Domestic Determinants of Net U. S. Foreign Investment

George M. Von Furstenberg

doi:10.5089/9781451930504.024.A001

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Domestic Determinants of Net U. S. Foreign Investment

Author: Mr. George M. Von Furstenberg¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1980

eISBN:: 9781451930504

Language:: English

Keywords:: SP; price level; rate of inflation; investment rate; public investment; price inflation; exchange rate depreciation; Public investment spending; Inflation; Private investment; Public sector; Central America; South America; Africa; Asia and Pacific; Caribbean; Global; saving rate; cost of capital; rate disturbance; saving-investment identity; rate residual; Foreign direct investment; Domestic savings; Private savings; Potential output; Output gap

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If the United States attempted to save more, would it also invest more? If so, would the increase be largely in foreign investment or in domestic investment? This paper tries to explore what evidence can be brought to bear on these questions by exploring the links between particular components of saving and investment in an income determination framework.

Abstract

I. Conceptual Background

There is now almost universal agreement that ex ante increases in the national saving rate lead to ex post increases in the investment rate in the long run. As the adjustment is unlikely to be instantaneous, aggregate demand and output will decline in the short run if such shifts in saving occur. There are disagreements on the speed of transition from the Keynesian impact effects to the classical outcomes. It is unlikely that these disagreements can be resolved empirically for the United States, because fiscal policy has not been used in such a way as to produce large and sustained shifts in the national saving rate.

Even if policy and behavior functions have been stable over the post-Korean period, the values of some of the arguments in these functions have changed, as have the national saving and domestic investment rates. National saving and domestic investment both respond positively to a variety of factors, particularly those associated with cyclical changes. Hence, a positive time-series correlation between national saving and domestic investment is to be expected even in open economies. Other factors, such as real interest rates or the net user cost of capital, including compensation for risk, may have opposite effects on national saving and domestic investment. Although changes in the relevant input variables are extremely difficult to measure, they must be expected to produce changes in net foreign investment whether or not the level of output is affected in the short run, because national saving and domestic investment are affected differently. The same holds for explanatory variables that appear significant in one or more saving functions but not in the domestic investment functions or vice versa. If movements in these variables induce changes in sectoral saving rates that are not mutually offsetting because of substitution among the different components of saving, net foreign investment must change as well.

Before specifying a simultaneous-equation model in which some of the cyclical and noncylical linkages between the components of national saving and domestic investment can be investigated, it may be useful to explore some of the theoretical possibilities in the simplest terms defensible.

Chart 1 shows the national saving and domestic investment schedules of two countries plotted against the real interest and net cost of capital rate, r.^¹ Schedules of this kind can be used only to illustrate what might happen soon after one of the two countries has been shocked out of equilibrium. ^² It is assumed that this shock is an increase in saving in country A that may be due either to a behavioral shift or to a parameter change in arguments other than r in the saving function of that country. In period 0 the negative net foreign investment (net imports) of country A, equal to CD, is matched by the positive net foreign investment (net exports) of country B, equal to EF. If r is equalized worldwide because the international mobility of capital is perfect, r must fall until GH matches IJ. For country A the result is that, from period 0 to period 1, national saving increases by KL, domestic investment by MN, and net foreign investment, while still negative (GH), increases by KL – MN. The increase in saving is thus used partly for higher domestic investment and partly to raise foreign investment.

If the investment schedule, IA_0,1, in Chart 1 were steeper than shown, r would have to decline more and this would necessarily imply a greater increase in the net foreign investment of country A before the two countries could reattain balance. If financial capital were immobile internationally, so that r remained at r₀ in country B, the real interest rate applicable in country A would have to fall below r₁ until the excess of domestic investment over national saving was restored to its original level (CD). In that case, the increase in saving would be entirely matched by the rise in domestic investment in country A.

Empirically, estimates of the private rate of return to private capital have differed almost as much within countries as between countries. ^³ Hence, whether there is a strong tendency for these rates of return to be equilibrated between countries or whether there are quasi-permanent differences across countries remains a moot question. Martin Feldstein and Charles Horioka (1980) have argued that the obvious tendency for covered international interest rate parity to hold on liquid low-risk financial instruments does not, by itself, imply equilibrium of the required rates of return on productive investment. In general, however, it seems safe to infer that an outward shift in the saving schedule of one country will increase both its net exports of goods and services, or net foreign investment, and its domestic investment to some degree.

Another illustration may be used to explore cyclical effects on net foreign investment versus domestic investment. Here, changes in the percentage gap between potential and actual output, g, rather than the real interest rate, r, are assumed to influence saving and investment in the short run. ^⁴ To assure stability, the investment schedule slopes down more steeply than the saving schedule in Chart 2. ^⁵ The starting position is arbitrarily assumed to involve the same equilibrium level of the output gap, g_o, in both countries. The assumption of a positive equilibrium level of the gap should surprise no one, since potential output, as officially estimated, for instance, in the United States, is higher than the long-run sustainable level of output consistent with non-accelerating inflation and other prerequisites of equilibrium. ^⁶ Deviations around this normal level of the gap are assumed to be transitory or cyclical, although the normal level may itself change, depending on how potential output is measured in different periods.

Now assume that with matching initial balances of net foreign investment of CD > 0 in country A and EF < 0 in country B, the short-run investment schedule shifts inward in country A. If the business cycles are synchronized, the level of gap rises to g₁ in both countries until GH is equal to IJ. In country A, domestic investment declines by MN, national saving by KL, and net foreign investment increases by MN – KL. Hence, the contractive shift in the domestic investment schedule of country A causes national saving to fall along with it, but net foreign investment increases. Qualitatively, one would not expect this conclusion to change if the gap increased more in country A than in country B. Only in the extreme, when country A has to do all the adjusting because the import surplus of country B remains fixed at EF,^⁷ would domestic investment fall by as much as national saving in country A. This would imply a gap greater than g₁ in that country, at which the horizontal difference between IA₁ and SA_0,1 in Chart 2 is equal to EF.

Rather than let output fall by this amount, the authorities of country A could, of course, attempt to reduce the national saving rate through increased fiscal deficits or reduced saving incentives for the private sector to check the cyclical decline. A policy link from shifts in the IA schedule to shifts in the SA schedule might thus be established that would reinforce the positive correlation between ex post changes in national saving and domestic investment. If the shift in the investment schedule is permanent rather than transitory, because it is due, for instance, to a decline in the rate of growth of potential output in country A, ^⁸ some permanent change would have to occur to restore the gap to its equilibrium value of g₀ in the long run. The fall in interest rates, analyzed in Chart 1, would help in this because it would shift the domestic investment schedule outward and the national saving schedule inward in both countries in the space represented in Chart 2.

As intimated by the title of this paper, both illustrations are based on the assumption that what happens to country A is due to developments in that country and not to shifts occuring abroad. This assumption may be appropriate for the United States, because the reserve currency status of the U. S. dollar gives it a large measure of freedom (due to the elasticity of foreign demand) in supplying dollar claims to the rest of the world. Second, cyclical disturbances or policy shifts originating in any one foreign country may be countered by shifts in other countries. Even if they are not, differences in the size of the internal market and the degree of diversification shield the United States from foreign influence more than would be the case in other industrial countries. ^⁹ Hence, the adjustment process illustrated for country A may be applicable to the United States.

Generalizing about the results of the experiments presented in the two charts, a shift in national saving may be expected to change domestic and foreign investment in the same direction in the United States. A shift in domestic investment, however, moves domestic saving in the same, and foreign investment in the opposite, direction under all but extreme assumptions. Positive time-series correlations between national saving and domestic investment would be expected in either case, whether or not the international mobility of capital is perfect. ^¹⁰ However, the important point established thus far is that net foreign investment is affected also. This provides the conceptual justification for estimating the latter from the balance of national saving and domestic investment.

Although it must be emphasized that net foreign investment as defined in the U. S. national income and product accounts refers to the current account balance (with some adjustments), ^¹¹ the balance of private and official capital movements and errors and omissions must, of course, balance this net foreign investment, or net exports. Thinking from the asset side, there is nothing unusual about an increase in national saving leading to an increase in the demand for both foreign and domestic financial assets, that is, increased net capital exports. Likewise, a fall in the domestic investment schedule stimulates capital exports if foreign demand for funds and investment opportunities hold up. If privately desired capital exports change by about as much as net exports of goods and services ex ante, there is little or no pressure on exchange rates that might trigger official intervention.

II. Analytical System

Leaving the detailed definition of variables to a later section, this section outlines the main features of the simultaneous-equation model used to investigate cyclical and other links between national saving and domestic investment rates. Section III details the specification of individual functions and derives the relationships that are solved in Section IV to reveal the non-cyclical factors that have caused the underlying rate of U. S. net foreign investment to fall over time. Section V discusses supply-linked versus demand-linked cyclical effects before proceeding to the overall conclusion in Section VI.

Three components comprising the net national saving rate and two components comprising the net domestic investment rate are analyzed in this section, where rates are generated by dividing by the net national product (NNP). These components are the government saving rate, GS, the personal saving rate, PS, and the corporate saving rate, CS, and then the fixed domestic investment rate, FI, and the rate of inventory change, IC. The estimated rate of net foreign investment, NF, is obtained from the estimated values of these variables as $\hat{G S} + \hat{P S} + \hat{C S} - (\hat{F I} + \hat{I C})$ .

CS appears in the PS equation because an increase in the corporate saving rate may be partially offset by changes in the personal saving rate. By contrast, CS is expected to have little effect on the current rate of net fixed investment, FI, because investment generally must be planned several quarters ahead in view of expected future profitability and production plans. In fact, fluctuations in the availability of internal financing were not found to influence the time path of fixed investment significantly, although there are some determinants which CS and FI have in common. Another link between the dependent variables considered was that PS may figure in the IC equation because a rise in PS may produce some (possibly undesired) inventory accumulation, but both prior expectations and the econometric evidence were weak on this point. Furthermore, there is no persuasive theory to suggest that GS should be an argument in the PS equation, although personal saving may very well respond to tax and transfer rates, fiscal surprises, and wealth effects of government debt. Of course, all saving rates react to cyclical conditions to some degree, and certain determinants of these rates may, in turn, modify the course of the cycle.

The PS equation contains four endogenous variables, one of which is another saving rate, CS. The rationale for this is that consumers “pierce the corporate veil” and subsume corporate saving in their personal saving decisions as if retained earnings had produced a roughly equivalent increase in household net worth. Other cyclical or cyclically affected variables in the PS equation are the output gap rate, GAP, the deviation of the rate of spending on consumer durables from its past average, CDUR, and the rate of government transfer payments, TRANS. Apart from having to complete the income determination framework through the estimation of GAP, the reason for treating the last three variables as endogenous is to avoid simultaneity bias that would arise if the actual rather than the expected levels of these variables were used in the regressions. Furthermore, there may be a substantial difference in the way households respond to the actual and the expected level of the rate of government transfer payments. Given that there is a stable cyclical pattern superimposed on an upward time trend in TRANS, any unexplained jump in TRANS would be both unexpected and fairly transitory (depending on the strength of the autoregression coefficient, p, in the error function u_t = ρu_t–1 + ϵ_t). Hence, more would be saved than would correspond to the expected level of TRANS. An analogous argument applies to the aggregate tax rate, TAX, where unusually high tax rates must be depressing personal saving by more than if the same level of TAX were no higher than expected.

All explanatory variables that are not reliably linked to the cycle, except for TAX, are treated as exogenous in this paper, although some of them are, of course, endogenous to a larger system than the one that can here be specified. These variables, which are identified in the next section, are represented by dots in the functions below, which are intended to highlight the simultaneous features and error linkages of the system. Thereafter, some of the solutions that can be derived from this system and some of the experiments that can be conducted with it are characterized briefly.

