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Energy and economic growth in the USA A multivariate approach

David I. Stern

This paper examines the causal relationship between GDP and energy use for the period 1947-90 in the USA. The relationship between energy use and economic growth has been

examined by both biophysical and neoclassical economists. In particular, several studies have

tested for the presence of a causal relationship (in the Granger sense> between energy use andeconomic growth. However, these tests do not allow a direct test of the relative explanatory powers of the neoclassical and biophysica2 models. A multivariate adaptation of the test-vector autoregression ( VAR) does allow such a test. A VAR of GDP, energy use, capital stock and

employment is estimated and Granger tests for causal relationships between the variables are carried out. Although there is no evidence that gross energy use Granger causes GDP, a measure ofjinal energy use adjustedfor changing fuel composition does Granger cause GDP.

Kqwords: Energy use; GDP; Causality

Some ecological economists, such as Ayres and Nair [S] have proposed a biophysical model in which energy is the sole primary factor of production as determined by the Laws of Thermodynamics. Though the literature of biophysical economics, such as the study by Cleveland et al [ 161, has provided much evidence of the importance of energy in economic production, these researchers start from an initial assumption of the importance of energy and do not control for the contribution of the other possible factors of production. Neoclassical economists such as Berndt [S] and Denison [ 19, 201 conclude that energy is not likely to be very important in causing economic growth. I believe that their conclusions were strongly influenced by their maintenance of a priori assumptions that energy influences economic growth only in certain ways, and that these maintained hypotheses influenced the construction of their empirical investigations. Research that could help assess the relative strengths of the biophysical and neoclassical explanations of economic production must use methods that incorporate a minimum of maintained hypotheses.

The author is with the Center for Energy and Environmental Studies, Boston University, 675 Commonwealth Avenue, Boston, MA 02215, USA.

Final manuscript received 23 November 1992.

Granger [26] tests can be seen as a methodology for testing the validity of maintained hypotheses [ 52, 533. Kraft and Kraft [ 361, Akarca and Long [3], Yu and Hwang [69], Abosedra and Baghestani [ 11, and others who used Granger tests to examine the presence or absence of a causal relationship between energy use and GNP in the USA obtained inconclusive results. Where significant results have been obtained, they contradict the postulates of biophysical econo- mics. These statistics may refute biophysical models or be the result of the inappropriate design ofthe tests.

This paper examines the relationship between energy, capital, labour and GDP in the US macroeconomy between 1947 and 1990. A vector autoregression (VAR) of energy, capital, labour and GDP is estimated. This methodology was developed by Sims [53] for carrying out macroeconomic modelling and hypothesis testing under a minimum of maintained hypotheses. The methodology al1ow.s for the examination of the ‘marginal’ causal relationships between the factors of production and output, by means of Granger causality tests. The results do not indicate that changes in gross energy use cause economic growth, but economic growth is found to Granger cause changes in gross energy use. However, there are scenarios under which this test would fail to detect a causal relationship. To account for one of these possibilities, I replace gross energy

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Energy and economic growth in the USA: D. I. Stern

use with an index of final energy use weighted for the changing fuel composition of the energy input, and obtain statistically significant results for causation running from energy use to GDP. Finally some conclusions are presented.

Literature review

One of the most important presentations of biophysical economics is the study of energy and the US economy by Cleveland et al [ 16 J. Though there has been much research since, it is still a good survey of the main propositions and empirical findings of biophysical economics. Their work represents a significant advance from the embodied energy theories of Odum and Odum [40] and Costanza [ 171 in integrating the biophysical approach with conven- tional economics and addressing central questions such as the sources of economic growth. Their principal finding is that there is a very strong correlation between energy use and GNP in the US economy (see Figure 1) and that changes in the energy/GNP ratio can largely be explained by shifts in the mix of fuels used and in the direct and indirect use of fuel. But studies of this type avoid testing the hard-core propositions [37] of biophysical economics that energy is the ultimate source of all economic value and the single primary factor of production. In particular, no tests are carried out where all possible

400 -

350 --

300 --

250 ~- 8

s c 200 --

E 150 -~

GEP

Figure 1. US gross energy use and GDP.

