Savings and Investment: Some International Perspectives.

Schmidt, Martin B.

Martin B. Schmidt [*]

Consistent with neoclassical growth models, recent estimates of the close association between domestic saving and investment rates may allow policy makers the opportunity to alter investment through the introduction of polices that alter domestic savings. However, such an interpretation presumes an endogenous investment response. Equally likely, at least theoretically, is that the close association is maintained by movements in domestic savings. The present paper explicitly examines the endogeneity of domestic saving and investment rates. For a subset of countries, including the United States, the results suggest that saving adjustments make up only a small portion of investment behavior.

1. Introduction

In recent years it has become common to lament the deterioration of domestic savings rates as one of the main causes of low GDP growth. The relation between the two represents the essence of most neoclassical growth models that suggest that decreased saving reduces domestic growth because of a reduction in investment opportunities. In this case policy prescriptions for increased economic growth are rather obvious: Introduce legislation that is intended to increase domestic saving rates.

The present paper is specifically interested in the link between a nation's saving and investment rates. Moreover, it is concerned with whether a nation's investment rate plays the suggested passive equilibrating role. To examine the endogenous responses of a nation's saving and investment rates, the paper focuses on recent empirical models that have characterized the long-run relation between domestic saving and investment. [1] The close association between the two suggests that a shock to one variable may produce an adjustment in the other variable. In this case such models hypothesize that policies that are intended to promote domestic saving may produce congruent investment responses. [2] However, such a policy prescription imputes a direction of causality that has not generally been the focus of these earlier studies. It is possible, at least theoretically, that the saving variable plays the equilibrating role.

To examine the endogenous responses of domestic saving and investment rates, the paper investigates both the long- and short-run properties of a nation's private saving and investment rates by incorporating the Johansen maximum likelihood methodology (MLE) to estimate vector error-correction (VEC) models for several countries. Furthermore, a more general approach is taken to investigating the endogenous saving and investment responses. Whereas short-run movements in the variables may be an outgrowth of deviations from the defined long-run equilibrium, they may also be produced by movements in the associated saving and investment lags. Finally, the paper examines saving and investment variance decompositions. The decompositions incorporate both responses simultaneously and describe the proportion of investment movements that may be ascribed to changes in savings.

Overall, the results suggest that the response to saving policies would differ dramatically across countries. Specifically, whereas the long-run estimates are similar for all nations, the short-run investment responses are considerably larger for France and Canada than they are for the United States, Japan, and the United Kingdom. Furthermore, the variance decomposition results for the United States and Japan suggest that only roughly 10% of the investment variance may be attributed to shocks in private saving. The United Kingdom produces a slightly larger value of roughly 24%. In contrast, France's value is close to 40% and Canada's is made up of approximately 58%. In the end, the results suggest that for a significant subset of countries the potential benefits of savings polices may be limited.

The plan of the paper is as follows: Section 2 describes the hypothesized saving-investment relation, the incorporated Johansen MLE methodology, and the associated VEC models. The following section describes the empirical results from analyzing both the long- and short-run behavior of saving and investment. Finally, section 4 provides a brief conclusion.

2. Assessing the Investment Response

In examining the relation between a nation's saving and investment rate, Feldstein and Horioka (FH) (1980) estimated the following (long-run) economic relation:

i/[y.sub.t] = [[beta].sub.0] + [[beta].sub.1] s/[y.sub.t] + [[epsilon].sub.t] (1)

where i represents domestic investment, s represents domestic saving, and y represents gross domestic product. To assess the value of [[beta.sub.1], FH examined data from 16 OECD countries over several subperiods and were unable to reject the hypothesis that [[beta].sub.1] = 1. Although numerous authors have debated the interpretation of Equation 1, the high degree of correlation between the two variables has been extended and replicated over many time periods, many econometric techniques, and across many nations. [3]

