CHAPTER THREE The Link Between Real Interest Rates and French Aggregate Private Investment

Paul Masson
Published Date:
October 1995
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Mark Taylor

The effect of movements in real interest rates on aggregate investment expenditure has traditionally been considered an important element of the monetary transmission mechanism (see, for instance, Miles and Wilcox (1991)). In France, the issue of the existence and strength of the link between real interest rates and real aggregate expenditure forms a crucial element of the current policy debate, given the tensions inherent in pursuing a firm nominal exchange rate policy in the face of high unemployment and weak macroeconomic activity.

This chapter is concerned with developing and estimating an empirical investment equation for France, using quarterly data for the period 1970–92. In particular, we search for the link between the real interest rate and the level of real aggregate private investment expenditure. We then use our empirical results to examine to what extent high real interest rates were responsible for the stagnation in French investment over the 1990–92 period, and whether reductions in real interest rates will significantly stimulate investment expenditure and so help lead the economy out of recession.

In contrast with much of the empirical evidence available on this issue, the results of our empirical investigation reveal the presence of statistically significant short-run and long-run effects of the real interest rate on French investment demand. The key to unearthing this relationship (and explaining why previous researchers have not detected it) appears to lie in the use of a methodological approach that is novel in empirical investment demand studies. This approach involves deriving an empirical model whose long-run solution is consistent with multiperiod optimizing behavior on the part of firms, but for which the short-run dynamics are largely determined by the data. While the resulting short-run investment function can be interpreted as deriving from dynamic optimization of firms in the presence of adjustment costs, it is capable of allowing for very rich short-run dynamics. In particular, there is a distinction made between the short-run and long-run elasticities of substitution between capital and labor. In the short run, we find that this elasticity is relatively low—which explains why simple accelerator models of investment have in the past been successful when estimated on French data—but in the long run the elasticity tends toward unity.1 The increased opportunity for substitution between capital and labor in the long run makes the implicit rental cost of capital goods, relative to the wage rate, increasingly important for investment decisions as time passes.

In the next section we motivate the analysis through a discussion of the relevance of the investment-interest rate nexus for the current policy debate. In Section II we give a very brief survey of previous empirical studies of aggregate investment on French data. In Section III we summarize our theoretical and empirical framework, the technical details of which are given more fully in Appendix I. The data are described in Section IV and our empirical results are summarized in Section V (and given in detail in Appendix II). In Section VI we use the estimated equation to carry out some counterfactual simulations assuming a higher growth of aggregate demand or lower real interest rates over the 1990–92 period. In Section VII we carry out some forecast simulation exercises, assuming alternative paths for real interest rates and output over the 1993-94 period. A final section concludes.

I. Investment and Interest Rates in France

For the ten years following the first Organization of Petroleum Exporting Countries (OPEC) oil price shock of 1974, the French investment-output ratio (gross fixed investment as a proportion of GDP) showed a more or less continuous decline, from close to 27 percent at the end of 1974 to less than 20 percent in 1984 (Chart 1). Although there was some reversal of this trend over the ensuing five years, investment again stagnated during the 1990-92 period. A prime suspect for one of the underlying causes of the recent stagnation in investment expenditure has been the very high level of real short-term interest rates.

Chart 1.France: Investment and Interest Rates

Source: INSEE; IMF Treasurer’s Department.

1Ratio of real investment expenditure of the secteur marchand to real GDP.

2Three-month money market rate less annualized growth in the GDP deflator in the following quarter.

During 1992-93, high nominal interest rates were needed in order to defend the franc’s parity against the deutsche mark, in the face of mounting speculative pressures and considerable turbulence within the European Monetary System (EMS) as well as a tight anti-inflationary stance of monetary policy in Germany. In the absence of strong French inflationary pressures, these high nominal rates translated into high real interest rates, despite the weakness of French economic activity and the clear desirability of easing monetary conditions. An apparent rise in market confidence in the franc, following the formation of the new Government in March 1993 and the announcement of new policy measures the following month, eased downward pressure on the franc somewhat, however, and German nominal interest rates also saw some slight reduction. The franc again came under strong speculative attack, exacerbating the policy dilemma over whether interest rate cuts should be reversed in the face of macroeconomic weakness. Even if this round of speculative attacks on the franc had not occurred, the link between interest rates and investment would still be an important policy issue for France.

