Policy Research Working Paper 8786
Adding Space to the International Business Cycle
Girum Dagnachew Abate
Luis Servén
Development Economics
Development Research Group
March 2019
Policy Research Working Paper 8786
Abstract
Growth fluctuations exhibit substantial synchronization countries—with proximity measured by bilateral trade link-
across countries, which has been viewed as reflecting a ages or geographic distance. The latent global factor shows
global business cycle driven by shocks with worldwide a strong positive correlation with worldwide TFP growth.
reach, or spillovers resulting from local real and/or finan- Countries’ exposure to global shocks rises with their open-
cial linkages between countries. This paper brings these ness to trade and the degree of commodity specialization
two perspectives together by analyzing international growth of their economies. Despite its simplicity, the empirical
fluctuations in a setting that allows for both global shocks model fits the data well, especially for advanced countries.
and spatial dependence. Using annual data for 117 coun- Ignoring the cross-country dependence of growth, by omit-
tries over 1970–2016, the paper finds that the cross-country ting spatial effects or common shocks (or both) from the
dependence of aggregate growth is the combined result analysis, leads to a marked deterioration of the empirical
of global shocks summarized by a latent common factor model’s in-sample explanatory power and out-of-sample
and spatial effects accruing through the growth of nearby forecasting performance.
This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the
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may be contacted at lserven@worldbank.org.
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Adding Space to the International Business Cycle
en∗
Girum Dagnachew Abate and Luis Serv´
The World Bank Group
Keywords: Growth, business cycle, common factors, spatial dependence
JEL classiﬁcation: F44, C23, F62
∗
Email addresses: gabate@worldbank.org, lserven@worldbank.org. We are indebted to Paul Elhorst for helpful
comments. The views expressed here are only ours and do not necessarily reﬂect those of the World Bank, its
executive directors, or the countries they represent.
1 Introduction
The international synchronization of business cycles has long attracted academic and
policy interest. From the academic viewpoint, understanding the factors behind the
cross-country comovement of output can help shed light on the empirical validity of
diﬀerent classes of theoretical models. From the policy perspective, quantifying the
degree of business cycle commonality is a primary consideration from the point of view
of optimal currency areas and, more broadly, to assess the merits of independent
stabilization policies.
An extensive empirical literature views the international comovement of growth as the
reﬂection of a global business cycle driven by shocks aﬀecting a multitude of countries.
Following the contribution of Kose, Otrok and Whiteman (2003), a number of studies
model the cycle as the combined eﬀect of a set of global and regional (and, in some cases,
sector-speciﬁc) latent common factors; see e.g., Kose, Otrok and Prasad (2012), Crucini,
Kose, and Otrok (2011), Mumtaz, Simonelli and Surico (2011), and Karadimitropoulou
and Leon-Ledesma (2013)). This literature ﬁnds that the international business cycle
can account for a major portion of cyclical GDP ﬂuctuations – as much as 40 percent of
their variance in the case of G7 countries, according to the results of Kose, Otrok and
Whiteman (2003).
Another strand of empirical literature stresses growth interdependence arising from
economic linkages between countries or regions. This is the approach taken by the
extensive Global VAR (GVAR) literature pioneered by Pesaran, Schuermann and Weiner
(2004), and recently surveyed by Chudik and Pesaran (2016), which underscores the
real and ﬁnancial dependence across countries that arises from their bilateral goods and
assets trade. The same basic mechanisms feature in several papers taking a spatial
perspective on growth empirics. Thus, Ho, Wang and Yu (2013) ﬁnd evidence of growth
spillovers due to bilateral trade linkages between OECD countries. In the context of
a Solow model, they conclude that the estimated rate of convergence is signiﬁcantly
higher once those spatial links are taken into account. Likewise, Wang, Wong and
Granato (2015) ﬁnd that the comovement of growth across countries is well explained
by the geographic distance between them.
These two empirical literatures share a common concern, namely the dependence of
economic growth across countries and regions. But methodologically they take very
diﬀerent views. The ﬁrst literature stresses shocks with global reach, aﬀecting all
countries or regions under consideration. The second literature puts the emphasis on
the linkages generating dependence between particular countries or regions. The two
views roughly correspond to the distinction between strong and weak cross-sectional
dependence, respectively. Strong dependence arises from pervasive common shocks. In
turn, weak dependence between speciﬁc countries primarily reﬂects their economic
and/or geographic proximity.1 Strong dependence is typically analyzed with factor
models (as done, for example, by Kose, Otrok and Whiteman (2003)), while weak
dependence is typically analyzed with spatial models highlighting geographic or
economic distance (as in, e.g., Ho, Wang and Yu (2013)).
1
Strong and weak cross-sectional dependence can be deﬁned in diﬀerent ways. One commonly-used deﬁnition
bases the distinction between them on the rate at which the largest eigenvalue of the covariance matrix of the
cross-section units rises with the number of units; see Bailey, Kapetanios and Pesaran (2015).
2
So far, the empirical literature on growth interdependence and international
business cycles has taken into account one or the other form of dependence – but not
both. However, identifying correctly the type of cross-sectional dependence at work
can be quite important for estimation of and inference on empirical growth models.
While details may depend on the speciﬁc model under consideration, ignoring strong
dependence in the estimation when it is present will generally lead to inconsistent
estimates if the omitted common shocks are correlated with the model’s regressors
(Pesaran and Tosetti (2011)). Conversely, introducing common factors in the
estimation when only weak dependence is at play may similarly yield inconsistent
estimates (Onatski (2012)). In turn, the consequences of neglecting spatial dependence
when it is present depend on its precise form. If spatial dependence accrues through
the model’s error term, ignoring it will only cause loss of eﬃciency; however, ignoring
spatial dependence in the dependent variable and/or the independent variables may
produce biased and inconsistent estimates of the parameters of the remaining variables
(LeSage and Pace (2009)).
In reality, however, the two forms of dependence are likely to be simultaneously
present. Indeed, growth in a given country is likely to be aﬀected by both global
shocks and shocks to economically nearby countries – with closeness deﬁned by
bilateral trade intensity, ﬁnancial linkages, and so on. The main contribution of this
paper is to bring both perspectives together. We analyze the international
comovement of GDP growth in a sample comprising more than 100 advanced and
emerging countries, using an encompassing empirical framework including both spatial
eﬀects and common factors. This allows us to assess quantitatively the respective roles
of strong and weak cross-sectional dependence in the observed patterns of GDP growth
across the world, and to illustrate the consequences of ignoring either (or both) of
them. To our knowledge, only Bailey, Holly and Pesaran (2016), who examine the
patterns of house prices across U.S. metropolitan areas, and Vega and Elhorst (2016),
who study regional unemployment trends across the Netherlands, have employed a
similarly encompassing approach.
We assume that spatial interactions between countries occur through growth itself.
This seems a natural way to model the linkages between national economies, and is the
same approach followed by Ho, Wang and Yu (2013), as well as the GVAR literature on
global business cycle dynamics. However, it also implies that the two-step estimation
methods employed by Bailey, Holly and Pesaran (2016), who assume that the interaction
occurs through the spatial error, are not applicable. Instead, we use the quasi-maximum
likelihood (QML) estimator recently introduced by Shi and Lee (2017), which permits
joint consideration of common factors and spatial dependence in a dynamic framework.
Because the factors and their loadings are treated as parameters, and their number
grows with sample size, they pose an incidental parameter problem that introduces
asymptotic bias in the QML estimator. The bias correction developed by Shi and Lee
(2017) addresses this issue.
In light of the earlier literature, we experiment with two alternative speciﬁcations of
the spatial weight matrix that summarizes interactions between countries. We use both
a bilateral trade weight matrix, as done by Ho, Wang and Yu (2013), and a bilateral
geographical distance weight matrix, as done by Wang, Wong and Granato (2015).
Our country sample contains both advanced and developing economies. The former
3
are likely to be more deeply integrated than the latter in the international economy,
and hence more exposed to the international business cycle. Hence we also estimate
the empirical growth model on a subsample of 21 advanced countries. This allows us to
assess diﬀerences between these countries and the rest regarding the extent and nature
of cross-sectional dependence.
Estimation results using the two alternative speciﬁcations of the spatial weight
matrix show that growth exhibits signiﬁcant inertia, somewhat higher in the advanced
country subsample than in the full sample. There is strong evidence of spatial eﬀects,
summarized by a positive contemporaneous spatial lag and a negative spatial-time lag,
with both statistically signiﬁcant in virtually all speciﬁcations, implying that local
interactions are important to understand the international comovement of growth.
However, the estimated spatial eﬀects are substantially larger when modeling spatial
dependence in terms of bilateral trade. Importantly, growth also reﬂects a latent
common factor, which we interpret as capturing the global business cycle. The factor
shows a robust positive correlation with a measure of worldwide total factor
productivity – as found by Crucini, Kose, and Otrok (2011) for G-7 countries.
The model does a good job at accounting for the pattern of growth across the world
and in particular its cross-country dependence. We ﬁnd that the global cycle – as
summarized by the common factor – and spatial interactions account for a substantial
portion of the variance of GDP growth – around a quarter in the full sample, and over
half in the advanced-country subsample.
Our results also speak to the determinants of countries’ exposure to global shocks,
an issue at the core of the policy debate. We ﬁnd that the impact of the common factor
on GDP growth is signiﬁcantly bigger in countries with more open trade accounts, and
those whose production structure is more tilted towards commodities.
