Saving and Growth: Granger Causality Analysis with

Saving and Growth: Granger Causality Analysis with Bootstrapping

on Panels of Countries

László Kónya

Department of Economics and Finance

School of Business

La Trobe University

Bundoora, VIC, 3086, Australia

Email: [email protected]

February 2004

1

Abstract

This paper investigates the possibility of Granger causality between the saving ratio (the

proportion of gross domestic saving in GDP) and the growth rate (annual percentage change

of real per capita GDP) in eighty-four countries of the world from 1961 to 2000. For technical

reason, on the basis of their per capita GDP in 1995, the countries have been classified as

high-income (at least 10000 $US), medium-income (between 1000 and 10000 $US) and low-

income (less than 1000 $US) countries, and the three panels of twenty-six, thirty and twenty-

eight countries, respectively, are considered separately. Granger causality is tested for with a

new panel-data approach based on SUR systems and Wald tests with country specific

bootstrap critical values. The results indicate two-way Granger causality between the saving

ratio and the growth rate in Austria, one-way causality from saving to growth in Ireland,

Trinidad & Tobago and the Central African Republic, and one-way causality from growth to

saving in Finland, France, Japan, Sweden, Switzerland and Niger. There is also some

support to causality from saving to growth in Mauritania and from growth to saving in Saudi

Arabia, but in all other cases there is no empirical evidence of Granger causality in either

direction.

JEL classification: C33, D90, E21, O49, O5.

Key words: causality, saving, economic growth, bootstrapping, panel data.

2

1 Introduction

For a decade or so, policy makers and academics alike have had shown renewed interest in

economic growth and its determinants, in particular, in the relationship between saving and

growth. The strong positive association between the share of saving or investment in GDP

and the per capita income growth rate is well documented in the literature (see e.g. Levine

and Renelt, 1992; Schmidt-Hebbel and Servén, 1999b), but the causal interpretation of this

observed contemporaneous correlation is ambiguous (see e.g. Deaton, 1999; Triantis, 1999;

Carroll, Overland and Weil, 2000; and Claus et al., 2001).

In the long run, economic growth requires investments in physical and human capital alike.

These investments are to be financed mainly from domestic saving, though savings in other

countries can also support one country’s investment. It is also fair to say that saving without

productive investments and their appropriate operation cannot guarantee economic growth.

Hence, strictly speaking, (domestic) saving is neither a necessary nor a sufficient condition for

growth, but it is certainly expected to enhance growth.

At first glance, the fact that higher-saving countries tend to enjoy faster income growth seems

to be incompatible with the closed-economy neoclassical growth model of Solow (1956). In

this model, a sudden increase in the saving rate raises the steady-state capital per efficiency

labour and output per efficiency labour ratios, but leaves the steady-state growth rate of

output per efficiency labour unaltered, so in the long run saving cannot cause growth. Yet, the

actual growth rate is not constant, it increases temporarily before resuming to its steady-state

value and the transition from the original equilibrium to the new equilibrium might be relatively

long. Ceteris paribus, the larger the elasticity of output with respect to capital, the slower the

transition. In the extreme case of unit elasticity of output with respect to capital and zero

elasticity of output with respect to labour, when the Solow growth model blends into the

Harrod-Domar model, an increase in the saving ratio has a permanent effect on the growth

rate. Even if we disregard this possibility, as Mankiw, Romer and Weil (1992) show, a

generalised version of the Solow model, which is augmented for human capital but still

maintains decreasing returns to scale, is reconcilable with the empirical evidence that higher

saving rates generate faster growth.

In all the models mentioned so far, the rate of technical progress is determined exogenously.

When this restriction is relaxed and technical progress is endogenised by making it depend

on the accumulation of knowledge and allowing for positive spillover effects and constant

returns to the broad concept of capital, which includes physical and human capital alike, as

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for example Lucas (1988) and Romer (1986, 1990) do, the growth rate can be raised

permanently by postponing consumption and increasing both types of capital simultaneously.

As regards the possibility of reverse causation, there are several reasonable explanations for

causality from income growth to saving as well (see Deaton, 1999). These include two

standard models of intertemporal choice based on the Flavin’s (1981) version of the

permanent income hypothesis and on the life-cycle hypothesis of Modigliani (1970, 1986),

respectively. Interestingly, although the permanent income hypothesis with finite life is

equivalent to a simple form of the life-cycle hypothesis, these models lead to different

predictions. Assuming constant optimal consumption, saving can be derived from the

permanent income hypothesis as having opposite sign but being equal in magnitude to the

discounted present value of all expected future changes in earnings. Hence, increases in

growth reduces saving. On the other hand, granted that income growth occurs across

generations but not within generations, in the life-cycle model there is a positive relationship

between income growth and saving. Other possible explanations, still within the general

framework of intertemporal choice under uncertain conditions, are based on precautionary

saving, liquidity constraints and habit formation. For example, Carroll, Overland and Weil

(2000) put forward such an example and show that a standard endogenous growth model

with habit formation in consumption can imply positive causality from growth to saving.

As mentioned before, there is abundant empirical literature on this issue. Many papers,

though, use household data, or report only contemporaneous correlation between saving and

growth and interpret the strong connection between them as evidence in favour of a causal

chain from saving to growth. Other papers explicitly test for Granger causality (precedence)

between saving and growth on the aggregate level, using time-series techniques for individual

countries or cross-section and/or panel data regressions for groups of countries. For example,

Sinha and Sinha (1998) study the relationship among private saving, public saving and

economic growth in Mexico (1960-1996) and, after a series of unit-root, cointegration and

causality tests, conclude that GDP growth positively Granger causes both types of saving, but

find no evidence of reverse causality. In a similar study for Sweden (1950-1996), the UK

(1952-1996) and the USA (1950-1997), Andersson (1999) reveals mutual causality between

saving and growth for the UK, causality from saving to GDP for Sweden, but no causality at

all for the USA. For different sets of countries Carroll and Weil (1994) detect positive Granger

causality running from growth to saving, but no hard evidence for causality in the other

direction, while Attanasio et. al. (2000) finds evidence of positive Granger causality in both

directions.

Unfortunately, these results tend to be sensitive to sample selection and model specification.

The fact that the temporal relationship between saving and growth differs across countries

casts doubt on the existence of a common pattern for groups of countries and questions the

4

validity of panel regressions that either assume country homogeneity, or allow for country

heterogeneity only by including country intercept dummy variables. On the other hand, the

disadvantage of the country-by-country time-series approach is that the analysis heavily

depends on the uni- and multivariate properties of the data, making preliminary unit-root and

cointegration tests crucial. However, the unit-root and cointegration test results are often

uncertain and contradictory, so the proper way to study causality is to consider all reasonable

assumptions and check whether the final conclusion regarding causality is sensitive to these

assumptions.1 If the final conclusion is robust, the researcher can be confident of it, otherwise

it is fair to admit that the sample information and/or the methods applied are not sufficient to

reach an unambiguous outcome.

This paper investigates the possibility of Granger causality between saving and growth in

eighty-four countries from 1961 to 2000. Contrary to previous studies, the present paper aims

to reveal the long-term relationship between saving and growth by exploiting the time-series

features of individual panel members, as well as the possible link between panel members. In

particular, we test for Granger causality between the saving ratio and growth rate with Wald

tests in seemingly unrelated regressions (SUR), using country specific bootstrap critical

values.2 This approach has two advantages. On the one hand, it does not require joint

hypotheses for all panel members, but allows for contemporaneous correlation across them,

making it possible to utilize the extra information provided by the panel data setting. On the

other hand, it is unnecessary to pre-test for unit roots and cointegration.

Our results indicate two-way Granger causality between the saving ratio and the growth rate

in Austria, one-way causality from saving to growth in Ireland, Trinidad & Tobago and the

Central African Republic, and one-way causality from the growth rate to the saving ratio in

Finland, France, Japan, Sweden, Switzerland and Niger. We have also found some support

to causality from saving to growth in Mauritania and from growth to saving in Saudi Arabia. In

all other cases, however, there is no empirical evidence of Granger causality between the

saving ratio and the growth rate in either direction.

