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COPYRIGHT 2000 MIT Press Journals
I. Introduction and Motivation
THE 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 ambiguous. Nonetheless, measuring such correlations is informative about the relative importance of various factors.
A natural 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 relationship 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 productivity 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, precautionary 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 interpreting Granger causality results.(1) Other saving-to-growth linkages 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 microeconomic 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 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 component, in that lagged saving rates are strongly correlated with current investment rates. It is therefore interesting to establish 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 correlation 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 consequence 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 analysis 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 methodological 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 asymptotics 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 variables, 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 T" asymptotic 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 which we consider the variables of interests and their interactions simultaneously. We conclude the section by analyzing the effects of introducing various controls normally 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 observed 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
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
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 hypothesis testing. In the analysis of country panels, it is conceptually 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 hereafter), 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)
(1a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(2a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are relevant for the Granger causality running from y to x, while the coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 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 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 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 implied by the dynamics of the system can be exploited to achieve efficiency.(5) In particular, at each point in time t, one 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 instruments increases very quickly. In our application, for instance, 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 N' estimators, 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, precludes 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 variables could differ across countries, possibly due to institutional reasons or differences...
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