Finally, the paper underscores the importance of properly addressing cross-sectional
dependence, both strong and weak, in cross-country growth empirics. Ignoring it, by
omitting both common factors and spatial eﬀects, leads to a gross overstatement of the
persistence of growth. It also weakens dramatically the estimated model’s in-sample ﬁt,
as well as its out-of-sample forecasting ability. Including either the common factor or
the spatial eﬀects helps mitigate these problems, but does not fully address the cross-
sectional dependence. Including both the factor and the spatial eﬀect yields the best
model performance, in terms of both in-sample ﬁt and out-of-sample forecasting.
The rest of the paper is organized as follows. Section 2 introduces the
factor-augmented dynamic spatial model of output growth employed in the paper.
Section 3 presents the data. Section 4 reports the results, and Section 5 provides some
conclusions.
2 Analytical framework
To study the international business cycle, we use a dynamic model that allows for both
pervasive cross-sectional dependence through common factors and localized dependence
through spatial linkages. We next describe the model and summarize our estimation
approach.
4
2.1 A factor-augmented dynamic spatial model of growth
Let git denote the real output growth in country i = 1, . . . , n at time t = 1, . . . , T , and
let gt = (g1t , ..., gnt ) . We assume that gt follows a spatial dynamic panel data (SDPD)
model of the form:
gt = ρWgt + βgt−1 + λWgt−1 + Ψ ft + Vt . (1)
Thus, each country’s real output growth is related to current real output growth in
(economically) neighboring countries, W gt , where W is an n × n spatial weight matrix;
lagged real output growth in the own country, gt−1 , as well as in neighboring countries
W gt−1 ; a set of r time-varying unobserved factors ft common to all countries; and a
stochastic disturbance Vt .
This general speciﬁcation allows for both spatial dependence, unobserved common
factors and growth persistence. Spatial dependence, embedded in the spatially-lagged
dependent variable Wgt as well as its time-lagged value Wgt−1 , reﬂects the eﬀects of
current and lagged real output growth of nearby countries on the real output growth of
a particular country, see e.g Ho, Wang and Yu (2013) and Ertur and Koch (2007). The
extent of spatial dependence is measured by the contemporaneous spatial autoregressive
parameter ρ and the space-time lag coeﬃcient λ.2 The relative contribution of each
country to the overall spatial eﬀect is measured by the spatial weight matrix W, which
can be understood as providing a measure of economic proximity between countries.
In turn, the unobserved common factors ft capture systemic shocks that aﬀect real
output growth across all countries. The n × r matrix of factor loadings Ψ measures the
(possibly heterogeneous) eﬀect of the factors on each country’s growth. Finally, growth
persistence is captured by the parameter β on the lagged endogenous variable.
Equation (1) nests various models as special cases. For example, in the absence of
spatial dependence (ρ = 0 and λ = 0), equation (1) simpliﬁes to a factor-augmented
model relating real output growth to observable lagged growth plus latent common
factors, see e.g. Kose, Otrok and Whiteman (2003), Jorg and Sandra (2016) or Moench,
Ng and Potter (2013).3
In these speciﬁcations, the spatial dependence between countries is parameterized by
the n × n spatial weight matrix W . The matrix is assumed to be non-stochastic, with the
properties (i) Wij ≥ 0 for i = j , and (ii) Wij = 0 for i = j . The ﬁrst property indicates
that the elements of W are non-negative known constants. The second property states
2
The parameter λ, termed ’diﬀusion parameter’ by Shi and Lee (2017), captures spatio-temporal correlations in
output growth that may result from partial adjustment or inter-temporal decision making by economic agents, see
e.g., Tao and Yu (2012).
3
Equation (1) can also be seen as a variant of the GVAR model of Chudik and Pesaran (2016) imposing constant
β, λ and ρ across. In turn, the common factor framework in (1) encompasses individual and time period ﬁxed eﬀects
as a particular case (Shi and Lee (2017)). To see this, consider the speciﬁcation
gt = ρ Wgt + βgt−1 + λ Wgt−1 + ζ + ιξt + εt ,
where ζ = (ζ1 ζ2 · · ζ ) are individual eﬀects, and ξt are time eﬀects with ι = (1 1 · · 1) , where
ζ1 ζ2 · · ζ 1 1· · 1
Ψn = and FT = .
1 1· · 1 ξ1 ξ2 · · ξ
5
that countries are not neighbors to themselves. In empirical applications the weight
matrix W typically is row-normalized, such that n i=j Wij = 1, see Anselin (1988).
Further, deﬁne S = (I − ρW ). Assuming that S is invertible, and letting A =
S −1 (βI + λW ), equation (1) can be written as gt = Agt−1 + S −1 (Ψ ft + Vt ). Recurrent
substitution yields
∞
gt = Ah S −1 (Ψ ft−h + Vt−h ). (2)
h=0
∞
With a row-normalized spatial weight matrix W , the sequence {Ah }h=0 is summable
in absolute value, and the initial condition g0 becomes asymptotically irrelevant when
T → ∞, provided the model’s parameters lie in the region Rs = {(ρ, β, λ) : β + (λ −
ρ)ωmin + 1 > 0, β + λ + ρ − 1 < 0, β + λ − ρ + 1 > 0, β + (ρ + λ)ωmin − 1 < 0}, where
ωmin is the smallest characteristic root of the weight matrix W, see Shi and Lee (2017).4
Equation (2) helps trace out the impulse responses to a unit shock in a given country
(i.e., a particular element of Vt ) both over time and across countries, as will be discussed
in Section 4.
2.2 Estimation approach
Estimation of the model (1) poses some special issues because of the simultaneous
presence of common factors and spatial eﬀects. Both features are also present in the
empirical speciﬁcation employed by Bailey, Holly and Pesaran (2016), who use a
two-stage approach to estimate their model: they estimate the common factors and
the model’s parameters at the ﬁrst stage, and the spatial eﬀects at the second stage.
In their case, however, the spatial eﬀects accrue through the error term, while here
they accrue through the dependent variable. This implies that the two-stage
estimation approach is not applicable in our setting. The reason is that ignoring the
spatial eﬀects in the ﬁrst-stage estimation, as done by Bailey, Holly and Pesaran
(2016), would yield inconsistent estimates.
In settings more similar to ours, Kuersteiner and Prucha (2015) propose a GMM-
type estimator, while Bai and Li (2015) develop a quasi-maximum likelihood (QML)
estimator. In this paper, we employ the QML estimation approach recently developed
by Shi and Lee (2017). We provide a brief outline next, and refer the reader to Shi and
Lee (2017) for the full details.
In equation (1), let Zt = (gt−1 , Wgt−1 ). Deﬁne the parameters of the model as
η = (δ , ρ) with δ = ( λ) , σ 2 , Ψ and FT . Then the quasi-log likelihood function of the
model in equation (1) is
T
1 1 1 1
L(η, σ , Ψ, FT ) = − log 2π − logσ 2 + log |S | − 2
2
(Sgt
2 2 n 2σ nT t=1
−Zt δ − Ψ f t ) × (Sgt − Zt δ − Ψ ft ). (3)
1 1
Dropping the constant term − 2 log 2π − 2 logσ 2 , this expression can be rewritten as
4
The parameter estimates reported below satisfy these restrictions in all cases.
6
T
1 1 1
L(η, Ψ, FT ) = log |S | − log (Sgt
n 2 nT t=1
−Zt δ − Ψ f t ) × (Sgt − Zt δ − Ψ ft ) . (4)
While here the number of common factors r is assumed to be known, for the
estimation it is determined using information criteria, as will be discussed below.
Due to the presence of the factors and their loadings, the number of parameters in
the model increases with the sample size. Focusing on η as the parameter of interest, and
concentrating out the factors and their loadings applying principal component analysis,
the concentrated log-likelihood is
L(η ) = max L (η, Ψ, FT )
FT ∈RT ×r ,Ψ∈Rn×r
1 1
=log |S | − log G(η ), (5)
n n
1 n K K
where G(η ) = nT i=r+1 µi (S − k=1 Zk δk )(S − k=1 Zk δk ) . The QML estimator is
derived from the optimization problem in equation (5). The estimate of the factor
loadings Ψ is computed from the eigenvectors associated with the ﬁrst r largest
eigenvalues of (S − K k=1 Zk δk )(S −
K
k=1 Zk δk ) . The estimate of FT is obtained
analogously by switching T and n.
The QML estimator of the regression coeﬃcients is consistent and asymptotically
normal. However, it may be asymptotically biased owing to an incidental parameters
problem that arises from the presence of predetermined regressors (the lagged
dependent variable) as well as the interaction between the spatial eﬀects and the factor
loadings. To tackle this issue, Shi and Lee (2017) develop a bias correction that yields
an asymptotically normal, properly-centered estimator.5 The estimations reported
below for the speciﬁcations including common factors employ the bias-corrected
estimator; Appendix B provides a brief description of the correction.
3 Data
We use a large cross-country data set drawn from the United Nations National
Accounts database. To circumvent potential outliers and data errors, we exclude (i)
very small economies with total population less than 500,000, owing to their often
extreme volatility; (ii) countries featuring any observations with annual real GDP
growth in excess of 40%; and (iii) countries with standard deviation of real GDP
growth exceeding 10%. This yields a balanced panel of 117 countries over the period
1970-2016.6 The sample countries account for more than 90% of world GDP in 2016.