The rest of this paper unfolds as follows. Section 2 is about some important technical issues,

including the data and its basic properties, the model, the estimation method and the Granger

causality test procedure. The empirical results of model estimation, causality tests and

sensitivity analysis are discussed in Section 3. The concluding remarks can be read in

Section 4. Finally, the data and the model are presented in the Appendix.

2 Technical Issues

1 For illustration, see for example Kónya (2000).

2 Originally Breuer, McNown and Wallace (2002) recommend a similar approach for unit-root testing. That test is

compared to other panel data unit root tests in Kónya (2001) and Holmes (2003).

5

Data and its basic properties

All data used in this study are from EconData, World Bank World Tables. The data set

comprises annual measures on the saving ratio (proportion of gross domestic saving in GDP,

percentage) and the growth rate (annual percentage change of real per capita GDP) of

eighty-four countries from 1961 to 2000.3 For technical reason, on the basis of per capita

GDP in 1995, these countries have been distributed into three groups.4

The high-income (at least 10000 $US per capita GDP in 1995) panel comprises 26 countries:

23 OECD countries (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Greece,

Iceland, Ireland, Italy, Japan, Republic of Korea, Luxembourg, the Netherlands, New Zealand,

Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, the United States), 2

countries from East Asia and the Pacific (Hong Kong, Singapore) and 1 country from the

Middle East and North Africa region (Israel).

In the medium-income (between 1000 and 10000 $US in 1995) panel there are 30 countries:

16 Latin American and Caribbean countries (Argentina, Barbados, Brazil, Chile, Columbia,

Costa Rica, Dominican Republic, Ecuador, El Salvador, Guatemala, Jamaica, Paraguay,

Peru, Trinidad & Tobago, Uruguay, Venezuela), 6 countries from East Asia and the Pacific

(Fiji, Indonesia, Malaysia, Papua New Guinea, Philippines, Thailand), 4 Middle Eastern and

North African countries (Algeria, Arab Republic of Egypt, Morocco, Saudi Arabia) 3 countries

from Sub-Saharan Africa (Botswana, Mauritius, South Africa) and 1 OECD country (Mexico).

Finally, the low-income (less than 1000 $US in 1995) panel comprises 28 countries: 18

countries from Sub-Saharan Africa (Benin, Burkina Faso, Burundi, Central African Republic,

Republic of Congo, Cote d’Ivoire, Ghana, Kenya, Lesotho, Madagascar, Malawi, Mauritania,

Niger, Nigeria, Rwanda, Senegal, Togo, Zambia), 5 Latin American and Caribbean countries

(Bolivia, Guyana, Haiti, Honduras, Nicaragua), 3 South Asian countries (Bangladesh, India,

Pakistan), 1 country from the Middle East and North Africa region (Syrian Arab Republic) and

1 from East Asia and the Pacific (China).

The time-series plots of the data series are in the Appendix. In many countries, the saving

ratio and the growth rate seem to follow similar patterns. In fact, there is a significantly

positive correlation at the 5 percent level between these two variables in 73% of the high-

3 Instead of annual data, several similar studies (like e.g. Carroll and Weil, 1994) use multiple-year averages. The

usual explanation for doing so is that, since growth theory focuses on the medium and long-run, cyclical variations must be at least diluted by using averages over a certain time span (Vanhoudt, 1998, p. 77). However, if the periodicity of the cycles is changing in time, or is constant but different from the selected time span, multiple-year averages are likely to distort, rather than eliminate business-cycle dynamics (Andersson, 1999, p. 7).

4 The estimation of a SUR system requires that there be less panel members than observations per variable.

6

income countries (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Greece,

Iceland, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Portugal, Spain,

Sweden, Switzerland), but only in 37% of the medium-income countries (Chile, Columbia,

Egypt, Guatemala, Indonesia, Jamaica, Mauritius, Paraguay, Saudi Arabia, South Africa,

Trinidad & Tobago) and in 29% of the low-income countries (Bangladesh, Burundi, China,

Cote d’Ivoire, Madagascar, Mauritania, Rwanda, Togo). All in all, in 38 out of 84 countries

(see Figures 1-3).5 Interestingly, in two medium- income countries (Barbados and Costa Rica)

the saving ratio and the growth rate have a significantly negative correlation.

The average or long-term saving ratios and growth rates are depicted in Figure 4. The three

groups of countries reflect two distinct patterns. Overall, the low-income countries are

characterised by low average saving ratios and growth rates, while the medium- and high-

income countries have relatively higher average saving ratios and growth rates.6 Within each

of the three country groups, there is a weak positive relationship between these variables, but

the linear regressions of average saving ratios on average growth rates prove to be

insignificant.7 This implies that although in 45% of the countries considered there is a positive

association between the saving ratio and the growth rate, a cross-country analysis based on

average values could not reveal this relationship.

Model

Within a country-by-country time-series setting the possibility of Granger causality between

two variables, say xt and yt, can be studied for each country individually using the following

bivariate VAR model:

, 1, 1, , , 1, , , 1, ,

1 1

, 2, 2, , , 2, , , 2, ,1 1

i i

i i

mly mlx

i t i i l i t l i l i t l i tl lmly mlx

i t i i l i t l i l i t l i tl l

y y x

x y x

α β γ ε

α β γ ε

− −= =

− −= =

= + + +

= + + +

∑ ∑

∑ ∑ (1)

5 Having 40 observations per variable, the approximate 95 percent confidence interval for the correlation coefficient

is (-0.3 ; 0.3). 6 There are three notable exceptions: Lesotho (low-income) has a negative average saving ratio, China (low-income)

has high saving ratio and growth rate, and Saudi Arabia (medium-income) has an extremely high saving ratio. 7 The coefficient of determination (R2) is 0.0680 for the high-income countries, 0.0111 for the medium-income

countries and 0.0029 for the low-income countries. Contrary to these results, Schmidt-Hebbel and Servén (1999b, p. 14) report a strong positive association between the average growth rates of real per capita GNP and average gross national saving ratios for the market economies over the 1965-1994 time periods.

7

Figures 1-3: Contemporaneous correlation coefficients between saving ratio and growth rate

Medium-Income Countries

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.7

Alge

riaAr

gent

ina

Barb

ados

Bots

wan

aBr

azil

Chi

leC

olum

bia

Cos

taD

omin

ican

Ecua

dor

Egyp

t,El

Salv

ado

Fiji

Gua

tem

alIn

done

sia

Jam

aica

Mal

aysi

aM

aurit

ius

Mex

ico

Mor

occo

Papu

a N

.Pa

ragu

ayPe

ruPh

ilippi

neSa

udi

Sout

hTh

aila

ndTr

inid

ad &

Uru

guay

Vene

zuel

Low-Income Countries

-0.10.00.10.20.30.40.50.60.7

Bang

lade

shBe

nin

Boliv

iaBu

rkin

aBu

rund

iC

entra

lC

hina

Con

go,

Cot

e d'

Ivoi

reG

hana

Guy

ana

Hai

tiH

ondu

ras

Indi

aKe

nya

Leso

tho

Mad

agas

car

Mal

awi

Mau

ritan

iaN

icar

agua

Nig

erN

iger

iaPa

kist

anR

wan

daSe

nega

lSy

rian

Arab

Togo

Zam

bia

High-Income Countries

-0.10.00.10.20.30.40.50.60.70.8

Aust

ralia

Aust

riaBe

lgiu

mC

anad

aD

enm

ark

Finl

and

Fran

ceG

reec

eH

ong

Kong

Icel

and

Irela

ndIs

rael

Italy

Japa

nKo

rea

Rep

.Lu

xem

bour

Net

herla

nds

New

Nor

way

Portu

gal

Sing

apor

eSp

ain

Swed

enSw

itzer

land

U.K

.U

.S.A

.

