determinants of world business cycles: some insights from...

Determinants of World Business Cycles: Some Insights

From a Flexible Dynamic Factor Model�

Charles Ka Yui Leung

Department of Economics and Finance, City University of Hong Kong

Peng Wang

Department of Economics, Hong Kong University of Science and Technology

December, 2015

Abstract

Using a dynamic factor model, we characterize the business cycles co-movement

among a panel of countries using a world factor, a country-speci�c factor, and an idio-

syncratic component. We allow correlated factors and then study the contribution of

each type of factor to the business cycle dynamics. We �nd that three world factors are

necessary to characterize the co-movement on the world level. Our analysis shows that

the three world factors correspond to the price dynamics, the consumption dynamics,

and the GDP growth dynamics respectively. We then compare the importance of the

world factor with that of the spill-over e¤ects from the country-speci�c factor. Then

we study how these factors are related to country shocks as well as other economic

variables. Our data set covers 23 countries, which include the G7, Four Little Dragons

(except Taiwan), Four Little Tigers (except Indonesia), and large developing economies

such as India and China, covering more than 75% of world total output.

�We are grateful to Sheng-Chen Hu, Yi-Chan Tsai, seminar participants of CEANA-TEA for helpfulcomments and Hong Kong Earmark Grant for �nancial support. Daisy Huang and Joe Ng provide capableresearch assistance. The work described in this paper was partially supported by a grant from the ResearchGrants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 146112]. Theusual disclaimer applied.

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This is the Pre-Published Version

1 Introduction

International business cycles has been a heavily researched area. In this paper, we use dy-

namic factor models to describe the business cycles co-movement among a panel of countries.

Given the data availability, our data set covers G7 (Canada, France, Germany, Italy, Japan,

the United Kingdom, and the United States), Four Little Dragons except Taiwan due to

incomplete data (Hong Kong, Singapore, South Korea), Four Little Tigers except Indone-

sia (Malaysia, Philippines and Thailand), and large developing economies such as India and

China. We apply a dynamic factor model with a multi-level factor structure that is similar to

Kose, Otrok, and Whiteman (2003) to conduct the analysis. Related work includes Gregory

and Head (1999), Kose, Otrok, and Whiteman (2008), Crucini, Kose, and Otrok (2011), etc.

Kose, et al (2003) decomposes the country macroeconomic variables into a world common

component, a regional common component, a country common component, and an idiosyn-

cratic error term. Speci�cally, a latent world factor is used to describe the co-movement

of the world economy, a latent regional factor for each economic region is used to describe

the co-movement among that region beyond the world-level co-movement. Then controlling

for the world and regional e¤ects, a latent country factor captures co-movement within a

country. In the literature, di¤erent factors are assumed to be independent of each other so

that one may separately identify all factors.

Our important departure from the framework of Kose et al. (2003) or Crucini et al.

(2011) is by allowing di¤erent factors to be correlated with each other. For example, the

world factor might be correlated with the historical country factors. As proved in Wang

(2012) and Bai and Wang (2014a, 2014b), the identi�cation of the multi-level factor model

only requires the factors from di¤erent levels are contemporarily uncorrelated. On the other

hand, identi�cation is still possible if, for instance, the world factor is correlated with the lags

of country factors, and the country factors themselves could have arbitrary serial correlation.

Such a framework allows us to identify the composition of the world factor and examine

individual country�s contribution to the world business cycles. In addition, we allow multiple

world factors to obtain a better characterization of the world business cycles.

2 Methodology

In this section, we present our main econometric methodology. In particular, we will use a

dynamic factor model to charaterize the international linkage among a panel of countries.

2


The model is designed for a large data environment, in the sense that the data set covers

a large number of countries over a long time, and for each country we also observe mutiple

economic variables. Let ycit denote variable i of country c that is observed in period t, where

i = 1; 2; :::; nc, c = 1; :::; n; t = 1; :::; T . Both n and T will be large in our analysis. Use fwt ,

a scalar for simplicity, to denote the unobserved global common factor which has a direct

impact on all countries in period t; use f ct , also a scalar, to denote the unobserved country-

speci�c factor of country c, which only has a direct impact on country c in period t. The

factors a¤ect the observable ycit through the following linear equation

ycit = �ci +

ci fwt + �

cifct + e

cit; (1)

where �ci is a constant, the coe¢ cients ci and �

ci are the factor loadings of the world factor

and the country factor respectively which measure the heterogeneous responses of country

variables to the factors, ecit is the serially uncorrelated error term. For notational convenience,

de�ne the following nc � 1 vectors

yct ��yc1t; :::; y

cnct

�0;

�c ��c1; :::; �

cnc

�0;

�c �� c1; :::;

cnc

�0;

�c ��c1; :::; �

cnc

�0;

ect ��ec1t; :::; e

cnct

�0;

and then the vector-form factor representation follows for each country c;

yct = �c + �c � fwt + �c � f ct + ect ; (2)