138

contributions of other factors of production are controlled for. In fact, the correlations of the labour input and capital input variables with GNP are greater than that of gross energy use and GNP. However, as biophysical economists assume from a thermodynamic perspective that there is an a priori causal relationship between energy use and the production of output, and that capital and labour are intermediate factors that require energy and materials for their production and maintenance [27], they do not interpret these correlations as evidence for a causal relationship. Of course, as Sayer [48] emphasized, attention must be paid to causal relations in empirical investigations, but other structures of causal relations are equally plausible a priori. Most neoclassical economists hold a priori assumptions, which translate into maintained hypotheses in econometric studies, that energy has a relatively minor role in economic production, and is an intermediate input produced by capital, labour and land that are the primary factors of production. Those neoclassical economists who suggest that energy might play a larger role in the economy, such as Hamilton [28] and Burbridge and Harrison [ 131, stop well short of the biophysical position. All of the following studies attempted to assess the effect of energy use or energy prices on economic output within a neoclassical framework.

Burgess [ 143 represents a methodological tradition following from the work of Hogan and Manne [31] and others, building a theoretical model based around a production function to test the effects of an increase in the world relative price of energy on potential GNP, income distribution, capital formation and economic welfare. This approach applies perhaps the most a priori restrictions, and is based entirely on simulations using a mathematical model without the introduction of any empirical data. Values for coefficients in the simulation are, however, taken in part from empirical studies. The conclusion is that real income losses due to the inflationary effects of an oil price rise may cause a greater income loss for capital than for labour, and a subsequent reduction in capital formation and potential GDP growth. However in an economy such as the USA a stimulus will occur to capital accumulation in the energy production sectors which may offset the decline in GDP in the rest of the economy. Biophysical economists regard this capital accumulation as a cost rather than a benefit of economic growth [ZS, 353.

One group of studies [8, 10, 19, 203 does not use rigorous mathematical or econometric methods but still incorporates many a priori restrictions on the types of interactions possible between energy and output. Bohi [lo] attempted to carry out a comprehensive survey of the role of energy in the

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overwhelming role for energy postulated by bio- physical economics. However, the assumptions are restrictive and the functional form may also introduce bias [19].

Renshaw [43] carried out a similar study of the energy-GNP relationship for 1949-79. He regressed the annual percentage change in GNP on the annual percentage changes in hours worked, real fixed private domestic investment, and energy use, and also a time trend and the Federal Reserve Board index of capacity utilization. He estimated that the energy output elasticity was 0.09 which was insignificantly different from zero. But the time trend coefficient was negative which casts doubt on the validity of the equation as a whole, as does a negative coefficient for the capacity utilization rate. The capital variable is definitely misspecified ~ the investment/output ratio is normally used in a growth equation of this type. Also the growth rates form does not allow for lagged effects of changes in the factors of production.

Kaufmann and Azary-Lee [34] used a similar production function approach to analyse substitution between energy and capital in the US forest products industry. Their estimate of the output elasticity of energy was 0.1295 which was remarkably close to Rasche and Tatom’s [42] estimate. However, this was an estimate for a single sector and the estimate of energy use is direct energy use not including energy used in the production of inputs and capital used in the sector. The fact that much energy is used indirectly is an important proposition of biophysical economics [16, 271.

A weakness of all studies based on production functions is that it is possible to estimate any form of the production function. A high correlation between energy use and economic growth may indicate that growth promotes energy use, but energy use may not be essential to economic growth. Jorgenson [33] suggests that energy may not be essential for economic growth per se, but that it is essential for implementing the majority of new technologies and thus for productivity growth. He follows Schurr et al [49, SO] and Rosenberg [46] who emphasized the links between the introduction of new energy technologies, especially electricity using technologies, and periods of intensive economic growth. Jorgenson [ 313 used econometric translog price functions for individual US industrial sectors to determine the bias in technical change in each of these sectors. In most sectors technical change was biased either towards an increased use of electricity or an increased use of non-electric energy. He explains that the slow-down in US productivity growth since 1973 was a direct result of the increases in energy prices and their impact on the implementation of new technologies. The

macroeconomy, in order to assess whether the oil price shocks of the 1970s were really responsible for the subsequent recessions in many countries. Bohi concluded that changes in money supply and not changes in energy prices were the cause of recessions in a number of Western countries. However Bohi’s analysis is rather weak as it is not based on econometric or rigorous mathematical methods. He mentions a number of econometric modelling efforts such as those of Hamilton [28], Burbridge and Harrison [ 131, and Hickman et al [ 301, which all reach opposite conclusions. However, these results are rejected in favour of his own descriptive methodology, despite Bohi’s apparent awareness of its limitations

