Theory-based measurement of the saving-investment correlation with an application to Norway.

Jansen, W. Jos ; Schulze, Gunther G.

I. INTRODUCTION

The findings of Feldstein and Horioka [19c,0] have led to numerous theoretical and empirical papers on the close correlation between domestic saving and domestic investment and its supposed implications for international capital mobility. Feldstein and Horioka [1980, 317] state that "with perfect world capital mobility, there should be no relation between domestic saving and domestic investment: saving in each country responds to the worldwide opportunities for investment while investment in that country is financed by the worldwide pool of capital." However, in a cross-country regression using period-averaged saving and investment figures for sixteen OECD countries, they obtain a significant coefficient close to unity and conclude that capital is rather immobile. This result constitutes the "Feldstein-Horicka puzzle," as it contradicts the widely held perception that capital is highly mobile across countries. Subsequent empirical work confirmed the close correlation, though its implication for the degree of capital mobility is a moot point (see Tesar [1991]).

This paper contributes to the understanding of the puzzle on both theoretical and empirical counts. First, we present a theory-based econometric specification for estimating saving investment correlations. Second, we discuss the possible usefulness of the estimates for detecting capital mobility. Third, we provide empirical results for the interesting case of Norway. We argue that Feldstein and Horioka's basic idea that the saving-investment correlation contains information about international capital mobility is correct, but that the interpretation of the estimated correlation value must be altered substantially in view of the results derived from modern macroeconomic models.

Our research is motivated by the observation that various regression equations have been used to measure the saving-investment correlation, but that none of them has a firm theoretical foundation. This in turn raises questions about the interpretation and comparability of the existing empirical results. We propose an econometric specification that is founded in intertemporal general equilibrium models, in which agents optimize under intertemporal budget constraints. We show that time-series studies have estimated misspecified equations and that cross-section studies are seriously flawed because they neglect dynamics. As a result the puzzle may turn out to be an artifact caused by measurement errors. However, the significance of reliable measurement of saving-investment correlations goes beyond solving the "Feldstein-Horioka puzzle," because they represent stylized facts open economy models should explain.

Norway serves as a suitable example to cement our methodological arguments with empirical evidence, thanks to its system of capital controls, which were phased out during the 1970s and 1980s, the oil discoveries and its small size. We demonstrate that the failure to take structural breaks into account seriously distorts the picture, making a strong case for careful diagnostic testing. Our main empirical result is that the "Feldstein-Horioka puzzle" does not exist for Norway.

The paper proceeds as follows. In section II we briefly summarize the state of the discussion regarding Feldstein and Horioka's findings. In section III we derive our specification from the theory, compare it to the previous specifications, and discuss how to make inferences about capital mobility. In section IV we sketch major developments in the post-war Norwegian economy, notably the abolition of capital controls and the emergence of the important oil sector. Section V presents the empirical results. Section VI summarizes and concludes.

II. THE FELDSTEIN-HORIOKA PUZZLE

Many authors have confirmed Feldstein and Horioka's result of a high and stable correlation of saving and investment for OECD countries, both in cross-country studies and in time-series studies. This finding can be regarded as a robust empirical regularity.(1) But does it really indicate low capital mobility, especially since the correlations remain relatively stable despite major deregulations of financial markets around 1974, for instance in the U.S., in Germany, and in the U.K.?

Several critiques of Feldstein and Horioka's interpretation have emerged that try to answer this question. The point most frequently raised is the endogeneity of saving, implying that third factors can produce a substantial correlation of saving (S) and investment (I) in the presence of full capital mobility.(2) This endogeneity problem can be tackled by averaging over longer periods to wash out business cycles, as Feldstein and Horioka [1980], Feldstein [1983], Tesar [1991] and others have done, or by adding the respective variable to the regression (Summers [1988], Feldstein and Bacchetta [1991]), or by using instrument variables, as done by Feldstein and Horioka [1980], Frankel [1986; 1991], and Dooley et al. [1987]. Yet, none of these procedures alters the results considerably.

A special form of endogeneity may arise from a government's reaction to incipient current account imbalances; especially variations in public saving may be used to offset fluctuations of private saving (inter alia Fieleke [1982], Tobin [1983], Westphal [1983], Summers [1988], and Bayoumi [1990]). However, an identification problem arises: the observed negative relationship between budget deficits and the private saving-total investment gap can be attributed to either endogenous government reactions with capital being highly mobile (Summers [1988]), or to a crowding-out effect of private investment by public borrowing, presupposing less than perfect capital mobility (Feldstein and Bacchetta [1991]).

Murphy [1984] and others argue that for large countries, an exogenous increase in domestic saving will feed back to an increase in investment demand via a lowered world interest rate. Moreover, larger countries tend to be more self-contained, and regional shocks may cancel out to a greater extent (Harberger [1980], Tobin [1983]). Yet, Frankel [1986] shows for the U.S. that the large country effect is far from being responsible for the high correlation.

Frankel [1986] and Dooley et al. [1987] have pointed out that for a saving-investment correlation close to zero, real interest rate parity must hold, a condition which is frequently violated (e.g. Cumby and Obstfeld [1984], Mishkin [1984; 1988]). The reason for this is the insufficient integration of goods markets, leading to non-zero currency premia; the ex ante purchasing power parities especially do not hold. However, inasmuch as real interest rates move in tandem (Cumby and Mishkin [1986]), only the smaller variations of the real interest rate differentials matter, not the differentials as such.(3)

Though these papers shed light on possible sources of positive saving-investment correlations in the presence of full capital mobility, the basic questions wait to be answered. This remains true even though the correlation based on annual data has been found to be considerably lower and variable (Sine [1992]).