The system of equations with adjustment for first-order serial correlation of the error terms has the following form:

\begin{matrix} G S_{t} = f (G A P_{t}, …) + ρ_{f} u_{f t - 1} + ε_{f t} & (1) \end{matrix}

\begin{array}{l} \begin{matrix} P S_{t} = g (G A P_{t}, C D U R_{t}, T R A N S_{t}, T A X_{t}, C S_{t}, . . .) \end{matrix} \\ + ρ_{g} u_{g t - 1} + ε_{g t} & (2) \end{array}

\begin{matrix} C S_{t} = h (G A P_{t}, …) + ρ_{h} u_{h t - 1} + ε_{h t} & (3) \end{matrix}

\begin{matrix} F I_{t} = j (G A P_{t - 1}, …) + ρ_{j} u_{j t - 1} + ε_{j t} & (4) \end{matrix}

\begin{matrix} I C_{t} = k (G A P_{t - 1}, …) + ρ_{k} u_{k t - 1} + ε_{k t} & (5) \end{matrix}

\begin{matrix} N F_{t} = G S_{t} + P S_{t} + C S_{t} - F I_{t} - I C_{t} & (6) \end{matrix}

\begin{matrix} G A P_{t} = m (G A P_{t - 1}, C D U R_{t}, N F_{t}) + ε_{m t} & (7) \end{matrix}

\begin{matrix} C D U R_{t} = n (G A P_{t - 1}, …) + ρ_{n} u_{n t - 1} + ε_{n t} & (8) \end{matrix}

\begin{matrix} T R A N S_{t} = p (G A P_{t - 1}, …) + ρ_{p} u_{p t - 1} ε_{p t} & (9) \end{matrix}

\begin{matrix} T A X_{t} = q (…) + ρ_{q} u_{q t - 1} + ε_{q t} & (10) \end{matrix}

In system estimation, NF_t is replaced by the linear combination of estimated values, ${\hat{G S}}_{t} + {\hat{P S}}_{t} + {\hat{C S}}_{t} - {\hat{F I}}_{t} - {\hat{I C}}_{t}$ , so that $N F_{t} - {\hat{N F}}_{t} = ε_{f t} + ε_{g t} + ε_{h t} - ε_{j t} - ε_{k t}$ yields the error in predicting the net foreign investment rate. This error will be used to determine the explanatory power of the indirect approach to estimating NF from the domestic components of saving and investment. Since

\begin{array}{l} \begin{matrix} {\hat{N F}}_{t} = \hat{f} + \hat{g} + \hat{h} - \hat{j} - \hat{k} + {\hat{ρ}}_{f} {\hat{u}}_{f t - 1} + {\hat{ρ}}_{g} {\hat{u}}_{g t - i} + {\hat{ρ}}_{h} {\hat{u}}_{h t - 1} \end{matrix} \\ - {\hat{p}}_{j} {\hat{u}}_{j t - 1} - {\hat{p}}_{k} {\hat{u}}_{k t - 1} & (11) \end{array}

under the indirect approach, a single-equation estimate of NF_t will not display a stable autoregressive structure unless the ps on the lagged error terms of the component equations are all of similar size. If they are not, lagged errors in the net foreign investment rate persist to different degrees, depending on where they have arisen.

Another useful insight suggested by the indirect approach is that the current error terms, ε_ts, while serially independent in any one of the national saving or domestic investment equations, are unlikely to be independent across equations at time t. If they were, then the conditionally expected error in NF _t would have to be equal to any ε_t that may be estimated in one of the national saving rates or to —ε_t if the error occurs in one of the domestic investment rates. Even if one views NF_t as residually determined, such a restriction would be both arbitrary and extreme, since those factors that produce a given ε_t in one equation may very well also contribute to the ε_t in another. For example, a spontaneous decline in confidence may affect both consumers and business investors more or less simultaneously, so that it may raise PS and lower FI for reasons not appearing in the equations.

Because the estimation technique employed here utilizes the full variance-covariance matrix of the error terms, it is not possible to address such questions as whether disturbances in national saving and investment rates are largely compensated within the system or in the net foreign investment rate. ^¹² Otherwise, if a positive value of the saving rate residuals tended to be matched by a positive value of domestic investment rate residuals, the Feldstein-Horioka (1980) hypothesis that policy measures to raise national saving rates increase domestic rather than foreign investment rates would be supported for the short run. Furthermore, since ε_t–1 is a component of u_{t -1} in equations (1) through (5), any such positive covariance of national saving and domestic investment rate disturbances might persist for some quarters, depending on the size and similarity of the respective ρs. However, if there were little relation between the ε_ts, then net foreign investment would absorb the disturbances arising in national saving or domestic investment in the short run. As already explained, no provision is made for disturbances originating abroad to affect the indirect estimate of NF_t. There would be no methodological objection to entering a composite of foreign potential output growth variables or of variables that are little influenced by variations in NF into the estimating equations for the domestic saving and investment rates without destroying the focus on the domestic determinants of net foreign investment chosen for this paper. Rather, the reasons for excluding such foreign exogenous variables from the final estimates subsequently reported are pragmatic. ^¹³

Just as it is not possible to determine econometrically how disturbances in one saving or investment component are associated with disturbances in other components in the short run, it is impossible to obtain empirical guidance on how maintained policy shifts affecting the national saving rate are reflected in domestic versus foreign investment rates in the long run. No large displacements appear to have occurred during the post-Korean period analyzed in this paper. Still, even though the fiscal policy rule imbedded in the GS function has changed little from one subperiod to the next in the sample, ^¹⁴ a change in that rule toward a permanently higher full employment (or zero GAP) budget surplus rate is experimentally conceivable. Particularly, if such a change is produced by reducing government purchases so as to leave TRANS and TAX unchanged at any given cyclical position, NF would be raised ex ante by the assumed rise in the GS function. However, NF is a positively signed argument in the GAP function on the absorption hypothesis, validated empirically later in this paper, that net exports are a positive function of the excess of domestic supply over domestic demand. This means that a rise in the national saving rate that exceeds the rise in domestic investment rates depresses output and increases the net foreign investment rate ex post. Thus, instead of obtaining long-run effects, we would be thrown back to short-term cyclical analysis in any such mental policy experiment with the model.

While the long-run effects of policy experiments with the government saving rate are unobservable, national saving and domestic investment rates have changed over time for reasons that are not just cyclical. Rather, solving the system at the endogenously determined equilibrium level of the output gap, with the explanatory variables taking on the values characteristic of different periods, reveals significant changes in the fundamental net foreign investment rate of the United States. To show what domestic factors may have contributed to this change is one major objective of this paper.

Beyond this, research on the interdependencies between domestic saving rates, on the one hand, and income determination, on the other, is valuable in its own right. Its results caution against linking cause and effect in this area through ceteris paribus assumptions that are at variance with actual experience. For instance, it is invalid to assume that an increase in corporate or government saving produces an increase in national saving the same as if personal saving had remained unaffected. One should also bear in mind that an ex ante increase in national saving does not produce an equal increase in investment in the short run. The fact that aggregate demand and output are reduced in the short run may have undercut the staying power of moves to lift the national saving rate politically. Even in the long run, raising national saving need not lead to an equal rise in the net stock of productive capital in the United States, because foreign investment is likely to increase also. ^¹⁵ A rise in net foreign investment due, for instance, to higher net exports of goods and services, and a corresponding reduction in net capital imports by the United States, may be just as beneficial to U. S. investors and to the world as a whole as increased domestic investment. Yet the effects on the gross domestic product (GDP) potential and on the real wages of U. S. labor are quite different. Conversely, it may be erroneous to assume that factors that have depressed national saving in the United States in the past have depressed its domestic net stock of capital equally.

III. Explanatory Variables and Specifications of Individual Functions

The government saving rate, GS, is the national income and product accounts surplus or deficit (—) of all levels of government combined divided by NNP. In the derivation of the official surplus estimate, government investment is not distinguished from other government expenditures and hence not treated as part of national saving and domestic investment. GS is assumed to reflect customary fiscal proprieties and built-in automaticities that make government saving fall whenever GAP increases. In addition, there is a lagged habitual policy response to past changes (U_–2 – U_–4) in the average quarterly civilian unemployment rate, U, which generally makes fiscal stimulus greatest in the early stages of an upswing.

Quarterly changes in U, DU, are a function of two preceding changes in GAP, (GAP_–1 – GAP_–2) and (GAP_–2 — GAP_–3), in the rate-of-change version of Okun’s Law. With U and hence DU expressed as a fraction of the labor force, the regression estimated from the first quarter of 1955 through the fourth quarter of 1978 is shown with t-values in parentheses.

\begin{matrix} U - U_{- 1} \equiv D \underset{(0.36)}{U = 0.00010} \underset{(8.22)}{+ 0.26531} (G A P_{- 1} - G A P_{- 2}) \\ \underset{(2.43)}{+ 0.7845} ({G A P}_{- 2} - {G A P}_{- 3}); {\bar{R}}^{2} = 0.514, \\ S E E = 0.00286, D - W = 2.012 (12) \end{matrix}

Hence, adding DU_–2 and DU_–3, 0.26531 (GAP_–3 – GAP_–5) + 0.07845 (GAP_–4 – GAP_–6), is substituted for U_–2 – U_–4 in cyclical experiments reported in a later section.

In addition to cyclical factors, GS may respond somewhat to differences between the actual inflation rate and the officially expected inflation rate, PI — EPI. The official price forecast, published in The Economic Report of the President, underlies the budget estimates appearing in the annual Budget of the United States Government. ^¹⁶ If inflation is higher than expected, the political tolerance for budget deficits is reduced under given cyclical conditions. The excess of the automatic inflation elasticity of government receipts over expenditures facilitates the adjustment normally desired. However, there is no reason to believe that GS is a rising function of the expected level of inflation, since notions about the acceptable or underlying rate of price increase have proved adaptable. Tax cuts have been voted periodically to offset the automatic effects of inflation on the budget balance. This completes the description of the fiscal policy rule that is implied in the budget stance customarily adopted in view of the economic conditions prevailing.

There are, however, certain identifiable anomalies, AN, that may obscure the basic pattern of the fiscal policy rule unless allowed for separately. Over the sample period these relate first to the budgetary manipulations that occurred during the escalation phase of the war in Viet Nam and second to the extraordinary response to the 1974–75 recession that took the form of large one-time tax rebates in the second quarter of 1975. Both anomalies originated at the federal level but distorted budgetary outcomes at all levels of government combined, since the Federal Government may react to budgetary anomalies at the state and local levels (for instance, the New York City default crisis that started in 1975) but not the other way around. Dividing the amounts involved at annual rates by NNP yields negative values of AN (unusually large deficits in view of prevailing conditions) during the third quarter of 1965 through the second quarters of 1968 and 1975. AN is zero in all other quarters. Its regression coefficient is expected to be around unity in the GS equation, on the assumption that these nonrandom disturbances were not compensated in other parts of the budget when they occurred.

Behaviorally, AN may be interpreted as a fiscal surprise or as unusual fiscal largesse that is not expected to last because it falls outside the normal parameters of budget policy. ^¹⁷ The aggregate tax rate, in particular, is unusually low, so that less is consumed and more is saved than if the same low level of GS and TAX had been generated without surprise because economic conditions were different. This explains the presence of AN in the personal saving function, in which its coefficient is expected to be negative given that AN ≤ 0.

The aggregate tax rate, TAX, is the national income and product accounts total of government receipts, excluding federal grants-in-aid to state and local governments, for the federal and state-local sectors combined divided by NNP. TAX is a rising function of TIME, a variable that takes on the value of 0 in the first quarter of 1955 and grows by increments of 1 in each quarter thereafter to 95 in the fourth quarter of 1978. Because the denominator of TAX is the tax base (NNP) and the cyclical elasticities of particular federal, state, and local revenue sources are scattered around unity, the average tax rate moves only negligibly with the cycle. Major downward deviations from the rising trend in TAX can be attributed to AN.