5
Vega and Elhorst (2016) also employ QML estimation in a setting featuring both spatial eﬀects and common
factors, specifying the latter as cross-sectional averages as in Pesaran and Tosetti (2011), and assuming that each
cross-sectional unit is too small to aﬀect the averages, so that they can be assumed exogenous – an assumption
unlikely to hold in our setting as the sample includes some very large economies.
6
We employ GDP growth data from the United Nations National Accounts database because it reaches up to
2016. In contrast, PWT data only reaches up to 2014. Over the common time sample, the correlation between the
GDP growth rates derived from both sources exceeds 0.99.
7
Because advanced countries feature higher trade and ﬁnancial integration (see Kose,
Terrones and Prasad (2004)) than other countries, which likely aﬀects their growth
comovement, we consider separately a sub-sample of 21 advanced economies. The full
list of countries is given in Table A1 in the appendix.
Real GDP is measured in constant U.S. dollars (expressed in international prices,
base 2010), and annual real output growth is computed as the ﬁrst diﬀerence of the log
of real GDP.
The spatial weight matrix that connects cross-sectional units (countries) is an
important element in the empirical implementation of the model. We measure the
economic distance between each pair of countries by the magnitude of their bilateral
trade, following the view that bilateral trade intensities capture economic interactions
and shock spillovers across countries, so that countries that trade more are
economically more connected, see e.g. Frankel and Rose (1998).
To construct the bilateral trade weight matrix, we use information on bilateral trade
taken from the IMF Direction of Trade Statistics (DOT). Speciﬁcally, for a pair of
countries i and j , i = j , entry i,j of the trade spatial weight matrix W is deﬁned as
Exportsij + Importsji
Wij = K =N ,
K =1 Exportsik + K =N
K =1 Importski
where Exportsij denotes the exports from country i to country j , and Importsji are
the imports of country i from country j . Once W has been computed, it is rescaled
dividing each of its elements by the sum of its corresponding row, so that the rows of
the rescaled matrix sum to unity.7
Alternatively, following Ertur and Koch (2007), we use a weight matrix W D based on
inverse squared distance. The elements of W D are deﬁned (before row normalization)
as
0 if i = j
W Dij =
dij −2 otherwise,
where dij is the great-circle distance between the capital cities of countries i and j .8
To assess the covariates of the common factors, we consider three candidate variables,
namely, (i) total factor productivity; (ii) policy uncertainty, and (iii) the U.S. short-term
real interest rate. Crucini, Kose, and Otrok (2011) ﬁnd that total factor productivity
is the leading driver of the business cycle of G-7 countries. They also ﬁnd a relatively
minor contribution of monetary policy. In turn, Baker and Bloom (2013) show that
policy uncertainty plays an important role in driving business cycles.
Total factor productivity (TFP) is computed from the standard Solow residual using
capital and labor inputs, and is drawn from the Penn World Tables version 9.0. Policy
7
Such row standardization of the weight matrix facilitates the interpretation of the model coeﬃcients, see Anselin
(1988).
8
The great-circle distance, the shortest distance between any two country capitals, is computed as: dij = radius ×
−1
cos [cos |longi − longj | coslati costlatj + sinlati sinlatj ] where radius is the Earth's radius, and lat and long are,
respectively, latitude and longitude for country capitals i and j . The latitude and longitude coordinates for each of
the country capitals in our sample were collected from the CEPII database.
8
uncertainty is measured using the U.S. policy uncertainty index of Baker, Bloom and
Davis (2016). The U.S. real interest rate is taken from the Fred dataset.
To assess the determinants of exposure to global shocks, we regress factor loadings
on a set of variables capturing countries’ policy and structural features, namely: (i)
trade openness measured as total exports plus imports as a percentage of GDP; (ii)
ﬁnancial openness measured by the Chinn-Ito index of capital account openness; (iii)
ﬁnancial depth, measured by domestic credit to the private sector as a percentage of
GDP; (iv) the extent of commodity specialization, measured by net real exports of
commodities over GDP as in Leamer (1984, 1995); (v) the degree of ﬂexibility of the
exchange rate regime, summarized by the index of de facto exchange rate arrangements
of Ghosh, Ostry, Kapan and Qureshi (2015); (vi) the size of the public sector measured
as government consumption as a percentage of GDP; and (vii) the size of the economy,
as captured by total population.
Figure 1: Average real output growth
Figure 1 depicts the time path of average real GDP growth for both the full and
advanced country samples. The trends are similar in both cases, although growth is
consistently higher in the former (3.6% on average over the entire sample period) than
in the latter (2.3%). The ﬁgure also shows major recessions at the time of the oil shock
of the mid 1970s as well as in 2008/09 following the global ﬁnancial crisis. Average
growth falls more sharply in the latter episode, and the fall is more severe for advanced
countries (see also Kose, Otrok and Prasad (2012)).
4 Empirical results
As a ﬁrst step, we compute the pairwise correlation of real output growth across
countries, and visualize it using network maps.9 Figure 2 shows the network map of
pairwise growth correlations for the full sample. The average and median correlations
are, respectively, 0.103 and 0.088. To avoid cluttering the ﬁgure, we only depict those
correlations above a threshold value of 0.4. In the network map, the correlation
9
Some studies, such as Ductor and Leiva-Leon (2016), use pairwise growth correlations to study business cycle
interdependence.
9
between two countries is indicated by the connecting line, and the position of the
countries is determined by the magnitude of the pairwise correlations, such that
countries that exhibit stronger correlations are located near each other. As shown,
most of the advanced economies locate near each other. There is a cluster of countries
featuring high pairwise correlations that comprises Austria, Belgium, Canada, France,
Germany, Italy, Spain, the Netherlands, USA and Colombia, among others. African
countries such as Togo, the Comoros and Burundi exhibit relatively low connection in
the system.
Figure 2: Real GDP growth correlation, all countries
Notes: The pairwise correlation between two countries is indicated by the
connecting line. Pairwise correlations less than 0.4 are dropped. If two countries
are not connected, it indicates the pairwise correlation is less than 0.4. The list of
countries and the corresponding codes are given in the appendix in Table A1.
Similarly, Figure 3 displays the network map of pairwise growth correlations for the
advanced countries. The average and median correlations are, respectively, 0.478 and
0.476. Because pairwise correlations are generally higher among advanced countries than
in the full sample, we use a higher threshold value of 0.6 in Figure 3. By this measure,
most of the advanced countries are connected with at least one country, except for
Greece, Ireland, Norway, New Zealand, and Switzerland. European Union countries
such as Belgium, Germany, France, the Netherlands, Portugal and Spain appear to be
connected with a larger number of countries than the rest.
10
Figure 3: Real GDP growth correlation, advanced countries
Notes: The pairwise correlation between two countries is indicated by the
connecting line. Pairwise correlations less than 0.6 are dropped. If two countries
are not connected, it indicates the pairwise correlation is less than 0.6. The list of
countries and the corresponding codes are given in the appendix in Table A1.
While the pairwise correlations indicated in Figures 2 and 3 provide a ﬁrst hint of the
extent of cross-sectional dependence of real output growth, a more formal assessment
can be made using two suitable statistics. The ﬁrst one is the cross-sectional dependence
(CD) test statistic of Pesaran (2015), which is based on a simple average of pairwise
NT N −1 N
correlation coeﬃcients. The statistic is given by N (N −1) i=1 ˆij
j =i+1 r where the
ˆij are the estimated pairwise correlation coeﬃcients. Under the null of weak cross-
r
d
sectional dependence, CD → − N (0, 1) for N → ∞ and large T ; see Pesaran (2015).
The second statistic is the exponent of cross-sectional dependence of Bailey,
Kapetanios and Pesaran (2015), deﬁned by the standard deviation of the
cross-sectional average of the observations. Speciﬁcally, the exponent α is given by
Std.(˜ xt ) = O(N α−1 ), where x ˜t is a simple cross-sectional average of observations
xit , i = 1, ...n; t = 1, ..., T deﬁned by x ˜t = N −1 N
i=1 xit . α takes a value between 0 and
1. A value of 1 indicates strong cross-sectional dependence, of the type usually
captured with (strong) factor models.10
Table 1 reports the Pesaran CD test statistic and the exponent of cross-sectional
10
In a general factor model setting the exponent of cross-sectional dependence can be interpreted as the rate at
which the factor loadings (fail to) die oﬀ as cross-sectional sample size increases, see Bailey, Kapetanios and Pesaran
(2015).
11
dependence of real GDP growth, for the full sample (left panel) and the advanced-
country sample (right panel). The CD test statistic is above 40 for both samples,
overwhelmingly rejecting the null. Table 1 also reports the exponent of cross-sectional
dependence α along with 95% conﬁdence bands, for both the advanced and full country
samples. The estimated value of α is 1 in the advanced-country sample (with a conﬁdence
region reaching well above 1) and .94 in the full sample. In both cases, the results point
to the presence of strong common factors in the output growth data, consistent with
the ﬁndings of, e.g., Kose, Otrok and Whiteman (2003).
Table 1: GDP growth: cross-sectional dependence
All countries Advanced countries
Pesaran CD statistic 42.343 41.661
Exponent of CSD 0.943 1.004
(0.906, 0.979) (0.905, 1.102)
Number of countries 117 21
Notes: GDP growth is the ﬁrst diﬀerence of the log of real GDP. ’Exponent of CSD’
is the exponent of cross-sectional dependence of Bailey, Kapetanios and Pesaran
(2015), and values in parenthesis are its 95% conﬁdence bands. The sample period
is 1970-2016.