III. MEASURING THE CORRELATION OF SAVING AND INVESTMENT: METHODOLOGICAL ISSUES

The regression of saving on investment looks into an unusual relation, because the regression equation cannot directly be derived from a theoretical model. It can neither be viewed as a structural relationship (it is not a behavioral relation in a model) nor as a reduced-form relation (it is not the solution of a system). Though there is no obvious candidate specification, surprisingly little attention has been devoted to the issue of specification. Instead, various econometric equations have been used to measure the supposedly same phenomenon without a systematic evaluation of their relative merits. The empirical literature provides correlations between the levels of saving and investment, between changes of saving and investment, and between the levels of saving and investment averaged over varying time-spans.

As will be demonstrated below, closer inspection of modern macroeconomic theory shows that the specifications used so far are incompatible with key theoretical insights. This incompatibility between theory and empirical practice has two consequences, which potentially invalidate the conclusions drawn from the existing empirical work. First, empirical estimates are probably biased due to misspecification. Second, it is not exactly clear what we can infer from estimates which come from different specifications, because we lack a theoretical guideline telling us how to interpret and to compare them (see also Genberg and Swoboda [1992]). For instance, are studies using period-averaged data in a cross-section as valuable for detecting capital mobility as studies using time-series data? Without a theory it is hard to tell. We believe that the confusion about the merits of the saving-investment correlation can be at least partly traced back to the mismatch of recent theoretical contributions and prevailing methods of measurement.

In this section we put forward a specification that is built upon modern macroeconomic theory and that is broad enough to cover opposing viewpoints concerning the factors producing the saving-investment correlation. We then survey the econometric specifications used in the literature and show that they are special cases of our specification. Finally, we address the issue of what we can infer from the correlation about the degree of capital mobility.

Specification of the Regression Equation

Our theoretical frame of reference consists of the open-economy variants of the modern macroeconomic theory, as expounded in Blanchard and Fischer [1989]. In both the infinitely lived representative agent models and the overlapping generations models, agents maximize (expected) life-time utility subject to an intertemporal budget constraint. Capital is assumed to be completely mobile, and hence agents can use the international capital market for smoothing their consumption.

We consider intertemporal general equilibrium models with steady states in which the current account, when suitably scaled (e.g. by output), is constant. Accordingly, saving and investment have a one-to-one relationship in the steady state. An example is the equality of saving and investment, implying that sustained current account deficits or surpluses are ruled out. In the short run, however, shocks to the system may push the economy out of the steady state and cause saving and investment to temporarily diverge from their steady-state values. These models are able to produce non-zero short-run saving-investment correlations despite perfect capital mobility. Examples are Buiter [1981], Persson and Svensson [1985], Obstfeld [1986], Matsuyama [1987], Finn [1990], Leachman [1991] and Koch [1992]. Both the sign and size of this endogenously produced saving-investment correlation depend on the nature and the size of the shock and the structure of the economy. The same holds true for the level of saving and investment in the new steady state.

The characteristics sketched above have important implications for the econometric specification. First, since the steady-state value of investment and saving depends on exogenous variables, which may be non-stationary, they may be non-stationary variables too. Second, the theory implies that saving and investment have a one-to-one relation in the steady state, regardless of their value. In other words, saving and investment are co-integrated variables. Engle and Granger [1987] prove that variables which exhibit these two properties have an error correction representation. Stationary variables can also be described by an error correction model. Consequently, the saving investment regression should be specified as an error correction model.

The simplest member of this class of specifications, which already serves our purpose, is

(1) [delta][IR.sub.t] = [alpha] + [beta][delta][SR.sub.t] + [gamma]([SR.sub.t-1]) - [IR.sub.t-1] +[delta][SR.sub.t-1] + [[epsilon].sub.t] where IR and SR denote the share in output of investment and saving, respectively, and [epsilon] is a well-behaved disturbance. The analytically relevant saving-investment correlation is the short-run correlation, defined between the changes of saving and investment, as measured by the parameter [beta]. This parameter is the empirical counterpart of the short-run reaction of saving and investment to shocks in theoretical models. The long-run relation between saving and investment can be derived as the steady-state solution:

(2) [alpha] + [gamma]([bar]SR - [bar]IR) + [delta] [bar]SR = 0.

If [delta]=0, the current account ([bar]SR - [bar]IR) equals some constant in the long run, while if [alpha] = [delta] = 0 it is zero. In both cases there exists a one-to-one long-run relation, as theory implies. Note that a one-to-one relation between SR and IR in the long run is perfectly compatible with full capital mobility. Testing parameter restrictions enables us to discern whether the steady-state relations suggested by modern open macroeconomic models are consistent with the data.(4) An affirmative finding would lend support to our claim that an error correction model reliably measures the saving-investment correlation.

Our theoretical frame of reference is broad enough to encompass (in principle) all explanations for zero and non-zero saving-investment correlations, including limited capital mobility, endogenous government behavior and real interest rate differentials. All explanations are consistent with the idea that in the long run the current account is constant and that saving investment dynamics are temporary phenomena. For example, Dooley et al. [1987] and Frankel [1991; 1992] assert that imperfectly integrated goods markets lie at the root of the positive saving-investment correlation. Sluggish price adjustment creates the temporary real interest rate differentials, that are the driving force behind saving-investment dynamics. The real interest rate differentials decline in the course of time, and the long-run equilibrium of a balanced or constant non-zero current account is eventually reached (Modjtahedi [1988], cf. fn. 7). Consequently, an error correction model should be used for measuring the saving-investment correlation, regardless of the prior beliefs about the interpretation of this correlation.