As was mentioned, the close association may afford a nation the ability to alter its investment levels by altering the nation's saving rate. However, this extension a priori assigns a direction of causality that is not part of Equation 1. To characterize the short-run responses that maintain the long-run relation, Feldstein and Bacchetta (FB) (1991) examined the response of a nation's domestic investment rate to the previous year's 'saving-investment' gap:

[delta][(i/y).sub.t] = [[alpha].sub.0] + [[alpha].sub.1] [[(s/y).sub.t-1] - [(i/y).sub.t-1]] + [[eta].sub.t]. (2)

FB estimated versions of Equation 2 for 23 OECD countries. Overall, their findings were consistent with a nation's investment rate responding endogenously to the nation's saving-investment gap. In this case, a nation's saving would Granger cause its investment level. [4] Furthermore, FB investigated whether a nation's saving rate held a similar response. The saving response was, however, generally of the wrong sign and often insignificant.

As is pointed out in Jansen and Schulze (1996), these two approaches are intimately related, so much so that they argue that the estimation of the equations in isolation would constitute an error in specification. Specifically, the FH saving-investment long-run estimation would be misspecified because of (i) the possible 'spurious' nature of the results, and (ii) even if the relation is not spurious, the formulation ignores the dynamic adjustment process that would maintain the long-run relation.

Although the FB short-run approach is not subject to the spurious concerns of Equation 1 and does attempt to capture the dynamic adjustment through the gap variable, the misspecification lies within the a priori assumption that the long-run relation between domestic saving and investment rates has a coefficient vector of (1.0, -1.0). A more efficient approach would entail allowing the available data to determine the coefficients. In addition, a more general approach to causality would incorporate and examine the responses of all significant lags of the two endogenous variables.

To correct for many of these specification concerns, Jansen and Schulze (1996) and Jansen (1996) combine the two approaches within the following VEC equation:

[delta][(i/y).sub.t] = [[delta].sub.0] + [[delta].sub.1][delta][(s/y).sub.t] + [[delta].sub.2][[(s/y).sub.t-1] - [(i/y).sub.t-1]] + [[delta].sub.3] [(s/y).sub.t-1] + [[eta].sub.t] (3)

where the lagged differenced saving terms are introduced to further capture the short-run dynamic adjustments and the additional lagged saving rate term allows the long-run relation to differ from unity. [5] Within Equation 3, the long-run relation, [[beta].sub.1], would equal (1 - [[[delta].sub.3]/[[delta].sub.2]whereas the short-run responses, [[alpha].sub.1], would equal [[delta].sub.2]. Jansen (1996) estimates versions of Equation 3 for 23 OECD nations. In general, Jansen's results suggest that national saving and investment rates are related, with coefficients (1.0, -1.0). Also, although the size of the shortrun responses differ substantially across nations, most nation investment rates respond endogenously. [6]

Unfortunately for the majority of the country saving-investment equations, Jansen is unable to estimate values for both [[delta].sub.2] and [[delta].sub.3]. To estimate these equations, Jansen drops the additional lagged saving rate term. However, once the term is omitted, Jansen continues to impose the unity restriction on the long-run relation. To correct for the difficulty of estimating the two simultaneously, the present paper estimates the long-run saving-investment relation with the Johansen MLE methodology. This approach integrates both the long- and short-run responses and may be summarized by the following general k-order VAR model:

[delta][X.sub.t] = [micro] + [[[sigma].sup.k-1].sub.i=1] [[gamma].sub.i][delta][X.sub.t-i] + [pi][X.sub.t-k] + [[epsilon].sub.t] (4)

where [X.sub.t] is a vector of I(1) variables at time t, the [[gamma].sub.i][delta][X.sub.t-1] terms account for the stationary variation related to the past history of the variables, and the [pi] matrix contains the cointegrating relations. [7] Furthermore, the [pi] matrix may be separated into two components, such that [pi] = [alpha][beta]', where the cointegrating parameters (the FH estimates) are contained within the [beta] matrix and the [alpha] matrix describes the weights with which each variable enters the equation (the FB estimates). Cointegration, then, requires that the [beta] matrix contains parameters such that [Z.sub.v], where [Z.sub.t] = [beta]'[X.sub.v] is stationary. Also, the a matrix is thought to represent the speed with which each variable changes to return the individual vectors to their respective long-run equilibrium and may be estimated from the error correction equations.