We use a vector autoregression of order one (VAR(1)) to model the dynamics of factors266664fwt

f 1t...

fnt

377775 = �266664fwt�1

f 1t�1...

fnt�1

377775+266664uwt

u1t...

unt

377775 ; (3)

where � is the conformable VAR coe¢ cient matrix, and ujt is the serially uncorrelated error

term. To simplify notation, we de�ne ft = [fwt ; f1t ; :::; f

nt ]0 and ut = [uwt ; u

1t ; :::; u

nt ]0 and thus

3


the VAR equation (3) is also given by

ft = �ft�1 + ut

We assume that fectg and fujsg are two independent groups. To separately identify theglobal factors fwt and the country factors f

ct , c = 1; :::; n, we make the following two assump-

tions about the VAR shocks and the factor loadings.

Assumption 1. The error term in the VAR equation is i.i.d normal with mean zero andidentity covariance: 266664

uwt

u1t...

unt

377775 � i:i:d:N (0; In+1) :Assumption 2. j1 > 0 for some 1 � j � n and �c1 > 0 for all c = 1; :::; n.

Bai and Wang (2014a) proved that under the above two assumptions, the dynamic factor

model as de�ned in (2) and (3) is identi�ed. Assumption 1 says that di¤erent factors do

not have contemporaneous impact on each other. This enables us to interpret uwt and uct

as the shocks to the world factor and the country factor respectively. The literature of

dynamic factor models usually assumes that di¤erent factors are independent of each other,

which requires the VAR coe¢ cient matrix � to be diagonal. Examples include Kose, et al

(2003), Crucini, et al (2011), among others. Our departure from the literature is to allow

factors to be cross-correlated, which translates into a non-diagonal �. The non-diagonal

� matrix allows us to study the impulse responses of country variables with respect to a

shock originated from other countries, and thus is able to capture the spill-over e¤ects. In

particular, we do not impose restrictions on the autoregressive coe¢ cient matrix �, except

that the eigenvalues of � all lie within the unit circle so as to guarantee stationarity. Such

�exibility allows us to study much richer impulse reponse functions than existing literature

and to answer important empricial questions concerning the international business cycles

comovement, such as the spill-over e¤ects of country shocks to the rest of the world economy

or the determinants of the world common factors. To see an example, consider country 1

is hit by a positive shock in period 1, i.e., �u11 = 1. At t = 1; only country 1 is a¤ected,

�y11 = �1 while �yc1 = 0 for all c 6= 1. At t � 2; it is easy to see that all factors, including

4


the world factor, are a¤ected by such a shock due to a non-diagonal �. In particular

�ft = �t�1 �

266666664

0

1

0...

0

377777775; t � 2:

This further implies that

�yct = [�c;�c] � �t�1 �

266666664

0

1

0...

0

377777775; t � 2:

An intrigue feature of model (2) and (3) is that one may study the dynamic impact of a

speci�c country shock to the world.

The model can be estimated by a number of methods such as the maximum likelihood

method or Bayesian method using Gibbs sampling. We will adopt a two-step method. In

step 1, we use the method of Wang (2012) to estimate the multi-level factor model (2). In

step 2, we perform a VAR analysis of the factor estimates from step 1 so as to obtain the

VAR coe¢ cient matrix �, which plays a crucial role in studying the spill-over e¤ects. If we

take a closer look at the matrix

� =

2664�00 � � � �0n...

. . ....

�n0 � � � �nn

3775 ;the parameter �0;j contains important information about how the world factor is linked to

country j: The dimension of � is large given the number of countries in our sample. One

may also impose some prior restrictions on � to incorporate prior belief on how countries

are interacted with each other. For example, if we assume that a country only indirectly

a¤ects another country through its impact on the world factor, then it implies a lot of zero

5


restrictions on �: The restricted � will look like

� =

266666664

�00 � � � � � � �0;n�1 �0n

�10 �11 0 � � � 0... 0

. . . . . ....

......

. . . . . . 0

�n0 0 � � � 0 �nn

377777775;

in which there are only 3n+1 parameters, instead of n2 in the unrestricted case, to estimate.

This framework can be easily extended to include region-speci�c factors and help to analyze

an economic region�s impact on the world factor. There are also other plausible ways to

restrict � so as to describe certain prior restriction on the relationship among factors.

3 Data

We collect our country data set from IMF�s International Financial Statistics (IFS). The

data set is on annual frequency, covering 23 countries from 1960 to 2010, which consists

of more than 75 percent of world total output. Our sample covers G7 (Canada, France,

Germany, Italy, Japan, the United Kingdom, and the United States), Four Little Dragons

except Taiwan (Hong Kong, Singapore, South Korea), Four Little Tigers except Indonesia

(Malaysia, Philippines and Thailand). We also include data on China, India, Australia, New

Zealand, Austria, Belgium, Denmark, Ireland, Norway, and Sweden. Our focus are on �ve

variables on prices and real economic activities that are available for all these countries:

CPI in�ation, in�ation on GDP de�ator, real GDP growth, growth rates on private �nal

consumption as well as public �nal consumption. This amounts to a total of 115 country

variables for 51 years.