Some of the explanations for non-zero saving-investment correlations have already been incorporated in the intertemporal general equilibrium framework. Bacchetta [1992] introduces capital controls and a regulated domestic financial sector into an open economy model a la Matsuyama [1987] and investigates the consequences of liberalization and deregulation. The stochastic overlapping generations two-country model (one small, one large country) in Finn [1990] generates, in spite of perfect capital mobility, differences in expected real rates of return.

When modelling saving-investment dynamics, care should be taken to detect structural breaks. It is a distinct possibility that different error correction models have governed the observed time series of saving and investment. Examples of events that may have caused structural breaks include the change in exchange rate regime (increase in exchange rate variability leading to real interest rate differentials; McKinnon [1987], Frankel and MacArthur [1988]), reduction in capital controls and deregulation of domestic financial systems, large changes in the price of oil, sectoral shifts and increased openness of economies. These considerations demonstrate the crucial importance of diagnostic testing in order to detect structural breaks. Yet, the empirical literature devotes little attention to diagnostic testing.(5)

Review of Previous Specifications

Empirical work on the saving-investment correlation has employed cross-section regressions as well as time-series regressions. The cross-section studies use the saving and investment rates for each country as observations, either for a particular year (Tesar [1991], Sinn [1992]) or averaged over some multi-year period (Feldstein and Horioka [1980] and other studies). Their regression equations are misspecified because they invariably concern a static relationship between saving and investment, instead of an error correction model, suggested by intertemporal general equilibrium models.(6) Moreover, the common practice of using period-averaged data makes the estimated saving-investment correlation unfit for assessing the degree of capital mobility on theoretical grounds. Sinn [1992] raises this point, arguing that the intertemporal budget constraint implies that saving and investment are approximately equal when averaged over long periods of time. His empirical analysis shows that averaging over decades creates an upward bias in the estimated saving-investment correlation.(7)

The time-series studies estimate the saving-investment correlation per country on the basis of time series, employing four different specifications. Frankel [1986; 1991] estimates the static equation

(3) [IR.sub.t] = [[theta].sub.0] + [[theta].sub.1][SR.sub.t] + [[epsilon].sub.t].

Because this specification ignores the dynamic adjustment process, it cannot adequately capture saving-investment dynamics. Feldstein [1983], Feldstein and Bacchetta [1991], and Bayoumi [1990] estimate the saving-investment relation in first differences:

(4) [Mathematical Expression Omitted]

Although eq. (4) measures a short-run correlation, it has no static equilibrium solution in the sense that nothing is implied regarding the relation of the levels of saving and investment in the steady state. The reason for Bayoumi [1990] to difference the time series was to make them stationary. However, eq. (4) is only correctly specified if there is indeed no long-run (cointegrating) relationship between saving and investment (Engle and Granger [1987]). Since theory maintains the opposite, eq. (4) is misspecified--it is overdifferenced.

Feldstein and Bacchetta [1991] introduce a lagged adjustment of investment to changes in saving and posit that investment reacts to the gap between investment and saving in the previous period:

(5) [delta][IR.sub.t] = [[psi].sub.0] + [[psi].sub.1]([SR.sub.t-1] - [IR.sub.t-1]) + [[epsilon].sub.t]

This specification restricts the short-run correlation between [IR.sub.t] and [SR.sub.t] to be zero and thus imposes limitations on the dynamic structure. Since it seems rather dubious that the data justify this restriction, eq. (5) is also misspecified.

Summarizing, specifications (3)-(5) are all found wanting, and estimating them may result in unwarranted inferences. Note that eqs. (3) to (5) are contained in our error correction model, eq. (1), as special cases enabling us to test the validity of the parameter restrictions in section V.(8) Our theoretical framework also gives us clues as to what the parameter restrictions entail. The static equation (3) and the equation in differences (4), which is essentially static, are both compatible with theories which do not look on saving and investment as solutions of an intertemporal decision problem.

Recently cointegration techniques have been employed for the time-series saving-investment regressions. Examples are Miller [1988], Leachman [1991], Vikoren [1994] and De Haan and Siermann [1994]. With the exception of Vikoren [1994], they all use the conventional Engle-Granger [1987] two-step procedure. In the first step the static regression (3) is run, and its residuals are then tested on stationarity in order to detect cointegration. Leachman [1991] found that for none of the twenty-three OECD countries were saving and investment cointegrated, and consequently that the difference equation (4) could be used to estimate the short-run saving-investment correlation. De Haan and Siermann [1994] challenge this result because of the low power of the cointegration test due to the short time series used (only twenty-five years). Using longer time series for ten countries they detect cointegration for several countries.

To our knowledge Vikeren [1994] is the first to apply an error correction model, discarding eqs. (4) and (5) as incompletely specified regression models. Using the model in Sachs [1981], he argues that the saving-investment regression should distinguish between the long-run correlation, which reflects the intertemporal budget constraint, and the short-run correlation, which could serve as an indicator of capital mobility. However, his theoretical model describes an economy which exists for two periods, in which only one investment and one saving decision are made. In the second period, investment is always zero and all income and wealth is consumed. This framework therefore precludes any interesting saving-investment dynamics. It takes a long- or infinitely lived economy to make a meaningful distinction between the short run and the long run. For this reason, Vikoren's theoretical results for the short-run and longhorn correlation are based on fallacious arguments, although the intuition behind them originates in general equilibrium models.