The steps involved in the Johansen approach are, briefly, to difference [X.sub.t] and regress [delta][X.sub.t], on [delta][X.sub.t-1], [delta][X.sub.t-2], ..., [delta][X.sub.t-k-1], and save the residual vector. Then [X.sub.t-k] is regressed on the future [delta][X.sub.t-1], [delta][X.sub.t-2], ..., [delta][X.sub.t-k-1] and [delta][Z.sub.t]. The resulting residual vector is also saved. This latter vector is nonstationary and contains the elements of the cointegrating vectors. Using reduced rank regression techniques, the covariance matrix of the two residual vectors is calculated and associated eigenvalues and cointegrating vectors are estimated.

In terms of directional causality, the use of cointegration techniques presents a difficulty since all of the included variables are assumed to be endogenous, and therefore cannot provide direct information on the exogeneity of the variables. However, Crowder (1998) offers straightforward tests for exogeneity through examination of the [[gamma].sub.i] and [alpha] estimates. Specifically, if [delta][X.sub.it] fails to respond to the defined long-run disequilibrium, that is, [[alpha].sub.i] = 0, then [X.sub.it] is said to be weakly exogenous. [8] In addition to weak exogeneity, strong exogeneity requires that [delta][X.sub.it] fail to respond to the incorporated (k) lags of [delta][X.sub.j], that is, [sigma][[gamma].sub.i] = 0. This may be accomplished through an F-test. Granger causality would then be found with the rejection of either strong or weak exogeneity.

The use of the Johansen MLE approach has additional benefits. Recently, Gonzalo (1994) has shown that the Johansen MLE approach is less sensitive to the choice of lag structure, that is, the choice of (k). As has been highlighted within the literature, the estimation of the long-and short-run estimates is sensitive to the choice. Specifically, a lag structure that is too high may overparameterize and may, therefore, reduce the power of the cointegration tests. However, a lag structure that is too low may not produce residuals that are white noise. In addition, Gonzalo demonstrates that the Johansen approach has stronger small-sample properties.

A final modification is made through the introduction of the nation's deficit rate as a conditioning variable. It has become common to introduce conditioning variables to eliminate unwanted influences that might affect the estimates of the cointegrating vectors. Because the variables are not part of any hypothesized vector, it would be inappropriate to include them within the cointegrating vector directly. However, these are influential and their effects should be accounted for.

The deficit variable is included for both theoretical and empirical concerns. [9] Theoretically, Summers (1988) and Artis and Bayoumi (1991) argue that current account targeting by national governments can lead to an endogenous 'government reaction function.' In this case changes in private sector savings may be offset by variations in public saving that may influence the estimated saving-investment estimation. Empirically, Bodman (1995) has shown that many nation's saving-investment relations are influenced by their deficit rate.

3. Empirical Results

To describe the long- and short-run behavior of the national private saving-investment relation, Tables 1-3 report the results for five countries: the United States, United Kingdom, Canada, France, and Japan. [10]

Unit Root and Lag Length Tests

A necessary condition for variables to be cointegrated is that each has a similar level of integration. Therefore, a beginning point for an analysis of long-run behavior must be an examination of the number of unit roots each of the included variables contains. To determine the integrated level of both investment and saving series, both augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests were performed. [11, 12] Overall, both ADF and PP tests indicate that all nation's saving and investment rates fail to reject the presence of a single unit root. In addition, consistent with the previous studies, they also suggest the absence of a second root. Therefore, the private saving and investment variables are estimated to be I(1) and may therefore be cointegrated.

