Abstract
Feldstein and Horioka (1980) argued that the correlation of saving and investment in a cross-section of countries may provide a test of global capital mobility. This paper argues that neither the long-run nor the short-run correlation can serve as a reliable basis for such a test. The intertemporal budget constraint implies that each country’s saving and investment should be cointegrated over time. Simulations show that the cross-section regressions used in the literature will produce correlations that strongly tend towards one, regardless of the degree of capital mobility. Although the short-run correlation is not affected by the intertemporal budget constraint, the empirical analysis shows it is primarily a country-specific business cycle fact.
I. Introduction
Feldstein and Horioka (1980) were the first to investigate the correlation between saving and investment with the aim to evaluate the degree of international capital mobility. In a closed economy (without any capital mobility) the saving-investment (SI) correlation is one, because saving necessarily equals investment, while under perfect capital mobility it is zero, because any gap between investment and saving can be borrowed or lent in the world capital market. In a cross-country regression involving period-averaged saving and investment rates of OECD countries, Feldstein and Horioka surprisingly found a correlation close to unity, from which they inferred low international capital mobility. Later empirical work confirmed the close correlation, although its implications for capital mobility are in dispute. 1/
This paper argues that the high SI-correlation for OECD countries found in cross-section studies reflects the cointegration of the saving and investment rates in the time dimension. 2/ This cointegration derives from two sources. First, intertemporal general equilibrium models, which assume perfect capital mobility, predict cointegration because of the intertemporal budget constraint. Second, limited capital mobility will reinforce the cointegration associated with the intertemporal budget constraint. We investigate the small sample behavior of the SI-correlation in various cross-section regressions, when the underlying time series of the saving and investment rate are cointegrated. Our Monte Carlo experiments indicate that the commonly used cross-section equations yield estimates of the SI-correlation strongly tending towards one. This is true even if saving and investment appear to be only “weakly” cointegrated and the intertemporal budget constraint does not seem to be particularly restrictive. Feldstein-Horioka tests based on such regressions are therefore not informative on the issue of global capital mobility.
We then examine whether a Feldstein-Horioka test can be based on the correlation between the changes of the saving and investment rates in a cross-section context, which is not affected by the intertemporal budget constraint. However, this short-run correlation probably reflects a mix of business cycle effects and capital mobility effects. We examine the short-run correlation’s behavior over time and its variation across countries to find out which of the two dominates. If there is a strong link between capital mobility and the correlation’s value we would expect the latter have exhibited a clear downward trend over the past few decades. However, we find that the variation of the correlation is across countries,
II. Social Assistance in Germany: Purpose and Development
Social assistance in Germany consists of two main programs: support for special circumstances, in particular for the re-integration of handicapped persons and for care (‘Hilfe in besonderen Lebenslagen’), and support in case of temporary or permanent loss of income (‘Laufende Hilfe zum Lebensunterhalt’). In the context of this paper, only the second element is of interest and, unless otherwise mentioned, the term social assistance will refer to this element. According to the principle of subsidiarity, it is the ultimate means of support that everyone with insufficient resources to make a living in Germany is entitled to, including non-nationals. Social assistance is needs based and individuals have a legal claim to receive social assistance, independent of whether they work or not. Strictly speaking, however, it is meant to be “help to work” in the sense that it ought to provide a basis from which an individual can and should try to obtain employment. 1/
Benefits consist of a basic allowance (DM 520 per month in 1994/95), an allowance for housing (DM 370 on average) and possibly one-time benefits (DM 140 on average). The average regular monthly allowance for an adult is therefore DM 890 (US$600), or DM 1,030 (US$700) including one-time payments. This is the lower bound of benefits for an adult. Benefits are higher for senior citizens, persons with physical disabilities, and for expectant mothers. Depending on age, benefits for children are 50–90 percent of the basic allowance for an adult.
1. Expenditures on social assistance
Expenditures on social assistance have soared over the last two decades (Chart 1, upper panel). While nominal GDP quadrupled from 1970 to 1990, total social assistance expenditures—including spending on those in special circumstances—went up by a factor of ten, and expenditure on social income maintenance alone went up by a factor of fifteen. Even though the basis for social assistance is a federal law [Bundessozialhilfegesetz (1962)], expenditures are borne by the Laender and local authorities. In total, the Laender spent 6 percent of their budgets on total social assistance in 1991 compared with 2 1/2 percent in 1970. 2/ The increase in expenditures is mainly due to a large increase in the number of recipients. However, increases in the real value of benefits per recipient have also contributed: deflated by the consumer price index, the basic allowance was in 1993 almost
Feldstein and Horioka considered (1) a long-run equilibrium relationship. They averaged the saving and investment rate (levels) of 16 OECD countries over various time-spans to avoid upward bias in βc due to business cycle effects. To their surprise, they found βC to be in the range 0.85 – 0.95, and had to reject the hypothesis of perfect capital mobility. Other authors confirmed their findings: the correlation is high during the 1960s and 1970s, while it decreases during the 1980s, although it remains high. 1/
2. Theoretical notions and time series regressions
The theoretical motivation behind the Feldstein-Horioka regression equation seems to consist of no more than the national income accounting identity. However, open-economy macroeconomics can provide additional insights as to the correct specification of the cross-section regression equation and the interpretation of the results. Since international macro-economic models typically analyze the behavior of a single small open economy over time, their implications refer to an SI-correlation that is estimated in a time series framework.
In the open-economy variants of intertemporal general equilibrium models agents maximize (expected) life-time utility subject to the inter-temporal budget constraint. Since financial capital is assumed to be completely mobile, agents can use the international capital market to smooth their consumption. There may be growth in the model due to technological progress or population growth, in which case the long-run saving rate and the investment rate may differ by a constant which is a function of the various model parameters. Hence, the current account (expressed as a ratio to GDP) is constant in the steady state. 2/ In the short run, all kinds of disturbances may temporarily push the system out of equilibrium. General equilibrium models are thus able to endogenously produce short-run SI-correlations, which may be positive, zero or negative, depending on the size and nature of the shock and the structure of the economy (see Finn 1990, Tesar 1991).
Modern macroeconomic theory thus looks upon saving-investment dynamics as temporary phenomena, whereas in the long run the intertemporal budget constraint keeps the saving and investment rate together. The current account is a stationary variable around a possibly non-zero mean. Hence, saving and investment rates are cointegrated with cointegrating vector (1,−1)’. 1/ An Error Correction Model (ECM) offers a very attractive statistical representation of saving-investment dynamics, because it is compatible with the fundamental results derived above. We can demonstrate this by considering a simple member of this class of specifications: 2/
where t is a time-index. The short-run SI-correlation βe shows which part of an increase in saving is invested at home. Since the estimate of βe represents the average contemporaneous comovement of saving and investment in response to shocks which have hit the economy in the past, it is an important summary statistic of the dynamic properties of the economy, and thus a stylized fact theoretical models need to explain (see Obstfeld 1986, Baxter and Crucini 1993 and Ghosh and Pesenti 1994).
If γ = 0, saving and investment are cointegrated with cointegrating vector (1,−1)’. 3/ The long-run (or cointegrating relation between the saving and investment rate is:
The time series of the current account (SR-IR) is stationary around −α/γ. If α = 0, it fluctuates around zero.