The error correction model approach integrates the two steps of the Engle-Granger procedure. Both long-run and short-run dynamics are simultaneously estimated. Testing whether [gamma] = 0 is equivalent to testing for cointegration. Moreover, Kremers, Ericsson and Dolado [1992] show that this cointegration test has considerably more power than the conventional one.

What Does the Saving-Investment Correlation Say about Capital Mobility?

Before turning to the empirical part of this paper, we address the crucial question whether the saving-investment correlation contains information about capital mobility and if so, in what sense. Feldstein and Horioka [1980] stated that full capital mobility implied a zero correlation whereas high positive correlations pointed to limited capital mobility. We argue that Feldstein and Horioka's basic idea that the saving-investment correlation contains information about international capital mobility is correct, but that the interpretation of the estimated correlation value must be altered substantially in view of the results derived from modern macroeconomic models.

Severely limited international capital mobility inevitably pins down the saving-investment correlation at a high positive value, regardless of the size and nature of the shocks the economy is exposed to. Note that this is a sufficient, but not a necessary condition for high positive correlations. As has been pointed out repeatedly in the literature, high positive correlations can also be generated in the presence of full capital mobility. Consequently, we cannot ascertain which phenomenon a high correlation signifies without additional information: low capital mobility or a correlation due to shocks, imperfectly integrated good markets, or the like under significant capital mobility. Relevant prior information comprises inter alia return differentials, direct measures of foreign exchange regulations, and structural breaks. On the other hand, small positive, zero, and negative correlations can only be generated if capital is sufficiently mobile. This implies that whenever we establish values of the saving-investment correlation to be in this range, we can unambiguously conclude that there is significant capital mobility.

The arguments above make clear that the correlation alone cannot be used to make inferences about the degree of capital mobility. For example, a correlation of 0.3 does not necessarily represent a lesser degree of capital mobility than a value of 0.1, since these values can (but need not) be produced under the same degree of (significant) capital mobility, reflecting different impacts of other factors. By the same token, it is not possible to associate a particular value of the correlation like Feldstein and Horioka's zero, or a range of values, with perfect capital mobility. Feldstein [1983,130] claimed that, strictly interpreted, the Feldstein-Horioka test was on "the extreme hypothesis of perfect capital mobility," whereas we argue that such a test is not possible: at best we can reach the qualitative result that significant capital mobility prevails. Without additional information, the saving-investment correlation can only be used to reject the hypothesis of capital immobility.(9)

When the saving-investment correlation is high, meaningful conjectures about capital mobility can be derived only by consulting further sources of information. For instance, zero return differentials and the absence of institutional rigidities point to substantial capital mobility. Strict capital controls lead to the reasonable suspicion of restricted capital mobility; still we do not know to what extent the low capital mobility is responsible for the high correlation. However, if a reliable time profile of factors influencing the correlation, in this case capital controls, is available and the saving-investment correlation reacts systematically and consistently to the varying restrictiveness of the regulations, we can conclude that the difference in the correlation value is caused by a different degree of interference in the free flow of capital. Only in this case can a difference in the estimated saving-investment value be said to reflect a difference in capital mobility.

IV. CAPITAL CONTROLS AND OIL DISCOVERIES--IMPORTANT NORWEGIAN PECULIARITIES

Norway offers several advantages for an empirical study. First, since it is a small country, the feedback effects of variations in domestic saving or investment via altered world market conditions can be neglected. Second, the Norwegian capital controls system, which varied in the degree of tightness, allows us to directly measure the effect of government behavior on capital mobility. Since the saving-investment correlation constitutes only an indirect measure of capital mobility, we can discern whether these two measures generate matching results.

By 1954, the beginning of our sample period, Norway had eliminated virtually all restrictions on current account transactions, while capital account transactions remained strictly regulated. Transborder portfolio investment was de facto prohibited, borrowing abroad required restrictively granted licenses and inward direct investment was made subject to concessions tied to certain conditions. The minor amount of outward direct investment was treated liberally. Narrow ceilings for banks' net foreign position were stipulated and nonresidents were restricted from holding Kroner accounts, just as residents were restricted from holding foreign exchange accounts. The shipping sector (including shipbuilding) and, later, the oil sector were exempted from exchange regulations and denied access to the domestic credit market due to their large and fluctuating finance requirements.

It is impossible to describe accurately the actual restrictiveness of the regulations, because it depends on the varying use of the authorities' discretionary scope, on which no systematic information is available. Typically, the lifting of a restriction was preceded by a more liberal handling of this restriction. The first noteworthy liberalization including a formal change in the regulations took place in June 1973, when the prohibition on buying Norwegian stocks was eased. The fall of 1978 marks the second important step: banks had to balance only their combined (spot and forward) foreign exchange position instead of meeting strict limits separately on both positions.

It followed a period of gradual and cautious liberalization, especially with regard to inward portfolio investment (fall 1979, spring 1982), but outward portfolio investment and bank regulations were also eased. A major liberalization package took effect in June 1984, affecting all sorts of transactions. Controls were tightened somewhat in 1985/86, but gradually dismantled thereafter. They were phased out by 1 July 1990. Regulations on the domestic credit market were dismantled more quickly than foreign exchange regulations. The official stipulation of almost all interest rates was discontinued in December 1977, but reintroduced for two years in September 1978, when a general wage and price freeze included all lending rates.