The VEC model also requires a lag structure to be selected. To investigate the optimal lag structure, both the Akaike Information Criterion and Schwarz Bayesian criterion tests for the various lags (1-12) were performed. The tests generally opt for a length of 4. [13]

The Estimated Number of Cointegrating Vectors

Whereas estimation of similar levels of integration allows for the possibility of cointegration between a nation's saving and investment rate, it does little to guarantee it or to describe the precise manner in which the variables are related. Therefore, the next step is to determine the number of cointegrating relations the two variables are estimated to produce. The choice is important because incorporating too few, relative to the true number, omits relevant error correction information, and incorporating too many distorts the distribution of the test statistics.

To determine the number of significant cointegrating vectors, the Johansen procedure evaluates the log likelihood ratio statistics of the estimated eigenvalues to determine the number that are significant, either by the maximal eigenvalue statistic, [[lambda].sub.max], or the trace statistic. Table I reports the maximal eigenvalue and trace tests for each nation. [14] Overall, both maximal eigenvalue and trace tests estimate one significant cointegrating vector. The one exception is Japan, whose second eigenvalue is also significant. However, such a result would seem implausible, as no common (permanent) trend would then exist.

The Estimated [beta] Values

It is possible with the use of Johansen and Juselius's (1992) procedure to obtain the estimated cointegrating coefficients, that is, the estimated [beta]'s. However, the identifying procedure requires one normalizing restriction. The restriction follows convention by normalizing on private investment rates, or that the cointegrating relation is defined as (1.0, [beta]). Table 2 reports the normalized estimates and their corresponding standard errors for the five countries. [15]

The results presented in Table 2 suggest that for most of the nations the long-run saving-investment relation is estimated close to (1.0, -1.0). The one exception is Japan, which has an estimate of (-0.81). However, as these coefficients are estimates, the question of their statistical significance is relevant. One approach to examine the significance of the estimated coefficient follows Kremers, Ericsson, and Dolado (1992). The authors show that the [beta]'s student t-statistic is approximately normally distributed. Therefore, all of the countries would reject the null of [beta] = 0, whereas none would reject the null of [beta] = -1.

Perhaps a more efficient approach to analyzing the acceptable range of [beta] would be to impose the delineating restrictions directly onto the investment-saving vector and examine the corresponding likelihood ratio statistic as described in Johansen and Juselius (1992). The Johansen and Juselius procedure also allows the researcher the ability to make such specific restrictions on the hypothesized vector. The system is reestimated with the overidentifying' restriction(s), and log-likelihood ratio statistics are then computed. The statistics are distributed [[chi].sup.2](n) where (n) represents the number of overidentifying restrictions. The last column of Table 2 reports associated likelihood ratio test statistics and p-values. The results are similar, as none of the countries rejects the hypothesized unitary coefficient.

The Short-Run Responses

As was mentioned earlier, the endogenous response of investment to changes in the saving rate provides important information for policy options. Such responses may be an outgrowth of either deviation from the defined long-run equilibrium, the saving-investment gap, or the incorporated saving lags.

The results of Tables 1 and 2 suggest the existence of a significant long-run relation between a nation's private saving and investment rates. In this case, deviations from long-run equilibrium must produce an adjustment(s) to reattain the defined equilibrium. For example, if the long-run relation were defined as in the case of Table 2 for the United States:

i/[y.sub.t] - 0.98. s/[y.sub.t] = [[epsilon].sub.sit]

where s, i, and y are defined as before, the error term, [[epsilon].sub.sit], represents the deviation away from the defined long-run equilibrium. In the case where [[epsilon].sub.sit] [greater than]0, some adjustment of the two variables must occur. The adjustment back to equilibrium would require the saving rate to rise or the investment rate to fall, or both. Theoretically, any combination of the two will clear the relation. Therefore, the saving rate should respond positively to [[epsilon].sub.sit], and the investment rate should move inversely to eliminate positive values of [[epsilon].sub.sit].