The aggregate transfer payments rate, TRANS, is here defined as the sum of all types of government expenditures other than government purchases of goods and services and federal grants-in-aid divided by NNP. Federal government transfer and interest payments to foreigners are also subtracted before dividing by NNP. Although TRANS thus includes net interest paid to domestic holders of government debt and subsidies less current surplus of government enterprises, the numerator is dominated by transfer payments to persons as defined in the national income and product accounts. Since transfer payments rise when GAP increases, the average transfer rate moves strongly countercyclically. From cycle to cycle, however, TRANS rises in step with TAX, since the simultaneous upward movement of taxes and transfer payments has been a basic characteristic of the sustained growth in the relative size of the public sector (including transfer payments) over the sample period.

There is one additional explanatory variable, also entered into the TAX equation, that has its strongest justification here. Since transfer payments, particularly old-age benefits, are contracted at one time and paid out at another, the size of the budget commitments they impose in relation to NNP on a pay-as-you-go basis is an inverse function of the rate of growth of potential output, POTGR. This rate is obtained as [(GNPK72 — GNPK72_–4)/GNPK72_–4], where GNPK72 is the Council of Economic Advisers’ estimate of potential output in 1972 dollars available from Data Resources, Inc. The same concept is used in constructing GAP as 1 — (GNP72/GNPK72), where GNP72 is the real value of actual gross national product (GNP).

An average of past levels of GAP, GAPA = 0.5 (GAP_–1 + GAP_–2), can be used as one of the explanatory variables of TRANS only after GAPA has been scaled. TRANS is the only dependent variable which has cyclical variations superimposed on a rising time trend; all other cyclically affected variables appear trendless. For this reason the expected effect of GAPA on TRANS is a function of the level of TRANS. ^¹⁸ TRANS is 0.057 in the first quarter of 1955 and 0.123 in the fourth quarter of 1978. One would therefore expect a given change in GAPA to change TRANS by an amount more than twice as large at the end of the sample period as at the beginning, if the percentage changes induced in TRANS are the same at both times. The ratio of real potential GNP in the current quarter to its level in the last quarter of the sample period, W, provides a suitable scaling factor of GAPA. ^¹⁹ Hence, the product of GAPA and W, GAPA W, is entered as the cyclical variable in the equation for TRANS. Since W equals 1 in the fourth quarter of 1978, GAPAW equals GAPA in that quarter, but W is less than 1 in all earlier quarters.

The personal saving rate, PS, is the national income and product accounts personal saving plus wage accruals less disbursements plus the statistical discrepancy, all divided by NNP. ^²⁰ The specification used for PS reflects first of all the permanent income theory, according to which households save a much larger proportion of transitory than of permanent income. This accounts for the presence of GAP in the equation, whose coefficient is expected to be negative.

Disposable personal income, whether current or permanent, may be too narrow a concept for saving decisions to be based on it exclusively. Rather, households may regard corporate saving (whose rate is denoted by CS) as increasing their personal net worth. They can then reduce personal saving when corporate retentions rise and still close the gap between actual net worth at the beginning and desired net worth at the end of the period to the same degree as otherwise planned. There may also be some degree of substitution between taxes and household consumption if households assume the spending of these taxes to generate current benefits similar to those obtained from personal consumption expenditures. ^²¹ Alternatively, taxes may be associated with future benefits similar to those that could be provided through personal saving for future consumption. This is particularly likely if paying taxes now is thought to entitle one to transfer payments in the future in view of the close link between changes in TAX and TRANS. ^²² For these reasons, components of NNP that are not contained in disposable income, that is, corporate retentions and taxes, may influence personal saving. It has also been suggested that not all components of disposable income affect personal saving equally. Thus, current transfer payments, which are not in NNP, may have an effect on personal saving which is stronger than that of other components of disposable income, just as the effect of taxes may be stronger than that of changes in disposable income due to other causes.

Having accounted for the presence of AN, GAP, CS, TAX, and TRANS in the equation for PS, three more variables, relating to liquidity, demographic, and measurement effects, remain to be explained. Given that the income velocity of M₂ has shown little, if any, trend over the sample period on a cyclically adjusted basis, changes in its inverse, the ratio of M₂ to the current dollar value of potential GNP (inflated by the GNP deflator, PGNP), DM = M₂/(PGNP)(GNPK72) — [M₂/(PGNP)(GNPK72)_–1, can be used to indicate recent changes in the liquidity of the household sector. A rise in DM should lower PS if increased liquidity of households raises their propensity to consume.

Because the proportion of young civilians, 25 through 34 years of age, in the total civilian population changed appreciably during the sample period, this ratio, YP, was entered as an additional explanatory variable. It fell from 0.145 in the first quarter of 1955 to a low of 0.113 in all of 1965 and then rose continuously to 0.155 by the end of the sample period. A high proportion of young persons in the aspiring, family-forming phase of the life cycle is likely to be associated with high consumption expenditures in relation to current income and a low PS.

Inclusion of the third variable, the deviation of the rate of personal expenditures on consumer durables (CD over NNP) from its past average over 16 preceding quarters, $C D U R = C D / N N P - Σ_{i = 1}^{16} {(C D / N N P)}_{- i} / 16$ is indicated simply on measurement grounds. The national income and product accounts concept of personal saving does not include net investment in consumer durables in PS. If households follow economists in regarding such investment as a use of saving rather than as a form of consumption, they may reduce PS, as measured in the national income and product accounts, by the amount of CDUR and still save as much as permanent-income theory and other factors would suggest. The coefficient on CDUR should therefore be around – 1. If households as a group save a little extra to acquire the initial equity in consumer durables, perhaps because of capital market imperfections or because some households would otherwise choose not to save at all, the degree of substitution may be less than one-to-one but it is unlikely to be more than one-to-one.

Deviations in the rate of net investment in consumer durables from trend, CDUR, both affect the current GAP and are affected by lagged values of GAP. The effect on CDUR is conveyed by preceding changes in income that have produced GAPA. In addition, CDUR responds to a weighted average of the difference between short and long interest rates, because the loan commitments of commercial banks to dealers and finance companies or of finance companies to dealers and thence the flow of consumer credit tend to be reduced when short-term credit is tight. The variables used to construct the current rate difference, SL, are the average quarterly market yield on 3-month treasury bills (RMGBS3NS in Data Resources, Inc.) and the corresponding yield on treasury securities at a constant maturity of 10 years (RMGFCM∂10NS). SL is –1.0 (percentage point) on average, reflecting normal backwardation of the term structure of interest rates. However, SL is positive in credit crunch periods such as fourth quarter 1966, third and fourth quarters 1969, and third quarter 1973 through third quarter 1974, and again in 1979, which is beyond the sample period. Because of response lags, the explanatory variable used in the equation for CDUR is the weighted average of past values of $S L, S L L A G = {0.125 S L}_{- 1} + 0.25 Σ_{i = 2}^{4} {S L}_{- i} + {0.125 S L}_{- 5}$ .

The corporate saving rate, CS, is the ratio of undistributed corporate profits with inventory valuation adjustment and capital consumption adjustment to NNP. There appears to have been little change in either the target payout ratio of after-tax reported profits or in the share of after-tax profits in NNP from cycle to cycle except for fairly short-lived effects of changes in the average tax rate on corporate profits. As a result, variations in CS are due mainly to cyclical factors affecting after-tax profits, to recent changes in the corporation income tax rate, and to the inflation adjustments that are made in measuring CS but not in the computation of profits reported for tax purposes.

A rise in the ratio of the inventory valuation adjustment to NNP (IVAC), in particular, is associated with a strong decline in CS suggesting that both taxes and dividends rise in relation to inflation-adjusted profits when inflation-induced inventory accounting profits get into reported profits. Since inventory valuation adjustment is negative when such paper profits are positive, the coefficient on IVAC is expected to be positive and at least equal to the average corporate tax rate on reported profits, TC, which is about 0.4. If inflation and IVAC had ever stabilized at a higher level during the sample period, some of the rise in the effective payout ratio might already have been reversed. Changes in the average corporate tax rate on reported profits from four quarters ago to the current quarter, TC04, and from eight quarters to four quarters ago, TC48, may have an effect on CS that is expected to taper off as more time is allowed for the capital stock to adjust. Because of the cyclically leading pattern of after-tax profits, CS is likely to respond negatively to the average level of the gap in the preceding half year, GAPA = 0.5 (GAP_–1 + GAP_–2), and to changes in that average, DGAPA = GAPA — GAPA_–1 = 0.5 (GAP_–1 — GAP_–3).

One last, basic factor that may be related to CS is the rate of growth of potential output, POTGR. Data Resources, Inc. estimates that this rate rose smoothly from 0.034 or 0.035 in the second half of the 1950s to 0.039 in the mid-1960s and then declined, not quite as continuously, to just under 0.030 at the end of the sample period. A decline in POTGR that is due to lower rates of neutral technical progress or declining growth in total factor productivity reduces the desired rate of net investment in NNP. It may also gradually depress the share of inflation-adjusted after-tax profits and CS. While a decline in the rate of potential output growth that is limited to a single country would not have to be associated with an appreciable decline in the net national saving rate or in any of its components if the international mobility of capital is perfect, ^²³ the composition of sectoral balance sheets would continue to change if national saving is maintained in the face of declining domestic investment rates.

This completes the discussion of the saving equations and of the ancillary relations for TAX, TRANS, and CDUR. The rates GS, PS, and CS sum to the national saving rate, with the statistical discrepancy included and capital grants received by the United States (net) excluded from the numerator. This rate is equal to the sum of the domestic and foreign net investment rates after the external capital grants are brought to the latter side of the accounts by subtracting them from net foreign investment. ^²⁴ Since the latter is to be estimated as the balance of national saving and domestic investment, we now turn to the specification of the domestic investment rates.

The rate of fixed investment, FI, is the ratio of net fixed investment (gross fixed investment minus capital consumption allowances with capital consumption adjustment) to NNP. Conceptually, net investment is a function of the difference between the actual stock of capital and the levels of that stock desired for future periods. Since some additions take years to complete, current investment can rarely do much to close the gap between the actual stock of capital and the stock one would like to have on stream right now. Instead, it is designed to help meet future requirements as they are currently perceived. Rather than model this time-distributed process explicitly, POTGR was identified as the variable governing the desired rate of capacity augmentation in the long run. Cyclical factors represented by GAPA may then determine the desired timing of such additions in the short run as completion schedules are stretched out or compressed.

The variable DGAPA is expected to capture the cyclically lagging pattern of fixed investment that is due to the high expense of terminating on-going investment projects when demand falls off and NNP (in the denominator of FI) declines from trend. It also reflects the inability to increase the investment rate immediately when demand strengthens and GAP declines, because planning, ordering, assembly, and installation take time. Hence, the coefficient on the disequilibrium variable, DGAPA, is expected to be positive.

The only other variable included in the FI equation, the short-long interest rate differential, SLLAG, is designed to capture the effects of increasing credit tightness on residential, more than on business, fixed investment in subsequent quarters. ^²⁵ The reasons for the disproportionate exposure of the housing sector to monetary policy, at least until the financial reforms of 1978 and 1979, are well known. ^²⁶ The possibility of ex ante crowding out of private fixed investment by perfectly substitutable government investment, raised by David and Scadding (1974), is ignored, since complementarity between these two types of investment is just as likely though difficult to measure.

The rate of change in inventories, IC, is the change in business inventories divided by NNP. On stock adjustment grounds, IC may be expected to be negatively related to the ratio of the stock of business inventories to final sales in the preceding quarter, (I/S)_–1 measured in 1972 dollars, which is available from the national income and product accounts since the fourth quarter of 1958 and is trendless. ^²⁷ In addition, the desired level of IC is expected to be lower the higher is GAPA. However, an increase in GAP over the preceding two quarters, represented by a positive DGAPA = 0.5 (GAP_–1 — GAP_–3), may well be associated with an undesired rise in IC. As in the equation for the fixed investment rate, FI, both equilibrium and disequilibrium elements are therefore present.