A traditional view among French economists, presumably derived from the empirical evidence discussed in the next section, is that real interest rates have little or no effect on investment expenditure. Certainly, any link that does exist between real interest rates and investment is likely to be complex, and interest rates clearly cannot explain all of the variation in investment. As Chart 1 shows, for example, the great decline in the aggregate investment-output ratio over the decade following the first OPEC oil price shock coincided with a sustained period of low and often negative ex post short-term real interest rates.

Nevertheless, economic theory does suggest that the real interest rate, operating through the implicit rental price of capital goods and in combination with other variables such as the relative price of labor and aggregate demand, should have some effect on real investment expenditure. In practice, however, empirical work on French aggregate investment has found little evidence of a link with the real interest rate. Rather, applied researchers have tended to favor the use of simple flexible accelerator-type models, where investment is explained solely by movements in aggregate output. Such a model would be implied by a fixed-coefficients production technology under a demand constraint: if a given amount of capital is required for producing a given amount of output, with no possibility of substituting between capital and labor, then the demand for new capital will depend on the expected level of output demand and will be largely insensitive to movements in the rental price of capital goods, and hence real interest rates.

We now turn to a discussion of existing empirical literature on this issue.

II. Empirical Investment Studies on French Data

Empirical investment studies,2 in France and elsewhere, may be classified into three broad categories: true neoclassical, competitive equilibrium models; quasi-neoclassical models; and accelerator models.

The true neoclassical model assumes perfectly elastic supplies of factors and perfectly elastic demand for output. The result is an investment function that, in the absence of adjustment costs or price uncertainty, is defined only for decreasing returns to scale (Jorgenson (1967), Coen (1969)). This is because with constant returns to scale the desired capital stock of the representative firm is infinitely large, while with increasing returns to scale the revenue function does not have a maximum. These problems illustrate the dangers of applying what is an essentially microeconomic theory of optimal capital accumulation at the aggregate level without allowing for the relevant features of aggregation, such as imperfectly elastic output demand.

Nevertheless, a number of researchers have estimated the true neoclassical model—in which investment is a function of relative factor rentals only—on aggregate French data (Schramm (1972), Muet (1979a, 1979b), Villa, Muet, and Boutillier (1980), Artus and Migus (1986)).3 Nearly all of these studies have reported disappointing results and have concluded that the true neoclassical model of investment is unrealistic at the aggregate level.

In a number of influential studies published during the 1960s,4 Jorgenson developed what became known as the neoclassical model of capital accumulation, but which we shall refer to as quasi-neoclassical. Jorgenson derives the desired level of the capital stock by equating the marginal product of capital with the user cost of capital, and then assumes lagged adjustment of the actual capital stock toward this desired level. The net result is an investment equation conditioned on output and the real user cost of capital. The problem with this approach is that only one of the first-order conditions for profit maximization is utilized; setting the marginal product of labor equal to the real wage rate and substituting into the Jorgenson model would yield the true neoclassical model where investment is conditioned only on relative factor rentals. Thus, the Jorgenson model is quasi-neoclassical. Muet (1979a) has estimated quasi-neoclassical models of investment for France, and reports largely disappointing results.

A close relative of the quasi-neoclassical model, but with a sounder theoretical footing, is the effective-demand investment model. This model explicitly recognizes an aggregate demand constraint, and so aggregate output (equal to demand if demand is less than notional supply) enters the investment function in addition to relative factor rentals.5

Output may also enter the investment function even in the absence of demand constraints if the production technology is assumed to be of the fixed-factor proportions, or Leontief, type. In the absence of a labor constraint, the desired capital stock will be directly proportional to output. Assuming a distributed lag adjustment of actual toward desired capital stock then results in the traditional flexible accelerator investment model, where investment is a function only of the change in output, with no effect of relative factor prices on the investment decision.

Demand-constrained investment models have been estimated for France, with some degree of success, by Artus and Muet (1980, 1981). These authors find, however, that the influence of relative factor rentals on investment “is weak compared to the acceleration effect of demand” (Artus and Muet (1980)). They also find that the elasticity of investment with respect to output demand—in theoretical terms, the inverse of the production function’s returns to scale—is insignificantly different from unity.

Simple flexible accelerator models of investment have been estimated for France by a number of researchers (e.g., Oudiz (1978), Muet (1978)—see Artus and Muet (1990) for a survey). These equations perform reasonably well and again provide evidence of constant returns to scale in production.