Studies estimating time series regressions do not address the issue of global capital mobility, but the narrower question how well an individual country is integrated in the world capital market. If the country is closed, it has to invest what it saves (and vice versa). In that case we expect high values for βe and γ and a zero value for a. If the country is open, it is able to borrow or lend the difference between saving and investment in the world capital market. In that case, βe is free to take on values ranging from, say, minus one to plus one, while we expect γ to be positive. Moreover, we expect a, βe and γ to differ across countries, because countries differ in economic structure and economic policies. The long-run SI-correlation cannot be used to gauge capital mobility, because a value of one is perfectly compatible with complete financial openness.
However, Jansen and Schulze (1996) and Jansen (1994a) argue that βe offers some limited possibilities to make inferences about capital mobility.
The ECM is related to two common specifications in the literature,
and
Since (4) is formulated in the levels of the saving and investment rate, it is conceptually comparable to the long-run relation (3). Indeed, it also serves as the cointegrating relation in the first step of the two-step Engle-Granger procedure, estimated by Leachman (1991) and De Haan and Siermann (1994). We therefore expect (4) to produce an SI-correlation close to one, regardless whether the economy is fully integrated in the world capital market or not. This makes β1 unfit as an indicator of capital mobility. Equation (5) is (2) with the restriction γ = 0. βd is conceptually comparable to βe. Since only differenced variables enter (5), it has no long-run solution and it is thus misspecified if saving and investment are cointegrated. It may therefore produce biased estimates.
Jansen (1994a) applies the ECM to 23 OECD countries for the period 1952–91, and systematically compares the outcomes to the ones obtained by alternative specifications and approaches. He finds that in general saving and investment are cointegrated in such a way that the current account is a stationary variable. Countries exhibit considerable differences in the short-run SI-correlation: for some countries βe is zero, for others it is one. A high contemporaneous SI-correlation does not appear to be a stylized fact of the typical industrialized country. Comparison of the results of (4) and (5) with the ECM results reveals that the equation in levels yields a β relatively close to one, while using differenced data leads to only a small upward bias.
The empirical findings of other papers employing a time series set-up are largely consistent with the above. Gundlach and Sinn (1992) reject a unit root (i.e., nonstationarity) for the current account for most OECD countries (exceptions are Germany, Japan and the US) in the period 1950–88, using Dickey-Fuller and Phillips-Perron (1988) unit root tests. Coakley, Kulasi and Smith (1995) analyzed 23 OECD countries over the period 1962–92 in a panel set-up. They strongly rejected the hypothesis that each country has a nonstationary current account on the basis of the t-bar statistic proposed by Im, Pesaran and Shin (1995). Argimón and Roldan (1994) find cointegration for five EC countries out of nine in the period 1960–88, employing the Johansen (1988) method. Using the Engle-Granger (1987) procedure, Leachman (1991) could not detect cointegration for any OECD country for the period 1960–84, but, as De Haan and Siermann (1994) point out, this is probably due to the small number of observations, which greatly reduces the power of the cointegration test. Using longer time series they find cointegration for many countries. Bayoumi (1990), Feldstein and Bacchetta (1991) and Leachman (1991), using differenced data, report βd-estimates which show considerable differences between countries. 1/
3. Lessons for the specification of the cross-section regression
The finding that saving and investment generally exhibit a long-run equilibrium relation in the post-war period has two important implications for the traditional cross-section analysis. The first one was pointed out by Sinn (1992), who observed that the intertemporal budget constraint implies that long-term averages of saving and investment figures are approximately equal. Using period-averaged data, as was done by Feldstein and Horioka and many others, will therefore drive the estimated cross-section SI-correlation (βc) towards one. However, Sinn’s empirical analysis shows that aggregation over time is not the main cause of the high saving investment correlation, as the regression on annual observations still yields high correlations, although the estimates are more variable and appear to decrease after 1973. Sinn’s point also applies to studies which use changes in decade-averages of saving and investment figures. These studies still find high SI-correlations. 2/
The second, and much more fundamental, implication concerns the use of the levels of the saving and investment rate. The time series studies cited above make clear that the saving and investment rate are cointegrated for many OECD countries in the postwar period. Saving and investment rates thus evolve over time according to an error correction mechanism (see Engle and Granger 1987), which is precisely what Jansen (1994a) found for the OECD countries.
What happens if we perform a cross-section regression over countries, with annual observations on data series that in the time domain are generated by an error correction mechanism? Since the regression equation in Feldstein and Horioka (1980) and Sinn (1992) is formulated in the levels of the variables, it is conceptually comparable to the long-run or cointegrating relation. As a result, the estimate of the cross-section SI-correlation (βc) will tend towards one, because the time series evidence points to a stationary current account, implying as cointegrating vector (1,−1)’. Pesaran and Smith (1995) prove that a cross-section regression using period-averaged levels of non-stationary variables yields a consistent estimate of the long-run effect, when the coefficients are randomly distributed. Van den Doel (1994, pp. 9–14) shows that this also holds for a cross-section regression using annual data.
Hence, the mere fact that the cross-section regression equation has always been framed in the levels of IR and SR (or in the changes in period-averages) could be the (statistical) explanation of the commonly found high estimates of βC. The high cross-section SI-correlation can be viewed as nothing more than a direct reflection of the fact that saving and investment are cointegrated in the time dimension, no matter what the degree of capital mobility is (see Jansen 1994b, and Coakley, Kulesi and Smith 1995). However, it would be jumping to conclusions to say that the observed cointegration chiefly reflects the influence of the intertemporal budget constraint, as imperfect capital mobility will make the degree of cointegration appear stronger. 1/ Because cross-section regressions in levels mix up effects of imperfect capital mobility and of the intertemporal budget constraint, they do not provide a reliable test of international capital mobility of the Feldstein-Horioka type.
III. Cross-Section Analysis With Cointegrated Data
In this section we study the behavior of various cross-section equations when the time series involved are non-stationary. There are two reasons why this is interesting. First, the result that the regression coefficient in cross-section level equations tends towards one is based on asymptotic reasoning. It holds if the number of countries is very large. However, empirical work typically concerns a small number of countries. Feldstein and Horioka’s paper analyses 16 countries, and this paper 23 countries; both samples are a long way from being large. Consequently, severe small sample bias is a distinct possibility, and the cointegration effect may not be strong enough to explain the close SI-correlation generally found in cross-section studies.
Second, the intertemporal budget constraint only implies that γ should be positive, not necessarily that it should be large. Given the low power of cointegration tests, the null-hypothesis of non-cointegration (γ = 0) is likely to be accepted in a sample of, say, 40 annual observations, if γ is small (say .10). 2/ Many countries will have seemingly non-cointegrated saving and investment time series, and the intertemporal budget constraint would seem hardly restrictive. This could lead one to believe that in such cases the intertemporal budget constraint alone cannot account for Feldstein and Horioka’s cross-section findings. It is therefore important to see how the Feldstein-Horioka cross-section regression fares when γ is small, and many countries thus have saving and investment rates that do not appear to be cointegrated (in short samples).
To get an impression of how strongly the cross-section correlation is driven towards one we carried out some Illustrative Monte Carlo experiments, in which we generated 250 data sets of dimensions comparable to the postwar OECD data set for different combinations of β and γ. Each data set consists of 40 annual observations for 25 countries. For each country the time series of the saving rate is generated as a random walk:
The investment rate is generated by an error correction mechanism:
The current account, SR-IR, is a stationary variable fluctuating around −αi, its country-specific equilibrium value. SR is weakly exogenous with respect to the cointegrating relation. Countries are assumed to have the same β and γ for the sake of the argument; they differ in initial conditions, equilibrium current account and shocks they experience. 1/ β takes on the values 0, .1, .3, .5 and .7; γ equals 0, .05, .1, .2, .35 and .5.