The rate of the potential output gap, GAP = 1 – GNP72/GNPK72, is also determined within the system. GAP is a function of cyclical momentum represented by its own lagged value (GAP_–1) and of new cyclical impulses. Two of these, I/S and IVAC, still appear with lags, because any output depressing effects of a high inventory-sales ratio or of high inventory profits and the ensuing cost increases are expected to materialize only after one quarter. A rise in (I/S)_–1 and in (the negative) IVAC_–1 should both increase GAP, calling for a positive coefficient on the former and a negative coefficient on the latter. ^²⁸ Deviations in the rate of spending on consumer durables from its past average, CDUR, and the rate of net foreign investment, NF, were, however, entered as simultaneous determinants of GAP. Another innovation is DM, the change in the ratio of M₂ to potential money GNP from the preceding quarter.

While the coefficients on CDUR and DM should clearly be negative in the GAP equation, the expected direction of the effect of NF is less clear. Ceteris paribus, a surge in net foreign investment due to foreign factors should reduce GAP. However, from an absorption viewpoint, a rise in NF is indicative of an increasing excess supply of domestic goods and services that would tend to raise GAP. As home demand slackens, export supply increases, and any increase in NF that may materialize ex post merely cushions the rise in GAP that would otherwise occur.

IV. Determinants of Underlying Balance of National Saving and Domestic Investment

The full-information maximum-likelihood estimates shown in Table 1 yield the expected coefficient signs in all cases where the direction of effects was clear a priori. ^²⁹ Some of the regression results bear on current controversies about the links between the components of private or national saving. These will be discussed in some detail before deriving the underlying level and cyclical behavior of the net foreign investment rate, NF, from the system estimated with data that include the July 1979 national income and product accounts revisions.

^{Table 1.}

Regression Results for Saving-Investment System

^¹The mnemonic definitions are as follows (for precise definitions and data sources see the text):

AN^*	Fiscal abnormalities or surprise rate
CDUR^*	Deviation of rate of spending on consumer durables from past average
CS^*	Corporate saving rate
DGAPA	Change in output gap rate, 0.5 (GAP_–1 + GAP_–2)
DM	Change in inverse of potential output velocity of M₂
FI^*	Net fixed domestic investment rate
GAP	Output gap rate
GAPA	Lagged average output gap rate, 0.5 (GAP_–1 + GAP_–2)
GS^*	Government saving rate
I/S	Ratio of inventories to final sales in constant dollars
IC^*	Rate of inventory change
IVAC^*	Rate of inventory valuation adjustment
NF^*	Net foreign investment rate
(PI – EPI)	Difference between actual and expected inflation rate
POTGR	Growth rate of potential output
PS^*	Personal saving rate
SLLAG	Lagged difference between short-term and long-term interest rates
TAX^*	Aggregate tax rate
TCQ4	Change in corporate profits tax rate over the past year
TC48	Change in corporate profits tax rate the year before last
TIME	Quarterly time dummy
TRANS^*	Aggregate government transfer payments rate
(U_–2 – U_–4)	Change in unemployment rate lagged as shown
YP	Proportion of young (25–34) civilian adults in total population
U_–1	Lagged error term with coefficient p
^*	Construction of rate involves division by NNP

^²The regression coefficient was constrained to equal -1 since the value of less than -1 [-1.28 (3.36)] otherwise found was regarded as too low.

^³The explanatory variable is GAPAW = GAPA × GNPK72/A in the equation for TRANS, where A is the level of potential real GNP (GNPK72) in the fourth quarter of 1978.

^⁴The explanatory variable is IVAC_–1 rather than IVAC in the equation for GAP.

^⁵The regression coefficient was constrained to equal -1 times the coefficient on TAX in this equation on the assumption (supported by the unconstrained regression results) that taxes net of transfers is the relevant explanator because the coefficients on TAX and TRANS do not differ significantly in absolute size.

^{Table 1.}

Regression Results for Saving-Investment System

		GS	PS	CS	FI	IC	GAP	CDUR	TRANS	TAX
Regression number:		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Independent variable ^¹
	Constant	0.00545	0.13087	0.00094	0.02577	0.11432	–0.05725	–0.00119	0.11465	0.31110
		(2.53)	(2.91)	(0.07)	(1.52)	(3.35)	(2.37)	(1.38)	(11.11)	(11.67)
	AN	0.87444	–0.72244							0.86164
		(8.83)	(4.10)							(10.15)
	CDUR		–1.0				–0.36660
			^⁽²⁾				(2.25)
	CS		–0.68149
			(8.32)
	DGAPA			–0.04589	0.03073	0.06972
				(1.68)	(0.71)	(1.07)
	DM		–0.17149				–0.20947
			(2.23)				(1.48)
	GAP	–0.45832	–0.08042	–0.07637
		(5.02)	(1.05)	(1.53)
	GAP_–1						0.92424
							(40.41)
	GAPA^³				–0.20949	–0.12896		–0.05588	0.27047
					(5.64)	(2.89)		(2.29)	(8.96)
	(I/S)_–1					–0.36770	0.20620
						(3.00)	(2.38)
	IVAC^⁴			0.65357			–0.23083
				(13.59)			(2.92)
	NF						0.35040
							(3.65)
	(PI – EPI)	0.01315
		(0.83)
	POTGR			0.83125	0.98086				–1.68247	–0.80751
				(2.11)	(1.98)				(6.12)	(1.22)
	SLLAG				–0.00266			–0.00297
					(2.46)			(4.17)
	TAX		–0.15363
			(0.87)
	TC04			–0.07603
				(4.40)
	IC48			–0.02662
				(1.57)
	TIME								0.000634 (23.30)	0.000822 (6.61)
									(23.30)	(6.61)
	TRANS		0.15363
			^⁽⁵⁾
	(U_–2 – U-₄)	–0.17468
		(3.39)
	YP		–0.22253
			(2.37)
	U_–1	0.91800	0.82048	0.88965	0.87079	0.65600	—	0.68518	0.66949	0.91186
		(30.57)	(28.39)	(25.50)	(20.94)	(11.16)		(10.87)	(11.27)	(26.94)
Identity
	NF (across)	1.0	1.0	1.0	–1.0	–1.0

^¹The mnemonic definitions are as follows (for precise definitions and data sources see the text):

AN^*	Fiscal abnormalities or surprise rate
CDUR^*	Deviation of rate of spending on consumer durables from past average
CS^*	Corporate saving rate
DGAPA	Change in output gap rate, 0.5 (GAP_–1 + GAP_–2)
DM	Change in inverse of potential output velocity of M₂
FI^*	Net fixed domestic investment rate
GAP	Output gap rate
GAPA	Lagged average output gap rate, 0.5 (GAP_–1 + GAP_–2)
GS^*	Government saving rate
I/S	Ratio of inventories to final sales in constant dollars
IC^*	Rate of inventory change
IVAC^*	Rate of inventory valuation adjustment
NF^*	Net foreign investment rate
(PI – EPI)	Difference between actual and expected inflation rate
POTGR	Growth rate of potential output
PS^*	Personal saving rate
SLLAG	Lagged difference between short-term and long-term interest rates
TAX^*	Aggregate tax rate
TCQ4	Change in corporate profits tax rate over the past year
TC48	Change in corporate profits tax rate the year before last
TIME	Quarterly time dummy
TRANS^*	Aggregate government transfer payments rate
(U_–2 – U_–4)	Change in unemployment rate lagged as shown
YP	Proportion of young (25–34) civilian adults in total population
U_–1	Lagged error term with coefficient p
^*	Construction of rate involves division by NNP

^²The regression coefficient was constrained to equal -1 since the value of less than -1 [-1.28 (3.36)] otherwise found was regarded as too low.

^³The explanatory variable is GAPAW = GAPA × GNPK72/A in the equation for TRANS, where A is the level of potential real GNP (GNPK72) in the fourth quarter of 1978.

^⁴The explanatory variable is IVAC_–1 rather than IVAC in the equation for GAP.

^{Table 1.}

Regression Results for Saving-Investment System

		GS	PS	CS	FI	IC	GAP	CDUR	TRANS	TAX
Regression number:		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Independent variable ^¹
	Constant	0.00545	0.13087	0.00094	0.02577	0.11432	–0.05725	–0.00119	0.11465	0.31110
		(2.53)	(2.91)	(0.07)	(1.52)	(3.35)	(2.37)	(1.38)	(11.11)	(11.67)
	AN	0.87444	–0.72244							0.86164
		(8.83)	(4.10)							(10.15)
	CDUR		–1.0				–0.36660
			^⁽²⁾				(2.25)
	CS		–0.68149
			(8.32)
	DGAPA			–0.04589	0.03073	0.06972
				(1.68)	(0.71)	(1.07)
	DM		–0.17149				–0.20947
			(2.23)				(1.48)
	GAP	–0.45832	–0.08042	–0.07637
		(5.02)	(1.05)	(1.53)
	GAP_–1						0.92424
							(40.41)
	GAPA^³				–0.20949	–0.12896		–0.05588	0.27047
					(5.64)	(2.89)		(2.29)	(8.96)
	(I/S)_–1					–0.36770	0.20620
						(3.00)	(2.38)
	IVAC^⁴			0.65357			–0.23083
				(13.59)			(2.92)
	NF						0.35040
							(3.65)
	(PI – EPI)	0.01315
		(0.83)
	POTGR			0.83125	0.98086				–1.68247	–0.80751
				(2.11)	(1.98)				(6.12)	(1.22)
	SLLAG				–0.00266			–0.00297
					(2.46)			(4.17)
	TAX		–0.15363
			(0.87)
	TC04			–0.07603
				(4.40)
	IC48			–0.02662
				(1.57)
	TIME								0.000634 (23.30)	0.000822 (6.61)
									(23.30)	(6.61)
	TRANS		0.15363
			^⁽⁵⁾
	(U_–2 – U-₄)	–0.17468
		(3.39)
	YP		–0.22253
			(2.37)
	U_–1	0.91800	0.82048	0.88965	0.87079	0.65600	—	0.68518	0.66949	0.91186
		(30.57)	(28.39)	(25.50)	(20.94)	(11.16)		(10.87)	(11.27)	(26.94)
Identity
	NF (across)	1.0	1.0	1.0	–1.0	–1.0

^¹The mnemonic definitions are as follows (for precise definitions and data sources see the text):

AN^*	Fiscal abnormalities or surprise rate
CDUR^*	Deviation of rate of spending on consumer durables from past average
CS^*	Corporate saving rate
DGAPA	Change in output gap rate, 0.5 (GAP_–1 + GAP_–2)
DM	Change in inverse of potential output velocity of M₂
FI^*	Net fixed domestic investment rate
GAP	Output gap rate
GAPA	Lagged average output gap rate, 0.5 (GAP_–1 + GAP_–2)
GS^*	Government saving rate
I/S	Ratio of inventories to final sales in constant dollars
IC^*	Rate of inventory change
IVAC^*	Rate of inventory valuation adjustment
NF^*	Net foreign investment rate
(PI – EPI)	Difference between actual and expected inflation rate
POTGR	Growth rate of potential output
PS^*	Personal saving rate
SLLAG	Lagged difference between short-term and long-term interest rates
TAX^*	Aggregate tax rate
TCQ4	Change in corporate profits tax rate over the past year
TC48	Change in corporate profits tax rate the year before last
TIME	Quarterly time dummy
TRANS^*	Aggregate government transfer payments rate
(U_–2 – U_–4)	Change in unemployment rate lagged as shown
YP	Proportion of young (25–34) civilian adults in total population
U_–1	Lagged error term with coefficient p
^*	Construction of rate involves division by NNP

^²The regression coefficient was constrained to equal -1 since the value of less than -1 [-1.28 (3.36)] otherwise found was regarded as too low.

^³The explanatory variable is GAPAW = GAPA × GNPK72/A in the equation for TRANS, where A is the level of potential real GNP (GNPK72) in the fourth quarter of 1978.

