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Saving, Growth, and Investment: A Macroeconomic Analysis Using a Panel of Countries

01 May 2000-The Review of Economics and Statistics (MIT Press 238 Main St., Suite 500, Cambridge, MA 02142-1046 USA journals-info@mit.edu)-Vol. 82, Iss: 2, pp 182-211

AbstractThis paper provides a descriptive analysis of the long- and short-run correlations among saving, investment, and growth rates for 123 countries over the period 1961-94. Three results are robust across data sets and estimation methods: i) lagges saving rates are positively related to investment rates; ii) investment rates Granger cause growth rates with a negative sign; iii) growth rates Granger-cause investment with a positive sign.

Summary (3 min read)

Introduction

  • And Motivation THE MAIN AIM of this paper is to provide an exhaustiveand careful descriptive analysis of the correlations among saving, investment, and growth rates.
  • It is therefore interesting to establish whether such a correlation survives also the introduction of various controls.
  • A dynamic link running from growth to investment might also hold.
  • While in recent years several authors have used panels of countries to study a variety of phenomena, no standard econometric methodology has been developed for the analysis of this type of data, a relative large panel of countries.

II. The Statistical Model and its Econometric Estimation

  • Preliminary to the empirical analysis, the authors discuss some econometric issues that are relevant to the study of the dynamic relationship between two or more variables observed over a relatively long time horizon and for a rather large number of countries.
  • Obviously, such a system cannot be estimated without imposing some restrictions on its parameters.
  • If the time-series variability is deemed sufficient to obtain reasonably precise estimates, one could specify the model by assuming that the parameters are constant over time and might be variable across countries.
  • Which of the two choices is feasible is often dictated by the data available.
  • An alternative way of thinking about the choice of estimation techniques is to consider whether the crosssectional or the time-series dimension has to increase in order to derive the asymptotic distributions used in hypothesis testing.

A. Large N (fixed T) Models

  • Many recent studies of data sets similar to the one the authors use have followed the microeconometric literature and applied estimators that rely on the cross-sectional variability to identify the model of interest.
  • If one is willing to assume that the residuals of the two equations are contemporaneously uncorrelated, on can instrument the laggedy’s in equation (1) and the laggedx’s in equation (2).
  • Even if one is interested in identifying long-run relationships, it is not obvious that averaging over fixed intervals will effectively eliminate businesscycle fluctuations and make easier the emergence of the relationships of interest.
  • As discussed by Pesaran and Smith (1995) (PS hereafter), if the coefficients of equation (1) and (2) are constant over time but vary across countries, techniques that impose parameter homogeneity do not yield consistent estimates.
  • Given these considerations, the best strategy is to estimate rich and flexible dynamic models that allow for differences in short- and long-run coefficients and use estimators that appeal to ‘largeT’ asymptotics to achieve consistency, while efficiently exploiting all the available information.

B. Contemporaneous Correlations and Rank Correlations between Saving, Investment, and Growth Rates

  • The authors start the analysis of the data set computing some simple correlation and rank correlation coefficients between the three variables that constitute the main focus of this study—namely the saving rate, the investment rate, and the 11 Another limitation is the fact that one is constrained to consider only some classes of error models.
  • In figure 1, the authors plot the contemporaneous correlation coefficients computed using all saving-growth pairs of a given year against time.
  • Again, it must be stressed that the number of countries that 15 As data set 1 is a not balanced panel, the country averages and the annual (cross section) correlations are computed using a different number of observations.
  • They report results obtained with and without the inclusion of a set of time dummies in their equations.
  • The experiments in columns 3 and 4 indicate that the assumption about the lack of contemporaneous correlation in the residuals of equation (1) and (2) is potentially quite important and might substantially affect their inferences.

A. A Dynamic Model with No Country Heterogeneity

  • The authors present a dynamic model for each of the three pairs of variables considered above, estimated with annual data and allowing for four lags of each of the two variables considered.
  • As discussed above, the authors estimate the model by OLS with country-specific intercepts.
  • The long-run effect of growth on saving is in general considerably larger than the sum of the lagged coefficients, reflecting a certain amount of persistence of saving rates:.
  • The coefficient on the first lag is significantly positive in all data sets, but the overall long-run effect turns out to be negative because of the effect of the additional lags.
  • Furthermore, both the short- and the long-run effects are quite similar to those in table 4.