It is precisely this term that policy makers may have some ability to manipulate. Policies that affect saving rates may be viewed as creating an initial wedge between these two variables. For example, a policy that increases savings, ceteris paribus, would create a negative [[epsilon].sub.sit] [less than]0. The policy maker would then hope that an endogenous rise in investment would follow. Table 3 reports the results of estimating these responses, that is, [alpha]'s. The disequilibrium residuals ([[epsilon].sub.sit-1]) were estimated with the quarterly [beta] estimates of Table 2. In addition, Table 3 reports the aggregate responses of investment and saving to the four lags of saving and investment. [16] Finally, the results of Wald tests, which examine the lags' aggregate significance, are reported.

Overall, the results suggest that whereas both investment and saving respond endogenously and in the correct manner to the associated disequilibrium, the saving responses are always larger. This is particularly true for the United Kingdom and Japan, which have the largest saving responses, 0.16 and 0.35, respectively. By contrast, France and Canada are the only countries that have investment responses over -0.10, with values of -0.16 and -0.15, respectively. The United States, United Kingdom, and Japan all have considerably smaller responses more closely associated with -0.07. In the end, although these results suggest some adjustment by investment, they also suggest a relatively stronger saving response. [17]

Another possible source of short-run adjustment is the responses of the investment and saving variables to movements in the associated lags contained within the VEC. However, as is highlighted in the latter part of Table 3, these are generally insignificant as a group. The exceptions are the significance of the savings lags within the United States saving equation and within both of Japan's equations. In addition, the investments lags are significant within the United Kingdom saving equation. These results do, however, foreshadow the variance decomposition results. Specifically, both Canada and France have, as a group, much larger investment responses to the incorporated saving lags than is reflected by their saving responses. This suggests that the impact of savings may be more important within these two countries.

To examine the dynamic impact of the long- and short-run estimates on the behavior of the two series, variance decompositions were performed for each nation's investment and saving variable. The decompositions are estimated from the VEC models contained within Table 3, which incorporate the results of Table 2. The decompositions characterize the response of the two variables to shocks to each variable. In this way, the decomposition integrates the short-run responses and provides an estimate of the impact of a shock in one variable on the other's future behavior. Within the variance decomposition, exogeniety represents the condition when a shock to one variable has little or no impact on the forecast variance of the other variable. For example, if saving were exogenous with respect to investment, innovations in savings should account for little of the variance of investment.

Consistent with the earlier results, the variance decompositions suggest that for many nations, domestic investment is largely determined by other factors than domestic saving rates. More specifically, although the proportion of French and Canadian variances, which are an outgrowth of saving innovations, are roughly 50%, the results for the other three countries continue to suggest that the success of saving polices may well be limited. The Untied States's value is only 10%, whereas Japan's is roughly 12%. The United Kingdom, because of the slightly larger saving lag response, has a slightly larger value of roughly 24%.

4. Conclusion

The present paper examines one possible implication of the high degree of correlation between a nation's saving rate and its investment rate. The close association of these variables may afford a nation the opportunity to use domestic policies to influence the domestic saving rate which may ultimately alter a nation's investment rate. However, the effectiveness of such policies requires not only a close association between the two variables but also an effective response by a nation's investment, that is, that a nation's saving rate Granger causes its investment rate.

To examine the short-run response of investment to changes in the domestic saving rate, the present paper modifies the FB approach by incorporating the Johansen MLE approach and examining more closely the associated error-correction responses. In addition, the additional lag significance is investigated. Finally, variance decompositions and the sensitivity of the responses, both long- and short-run, are examined with the use of a rolling-regression technique.

Overall, the results suggest that for a subset of countries the impact of saving polices may be limited. More specifically, although the long-run results for all incorporated countries are similar, for the United States, United Kingdom, and Japan, saving policies are likely to affect their investment rates only marginally. However, for France and Canada such polices are likely to have a much larger impact.

