NBER WORKING PAPER SERIESTRENDS AND CYCLES IN SMALL OPEN ECONOMIES:
MAKING THE CASE FOR A GENERAL EQUILIBRIUM APPROACH
Kan Chen
Mario Crucini
Working Paper 22460
http://www.nber.org/papers/w22460

NATIONAL BUREAU OF ECONOMIC RESEARCH
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Cambridge, MA 02138
July 2016

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Trends and Cycles in Small Open Economies: Making The Case For A General Equilibrium
Approach
Kan Chen and Mario Crucini
NBER Working Paper No. 22460
July 2016
JEL No. C55,C68,F41,F44
ABSTRACT
Economic research into the causes of business cycles in small open economies is almost always
undertaken using a partial equilibrium model. This approach is characterized by two key
assumptions. The first is that the world interest rate is unaffected by economic developments inthe small open economy, an exogeneity assumption. The second assumption is that thisexogenous interest rate combined with domestic productivity is sufficient to describe equilibrium
choices. We demonstrate the failure of the second assumption by contrasting general and partial
equilibrium approaches to the study of a cross-section of small open economies. In doing so, we
provide a method for modeling small open economies in general equilibrium that is no more
technically demanding than the small open economy approach while preserving much of thevalue of the general equilibrium approach.

Kan Chen
BBVA Research
2200 Post Oak Blvd
Houston, TX 77056
kan.chen@bbva.com
Mario Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu

1Introduction

The veracity of business cycles differs dramatically across countries. Figure 1 presents acomprehensive view: it displays the standard deviation of annual output and consumption
growth rates computed over the period 1971 to 2011 for 66 countries (countries are ranked
from the most to least volatile).1 The standard deviation of output growth ranges from anastounding 24.3% in Iraq (not shown) to a mere 1.58% in Australia; the median country is
Luxembourg (3.53%). An important goal of quantitative business cycle theory is to explainthese differences.
In this respect, the work-horse small open economy model has considerable appeal because it is possible to treat the world interest rate as given (i.e. determined in the rest-of-theworld), an exogeneity assumption and conduct a partial equilibrium analysis. Aguiar and
Gopinath (2007) is a recent leading example of this approach. They argue persuasively thatmuch of the cross-country heterogeneity in the veracity of business cycles is accounted forby differences in the relative importance of permanent and transitory shocks to total factor
productivity. The logic is simple. A permanent shock leads to larger jump in consumption
than a persistent, but transitory, shock because it entails a larger wealth effect. Output, toa reasonable first-approximation, follows the path of productivity and therefore inherits thevolatility and persistence properties of the shock itself. Altering the relative importance ofthe two shocks therefore allows one to match the standard deviation of output and consumption patterns displayed in Figure 1. Applying this method to 13 emerging and 13 developed
economies, Aguiar and Gopinath find that the permanent component accounts for 84% of
productivity growth for emerging markets compared to 61% for developed countries.2
The use of a partial equilibrium model comes at a cost however, as it fails to capture
any meaningful economic interactions across nations. The most obvious is the internationalcorrelation of business cycles. To fill this gap, we revisit the study of AG, using the twocountry general equilibrium model developed by Baxter and Crucini (1995). The BC model
1 The PWT 8.1 starts from 1951 and ends in 2011. The starting year of 1971 allows for a comprehensive
and balanced cross-country panel.
2 Note, they do not report a variance decomposition of output growth in their paper, though productivity
and output tend to move closely in neoclassical models of the business cycle.

1

is a natural choice because it shares virtually all features of preferences, technology and theasset market structure of AG, while closing the model by imposing world market clearing
in the goods market and the market for one-period non-contingent bonds.
In our simulations, the ‘home’ country is parameterized to mimic the business cycle ofan aggregate of (listed in descending economic size) the United States, Japan, the United
Kingdom, Germany, Italy, France, Canada and Australia (hereafter the G-8). This massive
economic block effectively determines the world interest rate (marginal product of capital).
The ‘foreign’ country is one of the 58 economies in our panel dataset. Individual countries
are rotated through in separate model simulations to produce the entire cross-section ofbusiness cycle implications that are consistent with the domestic and foreign business cycle
facts.
Total factor productivity in the G-8 is the sum of a pure random walk component and atransitory but persistent component. Matching the standard deviation of: i) consumption
growth, ii) income growth and iii) the consumption-GDP ratio for the G-8 block yields an estimated standard deviation of 0.9% (1.2%) for the innovation to the permanent (transitory)component. The persistence of the transitory component is 0.9. The implication of theseestimates is that the transitory component contributes 58% to the standard deviation of
TFP growth, compared to 42% for the stationary component. These estimates are broadly
consistent with the less structural approach of Crucini and Shintani (2015); they estimate
a bivariate error-correction model of output and consumption growth for each country of
the G-8 and find comparable contributions of stochastic trend and cycle shocks to output
growth.
For each country outside of the G-8, we match the standard deviation of output growth,
the standard deviation of consumption and the correlation of output and consumption
growth of each country with the output and consumption growth of the G-8 block. To
accomplish this – in addition to an idiosyncratic permanent and transitory shock to productivity in each country – we allow for a spillover from the G-8 permanent and transitory
shock. The productivity spillovers from the G-8 is the point of departure from the partial2