C. Growth and Investment Dynamic Model with Country Heterogeneity

  • One of the main advantages of using data that have a reasonably large time dimension is that one can investigate 23 Moreover, the first two lagged investment rates take very large coefficients: close to 1 in the first and close to20.3 in the second.
  • The authors also compute, as before, the short- and long-run multipliers for the causing variable.
  • In all other cases, the results obtained with the mean estimator are qualitatively identical to those obtained with the OLS estimator.
  • The authors conclude that, even if in their data set there is evidence of parameter heterogeneity across country, appropriately taking it into account does not modify the general picture obtained using estimators that erroneously impose homogeneity.
  • Note that, because of the presence of outliers, sometimes the mean group estimator is signed differently than the median individual estimate.

D. Three-Equation System

  • So far, the authors have been considering pair-wise tests of Granger causation.
  • In studying their three variables, there is no reason not to consider them jointly.
  • Rather than showing all estimates, the authors report the sum of the coefficients on the four lags considered and, in the case of the variables other than the dependent variable, the long-run effects.
  • If the authors consider the persistence of the three equations as measured by the sum of the coefficients on the lags of the dependent variable, they find that, as before, growth shows very little of it, while investment and saving rates are very persistent.
  • In general, this magnifies the size of the effects.

E. An Overall Evaluation and Some Extensions

  • The authors have already noticed that their results are, within the framework they have used, quite stable and robust.
  • While in table 7 the short- and the long-run multipliers are positive and usually significant, the introduction of controls reduces size and precision of the estimates in data set 2, and changes the signs in the case of data set 3.
  • Before turning to the discussion of the relationship between growth and saving, a small digression on the relevance of their evidence for the growth regressions initiated by the work of Barro (1991), Mankiw, Romer, and Weil (1992), and others is called for.

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SAVING, GROWTH, AND INVESTMENT:
A MACROECONOMIC ANALYSIS USING A PANEL OF COUNTRIES
Orazio P. Attanasio, Lucio Picci, and Antonello E. Scorcu*
Abstract—This paper provides a descriptive analysis of the long- and
short-run correlations among saving, investment, and growth rates for 123
countries over the period 1961–94. Three results are robust across data sets
and estimation methods: i) lagges saving rates are positively related to
investment rates; ii) investment rates Granger cause growth rates with a
negative sign; iii) growth rates Granger-cause investment with a positive
sign.
I. Introduction and Motivation
T
HE MAIN AIM of this paper is to provide an exhaustive
and careful descriptive analysis of the correlations
among saving, investment, and growth rates. We want to
establish what are the main (aggregate) ‘stylized facts’ that
link these variables. For such a purpose, we use a new data
set, gathered by the World Bank that contains a wide range
of variables for 150 countries over the post-WWII period.
The data set is probably the best panel of countries available
to date.
In what follows, we analyze both contemporaneous
correlations and dynamic models. Most of the analysis,
however, is focused on the dynamic relationships among the
variables of interest. We will be using the statistical concept
of Granger causality to denote the fact that a variable (the
caused one) is correlated with lagged values of the other
(after controlling for its own lags). Obviously, one should
refrain from giving a causal or structural interpretation to
these results.
We estimate flexible dynamic (reduced-form) models and
identify long-run and short-run correlations among the
variables of interest. The empirical regularities we document
should complement those observed in microeconomic data
sets and constitute the benchmark against which different
models of saving, consumption, and growth are evaluated.