More recent work on the French aggregate private investment function includes Artus and Sicsic (1990) and Muet and Véganzonès (1992), who fit a range of models to 1980s data. A major finding of these authors is that, while the effect of the real interest rate on investment, operating through the user cost of capital, was significant during the 1960s and 1970s, it becomes insignificant when the sample is extended to include the 1980s.

III. Theoretical and Empirical Framework

In Appendix I, we consider the investment decision of a representative firm facing a demand constraint on its output and producing according to a production function which is, at least in a long-run sense, of the traditional constant-returns Cobb-Douglas variety. We demonstrate that the solution to the firm’s optimization problem is a long-run investment demand function of the form

where I(t) is aggregate investment at time t, Y(t) is aggregate output, ρ(t) is the real user cost of capital, w(t) is the real wage rate, v(t) is a stationary disturbance term, π is a constant term, γt is a time trend that captures the effects of technical progress, and a is the share of labor in aggregate output (approximately 0.6 for France). The two noteworthy features of equation (1) are a long-run output elasticity of investment demand of unity and a negative investment demand elasticity with respect to relative factor rentals.

In Appendix I we also show that, given the existence of a long-run investment demand equation of the form (1), both dynamic optimization theory and certain statistical theorems can be employed to derive a short-run investment demand function of the form

where v(t) is the error correction or equilibrium error implicitly defined in equation (1), ξ(t) is a stochastic disturbance term, and γ4 < 0. The main interest of this equation is that it nests a flexible accelerator-type investment function (i.e., where investment is a function of lagged changes in output),6 but has a long-run solution that is of the form (1). In the short run, we expect γ4 and the γ3is to be small, reflecting limited short-run opportunities for capital-labor substitution. We expect γ4 to be negative and statistically significant, however, reflecting increased capital-labor substitution opportunities as time passes, with eventual steady-state convergence on the long-run investment demand function in equation (1).

Equations (1) and (2) are the two main equations estimated, although in Appendix II we also report estimates of a long-run aggregate production function for France, since the analysis is predicated on the assumption that this is approximately Cobb-Douglas—an assumption we test.

IV. Data

Quarterly data for the period 1970:I-1992:IV were obtained from the INSEE database on the following series for the secteur marchand (i.e., for the economy excluding public administration): real output (Y) and the output deflator (p), real gross investment expenditure (I) and the investment deflator (Q), total hours worked (L), the nominal hourly wage rate (W), and the nominal three-month money market interest rate (i). A corresponding real capital stock series was taken from OECD sources.7

Real wage (w) and real capital goods price (q) series were computed by deflating by the output deflator (i.e., w = W/p and q = Q/p). An ex post measure of the user cost of capital was constructed as

that is, the real price of capital goods multiplied by the opportunity cost of funds (real interest rate) and the quarterly depreciation rate, where the annual depreciation rate δ was set at 6 percent.8

V. Summary of the Empirical Results

Using very recent applied econometric techniques on the estimation of long-run economic relationships (Engle and Granger (1987), Johansen (1988), Phillips and Loretan (1991)), we obtained the following constrained estimate of equation (1):

This estimated equation is extremely encouraging in that the long-run coefficient constraints of a unit output elasticity, and of a negative relative factor rental elasticity equal in magnitude to the share of labor in aggregate output, are not rejected by the data (see Appendix II for further details).

The deviations from long-run equilibrium from this equation, that is, the fitted values of v(t), were then used to estimate a dynamic short-run investment function of the form in equation (2). This resulted in a highly stable estimated equation that fitted the data well, explaining some 55 percent of the quarterly percentage change in aggregate investment, and that passed a whole range of modern regression diagnostic tests. The stability of the estimated coefficients is particularly impressive. The short-run elasticity of investment demand with respect to relative factor rentals was estimated to be about -0.37, or roughly half the long-run elasticity of around -0.6, and to operate with a six-month lag. The estimated value of the adjustment coefficient, γ4 in equation (2), was approximately -0.02, implying a very slow adjustment toward the long-run or equilibrium level of investment demand: a 10 percent deviation from the long-run equilibrium level of investment generates an adjustment of only 0.2 percent in the current quarter.