4.1 Model estimation results
In order to estimate the factor-augmented dynamic spatial model (1), we ﬁrst need
to determine the number of unobserved common factors. To do so, we compute the
IC , BIC and HQ information criteria proposed by Choi and Jeong (2018) setting the
maximum number of factors to 5.11 The results are shown in Table 2. The upper panel of
the table reports results for the full sample, and the bottom panel reports results for the
advanced-country sample. For the full sample, both the IC and HQ criteria suggest one
factor while the BIC criterion suggests zero factors. For the advanced country sample,
the BIC and HQ suggest one factor while the IC criterion suggests two factors (by a
very narrow margin). We opt for employing one factor in all the estimations below.12
11
Setting the maximum number of factors to 3 gives very similar results.
12
Ductor and Leiva-Leon (2016) also employ a single factor to capture the common component of GDP growth
across countries.
12
Table 2: Model selection criteria
Criteria All countries
Number of factors
0 1 2 3 4
IC2 0.000 -0.054 -0.018 0.029 0.076
BIC 1.003 1.491 2.450 3.469 4.489
HQ 0.503 0.299 0.566 0.892 1.221
Advanced countries
IC2 0.000 -0.449 -0.452 -0.439 -0.408
BIC 0.144 -0.029 0.219 0.483 0.764
HQ 0.808 -2.903 -2.399 -1.749 -0.921
We turn to the main estimation results. Table 3 reports model estimates for the full
sample (left panel) and the advanced-country-sample (right panel). In each case, the two
columns in the table correspond to the two alternative spatial weight matrix-bilateral
trade and bilateral inverse distance.
Consider ﬁrst the full-sample results on the ﬁrst two columns of the table. The
coeﬃcient estimate of lagged output growth is positive and statistically signiﬁcant across
all speciﬁcations indicating a signiﬁcant degree of inertia in output growth.
Table 3: Estimation results
All countries Advanced countries
Weight matrix Trade Distance Trade Distance
gt−1 0.328 0.326 0.373 0.376
(24.748) (24.447) (12.020) (12.122)
W gt 0.286 0.110 0.422 0.195
(9.328) (5.120) (8.233) (3.941)
W gt−1 -0.104 0.035 -0.283 -0.262
(-2.069) (1.307) (-3.077) (-3.136)
Pesaran CD statistic -0.732 -0.825 0.161 -1.601
(p-value) (0.232) (0.205) (0.436) (0.055)
Exponent of CSD 0.402 0.511 0.766 0.362
R2 0.224 0.225 0.526 0.516
R¯2 0.198 0.199 0.489 0.478
Notes: GDP growth is the ﬁrst diﬀerence of the log of real GDP. ’Exponent of CSD’ is the exponent
of cross-sectional dependence of Bailey, Kapetanios and Pesaran (2015). The sample period covers
1970-2016.
Turning to the spatial eﬀects, the coeﬃcient estimate of the contemporaneous spatial
lag is positive and statistically signiﬁcant. Its magnitude is much bigger under the trade
13
weight matrix than under the distance matrix. The positive contemporaneous spatial
lag indicates that higher output growth in a country tends to raise growth of countries
nearby in terms of both bilateral trade and geographical distance. This result, consistent
with Ertur and Koch (2007) and Ertur and Koch (2011), implies that spatial spillover
eﬀects are important to understand growth, and countries cannot be treated as spatially
independent. Still, the parameter estimate on the spatial lag is much larger when using
the trade weight matrix than when using the distance matrix. Similarly, the space-time
lag is negative and statistically signiﬁcant under the trade weight matrix but becomes
insigniﬁcant under the distance weight matrix.
The factor-augmented dynamic model does a good job at capturing the
cross-sectional dependence shown in Table 1. The CD test statistic given in the
bottom panel of Table 3 ﬁnds little evidence of residual cross-sectional dependence.
The exponent of cross-sectional dependence also indicates no strong cross-sectional
dependence in the residuals of any of the speciﬁcations.
The estimates from the advanced-country sample, shown in the third and fourth
columns of Table 3, tend to follow the same sign and signiﬁcance patterns of the full-
country estimates. There are some diﬀerences, however. The estimated spatial eﬀects
are consistently larger, in absolute value, than in the full sample, likely reﬂecting the
deeper economic linkages among advanced countries relative to the rest. Like in the full
sample, the spatial eﬀects are also of larger magnitude under the trade weight matrix
than under the distance weight matrix. Further, under the latter speciﬁcation the
CD statistic hints at residual cross-sectional dependence – suggesting that geographic
distance does a poorer job than bilateral trade at capturing spatial dependence among
advanced countries.
The bottom panel of Table 3 also reports the R2 and its adjusted counterpart.13 The
model accounts for more than 20 percent of the variation of the dependent variable in
the full sample, and over 50 percent in the advanced-country sample. In the full sample,
the goodness of ﬁt is similar under both speciﬁcations of the spatial weight matrix, while
the trade matrix speciﬁcation provides the better ﬁt in the advanced country sample.
By this measure, the model’s explanatory power compares favorably with that of the
multilevel factor model of Kose, Otrok and Whiteman (2003), which accounts for some
17 and 42 percent of the variance of growth of the median country in its world and G7
samples, respectively.14
For the speciﬁcations estimated in Table 3, Tables A3 and A4 in the appendix further
report the correlation between the actual and ﬁtted values by country for the full and
advanced-country samples, respectively. The median value of the correlation is around
.45 for the full sample and over .70 for the advanced-country sample under both the
bilateral trade and inverse distance weight matrices. However, there is considerable
heterogeneity across countries, especially in the full sample. Guatemala, Romania and
Spain exhibit correlations above 0.75 under both weight matrices, while a handful of
poor countries, mostly in Sub-Saharan Africa (Benin, Burkina Faso, Guinea-Bissau,
Nepal, Senegal) show negative correlations. In the advanced country sample, two-thirds
13
R2 is measured by the square of the correlation between the actual and predicted values of the dependent
variable; see Elhorst (2014).
14
These ﬁgures are based on their Table 4, and comprise the contribution of both the global and the regional
factors in their model. Kose, Otrok and Prasad (2012) report very similar ﬁgures in their Table 1.
14
of the countries exhibit correlations above .7 under both the bilateral trade and the
distance weight matrices. In contrast, Australia and New Zealand exhibit much lower
correlations (around 0.3), indicating their (economic) remoteness within the system.
4.2 Transmission of spatial impacts
The fundamental implication of the dynamic spatial model is that a shock in a particular
country aﬀects growth not only in that country, but also in neighboring countries within
the spatial system. Incorporating the spatial interaction eﬀects helps better understand
the nature and magnitude of spillover eﬀects across countries. To illustrate the spatial
spillovers implied by the estimates of the model, consider equation (1) rewritten as:
gt = (I − ρW )−1 (βI + λW )gt−1 + (I − ρW )−1 (Ψ ft + Vt ). (6)
Then, recursive substitution shows that the eﬀect h-periods ahead of a one-time shock
to Vt is ∂g t+h
∂Vt
= [(I − ρW )−1 (βI + λW )]h (I − ρW )−1 . The short-run eﬀect is just
∂gt
∂Vt
= (I − ρW )−1 . Hence the impact of a shock hitting a particular country (i.e., a
shock to a particular element of Vt ) diminishes with distance at a rate that depends
on the elements of the weight matrix W and the spatial coeﬃcient ρ. It also declines
over time at a rate that depends on λ, β and ρ. The larger (in absolute value) these
parameters, the larger the eigenvalues of the transition matrix [(I − ρW )−1 (βI + λW )],
and the more persistent the eﬀects of the shock.
For illustration, Figure 4 reports the impact on selected countries of one-time shocks
to real output growth in the U.S., the U.K., Germany, Turkey, Mexico and Brazil. The
graphs show the response obtained with the full-sample estimates using the trade weight
matrix. In each case, the graphs show the contemporaneous response to a unit shock to
output growth, and the dynamics over the subsequent three years.15
The short-run eﬀects are, in some cases, fairly substantial. For example, a
1-percentage point shock to U.S. growth raises growth in Mexico by more than 0.8
percent. It also has sizable impacts on Brazil. Similarly, a shock to Germany raises
growth in Turkey by close to a quarter point.16
Convergence is monotonic and quite fast – after just three years, the impacts have
virtually vanished. The reason is that the eigenvalues of the transition matrix turn out
to be fairly small in absolute value (under 0.4), thus implying little persistence.
15
The standard deviation of the growth residuals is .04.
16
Under the distance speciﬁcation of the weight matrix, impacts (not reported) are much smaller.
15
Figure 4: Dynamic spatial impacts
To further illustrate the propagation of output shocks, we compute the
contemporaneous responses to a one-time shock to U.S., China and German output
growth using the full-sample estimates under the trade speciﬁcation of the weight
matrix. The results are summarized in Figure 5. In the ﬁgure, the direction of the
arrows indicates the transmission of shocks from the source country to the
(economically) neighboring countries, while the thickness of the line indicates the
magnitude of the shock spillovers. The closer a country is to the source country (in
terms of the trade weight matrix), the bigger is the spillover. Canada, Mexico,
Colombia and Haiti appear to be the most aﬀected by a U.S. output growth shock.
Output growth shocks in Germany and China have their largest impacts on Austria
and Hong Kong, respectively.