To get a �rst impression about the data, we �rst standardize all variables to have unit

variance, and then perform a variance decomposition to all the standardized country vari-

ables. The result is shown in Table 1.

Loosely speaking, Table 1 con�rms the notion of the �world factor�in the international

business cycles. Notice that the �rst two principal components (PC) �explain�more than

one third of all the variations in the data set. In the meantime, the subsequent principal com-

ponents also make non-trivial contributions to the �uctuations. While the �rst four leading

PC explain around 50 percent of the variation, the subsequent eleven principal components

combine to explain another 30 percent-plus of the variation. This suggests the co-existence

6


Principal component Variance explained Cumulative variance explained1 0.2600 0.26002 0.1077 0.36783 0.0741 0.44184 0.0617 0.50365 0.0545 0.55816 0.0523 0.61047 0.0395 0.65008 0.0325 0.68249 0.0323 0.714710 0.0262 0.740911 0.0243 0.765212 0.0213 0.786513 0.0203 0.806814 0.0184 0.825115 0.0178 0.8429

Table 1: Variance explained by the �rst 15 principal components.

of a world factor, as well as important country-speci�c factors in this international business

cycles data set. And it is natural to study whether there are non-trivial �spill-over� be-

tween the �world factor�and the country-speci�c factors. These queries seem to justify our

empirical analysis, which will be presented in the next section.

4 Empirical analysis: the benchmark case with one

world factor

Following the literature, we �rst the estimates of the benchmark case, where there is a

unique world factor and 23 country-speci�c factors. We believe that our estimated �world

factor�indeed catpure the international co-movements of the business cycles across countries.

To illustrate this point, we compare the time series plot of the world factor and that of

the in�ation-adjusted oil price in Figure 1. The oil price is chose because it is arguably

the most commonly used commodity in the world and previous studies �nd that the oil

price �uctuations do exert an impact on the macroeconomies of di¤erent countries.1 It

appears that the two process share certain degree of similarities in terms of dynamics. The

resemblance is not perfect though, given that the correlation coe¢ cient between these two

1The corresponding literature is too large to be revised here. Among others, see Hamilton (1983), Enge-mann et al. (2011).

7


series is 0.3621. The cross-sectional empirical distribution of loadings on the world factor is

show in Figure 2. In Figure 2, the horizontal axis shows the value of world factor loadings,

while the vertical axis shows the frequency count. Overall, Figure 2 demonstrates that some

country variables have substantially more exposure to the world factor as compared to others.

The majority of country variables move in the same direction with the world factor, with

only a few exceptions. For such exceptions, the value of the corresponding factor loading is

also relatively small.

1960 1970 1980 1990 2000 20102

1

0

1

2

3

4

5World factorOil price

Figure 1. World factor and the oil price (1960-2010).

8


0.4 0.2 0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18

20

Figure 2. Cross-sectional distribution of world factor loadings.

According to the factor representation, the total variation in the observables can be ac-

counted for by the world common component ci fwt , the country-speci�c common component

�cifct , and the idiosyncratic component e

cit. The overall variance decomposition shows that

such three components contribute to 24:10%, 33:66%, and 42:24% respectively of the total

variation in the observables. To further investigate di¤erent country�s exposure to di¤erent

factors, we perform variance decomposition on the country level based on the factor represen-

tation (2). Table 2 shows the result. Overall, the world factor has a substantial direct impact

on most of the countries in our sample, with only a few countries, such as China, India, and

Philippines, having much less direct exposure. For all countries, the country-speci�c factor

plays a notable role. China, India, and Philippines are largely a¤ected by their country

factor, and much lessly so by the world factor. All other countries in our sample have large

dual exposure to both world factor and country factor.

We also perform another variance decomposition that is applied to di¤erent variables. In

particular, we calculate the proportion of the variance of each variable that can be explained

by the world factor, which is de�ned as

V Wi =

PCc=1 (

ci )2 var (fw)PC

c=1 var (yci )

; i = 1; 2; :::;M;

with var (fw) = sample variance of ffwt ; t = 1; :::; Tg;

9


World factor Country factor World factor Country factorUS 0.3145 0.3653 China 0.0175 0.3247Canada 0.3425 0.3415 Hong Kong 0.1888 0.1949Japan 0.2531 0.3170 Korea 0.2530 0.5699Germany 0.1291 0.2512 Australia 0.2931 0.4503France 0.3316 0.2168 New Zealand 0.2197 0.3768UK 0.1932 0.3336 India 0.0515 0.5036Italy 0.4581 0.1452 Malaysia 0.1999 0.3211Austria 0.3595 0.2224 Philippines 0.0731 0.5773Belgium 0.2527 0.3370 Singapore 0.1955 0.3791Denmark 0.3782 0.2135 Thailand 0.2117 0.5088Irland 0.2673 0.2506Norway 0.2770 0.2079Sweden 0.2823 0.3340

Table 2: Variance explained by the world factor and the country-speci�c factor: country bycountry.