Thus, although we have found an effect of real interest rates on investment that is statistically significant and consistent with optimizing economic theory, the small magnitude of the relevant estimated coefficients and the extremely slow implied speed of adjustment toward long-run equilibrium (and increased capital-labor substitution possibilities) suggest that this link may not be economically important for practical policy purposes. This issue is explored in the following two sections.

VI. What Caused the Recent Decline in Investment?

The marked slowdown in French private investment over the 1990–92 period has been variously explained as due to the effect of high real interest rates operating through the user cost of capital, or the recession itself operating through a decline in output and an accelerator effect on investment. In an attempt to shed some light on this issue, we carried out three counterfactual experiments using our estimated investment equation.

In the first experiment, we held the short-term real interest rate constant, over the period 1990-92, at its 1989 average level of 6.3 percent per annum, as opposed to an actual path of the ex post real interest rate of between 6.7 and 8.2 percent over this period. Assuming no feedback effect on output, prices, or the wage level, we then used the equation to forecast investment dynamically over this three-year period. The percentage deviation of the forecast level of investment from the level predicted by the model with the real interest rate at its actual historical values was then computed.

In the second counterfactual exercise, the real interest rate was held at 5 percent per annum from 1990:I, and, in the third exercise, real output was assumed to grow at 2.5 percent per annum from 1990:I (with the real interest rate at its actual historical values). This growth rate, corresponding to the growth of output in 1990, is a somewhat higher growth path than was actually experienced, since aggregate output actually grew at some 0.7 percent in 1991 and 1.3 percent in 1992.

The results of these exercises, expressed as the percentage difference in the value of the simulated level of investment from the base simulation level, are given in Table 1. It appears that increases in the real interest rate may have had a significant negative impact on investment over the 1990–92 period. Indeed, the equation implies that holding the real rate at its average 1989 level would have led to real investment expenditures that were 9.25 percent higher by the end of 1992. This compares with a 6.75 percent simulated increase in real investment that follows when the 1990 average growth rate of output is projected over the period.

Table 1.Simulated Paths for Investment(Percentage deviations from base simulation)
Year and QuarterReal Interest Rate = 6.3 percentReal Interest Rate = 5 percentAnnual Growth of Output = 2.5 percent
Source: IMF staff calculations using equation (A16).
Source: IMF staff calculations using equation (A16).

Overall, these counterfactual exercises suggest that high real interest rates, as well as the decline in aggregate demand, may have played a significant role in the fall in the investment-output ratio over the 1990-92 period.

VII. Will Lower Real Interest Rates Stimulate Recovery Through Increased Investment?

The final question that we address is whether the prospective decline in real interest rates, as forecast in the September 1993 World Economic Outlook (WEO), could be expected to have a significant impact on investment expenditure. In examining this issue, we used our estimated equation to carry out three forecast simulation exercises.

In the first exercise, we forecast the growth path of real investment over the period 1993:III through 1994:IV, using values of all of the exogenous variables consistent with the September 1993 WEO forecast.

In the second exercise, we performed the same forecast simulation with the same WEO assumptions except that the real interest rate was held constant at its 1993:II level of 5.9 percent, rather than declining as foreseen in the WEO forecast to some 2.8 percent in 1994.

In the final forecast simulation, we used the WEO assumptions for real interest rates but assumed a higher growth rate for manufacturing output, equal to 1 percent per quarter.

The results of these exercises, expressed as the difference in the forecast level of investment at the end of 1994 from the level of investment produced by using the WEO forecast as assumptions, are given in Table 2. As the table shows, the interest rate effects on investment are again significant: failure to reduce the real interest rate by about 2 percentage points (to some 2.8 percent) by the end of 1994, leads to a simulated 10 percent fall in investment over the simulation period. On the other hand, increasing output growth to some 4 percent per annum (from the WEO forecast of -1 percent for 1993 and +1.1 percent for 1994) would increase real investment by 5 percent over the WEO base forecast by the end of 1994.

Table 2.Simulated Effects on Investment of Alternative Assumptions, 1993:III–1994:IV(Assumptions)
Real Interest Rate Unchanged from 1993:II Level ( = 5.9 percent p.a.)Quarterly Growth Rate of Manufacturing Output = 1 percent from 1993:III
Cumulative percentage increase in investment over base simulation−10.005.04
Note: The simulations assume paths for the exogenous variables consistent with the WEO forecast, except those indicated.Source: IMF staff calculations using equation (A16).
Note: The simulations assume paths for the exogenous variables consistent with the WEO forecast, except those indicated.Source: IMF staff calculations using equation (A16).