While the scope of this paper is not the estimation of a
structural model that links growth, saving, and investment
rates, it is worth thinking about the implications of some of
the standard models for the correlations we consider. The
theoretical predictions for both the long-run and short-run
correlations among the variables of interest are often ambigu-
ous. Nonetheless, measuring such correlations is informa-
tive about the relative importance of various factors.
Anatural theoretical framework that is used to think about
the correlation between saving and growth is the lifecycle
model. Such a model might imply both a long-run relation-
ship between past growth and current saving rates and
between future expected growth and current saving. If
wealth is accumulated during the first part of the lifecycle
and decumulated during retirement, population and/or pro-
ductivity growth might lead to higher aggregate saving, if
the saving of the young exceeds the dissaving of the old, in
the steady-growth equilibrium. However, it is easy to reverse
such prediction if one makes individual earning profiles
steep enough and lets the young borrow against their future
income. If the borrowing (negative saving) of the young is
large enough at the aggregate level, a strong productivity
growth might lead to a negative correlation between saving
rates and growth rates. The picture is further complicated if
one considers the possibility of liquidity constraints, precau-
tionary savings, habit formation, and general equilibrium
effects on the rate of return. In fact, the sign of the long-run
equilibrium correlation depends upon the precise shape of
the utility function, the demographic structure, the presence
of productivity changes, and other such factors.
The lifecycle model, in which individual saving is an
explicitly forward-looking variable, also predicts Granger
causation, possibly with a negative sign, running from
saving to growth. Rational individuals anticipating declines
in future income will increase savings. This is the ‘saving
for a rainy day’ mechanism illustrated, for instance, by
Campbell (1987), and it is worth stressing if nothing else to
emphasize that one should use particular caution in interpret-
ing Granger causality results.
1
Other saving-to-growth link-
ages are also possible through an (almost passive) physical
capital accumulation. Obviously, this link is only an indirect
one.
The considerations of the last three paragraphs clarify the
potential utility of measuring saving-growth correlations to
establish which of the various factors at play are more likely
to be of importance. For the same reason, it is important to
distinguish between long- and short-run effects and to
identify indirect effects through other variables, such as
investment rates. It should also be clear, however, that the
evidence we present can constitute only a piece of the
puzzle. If one is interested in explaining cross-country
differences in saving and growth (and their relationship), the
aggregate evidence should be complemented with microeco-
nomic evidence on the shape of earning profiles, age
distribution, and so forth. The dynamic relationship between
saving and growth rates has recently been studied by Carroll
Received for publication February 2, 1999. Revision accepted for
publication November 29, 1999.
* University College London Institute for Fiscal Studies and NBER,
Universita` di Bologna, and Universita` di Bologna, respectively.
We would like to thank Monica Paiella for skillful research assistance
and ManuelArellano, Steve Bond, Costas Meghir, Klaus Schmidt-Hebbel,
Luis Serve´n, and Farshid Vahid for useful comments. This paper was first
presented at the meeting ‘Saving in the World,’ January 15–16, 1998, at
the World Bank in Washington D.C., where we received valuable
comments from several participants and from our discussant Chris Carroll.
We are also grateful for detailed and useful comments from three
anonymous referees and an editor.
1
A short-run negative correlation emerges also in the standard IS-LM
framework, because a positive shock to saving leads to a subsequent
decline in income and production.
The Review of Economics and Statistics, May 2000, 82(2): 182211
r
2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

