(E.2), (E.5), (E.33)-(E.35), (E.36)-(E.37) we can obtain λ, cR , cN R , hR , hN R ,
ζ, revη0 and dg∗ .
42
A.3 Welfare measure
Consider two possible equilibria: r (reference) and a (alternative). The goal is to compute which
percentage of the consumption sequence of equilibrium r is the household willing to sacrifice to
be indifferent between the r and the a equilibria, denoted by λ, where indifference is measured in
terms of unconditional expected utility. Thus, it is implicitly defined as,
(∞
)
(∞
)
X
X
E
U(cat , hat ) = E
U((1 − λ)crt , hrt ) .
(E.50)
t=0
t=0
In some cases, the utility function is such that we can solve for λ explicitly,35 but in general this may
not be the case. We will the show how to approximate λ using a second order Taylor-expansion
around the steady state in the general case.
Let σ denote the perturbation parameter that scales the variance of all the shocks in the
model. It can be shown that up to second order the unconditional expectation of a generic variable
Xt is approximated by
σ2
ss
2
E {Xt } = X + Xσ
,
2
where Xσ2 reflects how the unconditional expectation depends on σ 2 .36 Thus, we redefine the lefthand side of (E.50) as V a (σ 2 ) to reflect the fact that it will depend on the perturbation parameter,
2
and its approximation is then V a (σ 2 ) ≈ V a,ss + Vσa2 σ2 , which can be easily computed with most
computational packages such as Dynare. Similarly, for a given value of λ, the right-hand side of
(E.50), defined as V r (λ, σ 2 ), can also be approximated only as a function of σ 2 (i.e. V r (λ, σ 2 ) ≈
2
V r,ss(λ) + Vσr2 (λ) σ2 for all λ).
Therefore, given that λ is implicitly defined as V a (σ 2 ) = V r (λ, σ 2 ), it is then clear that it
2
will be a function of σ 2 that can be approximated up to second order as λ(σ 2 ) ≈ λss + λσ2 σ2 . To
compute λss , notice the because in steady state σ = 0, (E.50) yields
V a (0) = V r (λss , 0).
In many cases λss can be solved for algebraically from that equation, and if not it can be found
with a numerical solver.
To obtain λσ2 , differentiate V a (σ 2 ) = V r (λ, σ 2 ) with respect to σ 2 and evaluate at the
steady state, which yields
V a2 − V r2 (λss )
λσ2 = σ r σss
Vλ (λ )
where Vλr (λss ) denotes the second-order accurate approximation of the derivative of V r (λ, σ 2 )
with respect
at the steady state λss . This is the second-order accurate approximation
P∞to λ evaluated
ss r
of −E { t=0 Uc ((1 − λ )ct , hrt )crt }, which can also be computed using Dynare or similar.
35
36
e.g. Schmitt-Grohe and Uribe (2004)
For instance, see Andreasen et al (2014).
43