It should also be noted that these single-equation simulation results are not dissimilar from those obtained from simulations of the IMF’s multiregion econometric model, MULTIMOD. In particular, MULTIMOD simulations for France suggest that a movement of 100 basis points in the real interest rate will move real investment by some 5 percent in the opposite direction over a one- to two-year period.9

VIII. Conclusion

In the appendices we have combined recent econometric techniques on the long-run properties of economic time series and economic theory to derive and estimate an empirical investment equation for France that is both consistent with economic theory and empirically tractable. The resulting equation, estimated on French quarterly data for the period 1970-92, performed well empirically, and suggested a statistically significant effect of real interest rates on aggregate investment demand, operating through the user cost of capital.

Simulations using the estimated equation suggested that the high level of real interest rates over the 1990-92 period may have been an important contributory factor in the decline in the investment-output ratio over the same period. Similarly, further forecast simulations suggested that failure to reduce real interest rates in the future may have important negative effects on aggregate investment.

As with all applied econometric studies, the results reported in this chapter should be interpreted with caution, and the reader may wish to consider the following points: It is clear that new econometric estimates do not have quite the same scientific authority as, for instance, new estimates of the speed of sound or of the gravitational constant. Thus, the forecast simulations reported above can only be taken as illustrative and indicative of the effects of real interest rate movements on real investment, rather than as definitive measures of these effects. In addition, the estimated effects of short rates on investment were obtained using a sample period during which short and long rates tended to move together. They may not give very accurate predictions for the last year, when the two rates have diverged considerably due to a sharply downward-sloping yield curve. As well as considering the reliability of a single estimate of the investment-interest rate nexus, one should also consider the implications of basing simulations on a single equation rather than on a full, general equilibrium model, although simulations using MULTIMOD do yield broadly similar results. On the other hand, our econometric results do provide a synthesis of received economic theory and the very latest econometric techniques, and they do in some sense encompass previous estimates of the French investment function.

Thus, the major conclusion that should be drawn from this study is really that the debate on the transmission mechanism of monetary policy in France should not be closed; in particular, it cannot be simply assumed or asserted that real interest rates will not affect aggregate investment expenditure.

Appendix I: Theoretical and Empirical Framework

Consider a representative firm producing according to a constantreturns Cobb-Douglas technology and facing a demand constraint. Its optimization problem is therefore one of cost minimization subject to a given level of output. Consider first the one-period static optimization problem

subject to

where w(t) and p(t) denote, respectively, the real wage and real user cost of capital at time t, L(t) and K(t) measure inputs of labor and capital at time t, and A(t) denotes total factor productivity at time t.

The solution to this problem can be expressed as a cost function of the form


By Shephard’s lemma, the factor demand schedules are given by the derivatives of the cost function with respect to the relevant factor price.10 Thus, we have the demand for the capital stock at time t given by


Taking logarithms of equation (A4),

To derive a relationship involving investment rather than the capital stock, we can employ the following identity:

where δ is the depreciation rate. In logarithms this expression becomes

Equation (A8) is identically equivalent to equation (A7), except for the approximation of the percentage change in the capital stock to Δ logK(t), which in any case is not essential. Note that, since K(t) > 0 for all t, equation (A7) implies that the term δ + logK(t) must be positive so long as gross investment, I(t), is positive. Thus, equation (A8) is a valid transformation of equation (A7).

We also assume that total factor productivity evolves according to

where ε(t) is a stationary (but possibly serially correlated) stochastic disturbance.

Substituting from equations (A8) and (A9) into equation (A5),


Now, if the time series for investment, output, level of the capital stock, and factor prices are integrated of order one (as most macroeconomic time series are), then from the definition of v(t) given in equation (A11), we see that equation (A10) must be a cointegrating relationship (Engle and Granger (1987)).

The analysis can be generalized to a multiperiod optimization problem as follows: note that unless there are costs of adjustment in the capital stock, the multiperiod optimization solution is equivalent to the static one-period solution just outlined. Thus, introducing costs of adjustment of the capital stock, the representative firm’s optimization problem can be represented as11

subject to equation (A2), where ß is a discount factor. From the Hamiltonian conditions for the solution of this problem, an expression can be derived that is identical to equation (A10) except for additional I(0) terms in the composite error term v(t), which nevertheless remains I(0). Thus, equation (A10) again emerges as a cointegrating relationship. This is the justification for equation (1), the long-run investment demand function used in the text.