On each generated data set we performed the following cross-section regressions (25 “country” observations):
where vji are assumed to be well-behaved disturbances, and where the numbers in square brackets denote the number of regressions per generated data set. Eq. (8a) is the original Feldstein-Horioka regression equation, using averages over 10 periods. Eq. (8b) uses “annual” data, as in Sinn (1992). Eq. (8c) is the Feldstein-Horioka equation in differences, featuring “decade-to-decade” changes. It was estimated by Feldstein and Horioka (1980) and Penati and Dooley (1984), among others. Eq. (8d) is the Sinn equation in differenced form: it correlates the “annual” changes in SR and IR. Eq. (8e) contains as an extra regressor the previous period’s current account in order to allow for dynamic adjustment. Eqs. (8d) and (8e) are the cross-section counterparts of the time series specifications (5) and (2) respectively, and have not been estimated before. The disturbance v4i can be written as ε1i + γ(SRi−IRi)t−1 + αiγ − c. Since none of its constituent parts is correlated with ΔSRi the estimate of βdcs will be unbiased. However, it will be inefficient compared to the estimate from (8e).
Columns 4–13 in Table 1 report the mean and standard deviation of the empirical distribution of the estimated parameters βjcs for various combinations of β and γ. For each combination, (8a) is run 1,000 times, (8c) 750 times, and (8b), (8d) and (8e) 10,000 times. We also examined the properties of the generated time series for each country separately, more specifically whether its saving and investment rate would appear to be cointegrated over a period of 40 years. The third column of Table 1 reports the rejection frequency of the null of non-cointegration, based on the cointegration test advocated by Kremers, Ericsson and Dolado (1992). 1/ We indeed find that if γ is small, non-cointegration is accepted in over 90 percent of the cases. If γ is small, a country’s saving and investment rate are in general not discernibly cointegrated in a sample of postwar period length.
Simulation Results: Cross-Section Regressions With Cointegrated Data
Simulation Results: Cross-Section Regressions With Cointegrated Data
| levels: decade | levels: annual | changes: decade | changes: annual | error correction | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| β | γ | Pcoint | SE(β) | SE(β) | SE(β) | SE(β) | SE(β) | ||||||
| .00 | .00 | .0226 | −.0380 | .3157 | −.0368 | .3160 | −.0219 | .3088 | −.0011 | .3210 | −.0021 | .3285 | |
| .05 | .0464 | .4264 | .2163 | .4056 | .2295 | .2738 | .2688 | .0005 | .3252 | −.0014 | .3288 | ||
| .10 | .0949 | .6176 | .1793 | .5903 | .2008 | .4740 | .2479 | .0015 | .3308 | −.0010 | .3295 | ||
| .20 | .2928 | .7673 | .1304 | .7391 | .1593 | .7076 | .2034 | .0030 | .3429 | −.0005 | .3324 | ||
| .35 | .7298 | .8401 | .0976 | .8166 | .1285 | .8611 | .1517 | .0045 | .3630 | −.0004 | .3333 | ||
| .50 | .9525 | .8678 | .0840 | .8488 | .1143 | .9247 | .1180 | .0056 | .3859 | −.0003 | .3514 | ||
| .10 | .00 | .0237 | .0566 | .3207 | .0556 | .3161 | .0781 | .3088 | .0989 | .3128 | .0978 | .3284 | |
| .05 | .0458 | .4736 | .2115 | .4554 | .2241 | .3449 | .2661 | .1005 | .3249 | .0985 | .3287 | ||
| .10 | .0899 | .6465 | .1731 | .6223 | .1936 | .5256 | .2436 | .1015 | .3302 | .0990 | .3294 | ||
| .20 | .2718 | .7818 | .1260 | .7569 | .1535 | .7363 | .1985 | .1029 | .3415 | .0995 | .3323 | ||
| .35 | .6936 | .8476 | .0952 | .8269 | .1245 | .8747 | .1474 | .1044 | .3605 | .0997 | .3400 | ||
| .50 | .9386 | .8727 | .0825 | .8560 | .1112 | .9321 | .1146 | .1055 | .3822 | .0999 | .3509 | ||
| .30 | .00 | .0227 | .2377 | .3162 | .2403 | .3165 | .2781 | .3088 | .2989 | .3210 | .2978 | .3283 | |
| .05 | .0432 | .5679 | .2029 | .5548 | .2144 | .4781 | .2615 | .3004 | .3244 | .2984 | .3286 | ||
| .10 | .0776 | .7041 | .1619 | .6864 | .1803 | .6288 | .2362 | .3014 | .3291 | .2989 | .3293 | ||
| .20 | .2284 | .8108 | .1180 | .7924 | .1427 | .7938 | .1898 | .3027 | .3392 | .2995 | .3321 | ||
| .35 | .6197 | .8627 | .0907 | .8476 | .1172 | .9020 | .1398 | .3042 | .3563 | .2998 | .3395 | ||
| .50 | .9078 | .8825 | .0796 | .8705 | .1056 | .9467 | .1083 | .3053 | .3760 | .3007 | .3498 | ||
| .50 | .00 | .0283 | .4215 | .3172 | .4249 | .3175 | .4781 | .3078 | .4989 | .3210 | .4978 | .3282 | |
| .05 | .0419 | .6623 | .1958 | .6543 | .2064 | .6293 | .2580 | .5003 | .3240 | .4983 | .3284 | ||
| .10 | .0718 | .7618 | .1522 | .7504 | .1690 | .7320 | .2303 | .5012 | .3282 | .4988 | .3291 | ||
| .20 | .1968 | .8398 | .1110 | .8279 | .1334 | .8513 | .1827 | .5025 | .3375 | .4994 | .3319 | ||
| .35 | .5592 | .8778 | .0868 | .8682 | .1109 | .9292 | .1335 | .5040 | .3532 | .4998 | .3391 | ||
| .50 | .8709 | .8922 | .0771 | .8850 | .1008 | .9614 | .1031 | .5052 | .3713 | .5002 | .3489 | ||
| .70 | .00 | .0310 | .6053 | .3187 | .6071 | .3188 | .6781 | .3088 | .6989 | .3210 | .6979 | .3285 | |
| .05 | .0429 | .7567 | .1904 | .7538 | .2003 | .7716 | .2556 | .7002 | .3238 | .6982 | .3282 | ||
| .10 | .0637 | .8195 | .1445 | .8144 | .1601 | .8352 | .2262 | .7011 | .3277 | .6986 | .3289 | ||
| .20 | .1742 | .8688 | .1051 | .8635 | .1259 | .9087 | .1775 | .7023 | .3364 | .6993 | .3317 | ||
| .35 | .5096 | .8928 | .0835 | .8889 | .1059 | .9564 | .1288 | .7038 | .3511 | .6998 | .3388 | ||
| .50 | .8430 | .9020 | .0749 | .8995 | .0969 | .9760 | .0992 | .7050 | .3682 | .7003 | .3483 | ||
| # regr. | 1,000 | 10,000 | 750 | 10,000 | 10,000 | ||||||||
Simulation Results: Cross-Section Regressions With Cointegrated Data
| levels: decade | levels: annual | changes: decade | changes: annual | error correction | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| β | γ | Pcoint | SE(β) | SE(β) | SE(β) | SE(β) | SE(β) | ||||||