Variables World factor variance contribution (V Wi )CPI 0.2965GDP de�ator 0.3159Real GDP 0.2252Real Private Consumption 0.2144Real Public Consumption 0.1530

Table 3: Variance contribution of the world factor: variable by variable.

and var (yci ) = sample variance of fycit; t = 1; :::; Tg:

Table 3 reports the variance contribution of the world factors for each variable. It is clear

that the world factor plays an important role explaining the variation for all the variables,

especially the price variables such as CPI and GDP de�ator.

To further address the issue of spill-over e¤ect, we perform the second step vector au-

toregression (VAR) analysis of all the factors and look at the impulse response functions.

Importantly, we have not imposed any restriction on the VAR coe¢ cient matrix. Figure 3

and Figure 4 show how the shocks to US factor and China factor a¤ect the factors of all

other countries. To interpret the graph, it is worth noting that the factors and the factor

loadings always appear as a product, and thus the direction of the change in the graph has

no real meaning without further sign restrictions. Since our purpose is to examine the overall

spill-over e¤ects, we just need to look at the scale of the impulse responses as well as the

10


con�dence bands. According to Figure 3 and 4, it appears that the shock to the US factor

a¤ects, besides itself, Canada, Hong Kong, India, Thailand in a statistically signi�cant way.

On the other hand, the point estimates show that the US factor has a substantial impact on

most other countries according to the economic size of the impulse response functions. As

for the case of China, the China factor seems to have statistically signi�cant spill-over e¤ects

on countries such as Austria, Denmark, and Germany. Again the point estimates could be

large for other countries. The reason behind the statistical insigni�cance might be due to

the limited sample size that is used to estimate the unrestricted VAR.

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of AUSTRALIA to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of AUSTRIA to US

.4

.2

.0

.2

.4

.6

2 4 6 8 10

Response of BELGIUM to US

.6

.4

.2

.0

.2

.4

2 4 6 8 10

Response of CANADA to US

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of CHINA to US

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of DENMARK to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of FRANCE to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of GERMANY to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of HK to US

.6

.4

.2

.0

.2

.4

2 4 6 8 10

Response of INDIA to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of IRLAND to US

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of ITALY to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of JAPAN to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of KOREA to US

.6

.4

.2

.0

.2

.4

2 4 6 8 10

Response of MALAYSIA to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of NORWAY to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of NZ to US

.6

.4

.2

.0

.2

.4

.6

2 4 6 8 10

Response of PHILIPPINES to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of SINGAPORE to US

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of SWEDEN to US

.6

.4

.2

.0

.2

.4

2 4 6 8 10

Response of THAILAND to US

.4

.2

.0

.2

.4

.6

2 4 6 8 10

Response of UK to US

.4

.2

.0

.2

.4

.6

.8

2 4 6 8 10

Response of US to US

.4

.2

.0

.2

.4

2 4 6 8 10

Response of WORLD to US

Figure 3. Impulse responses given one SD shock to the US factor.

11


.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of AUSTRALIA to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of AUSTRIA to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of BELGIUM to CHINA

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of CANADA to CHINA

.2

.0

.2

.4

.6

2 4 6 8 10

Response of CHINA to CHINA

.6

.4

.2

.0

.2

2 4 6 8 10

Response of DENMARK to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of FRANCE to CHINA

.6

.4

.2

.0

.2

.4

2 4 6 8 10

Response of GERMANY to CHINA

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of HK to CHINA

.2

.1

.0

.1

.2

.3

.4

2 4 6 8 10

Response of INDIA to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of IRLAND to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of ITALY to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of JAPAN to CHINA

.6

.4

.2

.0

.2

2 4 6 8 10

Response of KOREA to CHINA

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of MALAYSIA to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of NORWAY to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of NZ to CHINA

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of PHILIPPINES to CHINA

.4

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of SINGAPORE to CHINA

.3

.2

.1

.0

.1

.2

2 4 6 8 10

Response of SWEDEN to CHINA

.4

.2

.0

.2

.4

2 4 6 8 10

Response of THAILAND to CHINA

.4

.2

.0

.2

.4

2 4 6 8 10

Response of UK to CHINA

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of US to CHINA

.3

.2

.1

.0

.1

.2

.3

2 4 6 8 10

Response of WORLD to CHINA

Figure 4. Impulse responses given one SD shock to the China factor.