8

-50

-40

-30

-20

-10

0

10

20

30

40

50

-2 -1 0 1 2 3 4 5 6 7

Average growth rate

Aera

ge s

avin

g ra

te

High-Income Countries Medium-Income Countries Low-Income CountriesLinear trend Linear trend Linear trend

Figure 4: Average saving ratios versus growth rates

(1961-2000 averages by countries)

In these formulas, index i refers to the country (i = 1,..., N ), t to the time period (t = 1,..., T ), l

to the lag, and mly, mlx denote the longest lags in the system. The error terms, 1, ,i tε and 2, ,i tε ,

are supposed to be white-noises (i.e. they have zero means, constant variances and are

individually serially uncorrelated) that may be correlated with each other for a given country,

but not across countries.8 Moreover, it is assumed that yt and xt are stationary or cointegrated

so, depending on the time-series properties of the data, they denote levels or first

differences.9

With respect to this system, in country i there is one-way Granger causality running from X to

Y if in the first equation not all 1,iγ 's are zero but in the second all 2,iβ 's are zero, there is one-

way Granger causality from Y to X if in the first equation all 1,iγ 's are zero but in the second

not all 2,iβ 's are zero, there is two-way Granger causality between Y and X if neither all 1,iγ 's

8 ε 1,i,t and ε 2,i,t are correlated when there is feedback between X and Y, i.e. in the non-reduced form of (1), called

structural VAR, yt depends on xt and/or xt depends on yt. For a proof see Enders (2004, p. 266). 9 In case of cointegration, it is usually more appropriate to test for causality within a vector error correction, VEC,

framework. However, the usual Wald test in a level VAR remains valid if cointegration is ’sufficient’ in the sense of Toda and Phillips (1993), which is the case in bivariate cointegrated systems.

9

nor all 2,iβ ’s are zero, and there is no Granger causality between Y and X if all 1,iγ 's and

2,iβ 's are zero.10

As regards the estimation of (1), since for a given country both equations contain the same

predetermined, i.e. lagged exogenous and endogenous variables, the OLS estimates of the

parameters are consistent and asymptotically efficient.11 This suggests that the 2N equations

involved in the analysis can be estimated one-by-one, in any preferred order. For example,

we can divide the equations into two groups, the first one consisting of the equations on Y

and the second of the equations on X. In other words, instead of the N VAR systems like (1),

we can consider the following two sets of equations:

1 1

1 1

1 1

1, 1,1 1,1, 1, 1,1, 1, 1,1,1 1

2, 1,2 1,2, 2, 1,2, 2, 1,2,1 1

, 1, 1, , , 1, , , 1, ,1 1

:

mly mlx

t l t l l t l tl l

mly mlx

t l t l l t l tl l

mly mlx

N t N N l N t l N l N t l N tl l

y y x

y y x

y y x

α β γ ε

α β γ ε

α β γ ε

− −= =

− −= =

− −= =

= + + +

= + + +

= + + +

∑ ∑

∑ ∑

∑ ∑

(2a)

and

2 2

2 2

2 2

1, 2,1 2,1, 1, 2,1, 1, 2,1,1 1

2, 2,2 2,2, 2, 2,2, 2, 2,2,1 1

, 2, 2, , , 2, , , 2, ,1 1

:

mly mlx

t l t l l t l tl lmly mlx

t l t l l t l tl l

mly mlx

N t N N l N t l N l N t l N tl l

x y x

x y x

x y x

α β γ ε

α β γ ε

α β γ ε

− −= =

− −= =

− −= =

= + + +

= + + +

= + + +

∑ ∑

∑ ∑

∑ ∑

(2b)

Compared to (1), this alternative specification has two distinctive features. Firstly, each

equation in (2a), and also in (2b), has different predetermined variables. The only possible

link among individual regressions is contemporaneous correlation within the systems, which

might be due to the strong economic ties among several countries within each group. Hence,

these sets of equations are not VAR but SUR systems.12 Secondly, since we shall use country

specific bootstrap critical values, yt and xt are not supposed to be stationary, they denote the

10 This definition implies causality for one period ahead. This concept has been generalised by Dufour and Renault

(1998) to causality h periods ahead, and to causality up to horizon h, where h is a positive integer. 11 As Enders (2004, p. 281) points out, in spite of the possible correlation of the error terms across the two equations,

each equation can be estimated with OLS. However, if the lag lengths are allowed to be different in the equations, i.e. in the case of a near-VAR, then SUR is more efficient than OLS.

12 About the seemingly unrelated regressions model see, e.g. Greene (2003), Section 14.2.

10

levels of the saving ratio and the growth rate, irrespectively of the time-series properties of

these variables.

With respect to these SUR systems, in country i there is one-way Granger causality running

from X to Y if in (2a) not all 1,iγ 's are zero but in (2b) all 2,iβ ’s are zero, there is one-way

Granger causality from Y to X if in (2a) all 1,iγ 's are zero but in (2b) not all 2,iβ 's are zero,

there is two-way Granger causality between Y and X if neither all 1,iγ 's nor all 2,iβ 's are zero,

and there is no Granger causality between Y and X if all 1,iγ 's and 2,iβ 's are zero.

Estimation Method

The appropriate method to estimate (2a) and (2b) depends on the properties of the error

terms. If there is no contemporaneous correlation across countries, then each equation is a

classical regression. Consequently, the equations can be estimated one-by-one with OLS and

the OLS estimators of the parameters are the best linear unbiased estimators. On the other

hand, in the presence of contemporaneous correlation across countries the OLS estimators

are not efficient because they fail to utilise this extra information. In order to obtain more

efficient estimators, the equations in (2a), and also in (2b), must be stacked13 and the two

stacked equations can be estimated individually with the feasible generalised least squares or

maximum likelihood methods. In this study we use the SUR estimator proposed by Zellner

(1962).14

Prior to estimation, we have to specify the number of lags. This is a crucial step because the

causality test results may depend critically on the lag structure. In general, both too few and

too many lags may cause problems. Too few lags mean that some important variables are

omitted from the model and this specification error will usually cause bias in the retained

regression coefficients, leading to incorrect conclusions. On the other hand, too many lags

waste observations and this specification error will usually increase the standard errors of the

estimated coefficients, making the results less reliable.

Unfortunately, there is no simple rule to decide on the maximal lag, though there are formal

model specification criteria to rely on. Ideally, the lag structure is allowed to vary across

countries, variables and equation systems. However, for a relatively large panel like ours, this

would increase the computational burden substantially. For this reason in each system we

13 The stacked forms of (2a) and (2b) are shown in the Appendix. 14 The estimations were performed by the SUR routine of TSP4.5.

11

allow different maximal lags for Y and X, but do not allow them to vary across countries. This

means that altogether there are four maximal lag parameters. Assuming that their range is

1!4, we estimate (2a) and (2b) for each possible pair of mly1, mlx1 and mly2, mlx2 respectively,

and choose the combinations which minimize the Akaike Information Criterion (AIC) and

Schwartz Criterion (SC) defined as:

22lnk

N qAICT

= +W (3)

and

2

ln ln( )kN qSC TT

= +W (4)

where W is the estimated residual covariance matrix, N is the number of equations, q is the

number of coefficients per equation and T is the sample size, all in system k = 1, 2.

Occasionally, these two criteria select different lag lengths.

The SUR estimators are more efficient than the OLS estimators only if there is

contemporaneous correlation in the system. Therefore, it is of interest to test whether the

variance-covariance matrix of the errors is diagonal. For a given k, the null and alternative

hypotheses are as follows:

0 , , , ,: ( , ) 0 fork i t k j tH Cov i jε ε = ≠

, , , ,: ( , ) 0 for at least one pair ofA k i t k j tH Cov i jε ε ≠ ≠

If H0 is true there is no payoff to SUR. Assuming normality, Breusch and Pagan (1980), BP in

brief, suggested the following Lagrange multiplier test statistic:

1

2

2 1

N i

iji j

T rλ−

= =

= ∑∑ (5)

where rij is the estimated correlation coefficient between εk,i,t and εk,j,t (for a given k and i≠j)

from individual OLS regressions. Under H0, this statistic has an asymptotic chi-square

distribution with N(N -1) / 2 degrees of freedom.15

15 Greene (2003), p. 350.

12

Testing for Granger Causality

After having estimated (2a) and (2b), we test for Granger causality performing Wald tests with

country specific bootstrap critical values. Bootstrapping is basically a re-sampling method.16

The main issue is how to generate and use the bootstrap samples. For the sake of simplicity,

we focus on testing causality from X to Y in (2a). A similar procedure is applied for causality

from Y to X in (2b). The procedure is as follows.