An interesting implication of cointegration is that, by the Granger Representation Theorem (Engle and Granger (1987)), if investment is cointegrated with the right-hand-side variables in equation (A10), there must exist a dynamic error correction representation of the form

where v(t) is the error correction or equilibrium error implicitly defined in equation (A10), ξ(t) is a disturbance term, and γ4 < 0.

In the static, one-period case, the error correction form is hard to interpret. In the case of dynamic, multiperiod optimization, however, equation (A13) can be interpreted as the solution to the optimization problem in equation (A12), since it is well known that solutions to multiperiod quadratic costs of adjustment problems can be expressed as error correction equations (Nickell (1985), Taylor (1987)). This is the justification for equation (2), the short-run investment demand function used in the text.

Note that we could equally well have used equation (A6) as our cointegrating relationship, and derived an error correction equation analogous to equation (A13) in terms of ΔlogK rather than ΔlogI. The advantage of working with the latter is that this is the series in which we are primarily interested. Although, asymptotically, it should make no difference whatsoever which of these two forms the estimated error correction equation takes, the actual short-run dynamics may differ slightly between the two equations in small samples.

Appendix II: Detailed Empirical Results

I. Unit Root Tests

Table 3 lists the results of unit root tests applied to the logarithmic transformations of investment, output, hours worked, the capital stock, real wages, and the real user cost of capital. In every case, we cannot reject the hypothesis that the series are stationary in first differences, or integrated of order one (Engle and Granger (1987)).

II. The Long-Run Production Function

The theoretical and empirical framework outlined in Appendix I is predicated on the assumption that output, at least in the long run, is governed by a Cobb-Douglas technology in labor and capital. Thus our first task was to investigate whether or not a cointegrating relationship exists that approximates a Cobb-Douglas production function.

Table 4 reports results of estimating the long-run relationship between logY(t), logK(t), and logL(t) by ordinary least squares, Johansen (1988) maximum likelihood estimation, and Phillips-Loretan (1991) estimation. In each estimation method, allowance was made for a linear trend to enter the long-run relationship, capturing the assumption of an exponential trend in total factor productivity (equation (A9)).

Table 4.Cointegration Estimates of the Long-Run Production Function
(a).Ordinary least squares
log Y(t) = 0.637 logL(t) + 0.447 logK(t)
R2 = 0.99, ADF = -2.816
(b).Johansen maximum likelihood
i)Cointegration tests (r = number of cointegrating vectors)
Null hypothesisTRACE statistic5% critical valueNull hypothesisλ-max statistic5% critical value
r < 21.4623.762r = 2 vs. r = 31.4623.762
r < 19.21115.410r = 1 vs. r = 27.75014.069
r = 035.41329.680r = 0 vs. r = 126.20220.967
ii)Estimated cointegrating vector
logY(t) = 0.291 logL(t) + 0.886 logK(t)
(i)Estimated cointegrating vector
log Y(t) = 0.579 logL(t) + 0.523 logK(t)
(ii)Restricted cointegrating vector
log Y(t) = 0.6 logL(t) + 0.4 logK(t)
WALD(2) = 0.983
Notes: Allowance was made for a trend in the cointegrating equation in each case. Four lags were used in the VAR estimation for the Johansen method. For the Phillips-Loretan method, two lags of the cointegrating vector and two leads and lags of changes in investment and man-hours were used. In panel (c), WALD denotes a Wald test statistic for the restrictions, with marginal significance level in parentheses. The critical values for the ADF test in panel (a) are from MacKinnon (1991). The critical values in panel (b) are from Osterwald-Lenum (1992).
Notes: Allowance was made for a trend in the cointegrating equation in each case. Four lags were used in the VAR estimation for the Johansen method. For the Phillips-Loretan method, two lags of the cointegrating vector and two leads and lags of changes in investment and man-hours were used. In panel (c), WALD denotes a Wald test statistic for the restrictions, with marginal significance level in parentheses. The critical values for the ADF test in panel (a) are from MacKinnon (1991). The critical values in panel (b) are from Osterwald-Lenum (1992).