5 Empirical analysis: the number of factors

The benchmark case has demonstrated the signi�cant role played by both the world factor

and the country factors in explaining the dynamics of country business cycles. Impulse re-

sponses have show that there are notable interactions among di¤erent factors. However, there

may be more than one world factor as there are many political economic factors that could

a¤ect the business cycles in di¤erent economies. In the previous literature such as Kose et al.

(2003), a framework with a world factor and several regional factors is adopted. Thus, on top

of the world factor, there is a regional factor that drive the co-movements among countries

12


in the same geographical regions. This paper attempts to provide an alternative, which is

a framework consists of multiple world factors. To the best of our knowledge, this possibil-

ity has not been considered in the literature and therefore may provide a complementary

perspective on the world business cycles. This multiple world factor framework may also be

more consistent with the empirical regularity that bilateral trade is an important factor in

determining the business cycle comovements.2 We will examine whether additional world

factors bring new insights into our study. We start by estimating the following multiple

world factor (MWF) model with n = 2;

ycit = �ci +

nXj=1

cjifwjt + �

cifct + e

cit: (4)

Thus, fw1t and fw2t are both world factors that could simultaneously a¤ect all countries. A

variance decomposition country-by-country is shown in Figure 5. The horizontal axis de-

notes the 23 countries in our sample, and the vertical axis shows the variance within the

corresponding country that can be explained by the corresponding factor.

0 5 10 15 20 250

0.5

1World factor 1

0 5 10 15 20 250

0.5

1World factor 2

0 5 10 15 20 250

0.5

1Country factors

Figure 5. Variance decomposition with two world factors.

A very interesting observation is that the two world factors play di¤erent roles for di¤erent

countries. A country�s contemporaneous comovement with the world can be well explained

2Clearly, the literature is too large to be reviewed here. Among others, see Baxter and Kouparitsas(2005), Frenkel and Rose (1998), Di Giovanni and Levchenko (2010), and the reference therein.

13


by either one of the two world factors or both. On the other hand, some countries mainly

respond to the �rst world factor, while others to the second world factor. This implies a

single world factor might not enough to summarize the world business cycle comovement.

A natural question is whether we need three or more world factors to further improve the

model �t. We then estimate a MWF model with n = 3, maintaining the assumption of one

country-speci�c factor for each country. The corresponding variance decomposition results

are show in Figure 6. Compared to the �rst two world factors, the economic signi�cance of

the third world factor seems to be much smaller, explaining only a very small fraction of

variance for all countries. Similarly, Figure 7 shows the variance decomposition results when

four world factors are estimated. We note that while the fourth world factor can explain a

certain amount of variation for several countries, it does not seems to impact the majority of

countries in our sample. In this regard, the fourth world factor might be more appropriately

explained as a local factor among a small group of countries. Because our framework allows

dependence among country factors, it is possible that country factors are able to pick up

such observed local instead of global interactions. Based on the above �ndings, we consider

the case with two or three world factors to be a practical approximation for the study of

world business cycle comovements. Our subsequent empirical analysis will be based on the

MWF model with two or three world factors.

0 5 10 15 20 250

0.5

1World factor 1

0 5 10 15 20 250

0.5

1World factor 2

0 5 10 15 20 250

0.5

1World factor 3

0 5 10 15 20 250

0.5

1Country factors

Figure 6. Variance decomposition with three world factors.

14


0 5 10 15 20 250

0.5

1World factor 1

0 5 10 15 20 250

0.5

1World factor 2

0 5 10 15 20 250

0.5

1World factor 3

0 5 10 15 20 250

0.5

1World factor 4

0 5 10 15 20 250

0.5

1Country factors

Figure 7. Variance decomposition with four world factors.

5.1 Economic interpretation of the world factors

In the previous sections, we have noted the correlation between world factors and the oil

price. In this section, we carry out a more comprehensive study trying to understand the

economic meaning behind each world factor. Firstly, we compare the world factors estimated

from di¤erent models. We will consider four cases for the MWF model with n = 1; 2; 3; 4.

We will use MWF(1), ... , MWF(4) to denote the four cases. In Figure 8 to 11, we plot

the world factor estimates along with the NBER US recession periods, i.e., the shaded area.

It is interesting to note that the world factors estimated from di¤erent model speci�cations

share very similar dynamics. In the same time, the US recessions seem to accord with some

dynamics of the factors in certain episodes, especially the recent Great Recession.

15


1960 1970 1980 1990 2000 20102

1.5

1

0.5

0

0.5

1

1.5

2

2.5

3 US recessionMWF(1)MWF(2)MWF(3)MWF(4)

Figure 8. The �rst world factor estimates from MWF(1)-(4).

1960 1970 1980 1990 2000 2010

2

1.5

1

0.5

0

0.5

1

1.5

2

2.5US recessionMWF(2)MWF(3)MWF(4)

Figure 9. The second world factor estimates from MWF(2)-(4).