equilibrium approach and allows us to match international business cycle comovement ofconsumption and output.3
On average (across countries), the permanent shocks account for 45% of output growth indeveloping countries compared to 51% in developed countries. These results contrast sharply
with AG who attribute 84% of productivity growth to permanent shocks for emerging markets compared to 61% for developed countries. While there are a number of differences interms of the sample of countries and sample period, the main driver of the difference is ourgeneral equilibrium approach and the additional empirical discipline of matching international business cycle comovement. We demonstrate this in two ways.
First, we use a small open economy model to match national business cycle moments(excluding international comovement) in our cross-section and find the permanent shocks
must account for twice as much of output growth for developing countries compared todeveloped countries, which is even more skewed in the direction of AG’s earlier findings.
This demonstrates that our results using the same modeling approach as AG also imply
a dominant role for permanent shocks in developing countries. The even larger roll of thepermanent shock may be a consequence of the Great Recession.
Second, shocks to the exogenous interest rate play a non-trivial role, accounting for about
25% of output growth variation in the average country (both developing and developed).
Since the real interest rate is stationary in the model, it is impossible to determine the roleof permanent and transitory shocks in accounting for real interest rate fluctuations without
a general equilibrium model. To demonstrate the identification issue, when we incorporate
the international spillovers of productivity estimated from the general equilibrium model,
the real interest rate plays almost no role in the small open economy version despite the factthat the small open economy with spillovers of productivity produces virtually the same
variance decomposition as the general equilibrium model with spillovers.
The lessons here are stark. The logical contradiction of the small open economy approachis that any comovement of business cycles through productivity transmission (or endogenous
3 Consistent with the partial equilibrium approach, there are no productivity spillovers from the small
countries to the large countries: a block-exogeneity assumption.

3

propagation) must be attributed to domestic productivity or the “world” interest rate.
Any yet, the world interest rate is not determined by the business cycle of the small open
economy leading to a fundamental issue of identification and mis-specification of the variancedecomposition.

2

The one-sector stochastic growth model

Our use of the basic one-sector, two-country stochastic growth model is motivated by two
objectives. The first is to stay as close as possible to the model specification utilized by
AG. The second is to ensure that the general equilibrium and partial equilibrium versions of
the model are structurally compatible. Three sources of novelty are introduced into theseotherwise standard models. First, careful attention is given to international productivity
spillovers from the large G-8 block to each individual nation. Second, the cross-section ofcountries is comprehensive. Third, general equilibrium and partial equilibrium models are
explicitly compared. The general equilibrium model is the one-sector, two country, DSGE
model developed by Baxter and Crucini (1995). The partial equilibrium version of this modelomits the world goods market clearing condition and adds a stochastic process to capture
the evolution of the world interest rate.4 This section begins by quickly reviewing common
features of these two versions of the one-sector model and concludes with a discussion of thedifferences.

2.1

Preferences and technology

Individuals in each country have Cobb-Douglas preferences over consumption and leisure

U (Cjt , Ljt ) = β t

1[C θ L1−θ ]1−σ ,1 − σ jt jt(1)where parameter θ ∈ (0, 1), and the inter-temporal elasticity of substitution is 1/σ.
4 AG incorporate a domestic interest rate response to home debt relative to productivity, but this plays
a minor quantitative role in their exercise.

4

The final good is produced using capital and labor. The production function is CobbDouglas and each country experiences stochastic fluctuations in the level of factor productivity, Ajt ,1−α
Yjt = Ajt Kjt
Njt α .

(2)

The stochastic processes for productivity will involve both permanent and transitory components each potentially with a component common G-8 (world) component and an idiosyncratic or nation-specific component. These stochastic processes are described in more detailbelow.
The capital stock in each country, depreciates at the rate δ and is costly to adjust:Kjt+1 = (1 − δ)Kjt + φ(Ijt /Kjt )Kjt ,(3)

where φ(·) is the adjustment cost function. As in Baxter and Crucini (1995), adjustment
costs have the following properties: i) at the steady-state, φ(I/K) = I/K and φ0 (I/K) =1 so that in the deterministic solution to the model the steady state with and without
adjustment costs are the same and ii) φ0 > 0, φ00 < 0.