The results reported in Table 4 are reassuring in the sense that the three methods produce quite similar results. We are unable to reject the null hypothesis of noncointegration using an augmented Dickey-Fuller test applied to the cointegrating regression residuals. However, the poor power characteristics of the ADF test are well known and, using the Johansen techniques, we find strong evidence of a unique cointegrating vector.

The least squares results are also noteworthy in that the estimated coefficients are close to the values suggested by economic theory—that is, the sample factor shares in output of 0.6 and 0.4 for labor and capital, respectively. The Phillips-Loretan method, which has been shown to have superior small-sample performance (Phillips and Loretan (1991)), also produces coefficient estimates that are insignificantly different from their theoretical values.

Although we would not wish to claim that French manufacturing and business output can be completely explained by a simple Cobb-Douglas production function (see, e.g., Coe and Moghadam (1993)), these results nevertheless imply that the salient long-run characteristics can be captured by such a model. This at least allows us to investigate the existence of the implied long-run investment function.

III. The Long-Run Investment Function

The results of applying the various cointegration estimation methods to investment, output, the user cost of capital, and the wage rate, are given in Table 5. Note that, because of the difficulties in estimating nonlinear models with a very large number of parameters, we constrained factor rentals to enter in relative terms in the Phillips-Loretan estimation, thereby substantially reducing the dimensions of the parameter space.

Table 5.Cointegration Estimates of the Long-Run Investment Function
(a).Ordinary least squares
log I(t) = 2.138 logY(t) − 0.293 logρ(t) + 0.417 logw(t)
R2 = 0.96 ADF = −3.165
(b).Johansen maximum likelihood
i)Cointegration tests (r = number of cointegrating vectors)
Null hypothesisTRACE statistic5% critical valueNull hypothesisλ-max statistic5% critical value
r ≤ 32.6363.762r = 3 vs. r = 42.6363.762
r ≤ 222.53615.410r = 2 vs. r = 319.90014.069
r ≤ 145.22429.680r = 1 vs. r = 222.68820.967
r = 081.01747.210r = 0 vs. r = 135.79327.067
ii)Estimated cointegrating vector (corresponding to largest eigenvalue)
logI(t) = 0.960 logY(t) - 0.719 logρ(t) + 0.124 logw(t)
(i)Estimated cointegrating vector
logI(t) = 1.196 logY(t) - 0.199 logρ(t)/w(t)
(ii)Restricted cointegrating vector
logI(t) = 1.0 logY(t) - 0.6 logρ(t)/w(t)
WALD(2) = 0.074
Notes: Allowance was made for a trend in the cointegrating equation in each case. Four lags were used in the VAR estimation for the Johansen method. For the Phillips-Loretan method, two lags of the cointegrating vector and two leads and lags of changes in investment and man-hours were used. In panel (c), WALD denotes a Wald test statistic for the restrictions, with marginal significance level in parentheses. The critical values for the ADF test in panel (a) are from MacKinnon (1991). The critical values in panel (b) are from Osterwald-Lenum (1992).
Notes: Allowance was made for a trend in the cointegrating equation in each case. Four lags were used in the VAR estimation for the Johansen method. For the Phillips-Loretan method, two lags of the cointegrating vector and two leads and lags of changes in investment and man-hours were used. In panel (c), WALD denotes a Wald test statistic for the restrictions, with marginal significance level in parentheses. The critical values for the ADF test in panel (a) are from MacKinnon (1991). The critical values in panel (b) are from Osterwald-Lenum (1992).

Again, the results are encouraging in that broadly similar results are obtained using any of the three methods. We are again unable to reject, at the 5 percent level, noncointegration on the basis of a cointegrating regression ADF test, but find evidence of up to three cointegrating vectors using the Johansen method.

For all three methods, the estimated coefficients are correctly signed and, for the Johansen and Phillips-Loretan results, the output coefficients are close to unity. A Wald test of the restrictions that the output coefficient is unity and the coefficient on relative factor rentals is -0.6 is not rejected (panel (c)).

Overall, therefore, these results were very encouraging indeed, and strongly implied that a search for a stable, dynamic short-run investment function incorporating these long-run results would be fruitful.

IV. The Short-Run Investment Function

The next step was to estimate a short-run, dynamic error correction equation which could be interpreted as a short-run investment function. Since, in the previous section, we could not reject the theoretical restrictions on the long-run investment function, our error correction or equilibrium error term was defined as follows:

Starting with a general dynamic form corresponding to equation (A13) with n = 4 lags, we sequentially imposed statistically insignificant zero restrictions until a final parsimonious specification remained upon which no further statistically insignificant restrictions could be placed.