(P 6). Denison [ 19, 203 and Berndt [ 81 both examined

the possible size of the contribution of the rises in energy prices in 1973 and 1979 to the downturns in total factor productivity after those dates. Both concluded that higher energy prices could have only a very minor effect on productivity growth. Denison [20] pointed out that in both years the slowdown appeared to have started at least half a year prior to the rise in oil prices and he therefore doubted that oil prices could have been very important in causing the recession. But the rise in oil prices could have deepened the recession that was already under way [ 131. Based on the decline in the growth rate of the energy-output ratio from its 1948-73 average growth rate and the level of the energy-output ratio in 1973-81, Denison [20] estimated that higher energy prices led to a 0.14 percentage point decline in total factor productivity growth in the latter period relative to the former. The assumptions behind these calculations are, however, very restrictive in terms of the types of responses to energy prices that are considered. Berndt [S] reaches similar conclusions for similar reasons. He found it difficult to reach any solid conclusions using more sophisticated methods.

Some studies have introduced energy use as one variable of a vector of factors of production. These studies are generally less restrictive than the former groups. Rasche and Tatom [42] were perhaps the first to introduce energy use into an aggregate production function for the US economy. They estimated an aggregate production function for the USA between 1949 and 1975 using a CobbbDouglas function, but introduced various restrictive assumptions : energy use data were derived by the profit-maximizing condition from the relative energy/business sector price deflators rather than from actual consumption data. Similarly constant returns to scale were assumed in the economy as a whole and the sum of output elasticities was restricted to one. Their estimate of the energy output elasticity was 0.1363 which is low compared with the

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weakness in this argument is that Jorgensen estimated the factor bias in technical change using data for 1958-79, and he does not examine any change in the bias of technical change after 1973. As the value share of energy in costs increased after 1973, technical change was more likely to be directed to reducing energy costs. In other words historical data showing that productivity growth has tended to be accom- panied by energy intensification does not mean that energy intensification is essential to productivity growth per se. Jorgensen’s idea may be valid but is not adequately tested. He is perhaps unique among the neoclassical economists in considering the productivity as well as the quantity of energy use in the economy.

Various studies have attempted to determine whether there is a causal relationship between energy use and output and what the direction of causation is. Kraft and Kraft [36] found using Sims’ [ 523 causality test, that in the period 1950-70, GNP caused energy use and not vice versa. Akarca and Long [3] also used Sims’ test though they incorporated a contemporaneous term. They found that for the period 1950-68 causal relationships were insignificant unless the contemporaneous terms were included. Yu and Hwang [69] also found using Sims’ test that for the period 1947-79 no causality was present, while for 1973-81 using quarterly data causality was found to run from GNP to energy use. This last result suggests that the lack of causality found in other tests may be due to the annual lags used. Yu and Choi [68] also found a lack of causality in their international studies. Ammah-Tagoe [4] found using Sims’ test on annual data for Ghana for 1965-87 that a significant causal relationship ran from GDP to total energy use but not vice versa. Abosedra and Baghestani [l] used a Granger test with a contemporaneous term and first differenced logarithms of the time series for the USA. They found that for equations with contemporaneous terms mutual causation occurred, while in the equations without contemporaneous terms only data for 1947-74 showed any indication of causality from GNP to energy use. A possible problem with their test involving a contemporaneous term is the presence of simultaneity bias. I also argue that a test incorporating a contemporaneous term in the vector of independent variables cannot distinguish between instantaneous Granger causality and simple correlation. These and the other results indicate that there may be causality running from GNP to energy use though the majority of the effect may be transmitted in less than a year. None of these studies provides any evidence to corroborate the biophysical model.

There has been much criticism levelled at these techniques in the econometrics literature. Roberts and

Nord [44] found that the functional form of the time series affected the sensitivity of both Granger’s and Sims’ test. They found that data that had undergone logarithmic transformation showed no sign of causality while the untransformed data yielded significant results. This stands to reason as logarithmic transformation tends to reduce heteroscedasticity and increase the stationarity of the variables. However Chowdhury [ 151 found more disturbing results that give support to those who have doubted whether Granger causality was related to philosophical causality or economic exogeneity in any meaningful way. He found that a Granger test indicated that GNP causes sunspots ! A Sims test showed that prices caused sunspots ! None of the alternative hypotheses were validated. Prices and income may be exogenous in the sunspot equations, but sunspots are not endogenous in any meaningful philosophical or economic way.