(*.) Department of Economics, Portland State University, P.O. Box 751, Portland, OR 97207-0751, USA; E-mail schmidtm@pdx.edu.

I have benefited from helpful comments from Kent Kimbrough and two anonymous referees. However, I bear sole responsibility for all remaining errors.

Received April 2000; accepted February 2001.

(1.) The close association between national saving and investment rates has been highlighted by Murphy (1984), Obstfeld (1986), Miller (1988), Tesar (1991), Baxter and Crucini (1993), Bodman (1995), Barkoulas, Filizetkin, and Murphy (1996), Coakley, Kulasi, and Smith (1996), and Jansen (1996), as well as others.

(2.) An alternative interpretation is that where the degree of capital mobility is relatively small, polices that promote domestic saving must ultimately increase domestic investment. In contrast, if significant capital mobility exists, such policies would increase the flow of capital to international markets that may or may not affect the level of domestic investment. See, for example, Gordon (1997).

(3.) In the original analysis, Feldstein and Horioka hypothesized that the implication was little capital mobility. Recently, however, some authors have argued that the close association between the two simply highlights the 'solvency constraint' implied by the fact that a nation's balance of payments must be stationary, and is, therefore, not a test of capital mobility. See, for example, Coakley, Kulasi, and Smith (1996) or Jansen (1996).

(4.) See Enders (1995) for a description of the relation between Granger causality and the error-correction gap term.

(5.) See Banerjee et al. (1992).

(6.) Jansen (1996) fails to report the saving responses.

(7.) Johansen (1988), (1992a), or (1992b), or all.

(8.) The use of strong and weak exogeneity follows the definitions presented in Engle, Hendry, and Richard (1983).

(9.) In addition, the national deficit was subtracted from the national saving rate. The reason for this modification is twofold. The first is that this highlights the response of private saving that in the end is the main component of domestic legislation. The second is that failing to do so would create difficulty in that a component of the endogenous variable, the saving rate, would be the conditioning variable.

(10.) The specific quarterly data largely follow Bodman (1995). Specifically, gross private domestic investment is taken from gross fixed capital formation plus net additions to stock, and gross private saving is produced by adding net lending abroad to gross domestic product and subtracting private and government final consumption expenditures, as well as government saving. The deficit variable is gross government saving. Following the advice of an anonymous referee, I examined an alternative private saving definition. Largely following Jansen (1996), private domestic saving was created by adding net (net of government) private saving to net (again, net of government) private fixed capital consumption. This approach, however, produced qualitatively similar results. All data were obtained from the OECD Quarterly National Accounts.

(11.) As these results are consistent with earlier studies, the results are included in a data Appendix. See Miller (1998), Gulley (1991), Bodman (1995), Coakley, Kulasi, and Smith (1996), and Jansen (1996). The Appendix is available from the author upon request.

(12.) Both ADF and PP tests were also performed for the national deficit rates. Both tests indicate that the deficit rates are I(0). Therefore, its level was included.

(13.) In order to further investigate the choice, diagnostic tests (Godfrey's LM test--serial correlation, Ramsey's RESET test--functional form, Jarque-Bera test--normality, and White's LM test for heteroscedasticity) for the unrestricted VAR with four lags were examined. Overall, the results indicate that the system of equations with four lags is wellbehaved. In addition, the choice of four lags is consistent with most studies. These results are included in a data Appendix which is available from the author upon request.

(14.) The reported test statistics have been further adjusted by the correction factor suggested by Cheung and Lai (1993). These authors highlight with the use of Monte Carlo simulations that the original test statistics have poor small-sample properties. To correct for the possible bias, Cheung and Lai suggest the use of a correction factor of (0.9 [DF/T] + 0.1) where OF is the degrees of freedom and T represents the number of observations. The correction factor effectively reduces the likelihood test statistic.