2.2

Closing the model

Following Baxter and Crucini (1995), the two country general equilibrium model is closed
by imposing one intertemporal budget constraint and world goods market clearing. Theintertemporal budget constraint is:

PtB Bjt+1 − Bjt = Yjt − Cjt − Ijt(4)

where Bjt+1 denotes the quantity of bonds purchased in period t by country j. PtB is theprice of a bond purchased in period t and maturing in period t + 1. The bond is not statecontingent, it pays one physical unit of consumption in all states of the world. Implicitly
this defines, rt , the real rate of return for the bond (i.e., PtB ≡ (1 + rt )−1 < 1). The

5

price of this bond is endogenous in the two-country equilibrium model, determined by themarket-clearing condition in the world bond market.
The world goods market clearing condition is:

π0 (Y0t − C0t − I0t ) + πj (Yjt − Cjt − Ijt ) = 0,(5)where πj denotes the fraction of world GDP produced by country j. These weights arenecessary to define market clearing because the quantities in the constraint are in domestic
per capita terms.
The small open economy is closed with an inter-temporal budget constraint identical to(4). However, the discount rate follows an exogenous stochastic process describe below. In
addition, the following boundary condition is imposed:

lim β t pjt Bjt+1 = 0,t→∞where pjt is the multiplier on the inter-temporal budget constraint of the representative
agent in country j.
Parameterization of tastes and technology are set to values commonly used in the literature. The value of β is set to be 0.954, so that the annual real interest rate is 6.5%. The
parameter of relative risk aversion σ is 2 and labor’s share α in the production function is
0.58. In the Cobb-Douglas preference function, θ = 0.233. The depreciation rate of capital,
δ, is assigned a value of 0.10. The elasticity of the investment-capital ratio with respect toTobin’s Q is η = −(φ0 /φ00 ) ÷ (i/k) = 15.

2.3

Exogenous shocks

Moving from theory to quantitative implications requires estimation of the stochastic process for productivity in each country. Partial equilibrium models require specification ofstochastic processes for home country productivity and the domestic interest rate. Generalequilibrium models require the estimation of stochastic processes for both home and foreign
6

productivity since the interest rate is endogenous. Our specification and estimation method
for each of these stochastic processes is discussed in turn below.

2.3.1

Total factor productivity

Beginning with the G-8 aggregate, indexed by 0, the logarithm of productivity is the sum ofTa non-stationary and a stationary component, ln A0t = ln AP
0t +ln A0t . The non-stationary

component follows a pure random walk,

P
P
ln AP
0t = ln A0t−1 + ln ε0t ,(6)and the stationary component follows an AR(1) process:ln AT0t = ρ0 ln AT0t−1 + ln εT0t .

(7)

The innovations are drawn from independent normal distributions with different standardP
deviations: εT0t ∼ N (0, σ0T ), εP
0t ∼ N (0, σ0 ).

As the G-8 is by far the largest region and we assume that productivity spillovers are fromthe G-8 to each nation of the G-60 and not the reverse. Simulations of the closed economy
version of the benchmark model are used to estimate the parameters of the productivity
components of the G-8 (effectively this involves setting π = 1 in the general equilibrium
model described earlier). Inputs into the estimation are G-8 aggregates, constructed ascountry-size-weighted averages of output growth, consumption growth and the logarithm of
the consumption-output ratio.
Productivity parameters are chosen to match the observed sample variances of these three
key macroeconomic variables. The outcome of the moment-matching exercise is reported
in Table 1. The average difference (across countries) between the moments from the data
and from the model simulation, reported in the upper panel of the table, is less than 10%
in all cases. The estimated persistence of the stationary component of productivity is 0.90,
which, when converted to a quarterly estimate matches closely the existing closed economy
7real business cycle literature that focuses exclusively on persistent, but transitory shocks andoutput fluctuations at business cycle frequencies. It is interesting that the innovations to thepermanent and transitory components are of the same order of magnitude, with standard
deviations of 0.9 and 1.2, respectively. When combined with the estimated persistence of thestationary component, the implication is that the unconditional variance of the transitory
shock adds about 16% more to the variance of productivity growth than the permanent
shock.
The specification of total factor productivity of the small open economies (nations outsideof the G-8 block) is more novel. We have a no–spillover case and a spillover case. In the
no-spillover case, the structure is analogous to the G-8 specification:T
ln Ajt = ln AP
jt + ln Ajt .