Third, the emergence of the oil sector has a substantial impact on our analysis since it marks an important structural break. The first oil field (Ekofisk) was discovered in December 1969; because of high production costs oil field development became profitable on a large scale only after the first oil price shock of 1973-74 when prices quadrupled. The build-up of oil and gas production facilities was financed to a large extent by foreign capital resulting in record net capital imports. The oil bonanza spilt over to the mainland economy and caused the whole economy to boom. The rising importance of the oil sector is demonstrated by Figure 1, which plots the oil sector's share of gross investment and its share in GDP. All data were taken from OECD, National Accounts, as described in appendix A.

Lastly, the shipping and shipbuilding sector was extremely outward oriented. Shipping contributed around 10 percent to GDP until 1968, when its share started to decline considerably. During 1983 to 1986 a dramatic flagging out took place for tax reasons until the International Shipping Register was established in 1987, which reversed the trend.(10)

V. EMPIRICAL RESULTS

We estimate our error correction model (1) on annual data for Norway over the period 1954-89. Domestic investment is defined as the private sector's and government sector's net investment including the change in stocks; saving is the sum of private and government net saving. Both saving and investment are converted into rates by dividing them by net disposable income.(11) (10.) For further reference on capital controls see Norges Bank [1989] and Schulze [1992], for further reference on the economic development see Hodne [1983] and Galenson [1986].

Our main data source is the OECD National Accounts; for details see appendix A. Estimation of eq. (1) is done by OLS, after testing for the exogeneity of [delta]SR, the change in saving, by means of a Hausman [1978] test; see appendix B. The test indicates that ASR can be treated as an exogenous variable, so we refrain from using instrumental variables methods.

The estimation results shown in the first column of Table I (eq. (1)) reproduce the results in Vikoren [1994] despite minor differences in sample period, specification and estimation method.(12) The estimate for the short-run coefficient is not significantly different from zero at any reasonable significance level. Furthermore, the hypothesis that [alpha] = [delta] = 0, or saving equals investment in the long run, could not be rejected (F(2,33) statistic yields 0.54). All diagnostic tests are passed.

TABLE I
Saving-Investment Relations, Equations (1) and (6)
 eq. (1) eq. (6)

constant 0.001 0.010
 (0.02) (0.33)
[delta][SR.sub.t] -0.025
 (0.13)
[D.sub.(54-73)][delta][SR.sub.t] 0.655
 (2.02)
[D.sub.(74-78)][delta][SR.sub.t] -1.257
 (2.75)
[D.sub.(79-89)][delta][SR.sub.t] 0.012
 (0.06)
[SR.sub.t-1] - [IR.sub.t-1] 0.281 0.401
 (2.19) (3.30)+
[SR.sub.t-1] 0.029 -0.030
 (0.14) (0.17)
[sigma] 0.027 0.024
[R.sup.2] 0.174 0.372
DW 1.947 1.963
BG(1) 0.051 0.058
BG(2) 1.637 1.888
ARCH(1) 0.041 0.517
JB 0.555 1.327

H([delta][SR.sub.t]) 0.721 1.735

Sample period: 1954-89. Explanation of diagnostic
statistics and data sources: see appendix.
t-statistics in parentheses.

The zero estimate of the short-run coefficient indicates significant capital mobility. This is a striking result as it amounts to an "inverted" Feldstein-Horioka puzzle: we estimate a zero coefficient, while expecting a highly positive one due to severe capital controls that were in place during the greater part of the sample period. Our finding that saving equals investment in the long run accords with our theoretical framework, thereby providing supportive evidence for our approach.

Next, we look into possible structural breaks. To facilitate their detection, Figure 2 plots the time series for the saving and investment rate. During the sixties they moved closely together, but the behavior of both variables changed dramatically in the early seventies, when investment jumped to an all time high and saving plummeted to an all time low. The opposite movements can be attributed to the combined effect of discoveries of large oil and gas deposits and the sharp rise in the oil price in 1973, which made the exploitation of the oil fields on a large scale profitable.(13) Intertemporal consumption smoothing in response to an unanticipated wealth increase can explain the observed saving pattern. Consumption went up in anticipation of revenues from a new source of income. Since measured actual income lagged behind (see Figure 1), the observed saving rate was temporarily driven down. In the course of time, the expected income rise materialized and the saving rate returned to normal. The temporarily increased investment rate can be explained by the huge investments needed to build up the oil sector and by the attendant spill-over effects of the oil investments on the mainland sector. Together with the increased consumption demand, this added up to a buoyant investment climate.