(15.) The working paper version also incorporated a rolling regression approach to highlight the sensitivity of both the long-and short-run parameters to changes in sample periods. The rolling regression results suggested that the estimated coefficients were sensitive to changes in sample periods and further highlighted the misspecification concerns raised earlier. Overall the results suggest that for the United Kingdom and France the estimated [beta] coefficients were considerably larger than their hypothesized value for at least part of the 1980s. In contrast, for almost all of the 1980s, the opposite is true for Japan. The result is likely an outgrowth of the large capital outflows from Europe and large inflows into Asia during the 1980s. In any event, the results suggest that sample periods are a relevant concern when examining national saving-investment relations.

(16.) To examine whether the VEC equations are well-behaved", Breusch-Godfrey's LM test for serial correlation, JarqueBera test for normality, White's LM test for heteroscedasticity. and Ramsey's RESET test for functional form were examined. Overall, the tests indicate that the system's residuals are well-behaved. These results are included in a data Appendix which is available from the author upon request.

(17.) As with the earlier [beta] estimates, rolling regression estimates were computed for the two endogenous [alpha] estimates. These results were not as sensitive as the long-run estimates, suggesting that their relative behavior seems to be largely independent of the behavior of the long-run estimates.

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Table 1

Long-Run Cointegration Tests Based on Maximal Eigenvalue and Trace Test
of the Stochastic Matrix

 Eigenvalue Long-Run Cointegration Tests
Country: [lambda] [H.sub.0]:

United States
 0.136 r = 0
United Kingdom 0.001 r [less than or equal to] 1
 0.261 r = 0
 0.009 4 [less than or equal to] 1
Canada 0.171 r = 0
 0.026 r [less than or equal to] 1
France 0.241 r = 0
 0.014 r [less than or equal to] 1
Japan 0.341 r = 0
 0.067 r [less than or equal to] 1
[[lambda].sub.max] 99% r = 0 r = 1 15.69
 r [less than or 6.51
 equal to] 1 r = 2

 Long-Run Cointegration Tests
Country: [H.sub.a]: [[lambda].sub.max] [H.sub.0]:

United States
 r = 1 37.99 [*] r = 0
United Kingdom r = 2 0.045 r = 1
 r = 1 33.88 [*] r = 0
 r = 2 1.003 r = 1
Canada r = 1 27.69 [*] r = 0
 r = 2 4.01 r = 1
France r = 1 30.40 [*] r = 0
 r = 2 1.59 r = 1
Japan r = 1 65.17 [*] r = 0
 r = 2 10.86 [*] r = 1
[[lambda].sub.max] 99% trace = 99% r = 0
 r = 1


 Long-Run Cointegration Tests
Country: [H.sub.a]: Trace

United States
 4 [greater than or equal to] 1 38.04 [*]
United Kingdom 4 [greater than or equal to] 2 0.045
 r [greater than or equal to] 1 34.88 [*]
 4 [greater than or equal to] 2 1.003
Canada r [greater than or equal to] 1 31.69 [*]
 r [greater than or equal to] 2 4.01
France r [greater than or equal to] 1 31.99 [*]
 r [greater than or equal to] 2 1.59
Japan r [greater than or equal to] 1 76.03 [*]
 r [greater than or equal to] 2 10.86 [*]
[[lambda].sub.max] 99% r [greater than or equal to] 1 16.31
 r [greater than or equal to] 2 6.51
Table 2.

Exact-Identifying Values for the Cointegrating Vectors: Normalized
Johansen & Juselius' [beta] Estimates

 Variables: LR Statistics:
Country inv/y sav/y Overidentifying Restriction(s):