The permanent component of TFP in country j is,

P
P
ln AP
jt = ln Ajt−1 + ln εjt ,(8)and the stationary component is an AR(1) process :ln ATjt = ρj ln ATjt−1 + ln εTjt .

(9)T
As was the case of innovations to the components of TFP of the G-8, εP
jt , εjt , are i.i.d.

draws from normal distributions both with mean zero, but different standard deviations.
For expositional convenience, the distributions are expressed as: εTjt ∼ N (0, vjT σ0T ), εP
jt ∼N (0, vjP σ0P ). Thus, vjP and vjT , are the standard deviations of the innovations to the permanent and temporary components of productivity in country j relative to their counterpartsin the G-8, estimated earlier. For purposes of parsimony and tractability, the persistenceof the transitory component of TFP in all countries is set equal to its G-8 counterpart:ρj = ρb0 = 0.90 ∀j.5
5 While this choice of persistence for the stationary component is based on maintaining some aspects of8

The second specification of total factor productivity is the correctly specified one in
the sense that it is estimated by simulating the two country general equilibrium model.
Specifically, with the G-8 productivity processes estimated from the closed economy generalequilibrium model, the stochastic process for TFP in the small open economy in the twoTP
P
country general equilibrium model is specified as: ln Ajt = ln AP
jt + ln Ajt + ωj ln A0t +ωjT ln AT0t .

The parameters ωjP and ωjT are factor loadings capturing non-stationary andstationary productivity spillovers from the G-8 to country j. These spillovers are necessary
to match international business cycle comovement patterns across the G-8 and individual
small open economies in our panel data.
Thus, the correct structural model is taken to be the two-country general equilibrium
model with a block-recursive bivariate model for TFP of country j and the G-8 (j = 0):

 
ln
A
jt 
 1


=
0
ln A0t


1

ωjP

0

1

ln AP
jt







T 
ln
A
ωjT  
jt 

 .


P 
ln
A
1

0t 


ln AT0t

As a matter of accounting, the true productivity process of the small open economy is thesum of four terms, the first two terms are permanent and temporary components coming from domestic productivity and the second two terms are permanent and temporary
productivity spillovers from the G-8.
Naturally, the response of an open economy to a permanent or temporary productivity
shock will depend on whether the shock is of home or foreign origin. As we shall see, thespillovers are necessary to match the international correlation of business cycles, which areabsent from the set of moments available using the partial equilibrium approach. This iswhat distinguishes general equilibrium analysis from partial equilibrium analysis of internatractability and symmetry across countries, it turns out this is equivalent to a quarterly persistence of 0.96
and thus consistent with the findings of Aguiar and Gopinath (2007). They estimated persistence of theirtransitory component of productivity at the quarterly frequency of 0.97 for Canada and 0.95 for Mexico,
respectively. Moreover, they find this value is close to what the persistence of transitory component of
productivity equals for a number of other developed countries.

9tional business cycles.
To estimate the nation-specific factor loadings on G-8 productivity components, ωjP andωjT , and the relative standard deviations of nation-specific productivity innovations, vjT and
vjP , the general equilibrium open economy model is used. Specifically, in each simulation,
the G-8 takes the role of the home economy and nation j (a nation outside the G-8) takes
the role of the foreign economy in the model. The relative size of the small country is set
to the fraction of world GDP that country produces, on average, over the sample period of
observation. The model is simulated for a range of values for the innovation variance of thepermanent and transitory shock to the small country relative to the G-8 value (keeping theG-8 processes as previously estimated) to match: i) the variance of GDP growth of countryj; ii) the variance of consumption growth of country j; iii) the correlation of GDP growth
between the G-8 and country j. and iv) the correlation of consumption growth between the
G-8 and country j.
The heterogeneity of business cycles across developing and developed countries is stark(see Table 2). The standard deviation of output growth is almost twice as high in developing
countries compared to developed countries, 4.93 versus 2.60. Notice also that the standard
deviation of consumption is higher than that of output in developing countries (5.93 versus
4.93) while it is lower in developed countries (2.12 versus 2.60). Recall that the permanent
income reasoning of AG plays a key role in their attributing a dominant role for permanent
shocks in developing countries to match this ranking. The additional moments to be matchedin the general equilibrium model are the international comovement of consumption growthand output growth. These correlations are also quite distinct across the two groups withstrong positive comovement of income growth (0.62) between the median developed economy
and the G-8 and positive, but lower consumption growth correlations (0.47). In contrast,
the median developing country has a near zero correlation with the G-8 business cycle byeither measure (output or consumption growth).6
6 Backus, Kehoe and Kydland (1992) coined the phrase ‘international comovement puzzle’ in recognition
that models featuring complete financial markets predict consumption growth correlations be near unity,
bounding the output correlation from above. There work focused on developed nations within the G-8
block. The puzzle is preserved in the developed nations sample and the puzzle worsens dramatically when
the sample is extended to developing countries.