16


1960 1970 1980 1990 2000 2010

3

2.5

2

1.5

1

0.5

0

0.5

1

1.5

US recessionMWF(3)MWF(4)

Figure 10. The third world factor estimates from MWF(3) and (4).

1960 1970 1980 1990 2000 2010

2

1

0

1

2

3 US recessionMWF(4)

Figure 11. The fourth world factor estimates from MWF(4).

17


Group name Variable included in the groupCPI CPI in�ationDe�ator GDP de�ator in�ationGDP Real GDP growthPrivCon Real private consumption growthPubCon Real public consumption growth

Table 4: Group the data variable-by-variable.

Given that one of our primary objectives is to �nd out the economic meaning of these

world factors, we need to go beyond the US perspective. In the following study, we di-

vide the data into �ve groups, each group corresponding to one economic variable as being

demonstrated by Table 4.

For each group, we extract one factor by principal component analysis. We denote

the resulting �ve factors as CPI factor, De�ator factor, GDP factor, PrivCon factor, and

PubCon factor respectively. Figure 8-10 imply that we may focus on the factors estimated

from MWF(3) or MWF(4). Figure 12 plots the �rst world factor agains the CPI factor

and the De�ator factor, from which we note that the three factors share almost the same

dynamics. This suggests that the �rst world factor largely re�exes the price dynamics. We

may thus call the �rst world factor the �Price Factor.�Figure 13 shows the second world

factor along with the PrivCon factor and the PubCon factor, all three being very close to each

other. Thus the second world factor might pick up the dynamics in consumption. We will

thus call the second world factor the �Consumption Factor.�Similarly, Figure 14 plots the

third world factor and the GDP factor. We also notice that the dynamics of the third world

factor largely resembles that of the GDP factor. We may then call the third world factor the

�Growth Factor.�In Table 5, we report the correlation coe¢ cients between di¤erent factors.

Note that the �rst three world factors are all correlated with the oil price in�ation. The

last row of Table 5 shows only minor correlation between the fourth world factor and other

economic factors as well as the oil price in�ation. This provides further evidence that we

may focus on the model MWF(3). In general, we may also explain the �rst world factor as

an indicator for nominal activities, and the second and the third world factors as indicators

for the real economic activities.

18


1960 1970 1980 1990 2000 20101.5

1

0.5

0

0.5

1

1.5

2

2.5

3 US recessionWorld factor 1CPI factorDeflator factor

Figure 12. The Price Factors.

1960 1970 1980 1990 2000 2010

2

1.5

1

0.5

0

0.5

1

1.5

2

US recessionWorld factor 2PrivCon factorPubCon factor

Figure 13. The Consumption Factor.

19


Factor name CPI De�ator PrivCon PubCon GDP OilWorld factor 1 0.9842 0.9776 0.2112 0.1284 0.0323 0.3650World factor 2 0.0553 0.1588 0.9572 0.9424 0.4729 0.3048World factor 3 0.0819 0.0072 0.1386 0.2670 0.8592 0.4516World factor 4 0.0323 0.0404 0.0170 0.0762 0.0236 0.0484

Table 5: Cross correlation between factors.

1960 1970 1980 1990 2000 2010

3

2.5

2

1.5

1

0.5

0

0.5

1

1.5

US recessionWorld factor 3GDP factor

Figure 14. The Growth Factor.

5.2 Are there regional e¤ects

Figure 5 in the above section shows that some countries are collectively more responsive to

certain world factors. To take a closer look, we report the variance decomposition in Table

6.

According to the relative importance of each world factor, we can categorize coutries into

several groups. To see an example, US and Canada mainly respond to both the Price Factor

(world factor 1) and the Growth Factor (world factor 3), but not so much to the Consumption

Factor (world factor 2). This implies that US and Canada share similar business cycle

20


ID Country name World factor 1 World factor 2 World factor 3 Country factor1 US 0.3331 0.0126 0.1674 0.20862 Canada 0.3524 0.0613 0.1067 0.32723 Japan 0.1975 0.1563 0.0945 0.28034 Germany 0.0993 0.3392 0.0863 0.11585 France 0.3584 0.3293 0.1490 0.09016 UK 0.2226 0.2369 0.0866 0.22937 Italy 0.5290 0.3285 0.1202 0.07368 Austria 0.3191 0.3813 0.1068 0.15849 Belgium 0.2930 0.3278 0.0783 0.266910 Denmark 0.3963 0.3524 0.1413 0.068911 Irland 0.3345 0.2392 0.0711 0.220012 Norway 0.2627 0.3011 0.1032 0.185413 Sweden 0.3166 0.2695 0.0673 0.258514 China 0.0268 0.0367 0.0274 0.307115 Hong Kong 0.1733 0.1683 0.0690 0.184316 Korea 0.2368 0.0446 0.0486 0.572017 Australia 0.3144 0.1536 0.0564 0.344818 New Zealand 0.2567 0.2184 0.0395 0.180519 India 0.0553 0.0314 0.0415 0.504020 Malaysia 0.1713 0.1043 0.0953 0.316921 Philippines 0.1022 0.1074 0.0267 0.576022 Singapore 0.1733 0.0913 0.0760 0.359823 Thailand 0.1785 0.1464 0.0606 0.4459

Table 6: Variance explained by the world factors and the country-speci�c factor: country bycountry.