The resulting parsimonious specification was as follows:

The estimated short-run equation is quite encouraging in that a reasonable fit is obtained with well-determined coefficients that are intuitively of the correct sign, and the equation also passes a battery of regression diagnostics.12

When the model is estimated retaining the last five years of data for postsample forecasting tests, we obtain

Clearly, the equation parameters appear to be stable and the fit and regression diagnostics are again satisfactory. Particularly impressive are the results of the Chow (1960) and the Hendry (1979) tests for predictive failure over the last five years of the sample (CHOW and HF respectively): they are both highly insignificant.

As a comparison, we also estimated an accelerator model of investment of the kind estimated by Muet and Véganzonès (1992):

This resulted in an estimated equation with an R2 of 0.47 and a Durbin-Watson statistic of 0.28 (suggesting dynamic misspecification). We then carried out formal tests of the two estimated equations as alternative models of investment. First, we multiplied the fitted values from equation (A17) by Y(t) and took logarithms and then first differences of the resulting series, to obtain implied fitted values of ΔlogI(t). Regressing the actual values of ΔlogI(t) onto the fitted values of ΔlogI(t) from the estimated error correction model and the implied fitted values from the accelerator model (using superscripts ecm and acc to denote fitted values from the error correction and accelerator models respectively), we obtained

where standard errors are given in parentheses. Clearly, the implied fitted values of the accelerator model contain no extra information with respect to the growth of investment over the information supplied by the error correction model. In that sense, the error correction model encompasses the accelerator model (Mizon (1984)).

To avoid the charge of unduly biasing the test against the pure accelerator model, we also carried out the converse exercise of calculating the implied fitted values of [I(t)/Y(t)] from the estimated error correction model [I(t)IY(t)]ecm, and regressed the actual values of [I(t)/Y(t)] onto these and the fitted values from the accelerator model [I(t)/Y(t)]acc, obtaining

Again, the pure accelerator model provides no additional information and is encompassed by the error correction equation.


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Technically, the short-run production technology appears to be closer to the Leontief or fixed factor proportions type, while the long-run production function appears well approximated by a Cobb-Douglas function.

This survey is highly selective. A more thorough and comprehensive survey of the theory and evidence relating to the French investment function can be found in Artus and Muet (1990).

See Schramm (1970) and Jorgenson (1967) for applications to U.S. data.

For instance, Jorgenson (1967), Jorgenson and Stephenson (1967a, 1967b, 1969a, 1969b), and Hall and Jorgenson (1971).

In the Jorgenson model, investment is conditioned on output and the real user cost of capital rather than relative factor rentals alone or relative factor rentals and output. It really is, therefore, “neither fish nor fowl.”

The usual accelerator model explains investment or the investment-output ratio as a function of changes in output, rather than having changes in investment as the dependent variable. In this chapter, however, we shall speak of the whole class of investment functions in which investment is explained solely by a distributed lag of changes in output as flexible accelerator-type models.

Flux et Stocks de Capital Fixe, OECD, Paris.

This value was suggested by economists at the French Direction de la Prévision. Setting δ as low as 2 percent per annum or as high as 15 percent per annum made no qualitative difference—and slight quantitative difference—to the results reported below.

Although, in MULTIMOD, some of the effect on investment comes indirectly through the effect on output. See Masson, Symansky, and Meredith (1990).

A proof of Shephard’s lemma can be found in Varian (1978), chap. 1.

Note that, for simplicity, we assume certainty equivalence.

AR(4, 75) is a test for up to fourth-order residual serial correlation; ARCH(1, 77) and ARCH(4, 71) are tests for first-order and up to fourth-order autoregressive conditional heteroscedasticity in the residuals; WHITE(18, 60) is White’s (1980) test for general heteroscedasticity or functional misspecification; HETX2(10, 68) is a test for heteroscedasticity based on the squares of the regressors; RESET(3, 76) is a test for nonlinear specification, based upon adding powers of the fitted values to the regression. All test statistics are distributed as F under the null hypothesis with the indicated degrees of freedom. A discussion of the diagnostic tests can be found in Cuthbertson, Hall, and Taylor (1992).

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