10

The stochastic processes for productivity, by allowing for both idiosyncratic and common
components to permanent and transitory movements in national productivity is able tocapture both the standard deviation patterns of income and consumption growth in eachnation as well as the correlation of business cycles between each nation and the G-8 block.
It is not surprising, for example, that the standard deviation of productivity innovations are
estimated to be much higher in developing countries. Less obvious and more interesting is
a comparison of the two components that determine country-specific component of national
productivity: the innovations to the permanent component to productivity has a standard
deviation three times that of the G-8 (3.13) and that stationary component has a standard
deviation of twice that of the G-8 (1.98). In contrast, the country specific components
of national productivity are relatively smooth for the developed countries: the permanent
component has a standard deviation of innovations 0.61 times that of the G-8 and thestationary component is 0.78 times that of the G-8.
Turning to the factor loadings linking national productivity to the G-8 productivity
levels, the spillover from G-8 productivity shocks to productivity level in the developed
world is positive for both permanent and transitory shocks, but the permanent shock has
a factor loading of 1.83, almost three times that of the transitory component (0.67). The
factor loadings for developing countries are both smaller and the loading on the permanent
G-8 shock is actually negative. This pattern of spillovers are required to match the low
correlation of output growth (0.09) and negative correlation of consumption growth (-0.08)
between the G-8 and developing countries. This is where the general equilibrium incomplete
markets model is particularly useful. Essentially, what matters for consumption comovement
is the correlation of wealth in each country with that of the G-8 block. The negative factor
loading on the permanent G-8 shock for developing countries shifts output and particularly
consumption comovement toward zero for that group of nations.

112.3.2

Interest rate shocks

In the SOE model, domestic productivity shocks play a central role as they should, just as is
the case in the general equilibrium model. However, unlike the general equilibrium model,
foreign productivity shocks are not explicitly included in the set of exogenous shocks facedby small open economies and interest rate shocks are intended to summarize the relevantinternational business cycle spillovers. As there has not been any systematic research into
the ability of interest rate disturbances to capture the response of a small open economy toanything other than an an unexpected change in the interest rate itself, it seems essential
to elucidate the issue.
To explore the implications of exogenously specified interest rates we assume as Mendoza(1991) did that the discount rate follows an AR(1) process:B
B
ln Pjt= γj ln Pjt+ ln εB
jt ,(10)

where 0 < γj < 1 denotes the persistence of the logarithm of the bond price, and εB
jt is aniid draw from a normal distribution with zero mean and standard deviation σjP B .7
From a general equilibrium perspective, the bond price is redundant as it is determinedalmost entirely by G-8 productivity when the model is closed. When added as a separate
forcing process in the small open economy model along with the productivity processes,
some of the variance of output and consumption that should be attributable to domestic or
foreign productivity is incorrectly attributed to the real interest rate. Turning to the results,
Table 3 reports the persistence and innovation variance of the bond price for the two groupsof countries for two parameterizations. The column labeled “Yes” is the case in which G-8
productivity spillovers are included and the case labeled “No” are the case in which thesespillovers are absent. The contrast of these cases is intended to explore the consequences of
7 Recent extensions of this basic approach allow for a differential to arise between the domestic interest
rate and the world interest rate and for that differential to be a function of domestic productivity, as Uribe
and Yue (2006). The latter formulation is intended to allow for the possibility that changes in domestic
productivity change the probability of default and this feeds back into banks willingness to lend. While
this is an important extension of the basic framework, this formulation, once again, abstracts from thedifferential response of a country to a home and global productivity change.

12

ignoring international business cycle comovement in the moment matching exercise.
Beginning with the no-spillover case, which is most relevant to partial equilibrium calibration, the persistence averages 0.54 for developing countries and 0.69 for developed countries
while the standard deviation averages about 5.5 basis points. Including spillovers from theG-8 significantly reduces the role of interest rate shocks by: reducing the persistence needed
for both groups of countries and, particularly for the developing countries while cutting theinnovation variance in half. The diminished role of the interest rate shocks when spillovers
are included goes in the right direction in terms of general equilibrium reasoning, but amore direct evaluation is to examine the output variance decomposition across the model
variants, to which we now turn.