and Weil (1994), who explicitly used the concept of Granger
causation. We will analyze Carroll and Weil results in detail,
partly for their intrinsic interest and partly to illustrate some
of the methodological points that we want to make.
When considering the association between saving and
investment rates, it is natural to think in terms of the
integration (or lack of) of international financial markets.
Indeed, in an influential contribution, Feldstein and Horioka
(1980) interpreted the cross-country correlation between
saving and investment rates as evidence of low international
capital mobility. In this case, saving is likely to be a limiting
factor for investment. A saving-to-investment link could
therefore arise because ‘an increase in national saving has a
substantial effect on the level of investment’ (Feldstein and
Bacchetta (1991)), as investment must be supported by
saving and domestic firms compete for the flow of available
domestic saving.
This interpretation has often been challenged: In fact, in
the long run, technological variables and the demographic
structure of the population could drive both variables,
thereby inducing positive correlation even with perfect
capital mobility (Baxter and Crucini (1992); Taylor (1994).
2
Our results show that the correlation between saving and
investment is, indeed, a robust finding. Moreover, we show
that such a correlation has an important dynamic compo-
nent, in that lagged saving rates are strongly correlated with
current investment rates. It is therefore interesting to estab-
lish whether such a correlation survives also the introduction
of various controls.
Obviously, Granger causation running from investment to
saving is also possible. While the exact mechanisms at work
are hard to spell out in detail, if an increased demand for
capital goods stimulates saving—maybe through interest
rate effects or the endogenous development of the financial
instruments that permit the mobilization of saving—saving
might adjust to investment.
The positive contemporaneous association between rate
of investment and growth is usually explained in terms of a
causal link running from the former variable to the latter.
Several well-known theoretical explanations can be offered
for such a link. Some growth models, for instance, suggest
that a rise in productivity growth causes both growth rates
and investment rates to move together (possibly coupled
with the accumulation of human capital). This is the type of
mechanism mentioned, for instance, by Barro (1991) when
considering the simultaneous determination of growth and
investment rates (as well as fertility rates) and investigated
empirically more recently by Caselli, Esquirrel, and Lefort
(1995) and Islam (1996). In what follows, we stress, once
again, the dynamic nature of the relationship between
investment and growth and show that the dynamic correla-
tion can be quite different from the contemporaneous ones.
A dynamic link running from growth to investment might
also hold. Higher growth might drive saving up, leading in
turn to higher investment. However, Blomstrom, Lipsey, and
Zejan (1996) suggest that accumulation might be a conse-
quence of the growth process, ignited by the growth-based
saving change. Furthermore, higher growth can enhance
future growth expectations and returns on investment.
Provided that saving (possibly raised by the growth process)
is not a limiting factor, the accumulation of physical capital
will finally take place.
While in recent years several authors have used panels of
countries to study a variety of phenomena, no standard
econometric methodology has been developed for the analy-
sis of this type of data, a relative large panel of countries.
The second contribution of our paper is a methodological
one. We precede the empirical analysis with a discussion of
alternative econometric techniques and of the related meth-
odological issues.
In standard panel data analysis, the presence of fixed
effects correlated with the variables on the right-hand side of
the equations of interest constitutes an important concern.
The issue is particularly serious in the analysis of dynamic
systems, in which the hypothesis of strong exogeneity of the
independent variables is obviously untenable. However,
while these problems are certainly relevant, the analysis of a
panel of countries puts the researcher in a slightly different
environment than that faced by an econometrician studying
large panels of individual observations. The main difference
is in the fact that, unlike with household-level data, in which
typically N (the number of individuals) is large and T (the
number of periods) is small, in analyzing a panel of
countries, N and T tend to have the same order of magnitude.
Furthermore, it is more natural to think about the asymp-
totics of the problem as T-asymptotics rather than
N-asymptotics. This will have an effect on the choice of
techniques used in the analysis. Finally, if one is interested in
characterizing the dynamic relationship among several vari-
ables, it is more natural to use concepts from the time-series
literature and use the N dimension of the sample to allow for
differences among countries that can be of independent
interest.
The rest of the paper is organized as follows. In section II,
we discuss some methodological issues relevant for the
econometric analysis of dynamic models using panels of
countries. In section III, we briefly describe the data set and
present some evidence on the static correlations among the
variables of interest. In section IV, we analyze the robustness
of the Carroll and Weill results by using their estimators on
the new data set and also considering different econometric
techniques and different frequencies of the data. In section V,
instead, we switch to the analysis of annual data and apply
three different types of estimators. We first assume that the
total number of time observations we have is large enough to
allow us to use ‘big Tasymptotic approximations. We then
present some results obtained using a ‘fixed T estimator.
Next, we allow for across-country heterogeneity in the
dynamic effects that link the three variables of interest.
Finally, we present the estimates of a trivariate model in
2
Arguments based on the intertemporal country’s budget constraint lead
to the same conclusion (Argimon and Roldan (1994)).
183SAVING, GROWTH, AND INVESTMENT

