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

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.

## 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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### Cites background or result from "Saving, Growth, and Investment: A M..."

...Our results are consistent with those reported by Carroll and Weil (1994) and Attanasio et al. (2000). When the national saving rate is considered as the dependent variable, we first find that this rate is as persistent as the investment rate....

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...(1996) and Attanasio et al. (2000) also find a negative impact of lagged investment on economic growth....

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##### References

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### "Saving, Growth, and Investment: A M..." refers background or methods in this paper

...…countries while they are allowed, at least in principle, to vary over time.6 Typically, some Panel Data estimator that allows for the presence of fixed effects, such as those proposed by Holtz-Eakin, Newey and Rosen (1988), (HNR from now on), and Arellano and Bond (1991) (AB from now on) is used....

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...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....

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### "Saving, Growth, and Investment: A M..." refers background or methods in this paper

...Arellano and Bover (1995) show that one can express the model in terms of orthogonal deviations9 to obtain a simple way of computing the HNR or AB estimator....

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...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....

[...]

...…Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies 58, 277-297 _________ and O. Bover (1995): "Another Look at the Instrumental Variable Estimation of Error-Components Models," Journal of Econometrics, 18, 47- 82....

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