16
Figure 5: The short-run spatial transmission of shocks
(a) US
(b) China
17
(c) Germany
Notes: The graph shows the short-run transmission of a one-time shock from the
U.S., China and Germany to other countries. The thickness of the arrows in the
graph indicates the magnitude of the impact, i.e the thicker the arrow, the bigger the
impact.
4.3 The common factor and the global business cycle
A crucial element of the empirical model is the unobserved common factor driving output
growth around the world. Figure 6 depicts the common factors obtained from the model
estimation under each of the weight matrices, for both the advanced-country and the full
sample, along with the growth rate of world and advanced-country GDP. In both cases
the common factor tracks aggregate GDP growth fairly closely. For the full country
sample, the correlation of the factor with world GDP growth is .64 and .61 under the
trade and distance weight matrix, respectively. For the advanced-country subsample,
the correlations are .78 and .79.
Consistent with the ﬁndings of Kose, Otrok and Whiteman (2003), the swings in the
estimated factors reﬂect major economic episodes of the last four and a half decades –
the recessions of the mid 1970s and early 1980s, the downturn of the early 1990s, and
the ﬁnancial crisis of 2008/09. The estimated common factors are very similar across
the bilateral trade and distance matrix speciﬁcations in Table 3. For the full country
sample, their pairwise correlations exceed .92; for the advanced-country sub-sample they
exceed .97.
18
Figure 6: Output growth and common factor
(a) All countries
(b) Advanced countries
Kose, Otrok and Whiteman (2003) and Crucini, Kose, and Otrok (2011) also ﬁnd a
common factor behind worldwide and G-7 GDP growth, respectively. The latter paper
also examines the drivers of the G-7 common factor, and concludes that productivity
growth plays the leading role, in accordance with standard real business cycle models.
In contrast, measures of monetary and ﬁscal policy, oil prices, and the terms of trade
are much less important. On the other hand, more recent work by Baker and Bloom
(2013) and Baker, Bloom and Davis (2016) shows that policy uncertainty also plays
a signiﬁcant role in driving business cycles among advanced countries, with increased
uncertainty resulting in declines in aggregate output, investment, and employment.
19
Table 4: Factor covariates, trade and distance weight matrices
Variable Trade weight matrix
I II III IV
∆ TFP 0.945 3.131
(2.840) (1.920)
Uncertainty -0.149 -0.134
(-1.840) (-1.600)
Real interest rate -0.391 -0.413
(-1.490) (-1.260)
No. of obs. 43 45 45 43
R2 0.165 0.078 0.034 0.343
Distance weight matrix
∆ TFP 5.435 4.958
(2.940) (2.530)
Uncertainty -0.221 -0.142
(-1.950) (-1.270)
Real interest rate -0.027 0.127
(-0.070) (0.360)
No. of obs. 43 45 45 43
R2 0.285 0.134 0.000 0.345
Notes: The dependent variable is the common factor from the full
sample estimates in Table 3. ∆ TFP is the ﬁrst diﬀerence of
total factor productivity (TFP), Uncertainty is the log of the U.S.
economic policy uncertainty index taken from Baker, Bloom and
Davis (2016), Real interest rate is the U.S. real short-term interest
rate. T-statistics in brackets computed with heteroskedasticity and
autocorrelation consistent (HAC) standard errors. The regressions
include a constant.
To assess the covariates of the global business cycle in our much broader country
sample, Table 4 presents regressions of the estimated common factor on total factor
productivity, policy uncertainty, and the U.S. short-term interest rate, taken as a
measure of global monetary conditions. The upper panel reports the results obtained
using as dependent variable the common factor derived from the model using the trade
weight matrix, and the bottom panel reports the results obtained with the factor
estimated when using the bilateral distance weight matrix.
The univariate regression results show that total factor productivity is positively
correlated with the common factor, corroborating the ﬁndings of Crucini, Kose, and
Otrok (2011) using data for G-7 countries. Next, the uncertainty index shows a
negative sign with a statistically signiﬁcant coeﬃcient, showing that the adverse eﬀect
of uncertainty on output found by Baker, Bloom and Davis (2016) among major
advanced countries also holds in our larger country sample. In turn, the U.S.
short-term real interest rate is negatively correlated with the global factor under both
20
conﬁgurations of the weight matrix, likely reﬂecting the action of supply-side monetary
shocks (demand-side shocks should result in a positive sign). However, the regression
coeﬃcient is statistically insigniﬁcant under both weight matrices. Finally, the last
column of the table shows that when all three variables are considered jointly, they can
account for over one-third of the variation in the common factor. However, only TFP
growth remains statistically signiﬁcant.
4.4 The exposure to the global business cycle
As already noted, the common factor driving output growth across the world can be
interpreted as a summary representation of the global business cycle. A natural question
is what determines countries’ exposure to the cycle – or, in other words, the sensitivity
of their output growth to global shocks.
In our model, the factor loadings measure the response of each country’s output
growth to the common shocks. The estimated loadings (shown in Figure 7) are very
similar across the two speciﬁcations in Table 3: in the full country sample, their pairwise
correlations exceed .96, while for the advanced-country sample the correlation exceeds
.98. The loadings are positive in all cases, indicating that the global cycle aﬀects the
growth rate of all countries in the same direction. However, the magnitude of the
loadings displays considerable variation across countries. In the full sample, the largest
loadings belong to Botswana, Qatar and China when using the trade-based matrix,
and Botswana, Qatar and Singapore when using the distance weight matrix. In the
advanced-country sample, the largest loadings correspond by far to Ireland, followed by
Portugal and Finland, in both the trade-based and distance weight matrices.
Figure 7: Factor loadings
(a) All countries
21
(b) Advanced countries
It seems plausible to expect the loadings to vary systematically with key features of
countries’ structural and policy framework – such as their degree of ﬁnancial development
and/or international ﬁnancial integration. To verify this conjecture, we regress the full-
sample factor loadings on selected policy and structural indicators using the full-sample
results.
Speciﬁcally, the variables we consider are trade openness, capital account openness,
ﬁnancial depth, commodity specialization, the degree of ﬂexibility of the exchange rate
regime, the relative size of the public sector, and country size.
On theoretical grounds, trade openness should raise business cycle interdependence
by facilitating the transmission of shocks across countries, see Kose and Yi (2006),
Ductor and Leiva-Leon (2016) and Barrot, Calder´ on and Serv´ en (2018). In turn,
ﬁnancial openness plays in principle a more ambiguous role, as it might allow better
diversiﬁcation of real shocks but at the same time expose the economy to external
ﬁnancial disturbances. The same applies to domestic ﬁnancial depth. Next, a higher
degree of commodity specialization should raise the economy’s exposure to global
cycle, to the extent that it is partly driven by commodity price shocks; indeed,Barrot,
Calder´ on and Serv´en (2018) ﬁnd that commodity-intensive developing economies are
more vulnerable than the rest to both real and ﬁnancial external shocks.
In turn, exchange rate ﬂexibility helps cushion external real shocks (e.g., Broda
(2004)), but its ability to provide insulation from global ﬁnancial disturbances remains
debated. Inﬂuential work by Rey (2013) fails to ﬁnd any diﬀerence across exchange
rate regimes regarding their ability to shelter the economy from external (ﬁnancial)
shocks.17 We also include public sector size, as measured by government consumption
relative to GDP. The theoretical expectation is that a bigger public sector should help
mitigate the impact of global disturbances. Finally, following Redding and Venables
17
We employ the de facto classiﬁcation compiled by Ghosh, Ostry, Kapan and Qureshi (2015), which distinguishes
between ﬁxed, intermediate, and ﬂoating regimes. As used here, an increase in the value of the indicator variable
denotes a more ﬂexible regime.
22
(2004), we also include average population as a proxy measure of country size. In
theory, a smaller country may exhibit higher growth ﬂuctuations either because the
world interest rate is less sensitive to shocks occurring in that country and/or small
countries have relatively fewer ﬁrms and, thus are subject to higher growth ﬂuctuations,
see Giovanni and Levchenko (2012).
As the factor loadings do not change over time, the regressions only make use of the
cross-sectional variation, and therefore the explanatory variables are measured by their
respective average over the entire 46-year time sample. Over this time span, they have
surely undergone major changes, which should tend to obscure their relationship with the
loadings. Hence the regressions probably understate the strength of that relationship.
Table 5: Loading covariates regression, all countries
Variable Trade weight matrix
I II III IV V VI VII VIII
Trade opnness 0.019 0.019
(2.390) (1.750)
Financial openness -0.005 -0.003
(-0.97) ( -0.490)
Financial depth -0.003 -0.008
(-0.640) (-1.300)
Commodity specialization 0.012 0.012
(4.12) (2.790)
Exchange rate ﬂexibility -0.007 -0.007
(-0.81) (-0.750)
Public sector size -0.0004 -0.001
(-0.480) (-0.960)
Population -0.0004 0.005
(-0.130) (1.460)
R2 0.061 0.008 0.004 0.162 0.005 0.002 0.000 0.220
Distance weight matrix
Trade opnness 0.022 0.020
(2.660) (1.800)
Financial openness 0.001 0.0002
(0.230) (0.030)
Financial depth 0.0027 -0.005
(0.510) (-0.700)
Commodity specialization 0.011 0.011
(3.770) (2.630)
Exchange rate ﬂexibility -0.004 -0.003
(-0.500) (-0.320)
Public sector size -0.0002 -0.001
(-0.310) (-0.760)
Population 0.0002 0.006
(0.080) (1.580)
R2 0.081 0.001 0.003 0.144 0.002 0.041 0.001 0.247
Notes: The table shows regression of the factor loadings from the full sample estimates in Table 3 on the
variables shown. An increase in the value of the exchange rate regime variable denotes a more ﬂexible regime.