21


dynamics on the world level. Another group includes France, Italy, Austria, Denmark, and

Norway, which respond to all three world factors. Not like the rest of the countries in the

sample, China and India do not show much response to any of the three world factors.

Instead, their business cycle dynamics is mainly driven by country factors. For countries

such as France, Italy, and Denmark, their country factors play only a minor role. In terms of

overal importance, the Price Factor ranks the �rst, and then followed by the Consumption

Factor and the Growth Factor.

Two observations are immediate. First, each group conists of nations from di¤erent

continents. For instance, Group 1 consists of Canada which is from the North American;

France and Germany which are from Europe, and Hong Kong and India which are from

Asia. Second, it is interesting to notice that geography may not completely determine the

contemporaneous co-movement among countries. For example, US and Canada, which share

a long border, respond to di¤erent world factors. Likewise, Australia and New Zealand, the

geographically closest country to each other, do not share the same world factor. Clearly, it

does not invalidate the idea of regional shocks. It is clear that continential European countries

such as Austria, France, Germany, and Denmark are signi�cantly a¤ected by the world

factor 1. Similarly, Northern European countries like Norway and Sweden, and Southeast

Asian countries such as Philippines, Singapore, and Thailand are signi�cantly in�uenced

by the world factor 2. One interpretation is that �economic region�such as bilateral trade

relationship, or sharing the same trading partners, may be as important as the �geographical

region�. It is also possible that since our sample consists of a much smaller set of countries,

which leads to a di¤erent identi�cation of �world factors�. Clearly, it is beyond the scope of

this paper to resolve the issue and we leave this to future research.

In addition, we �nd that country factors or world factors could have indirect impact

on di¤erent economies. For example, the US factor might have an impact on future world

factors, which in turn a¤ect Canada and other countries. Likewise, the �rst world factor

might a¤ect future world factors and country factors, which in turn a¤ect all countries. Al-

though by identi�cation restrictions, the contemporaneous correlations among world factors

and country factors are zero, they can have cross-correlation at longer lags. Figure 15 to

Figure 21 show that although uncorrelated at lag 0, di¤erent factors demonstrate substan-

tial correlation at lags other than zero. To formally study the overall interactions among

countries, We will perform a VAR analysis of all the factors in the next section.

22


10 5 0 5 100.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

0.5

lags

corr(g1(t),g2(tlag)

Figure 15. Cross correlation between world factor 1 and 2 over time.

10 5 0 5 100.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

0.5

lags

corr(g1(t),g3(tlag)


23


10 5 0 5 100.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

0.5

lags

corr(g2(t),g3(tlag)


10 5 0 5 100.5

0

0.5corr(g1(t),US(tlag)

10 5 0 5 100.5

0

0.5corr(g2(t),US(tlag)

10 5 0 5 100.5

0

0.5

lags

corr(g3(t),US(tlag)

Figure 18. Cross correlation between the world factors and the US factor.

24


10 5 0 5 100.5

0

0.5corr(g1(t),Japan(tlag)

10 5 0 5 100.5

0

0.5corr(g2(t),Japan(tlag)

10 5 0 5 100.5

0

0.5

lags

corr(g3(t),Japan(tlag)

Figure 19. Cross correlation between the world factors and the Japan factor.

10 5 0 5 100.5

0

0.5corr(g1(t),China(tlag)

10 5 0 5 100.5

0

0.5corr(g2(t),China(tlag)

10 5 0 5 100.5

0

0.5

lags

corr(g3(t),China(tlag)

Figure 20. Cross correlation between the world factors and the China factor.

25


10 5 0 5 100.5

0

0.5corr(g1(t),HK(tlag)

10 5 0 5 100.5

0

0.5corr(g2(t),HK(tlag)

10 5 0 5 100.5

0

0.5

lags

corr(g3(t),HK(tlag)

Figure 21. Cross correlation between the world factors and the HK factor.

5.3 VAR analysis

This section conducts VAR analysis for the three world factors and 23 country factors. The

main purpose is to characterize the interactions among di¤erent factors over time. To make

the analysis feasible, we impose a few restrictions on the VAR. In particular, we assume

that a group of country factors do not Granger cause other factors. Such a list of countries

26


includes Austria, Belgium, Denmark, Irland, Norway, Sweden, Philippines, Singapore.