3

Variance Decomposition

With the calibration of the DGSE and SOE models complete, we are in a position to computevariance decomposition of output growth into the underlying exogenous sources of variation
under the null and alternative model. Recall, the null model is the two-country generalequilibrium model with international productivity spillovers.
Table 4 reports the results using the small open economy model without spillovers as
this corresponds most closely to the analysis of AG. Beginning with the pooled results for
all countries the permanent and transitory shocks account for virtually identical fractionsof output growth fluctuations, 37% (74% combined). The world interest rate accounts forthe remaining 26%. However, these averages obscure heterogeneity in the cross-section.
Dividing the sample into developing and developed countries the asymmetry point out by
AG shows up vividly: the permanent shock accounting for about 43% of the variance indeveloping countries compared to 23% in the case of developed economies. The interest rate
plays a relative minor role in both cases, but is more important for the developed economies
than the developing economies.
This no-spillover benchmark is even more stark in amplifying the role of permanent

13

shocks in developing countries than the original AG result. The result is sensitive to thesample of countries. Using 20 countries that are common across our study and theirs, thepermanent shock accounts for 30% for developing countries and 22% in developed countries.
The sensitivity to countries included in the analysis reflects substantial differences in businesscycle variability within each group, an issue we address below.
Turning to Table 5, the result when the simulation model is correctly specified as atwo country general equilibrium model with productivity spillovers, the asymmetry in thecontribution of permanent and transitory shocks across the country groups is now the reverseof what AG found. That is, the permanent shocks now play a relatively more important rolein the case of the developed countries, 51% versus 45% for developing countries. Notably
this tendency is even more pronounced in the narrower sample used by AG (51% versus35%). The right-most panel uses the partial equilibrium model with spillovers to show thatwhen the productivity processes of correctly specified, the partial equilibrium approachgives quantitatively similar results. However, this should not be construed as indicating thepotential for the partial equilibrium model to correctly identify the relevant business cycle
shocks. Recall, the spillover case was based upon the general equilibrium simulations that
also matched international business cycle comovement.
Further problems of identification are evident in the lower panel of Table 5, which breaks
the permanent and transitory components into the contributions of home productivity andG8 spillovers. In particular, the small open economy model does not reproduce the correct decomposition of the permanent and temporary components into home and foreign(spillovers). For example, in the case of developed countries, the correct decomposition of
the permanent shocks is to assign 42.7% of the variation to a spillover from the G-8. The
small open economy model assigns 30.9% to this spillover. The reason the prediction is so
far off is that the small open economy predicts that agents will respond in the same fashion
to shocks of domestic or foreign origin provided they have the same stochastic properties(i.e. permanent or transitory) whereas this is obviously not the case in a general equilibrium context where the source of the shock is of paramount importance in determining thequantitative response and often the sign of the response.
14

The results are even more apparent at the country level since the specification errors
tend to highly skewed. Figure 2 depicts the fraction of output growth variance attributable
to the permanent shocks (home and G-8 spillover) predicted by the general equilibrium andpartial equilibrium models. Since the interest rate is endogenous in the general equilibrium
model, the fraction of variance attributed to productivity is typically an upper envelope ofthat predicted by the small open economy. The reader is reminded that in this exercise
the spillovers estimated using the general equilibrium model are included in the partial
equilibrium simulations in this comparison to give the partial equilibrium model the best
chance of matching the general equilibrium null model. Since the spillovers are not identified
in the partial equilibrium model these comparisons should be viewed as lower bounds onthe errors: only if the productivity processes could be directly observed would this small
open economy specification be feasible to simulate and compare to the small open economy
results in Figure 2.
Figure 3 presents a more pragmatic comparison. It contrasts the small open economy
approach under the correct specification with productivity spillovers from G-8 and the morecommon practice (as in AG) where the small open economy model is simulated with only
domestic permanent and transitory shocks. Note that the small open economy approach getsthe correct variance decomposition on average (across countries) even when spillovers are
ignored. However, the errors of variance accounting country-by-country are obviously very
substantial and not randomly distributed in the cross-section. The role of permanent shocks
is underestimated when spillovers are ignored for developed economies, but overestimatedwhen spillovers are ignored in the case of developing countries.