Sims and others developed a more comprehensive form of econometric analysis : vector autoregression (VAR) [47, 531. VAR was seen by Sims [53] and Sargent [ 473 as a method of carrying out econometric analysis with a minimum of a priori assumptions about economic theory. The VAR approach to econometrics has also come under very heavy fire in the literature. The critics, such as Epstein [22] and Darnell and Evans [ 181, do, however, argue that the only useful purpose of a VAR in testing economic theory is as a multivariate Granger causality test. In this paper, I use VAR as a generalized method of testing a priori assumptions by means of the multivariate Granger test, prior to the construction of econometric models used to test more detailed hypotheses. VAR is being introduced in this way in an increasingly large number of empirical studies.

The advantage of multivariate Granger tests over bivariate Granger tests is that they can help avoid spurious correlations and can aid in testing the general validity of the causation test. If Chowdhury [ 151 had estimated a VAR on sunspots, GNP, and, for example, the Sun’s magnetic activity, he may have found causation between magnetic activity and sunspots but none between income and the other variables, once the causal effect of magnetic activity was taken into account. Though a VAR cannot, due to limits on degrees of freedom, include all variables that may be causally related to the principal variable under investigation, some attempt can be made to include as many as possible. In the context of the energy-output relationship, including capital and labour in the VAR might help avoid any spurious correlations between energy and output. If no causal relationships are found between any of the variables and output, doubt will be cast on the sensitivity of the test to causal relationships between output and the

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factors of production, as most of the principal factors of production will be included in the equation. A lack of sensitivity could be due to a misspecified lag length, insufficiently frequent observations, or the lack of Granger causality even if philosophical causation occurs. Also, in the bivariate test, if the capital and labour inputs decrease while energy increases, one may not see any Granger causation from energy to output. The VAR approach holds the inputs of the other factors of production constant and allows one to observe the marginal effect of energy use on output. Finally, it allows the investigation of indirect channels of causation from energy use to GDP as it incorporates equations explaining the level of the capital and labour inputs.

Hamilton [28], Burbridge and Harrison [ 131, and Mork [39] used vector autoregressions in the energy-output context. Hamilton [28] used Sims’ [53] VAR, with the addition of a seventh equation to account for oil prices, to examine the relationship between oil prices and the US economy in 1949-72. Hamilton found that changes in oil prices Granger- caused changes in GNP and unemployment whereas oil prices were exogenous in the system. Mork [39] extended Hamilton’s [28] analysis to the late 1970s and the 1980s when oil prices both rose and declined. He found that there was no causal relationship between oil prices and GNP in periods of declining oil prices. Burbridge and Harrison [ 131 used a slightly different set of variables (oil prices, non-domestic OECD growth, real interest rates, money supply, wages, consumer prices and industrial production) for 1962-82 in the USA, Japan, Germany, UK and Canada. They reached essentially the same conclu- sions as Hamilton [28] for the 1973-74 recession. But for the early 1980s recession Burbridge and Harrison [ 131 find little evidence that the changes in oil prices in 1979-80 had much of an effect on industrial output or inflation. One problem with each of these three researchers’ analyses is the seemingly unreasonable a priori exclusion of factor inputs from the output equation which reflects the biases of conventional macroeconomic theory.

Multivariate causality test

A four equation VAR was set up on annual US GDP, energy input, capital input and labour input for 1947-90. US GDP data are in constant 1982 dollars and are from the National Income and Product Accounts as formulated prior to the 1991 comprehensive revision 1611. This is as, at the time of writing, the new estimates were only available from 1959 on. I

define the capital input as the net capital stock multiplied by the rate of employment of labour. I prefer this measure to the Federal Reserve capital utilization rate, as the latter only refers to capital in the manufacturing sector. The net capital stock is defined as the sum of net fixed private non-residential capital and net fixed government-owned capital. The net capital stock is in 1987 prices as these were available from 1925 on. The labour input is measured by full-time equivalent employees. The energy input is measured in British thermal units (1 Btu = 252 calories = 1059 Joules). Full details of data sources are supplied in the Appendix. The generalized form of the VARs used in this paper is:

f(GDP,) = 4,Ql + u11 (1)