Step 1: Estimate (2a) under the null hypothesis that there is no causality from X to Y (i.e.

assuming the γ1,i,l = 0 restriction for all i and l ) and obtain the residuals

1

0 , , , 1, 1, , ,1

ˆˆmly

H i t i t i i l i t ll

e y yα β −=

= − −∑ for i = 1,..., N and t = 1,..., T.

From these residuals develop the N×T 0 , ,[ ]H i te matrix.

Step 2: Re-sample these residuals. In order to preserve the contemporaneous cross-

correlation structure of the error terms in (2a), do not the draw the residuals for

each country one-by-one, but rather select randomly a full column from the 0 , ,[ ]H i te

matrix at a time. Denote the selected bootstrap residuals as 0

*, ,H i te , where t = 1,...,

T* and T* can be greater than T.

Step 3: Generate a bootstrap sample of Y assuming again that X does not cause it, i.e.

using the following formula:

1

0

* * * *, 1, 1, , , , ,

1

ˆˆ , 1,...,mly

i t i i l i t l H i tl

y y e t Tα β −=

= + + =∑ (6)

Step 4: Substitute *,i ty for , ,i ty estimate (2a) without imposing any parameter restriction on it,

and for each country perform a Wald test implied by the no-causality null

hypothesis.

Step 5: Develop the empirical distributions of the Wald test statistics repeating steps 2-4

many times, and specify the bootstrap critical values by selecting the appropriate

percentiles of these sampling distributions.

There are a few remarks to be made. The maximal lags are allowed to vary between 1 and 4,

inclusively. In Steps 2 and 3, depending on the lag structure, we draw at least T* = 68

16 About bootstrapping in general see e.g. Maddala and Kim (1998, 10.2).

13

bootstrap residuals and generate the same number of bootstrap *,i ty values for each country.

To commence the recursive algorithm defined by (6), the first 2-5 *,i ty values are set equal to

zero and, to minimize the effect of this initialisation onto the results, in Step 4 the Wald tests

are performed over only the last 34-37 values. In Step 5, the bootstrap distribution of each

test statistic is derived from 10,000 replications.

3 Empirical Results

For each country group, the analysis consisted of three stages. First we estimated (2a) and

(2b) with SUR for all possible pairs of maximal lags, and selected mly1, mly2, mlx1 and mlx2 by

minimizing the model selection criteria (3) and (4). Interestingly, in all cases, AIC and SC took

their smallest values at a single lag for each variable. Then, we performed the BP test on (2a)

and (2b) with a single lag. In every case it was possible to reject the null hypothesis of no

contemporaneous correlation within the system even at the half percent significance level,

justifying the application of SUR. Finally, we tested for Granger causality with Wald tests and

country specific bootstrap critical values from saving ratio to growth rate and from growth rate

to saving ratio. Since our main interest is in testing for causality, only these latter results are

reported in this paper.17

Granger Causality Results

The Granger causality test results for the null hypothesis that the saving ratio does not cause

the growth rate can be found in Table 1. Notice that the bootstrap critical values vary

considerably from country to country, and that they are substantially higher than the

corresponding chi-square critical values usually applied with the Wald test.18 In fact, they are

so high, that at the ten percent or lower significance level we can reject the null hypothesis

only for five countries: Austria, Ireland, the Netherlands, Trinidad & Tobago and Burundi. In

these cases the point estimates of the coefficient of the lagged saving ratio, i.e. 1̂γ , are all

positive (0.340 for Austria, 0.247 for Ireland, 0.361 for the Netherlands, 0.387 for Trinidad &

Tobago, 0.625 for Burundi), that is they have the logical sign. They suggest that a one

percentage point increase of the saving ratio implies a 0.247 to 0.625 percentage point

increase of the growth rate a year later.

17 On request, all the details are available to interested readers. 18 The chi-square critical values for one degree of freedom, i.e. for Wald tests with a single restriction, are 6.6349

(1%), 3.8415 (5%) and 2.7055 (10%).

14

Table 1: Granger causality from saving ratio to growth rate;

Wald tests with bootstrapping, mly= mlx=1

Bootstrap Critical Values Country 1̂γ Test. Stat.

1% 5% 10%

Bootstrap p-value


Australia -0.338 15.7687 51.3467 27.9279 18.5124 0.13

Austria 0.340 23.6255 43.2185 22.2897 15.1186 0.05**

Belgium 0.115 8.0064 78.5239 46.3498 32.4158 0.44

Canada -0.111 2.4011 70.4232 38.6603 26.5552 0.63

Denmark -0.040 0.5119 67.4983 38.2752 26.2758 0.82

Finland -0.250 7.3501 73.0468 37.2492 25.3928 0.37

France 0.177 20.9408 65.0952 38.0125 26.2656 0.14

Greece 0.121 3.0022 46.0960 23.4940 16.2580 0.46

Hong Kong -0.160 4.8548 59.9534 31.0694 20.9566 0.42

Iceland 0.307 9.8460 34.1007 19.1581 13.2553 0.16

Ireland 0.247 29.6086 43.2594 23.5829 16.0528 0.04**

Israel -0.002 0.0021 50.0791 27.2313 17.8186 0.96

Italy 0.279 12.6021 60.7082 32.8782 21.9681 0.21

Japan -0.037 0.1885 62.5359 33.8663 23.6218 0.88

Korea Rep. 0.016 0.2127 38.3025 20.9026 14.1693 0.84

Luxembourg -0.007 0.0209 59.8193 31.6124 20.9949 0.96

Netherlands 0.361 31.9763 71.2150 39.4945 27.0135 0.08*

New Zealand -0.010 0.0028 66.2155 33.5541 22.1383 0.99

Norway 0.082 1.9923 54.8085 29.7316 20.2984 0.61

Portugal 0.158 3.1764 88.6382 47.9678 32.9351 0.60

Singapore -0.023 3.1899 60.5334 28.7711 19.5295 0.48

Spain -0.174 3.3034 57.8551 31.2381 20.8093 0.50

Sweden -0.127 3.6461 61.5158 33.4450 23.0439 0.51

Switzerland -0.105 3.5787 52.3685 28.8411 19.7054 0.48

UK -0.151 4.4086 64.5787 36.1282 25.2682 0.49

USA -0.257 8.4672 66.4818 37.6079 26.0329 0.35

15

Table 1 cont.


1% 5% 10%

Bootstrap p-value


Algeria 0.055 0.5005 91.7048 48.6977 32.3906 0.84

Argentina -0.056 0.2818 95.3766 51.5353 34.2340 0.88

Barbados -0.012 0.0217 98.5507 49.8252 34.5186 0.97

Botswana -0.041 4.5724 108.4213 54.5314 37.2686 0.56

Brazil -0.288 4.9925 119.0029 61.6636 42.5040 0.57

Chile 2.992 2.9917 108.1988 59.1020 40.9687 0.65

Columbia 0.151 8.6646 125.5408 65.6551 46.1699 0.48

Costa Rica -0.132 9.8979 132.0316 71.3911 49.8104 0.47

Dominican Rep. -0.110 0.3704 85.4277 40.2059 26.7838 0.84

Ecuador -0.102 1.7352 93.1684 49.2057 33.7326 0.70

Egypt, Arab Rep. -0.207 5.7848 100.1075 53.0945 35.5552 0.50

El Salvador -0.065 2.0319 119.0146 66.2455 45.4494 0.72

Fiji -0.059 0.2085 120.0667 59.1051 40.0183 0.91

Guatemala -0.023 0.2732 134.3739 74.7315 55.1663 0.92

Indonesia 0.032 1.5584 98.4600 54.0959 36.6437 0.74

Jamaica 0.460 30.4794 102.2415 52.6800 35.8329 0.13

Malaysia 0.005 0.0452 114.9538 64.9606 45.7745 0.96

Mauritius 0.280 13.6866 99.9736 51.4443 35.9731 0.30

Mexico -0.015 0.0304 98.9824 50.5733 33.6640 0.96

Morocco -0.288 9.8000 84.9937 42.1114 28.7297 0.37

Papua New Guinea -0.100 5.1423 77.3147 41.2272 27.5733 0.45

Paraguay 0.132 6.5146 103.7357 55.1407 38.1417 0.50

Peru 0.003 0.0037 106.7329 55.4368 37.9625 0.99

Philippines -0.088 1.5959 91.6419 48.4485 31.6956 0.70

Saudi Arabia 0.030 0.6376 95.2967 53.0880 36.8823 0.82

South Africa 0.236 4.4020 95.1064 49.1641 31.9814 0.53

Thailand -0.064 1.9960 95.0619 46.9925 32.4828 0.67

Trinidad & Tobago 0.387 128.5246 104.9756 58.2251 38.5547 0.01***

Uruguay 0.060 0.7546 158.0392 77.8367 52.3517 0.84

Venezuela 0.138 5.7076 87.3378 45.6075 30.8603 0.46

16

Table 1 cont.