which we consider the variables of interests and their
interactions simultaneously. We conclude the section by
analyzing the effects of introducing various controls nor-
mally used in the literature. In section VI, we summarize and
interpret the main results.
II. The Statistical Model and its Econometric Estimation
Preliminary to the empirical analysis, we discuss some
econometric issues that are relevant to the study of the
dynamic relationship between two or more variables ob-
served over a relatively long time horizon and for a rather
large number of countries.
A general representation of a dynamic model linking two
variables x and y is
y
i,t
⫽␣
0
j1
q
i,t,j
y
y
i,tj
j1
p
i,t,j
y
x
i,tj
⫹␺
t
y
f
i
y
u
i,t
y
(1)
x
i,t
⫽␤
0
j1
m
i,t,j
x
y
i,tj
j1
n
i,t,j
x
x
i,tj
⫹␺
t
x
f
i
x
u
i,t
x
(2)
Obviously, such a system cannot be estimated without
imposing some restrictions on its parameters. This can be
done either in the time series or in the cross-sectional
dimension. If the time-series variability is deemed sufficient
to obtain reasonably precise estimates, one could specify the
model by assuming that the parameters are constant over
time and might be variable across countries. On the other
hand, if one wants to exploit the cross-sectional variability,
one might let the parameters differ over time, while being
constant across countries. Which of the two choices is
feasible is often dictated by the data available. However,
when the time and cross-sectional dimensions are roughly of
the same order of magnitude (as it is in the case at hand), one
faces a real choice whose solution should be dictated by the
nature of the phenomenon one is studying.
An alternative way of thinking about the choice of
estimation techniques is to consider whether the cross-
sectional or the time-series dimension has to increase in
order to derive the asymptotic distributions used in hypoth-
esis testing. In the analysis of country panels, it is conceptu-
ally awkward to consider N that goes to infinity. On the other
hand, the analysis that lets T go to infinity is the standard
practice in time-series analysis.
3
Furthermore, if one is
interested in studying the dynamic relationship between two
or more variables, either by testing the existence of Granger
causality or, more generally, by characterizing the dynamic
relationship between the variables under study, it seems
natural to consider a model that is flexible, but stable, over
time. The analysis of heterogeneity in impluse-response
functions across countries might be also interesting in its
own right.
A. Large N (fixed T) Models
Many recent studies of data sets similar to the one we use
have followed the microeconometric literature and applied
estimators that rely on the cross-sectional variability to
identify the model of interest. This amounts to imposing
constancy of the parameters in equation (1) and (2) across
countries, while, at least in principle, allowing them to vary
over time. Typically, estimators with fixed effects, such as
those proposed by Holtz-Eakin, Newey, and Rosen (1988)
(HNR hereafter) and Arellano and Bond (1991) (AB hereaf-
ter), are used. The model is often specialized to the
following expression, to impose constancy of the parameters
not only across equations, but also over time:
4
y
i,t
⫽␣
0
j1
q
j
y
y
i,tj
j1
p
j
y
x
i,tj
f
i
y
u
i,t
y
(1a)
x
i,t
⫽␤
0
j1
m
j
x
y
i,tj
j1
n
j
x
x
i,tj
f
i
x
u
i,t
x
(2a)
The coefficients
j
x
are relevant for the Granger causality
running from y to x, while the coefficients
j
y
are relevant for
the Granger causality running in the opposite direction. We
assume that the residuals of the two equations of the system
are uncorrelated with the variables on the right side and are
i.i.d. The two variables, however, are in principle correlated
at a point in time; that is, the covariance between u
i,t
x
and u
i,t
y
is not necessarily zero. Notice that, because of the presence
of fixed effects, none of the observable variables on the
right-hand side of the two equations is strongly exogenous.
To eliminate the bias caused by the presence of fixed
effects, these equations are typically estimated in first
differences. As first-differencing induces MA(1) residuals,
one has to use some instrumental-variable technique. HNR
and AB stress that, when the cross-sectional dimension
identifies the model, all the orthogonality restrictions im-
plied by the dynamics of the system can be exploited to
achieve efficiency.
5
In particular, at each point in time t, one
3
Also, from a practical point of view, it is often not obvious that
increasing the number of the included countries provides additional
information, when the quality of the data decreases as more countries are
considered.
4
As such a system is typically estimated using N-asymptotics. The latter
assumption can be easily relaxed. (See HNR (1988) for instance.)
5
Notice that, in both equations, we need to instrument both the
(one-period) lagged ys and the lagged xs. If one is willing to assume that
the residuals of the two equations are contemporaneously uncorrelated,
one can instrument the lagged ys in equation (1) and the lagged x’s in
equation (2).
184 THE REVIEW OF ECONOMICS AND STATISTICS