| .00 | .00 | .0226 | −.0380 | .3157 | −.0368 | .3160 | −.0219 | .3088 | −.0011 | .3210 | −.0021 | .3285 | |
| .05 | .0464 | .4264 | .2163 | .4056 | .2295 | .2738 | .2688 | .0005 | .3252 | −.0014 | .3288 | ||
| .10 | .0949 | .6176 | .1793 | .5903 | .2008 | .4740 | .2479 | .0015 | .3308 | −.0010 | .3295 | ||
| .20 | .2928 | .7673 | .1304 | .7391 | .1593 | .7076 | .2034 | .0030 | .3429 | −.0005 | .3324 | ||
| .35 | .7298 | .8401 | .0976 | .8166 | .1285 | .8611 | .1517 | .0045 | .3630 | −.0004 | .3333 | ||
| .50 | .9525 | .8678 | .0840 | .8488 | .1143 | .9247 | .1180 | .0056 | .3859 | −.0003 | .3514 | ||
| .10 | .00 | .0237 | .0566 | .3207 | .0556 | .3161 | .0781 | .3088 | .0989 | .3128 | .0978 | .3284 | |
| .05 | .0458 | .4736 | .2115 | .4554 | .2241 | .3449 | .2661 | .1005 | .3249 | .0985 | .3287 | ||
| .10 | .0899 | .6465 | .1731 | .6223 | .1936 | .5256 | .2436 | .1015 | .3302 | .0990 | .3294 | ||
| .20 | .2718 | .7818 | .1260 | .7569 | .1535 | .7363 | .1985 | .1029 | .3415 | .0995 | .3323 | ||
| .35 | .6936 | .8476 | .0952 | .8269 | .1245 | .8747 | .1474 | .1044 | .3605 | .0997 | .3400 | ||
| .50 | .9386 | .8727 | .0825 | .8560 | .1112 | .9321 | .1146 | .1055 | .3822 | .0999 | .3509 | ||
| .30 | .00 | .0227 | .2377 | .3162 | .2403 | .3165 | .2781 | .3088 | .2989 | .3210 | .2978 | .3283 | |
| .05 | .0432 | .5679 | .2029 | .5548 | .2144 | .4781 | .2615 | .3004 | .3244 | .2984 | .3286 | ||
| .10 | .0776 | .7041 | .1619 | .6864 | .1803 | .6288 | .2362 | .3014 | .3291 | .2989 | .3293 | ||
| .20 | .2284 | .8108 | .1180 | .7924 | .1427 | .7938 | .1898 | .3027 | .3392 | .2995 | .3321 | ||
| .35 | .6197 | .8627 | .0907 | .8476 | .1172 | .9020 | .1398 | .3042 | .3563 | .2998 | .3395 | ||
| .50 | .9078 | .8825 | .0796 | .8705 | .1056 | .9467 | .1083 | .3053 | .3760 | .3007 | .3498 | ||
| .50 | .00 | .0283 | .4215 | .3172 | .4249 | .3175 | .4781 | .3078 | .4989 | .3210 | .4978 | .3282 | |
| .05 | .0419 | .6623 | .1958 | .6543 | .2064 | .6293 | .2580 | .5003 | .3240 | .4983 | .3284 | ||
| .10 | .0718 | .7618 | .1522 | .7504 | .1690 | .7320 | .2303 | .5012 | .3282 | .4988 | .3291 | ||
| .20 | .1968 | .8398 | .1110 | .8279 | .1334 | .8513 | .1827 | .5025 | .3375 | .4994 | .3319 | ||
| .35 | .5592 | .8778 | .0868 | .8682 | .1109 | .9292 | .1335 | .5040 | .3532 | .4998 | .3391 | ||
| .50 | .8709 | .8922 | .0771 | .8850 | .1008 | .9614 | .1031 | .5052 | .3713 | .5002 | .3489 | ||
| .70 | .00 | .0310 | .6053 | .3187 | .6071 | .3188 | .6781 | .3088 | .6989 | .3210 | .6979 | .3285 | |
| .05 | .0429 | .7567 | .1904 | .7538 | .2003 | .7716 | .2556 | .7002 | .3238 | .6982 | .3282 | ||
| .10 | .0637 | .8195 | .1445 | .8144 | .1601 | .8352 | .2262 | .7011 | .3277 | .6986 | .3289 | ||
| .20 | .1742 | .8688 | .1051 | .8635 | .1259 | .9087 | .1775 | .7023 | .3364 | .6993 | .3317 | ||
| .35 | .5096 | .8928 | .0835 | .8889 | .1059 | .9564 | .1288 | .7038 | .3511 | .6998 | .3388 | ||
| .50 | .8430 | .9020 | .0749 | .8995 | .0969 | .9760 | .0992 | .7050 | .3682 | .7003 | .3483 | ||
| # regr. | 1,000 | 10,000 | 750 | 10,000 | 10,000 | ||||||||
As a benchmark case we analyze the case in which saving and investment are not correlated, neither in the long run nor in the short run: β = 0 and γ = 0. All equations produce zero correlations in this case. The overall impression Table 1 gives is that cointegration of saving and investment (i.e., γ > 0) strongly pushes the estimate of β towards one for level equations. Even when the intertemporal budget constraint does not seem to act as much of a constraint on the country level (i.e., γ is small), we find this strong tendency towards one, even if the true contemporaneous correlation β is zero. The mean of the β1cs estimates is closer to one the higher the error correction parameter γ. A large estimate of β1cs can occur in case of a large β, but also in case of a zero beta. As Sinn (1992) found, use of period-averaged data instead of annual data reinforces the tendency towards one, but only marginally. In addition, it produces smaller standard errors of the estimator (if γ > 0). Employing decade-to-decade changes as in (8c) weakens the drive toward one somewhat, but it remains strong. It appears that OLS estimation of a static cross-section equation does a very good job in filtering out the cointegrating relation.
Things are quite different for the equations based on annually differenced data, (8d) and (8e). In both cases the contemporaneous correlation is estimated unbiasedly, but the estimates display a large variability. Inclusion of an error correction term leads to a small efficiency gain (smaller standard errors), which is larger for larger γ. Jansen (1994a) similarly found for time series regressions that using differenced data does not greatly affect the estimate of the contemporaneous SI-correlation (βd) in comparison with the one obtained by the ECM (βe). 1/
The Monte Carlo experiments show that the original Feldstein-Horioka regression equation is fundamentally flawed. It will yield estimates which strongly tend towards one because of the intertemporal budget constraint and possibly because of limited capital mobility. There is no way of identifying the individual contributions of the two. Large cross-section estimates are likely, even when the intertemporal budget constraint does not seem to be particularly restrictive for the intertemporal behavior of individual countries (small γ). This holds, even if all countries are perfectly integrated in the world capital market according to the Feldstein-Horioka criterion (i.e., β = 0). As a result, high saving-investment correlations are in no way inconsistent with full capital mobility. Cross-section regressions in levels are therefore unfit for measuring or testing capital mobility.