Judging by the graph, investment and saving were positively correlated until the oil boom and negatively correlated for the period 1974-78, while thereafter there is no clear correlation. So it could well be that the zero correlation we have found masks structural shifts in the parameters. We have investigated this possibility by reestimating eq. (1) allowing the parameters to vary. We specified three regimes: 1954-73, 1974-78 and 1979-89.(14) The second column of Table I reports the estimates of the error correction model with time-variable short-run coefficients,

(6) [delta][IR.sub.t] = [alpha] + ([[beta].sub.1][D.sub.1] + [[beta].sub.2][D.sub.2] + [[beta].sub.3][D.sub.3])[delta][Sr.sub.t] + [gamma]([Sr.sub.t-1] - [IR.sub.t-1]) + [delta][Sr.sub.t-1] + [[epsilon].sub.t]

where [D.sub.i] (i = 1,2,3) denote dummies that are one during subperiod i, and zero otherwise.(15) The hypothesis that the short-run coefficient is constant is rejected at the 1 percent level (F(2,30) is 6.05) and, again, we cannot reject the hypothesis that saving equals investment in the long run (F(2,30) is 0.62). The fit is much better now and the diagnostic statistics do not indicate any trouble. We checked the stability of eq. (6) by testing for structural breaks in the first and third subperiod. We specifically looked for whether the short-run coefficient changed after 1984, when a major liberalization package concerning foreign exchange regulations took effect, or after 1986, when the oil price collapsed. In all cases we are unable to reject our empirical model at the 5 percent significance level.(16)

The estimates show that the short-run correlation is 0.7 from the fifties to the early seventies, when indeed rather strict capital controls were in place. It is negative during Norway's structural adjustment to the oil discoveries, and zero after 1978. Accordingly, the Feldstein-Horioka criterion as set out in section III diagnoses significant capital mobility for the period after 1973. There exists corroborating evidence for this result. As argued in Jansen and Schulze [1994], the Norwegian money market was basically well-integrated in the world market during the 1980s. They also failed to find any statistically significant influences of the--declining--controls on stock return differentials in the 1980s, although this may be due to the low power of the tests. Moreover, the exchange controls were gradually being dismantled, while the shipping and the growing oil sector had free access to the world capital market to finance their huge and fluctuating investments. The freedom of the large oil sector to import capital effectively amounts to a lowering of capital controls for the nation as a whole.

Our finding of significant capital mobility does not imply that the restrictions on cross-border portfolio investment were necessarily ineffective, because the saving-investment correlation relates to net total capital flows and not to net flows of a particular asset. We have merely established the existence of enough open channels between Norway and the world capital market to allow Norway to smooth its aggregate expenditure. Since the time pattern of the short-run correlation is consistent with other information on capital mobility, like asset return differentials and the historical evolution of the regulations, we conclude that the "Feldstein-Horioka puzzle" does not exist for Norway.

We next assess the empirical relevance of our criticism of other specifications, which is based on theoretical notions. Since our error correction model (1) encompasses the static equation (3), the equation in differences (4) and the partial adjustment equation (5) we are able to test these alternatives against our model. Each of the alternatives implies two restrictions on the error correction model specification (see footnote 8). Since we have found structural breaks, we use period-dependent parameters, and hence the error correction model counts twelve parameters and the number of restrictions is six in each case. Table II presents the F-statistics.

TABLE II
Test of Alternative Specifications against the Error
Correction Model

static, eq. (3) 2.86
difference, eq. (4) 5.47
partial adjustment, eq. (5) 2.94
critical [F.sub.0.05] (6,24) 2.51

The three alternative regression equations are all rejected in favor of the error correction model. The results for eq. (4) reveal that neglecting the long-run equilibrium is particularly harmful. This outcome provides additional evidence that an error correction model is the most suitable equation for measuring the saving-investment correlation.

Since the emergence of the oil sector marks a structural break, it could be that the low estimate of the aggregate saving-investment correlation chiefly reflects the large and volatile flows of foreign capital into and out of the oil sector. According to this interpretation the non-oil economy is still rather insulated. As a check on the robustness of our results we have therefore estimated a separate saving-investment relation for the non-oil economy. This is not a straightforward affair, because data on saving disaggregated by industry are not available (data on investment are). We surmounted the data availability problem by estimating a system of two saving-investment relations (for the oil and non-oil sectors) jointly with an equation for the oil sector's retained profits. Retained profits were the only domestic funds available to the oil sector as it was not allowed to borrow in the domestic market. The remainder of domestic saving is at the disposal of the non-oil sector. Retained profits are assumed to depend on operating surplus and oil price (lagged one period). Estimation of the system outlined above yields estimates for the non-oil sector which resemble those in Table I. The short-run saving-investment correlation is 0.70 prior to 1974, -0.87 during the oil boom, and 0.04 thereafter.(17)

VI. CONCLUSION

The correlation between saving and investment is at the core of modern macroeconomics since it represents an important stylized fact which the theory has to explain. Reliable measurement of the correlation requires an econometric specification with a sound theoretical foundation in order to avoid biased results and to allow meaningful interpretations.

Only error correction models meet this requirement because up-to-date intertemporal general equilibrium models imply a cointegrating relation between saving and investment. In the most obvious and most frequently analyzed case, saving equals investment in the steady state and deviations from this equality (current account imbalances) are temporary phenomena. The specifications used up until now are seriously flawed because they ignore either the dynamics or the steady-state relation between saving and investment. Drawing on Feldstein and Horioka [1980], we argue that the possibility of deriving inferences about capital mobility from the saving-investment correlation is asymmetric. While low or negative correlations presuppose significant capital mobility, high correlations can be produced under both low and high capital mobility. Without additional information it is impossible to identify which state prevails in the latter case.