1% 5% 10%

Bootstrap p-value


Bangladesh 0.060 0.6987 64.2261 34.8607 24.3230 0.78

Benin 0.030 0.0834 59.3218 30.9764 20.3008 0.91

Bolivia -0.005 0.0145 74.2412 37.3383 24.6840 0.97

Burkina Faso 0.165 7.9981 57.7168 31.0566 21.1407 0.31

Burundi 0.625 29.4133 60.8294 32.5693 22.7695 0.07*

Central African Rep. 0.244 15.7680 63.9216 33.8054 22.5582 0.17

China -0.020 0.0996 58.9317 32.3302 58.9317 0.91

Congo, Rep. -0.045 1.0827 63.1680 32.7329 22.1115 0.70

Cote d'Ivoire 0.381 14.9844 70.6033 36.0192 24.3962 0.20

Ghana 0.022 0.0570 86.3536 45.3777 31.1445 0.94

Guyana 0.176 15.6125 91.2107 49.0552 33.0844 0.26

Haiti 0.173 6.0021 65.1895 34.1591 23.5450 0.39

Honduras -0.118 2.8888 59.9850 32.6845 22.9640 0.54

India 0.528 16.5326 52.5740 28.9989 19.9654 0.14

Kenya 0.249 11.7012 84.1549 44.9063 30.7580 0.30

Lesotho -0.058 3.2962 65.7236 34.2073 23.1023 0.53

Madagascar 0.217 1.9163 82.9124 43.4190 29.6587 0.67

Malawi -0.124 5.1104 60.3250 32.1070 22.4133 0.44

Mauritania 0.123 18.6270 69.4418 39.8351 27.4330 0.19

Nicaragua -0.197 7.7791 54.7666 28.5955 19.3795 0.30

Niger 0.090 0.4910 74.9443 39.2169 26.8764 0.83

Nigeria -0.174 4.0142 66.0100 35.2884 24.2040 0.49

Pakistan -0.049 0.6703 81.8932 43.1035 31.0168 0.81

Rwanda -0.509 19.9900 172.8405 45.1100 26.7036 0.14

Senegal 0.148 3.1719 63.6027 33.1146 22.5956 0.52

Syrian Arab Rep. -0.411 4.7276 62.5578 32.1757 22.3344 0.43

Togo 0.015 0.1396 84.0475 42.9647 28.8510 0.91

Zambia 0.057 2.9464 54.3379 28.8623 19.4486 0.52

Note: ***, ** and * indicate significance at the 1, 5 and 10 percent levels, respectively.

17

The results for reverse Granger causality, that is for the null hypothesis that the growth rate

does not cause the saving ratio, are shown in Table 2. There are only seven countries for

which this hypothesis can be rejected at the ten percent or lower significance level: Finland,

France, Japan, Sweden, Switzerland, Saudi Arabia and Niger. The corresponding point

estimates of the coefficient of the lagged growth rate are again all positive (0.342 for Finland,

0.265 for France, 0.241 for Japan, 0.308 for Sweden, 0.248 for Switzerland, 0.670 for Saudi

Arabia, 0.278 for Niger), that is they also have the logical sign. They suggest that a one

percentage point increase of the growth rate implies a 0.241 to 0.670 percentage point

increase of the saving ratio in the following year.

Compared to the number of countries considered, Granger non-causality in either direction

can be rejected relatively rarely. The rejection rate is only about 14% for the high-income

countries and even lower, 3 and 3.5%, for the medium-income and low-income countries,

respectively.

Sensitivity Analysis

In order to check the robustness of the causality results, we have deliberately overfitted (2a)

and (2b). Although the overall AIC, SC measures (3) and (4) support a single lag for both

variables (mlyk = mlxk = 1) in each system, this specification is not necessarily the best for

every country. For this reason, we re-estimated both systems with two alternative lag

structures: mlyk = 1, mlxk = 2 and mlyk = 2, mlxk = 1 (k = 1, 2). For each country and each

specification, we re-performed the causality tests and calculated the following single-equation

versions of (3) and (4):

( )2 2ln ˆi ii

qAICT

σ= + (3*)

and

( )2ln ln( )ˆi ii

qSC TT

σ= + (4*)

where i refers to the country (i = 1, 2, …, N) and 2ˆ iiσ is the estimated variance of the residuals

from the i th equation, that is the (i,i)th element of the estimated residual covariance matrix W.

In the case of conflicting causality test results for a given country, we prefer the specification

with the lowest AICi and/or SCi value.

18

Table 2: Granger causality from growth rate to saving ratio;

Wald tests with bootstrapping, mly= mlx=1


1% 5% 10%

Bootstrap p-value


Australia -0.084 1.7045 58.9178 29.3190 20.2017 0.62

Austria 0.195 11.5944 75.0598 42.2922 29.6411 0.30

Belgium 0.217 14.7411 67.0091 36.3050 25.6297 0.21

Canada 0.160 10.6232 70.2778 40.2054 27.6723 0.31

Denmark 0.120 5.3541 69.1374 35.9585 25.1984 0.44

Finland 0.342 44.4519 70.3267 35.7500 24.2745 0.04**

France 0.265 55.8097 73.0986 43.5010 30.8939 0.03**

Greece 0.148 6.1584 79.2685 42.5212 29.6589 0.46

Hong Kong -0.026 0.1904 54.4445 28.5742 19.6722 0.86

Iceland -0.119 5.8754 57.4611 29.3251 19.3751 0.35

Ireland 0.012 0.0227 51.0019 28.3578 19.5389 0.96

Israel -0.023 0.0548 72.7827 38.3813 26.2710 0.95

Italy 0.005 0.0104 54.5880 28.0322 19.5399 0.97

Japan 0.241 100.2680 72.9899 40.3424 27.1557 0.01**

Korea Rep. -0.053 1.1323 64.4011 33.3870 22.6720 0.70

Luxembourg 0.275 5.3482 65.9917 33.0069 21.7767 0.39

Netherlands -0.072 3.0116 67.9229 35.9924 24.1749 0.55

New Zealand -0.012 0.0392 73.3161 38.2097 26.0124 0.95

Norway -0.137 3.2629 60.1460 31.5247 21.4183 0.51

Portugal 0.123 1.8790 68.4593 35.3426 23.3315 0.64

Singapore -0.865 6.2432 75.6858 39.7958 27.4660 0.43

Spain 0.099 11.0670 71.8929 41.3588 28.3216 0.30

Sweden 0.308 24.7599 64.4207 36.0165 24.7593 0.10*

Switzerland 0.248 47.5127 69.2604 35.7798 24.2172 0.03**

UK 0.040 0.9058 51.9539 29.5059 19.6474 0.72

USA 0.034 0.5882 55.1693 28.3197 19.2794 0.77

19

Table 2 cont.