 [[chi].sup.2](n)Statistic
United States 1.00 -0.98 [*] [beta] = 0.00: [[chi].sup.2]
 (1)statistic = 35.03 (0.00)
(59q2-99q1) (0.02) [beta] = -1.00: [[chi].sup.2]
 (1)statistic = 0.63 (0.43)
United Kingdom 1.00 -1.08 [*] [beta] = 0.00: [[chi].sup.2]
 (1)statistic = 31.22 (0.00)
(70q2-99q1) (0.05) [beta] = -1.00: [[chi].sup.2]
 (1)statistic = 2.86 (0.09)
Canada 1.00 -0.99 [*] [beta] = 0.00: [[chi].sup.2]
 (1)statistic = 21.47 (0.00)
(61q2-99q1) (0.04) [beta] = -1.00: [[chi].sup.2]
 (1)statistic = 0.08 (0.78)
France 1.00 -1.09 [*] [beta] = 0.00: [[chi].sup.2]
 (1)statistic = 26.85 (0.00)
(70q2-98q3) (0.07) [beta] = -1.00: [[chi].sup.2]
 (1)statistic = 1.11 (0.29)
Japan 1.00 -0.81 [*] [beta] = 0.00: [[chi].sup.2]
 (1)statistic = 21.29 (0.00)
(59q2-98q4) (0.17) [beta] = -1.00: [[chi].sup.2]
 (1)statistic = 0.58 (0.45)

Each equation contains an exogenous domestic deficit rate (conditioning
variable) and trend term. The estimates have been normalized and are
reported with their respective standard errors.

(*)represents significance at the 1% critical level (see Kremers,
Ericsson, and Dolado 1992). The (n) overidentifying restrictions are
imposed on the estimated matrix and the log-likelihood ratio tests are
by the method suggested in Johansen and Juselius (1992). The ratio test
statistics estimated [chi](n) p-values are reported in parentheses.
Table 3.

Weak and Strong Exogenity Tests



Country Eq: [alpha]'s

United States [delta][(s/y).sub.t] 0.109 (0.00)
(59q2-99q1) [delta][(i/y).sub.t] -0.070 (0.04)
United Kingdom [delta][(s/y).sub.t] 0.166 (0.00)
(70q2-99q1) [delta][(i/y).sub.t] -0.067 (0.00)
Canada [delta][(s/y).sub.t] 0.148 (0.00)
(61q2-99q1) [delta][(i/y).sub.t] -0.199 (0.0)
France [delta][(s/y).sub.t] 0.161 (0.00)
(70q2-98q3) [delta][(i/y).sub.t] -0.130 (0.00)
Japan [delta][(s/y).sub.t] 0.356 (0.00)
(59q2-98q4) [delta][(i/y).sub.t] -0.066 (0.00)

 Wald Test:
 [sigma] [sigma] [delta][(i/y).sub.t-j]
Country [delta][(i/y).sub.t-j] = 0

United States -0.171 1.111 (0.29)
(59q2-99q1) -0.204 0.978 (0.32)
United Kingdom -0.588 3.753 (0.05)
(70q2-99q1) -0.052 0.056 (0.81)
Canada -0.205 0.205 (0.37)
(61q2-99q1) -0.045 0.068 (0.79)
France -0.171 0.809 (0.37)
(70q2-98q3) -0.016 0.008 (0.93)
Japan 0.367 0.008 (0.93)
(59q2-98q4) -0.048 0.086 (0.77)

 Wald Test:
 [sigma] [sigma] [delta][(i/y).sub.t-j]
Country [delta][(s/y).sub.t-j) = 0

United States -0.593 7.160 (0.01)
(59q2-99q1) -0.359 2.019 (0.15)
United Kingdom 0.076 0.076 (0.72)
(70q2-99q1) -0.122 0.638 (0.42)
Canada 0.009 0.002 (0.97)
(61q2-99q1) -0.145 0.763 (0.38)
France -0.167 0.471 (0.49)
(70q2-98q3) -0.299 1.442 (0.23)
Japan -1.605 86.398 (0.00)
(59q2-98q4) -0.428 26.279 (0.00)

Notes: In addition to a deficit rate and trend term, each equation
contains four lags of the differenced saving and investment rates. The
[epsilon]s[i.sub.t-j]'s were computed from the results presented in
Table 2. P-values are in parentheses.