IV. A “Dynamic” Feldstein-Horioka Regression Equation
The question thus arises whether we can implement Feldstein and Horioka’s test of international capital mobility empirically. How can we separate the effects of the intertemporal budget constraint and those of limited capital mobility? The natural way to accomplish this is to focus on the short-run dynamics of saving and investment. This section investigates empirically whether switching to a short-run version of the Feldstein-Horioka cross-section equation throws any light on the link between capital mobility and the saving-investment correlation. To this end we examine the behavior of the short-run correlation, and look how it varies over time and across countries.
Estimates of the cross-section correlation between the annual changes of the saving and investment rate are not affected by the intertemporal budget constraint, since it only restricts the long-run behavior of saving and investment. By contrast, restrictions on capital flows may still give rise to positive short-run SI-correlations, as Feldstein and Horioka’s idea can also be applied to the changes of saving and investment: under perfect capital mobility an increase in domestic investment need not be matched by an increase in national saving. Consequently, the change in the contribution to the world pool of savings (ΔSR) by a country should be uncorrelated with the change in its use of that pool (ΔIR). On the other hand, as argued in Section II.2, positive short-run saving-investment correlations can be endogenously produced under perfect capital mobility as the economy adjusts to shocks. Hence, estimates of short-run SI-correlations may chiefly reflect business cycle phenomena. If capital mobility effects dominate we would expect a clear downward trend over time in the value of the correlation, as it is widely believed that capital mobility has greatly increased since the early 1970s. If business cycle effects dominate we would expect systematic differences across countries, and variation over time, but no strong trend.
Table 2 reports the estimates of (8e) for 37 years (1955–91). We use (8e) because the simulation results indicate that it is the most attractive specification to generate an unbiased estimate of the contemporaneous SI-correlation. The error correction term (SRi-IRi)t−1 serves as a control variable for dynamic adjustment. 1/ The data used are gross investment and gross saving, expressed as a share of GDP, of 22 OECD countries. 2/ To put our results into perspective we also report the estimates of β1cs from (8b), which uses the levels. Figure 1 depicts the evolution of both β-coefficients.
Cross-Section Saving-Investment Regressions, 1995–91
Cross-Section Saving-Investment Regressions, 1995–91
| Levels | Error Correction | |||||
|---|---|---|---|---|---|---|
| Year | β1 | t-stat | R2 | βe | t-stat | R2 |
| 1955 | .8374 | (7.03) | .7076 | .1796 | (0.73) | .2046 |
| 1956 | .8794 | (11.3) | .8641 | .5120 | (1.93) | .5105 |
| 1957 | .9108 | (8.66) | .7871 | .5146 | (2.02) | .0558 |
| 1958 | .7792 | (6.21) | .6525 | .3115 | (0.83) | .1031 |
| 1959 | .7602 | (9.04) | .8014 | .8284 | (3.67) | .6242 |
| 1960 | .8294 | (11.1) | .8523 | .4649 | (2.77) | .8327 |
| 1961 | .8507 | (9.22) | .8002 | .3670 | (1.42) | .1877 |
| 1962 | .9042 | (12.5) | .8813 | .6749 | (3.14) | .3487 |
| 1963 | .9109 | (11.5) | .8627 | .3941 | (1.92) | .0747 |
| 1964 | .9102 | (11.9) | .8699 | .6323 | (2.46) | .3130 |
| 1965 | .8057 | (7.57) | .7281 | .6976 | (2.04) | .0941 |
| 1966 | .8569 | (10.1) | .8241 | .8563 | (4.12) | .6011 |
| 1967 | .8504 | (9.78) | .8185 | .5356 | (2.92) | .4414 |
| 1968 | .8144 | (12.1) | .8730 | .7157 | (3.45) | .3209 |
| 1969 | .7708 | (8.79) | .7841 | .6538 | (2.56) | .2097 |
| 1970 | .8466 | (10.4) | .8372 | .7365 | (3.18) | .4778 |
| 1971 | .8785 | (9.93) | .8229 | .4579 | (1.79) | .1199 |
| 1972 | .8339 | (11.6) | .8648 | .6037 | (3.73) | .4487 |
| 1973 | .9722 | (9.46) | .8082 | .5782 | (1.78) | .0633 |
| 1974 | .7214 | (4.21) | .4438 | .4180 | (1.88) | .0741 |
| 1975 | .8186 | (4.36) | .4615 | .5756 | (1.99) | .1605 |
| 1976 | .6359 | (2.89) | .2595 | .5546 | (1.96) | .0964 |
| 1977 | .4792 | (2.12) | .1421 | .6474 | (3.87) | .3827 |
| 1978 | .7375 | (4.82) | .5138 | .9507 | (3.54) | .5394 |
| 1979 | .7191 | (4.73) | .5041 | .0482 | (0.20) | .0479 |
| 1980 | .7285 | (6.42) | .6569 | .2098 | (0.80) | .4025 |
| 1981 | .5865 | (3.33) | .3250 | .6078 | (3.80) | .4376 |
| 1982 | .6059 | (3.38) | .3313 | .5363 | (3.30) | .2989 |
| 1983 | .5909 | (4.31) | .4552 | .5550 | (2.50) | .4889 |
| 1984 | .4993 | (4.36) | .4621 | .6767 | (1.44) | .2316 |
| 1985 | .3907 | (3.52) | .3523 | .4250 | (2.17) | .1226 |
| 1986 | .5092 | (4.08) | .4268 | −.0863 | (0.50) | .2403 |
| 1987 | .6691 | (6.85) | .6862 | .8453 | (3.04) | .5324 |
| 1988 | .6834 | (5.93) | .6191 | .2956 | (1.01) | .0019 |
| 1989 | .5800 | (5.33) | .5659 | .0359 | (0.13) | .0138 |
| 1990 | .6014 | (6.20) | .6409 | .5463 | (1.94) | .3820 |
| 1991 | .6254 | (6.67) | .6741 | .6963 | (4.47) | .5531 |
| av(β1) | av(βe) | sd(β1) | sd(βe) | c(β1,βe) | ||
| 55–91 | .7401 | .5177 | .1438 | .2394 | .1717 | |
| 55–73 | .8527 | .5639 | .0547 | .1762 | −.1315 | |
| 74–91 | .6212 | .4690 | .1071 | .2892 | .0617 | |
Cross-Section Saving-Investment Regressions, 1995–91
| Levels | Error Correction | |||||
|---|---|---|---|---|---|---|
| Year | β1 | t-stat | R2 | βe | t-stat | R2 |
| 1955 | .8374 | (7.03) | .7076 | .1796 | (0.73) | .2046 |
| 1956 | .8794 | (11.3) | .8641 | .5120 | (1.93) | .5105 |
| 1957 | .9108 | (8.66) | .7871 | .5146 | (2.02) | .0558 |
| 1958 | .7792 | (6.21) | .6525 | .3115 | (0.83) | .1031 |
| 1959 | .7602 | (9.04) | .8014 | .8284 | (3.67) | .6242 |
| 1960 | .8294 | (11.1) | .8523 | .4649 | (2.77) | .8327 |
| 1961 | .8507 | (9.22) | .8002 | .3670 | (1.42) | .1877 |
| 1962 | .9042 | (12.5) | .8813 | .6749 | (3.14) | .3487 |
| 1963 | .9109 | (11.5) | .8627 | .3941 | (1.92) | .0747 |
| 1964 | .9102 | (11.9) | .8699 | .6323 | (2.46) | .3130 |
| 1965 | .8057 | (7.57) | .7281 | .6976 | (2.04) | .0941 |
| 1966 | .8569 | (10.1) | .8241 | .8563 | (4.12) | .6011 |
| 1967 | .8504 | (9.78) | .8185 | .5356 | (2.92) | .4414 |
| 1968 | .8144 | (12.1) | .8730 | .7157 | (3.45) | .3209 |
| 1969 | .7708 | (8.79) | .7841 | .6538 | (2.56) | .2097 |
| 1970 | .8466 | (10.4) | .8372 | .7365 | (3.18) | .4778 |