4

Concluding remarks

In this paper we have compared the performance of a standard SOE model with an analytically comparable two-country DSGE model. We conducted variance decomposition for
58 small economies using both models. We find that the main limitation of the SOE modelis that it cannot capture the role of TFP spillovers from the G-8 since it ignores interna15

tional business cycle correlation in the moment-matching exercise. This result is robust in
the entire cross-section of nations, but is more quantitatively important for small developed countries, who share more of a stochastic trend in productivity with the G-8 than dodeveloping countries.
The exercise shows that is simply not true that the small open economy framework isjustifiable on the grounds that small economies do not affect the world interest rate. The
practical difficulty with the small open economy approach is that is greatly limits the abilityof researchers to capture the differential national responses of internationally integrated
economies to common and idiosyncratic shocks, be they permanent or transitory in nature.
What matters is not just how persistence the shocks are, but also how idiosyncratic theyare.
Our paper has provided a methodology that allows researchers to study economic interactions of a large number of heterogeneous and small open economies in general equilibrium
without exploding the dimensionality of the state space. Essentially it boils down to modeling a large aggregate economic region in general equilibrium with a small open economy.
One limitation of way this approach is developed here is that it abstracts from the possibility that shocks outside of the G-8 are large enough to alter the world interest rate. With
the emergence of the BRICs, for example, it seems important to extend the approach toallow for more than one block of nations to alter the equilibrium dynamics of the smaller
economies that comprise the rest of the world. We leave this extension to future work.

16

References
Aguiar, M. and G. Gopinath, “Emerging Market Business Cycles: The Cycle is theTrend,” Working Paper 10734, National Bureau of Economic Research, September 2004.
———, “Emerging Market Business Cycles: The Cycle is the Trend,” Journal of Political
Economy 115 (2007), 69–102.
Backus, D. K., P. J. Kehoe and F. E. Kydland, “International Real Business Cycles,”The Journal of Political Economy 100 (1992), 745–775.
Baxter, M. and M. J. Crucini, “Explaining Saving-Investment Correlations,” American
Economic Review 83 (June 1993), 416–36.
———, “Business Cycles and the Asset Structure of Foreign Trade,” International economic
review 36 (1995), 821–854.
Burstein, A., C. Kurz and L. Tesar, “Trade, production sharing, and the internationaltransmission of business cycles,” Journal of Monetary Economics 55 (2008), 775 – 795.
Calvo, G. A. and E. G. Mendoza, “Capital-Markets Crises and Economic Collapse in
Emerging Markets: An Informational-Frictions Approach,” American Economic Review
90 (May 2000), 59–64.
Chari, V., P. Kehoe and E. R. McGrattan, “Sudden Stops and Output Drops,”
Working Paper 11133, National Bureau of Economic Research, February 2005.
Crucini, M., The Transmission of Business Cycles in the Open Economy, Ph.D. thesis,
University of Rochester (1991).
Crucini, M. J., “Country Size and Economic Fluctuations,” Review of International Economics 5 (1997), 204–220.
Crucini, M. J., A. Kose and C. Otrok, “What are the driving forces of international
business cycles?,” Review of Economic Dynamics 14 (2011), 156–175.

17

Crucini, M. J. and M. Shintani, “Measuring international business cycles by saving fora rainy day,” Canadian Journal of Economics/Revue canadienne d’économique 48 (2015),
1266–1290.
de Walque, G., F. Smets and R. Wouters, “An Estimated Two-Country DSGE Modelfor the Euro Area and the US Economy,” Technical Report, European Central Bank, 2005.
Devereux, M. B. and A. Sutherland, “A portfolio model of capital flows to emerging
markets,” Journal of Development Economics 89 (2009), 181 – 193.
Feenstra, R. C., R. Inklaar and M. P. Timmer, “The next generation of the Penn
World Table,” The American Economic Review 105 (2015), 3150–3182.
Garcia-Cicco, J., R. Pancrazi and M. Uribe, “Real Business Cycles in Emerging
Countries?,” American Economic Review 100 (2010), 2510–31.
Heathcote, J. and F. Perri, “Financial autarky and international business cycles,”Journal of Monetary Economics 49 (2002), 601 – 627.
Mendoza, E. G., “Real Business Cycles in a Small Open Economy,” American Economic
Review 81 (September 1991), 797–818.
———, “Sudden Stops, Financial Crises, and Leverage,” American Economic Review 100(2010), 1941–66.
Neumeyer, P. A. and F. Perri, “Business cycles in emerging economies: the role ofinterest rates,” Journal of Monetary Economics 52 (2005), 345 – 380.
Obstfeld, M. and K. Rogoff, “The Six Major Puzzles in International Macroeconomics:
Is There a Common Cause?,” Working Paper 7777, National Bureau of Economic Research, July 2000.
Quah, D., “The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds,” Econometrica 60 (1992), 107–118.