.4

.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 1 0


.4

.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 1 0

Response of US to WORLD1

.4

.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 1 0


.4

.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 1 0


.8

.4

.0

.4

.8

1 2 3 4 5 6 7 8 9 1 0

Response of WORLD1 to US

.8

.4

.0

.4

.8

1 2 3 4 5 6 7 8 9 1 0

Response of WORLD1 to WORLD1

.8

.4

.0

.4

.8

1 2 3 4 5 6 7 8 9 1 0


.8

.4

.0

.4

.8

1 2 3 4 5 6 7 8 9 1 0


0 .5

0 .0

0 .5

1 .0

1 2 3 4 5 6 7 8 9 1 0


0 .5

0 .0

0 .5

1 .0

1 2 3 4 5 6 7 8 9 1 0


0 .5

0 .0

0 .5

1 .0

1 2 3 4 5 6 7 8 9 1 0


0 .5

0 .0

0 .5

1 .0

1 2 3 4 5 6 7 8 9 1 0


0 .4

0 .0

0 .4

0 .8

1 .2

1 2 3 4 5 6 7 8 9 1 0


0 .4

0 .0

0 .4

0 .8

1 .2

1 2 3 4 5 6 7 8 9 1 0


0 .4

0 .0

0 .4

0 .8

1 .2

1 2 3 4 5 6 7 8 9 1 0


0 .4

0 .0

0 .4

0 .8

1 .2

1 2 3 4 5 6 7 8 9 1 0


Response to Nonf actorized One S.D. Innov ations with 2 S.E. Error Bands

Figure 22. Interactions among US and the three world factors.

. 3

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of AUSTRALIA to US

. 3

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of CANADA to US

. 3

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of CHINA to US

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of FRANCE to US

. 1

. 0

. 1

2 4 6 8 10

Response of GERMANY to US

. 15

. 10

. 05

. 00

. 05

. 10

2 4 6 8 10


. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of INDIA to US

. 1

. 0

. 1

2 4 6 8 10

Response of ITALY to US

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of JAPAN to US

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of KOREA to US

. 4

. 2

. 0

. 2

. 4

2 4 6 8 10

Response of MALAYSIA to US

. 2

. 1

. 0

. 1

. 2

. 3

. 4

2 4 6 8 10

Response of NZ to US

. 4

. 2

. 0

. 2

. 4

2 4 6 8 10

Response of PHILIPPINES to US

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of SINGAPORE to US

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of THAILAND to US

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of UK to US

. 4

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10


. 2

. 1

. 0

. 1

. 2

. 3

. 4

2 4 6 8 10


. 4

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10


. 4

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10


Response to Nonfactorized One S.D. Innovations with 2 S.E. Error Bands

27


Figure 23. Responses of countries to US shock.

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of AUSTRALIA to CHINA

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of CANADA to CHINA

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10

Response of CHINA to CHINA

. 10

. 05

. 00

. 05

. 10

2 4 6 8 10

Response of FRANCE to CHINA

. 12

. 08

. 04

. 00

. 04

. 08

. 12

2 4 6 8 10

Response of GERMANY to CHINA

. 04

. 00

. 04

. 08

. 12

. 16

2 4 6 8 10


. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of INDIA to CHINA

. 10

. 05

. 00

. 05

. 10

. 15

2 4 6 8 10

Response of ITALY to CHINA

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of JAPAN to CHINA

. 4

. 3

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of KOREA to CHINA

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of MALAYSIA to CHINA

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of NZ to CHINA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of PHILIPPINES to CHINA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of SINGAPORE to CHINA

. 3

. 2

. 1

. 0

. 1

. 2

2 4 6 8 10

Response of THAILAND to CHINA

. 10

. 05

. 00

. 05

. 10

. 15

2 4 6 8 10

Response of UK to CHINA

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of US to CHINA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of WORLD1 to CHINA

. 4

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10


. 4

. 2

. 0

. 2

. 4

. 6

2 4 6 8 10



Figure 24. Responses of countries to China shock.

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to AUSTRALIA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to CANADA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10


. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to FRANCE

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to GERMANY

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to HK

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to INDIA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to ITALY

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to JAPAN

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to KOREA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to MALAYSIA

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to NZ

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to PHILIPPINES

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to SINGAPORE

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to THAILAND

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to UK

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10


. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10

Response of HK to WORLD1

. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10


. 3

. 2

. 1

. 0

. 1

. 2

. 3

2 4 6 8 10



Figure 25. Response of Hong Kong to country shocks and world factor shocks.

28


6 Conclusion

Using a dynamic factor model, we �nd that both the world factor and the country-speci�c

factors play important roles in explaining country business cycles. Two world factors prove

to provide adequate characterization of the world co-movement. There are also high degree

of heterogeneity though in terms of countries�exposure to di¤erent types of factors. There

are also substantial interactions among di¤erent factors.

29


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31


determinants of world business cycles: some insights from...

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