1% 5% 10%

Bootstrap p-value


Algeria 0.100 6.8028 142.6243 73.7526 48.6411 0.52

Argentina 0.033 0.6138 107.1270 55.2907 37.5515 0.83

Barbados -0.018 0.1021 122.1390 65.7125 43.9966 0.94

Botswana 0.218 2.9440 114.4384 59.8585 40.2657 0.66

Brazil 0.006 0.0185 102.6791 54.3333 36.9004 0.98

Chile -0.187 13.2181 137.5215 71.4694 49.2870 0.40

Columbia -0.036 0.2097 110.1605 55.9953 37.7553 0.90

Costa Rica -0.092 1.1929 106.4896 56.7877 38.2853 0.76

Dominican Rep. 0.093 4.6907 127.1799 65.6405 43.0715 0.56

Ecuador -0.004 0.0090 127.7617 70.5524 48.5436 0.99

Egypt, Arab Rep. 0.274 22.4663 135.1104 69.9897 48.3052 0.27

El Salvador 0.169 7.6193 122.7106 62.1723 40.4181 0.46

Fiji 0.028 0.3881 121.1364 65.6252 43.1864 0.88

Guatemala 0.117 6.3210 116.4657 61.2834 41.3768 0.51

Indonesia 0.290 19.0127 145.6695 67.0024 42.6497 0.25

Jamaica 0.344 28.7605 118.0988 62.9272 42.1175 0.17

Malaysia -0.141 3.7346 100.8638 49.8880 33.0066 0.56

Mauritius -0.218 6.0788 118.8859 62.2649 43.2173 0.51

Mexico -0.018 0.1116 106.4500 56.8986 38.7325 0.93

Morocco -0.083 9.0255 126.5212 65.2234 43.1509 0.45

Papua New Guinea 0.345 20.8434 133.0222 72.9047 49.3188 0.29

Paraguay -0.021 0.0859 128.2619 72.1158 50.2122 0.95

Peru 0.113 4.8441 121.9641 63.2953 43.1352 0.58

Philippines 0.066 1.0243 146.6040 73.0870 48.5939 0.81

Saudi Arabia 0.670 66.6762 121.7180 67.5189 46.4831 0.06*

South Africa -0.140 10.6106 127.6984 71.0721 48.6045 0.45

Thailand 0.125 6.5015 107.2864 54.4743 34.9956 0.46

Trinidad & Tobago 0.036 0.2724 149.4539 78.7276 55.9595 0.92

Uruguay -0.167 4.7095 127.8116 65.3718 42.5186 0.56

Venezuela -0.159 12.6992 157.9070 84.6755 59.2651 0.47 Table 2 cont.

20


1% 5% 10%

Bootstrap p-value


Bangladesh -0.038 0.2024 78.2550 38.5674 25.1241 0.88

Benin 0.044 0.4860 103.6167 53.3225 36.1000 0.85

Bolivia 0.061 0.1832 96.1208 42.9326 28.0554 0.89

Burkina Faso -0.368 18.7380 85.4405 45.2536 30.1203 0.20

Burundi -0.123 6.9860 94.3007 50.6191 34.7074 0.46

Central African Rep. 0.180 3.7823 82.9141 42.8307 29.7724 0.55

China 0.209 21.1959 100.9221 44.6137 27.0276 0.14

Congo, Rep. 0.046 0.1438 84.2461 43.1496 28.4053 0.91

Cote d'Ivoire -0.038 0.2101 82.5931 41.2137 28.3177 0.89

Ghana 0.196 5.7981 79.4880 41.1778 27.4051 0.43

Guyana 0.344 10.0724 84.0413 43.0203 28.7741 0.31

Haiti 0.181 10.3062 72.4883 41.1334 27.7515 0.31

Honduras 0.212 7.9420 83.1172 43.8105 30.6271 0.39

India 0.098 5.0037 78.3117 40.3828 26.9450 0.46

Kenya -0.028 0.1523 77.2680 40.8304 27.5779 0.90

Lesotho 0.041 0.0703 61.6439 33.8370 22.0182 0.92

Madagascar 0.055 0.7864 73.8468 37.6401 25.0090 0.76

Malawi -0.154 8.4182 73.8240 37.9119 26.2072 0.34

Mauritania 0.026 0.0400 82.9308 42.7034 27.9570 0.95

Nicaragua 0.274 10.7901 102.1096 44.2628 28.4193 0.29

Niger 0.278 35.4965 90.8551 46.4273 31.0170 0.08*

Nigeria 0.149 4.3054 79.5079 42.0576 28.7484 0.51

Pakistan -0.104 2.5247 80.7374 43.8291 29.6604 0.62

Rwanda -0.028 0.1700 135.8177 44.4371 26.6979 0.88

Senegal -0.118 3.4280 82.5422 46.2225 31.9389 0.59

Syrian Arab Rep. -0.027 0.7019 83.0561 45.5500 30.9868 0.79

Togo -0.051 0.1450 91.2241 46.3752 30.4502 0.91

Zambia -0.110 0.4911 82.0245 41.0871 27.5307 0.83

Note: : ***, ** and * indicate significance at the 1, 5 and 10 percent levels, respectively.

21

For most of the countries, 70 out of 84, the Granger causality tests over the three different

specifications led to the same conclusion, so in this sense our results are fairly robust. The

contradicting cases are shown in Table 3. Clearly, despite the conflicting outcomes, on the

basis of country specific AIC and SC, we can still maintain our original conclusions most of

the time.

Table 3: Contradicting Granger causality test results;

Wald tests with bootstrapping and alternative lag structures

Granger causality from saving ratio to growth rate

Lag structure

mlyk = mlxk = 1 mlyk = 1, mlxk = 2 mlyk = 2, mlxk = 1

Country AIC SC p AIC SC p AIC SC p

Austria 2.225 2.354 0.05** 2.311 2.485 0.11 2.307 2.481 0.06*

Ireland 3.317 3.446 0.04** 3.367 3.541 0.04** 3.383 3.557 0.05**

Netherlands 2.156 2.285 0.08* 2.050 2.225 0.55 2.090 2.264 0.28

Burundi 6.829 6.957 0.00*** 6.718 6.890 0.12 6.905 7.078 0.11

Central Afr. Rep. 5.389 5.516 0.17 5.160 5.333 0.07* 5.349 5.521 0.11

Mauritania 6.734 6.862 0.19 6.852 7.025 0.31 6.706 6.878 0.09*

Granger causality from growth rate to saving ratio

Lag structure

mlyk = mlxk = 1 mlyk = 1, mlxk = 2 mlyk = 2, mlxk = 1

Country AIC SC p AIC SC p AIC SC p

Austria 0.207 0.336 0.30 -0.056 0.118 0.01*** 0.257 0.431 0.27

Denmark 0.937 1.066 0.44 1.029 1.203 0.08* 0.927 1.101 0.58

Finland 1.694 1.824 0.04** 1.698 1.872 0.11 1.733 1.907 0.01***

France -0.833 -0.704 0.03** -0.723 -0.549 0.14 -0.737 -0.563 0.21

Iceland 2.279 2.408 0.35 2.300 2.474 0.21 2.323 2.497 0.09*

Sweden 0.613 0.743 0.10* 0.616 0.790 0.14 0.748 0.922 0.35

Indonesia 5.343 5.471 0.25 5.352 5.524 0.16 5.361 5.534 0.08*

Saudi Arabia 6.978 7.106 0.06* 7.087 7.259 0.07* 6.966 7.138 0.15

Niger 5.029 5.157 0.08* 5.088 5.260 0.13 5.142 5.314 0.07*

Note: p refers to the bootstrap p-value. In each row the items in bold are the lowest AIC and SC values and the corresponding p-values. : ***, ** and * indicate significance at the 1, 5 and 10 percent levels, respectively.

22

There are only 6 cases where they have to be revised. Namely, there is probably no Granger

causality from the saving ratio to the growth rate in the Netherlands and in Burundi, while

there is support for Granger causality from the saving ratio to the growth rate in the Central

African Republic, and from the growth rate to the saving ratio in Austria. In the remaining two

cases, Mauritania and Saudi Arabia, AIC and SC support different outcomes.

4 Summary

In this paper we have studied the possibility of Granger causality between the saving ratio

and the growth rate in eighty-four countries from 1961 to 2000. For technical reason, on the

basis of their per capita GDP in 1995, the countries have been classified as high-income (at

least 10000 $US), medium-income (between 1000 and 10000 $US) and low-income (less

than 1000 $US) countries, and the three panels of twenty-six, thirty and twenty-eight

countries, respectively, have been considered separately.

A new panel-data approach has been applied which is based on SUR systems and Wald

tests with country specific bootstrap critical values. This approach has two advantages. On

the one hand, it does not assume that the panel is homogeneous, so it is possible to perform

Granger-causality tests on each individual panel member separately. However, since

contemporaneous correlation is allowed across countries, it makes it possible to exploit the

extra information provided by the panel data setting. On the other hand, this approach does

not require pretesting for unit roots and cointegration, though it still requires the specification

of the lag structure. This is an important feature since the unit-root and cointegration tests in

general suffer from low power. Different tests often lead to contradictory outcomes, so the

conclusions drawn from them are usually conditional on some more or less arbitrary decisions

made by the researcher.