^⁴The explanatory variable is IVAC_–1 rather than IVAC in the equation for GAP.

Fiscal anomalies, AN, are not compensated in other parts of the consolidated budget, so that they reduce GS at a rate that is not significantly different from one-to-one. Furthermore, such anomalies are due principally to the tax rate being unusually low in view of the economic conditions prevailing, as the coefficient on AN in TAX is 0.86. Although AN was zero or negative during the sample period, the coefficients on AN and TAX in the PS equation suggest that almost 90 per cent of an unusual and unsustained increase in TAX, which would yield a positive AN, would be offset by a decline in the personal saving rate. However, the normal growth in TAX reduces PS by only 15 per cent of the amount involved. Furthermore, since the coefficient on TIME is 0.000822 in the TAX equation and 0.000634 in the TRANS equation, the accompanying rise in TRANS offsets about three fourths of this effect. The small rise in TAX — TRANS, which amounts to 0.000188 a quarter or 0.0075 a decade in relation to NNP, has been all but eliminated by the decline in the potential output growth rate, POTGR, since the late 1960s. This decline is almost twice as powerful in raising TRANS as in raising TAX, so that a fall in POTGR from 0.036 in 1968 to 0.030 in 1978 by itself lowers TAX — TRANS by 0.0052. The simultaneous rise of TAX and TRANS, produced by the combination of TIME and falling POTGR has left the personal saving rate almost untouched by the growth of the welfare state over the past decade. However, this result should not be viewed as indicative of the behavioral independence of PS from fiscal variables which has been postulated in the name of ultrarationality by others. ^³⁰ Rather, it shows such constancy to be a happenstance of roughly equal cycle-average growth in TAX and TRANS, particularly over the past decade, which may not continue. ^³¹

Unlike ultrarationality applied to net taxes, the hypotheses that corporate saving in large part substitutes for personal saving and that net investment in consumer durables also substitutes for personal saving, as measured in the national income and product accounts, are supported by the regression results. The coefficient on CDUR in the PS equation was not significantly different from —1 and ultimately constrained to that value. The coefficient on CS, —0.68, while significantly different from —1, still showed a very high degree of offset, so that a change in the estimated value of CS changes the net private saving rate only by one third as much. This has important implications for the effect of IVAC and POTGR on the difference, NF, between the national saving rate, NS = GS + PS + CS, and the domestic investment rate, NI = Fl + IC. For while a rise in the growth rate of potential output, POTGR, increases the corporate saving and fixed investment rates, CS and Fl, about equally, thereby making their basic (noncyclical) correlation positive, ^³² much of the effect of POTGR on CS is offset in PS. The net result is that a decline in POTGR increases NF by depressing NI more than NS. Similarly, only about one third of the strong effect of IVAC on CS comes through in NS. Thus, the tax and payout raising effects of inflation-induced inventory profits fall much more strongly on corporate saving than on national saving. One may infer from this that any economic development or any legislative or accounting change that affects CS will change the composition of national saving more than its level. ^³³

basic determinants of net foreign investment rate

Having discussed particular regression results and the linkages between individual components of the national saving and domestic investment rates, the system can be solved at a non-cyclical level of GAP. To reveal the underlying rate of NF predicted by the system of equations at five-year intervals, IVAC, POTGR, TIME, W, and YP were allowed to take on their actual values in the last quarters of 1958, 1963, 1968, 1973, and 1978. However, (I/S)_–1 (=I/S) was held at its sample mean of 0.279 and SLLAG at -1.0 in each of the five quarters chosen to conform to the assumption of noncyclicality. With AN, DGAPA, DM, PI – EPI, TC04, and U_–2 – U_–4 all zero, with GAP = GAP_–1, and with GAPAW = W(GAP), the solutions obtained for the saving and investment rates in Table 1 after substituting for CDUR, TRANS, and TAX are

\begin{matrix} G S = 0.0545 - 0.45832 G A P & (13) \end{matrix}

\begin{matrix} P S = 0.10124 + 0.02751 G A P + 0.04155 W (G A P) \\ - 0.44540 I V A C - 0.70091 P O T G R \\ - 0.22253 Y P - 0.000029 T I M E \\ = 0.00297 S L L A G & (14) \end{matrix}

\begin{array}{l} C S = 0.00091 - 0.07367 G A P + 0.6357 I V A C \\ + 0.83125 P O T G R & (15) \end{array}

therefore,

\begin{matrix} N S = 0.10763 - 0.50718 G A P + 0.04155 W (G A P) \\ + 0.20817 I V A C + 0.13034 P O T G R \\ - 0.22253 Y P - 0.000029 T I M E \\ + 0.00297 S L L A G & (16) \end{matrix}

\begin{matrix} F I = 0.05877 - 0.20949 G A P + 0.98086 P O T G R \\ - 0.00266 S L L A G & (17) \end{matrix}

\begin{matrix} I C = 0.11432 - 0.12896 G A P - 0.36770 I / S & (18) \end{matrix}

therefore,

\begin{array}{l} N I = 0.14009 - 0.33845 G A P + 0.98086 P O T G R \\ - 0.36770 I / S & (19) \end{array}

\begin{array}{l} N F = N S - N I = - 0.3246 - 0.16873 G A P \\ + 0.04155 W (G A P) \\ - 0.85052 P O T G R + 0.20817 I V A C \\ - 0.22253 Y P \\ - 0.000029 T I M E + 0.36770 I / S \\ + 0.00563 S L L A G \\ = 0.06450 - 0.16873 G A P + 0.04155 \\ W (G A P) \\ - 0.85052 P O T G R + 0.20817 I V A C \\ - 0.22253 Y P - 0.000029 T I M E (20) \end{array}

Using the values of IVAC, POTGR, YP, TIME, and W given in Table 2, the specific solutions of equation (20) are derived and are shown in the bottom panel of that table. These equations show that the basic supply of national saving is lowered more than the demand for domestic investment, so that NF is less the higher the level of GAP. The degree of response has declined over time because of the expansion of countercyclical transfer programs in relation to NNP indicated by W. Since there can be only one equilibrium level of GAP at any one time, a second relation is needed to determine it. Solving the cyclically unchanging version of the GAP equation in Table 1 (shown below as equation (21)) for NF after substituting for CDUR supplies the other blade of the scissors. Unlike equation (20), equation (22) has NF rise with GAP, because a rise in GAP is due to growing excess supply of national saving over domestic investment.

^{Table 2.}

Specific Solutions for Underlying (GAP, NF) Combination and Variable Levels and Equations Used to Derive Them

^¹I/S is held at 0.279 and SLLAG at -1.0 throughout.

^{Table 2.}

Specific Solutions for Underlying (GAP, NF) Combination and Variable Levels and Equations Used to Derive Them

		Conditioning Variables ^¹					Solution
		IVAC	POTGR	TIME	W	YP	GAP	NF
Fourth quarter
	1958	–0.00214	0.03456	15	0.50775	0.131	0.01778	0.00245
	1963	–0.00114	0.03809	35	0.60423	0.115	0.01639	0.00290
	1968	–0.00453	0.03547	55	0.72649	0.118	0.02515	0.00205
	1973	–0.01552	0.03287	75	0.86265	0.137	0.03372	–0.00384
	1978	–0.01432	0.02985	95	1	0.155	0.02545	–0.00436
		Equation (20): NF =				Equation (22): NF =
Fourth quarter
	1958		0.00508 – 0.14763 GAP			–0.00035 + 0.15773 GAP
	1963		0.00525 – 0.14362 GAP			0.00031 + 0.15773 GAP
	1968		0.00553 – 0.13854 GAP			–0.00192 + 0.15773 GAP
	1973		0.00064 – 0.13289 GAP			–0.00916 + 0.15773 GAP
	1978		–0.00112 – 0.12718 GAP			–0.00837 + 0.15773 GAP

^¹I/S is held at 0.279 and SLLAG at -1.0 throughout.

^{Table 2.}

Specific Solutions for Underlying (GAP, NF) Combination and Variable Levels and Equations Used to Derive Them

		Conditioning Variables ^¹					Solution
		IVAC	POTGR	TIME	W	YP	GAP	NF
Fourth quarter
	1958	–0.00214	0.03456	15	0.50775	0.131	0.01778	0.00245
	1963	–0.00114	0.03809	35	0.60423	0.115	0.01639	0.00290
	1968	–0.00453	0.03547	55	0.72649	0.118	0.02515	0.00205
	1973	–0.01552	0.03287	75	0.86265	0.137	0.03372	–0.00384
	1978	–0.01432	0.02985	95	1	0.155	0.02545	–0.00436
		Equation (20): NF =				Equation (22): NF =
Fourth quarter
	1958		0.00508 – 0.14763 GAP			–0.00035 + 0.15773 GAP
	1963		0.00525 – 0.14362 GAP			0.00031 + 0.15773 GAP
	1968		0.00553 – 0.13854 GAP			–0.00192 + 0.15773 GAP
	1973		0.00064 – 0.13289 GAP			–0.00916 + 0.15773 GAP
	1978		–0.00112 – 0.12718 GAP			–0.00837 + 0.15773 GAP

^¹I/S is held at 0.279 and SLLAG at -1.0 throughout.

\begin{array}{l} G A P = - 0.05681 + 0.94473 G A P \\ - 0.23083 I V A C + 0.35040 N F \\ + 0.20620 I / S + 0.00109 S L L A G \\ = - 0.00037 \\ + 0.4473 G A P - 0.23083 I V A C \\ + 0.35040 N F (21) \end{array}

\begin{matrix} N F = 0.00106 + 0.15773 G A P + 0.65876 I V A C & (22) \end{matrix}

Equation (20) may be thought of as the demand for net foreign investment schedule, since the demand for investment assets, represented by national saving, exceeds the supply, represented by domestic investment, by NF. Similarly, equation (22) may be interpreted as the supply schedule of NF, which is derived from the difference between domestic levels of production and absorption in an income determination framework. Specific solutions of equation (22) are shown in Table 2 for the five quarters selected.

In each quarter the intersection of the negatively sloped demand schedule and the positively sloped supply schedule simultaneously determines cyclically unchanging levels of NF and GAP. If the slope of the demand schedule had been found to be positive in equation (20), income determination would not be stable in a closed economy, because a greater fall in domestic investment than in national saving would then be induced by a cyclical decline. In that case, the output depressing effects of any exogenous contractive impulse would not be contained by the rise in the output gap. In an open economy with a positively sloped supply schedule in (GAP, NF) space, the process of income determination would be stable even with a positively sloped demand schedule, provided the slope of the latter (with NF on the vertical axis) exceeds that of the former. As the demand and supply schedules shift and as the estimated slope of the demand schedule changes because of the growing weight (W) of transfer payments (see the intercepts and slopes in the bottom panel of Table 2), the point of intersection of these schedules changes with the noncyclical conditions characteristic of specified quarters. The result is that the sustainable level of output relative to the official estimate of potential output, and hence the equilibrium level of GAP, changes somewhat from period to period.