Population is the average population (in millions) during 1970-2016. T-statistics in brackets computed with
heteroscedasticity-consistent standard errors. The regressions include a constant.
23
Table 5 reports the regression results using the factor loadings as dependent
variable. The upper panel reports the results obtained from the trade weight matrix,
and the bottom panel reports the results obtained using the distance weight matrix.
The univariate regressions show that exposure to the global business cycle signiﬁcantly
increases with countries’ trade openness and commodity specialization, consistent with
the results of Barrot, Calder´on and Serv´ en (2018). This also holds true for regression
results using all the variables jointly, as shown in the ﬁnal column of the table. The
remaining variables are insigniﬁcant in both the univariate and the multivariate
regressions.
4.5 Sensitivity analysis
Finally, we examine the sensitivity of our main results to alternative ways of modeling
the cross-country dependence of output growth. Our methodological setting employs
both common factors and spatial eﬀects, in contrast with the earlier literature that
opts for one or the other. We next assess how this choice aﬀects our results. For this
purpose, we re-estimate the model omitting the common factor and the spatial eﬀects
– ﬁrst jointly and then in turn.18
The results are shown in Table 6. In the ﬁrst column, cross-sectional dependence is
ignored altogether, and common factors and spatial eﬀects are both omitted – i.e., in
terms of equation (1), we impose ρ = λ = 0 and Ψ = 0. In the second column, the
model includes a common factor but no spatial eﬀects (i.e., ρ = λ = 0). The last two
columns rule out common factors (i.e., Ψ = 0) but allow for spatial eﬀects described by
the two alternative speciﬁcations of the spatial weight matrix. The top panel of Table
6 reports the results obtained with the full sample, and the bottom panel reports those
obtained with the advanced-country sample.
The ﬁrst column of Table 6 shows that ignoring cross-sectional dependence leads to
distorted parameter estimates and to a marked deterioration of the model’s empirical
performance relative to that achieved when both spatial eﬀects and common factors
are allowed for (shown in Table 3). The parameter estimate on the lagged dependent
variable almost doubles relative to that in Table 3. Moreover, in both samples the CD
statistic and the exponent of cross-sectional dependence show overwhelming evidence of
(strong) residual dependence. In addition, the overall ﬁt of the model, as measured by
the R2 , is quite poor.
The second column of Table 6 adds a common factor but omits spatial eﬀects. The
parameter estimates of the lagged dependent variable are now much closer to those in
Table 3. In the full sample, both the CD statistic and the exponent of cross-sectional
dependence fall sharply indicating no cross-sectional dependence in the residuals. In the
advanced country sample, on the other hand, both the CD statistic and the exponent
of cross-sectional dependence also fall sharply relative to those in the ﬁrst column, but
still hint at dependence among the residuals. Finally, the ﬁt of the model shows a
considerable improvement relative to the preceding column.
18
Ertur and Musolesi (2017) also compare the estimates obtained from a factor model with those obtained from
a spatial model.
24
Table 6: Robustness checks
All countries
Spatial only
None Factor only Trade Distance
gt−1 0.592 0.329 0.379 0.400
(43.024) (24.666) (29.583) (31.170)
W gt 0.607 0.304
(31.186) (16.023)
W gt−1 0.003 0.177
(0.124) (8.084)
Pesaran CD statistic 49.889 -0.861 12.526 31.885
(p-value) (0.000) (0.195) (0.000) (0.000)
Exponent of CSD 0.910 0.462 0.670 0.827
R2 0.129 0.219 0.168 0.143
R¯2 0.074 0.194 0.166 0.132
Advanced countries
Spatial only
None Factor only Trade Distance
gt−1 0.683 0.376 0.428 0.438
(16.645) (11.983) (14.219) (14.418)
W gt 0.735 0.659
(32.452) (26.132)
W gt−1 -0.193 -0.147
(-4.612) (-3.440)
Pesaran CD statistic 40.773 2.166 3.080 7.673
(p-value) (0.000) (0.015) (0.001) (0.000)
Exponent of CSD 1.004 0.770 0.683 0.789
R2 0.163 0.503 0.461 0.424
R¯2 0.082 0.462 0.458 0.423
Notes: GDP growth is the ﬁrst diﬀerence of the log of real GDP. ’Exponent of CSD’ is
the exponent of cross-sectional dependence of Bailey, Kapetanios and Pesaran (2015).
The sample period covers 1970-2016.
The last two columns of Table 6 report estimates including spatial eﬀects, for each
of the two versions of the spatial weight matrix we consider, but excluding the common
factor. In all cases, the estimates of the parameter on the lagged dependent variable
exceed the values shown in Table 3, likely exaggerating the persistence of growth. In
turn, the spatial eﬀects are strongly signiﬁcant, except for the space-time lag under
the trade matrix in the full sample. In fact, the magnitude and the signiﬁcance of the
spatial lag parameter appear substantially overstated relative to the results shown in
25
Table 3. In turn, the cross-sectional dependence statistics show in general lower values
than in the ﬁrst column of Table 6, but the CD statistic still shows signiﬁcant evidence
against the null of weak dependence, suggesting that the spatial eﬀects alone do not do
enough to ameliorate the dependence in the data. Both the exponent of cross-sectional
dependence and the CD statistic are higher in both samples under the distance weight
matrix, which seems to imply that the problem is more acute in that setting. Lastly,
the overall ﬁt of the model, as measured by R2 , improves substantially relative to the
ﬁrst column with the addition of the spatial variables, but remains lower than that of
the factor-only model in the second column of the table. The same applies to the R ¯2,
even though the inclusion of the factor uses up a considerable number (i.e., T + N ) of
degrees of freedom.
Overall, comparison of Tables 3 and 6 shows that both the common factor and the
spatial eﬀects contribute to the model’s empirical performance – they complement each
other in their ability to account for cross-sectional dependence, and to track the variation
of the dependent variable. Inspection of the R ¯ 2 suggests that the encompassing models
in Table 3 provide the best ﬁt to the data despite their consumption of degrees of
freedom.
Table 7 reports further robustness checks on the speciﬁcation of the empirical model.
The ﬁrst two columns add to the baseline speciﬁcation in column 1 of Table 3 a spatial
error term. The spatial error is signiﬁcant only in the full-sample under the distance
weight matrix, where the contemporaneous spatial lag coeﬃcient becomes negative. The
rest of the estimates show little change relative to the baseline. In the advanced-country
sample, the parameter estimates of the space-time lag variable are insigniﬁcant, as is
that of the spatial lag under the distance weight matrix. The CD statistic suggests the
presence of residual cross-sectional dependence.
The third and fourth column employ two factors in the estimation, rather than the
single factor used in the baseline speciﬁcation as dictated by the information criteria.
The main consequence is that the spatial lag coeﬃcient becomes larger, especially under
the trade weight matrix. The spatial eﬀects follow the same pattern as in Table 3 – the
estimated coeﬃcients are larger (in absolute value) under the trade weight matrix than
under the inverse distance weight matrix. With an additional factor, the ﬁt of the model
improves relative to that in Table 3. However, in the advanced-country sample the CD
statistics continue to show evidence against the null of weak cross-sectional dependence.
26
Table 7: Further robustness checks
All countries
Spatial error Two factors
Trade Distance Trade Distance
gt−1 0.328 0.330 0.334 0.329
(24.730) (24.649) (24.842) (24.466)
W gt -0.316 -0.211 0.355 0.114
(-0.046) (-1.928) (12.276) (5.324)
W gt−1 0.077 0.144 -0.134 0.024
(0.038) (3.237) (-2.846) (0.919)
Spatial error 0.646 0.305
(0.095) (3.067)
Pesaran CD statstic 1.190 3.203 -0.580 -0.577
(p-value) (0.117) (0.001) (0.281) (0.282)
Exponent of CSD 0.694 0.701 0.487 0.482
R2 0.222 0.240 0.311 0.305
R¯2 0.197 0.215 0.260 0.258
Advanced countries
Spatial error Two factors
Trade Distance Trade Distance
gt−1 0.341 0.376 0.426 0.378
(10.884) (11.006) (13.983) (11.855)
W gt 0.539 0.211 0.779 0.244
(2.663) (0.294) (42.005) (5.051)
W gt−1 0.015 -0.262 -0.245 -0.123
(0.096) (-1.238) (-6.567) (-1.672)
Spatial error 0.390 -0.007
(1.428) (-0.009)
Pesaran CD statstic 4.060 -1.537 2.391 -3.381
(p-value) (0.000) (0.062) (0.008) (0.000)
Exponent of CSD 0.735 0.370 0.638 0.477
R2 0.572 0.516 0.694 0.630
R¯2 0.537 0.479 0.643 0.570
Notes: GDP growth is the ﬁrst diﬀerence of the log of real GDP. ’Exponent of
CSD’ is the exponent of cross-sectional dependence of Bailey, Kapetanios and
Pesaran (2015). The sample period covers 1970-2016.
4.6 Forecasting performance
Properly accounting for cross-sectional dependence can help improve the accuracy and
eﬃciency of growth forecasts. This has been illustrated by Bjornland, Ravazzolo, and
27
Thorsrud (2017) in the context of a latent factor model featuring one global factor.