In order to check how sensitive the Granger causality test results are to lag selection, we

have repeated the calculations on three different specifications, but our final conclusions were

affected in only a few cases.

All things considered, we are confident to conclude that there is two-way Granger causality

between the saving ratio and the growth rate in Austria, there is one-way causality from

saving to growth in Ireland, Trinidad & Tobago and the Central African Republic, and from

growth to saving in Finland, France, Japan, Sweden, Switzerland and Niger. Our results also

lend some support to causality from saving to growth in Mauritania and from growth to saving

in Saudi Arabia. In all other cases, however, there is no empirical evidence of Granger

causality between the saving ratio and the growth rate in either direction.

23

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Economics, vol. 22, pp. 3-42,

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Growth and Trade: Essays in Honour of Sir Roy Harrod, Clarendon Press, Oxford. pp.

197-225.

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25

Romer, P.M. (1986): Increasing Returns and the Long-Run Growth, Journal of Political

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pp. 348-368.

26

1960 1965 1970 1975 1980 1985 1990 1995 2000

29

28

27

26

25

24

23

22

21

20

8

6

4

2

0

-2

-4

-6

Australia

1960 1965 1970 1975 1980 1985 1990 1995 2000

32

31

30

29

28

27

26

25

24

23

22

7

6

5

4

3

2

1

0

-1

Austria

Appendix

Data The following figures exhibit the data used in this study. In each plot the saving ratio (1960-

2000, percentage) is measured on the left vertical axis and is illustrated by the smooth line,

while the growth rate (1961-2000, percentage) is measured on the right vertical axis and is

illustrated by the dashed line.


1960 1965 1970 1975 1980 1985 1990 1995 2000

30

28

26

24

22

20

18

16

7

6

5

4

3

2

1

0

-1

-2

Belgium

1960 1965 1970 1975 1980 1985 1990 1995 2000

27

26

25

24

23

22

21

20

19

18

17

6

4

2

0

-2

-4

-6

Canada

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

28

26

24

22

20

18

16

10

8

6

4

2

0

-2

-4

Denmark

1960 1965 1970 1975 1980 1985 1990 1995 2000

32

30

28

26

24

22

20

18

10

8

6

4

2

0

-2

-4

-6

-8

Finland

27

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

35

30

25

20

15

15

10

5

0

-5

-10

Hong Kong

1960 1965 1970 1975 1980 1985 1990 1995 2000

34

32

30

28

26

24

22

20

18

12

10

8

6

4

2

0

-2

-4

-6

-8

Iceland

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

35

30

25

20

15

10

10

8

6

4

2

0

-2

Ireland

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

-5

14

12

10

8

6

4

2

0

-2

-4

Israel

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

29

28

27

26

25

24

23

22

21

20

8

6

4

2

0

-2

-4

Italy

1960 1965 1970 1975 1980 1985 1990 1995 2000

42

40

38

36

34

32

30

28

26

12

10

8

6

4

2

0

-2

-4

Japan

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

27

26

25

24

23

22

21

20

19

6

5

4

3

2

1

0

-1

-2

France

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

10

8

6

4

2

0

-2

-4

-6

-8

Greece

28

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

35

30

25

20

15

10

5

0

12

10

8

6

4

2

0

-2

-4

-6

-8

Korea, Rep.

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

29

28

27

26

25

24

23

22

7

6

5

4

3

2

1

0

-1

-2

Netherlands

1960 1965 1970 1975 1980 1985 1990 1995 2000

26

24

22

20

18

16

14

12

10

8

15

10

5

0

-5

-10

Portugal

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

27

26

25

24

23

22

21

20

12

10

8

6

4

2

0

-2

Spain

1960 1965 1970 1975 1980 1985 1990 1995 2000

45

40

35

30

25

20

15

10

10

8

6

4

2

0

-2

-4

-6

-8

Luxembourg

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

27

26

25

24

23

22

21

20

19

8

6

4

2

0

-2

-4

-6

-8

New Zealand

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

38

36

34

32

30

28

26

6

5

4

3

2

1

0

-1

Norway

1960 1965 1970 1975 1980 1985 1990 1995 2000

60

40

20

0

-20

-40

-60

-80

12

10

8

6

4

2

0

-2

-4

Singapore

29

1960 1965 1970 1975 1980 1985 1990 1995 2000

33

32

31

30

29

28

27

26

25

24

23

8

6

4

2

0

-2

-4

-6

-8

Switzerland

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

27

26

25

24

23

22

21

20

19

18

6

5

4

3

2

1

0

-1

-2

-3

Sweden

1960 1965 1970 1975 1980 1985 1990 1995 2000

22

21

20

19

18

17

16

15

14

7

6

5

4

3

2

1

0

-1

-2

-3

United Kingdom

1960 1965 1970 1975 1980 1985 1990 1995 2000

22

21

20

19

18

17

16

15

8

6

4

2

0

-2

-4

United States

30


1960 1965 1970 1975 1980 1985 1990 1995 2000

45

40

35

30

25

20

15

10

30

20

10

0

-10

-20

-30

Algeria

1960 1965 1970 1975 1980 1985 1990 1995 2000

34

32

30

28

26

24

22

20

18

16

14

15

10

5

0

-5

-10

Argentina

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

12

10

8

6

4

2

0

-2

-4

-6

Barbados

1960 1965 1970 1975 1980 1985 1990 1995 2000

60

50

40

30

20

10

0

-10

20

15

10

5

0

-5

Botswana

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

26

24

22

20

18

16

12

10

8

6

4

2

0

-2

-4

-6

-8

Brazil

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

25

20

15

10

5

10

5

0

-5

-10

-15

Chile

1960 1965 1970 1975 1980 1985 1990 1995 2000

26

24

22

20

18

16

14

12

6

4

2

0

-2

-4

-6

Colombia

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

26

24

22

20

18

16

14

12

10

8

8

6

4

2

0

-2

-4

-6

-8

-10

-12

Costa Rica

31

1960 1965 1970 1975 1980 1985 1990 1995 2000

24

22

20

18

16

14

12

10

8

6

4

15

10

5

0

-5

-10

-15

-20

Dominican Rep.

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

28

26

24

22

20

18

16

14

12

10

20

15

10

5

0

-5

-10

Ecuador

1960 1965 1970 1975 1980 1985 1990 1995 2000

20

18

16

14

12

10

8

6

4

12

10

8

6

4

2

0

-2

Egypt, Arab Rep.