What happens to the associated equilibrium level of NF is much more important. The solutions on the right side of the top panel in Table 2 show that there has been little change in the underlying level of NF from the last quarter of 1958 to that of 1968, although the equilibrium level of GAP crept up in the mid-1960s from below to above its sample-period average of 2.2 per cent (0.022). However, there was a large change in the underlying level of NF in the succeeding decade, with NF declining from 0.0021 in the fourth quarter of 1968 to –0.0044 in the fourth quarter of 1978 without further significant changes in GAP. The 0.0065 decline in the underlying net foreign investment rate, most of which occurred between the fourth quarter of 1968 and the fourth quarter of 1973, represents a swing of $13 billion (annual rate) at a fourth quarter 1978 NNP of around $2,000 billion. From the absorption perspective, the balance between net national saving and net domestic investment rates has therefore become distinctly less favorable to net foreign investment over the past decade. This has occurred in spite of the decline in the net domestic investment rate, because the net national saving rate has fallen even more. The relations between the various changes and the factors that have caused the equilibrium levels of these rates to change are spelled out next.

components of change

With the equilibrium level of the output gap given by the solution of the two equations in Table 2, the corresponding underlying levels of all national saving and investment rates can be derived for the quarters selected using equations (13) through (15) and (17) through (18). As shown in the top panel of Table 3, the underlying national saving rate declined by 0.014 from the fourth quarter of 1958 to the fourth quarter of 1978, with GS down by 0.004, PS up by 0.002, and CS down by 0.012. The decline in GS was due entirely to the rise in the equilibrium level of GAP. While there would have been no change in the underlying level of GS if the output gap were held constant, the underlying government deficit in relation to NNP has risen because the official estimate of potential output has exceeded the equilibrium level of output since the mid-1960s proportionately more than before. The personal saving rate has risen slightly because part of the decline in corporate saving was compensated in the personal sector. Specifically, increasingly large negative values of IVAC in equation (14) raised PS by 0.005 and the decline in the growth rate of potential output, POTGR, added 0.003. However, the rise in the proportion of young civilian adults in the population, YP, subtracted 0.005, and the combined effect of changes in GAP, W(GAP), and TIME was —0.024. Changes in the equilibrium level of the gap and the rise in tax and transfer rates thus had little net effect on the personal saving rate. Almost the entire decline in CS is due to IVAC and POTGR rather than to the rise in the equilibrium level of GAP. The change in the rate of the inventory valuation adjustment, IVAC, subtracts 0.008 and the decline in POTGR subtracts 0.004 from the underlying level of the corporate saving rate over the 20-year period starting in the fourth quarter of 1958.

^{Table 3.}

Underlying Saving and Investment Rates Calculated with Conditioning Variables Characteristic of Selected Quarters

^¹As fractions of NNP.

^²These entries are identical to those in the corresponding last column of Table 2.

^³The change in the net domestic investment rate in per cent of the change in the national saving rate.

^⁴The change in the net foreign investment rate in per cent of the change in the national saving rate.

^{Table 3.}

Underlying Saving and Investment Rates Calculated with Conditioning Variables Characteristic of Selected Quarters

			Net Saving Rates ^¹				Net Investment Rates^¹
			Government GS (1)	Personal PS (2)	Corporate CS (3)	National NS (4)=(1)+(2)+(3)	Fixed FI (5)	Inventory IC (6)	Domestic NI (7)=(5)+(6)	Foreign ^² NF (8)=(4)–(7)
	Fourth quarter
		1958	–0.00270	0.04628	0.02691	0.07049	0.05860	0.00944	0.06804	0.00245
		1963	–0.00206	0.04633	0.03060	0.07487	0.06235	0.00962	0.07197	0.00290
		1968	–0.00607	0.04902	0.02554	0.06849	0.05795	0.00849	0.06644	0.00205
		1973	–0.01000	0.05161	0.01554	0.05715	0.05361	0.00738	0.06099	–0.00384
		1978	–0.00621	0.04823	0.01445	0.05647	0.05238	0.00845	0.06083	–0.00436
Change (Δ) From			To	ΔNS	ΔNI	ΔNF	100(ΔNI/ΔNS)^³		100 (ΔNF/ΔNS)^⁴
	Fourth quarter
1958			1963	0.00438	0.00393	0.00045	89.7		11.3
1963			1968	–0.00638	–0.00533	–0.00085	86.7		13.3
1968			1973	–0.01134	–0.00545	–0.00589	48.1		51.8
1973			1978	–0.00068	–0.00016	–0.00052	23.5		76.5
1958			1978	–0.01402	–0.00721	–0.00681	51.4		48.6

^¹As fractions of NNP.

^²These entries are identical to those in the corresponding last column of Table 2.

^³The change in the net domestic investment rate in per cent of the change in the national saving rate.

^⁴The change in the net foreign investment rate in per cent of the change in the national saving rate.

^{Table 3.}

Underlying Saving and Investment Rates Calculated with Conditioning Variables Characteristic of Selected Quarters

			Net Saving Rates ^¹				Net Investment Rates^¹
			Government GS (1)	Personal PS (2)	Corporate CS (3)	National NS (4)=(1)+(2)+(3)	Fixed FI (5)	Inventory IC (6)	Domestic NI (7)=(5)+(6)	Foreign ^² NF (8)=(4)–(7)
	Fourth quarter
		1958	–0.00270	0.04628	0.02691	0.07049	0.05860	0.00944	0.06804	0.00245
		1963	–0.00206	0.04633	0.03060	0.07487	0.06235	0.00962	0.07197	0.00290
		1968	–0.00607	0.04902	0.02554	0.06849	0.05795	0.00849	0.06644	0.00205
		1973	–0.01000	0.05161	0.01554	0.05715	0.05361	0.00738	0.06099	–0.00384
		1978	–0.00621	0.04823	0.01445	0.05647	0.05238	0.00845	0.06083	–0.00436
Change (Δ) From			To	ΔNS	ΔNI	ΔNF	100(ΔNI/ΔNS)^³		100 (ΔNF/ΔNS)^⁴
	Fourth quarter
1958			1963	0.00438	0.00393	0.00045	89.7		11.3
1963			1968	–0.00638	–0.00533	–0.00085	86.7		13.3
1968			1973	–0.01134	–0.00545	–0.00589	48.1		51.8
1973			1978	–0.00068	–0.00016	–0.00052	23.5		76.5
1958			1978	–0.01402	–0.00721	–0.00681	51.4		48.6

^¹As fractions of NNP.

^²These entries are identical to those in the corresponding last column of Table 2.

^³The change in the net domestic investment rate in per cent of the change in the national saving rate.

^⁴The change in the net foreign investment rate in per cent of the change in the national saving rate.

The decline in the net domestic investment rate is about half as large as the decline in the national saving rate, or 0.007 rather than 0.014, from fourth quarter 1958 to fourth quarter 1978. Over this period, the underlying fixed investment rate fell by 0.006, with two thirds of the decline due to the fall in POTGR and one third due to the higher equilibrium level of GAP. The rise in the equilibrium level of GAP simply indicates that the equilibrium level of real output has grown less rapidly since the mid-1960s than the official estimate of the rate of growth of potential output would suggest. The underlying rate of inventory change, IC, was also affected by the slowdown communicated through the last factor, with IC declining by 0.001.

With regard to the interest stimulated by the Feldstein-Horioka (1980) finding that national saving rates and domestic investment rates differ by similar amounts between countries, the most important result lies elsewhere: almost half of the decline in the underlying national saving rate of the United States was matched by a decline in net foreign and not net domestic investment. As highlighted in the bottom panel of Table 3, while the time-series analogue of the link postulated by Feldstein and Horioka held under the basic (noncyclical) conditions prevailing up to the mid-1960s, it has been less descriptive of the outcomes observed since that time. Furthermore, in each instance net foreign investment changes in the same direction as national saving, as the conceptual considerations raised at the beginning of this paper had suggested. For the period fourth quarter 1958 through fourth quarter 1978 as a whole, the U.S. experience appears to suggest that changes in national saving rates change the domestic investment rates only half as much, with the constellation of changes that occurred between the fourth quarter of 1968 and the fourth quarter of 1973 dominating the outcome. Of course, this result may be so sample-specific as to apply only to those factors that have caused the national saving rate to change in the past and not to policy measures of unprecedented staying power, composition, or focus that may be used to do so in the future.

V. Cyclical Aspects

While it is important to abstract from cyclical and transitory effects to measure the underlying net foreign investment, it is also useful to attempt to measure the effects of cyclical developments in the domestic economy on the balance between national saving and domestic investment. Assuming that the noncyclical variables, IIS, IVAC, POTGR, SLLAG, TIME, W, and YP take on the values shown for the fourth quarter of 1978 in Table 2, using equation (12) to substitute for (U_–2 – U_–4), and holding all other noncyclical variables at zero, provides the following dynamic forms of equations (20) and (22):

\begin{array}{l} N F = - 0.00112 - 0.56306 G A P \\ + 0.18335 G A P_{- 1} + 0.21794 G A P_{- 2} \\ - 0.01175 G A P_{- 3} - 0.01370 G A P_{- 4} \\ + 0.04634 G A P_{- 5} + 0.01370 G A P_{- 6} & (23) \end{array}

\begin{array}{l} N F = - 0.00837 + 2.85388 G A P \\ - 2.6690 {G A P}_{- 1} - 0.02925 {G A P}_{- 2} & (24) \end{array}

Combining these equations and normalizing yields

\begin{matrix} G A P = 0.002122 + 0.83415 {G A P}_{- 1} + 0.07235 {G A P}_{- 2} \\ - 0.00344 {G A P}_{- 3} - 0.00404 {G A P}_{- 4} \\ + 0.01356 {G A P}_{- 5} + 0.00401 {G A P}_{- 6} & (25) \end{matrix}

The stationary solution of this equation yields GAP of 0.02545, the same as in Table 2. The largest of the six roots of this equation is 0.9273, with the maximum absolute value of (the real part of) all other roots being 0.2765. There are four oscillatory solutions among the latter. Because the solution of the sixth-order difference equation is dominated by a single real root of around 0.93, it converges gradually with only slight oscillations in the absence of new disturbances. Starting with a suitable set of initial conditions, we can remain at the intersection of the dynamic demand and supply equations (23) and (24) only if successive values of GAP are generated from the difference-equation solution. Since that solution yields a path that converges rather smoothly to a steady level, it does not provide insights into the behavior of NF over recurring 4-to-5-year cycles of the kind actually experienced in recent years.

To achieve greater realism one could proceed to analyze disequilibrium versions of the system by introducing errors that allow the solution for NF to be off either the demand or the supply curve. Explaining how this can be done is useful to show that the way in which domestic cyclical factors may affect NF depends very much on where shocks or errors originate in the economy.

Assume, for instance, that errors, 6, arise only in the GAP equation that was used to obtain equation (24):

\begin{array}{l} G A P = 0.00293 + 0.93448 G A P_{- 1} + 0.01025 G A P_{- 2} \\ + 0.35040 N F + ε & (26) \end{array}

Then NF is given by equation (23) with $G A P = (\hat{G} A P + ε)$ substituted for GAP, since NF is assumed to have been precisely what it would have been if GAP had been as predicted. Substituting from equation (23) for NF in equation (26), one can then generate recurring cycles molded as verisimilarly as one pleases by a recurring error pattern. This is done by simulating equation (26) over successive cycles, from arbitrary initial conditions on the lagged values of GAP until the cycle is resonant or independent of these conditions. The reference cycle perpetuated with periodic infusions of s yields the values of $(\hat{G} A P + ε)$ and the lagged values of GAP required to solve equation (23) for NF. The solution lies on the demand but off the supply curve for NF.

Unless one believes that equiproportional unexplained shrinkages or expansions in all components of aggregate demand and supply that leave the rates NS and NI and hence NF unchanged while altering GAP are in some way representative of real world cyclical disturbances, the result would be uninteresting except as a special case. It would also be unsurprising, since being off the supply curve while moving along the dynamic demand curve would only tell us what we already know from the noncyclical solution: the negatively sloped demand curve in (GAP, NF) space has NF move procyclically in this experiment. ^³⁴

More representative, countercyclical movements can be generated by attaching the error to any of the components of NF combined in equation (23), while requiring equation (24) to hold at all times when $N F = \hat{N} F + ε$ is substituted for NF. This implies that we must now remain on the dynamic supply curve, since specified errors take us off the demand curve in this alternative polar case. Assume, for instance, that an unexplained decline occurs in the rate of inventory change so that NI is reduced and NF is raised by a negative ε_k in IC. Initially, GAP is unchanged, but since ε_k reduces $\hat{I C}$ by ${\hat{ρ}}_{K} {\hat{u}}_{k t - 1}$ in the next quarter (see equation (5)), NF will grow and so must GAP, since s is now required to be zero in equation (26).