can use as valid instruments all the variables from time 1 to
time t s 1 (where s max (m, n, p, q).
6
While the application of the HNR or AB estimators is
conceptually straightforward, a few important caveats are in
order when the time dimension is not small and when the
focus is on a dynamic phenomenon such as Granger
causality. As T increase, the number of admissible instru-
ments increases very quickly. In our application, for in-
stance, with two variables whose lags are valid instruments,
m n p q 1, t 35, and N 50 (as it is
approximately the case in some of the results presented
below), by the time we get to the end of the sample, there are
close to seventy valid instruments for no more than fifty
cross-sectional observations. It is obvious that one cannot
use all of them. In cases like this, it is advisable to use only a
limited number of lagged variables as instruments.
An alternative way to tackle the problem, which has often
been employed, is to use n-year averages (with n usually
equal to 5 or 10), therefore artificially reducing the time-
series dimension of the sample. This filtering is meant to
capture long-run relationships and abstract from fluctuations
of business-cycle frequencies. We favor the use of methods
that explicitly use the time-series variation and possibly
explore the existence of heterogeneity across countries.
Even if one wants to use the ‘large Nestimators, we argue in
favor of annual observations rather than n-year averages.
Some of the reasons follow.
7
1. Annual data provide information that is lost when
averaging.
2. Even if one is interested in identifying long-run
relationships, it is not obvious that averaging over
fixed intervals will effectively eliminate business-
cycle fluctuations and make easier the emergence of
the relationships of interest. The length of the interval
over which averages are computed is arbitrary, and
there is no guarantee that business cycles are cut in the
right way, as their length varies over time and across
countries.
3. By averaging, one commits oneself to the use of
cross-sectional variability to estimate the parameters
of interest and discards the possibility of considering
cross-sectional heterogeneity in the parameters. This
limitation might be particularly severe when one
analyzes several countries that could differ in many
dimensions.
4. By averaging, an overall effect over a given time
window is measured. In the case at hand, what we
know about the economic relationship among the
variables involved indicates that contrasting forces are
often at work. The dynamic interplay of these forces
could well result in significant but opposed effects,
maybe acting with different lags, that might eventually
cancel out once averaged. Focusing only on the
long-run effect, provided averaging does that, pre-
cludes the analysis of such short-run effects.
8
B. Large T (fixed N) Models
An alternative to methods based on ‘large N asymptotics
is to assume that the parameters are constant over time and
exploit the time-series variability to estimate them. In such a
situation, we can introduce flexibility in the cross-sectional
dimension and let the coefficients of interest vary across
countries.
The coefficients of our model represent the lagged effects
of growth, saving, and investment on the same variables.
However, the underlying mechanisms linking those vari-
ables could differ across countries, possibly due to institu-
tional reasons or differences in preferences.
9
The question,
then, is to determine whether the econometric techniques
that we have illustrated—all assuming constancy across
countries of the underlying parameters—are still appropriate
in the case in which those parameters are heterogeneous.
The answer to this question obviously depends on the
nature of the variation and on the general properties of the
model. As discussed by Pesaran and Smith (1995) (PS
hereafter), if the coefficients of equation (1) and (2) are
constant over time but vary across countries, techniques that
impose parameter homogeneity do not yield consistent
estimates. Responsible of the bias—which persists regard-
less of the size of N, T, and of any choice of instruments—is
the dynamic nature of the model. On the other hand, a mean
group estimator, obtained by averaging the individual coun-
tries estimates, is unbiased and consistent.
While wrongly assuming parameter constancy across
countries implies biased estimates of the underlying average
effects, a parsimoniously parameterized model yields more-
precise estimates. Within this familiar tradeoff between
consistency and efficiency, the choice between homoge-
neous ‘pooled’estimators and their heterogeneous counter-
parts does not reside in a formula, but boils down to a
case-by-case problem of model selection.
10
6
By using a GLS-type transformation to account for the MA structure of
the residuals, one obtains a further gain in efficiency. Arellano and Bover
(1995) show that one can express the model in terms of orthogonal
deviations to obtain a simple way of computing the HNR or AB estimator.
7
The same considerations arise also in different frameworks. For
example, the Feldstein-Horioka type regressions have been recently
estimated on annual series rather than on the more conventional time
averages. See, among others, Sinn (1992).
8
It has also been argued that the consideration of time averages reduces
the relevance of measurement error. Of course, this argument is valid only
if measurement errors are not perfectly correlated over time.
9
In such a situation, rather than in the complete characterization of the
coefficients in all countries, one might be interested in the average
coefficient.
10
Baltagi and Griffin (1997) compare out-of-sample forecast perfor-
mances of an array of homogeneous and heterogeneous estimators. They
find that pooled estimators fare relatively well, thus showing (for the
particular case at hand) that the heterogeneity inevitably characterizing
different countries, and the ensuing pooled estimates’ bias, should not
necessarily lead to the rejection of the homogeneity assumption.
185SAVING, GROWTH, AND INVESTMENT