They ﬁnd that exploiting the informational content of the common factor improves the
accuracy of growth forecasts across a large panel of countries.
Our empirical setting is diﬀerent for two reasons. First, it features a lagged dependent
variable. Second, it includes spatial eﬀects in addition to a common factor. To assess
the forecasting performance of our model, and in particular the respective contributions
of the spatial eﬀects and the common factor, we divide the sample into an estimation
period from 1970 to 2013 and a forecasting period from 2014 to 2016. We estimate
the model over the former period under both the distance and trade matrices, in the
latter case using a re-computed trade weight matrix covering the years 1970 to 2013.
We do this for the full model as well as the reduced models of Table 6 that exclude the
common factors and/or the spatial eﬀects – a total of four model versions under each
weight matrix and country sample. Finally, for each of the model versions featuring a
common factor, we ﬁt an autoregressive model to the estimated factor; in every case, an
AR(1) process proved suﬃcient.
Equipped with these estimates, we compute out-of-sample dynamic forecasts up to
3 years ahead. The results are reported in Table 8. The prediction performance is
measured by the root mean square error (RMSE). The upper panel reports results for
the full sample and the lower panel reports the results for the advanced country sample,
using the trade weight matrix (left three columns) and the distance weight matrix (right
three columns).
Overall, three facts stand out. First, neglecting cross-sectional dependence
altogether – by omitting both spatial eﬀects and common factors – results in abysmal
forecasting performance in all cases, especially markedly in the advanced-country
subsample. Second, in most cases the model with both common factors and spatial
eﬀects exhibits the best performance. This accords with the ﬁnding in the preceding
section that such model also oﬀers the best in-sample ﬁt. The main exception is the
speciﬁcation using the inverse distance weight matrix in the full-sample, under which
the factor-only model does best at forecasting. Third, the factor-inclusive models with
and without spatial eﬀects exhibit very similar forecasting performance – in general,
both outperform the spatial-only model (except for the 3-year forecast horizon in the
full-sample, trade-matrix case), by a margin that is especially large in the
advanced-country sample.
28
Table 8: Out-of-sample dynamic forecast performance (RMSE, percent)
All countries
Trade weight matrix Distance weight matrix
Forecast horizon 1 year 2 years 3 years 1 year 2 years 3 years
CSD speciﬁcation
None 2.870 4.605 3.733 2.870 4.605 3.733
Factor only 2.133 3.965 3.337 2.133 3.965 3.337
Spatial only 2.262 4.077 3.255 2.333 4.203 3.376
Factor and spatial 2.094 3.951 3.316 2.146 3.981 3.357
Advanced countries
Trade weight matrix Distance weight matrix
None 2.079 5.143 1.955 2.079 5.143 1.955
Factor only 1.541 4.562 1.016 1.541 4.562 1.016
Spatial only 1.930 5.045 1.671 1.926 5.050 1.690
Factor and spatial 1.521 4.498 0.957 1.491 4.475 0.999
Notes: The table shows the RMSE of dynamic forecasts over 2014-2016 obtained
with model estimates using data for 1970-2013 under alternative speciﬁcations of
cross-sectional dependence. Speciﬁcations including a common factor use an AR(1)
model to predict its future values.
5 Conclusion
Output growth displays substantial comovement across countries. Existing empirical
literature has modeled the cross-sectional dependence of growth as reﬂecting either
localized linkages across countries or regions, or pervasive common shocks – i.e., weak
and strong cross-sectional dependence, respectively. In this paper we have brought
both perspectives together by assessing the international comovement of GDP growth
in a setting that allows for both spatial dependence and latent common factors, using
annual GDP growth data over the years 1970–2016 for 117 advanced and developing
countries.
In the paper’s empirical setting, the dynamics of growth reﬂect the action of global
common factors as well as spatial eﬀects accruing through the growth of economically
neighboring countries. Estimation employs a bias-corrected quasi-maximum likelihood
procedure recently developed by Shi and Lee (2017), alternatively considering all 117
sample countries, or a subsample of 21 advanced economies. To capture the interactions
among countries, we employ two alternative spatial weight matrices – one based on
bilateral trade, and another based on geographic distance. To determine the number
of latent common factors driving GDP growth across the world, we use a variety of
information criteria. On the whole, they indicate the presence of a single factor for both
country samples considered.
Under the two alternative speciﬁcations of the spatial weight matrix and for the
29
two samples considered, growth reﬂects the action of global shocks, as captured by a
latent common factor which, as in Kose, Otrok and Whiteman (2003), we interpret as
summarizing the ’global business cycle’. Also, growth displays signiﬁcant inertia. In
addition, there is strong evidence of spatial eﬀects, both contemporaneous and lagged
– although their magnitude is consistently larger under the trade weight matrix than
under the spatial weight matrix. The implication is that both global shocks and local
interactions are important to understand the cross-country comovement of output
growth.
In turn, the estimated common factor is strongly positively correlated with worldwide
TFP growth, in line with the predictions of the standard real business cycle model.
Despite its simplicity, the empirical model does a good job at accounting for observed
growth patterns: it accounts for over 50 percent of the variation of GDP growth in the
advanced-country subsample, and over 20 percent in the full country sample.
Our results also shed light on the determinants of countries’ exposure to global shocks,
an issue at the core of the policy debate. We ﬁnd that the impact of the common factor
on real output growth is bigger in countries that exhibit higher trade openness and a
larger degree of specialization on commodities.
Our results also illustrate the consequences of improperly ignoring cross-sectional
dependence when analyzing cross-country growth patterns. Omitting both common
factors and spatial eﬀects from the empirical model causes major distortions in the
parameter estimates, leading in particular to a gross overstatement of the persistence
of growth. It also results in a sharp deterioration of the model’s explanatory power,
as well as its out-of-sample forecasting performance. Adding the common factor, while
still omitting spatial eﬀects, helps correct these problems, but leaves evidence of residual
dependence in the advanced-country sample. In turn, allowing for spatial eﬀects, while
omitting the common factor, also improves the ﬁt and parameter estimates, but leads
to overstated spatial eﬀects, strong residual dependence, and – in virtually all scenarios
considered – inferior forecasting performance.
In summary, the paper’s encompassing speciﬁcation including common factors along
with spatial eﬀects oﬀers the best performance in terms of both in-sample ﬁt and out-of-
sample forecasting. Overall, these results conﬁrm the need to account for cross-sectional
dependence, both strong and weak, in empirical modeling of growth across countries.
30
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Appendix A: Additional tables
Table A1: List of countries
All countries Advanced countries
Country ISO Code Country ISO code Country ISO Code
1 Albania ALB 61 Lesotho LSO 1 Australia AUS
2 Algeria DZA 62 Madagascar MDG 2 Austria AUT
3 Angola AGO 63 Malawi MWI 3 Belgium BEL
4 Argentina ARG 64 Malaysia MYS 4 Canada CAN
5 Australia AUS 65 Mali MLI 5 Denmark DNK