Compared with the previous experiment, the additional complication that arises here is that errors introduced into NF persist to different degrees depending on the size of the serial correlation coefficient (p) estimated for each of its components. These coefficients range from 0.66 (IC) to 0.92 (GS) in Table 1. The degree to which NF and hence GAP are affected by any shock thus depends on how the shock is introduced. Since it seems safe to assume that the source of the disturbance will vary over time by sector and between the supply and demand sides, the cyclical response pattern of NF is unlikely to be stable. In particular, both procyclical and countercyclical episodes may be observed, although countercyclical responses arising from disturbances in the components of aggregate domestic demand may predominate historically.

VI. Conclusion

As suggested in the first section of this paper, the domestic saving-investment approach to the determination of the current account balance (more precisely, net foreign investment) may be appropriate for some countries and periods but not for others. Because the size of its internal market gives the United States a special status in the world economy, making it less subject to feedback effects from abroad than any other country, this approach has the greatest chance to yield useful insights when applied to the United States. It can help to identify factors that appear to influence net foreign investment because they affect national saving and domestic investment differently.

Whether the indirect approach to estimating the net foreign investment rate, NF, from the balance of the other elements of the saving-investment identity also yields reasonably good predictions of the actual NF is another question. It is quite possible that estimated errors that appear small in relation to the domestic saving and investment rates ^³⁵ combine in such a way as to yield large errors in relation to NF in the United States. ^³⁶ If factors influencing national saving caused matching movements in domestic investment, the indirect approach to estimating the net foreign investment rate of the United States might have no explanatory power at all for the latter. Fortunately, this does not appear to be the case.

The research strategy of estimating NF from the other side yields a predicted value of the net foreign investment rate, $\hat{N F} = \hat{N S} - \hat{N I}$ , that explains 80 per cent of the variation in NF, as shown below.

\begin{array}{l} N F \underset{(0.06)}{= 0.00002} + \underset{(19.44)}{1.03100} (\hat{N S} - \hat{N I}) & (27) \\ {\bar{R}}^{2} = 0.082, S E E = 0.00283, D - W = 1.242 \end{array}

Regressing NF on $\hat{N F}$ with a constant shows that the intercept is almost precisely zero and the coefficient on $\hat{N} F$ very close to 1, as one would expect if the indirect estimate of NF is unbiased. Even though a standard error of estimate of 0.00283 in relation to NNP suggests that errors of $5.7 billion or more (with a fourth quarter 1978 NNP of around $2,000 billion) may occur with a probability of one third, the actual variations in NF have frequently been much larger from quarter to quarter at annual rates, so that the explanatory power of equation (27) is quite high. ^³⁷

It is concluded, therefore, that domestic factors relating to the supply of national saving and the demand for investing in the United States have important repercussions on the state of its foreign balance and not just on other domestic components of saving and investment. The fact that the U. S. economy is open and that government actions may have external effects cannot safely be ignored in the discussion of policy initiatives to raise the rate of capital formation and productivity and hence the growth path of the United States, even if there is little historical experience with such initiatives. Conversely, the contribution to external adjustment of measures to raise the national saving rate may be greater than implied in recent research on the adequacy of saving and investment in the United States. This applies especially at times when the rest of the world would welcome a reduction in the current account deficit of the United States and take no measures to oppose it.

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Mr. von Furstenberg, Chief of the Financial Studies Division of the Research Department, was formerly Professor of Economics at Indiana University and a Senior Staff Economist of the U.S. President’s Council of Economic Advisers.

Equating the real interest rate on saving to the real net user cost of capital rate relevant for fixed investment is purely illustrative in Chart 1. No rate of return variables survived in the final empirical estimates reported later in this paper.

If technological progress is either absent or purely labor augmenting, the natural growth rate of an economy is equal to the growth rate, n, of (augmented) labor inputs in the steady state. Net investment per head (per unit of labor input), i, is then i = nk + k, where k is capital per head. Assuming that k = f (k_d — k), f’ > 0, where the desired amount of capital per head, k_d, varies (inversely) with the real interest rate and other factors, a decline in r changes i more in the short run (k > 0) than in the long run (k = 0). In the long run, i = nk = nk_d is raised by the decline in r only to the extent capital deepening has raised k. Hence, the investment schedule shown in Chart 1 changes with the time allowed for adjustments to take place. A decline in the natural growth rate, however, reduces net investment per head in both the short run and the long run.

Analogously, private saving per head, s, is $s = n w + \dot{w}$ where w is private net worth per head. Assuming that $\dot{w}$ = g (w_d — w), g’ > 0, it is unclear whether s is raised or lowered by a decline in r in the short run, since the sign of ∂w_d/∂r and hence ∂(w_d — w)/∂r is theoretically indeterminate even though ∂w/∂r < 0 in the short run. However, a temporary rise in interest rates that does not alter the expected life-cycle rate of return on saving because it is expected to alternate with lower rates in the future has only negligible effects on permanent income. This would allow the positive substitution effects to dominate the short-term response of saving. If ∂w_d/∂r > 0, ∂s/∂r must be positive also, as assumed in Chart 1. Turning to the effects of the natural growth rate, a reduction in n that is due to a fall in the growth rate of population and labor inputs may well lower the stock of “hump-saving” in life-cycle models because of the associated shifts in the age structure of the population. However, a reduction in n that is due to the decline in the rate of labor augmenting technological progress is likely to lead to an increase in the desired average stock of net worth per head in the economy, w_d, since households must save sooner in their life cycle to distribute consumption optimally over their lifetime when the growth of household income with advancing age is expected to be lower. Because the decline in the rate of growth of potential output over the past decade has been due principally to the latter factor in the United States, saving may have been stimulated on that account, ceteris paribus, but this effect is far less certain than the depressing effects on domestic investment. Again, however, the short-run and the long-run effects may differ.

Harberger (1980) reports estimates ranging from 7.8 per cent (1947–57) to 12.7 per cent (1955–66) for the United States. The estimates of 6.3 per cent for Canada (1965–69) and 7.1 per cent for India (1955–59) contrast with 12.0 per cent estimated for Colombia (1967).

Using the rudimentary functions specified in footnote 2, with g now denoting the potential output gap rate, ∂(k_d – k)/∂g < 0 and hence k < 0 and net investment per head is depressed when the gap widens cyclically. On the saving side, ∂(w_d – w)/∂_g < 0 on permanent income grounds, since a transitory rise in the output gap that is associated with a temporary depression of private incomes below trend leads to little change in consumption compared with saving.

Since cyclical deviations are expected to be transitory, their effect is weaker on investment than on saving. Because a reversal of the cyclical decline is expected, the capital stock desired for future years may be little affected, and only investment that can quickly be put in place and started up may be discouraged or deferred by a cyclical decline.

The potential output series used later in this paper, prepared by the President’s Council of Economic Advisers, involves a benchmark unemployment rate of 5.1 per cent that is consistent with a zero level of the output gap in 1978. This rate is well below the natural unemployment rate deduced by most economists (see U.S. President (1979), pp. 72–76).

In the absence of J-curve effects, a depreciation of country B’s currency would presumably be required to shield its net exports from the effects of cyclical declines abroad. However, it is unlikely that country B can obtain such a depreciation in real terms when private capital movements are free, even if commodities are differentiated to some extent by country of origin. Hence, this polar case is again implausible.

Cause and effect are often confused by those who argue that an endogenous decline in the rate of investment lowers the rate of growth of potential output. As explained in footnote 2, the natural growth rate of an economy is not normally a function of k or k_d. Outside the steady state, the stock of capital may enter into empirical estimates of potential output growth if k is changing, for instance, because capital deepening is induced by a permanent decline in r. Recurring cyclical disturbances, however, lead to investment being higher than normal during one part of the cycle and below normal in the other part. Hence, there is no reason for the growth rate of potential output to change or for future levels of potential output to be systematically different from what they would have been if the past cyclical disturbances around the normal level of the gap had not occurred.

The comparative insulation of the United States has been documented in a number of studies. Dornbusch and Krugman (1976, p. 568) point out, for instance, that export prices in the seven major industrial countries show considerable responsiveness to competitors’ prices except in the United States.

By contrast, whether or not there is a close correlation between national saving and domestic investment across countries rather than over time within countries depends very much on the international mobility of certain types of financial capital, as Feldstein and Horioka (1980) have pointed out.

In these accounts, net foreign investment is defined as net exports of goods and services plus net capital grants received by the United States minus net transfer payments from persons and government to foreigners and minus interest paid by government to foreigners. Since capital grants are rarely received or bestowed by the United States, the main difference between the balance on current account on the balance of payments accounts basis and net foreign investment on the national income and product accounts basis lies in the treatment of the net reinvested earnings of incorporated affiliates of U. S. direct investors. Not being part of the U. S. gross national product, such earnings are not treated as an export of services in the national income and product accounts but netted directly against the corresponding capital export. As a result, net foreign investment was $9.7 billion lower than the balance on current account in 1978.

By definition, E(∊_i,∊_j) = Ω, where the elements of the error variance-covariance matrix Ω are symmetric. Now let ξ_i,ξ_j be independently distributed normal random variates, N(0,1) with E(ζζ’) = I, that serve to generate disturbances in the corresponding errors ∊_i,∊_j and thence in all correlated errors. To determine how changes in the vector of ∊s are related to the random variations in ξ, one would have to find a matrix, L, such that ∊ = Lξ. L would have to satisfy the condition Ω = LL’, so that E(∊∊’) = LIL’ for ∊∊’ = Lξξ, L’. The L that satisfies this condition is not unique, although a unique L can be found if restrictions on the form of L are accepted. One such restriction is that L is lower triangular. One implication of this restriction would be that changes in the e referring to the first equation would affect all ∊s, while changes in the ξ referring to the last equation would affect only the corresponding ∊ and no other. If L were upper triangular, the reverse would hold. Thus, unless there are economic reasons for imposing a particular form on L, L and the relation between ∊ and ξ are arbitrary and underdetermined.

Although the rate of growth of potential output declined in a number of industrial countries during the 1970s, and not just in the United States, the same is not necessarily true for developing countries (including oil exporting countries) and compatible estimates are difficult to obtain. The failure of terms-of-trade effects (the net absorption deflator relative to the NNP deflator) to yield significant results in the PS equation and of foreign cyclical effects to help explain the net retained earnings originating in the rest of the world is detailed in von Furstenberg (1980 a). Furthermore, a variable representing the relative price of energy (the ratio of the wholesale price index for fuels and related products and power to the general wholesale price index) failed to be significant in either the CS or the FI equation reported in this paper, although jumps in this ratio are positively associated with inventory profits (negatively with the inventory valuation adjustment) and negatively with the rate of growth of potential output.

See the F-tests for three subperiods reported in von Furstenberg (1980 a). It has been pointed out to the author that the adjustment for first-order serial correlation may contribute to this result, although p ranged from 0.86 to 0.58 in the subperiods, compared with 0.81 in the combined run. As explained in Section IV of this paper, the rule by which fiscal policy is made is stable only with respect to the official estimate of GAP and not with respect to deviations from the equilibrium level of income as later derived.

Feldstein and Horioka (1980) would expect most or all of the stimulus to go to net domestic investment in the long run; Artus (1980) expects to see it in net foreign investment; and Lederer (1980) expects both investment components to be affected in the full employment context, since savers increase their demand for foreign and domestic assets when the supply of national saving shifts outward. In earlier work, Feldstein (1975) and Boskin (1978), like many others, assumed a one-to-one correspondence between those reductions in the national saving rate that they attributed to the wealth effects of government social security programs or to the taxation of interest income received by U.S. taxpayers and reductions in the net stock of capital (as well as potential output and welfare) in the United States as if the openness of the U.S. economy could be ignored in the evaluation of the economic effects of government programs.