C. Large N or Large T?
As in our data set N and T are roughly of the same order of
magnitude, the presence of a tension between flexibility in
the time-series and in the cross-sectional dimension is
evident. The resolution of this tension, absent in the analysis
of individual data surveys in which T is typically small and
inferences are conducted using ‘large N asymptotics, obvi-
ously affects the model specification and the choice of
estimators.
Given these considerations, the best strategy is to estimate
rich and flexible dynamic models that allow for differences
in short- and long-run coefficients and use estimators that
appeal to ‘large Tasymptotics to achieve consistency, while
efficiently exploiting all the available information. These
models can and should also consider the possibilities that the
(dynamic) relationships of interest are different across
countries.
Obviously, the proposed approach imposes different types
of constraints on the researcher. The most important is the
necessity to consider coefficients that are constant over time.
Obviously, it is necessary to assume that the available
sample period is long enough to allow for reasonably precise
estimates of time-invariant country coefficients.
11
Partly
because of these reasons and partly to make our analysis
comparable to a large body of the literature, we present
results obtained estimating both classes of models discussed
in this section.
III. The Data Set
A. The Nature of the Data Set and its Construction
As mentioned in the introduction, we use a new panel of
countries (the World Saving Database) recently gathered at
the World Bank. As the data-gathering effort is described in
detail by Loayza et al. (1998), here we provide a very brief
discussion of the structure of the panel, focusing in particu-
lar on those aspects that are relevant for our analysis. With
the exception of total population figures, originating from
the World Bank database, all the data are from National
Accounts and follow their standard conventions. The data-
base includes 150 countries and spans the years 1960 to
1995. However, not all variables are available for every
country and for every year. In particular, the population data
cover the period 1960 to 1994 only. As a consequence, our
analysis is restricted to those years.
For each country, the variables that we use are the rate of
growth of annual, real, per capita gross national product, the
saving rate, and the rate of investment. All these series are
measured in local currencies. The saving rates are computed
as nominal gross national saving over nominal gross na-
tional income, while the investment rates are computed as
nominal gross fixed investment over nominal gross national
product. Growth is measured as the rate of growth in real per
capita GNP (deflated with the GDP deflator).
12
We use three different samples of countries. The first is as
close as possible to the whole set of countries included in the
World Bank database. We exclude only those countries
whose annual income, saving, or investment were not
recorded at all or are recorded for less than a five-year
interval, and those countries for which the relevant series
have missing values in the middle of the sample period. This
procedure leaves us with a sample consisting of 123
countries. We call this our ‘whole’ sample. The other two
samples trade-off the T and N dimension. The second sample
consists of the fifty countries for which all variables are
available every year in the interval 1965–1993. Our third
sample consists only of those countries whose variables are
available every year from 1961 to 1994. Only 38 countries
are included. We also use, for comparison purposes only, the
Carroll and Weil (1994) 64-countries sample. All countries
in this sample are also in our whole sample, with the
exception of Tanzania and Zimbabwe, which were excluded
because of the unavailability of data.
13
In the next section, we analyze Carroll and Weil’s full
sample results, in addition to the analysis based on annual
data. We also look at nonoverlapping, five-year averages of
growth, saving, and investment rates for each country.
14
The
information on the number of countries in each of the data
sets we use is summarized in table 1.
B. Contemporaneous Correlations and Rank Correlations
between Saving, Investment, and Growth Rates
We start the analysis of the data set computing some
simple correlation and rank correlation coefficients between
the three variables that constitute the main focus of this
study—namely the saving rate, the investment rate, and the
11
Another limitation is the fact that one is constrained to consider only
some classes of error models. For instance, if the residuals of the model in
equation (1) and (2) are of the autoregressive type and there are fixed
effects, it is impossible to find instruments that identify the relationships of
interest.
12
To avoid the loss of a large number of observations, we did not perform
any PPP adjustment. The same applies to the deflation of GNP by the GDP
deflator.
13
Dropping these countries from this sample does not change the results
in any significant way.
14
Given the period covered by our sample, for each country, the first
observation on average growth is in fact a four-year average. If there were
no missing values, we would have seven observations for each country.
However, many observations are missing for the first sample considered.
This implies that, for these countries, the averaged data can sometimes
result from the averaging of relatively short series. Obviously, this problem
does not arise when using the balanced data sets.
TABLE 1.—DESCRIPTION OF THE DATA SET
Number of
Countries
Of Which With
Data 1961–1994
(1965–1993 for
Data Set 2)
Average Number of
Years Per Country
Data set 1 123 38 24
Data set 2 50 50 29
Data set 3 38 38 34
CW data set 64 64 29 (5-year average)
186 THE REVIEW OF ECONOMICS AND STATISTICS

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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Saving, growth, and investment: a macroeconomic analysis using a panel of countries" ?

This paper provides a descriptive analysis of the longand short-run correlations among saving, investment, and growth rates for 123 countries over the period 1961–94.