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

10

5

0

-5

-10

-15

El Salvador

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

26

24

22

20

18

16

14

12

10

8

15

10

5

0

-5

-10

Fiji

1960 1965 1970 1975 1980 1985 1990 1995 2000

20

18

16

14

12

10

8

6

8

6

4

2

0

-2

-4

-6

-8

Guatemala

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

35

30

25

20

15

10

5

0

-5

10

5

0

-5

-10

-15

-20

Indonesia

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

25

20

15

10

5

15

10

5

0

-5

-10

Jamaica

32

1960 1965 1970 1975 1980 1985 1990 1995 2000

50

45

40

35

30

25

20

15

10

8

6

4

2

0

-2

-4

-6

-8

-10

Malaysia

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

5

20

15

10

5

0

-5

-10

-15

Mauritius

1960 1965 1970 1975 1980 1985 1990 1995 2000

32

30

28

26

24

22

20

18

16

14

10

8

6

4

2

0

-2

-4

-6

-8

-10

Mexico

1960 1965 1970 1975 1980 1985 1990 1995 2000

22

20

18

16

14

12

10

8

6

10

8

6

4

2

0

-2

-4

-6

-8

-10

Morocco

1965 1970 1975 1980 1985 1990 1995 2000

45

40

35

30

25

20

15

10

5

0

-5

15

10

5

0

-5

-10

Papua New Guinea

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

25

20

15

10

5

0

12

10

8

6

4

2

0

-2

-4

-6

-8

Paraguay

1960 1965 1970 1975 1980 1985 1990 1995 2000

45

40

35

30

25

20

15

10

15

10

5

0

-5

-10

-15

Peru

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

28

26

24

22

20

18

16

14

12

6

4

2

0

-2

-4

-6

-8

-10

-12

Philippines

33

1960 1965 1970 1975 1980 1985 1990 1995 2000

90

80

70

60

50

40

30

20

10

0

15

10

5

0

-5

-10

-15

-20

Saudi Arabia

1960 1965 1970 1975 1980 1985 1990 1995 2000

32

30

28

26

24

22

20

18

16

8

6

4

2

0

-2

-4

-6

-8

South Africa

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

35

30

25

20

15

10

15

10

5

0

-5

-10

-15

Thailand

1960 1965 1970 1975 1980 1985 1990 1995 2000

50

45

40

35

30

25

20

15

12

10

8

6

4

2

0

-2

-4

-6

-8

Trinidad & Tobago

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

5

0

8

6

4

2

0

-2

-4

-6

-8

-10

-12

Uruguay

1960 1965 1970 1975 1980 1985 1990 1995 2000

50

45

40

35

30

25

20

15

8

6

4

2

0

-2

-4

-6

-8

-10

-12

Venezuela

34


1960 1965 1970 1975 1980 1985 1990 1995 2000

20

15

10

5

0

-5

15

10

5

0

-5

-10

-15

-20

Bangladesh

1960 1965 1970 1975 1980 1985 1990 1995 2000

10

5

0

-5

-10

-15

8

6

4

2

0

-2

-4

-6

-8

Benin

1960 1965 1970 1975 1980 1985 1990 1995 2000

50

45

40

35

30

25

20

15

10

5

5

0

-5

-10

-15

-20

Bolivia

1960 1965 1970 1975 1980 1985 1990 1995 2000

15

10

5

0

-5

-10

8

6

4

2

0

-2

-4

-6

Burkina Faso

1960 1965 1970 1975 1980 1985 1990 1995 2000

12

10

8

6

4

2

0

-2

-4

-6

-8

20

15

10

5

0

-5

-10

-15

-20

Burundi

1960 1965 1970 1975 1980 1985 1990 1995 2000

15

10

5

0

-5

-10

8

6

4

2

0

-2

-4

-6

-8

-10

-12

Central African Rep.

1960 1965 1970 1975 1980 1985 1990 1995 2000

45

40

35

30

25

20

15

10

15

10

5

0

-5

-10

-15

-20

-25

-30

-35

China

1960 1965 1970 1975 1980 1985 1990 1995 2000

70

60

50

40

30

20

10

0

-10

-20

20

15

10

5

0

-5

-10

-15

Congo, Rep.

35

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

5

15

10

5

0

-5

-10

-15

-20

Cote d'Ivorie

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

10

5

0

-5

-10

-15

-20

Ghana

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

5

0

10

5

0

-5

-10

-15

-20

Guyana

1960 1965 1970 1975 1980 1985 1990 1995 2000

15

10

5

0

-5

-10

-15

10

5

0

-5

-10

-15

-20

Haiti

1960 1965 1970 1975 1980 1985 1990 1995 2000

28

26

24

22

20

18

16

14

12

10

8

8

6

4

2

0

-2

-4

-6

Honduras

1960 1965 1970 1975 1980 1985 1990 1995 2000

24

22

20

18

16

14

12

8

6

4

2

0

-2

-4

-6

-8

India

1960 1965 1970 1975 1980 1985 1990 1995 2000

30

25

20

15

10

5

0

20

15

10

5

0

-5

-10

-15

Kenya

1960 1965 1970 1975 1980 1985 1990 1995 2000

-10

-20

-30

-40

-50

-60

-70

-80

-90

25

20

15

10

5

0

-5

-10

-15

-20

Lesotho

36

1960 1965 1970 1975 1980 1985 1990 1995 2000

10

8

6

4

2

0

-2

10

5

0

-5

-10

-15

Madagascar

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

-5

-10

15

10

5

0

-5

-10

-15

Malawi

1960 1965 1970 1975 1980 1985 1990 1995 2000

40

30

20

10

0

-10

-20

25

20

15

10

5

0

-5

-10

Mauritania

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

0

-5

-10

-15

-20

10

5

0

-5

-10

-15

-20

-25

-30

-35

Nicaragua

1960 1965 1970 1975 1980 1985 1990 1995 2000

18

16

14

12

10

8

6

4

2

0

-2

10

5

0

-5

-10

-15

-20

-25

Niger

1960 1965 1970 1975 1980 1985 1990 1995 2000

35

30

25

20

15

10

5

0

20

15

10

5

0

-5

-10

-15

-20

Nigeria

1960 1965 1970 1975 1980 1985 1990 1995 2000

16

14

12

10

8

6

4

8

6

4

2

0

-2

-4

Pakistan

1960 1965 1970 1975 1980 1985 1990 1995 2000

20

10

0

-10

-20

-30

-40

-50

30

20

10

0

-10

-20

-30

-40

-50

-60

Rwanda

37

1960 1965 1970 1975 1980 1985 1990 1995 2000

15

10

5

0

-5

-10

15

10

5

0

-5

-10

Senegal

1960 1965 1970 1975 1980 1985 1990 1995 2000

60

50

40

30

20

10

0

-10

15

10

5

0

-5

-10

-15

-20

Togo

1960 1965 1970 1975 1980 1985 1990 1995 2000

60

50

40

30

20

10

0

-10

15

10

5

0

-5

-10

-15

Zambia

1960 1965 1970 1975 1980 1985 1990 1995 2000

25

20

15

10

5

20

15

10

5

0

-5

-10

-15

Syrian Arab Rep.

38

Model For the ith panel member (2a) and (2b) can be written in matrix form as

1, 1, 1, 1, 1, 1,i i i i i i iα * *Y = ι +Y β + X γ + ε (2a*)

and 2, 2, 2, 2, 2, 2,i i i i i i iα * *X = ι +Y β +X γ +ε (2b*) where 4 is a T ×1 vector of ones, Yi and Xi are T ×1 vectors of the observed values of Y and X,

*1,iY , *

1,iX , *2,iY and *

2,iX are T ×1 vectors of the values of the error variables, ∀1,i and ∀2,i are the

intercept terms, and 1,iβ , 1,iγ , 2,iβ and 2,iγ are mly1×1, mlx1×1, mly2×1 and mlx2×1 vectors of

the slope coefficients, all for country i.

Stacking the equations for all i (i = 1,..., N ), the two sets of equations can be written as * *

1 1 1 1 1 1= + + +Y α Y β X γ ε (2a**)

and * *2 2 2 2 2 2= + + +X α Y β X γ ε (2b**)

where

1

2

:

N

=

YY

Y

Y

,

1

2

:

N

=

XX

X

X

,

1,1

1,21

1,

:

N

αα

α

=

ιι

α

ι

,

2,1

2,22

2,

:

N

αα

α

=

ιι

α

ι

,

1,1

1,21

1,

:

N

=

εε

ε

ε

,

2,1

2,22

2,

:

N

=

εε

ε

ε

are N T × 1 vectors,

*1,1

*1,2*

1

*1,

...

...: : : :

... N

=

Y 0 00 Y 0

Y

0 0 Y

,

*1,1

*1,2*

1

*1,

...

...: : : :

... N

=

X 0 00 X 0

X

0 0 X

*2,1

*2,2*

2

*2,

...

...: : : :

... N

=

Y 0 00 Y 0

Y

0 0 Y

,

*2,1

*2,2*

2

*2,

...

...: : : :

... N

=

X 0 00 X 0

X

0 0 X

are N T ×N mly1, N T ×N mlx1, N T ×N mly2 and N T ×N mlx2 matrices, and

39

1,1

1,21

1,

:

N

=

ββ

β

β

,

1,1

1,21

1,

:

N

=

γγ

γ

γ

,

2,1

2,22

2,

:

N

=

ββ

β

β

,

2,1

2,22

2,

:

N

=

γγ

γ

γ

are N mly1×1, N mlx1×1, N mly2×1 and N mlx2×1 vectors.

Documents

Saving and Growth: Granger Causality Analysis with