| 1971 | .8785 | (9.93) | .8229 | .4579 | (1.79) | .1199 |
| 1972 | .8339 | (11.6) | .8648 | .6037 | (3.73) | .4487 |
| 1973 | .9722 | (9.46) | .8082 | .5782 | (1.78) | .0633 |
| 1974 | .7214 | (4.21) | .4438 | .4180 | (1.88) | .0741 |
| 1975 | .8186 | (4.36) | .4615 | .5756 | (1.99) | .1605 |
| 1976 | .6359 | (2.89) | .2595 | .5546 | (1.96) | .0964 |
| 1977 | .4792 | (2.12) | .1421 | .6474 | (3.87) | .3827 |
| 1978 | .7375 | (4.82) | .5138 | .9507 | (3.54) | .5394 |
| 1979 | .7191 | (4.73) | .5041 | .0482 | (0.20) | .0479 |
| 1980 | .7285 | (6.42) | .6569 | .2098 | (0.80) | .4025 |
| 1981 | .5865 | (3.33) | .3250 | .6078 | (3.80) | .4376 |
| 1982 | .6059 | (3.38) | .3313 | .5363 | (3.30) | .2989 |
| 1983 | .5909 | (4.31) | .4552 | .5550 | (2.50) | .4889 |
| 1984 | .4993 | (4.36) | .4621 | .6767 | (1.44) | .2316 |
| 1985 | .3907 | (3.52) | .3523 | .4250 | (2.17) | .1226 |
| 1986 | .5092 | (4.08) | .4268 | −.0863 | (0.50) | .2403 |
| 1987 | .6691 | (6.85) | .6862 | .8453 | (3.04) | .5324 |
| 1988 | .6834 | (5.93) | .6191 | .2956 | (1.01) | .0019 |
| 1989 | .5800 | (5.33) | .5659 | .0359 | (0.13) | .0138 |
| 1990 | .6014 | (6.20) | .6409 | .5463 | (1.94) | .3820 |
| 1991 | .6254 | (6.67) | .6741 | .6963 | (4.47) | .5531 |
| av(β1) | av(βe) | sd(β1) | sd(βe) | c(β1,βe) | ||
| 55–91 | .7401 | .5177 | .1438 | .2394 | .1717 | |
| 55–73 | .8527 | .5639 | .0547 | .1762 | −.1315 | |
| 74–91 | .6212 | .4690 | .1071 | .2892 | .0617 | |
Cross-Section SI-Correlations
(Annual estimates)
Citation: IMF Working Papers 1996, 100; 10.5089/9781451852356.001.A001
Cross-Section SI-Correlations
(Annual estimates)
Citation: IMF Working Papers 1996, 100; 10.5089/9781451852356.001.A001
Cross-Section SI-Correlations
(Annual estimates)
Citation: IMF Working Papers 1996, 100; 10.5089/9781451852356.001.A001
The two measures of the SI-correlation show markedly different behavior. The results can be summarized in four points. First, the estimates of β1cs are .74 on average, while those of βecs are .52 on average. Second, the estimate of βecs is highly variable over time: it takes on all values between zero and one. By contrast, estimates of β1cs are generally greater than one half. Third, estimates of both β1cs and βecs tend to be lower and more variable after 1973, the change being more pronounced for β1cs. This decrease is consistent with the results in Jansen (1994a) who found for several countries a lower β or γ after 1973. Fourth, the estimates of β1cs and βecs, which are supposedly both measures of the degree of international capital mobility, actually exhibit very low correlation. This is a strong reminder that β1cs and βecs stand for fundamentally different phenomena: β1cs measures the long-run SI-correlation and βecs the contemporaneous (short-run) SI-correlation.
The Feldstein-Horioka puzzle does not show up in case of the short-run cross-section SI-correlation. In some years ΔSR and ΔIR were highly correlated across countries (e.g., in 1966 and 1978), whereas in others they appeared to be completely uncorrelated (e.g., in 1979 and 1989). The short-run correlation appears to move unrestrictedly between zero and one, especially after 1973. This finding is inconsistent with structurally low capital mobility. Furthermore, being so volatile, the short-run correlation cannot be considered as a measure of capital mobility for any practical purpose. Rather, the evidence suggests that the short-run correlation reflects the adjustment to common shocks, which may sharply differ across years, or to country-specific shocks. 1/ In the latter case the short-run cross-section SI-correlation has no economic meaning.
The high variability of the βecs-estimates raises the interesting question whether the βecs-estimates actually differ across time periods. A pooled time series cross-section regression (with fixed effects) offers a simple framework for a formal test of the time-invariance of βecs. Table 3 reports estimates based on the following regression equation:
Pooled Saving-Investment Regressions
Base regression: ΔIRit = Σat + βΔSRit + Σ γt(SRi-IRi)t−1
Pooled Saving-Investment Regressions
Base regression: ΔIRit = Σat + βΔSRit + Σ γt(SRi-IRi)t−1
| A. 808 observations (22 countries, 1955–91) | ||||||||||||
| Model | # par | α | β | γ | F-test α(t),γ(t) | average β(t) | vI,v2 | F-test β(t)=β | average β(i) | v1, v2 | F-test β(i)β | |
| (1) | α β γ | 3 | .0023 (3.53) | .5632 (16.0) | .2469 (11.6) | .5687 | 36,769 | 1.8304 [.0024] | .6858 | 21,784 | 5.4509 [.0000] | |
| (2) | α(t) β γ | 39 | .4891 (13.0) | .2160 (10.3) | 3.7100 [.0000] | .5083 | 36,733 | 1.0541 [.3849] | .6146 | 21,748 | 4.4515 [.0000] | |
| (3) | α β γ(t) | 39 | .0021 (3.32) | .5756 (16.0) | 2.1308 [.0002] | .5950 | 36,773 | 1.7663 [.0041] | .6971 | 21,748 | 5.5639 [.0000] | |
| (4) | α(t) β γ(t) | 75 | .4953 (13.1) | 3.1391 [.0000] | .5177 | 36,697 | 1.2070 [.4502] | .6245 | 21,712 | 4.4461 [.0000] | ||
| B. All observations excluding: 800 observations | ||||||||||||
| Model | # par | α | β | γ | F-test α(t),γ(t) | average β(t) | v1, v2 | F-test β(t)−β | average β(i) | v1, v2 | F-test β(i)=β | |
| (1) | α β γ | 3 | .0019 (3.12) | .6199 (17.8) | .2336 (11.4) | .6055 | 36,761 | 1.5410 [.0235] | .7021 | 21,776 | 3.7112 [.0000] | |
| (2) | α(t) β γ | 39 | .5354 (14.2) | .2050 (10.2) | 3.7163 [.0000] | .5482 | 36,725 | 0.8391 [.7362] | .6130 | 21,740 | 2.9975 [.0000] | |
| (3) | α β γ(t) | 39 | .0018 (3.00) | .6385 (17.8) | 2.0524 [.0003] | .6406 | 36,725 | 1.6871 [.0078] | .7179 | 21,740 | 3.7690 [.0000] | |
| (4) | α(t) β γ(t) | 75 | .5471 (14.4) | 3.1490 [.0000] | .5640 | 36,689 | 0.9497 [.5552] | .6273 | 21,704 | 2.9532 [.0000] | ||
Pooled Saving-Investment Regressions
Base regression: ΔIRit = Σat + βΔSRit + Σ γt(SRi-IRi)t−1
| A. 808 observations (22 countries, 1955–91) | ||||||||||||
| Model | # par | α | β | γ | F-test α(t),γ(t) | average β(t) | vI,v2 | F-test β(t)=β | average β(i) | v1, v2 | F-test β(i)β | |
| (1) | α β γ | 3 | .0023 (3.53) | .5632 (16.0) | .2469 (11.6) | .5687 | 36,769 | 1.8304 [.0024] | .6858 | 21,784 | 5.4509 [.0000] | |
| (2) | α(t) β γ | 39 | .4891 (13.0) | .2160 (10.3) | 3.7100 [.0000] | .5083 | 36,733 | 1.0541 [.3849] | .6146 | 21,748 | 4.4515 [.0000] | |
| (3) | α β γ(t) | 39 | .0021 (3.32) | .5756 (16.0) | 2.1308 [.0002] | .5950 | 36,773 | 1.7663 [.0041] | .6971 | 21,748 | 5.5639 [.0000] | |