Applying the error correction model to Norwegian annual data for 1954-89 underpins our methodological arguments. The long-run relation between saving and investment is consistent with the steady-state equality and the error correction model also outperforms previous specifications empirically. Moreover, we demonstrate the need for careful testing for structural breaks. While regressing over the whole sample period would have created an "inverted Feldstein-Horioka puzzle" (zero short-run correlation despite strict capital controls during the larger part of the sample), we detect that the oil boom breaks the sample period into three regimes, for which the short-run correlation accords with the history of Norwegian capital controls. The correlation is positive and high in the times of tight controls prior to the oil boom, negative during the oil boom of 1974-78, when Norway adjusted to the unanticipated increase in wealth and investment demand, and zero thereafter, when controls were gradually dismantled. This time pattern holds even if we control for the influence of the oil sector, which was not affected by capital controls. The "Feldstein-Horioka puzzle" does not hold for Norway: capital has been shown to be mobile from 1974 onwards and we find a remarkable coincidence between the tightness of capital controls and the value of the saving-investment correlation.

As for future research, a panel design seems to be the most suitable econometric framework to estimate the saving-investment correlation since it allows for the incorporation of both dynamics and cross-country parameter restrictions. An additional advantage of the panel design lies in the more efficient estimation, thanks to the exploitation of the contemporaneous correlation of the disturbances reflecting common shocks. Stylized facts, like structural breaks and similarities in saving-investment dynamics across (subsets of) countries, can easily be established by testing parameter restrictions. Note that the panel design is a generalization of the design used by Feldstein and Horioka, who impose the restriction that the saving investment correlation is equal both across countries and over time.

In the end we may find that the result found for Norway carries over to other countries so that the "Feldstein-Horioka puzzle" would cease to exist, or be confined to a group of countries. This outcome is not necessary, but even if Norway turns out to be an exception and the puzzle is confirmed in general, it will have been given a much firmer statistical foundation than it currently enjoys.

APPENDIX

A. Data Sources

The main source of the data is the OECD National Accounts, Volume 11, published annually by the OECD. Table 1 (Main aggregates) contains all the data needed to compute the investment and saving rate as defined in the main text.

Gross investment for the oil sector is taken from table 3, line 7, (Gross fixed capital formation by kind of activity) and depreciation and operating surplus are taken from table 13, line 7, (Cost components of value added by kind of activity). Comparable data for the shipping sector were made available by the Central Bureau of Statistics in Oslo. Total operating surplus is taken from table 1. The price of oil is taken from International Financial Statistics, published by the International Monetary Fund, table Commodity prices, line 456.

Concerning the instruments used in the Hausman exogeneity test, defense spending is taken from OECD National Accounts, table 5 (Total government outlays by function and type), direct taxes from table 6 (Accounts for general government) and wage income from table 1. The dependency ratio is defined as the ratio between the number of people aged less than fifteen or more than sixty-five years old and the number of people aged fifteen to sixty-five years old. Data are taken from the Labour Force Statistics, published by the OECD, table 1. All instruments (except the demographic variable) are expressed as shares of net disposable income.

B. Explanation of the Test Statistics in the Tables

The variable [sigma] is the standard error of the regression, [R.sup.2] the coefficient of multiple correlation adjusted for degrees of freedom, and DW the Durbin-Watson statistic. BG(1) and BG(2) are Breusch-Godfrey statistics, testing for first- and second-order autocorrelation in the residuals, respectively. Their distribution under the null hypothesis of zero autocorrelation is [chi square] (1) and [chi square] (2), respectively. ARCH(1) tests for first-order autoregressive conditional heteroscedasticity, see Engle [1982]. Its distribution under the null hypothesis of homoscedasticity is [chi square](1) JB is the Jarque-Bera statistic testing for nonnormality of the residuals. Its distribution is [chi square](2) under the null hypothesis of normality.

H([delta][Sr.sub.t]) denotes the Hausman-test, which is conducted by regressing [delta][Sr.sub.t] on a set of instruments and using the residuals of that projection as an additional regressor in the original regression. In the case of exogeneity the projection residuals have no additional explanatory power. The test statistic is the t-value of the added variable's parameter estimate. As instruments we used one- and two-period lagged values of saving and investment, one-period lagged wage income and direct taxes, current defense spending, and the dependency ratio. The latter two instruments were also employed by Dooley et al. [1987] and Frankel [1991]. W. JOS JANSEN and GUNTHER G. SCHULZE, Tinbergen Institute, Erasmus University Rotterdam and University of Konstanz, currently at Stanford University. Financial Support of the German Research Foundation is greatly appreciated. Jansen wishes to thank Hanslurgen Vosgerau and the SFB 178 for their hospitality during his stay in Konstanz in 1992. We are very much indebted to Birger Vikoren and many of his colleagues from Norges Bank and the people from the Norwegian Central Bureau of Statistics for providing data and information. We thank Max Albert, Peter Broer, Angelika Eymann, Karl-Josef Koch, Gerd Ronning Otto Swank, two anonymous referees and Birger Vikoren for helpful and inspiring discussions.