6 Austria AUT 66 Mauritania MRT 6 Finland FIN
7 Bahrain BHR 67 Mauritius MUS 7 France FRA
8 Bangladesh BGD 68 Mexico MEX 8 Germany DEU
9 Belgium BEL 69 Mongolia MNG 9 Greece GRC
10 Benin BEN 70 Morocco MAR 10 Ireland IRL
11 Bhutan BTN 71 Mozambique MOZ 11 Italy ITA
12 Bolivia BOL 72 Myanmar MMR 12 Japan JPN
13 Botswana BWA 73 Namibia NAM 13 Netherlands NLD
14 Brazil BRA 74 Nepal NPL 14 New Zealand NZL
15 Bulgaria BGR 75 Netherlands NLD 15 Norway NOR
16 Burukina Faso BFA 76 New Zealand NZL 16 Portugal PRT
17 Burundi BDI 77 Nicaragua NIC 17 Spain ESP
18 Cambodia KHM 78 Niger NER 18 Sweden SWE
19 Cameroon CMR 79 Nigeria NGA 19 Switzerland CHE
20 Canada CAN 80 Norway NOR 20 United Kingdom GBR
21 Chad TCD 81 Oman OMN 21 United States USA
22 Chile CHL 82 Pakistan PAK
23 China CHN 83 Panama PAN
24 Colombia COL 84 Paraguay PAR
25 Comoros COM 85 Peru PER
26 Costa Rica CRI 86 Philippines PHL
27 Cyprus CYP 87 Poland POL
28 Cote d’Ivoire CIV 88 Portugal PRT
29 Congo, Dem. Rep COG 89 Qatar QAT
30 Denmark DNK 90 Korea, Dem. Peopl’s R. KOR
31 Djibouti DJI 91 Romania ROM
32 Dominican Republic DOM 92 Saudi Arabia SAU
33 Ecuador ECU 93 Senegal SEN
34 Egypt EGY 94 Sierra Leone SLE
35 El Salvador SLV 95 Sigapore SGP
36 Ethiopia ETH 96 South Africa ZAF
37 Fiji FJI 97 Spain ESP
38 Finland FIN 98 Sri Lanka LKA
39 France FRA 99 Sudan SDN
40 Germany DEU 100 Swaziland SWZ
41 Ghana GHA 101 Sweden SWE
42 Greece GRC 102 Switzerland CHE
43 Guatemala GTM 103 Syria SYR
44 Guinea GIN 104 Thailand THA
45 Guinea Bissau GNB 105 Togo TGO
46 Haiti HTI 106 Trinidad and Tobago TTO
47 Honduras HND 107 Tunisia TUN
48 Hong Kong HKG 108 Turkey TUR
49 Hungary HUN 109 Uganda UGA
50 India IND 110 United Arab Emirates ARE
51 Indonesia IDN 111 United Kingdom GBR
52 Iran IRN 112 United Republic, Tanzania TZA
53 Ireland IRL 113 United States USA
54 Isreal ISR 114 Uruguay URY
55 Italy ITA 115 Venezuela VEN
56 Jamaica JAM 116 Viet Nam VNM
57 Japan JPN 117 Zambia ZAM
58 Jordan JOR
59 Kenya KEN
60 Lao PDR LAO
34
Table A2: Data sources and deﬁnition
Variable Deﬁnition Source
GDP growth The ﬁrst diﬀernce of log real GDP United Nations National Accounts
Bilateral Trade Bilateral trade ﬂow IMF (DOTS)
Total factor productivity Computed from Solow residual using labor and capital inputs PWT
35
Trade openness Sum of total exports and imports over GDP WDI
Commodity intensity Net Exports of Commodities over GDP UN/COMTRADE
Exchange rate ﬂexibility De facto exchange rate regime Gosh, Ostry and Qureshi (2015)
Financial depth Domestic credit to private sector (% of GDP) WB, WDI
Capital account openness Chin-Ito Index of Capital account Liberalization Chin-Ito
Short-term real interest rate U.S. short-term real interest rate FRED
Uncertainty U.S. economic policy uncertainty index Baker, Bloom and Davis (2016)
Public sector size Government consumption (% of GDP) WDI
Population Average population in millions United Nations National Accounts
Table A3: Correlation between actual and ﬁtted values: All countries, trade and distance weight
matrices
Country Trade Distance Country Trade Distance
Albania 0.356 0.382 Malawi 0.001 -0.023
Algeria 0.019 0.026 Malaysia 0.561 0.590
Angola 0.457 0.504 Mali 0.046 -0.027
Argentina 0.344 0.383 Mauritania 0.162 0.177
Australia 0.206 0.183 Mauritius 0.275 0.337
Austria 0.632 0.523 Mexico 0.665 0.544
Bahrain 0.392 0.334 Mongolia 0.645 0.659
Bangladesh 0.234 0.326 Morocco -0.149 -0.201
Belgium 0.660 0.613 Mozambique 0.525 0.457
Benin -0.088 -0.077 Myanmar 0.566 0.554
Bhutan 0.270 0.312 Namibia 0.444 0.344
Bolivia 0.645 0.693 Nepal -0.137 -0.141
Botswana 0.505 0.596 Netherlands 0.733 0.598
Brazil 0.617 0.630 New Zealand 0.345 0.345
Bulgaria 0.634 0.645 Nicaragua 0.268 0.290
Burkina Faso -0.029 -0.086 Niger 0.053 0.051
Burundi 0.117 0.102 Nigeria 0.478 0.465
Cambodia 0.565 0.571 Norway 0.639 0.601
Cameroon 0.501 0.516 Oman 0.180 0.150
Canada 0.742 0.683 Pakistan 0.133 0.176
Chad 0.265 0.278 Panama 0.360 0.372
Chile 0.495 0.528 Paraguay 0.473 0.477
China 0.029 0.053 Peru 0.495 0.500
Colombia 0.671 0.690 Philippines 0.642 0.620
Comoros 0.044 0.147 Poland 0.623 0.630
Costa Rica 0.612 0.588 Portugal 0.688 0.597
Cyprus 0.446 0.482 Qatar 0.543 0.532
Cote d’Ivoire 0.355 0.348 Korea, Dem. Peopl’s R. 0.417 0.404
Congo, Dem. Rep 0.746 0.774 Romania 0.778 0.794
Denmark 0.548 0.472 Saudi Arabia 0.443 0.510
Djibouti 0.165 0.210 Senegal -0.127 -0.170
Dominican Republic 0.448 0.474 Sierra Leone 0.399 0.397
Ecuador 0.483 0.501 Sigapore 0.602 0.627
Egypt 0.269 0.301 South Africa 0.644 0.641
El Salvador 0.748 0.715 Spain 0.811 0.760
Ethiopia 0.383 0.373 Sri Lanka 0.259 0.223
Fiji 0.000 0.017 Sudan 0.218 0.213
Finland 0.688 0.674 Swaziland 0.445 0.418
France 0.764 0.714 Sweden 0.547 0.470
Germany 0.645 0.598 Switzerland 0.605 0.565
Ghana 0.469 0.479 Syria 0.318 0.322
Greece 0.568 0.557 Thailand 0.557 0.534
Guatemala 0.855 0.880 Togo 0.203 0.198
Guinea 0.104 0.086 TrinidadTobago 0.703 0.692
Guinea-Bissau -0.211 -0.184 Tunisia 0.298 0.284
Haiti 0.191 0.221 Turkey 0.309 0.296
Honduras 0.579 0.548 Uganda 0.517 0.525
Hong Kong 0.572 0.681 United Arab Emirates 0.417 0.468
Hungary 0.658 0.668 United Kingdom 0.516 0.374
India 0.015 0.035 United Republic,Tanzania 0.515 0.472
Indonesia 0.495 0.465 United States 0.601 0.605
Iran 0.383 0.375 Uruguay 0.626 0.687
Ireland 0.419 0.408 Venezuela 0.427 0.441
Isreal 0.409 0.402 Viet Nam 0.252 0.283
Italy 0.720 0.645 Zambia 0.336 0.329
Jamaica 0.416 0.322 Median 0.448 0.465
Japan 0.624 0.580
Jordan 0.508 0.511
Kenya 0.495 0.479
Lao PDR 0.041 0.019
Lesotho 0.271 0.252
Madagascar -0.042 -0.143
36
Table A4: Correlation between actual and ﬁtted values: Advanced countries, trade and distance
weight matrices
Country Trade Distance
Australia 0.338 0.331
Austria 0.705 0.677
Belgium 0.755 0.745
Canada 0.793 0.780
Denmark 0.709 0.712
Finland 0.829 0.841
France 0.850 0.859
Germany 0.767 0.808
Greece 0.644 0.646
Ireland 0.682 0.598
Italy 0.822 0.828
Japan 0.701 0.721
Netherlands 0.823 0.814
NewZealand 0.320 0.327
Norway 0.638 0.663
Portugal 0.805 0.806
Spain 0.880 0.874
Sweden 0.729 0.751
Switzerland 0.641 0.655
UnitedKingdom 0.711 0.728
UnitedStates 0.779 0.816
Median 0.729 0.745
37
Appendix B: Bias correction procedure
Here we brieﬂy summarize the bias correction proposed by Shi and Lee (2017). In
order to derive the limiting distribution of the estimators η ˆT and the associated
asymptotic bias, consider G(η ) = nT i=r+1 µi (S − k=1 Zk δk )(S − K
1 n K
k=1 Zk δk ) from
equation (5) is expressed around the initial value η0 . Under appropriate assumptions,
using the perturbation theory of linear operators the limiting distribution of ηˆ around
η0 can be derived as
√ d
η − η0 ) − (σ0
nT (ˆ 2
− N (0, Q−1 (Q + Σ)Q−1 ),
Q)−1 ϕ→ (A1)
σ2 T −1
where ϕ = (ϕβ , ϕλ , 01 × (K − 2), ϕρ ) , with ϕβ = − √nT
0
h=1 tr(J0 PFT Jh )tr(Ah−1 S −1 )
2 T −1
σ 0 h−1 −1
ϕλ = − √ nT h=1 tr (J0 PFT Jh )tr (W A S ),
2
σ0 T −1
ϕρ = − √nT h=1 tr(J0 PFT Jh )tr(βG + λGW )Ah−1 S −1 + T σ 2 ( r0 tr(G − tr(Pψ G)),
n 0 n
A = S −1 (βI + λW ), S = I − ρW, G = W S −1 , Jh = (0T ×(T −h) , IT , 0T ×h ) ,
0 ... 0 0
. . .
. . .
. . .
1
QT = π π +
2 T T
0 . . . 0 0 0
nT σ0
0 . . . 0 Υ
K +1,K +1 ΥK +1,K +2
0 . . . 0 ΥK +1,K +2 ΥK +2,K +2
where πT = (π1 . . . πK +1 0), with πk = vec(MT Zk MF ), k = 1, . . . , K + 1;
1 1 1
ΥK +1,K +1 = n tr(GG ) + n tr(G2 ) − 2( n tr(G))2 ,
1
ΥK +1,K +2 = n tr(GG ˜ ) + 1 tr(G˜ 2 ) − 2( 1 tr(G˜ ))2
n n
1
ΥK +2,K +2 = n ˜G
tr(G ˜ 2 ) − 2( 1 tr(G
˜ ) + 1 tr(G ˜ ))2 , and the expression for Σ is given in Shi
n n
and Lee (2017).
Equation (A1) indicates that the limiting distribution of η ˆ may deviate from η0 with
2 −1
an asymptotic bias term (σ0 Q) ϕ. In our SDPD the bias comes from the predetermined
control variables and the interactions of the spatial eﬀects and factor loadings.
Under some additional assumptions, the bias corrected estimator is given by
ˆbc = η
η ˆ )−1 √1 ϕ.
σ2Q
ˆ − (ˆ ˆ
nT
38