| (4) | α(t) β γ(t) | 75 | .4953 (13.1) | 3.1391 [.0000] | .5177 | 36,697 | 1.2070 [.4502] | .6245 | 21,712 | 4.4461 [.0000] | ||
| B. All observations excluding: 800 observations | ||||||||||||
| Model | # par | α | β | γ | F-test α(t),γ(t) | average β(t) | v1, v2 | F-test β(t)−β | average β(i) | v1, v2 | F-test β(i)=β | |
| (1) | α β γ | 3 | .0019 (3.12) | .6199 (17.8) | .2336 (11.4) | .6055 | 36,761 | 1.5410 [.0235] | .7021 | 21,776 | 3.7112 [.0000] | |
| (2) | α(t) β γ | 39 | .5354 (14.2) | .2050 (10.2) | 3.7163 [.0000] | .5482 | 36,725 | 0.8391 [.7362] | .6130 | 21,740 | 2.9975 [.0000] | |
| (3) | α β γ(t) | 39 | .0018 (3.00) | .6385 (17.8) | 2.0524 [.0003] | .6406 | 36,725 | 1.6871 [.0078] | .7179 | 21,740 | 3.7690 [.0000] | |
| (4) | α(t) β γ(t) | 75 | .5471 (14.4) | 3.1490 [.0000] | .5640 | 36,689 | 0.9497 [.5552] | .6273 | 21,704 | 2.9532 [.0000] | ||
where v is a well-behaved disturbance term. DT is a dummy variable, which is one for observations from period τ, and zero otherwise. Country-Index i denotes the country and time-index t denotes the year (1955–1991, 37 years) of a particular observation. Pooling yields 808 observations. The difference between estimation of the full-blown version of (9) and estimation of (8e) for 37 years separately, as in Table 2, amounts to the stochastic assumption that the variance of the disturbance v is equal across years. Since the estimates of (9) are very close to the ones reported in Table 2, they are not reported here. Line 1 of Table 3 shows the benchmark case of constant parameters, which yields a highly significant estimate of β of .56. The estimate of γ is also highly significant, indicating strong support for cointegration of saving and investment.
Lines 2–4 show various restricted versions of (9). The hypotheses of a constant αT and a constant γT are strongly rejected, making the model in line 4 the appropriate null-hypothesis in a test of the time-invariance of βT. We get a markedly lower estimate of β when the intercept is time-varying. The difference of about .07 can be attributed to positively correlated shocks across countries. Such shocks make that the investment rates of countries tend to move in the same direction. Time-variation of the feedback coefficient γ hardly affects the estimate of β. Testing whether βT is constant over time involves 36 parameter restrictions. The F-test of the hypothesis βT = β in line 4 points to easy acceptance. 1/ To assess the robustness of the results, we dropped from the sample the eight most influential observations (1% of the total), reducing the sample size to 800 observations, and re-estimated all equations. The outcomes are reported in lines 5–8. The equation with time-invariant parameters now yields .62 as the estimated β. Making α and γ time-varying reduces the β-estimate to .55. The empirical evidence moves in the direction of a constant short-run SI-correlation as all F-tests have larger marginal significance levels. 2/
The finding of a time-invariant short-run saving-investment correlation suggests that this correlation has little to do with the degree of capital mobility, since it is widely believed that capital mobility has greatly increased over the past three decades. Moreover, how should we interpret a constant β in the light of the time series evidence pointing to considerable cross-country differences in β See, for example, Obstfeld (1986), Feldstein and Bacchetta (1991), Leachman (1991) and Jansen (1994a). To clarify this issue, the last column of Table 3 reports F-tests of the hypothesis that all countries have the same short-run SI-correlation. The hypothesis is overwhelmingly rejected in all cases. The estimate of the time-invariant β in Table 3 thus obscures systematic country differences and should be interpreted as a biased average of country-specific SI-correlations. The short-run cross-section SI-correlation is therefore not interesting from a theoretical point of view. The heterogeneity bias is about −.12 (panel A), which reduces to about −.08 after the sample has been purged of its most extreme observations. Country-specific SI-correlations are in agreement with macroeconomic theory: countries that differ in economic structure, government policies and so on, will probably exhibit different saving-investment dynamics. In this respect the SI-correlation is no different from other business cycle facts, which also display differences across countries (Danthine and Donaldson 1993).
The evidence presented in this section suggests that the variation in the short-run SI-correlation is across countries, and not across time. Such a pattern supports the view that this correlation mainly reflects business cycle influences (i.e., adjustments to supply and demand shocks), and not the degree of international capital mobility. Our conclusion is that Feldstein and Horioka’s original test of international capital mobility, which implies a cross-country concept of the SI-correlation, is not feasible. The (long-run) correlation from the Feldstein-Horioka equation in levels measures the combined effect of the intertemporal budget constraint and limited capital mobility. The correlation from the short-run cross-section equation appears to be dominated by business cycle effects that drown out any systematic effects of limited capital mobility.
V. Summary and Conclusions
Feldstein and Horioka (1980) argued that the correlation between investment and saving in a cross-section of countries in a certain period may serve as an indicator of the degree of international capital mobility in that period. Accordingly, they interpreted the high correlation they found as evidence of low capital mobility among OECD countries.
This paper argues that the high saving-investment correlation generally found in cross-section studies reflects the cointegration of each country’s saving and investment rate in the time dimension. Saving and investment exhibit a long-run relationship, which takes the form of a stationary current account. This is a direct consequence of the intertemporal budget constraint of a completely open economy. On the other hand, restrictions on a country’s cross-border capital flows will reinforce the effect of the intertemporal budget constraint on the stationarity of its current account. Hence, cointegration of a single country’s saving and investment over time may reflect two phenomena, one that is not related to capital mobility, and one that is.