(1.) Cf. inter alia Fieleke [1982], Feldstein [1983], Penati and Dooley [1984], Summers [1988], Dooley et al. [1987], Bayoumi [1990], Artis and Bayoumi [1991], Feldstein and Bacchetta [1991], and Tesar [1991] for cross-country analyses and Frankel [1986], Obstfeld [1986; 1989], Bayoumi [1990], and Tesar [1991] for timeseries studies. An exception is Frankel [1991], who obtains low coefficients for the U.S. in the eighties due to the large current account deficits ("Reaganomics"). Murphy [1984], Obstfeld [1986], Dooley et al. [1987], and Wong [1990] analyze correlations for smaller industrialized or developing countries, which are found to be lower on average. (2.) Among the factors mentioned are the procyclicality of saving and investment, population growth (Summers [1988], Obstfeld [1986]), productivity and other shocks (e.g. Obstfeld [1986, 74-82]), and non-traded goods (Murphy [1986], Wong [1990]). (3.) Dooley et al. [1987, 506, eq. (3)] show that, for the saving-investment correlation to be zero, it is necessary that the covariance between the real interest rate differential and the saving rate is zero. This condition, however, is satisfied, not only if the real interest rate differentials are zero, but also if they are constant. Modjtahedi [1988] finds that the differentials converge to a constant value after six months, which can be explained by stable tax differentials. (4.) The requirement that dynamic equations be consistent with the long-run equilibrium originates from Davidson, Hendry, Srba and Yeo [1978], who introduced the influential error correction model. Note that the exact lag structure of the error correction model cannot directly be derived from a theoretical model, but has to be determined by the data. (5.) Feldstein [1983], Feldstein and Bacchetta [1991], and Leachman [1991] do not even report Durbin-Watson statistics. Bayoumi [1990] observes that satisfactory Durbin-Watson statistics were found for most regressions. Frankel [1986, 1991], estimating regressions in levels, finds low Durbin-Watson statistics. He proceeds by assuming first-order autocorrelated errors, but does not adjust his dynamic specification. Vikoren [1994] reports a full set of diagnostic statistics. (6.) The regression equation is eq. (3) in the main text, with time index t replaced by country index i. (7.) Sinn derives his result in a non-growth framework. The drift of his argument still holds when there is growth. The time-invariance of the intertemporal budget constraint also offers an explanation why the estimated correlation in the cross-section studies has decreased only slowly over time. (8.) The restrictions are: [beta] - [delta] = 1, [gamma] = 1 for (3), [delta] = [gamma] = 0 for (4), and [delta] = [beta] = 0 for (5). (9.) We cannot reject the hypothesis of capital mobility and we must not regard high correlations in itself "as evidence that there are substantial imperfections in the international capital market" (Feldstein [1983, 131]), because high correlations can have very different, complex causes, only one of which is low capital mobility. On the other hand, since we can only ascertain significant capital mobility, but not the degree of capital mobility, low correlations found for many less developed countries (Dooley et al. [1987]) do not necessarily contradict the notion that these countries are only imperfectly integrated in world capital markets. They do, however, refute the idea of capital immobility. (11.) Using gross investment and gross saving expressed as shares of GDP hardly affects the results. We have tested for the significance of up to two extra lags in our error correction model, which were however found highly insignificant.

We examined the time series properties of the saving rate and investment rate (SR and IR) by carrying out the Augmented Dickey-Fuller (ADF) test. Addition of the one-period lagged first difference of the variable in question sufficed to make the residuals of the ADF regression appear white noise. The ADF (1) statistic for IR was -3.07 (almost significant at the 10 percent level) and for SR it was -4.30 (significant at the 1 percent level). Critical values for our sample size were calculated on the basis of MacKinnon [1991]. In view of the low power of the ADF test in small samples, we conclude that the saving rate and the investment rate can be considered stationary in levels. This outcome concurs with Vikoren [1994], but Leachman [1991] found non-stationarity. We ascribe this difference to Leachman's shorter sample period (1960-84) compared to ours (195-89).

Although the use of shares is standard practice in empirical work, Ronning [1992] points out that this may render OLS inefficient. The transformation into shares confines the values of the time series to a specific interval and this may give rise to non-normal and heteroscedastic disturbances. However, our diagnostic tests always point to normality and homoscedasticity of the residuals and hence the use of OLS is warranted. (12.) Vikoren employs an error correction model similar to ours. However, he does not allow for structural breaks. This leads to incorrect inferences concerning the dynamic behavior of saving and investment. Moreover, he does neither test for the validity of alternative models, nor does he control for the influence of the oil sector. (13.) Dooley et al. (1987, footnote 7) mention the possibility of a negative saving-investment correlation in case of oil discoveries. However, they do not explain this phenomenon. (14.) We also investigated other subdivisions of the sample period. The division for which results are reported generates the highest likelihood. Note that the second subperiod coincides with the first investment boom in the oil sector (cf. section IV), thereby also providing intuition for this split-up. (15.) We report a constrained version because the 12 parameter specification is overfitted for the second subperiod (4 parameters for 5 observations). The 6 parameter restrictions that eq. (6) implies cannot be rejected at the 5% level as F(6,24) is 2.14. The hypothesis of no structural break is rejected at the 1% level: F(8,24) is 3.46. (16.) We reject a different regime in 1954-63 and 1964-73: F(4,20) = 0.95. Likewise, we reject different p35 between 1979-1984 and 1985-89 or 1979-86 and 1986-89: the F(1,29) statistics are 1.90 and 3.43, respectively. To assess the effect of the gradual dismantling of capital controls on p3, we applied the Wilton-Reid technique, which specifies the parameter as an n-degree polynomial of time. We chose n=3 to allow for an inflection point. Testing for the joint significance of the three additional parameters yields an F(3,27) statistic of only 0.95. See Wilton [1975] and Reid [1977] for a description of this method and Dooley and Isard [1980] for an application to the analysis of the effects of capital controls on interest rate differentials. (17.) Details on the estimated system and the results are in the working paper version of this article (Jensen and Schulze [1993]) which is available upon request. It also reports estimates of equations (1) and (6) for the non-oil sector under the extreme assumption that all oil sector investment was financed by foreign sources.

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