18

Schmitt-Grohe, S. and M. Uribe, “Closing small open economy models,” Journal ofInternational Economics 61 (2003), 163 – 185.
Uribe, M. and V. Z. Yue, “Country spreads and emerging countries: Who drives whom?,”
Journal of International Economics 69 (2006), 6 – 36.

19

TABLE 1 – ESTIMATES of G-8 PRODUCTIVITY PROCESSES
Data

Model

GDP growth

1.78

1.80

Consumption growth

1.14

1.14

Consumption-GDP ratio

1.22

1.20

Standard deviation of:

G-8 productivity parameters
Std. dev. of permanent innovation

0.9

Persistence

0.90

Std. dev. of transitory innovation

1.2

Notes: The upper panel reports the moments of G-8 data in the first column that arematched with the model simulations reported in the second column. The closed economy
version of the model is simulated 2,700 times with the range of parameters as follows:ρb0 ∈ [0.40, 0.95], σb0T ∈ [0.006, 0.02] and σ
b0p ∈ [0.006, 0.02]. The parameters that best fit themodel to the data are reported in the lower panel.

20

TABLE 2 – ESTIMATES of G-60 PRODUCTIVITY PROCESSES
Developing

Developed

Data

Model

Data

Model

Std. Dev. of GDP

4.93

5.51

2.60

2.87

Std. Dev. of consumption

5.93

5.61

2.12

2.46

Corr. with G-8 GDP

0.09

0.09

0.62

0.61

Corr. with G-8 consumption

-0.08

-0.06

0.47

0.37

Innovation standard deviations
relative to G-8 counterparts
vjP ∈ [0.1, 15]

3.13

0.61

vjT ∈ [0.1, 15]

1.98

0.78

ωjP ∈ [−15, 15]

-0.53

1.83

ωjT ∈ [−15, 15]

0.40

0.67

Factor loadings on G-8 spillovers

21

TABLE 3 – BOND PRICE SHOCK PARAMETERS
Developing

Developed

Spillovers

Yes

No

Yes

No

Persistence

0.30

0.54

0.24

0.69

Innovation standard deviations

0.003

0.006

0.004

0.005

22

TABLE 4. OUTPUT VARIANCE DECOMPOSITIONS, SMALL OPEN ECONOMY MODEL
Variance Decomposition
Total

Number

Std. dev.

ofofCountries

OutputSource of shock

Home

Home

World

Type of shock

Permanent

Transitory

Interest rate

All Countries

36.93

36.97

26.10

100

58

4.3

Developing

43.13

30.51

26.37

100

40

4.9

Developed

23.15

51.34

25.51

100

18

2.8

AG Sample

25.70

46.72

27.58

100

20

3.1

Developing

29.97

43.03

27.00

100

9

4.0

Developed

21.81

50.07

18.12

100

11

2.3

Notes:Productivity spillovers are abstracted from in this specification because they would
not be identified using the small open economy model.

23

TABLE 5. OUTPUT VARIANCE DECOMPOSITIONS, MODEL COMPARISONS
Model

DSGE

SOE

Source of shock

Home + G8

Home + G8

Home + G8

Home + G8

Interest

Type of shock

Permanent

Transitory

Permanent

Transitory

rate

All Countries

46.9

53.1

41.3

53.2

5.4

Developing

45.2

54.8

42.8

54.4

2.7

Developed

50.8

49.2

38.0

50.5

11.5

Aguiar and Gopinath

43.3

56.7

32.6

57.0

10.4

Developing

34.9

65.1

30.2

64.0

5.8

Developed

51.0

49.0

34.8

50.8

14.4

Source of shock

Home

G8

Home

G8

Home

G8

Home

G8

Interest

Type of shock

P

P

T

T

P

P

T

T

rate

All Countries

23.6

23.4

38.5

14.6

22.5

18.8

37.9

15.3

5.4

Developing

30.6

14.6

44.2

10.6

29.5

13.4

43.6

10.8

2.7

Developed

8.1

42.7

25.8

23.4

7.1

30.9

25.3

25.2

11.5

24

Figure 1. International Business Cycles
0.15

0.1

0.05

0

Output std. dev.

Consumption std. dev.

25

Figure 2. Proportion of output growth variance accounted for by permanent shocks:
Comparison of DSGE model and SOE with productivity spillovers
100
90
80
70
60
50
40
30
20
10
0

DSGE permanent component

SOE permanent component with spillovers

26

Figure 3. Proportion of output growth variance accounted by permanent shocks:
Comparison of SOE model with productivity spillovers to SOE model without spillovers
100
90
80
70
60
50
40
30
20
10

0

SOE permanent component (with spillovers)

SOE permanent component (w/o spillovers)

27