This paper focuses on the consequences of the cointegration property for the traditional cross-section saving-investment regression, which attempts to assess global capital mobility. The conventional equation is formulated in the levels of the variables. We investigate in Monte Carlo simulations the small sample behavior of the saving-investment correlation in various cross-section regressions, if the underlying time series of the saving and investment rate are cointegrated. We find that the cross-section regressions commonly used in the literature yield an estimate of the saving-investment correlation that strongly tends towards one. This is even true if saving and investment appear to be only “weakly” cointegrated (small error correction coefficient γ), and the intertemporal budget constraint does not seem to be particularly restrictive on the level of a single country. Moreover, we still find high correlations if the contemporaneous correlation β is zero, and all countries are perfectly integrated in the world capital market according to the Feldstein-Horioka criterion. Conventional cross-section regressions are thus likely to produce high saving-investment correlations, regardless whether the degree of international capital mobility is high or low. Consequently, the Feldstein-Horioka test as conducted in the literature is not informative.
In our empirical section we therefore investigate the contemporaneous (or short-run) saving-investment correlation in a cross-section of countries. The intertemporal budget constraint does not affect this type of correlation, whereas restrictions on capital flows still do. However, business cycle effects may now play the distorting role. We examine the short-run correlation’s behavior over time and across countries in order to find out which effect dominates. If the short-run correlation truly measures the degree of global capital mobility, it should decline sharply over time. However, we find that the short-run correlation mainly varies across countries, and not over time. The finding of rather stable country-specific short-run saving-investment correlations suggests that these correlations are produced in the process of adjustment to supply and demand shocks.
The simulation results and the empirical results in this paper demonstrate the impossibility of a reliable test of Feldstein and Horioka’s basic idea that the correlation of saving and investment in a cross-section of countries provides information on the degree of international (global) capital mobility. This is not to say that economists should lose interest in saving-investment correlations. Both the long-run and the short-run saving-investment correlation are interesting variables on the level of an individual country. The long-run correlation provides a test of the relevance of the intertemporal budget constraint, which is one of the cornerstones of modern open-economy macroeconomics. The short-run correlation is an important business cycle fact. Estimation of these country-specific saving-investment correlations requires a time series or panel data framework.
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This paper was written while I was a guest at the Research Department. I would like to thank, without implication, Tamim Bayoumi, Peter Broer, Menzie Chinn, Laura van Geest, André Lucas, Paul Masson, Ron Smith and Otto Swank for helpful comments on earlier drafts, and the Research Department for hospitality.
See Tesar (1991) for a review article.
Evidence on the cointegration of the saving and investment rate can be found in the time series studies by Gundlach and Sinn (1992) and Jansen (1994a), among others.
See BMA (1994, Chapters 19 and 20) for a comprehensive overview of the characteristics of social assistance. A very comprehensive treatment of the sociological problems of social assistance and poverty in Germany can be found in Hauser and Hubinger (1993), and in Leibfried and Leisering (1995).
Erbe and Erbe (1993, p. 588).
Cross-section regression results were reported by Feldstein (1983), Penati and Dooley (1984), Dooley, Frankel and Mathieson (1987), Feldstein and Bacchetta (1991), Tesar (1991), Sinn (1992), and others.
Blanchard and Fischer (1989) provide an exposition of intertemporal general equilibrium models. Obstfeld (1986) and Leachman (1991) derive steady state expressions for the saving rate, the investment rate and the current account for specific overlapping generations models. Masson, Kremers and Horne (1994) show for the US, Germany and Japan that net foreign assets are a function of demographic factors and government debt in long-run equilibrium.
See Jansen and Schulze (1996), Vikoren (1994), Jansen (1994a), Levy (1996), and Coakley, Kulasi, and Smith (1995), among others.
The ECM is kept as simple as possible to facilitate the exposition. Extra lags of SR and IR generate richer SI-dynamics, but are not essential to the discussion. In empirical applications the exact lag structure has to determined by the data, since it cannot directly be derived from a theoretical model. Jansen (1994a) finds statistically significant additional lags (mostly one) for 9 of the 23 OECD countries.
Kremers, Ericsson and Dolado (1992) show that the t-statistic of the error correction coefficient γ provides a more powerful test for cointegration than the two-step Engle-Granger (1987) procedure.
None of the cited papers, nor Jansen (1994a), tests whether these differences are statistically significant. Section IV below presents such a formal statistical test.
See, for instance, Feldstein and Horioka (1980), Penati and Dooley (1984), and Dooley, Frankel, and Mathieson (1987).
In the past governments and central banks have cared about the current account (and some probably still care), giving rise to (long-run) current account targeting (see Summers 1988). The feedback of (lagged) current account imbalances into monetary and fiscal policy will result in a more stable current account, which will also make it easier to establish statistically significant cointegration.
Jansen (1994a) found that the standard error of the γ estimate typically exceeds .10. The associated t-statistic is the cointegration test advocated by Kremers, Ericsson and Dolado (1992). With critical values around 3, it will prove hard to detect cointegration when γ is less than .30.
The numerical values of the variances of the disturbances appearing in (6) and (7) are chosen so as to generate time series with mean and variability comparable to the historically observed saving and investment rate series. The series are started from a situation of equilibrium with IR equaling .25. The initial value of SR is thus .25−α. The length of the series is 50 observations. The first 10 observations are dropped to weaken the influence of the starting conditions. We restart after 50 periods to avoid unreasonable values for SR and IR, which are unavoidable when SR is generated by a random walk process.
The rejection frequency is based on 6250 cointegration tests (25 countries × 250 data sets) involving 40 annual observations. As recommended by Kremers, Ericsson and Dolado (1992), we use the 5 percent critical value of the Dickey-Fuller distribution.
As a sensitivity analysis we also performed the simulations for the following process of the saving rate
SR is stationary around mean .25, but it will often resemble a random walk over a time-span of 40 observations. (Using Dickey-Fuller tests non-stationarity was accepted in 94% of the cases.) Because it is hard to believe that the saving rate truly is a random walk, a stationary process with slow mean reversion is probably closer to reality. However, the simulation results are essentially the same. Level equations strongly drive β towards one, and (8d) and (8e) estimate the short-run correlation without bias.
Estimation of (8d) does not change the main results of Section IV. The estimation results are available from the author upon request.
Source of the data is the OECD National Accounts. The sample includes all OECD countries, except for Luxembourg and Iceland. Both countries are extremely small and special cases. Luxembourg is routinely excluded in similar empirical work because it has a large international banking sector (see Als 1988). Iceland experienced high and variable inflation and has an ill-diversified economy. Including Iceland would exert a downward influence on the cross-section SI-correlation, since it has an atypical, negative SI-correlation. Annual data for IR and SR are available for 1954–91 for all countries, except Turkey (1960–91).
It is remarkable that two very low short-run correlations occur in years in which there was an oil price shock (1979 and 1986). Matsuyama (1987), and Jansen and Schulze (1996) offer explanations why oil price changes may give rise to a negative SI-correlation.
For the sake of completeness we also report the test for the other null-models. The hypothesis is easily accepted in case of a time-varying α (line 2), while rejected at the 1% level in case of a constant αT (lines 1 and 3).
Influential observations were identified by their DFBETAS-statistics. See the note at the bottom of Table 3 for details. We also investigated whether we could find a single structural break in β in the period 1962–1989. The associated t-statistic was never significant, and in about 90 percent of the cases below one.