For details, see von Furstenberg (1980 a). The idea of using the officially forecasted inflation rate stems from Fellner (1976), pp. 118–24.

See von Furstenberg (1980 a) for the derivation of AN. AN was not found to be statistically significant in the CDUR equation, and any fiscal surprise that may affect CS is captured directly in the CS equation via changes in the corporation income tax rate.

Let the levels of government transfer payments, X, and NNP, Y, both be functions of time, t, and GAP, k, so that X = f(t,k), Y = g(t,k). Then the change in the transfer rate, d(X/Y) = ∂(X/Y)∂t + (X/Y)((∂Y/∂k)/x — ((∂Y/∂k)/Y). Assuming that ∂(X/Y)/∂T and (∂∂K)/X are constant, and given that (∂Y/∂k)/Y is constant by definition, d(X/Y) = a₀ + a₁ (X/Y). Hence, the coefficient on GAP would be the variable a, (Pr. Thus, GAP must be multiplied by (X/Y) or a cyclically neutral proxy variable that rises at the same average rate as X/Y before an unbiased coefficient can be expected.

W rises by a factor of 2.2 from first quarter 1955 to fourth quarter 1978, the same as the rise in TRANS, and deviations in the rates of growth are small in the interim because of the steady growth in both series.

Adding the difference between wage accruals and disbursements, which is charged against corporate and government saving in the national income and product accounts, to PS amounts to converting wages and salaries in disposable income from a cash basis to an accrual basis for consistency. Adding the statistical discrepancy to personal saving is more problematic although commonly done. See, for instance, Boskin (1978). The author has been advised that the excess of flow-of-funds saving of households and unincorporated businesses over personal saving and consideration of net incomes earned in illegal activities suggest that disposable personal income and personal saving are both underestimated in the national income and product accounts, so that adding the (generally positive) statistical discrepancy to personal saving appears warranted. If one further nets interest paid by consumers to business against interest received by consumers from business so as to exclude this item from both disposable income and personal outlays, the remaining differences between unity and the share of redefined disposable income in NNP is CS + TAX — TRANS, where CS is the corporate saving rate.

See David and Scadding (1974), Howrey and Hymans (1978), Buiter and Tobin (1979), and von Furstenberg (1981) for the original proposition and its subsequent examination.

This view is implied in Tanner’s (1979, p. 319) statement that “households perceive an extra dollar of government saving and of corporate saving in exactly the same way—both contribute equal amounts to the household’s perception of its life-cycle resource availability,” provided GS is varied by changing TAX or TRANS in such a way that the net tax rate, TAX—TRANS, is affected.

If a small, worldwide reduction in the rate of return on saving reduces saving in other countries and stimulates capital deepening everywhere, an increase in net foreign investment by the country experiencing a decline in its rate of potential output growth is feasible. It is also feasible if growth opportunities rise in other countries without a corresponding rise in their national desire to save. However, if growth opportunities decline elsewhere as well, not every country is likely to be able to maintain the net national saving rate at its former level. If the international mobility of capital is imperfect, some countries will experience steeper declines than others in rates of return on saving, so that the old rates of national saving may become allocatively excessive over time in some countries, depending on their natural rate of growth. For a discussion of some related aspects see Artus (1980).

Dividing the result by NNP yields the net foreign investment rate, NF, used in this paper, which treats capital grants received by the United States (net) the same as in the current account (balance of payments accounts basis). See footnote 11.

The equation lacks a net user cost of capital variable, although certain measures that have been used in lieu of such a variable, such as Tobin’s “q,” are correlated with included variables. The variable q appears to respond positively to the potential output growth rate and negatively to GAP and perhaps to credit crunches reflected in SL, apart from displaying high serial correlation. Lagged values of q were not found to be statistically significant when added in the equation for FI.

See, for instance, Jaffee and Rosen (1979).

I/S was held at its 1959 average value of 0.278 prior to the fourth quarter of 1958. This value is close to the average of 0.279 for the entire sample period. Only the year-end ratios are reported in the, national income and product accounts prior to 1959; these ratios range from 0.279 to 0.289 from 1954 to 1958, with unknown variations in between.

A past surge of inventory profits due to materials cost inflation tends to erode corporate profit margins and to reduce business and consumer purchasing power in subsequent quarters. These effects would, of course, not all go away if all corporations switched from a first in, first out to a last in, first out basis so that IVAC would become negligible. IVAC is, therefore, used as a convenient proxy for materials cost inflation over the sample period.

Some of the effects estimated were, however, extremely small. Thus, a maximum difference of 5 percentage points between the actual and the officially expected inflation rate that yielded a (PI — EPI) of around 0.05 in several quarters of 1973 and 1974 would raise GS by a mere 0.0007, or by less than one thousandth of NNP. With an NNP of around $2,000 billion at the end of the sample period, such a shock would lower the government deficit by $1 billion to $2 billion at an annual rate. A rise in SLLAG by one percentage point from its mean of —1.0, which would indicate a transition from normal backwardation of the term structure of interest rates to the threshold of a credit crunch, also has only rather slight effects. Both Fl and CDUR would be reduced by about 0.003, while PS would be raised by an equal amount because of the decline in CDUR. The effect of changes in the cyclically adjusted version of Marshall’s “k,” DM, are negligible as well, because changes above ±0.004 are rare. A positive change of this size would reduce PS and GAP by about 0.0008 directly, or by less than one thousandth of NNP.

See David and Scadding (1974). Another inference drawn from rationality is that households offset government saving whether or not changes in government saving are due to cyclical variations in net taxes (TAX – TRANS), as they usually are, or to changes in government purchases. For a statement of this position and its critique, see Barro (1978), including the comments by Feldstein on pp. 42–45.

While the coefficient on TAX is not statistically significant, the coefficient on AN is. This is pertinent to appraising the possible effects of fiscal actions, since David and Scadding (1974) made no distinction between changes in net taxes that are part of the rule and those that deviate from it in arguing that the private saving rate and the government saving rate are independent.

Given that there is also some cyclical simultaneity, although CS is leading and FI is lagging behind the cycle, the close correlation between CS and the corporate component of FI found by Feldstein and Horioka (1980) across countries for 15-year averages of these rates is likely to hold also within any country over time. Their challenge to identify common causes of the variation in both national saving and domestic investment that could explain their covariation even in a world of perfect capital mobility can be met by pointing to persistent international differences in the rates of growth of potential output. The lower the rate of output growth, and hence the rate of net domestic investment relative to NNP, the less internal financing is required in relation to NNP if the financial structure of corporations is to remain unchanged.

This applies, for instance, to changes in the average corporate profits tax rate, which are found to have a strong effect on CS in the first year, although the effect declines rapidly thereafter. Raising the corporate tax rate by 10 percentage points (TC04 = 0.10) amounts to raising the ratio of such taxes to NNP by about 1 per cent, or 0.01 of NNP. Since the effect of such an action is a reduction of CS by 0.0076 of NNP in the first year, about three fourths of the added taxes are initially paid out of corporate saving.

This was confirmed experimentally by generating recurring 15-quarter cycles through an error pattern of ε = 0.005, 0.01, 0.015, 0.01, 0.005 in the first 5 quarters of each cycle. After 19 simulation cycles, GAP began to repeat itself to six places of decimals every 15 quarters, although the amplitude of the resonant cycle so generated was quite small (0.028 from the peak in the fifteenth quarter to the trough in the fifth). NF was highest in the first quarter (-0.00142) at the beginning of the recession and lowest in the fourth (-0.00650) toward its end, compared with —0.00436 in the noncyclical solution (Table 2). Thus, NF is fairly synchronized with the cycle and moves procyclically in this experiment.

The Carter-Nagar ${\bar{R}}^{2}$ of the combined system estimated in Table 1 was 0.961. While the chi-square value of the log-likelihood ratio (758) exceeded the critical value for consistency of overidentifying restrictions in the upper tail, this consistency test is known to be overly severe in cases involving less than several hundred observations.

This is less likely to happen in countries such as the Federal Republic of Germany and Japan, where positive values of NF have frequently been equal to a substantial fraction of the national saving rate or in some developing countries where large negative values of NF have been encountered in relation to the size of their economies or saving rates. For comparisons of the Federal Republic of Germany and Japan with the United States in this regard, see Kindleberger (1976) and McKinnon (1978).

A less attractive feature of equation (27) is that there remains evidence of significant serial correlation, as the Durbin-Watson statistic is only 1.24. Such correlation should have been eliminated, but apparently was not removed completely by the adjustment for autocorrelation in all the equations on the other side of the saving-investment identity, if the autoregressive process in each was of the first order assumed. Estimating all the equations in Table 1 by ordinary least squares showed that the equation for inventory change, IC, had the worst fit $({\bar{R}}^{2} = 0.53)$ , while the equation for the government saving rate, GS, had the lowest Durbin-Watson statistic (1.517). Specification problems are most likely to be concentrated in these two sectors. Since changes in stocks, particularly of crude materials, may have a direct influence on the net exports recorded in the national income and product accounts, errors in IC may have a particular bearing on NF.

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IMF Staff papers: Volume 27 No. 4

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1980: Issue 004

Publisher:: International Monetary Fund

ISBN:: 9781451930504

ISSN:: 1020-7635

Pages:: 236

DOI:: https://doi.org/10.5089/9781451930504.024

Keywords
I. Conceptual Background
II. Analytical System
III. Explanatory Variables and Specifications of Individual Functions
IV. Determinants of Underlying Balance of National Saving and Domestic Investment
- basic determinants of net foreign investment rate
- components of change
V. Cyclical Aspects
VI. Conclusion
REFERENCES

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Adjustment of Interest Rate and Net Foreign Investment to Shift in Saving Schedule of Country A from Period 0 to 1

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Adjustment of OutputGap and Net Foreign Investment to Shift in Domestic Investment Schedule of Country A From Period 0 TO 1

^{Table 3.}

Underlying Saving and Investment Rates Calculated with Conditioning Variables Characteristic of Selected Quarters

			Net Saving Rates ^¹				Net Investment Rates^¹
			Government GS (1)	Personal PS (2)	Corporate CS (3)	National NS (4)=(1)+(2)+(3)	Fixed FI (5)	Inventory IC (6)	Domestic NI (7)=(5)+(6)	Foreign ^² NF (8)=(4)–(7)
	Fourth quarter
		1958	–0.00270	0.04628	0.02691	0.07049	0.05860	0.00944	0.06804	0.00245
		1963	–0.00206	0.04633	0.03060	0.07487	0.06235	0.00962	0.07197	0.00290
		1968	–0.00607	0.04902	0.02554	0.06849	0.05795	0.00849	0.06644	0.00205
		1973	–0.01000	0.05161	0.01554	0.05715	0.05361	0.00738	0.06099	–0.00384
		1978	–0.00621	0.04823	0.01445	0.05647	0.05238	0.00845	0.06083	–0.00436
Change (Δ) From			To	ΔNS	ΔNI	ΔNF	100(ΔNI/ΔNS)^³		100 (ΔNF/ΔNS)^⁴
	Fourth quarter
1958			1963	0.00438	0.00393	0.00045	89.7		11.3
1963			1968	–0.00638	–0.00533	–0.00085	86.7		13.3
1968			1973	–0.01134	–0.00545	–0.00589	48.1		51.8
1973			1978	–0.00068	–0.00016	–0.00052	23.5		76.5
1958			1978	–0.01402	–0.00721	–0.00681	51.4		48.6

^¹As fractions of NNP.

^²These entries are identical to those in the corresponding last column of Table 2.

^³The change in the net domestic investment rate in per cent of the change in the national saving rate.

^⁴The change in the net foreign investment rate in per cent of the change in the national saving rate.

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Abstract

I. Conceptual Background

II. Analytical System

III. Explanatory Variables and Specifications of Individual Functions

IV. Determinants of Underlying Balance of National Saving and Domestic Investment

basic determinants of net foreign investment rate

components of change

V. Cyclical Aspects

VI. Conclusion

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