&f(K) = x:,a2 + Uzt (2)

.f(Jk) = a3 + U3t (3)

f(E,) = 04 + u41 (4)

x:, = Cl,f(GDP,-,), . . . ,f(GDP,-,I,

f(K,-I ), . . * 9 f(K,-,L

f(L 113 . . . > f(-L,L

f(J%-I 12 . . .Y f(L)1 (5)

where GDP is gross domestic product, K is capital input, L is labour input, and E is energy input. f( ) is a function, and r is the number of lags. The ai are ((4. r ) + 1) x 1 vectors of regression coefficients. There are two major specification issues for a VAR in this context: functional form and lag length. Four functional forms were considered : logarithms with no differencing, first differences of logarithms, levels with no differencing, and first differences of levels. Four lag lengths were also considered : one, two, three and four annual lags. Differencing is often advocated to achieve the residual whiteness conditions required for causality tests [50]. In order to determine the optimum lag length for the VAR, I used the likelihood ratio test proposed by Sims [53] :

(T - c)lln(U) - ln(l~,I)I (6)

where T is the number of observations, & and Z” are the restricted and unrestricted residual covariance matrices, and c is a correction factor equal to the number of independent variables in one of the unrestricted equations. The statistic is asymptotically distributed as ~2, where k is equal to the number of restrictions, in this case the product of the number of omitted lags, the number of variables, and the number of equations. The null hypothesis H, is that the smaller restricted lag length is true.

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Table 1. Likelihood ratio tests for lag length: levels model.

Null hypothesis H, : lag length =

I 2 3

Alternative hypothesis H, : lag length = 2 43.2453

0.0003

3 57.1542 19.4889 0.0041 0.2441

4 64.8634 33.6041 16.1765 0.0527 0.3896 0.4407

Nofe: Significance levels of I* statistics in italics. Sample period is 1951-90.

Table 2. Likelihood ratio tests for lag length : first-ditTerenced levels model

Null hypothesis H, : lag length =

1 2 3

Alternative hypothesis H, : lag length = 2 13.3201 _ _

0.6492

3 29.5368 10.3115 _

0.5918 0.8499

4 34.1529 24.3848 15.6591 0.9342 0.8302 0.4770

Note: Significance levels of x2 statistics in italics. Sample period is 1952-90.

Tables l-4 present the likelihood ratio tests for lag length for each of the four different functional forms. I selected a 5% level of significance for all these tests. In the undifferenced levels model (Table 1) the single lag model is clearly rejected. In the test between two and three lags, the two lag model is accepted. Therefore two lags was chosen as the optimal length. In the first-differenced levels model (Table 2 ) the single lag structure is accepted in tests against all three alternative hypotheses. In the case of the undifferenced logarithmic model (Table 3), the single lag structure is rejected in tests against all three alternative hypotheses and the two lag structure is accepted in a test against the alternative three lag structure. Finally a lag length of one was selected for the first-differenced logarithmic model (Table 4) in tests against all the alternative hypotheses.

To determine the most appropriate functional form I use the Akaike Information Criterion (AIC) [Z] . For the levels and differenced levels models AIC takes the form :

AIC = 1 + ln(2l-I) + ln(a’) + q

where k is the number of regressors and T the number of observations. 0 is the standard error of the appropriate regression. For the logarithmic and differenced logs models AIC takes the form [29] :

AIC= 1 +ln(2n)+ln(o’)+~ k+ i ln(y ) T[ f=l ‘] (8)

where y is the untransformed dependent variable. Table 5 presents the AIC for each equation of the selected version of each model. With the exception of the energy equation, the logarithmic model is superior to the other three models. The mean of the AIC for the four equations is also lowest in this case. Therefore the un-differenced logarithmic model was selected for all further tests.

Table 6 presents the results of the Granger tests, the adjusted multiple correlation coefficient, fi2, and the Box-Pierce [ 121 Q-statistic for each equation of the logarithmic model. All the equations easily pass the residual whiteness test at the 10% level and fit the

Table 3. Likelihood ratio tests for lag length: logarithmic model.

Null hypothesis HO: lag length =

1 2 3

Alternative hypothesis H, : lag length = 2 51.6345 _ _

0.0000

3 47.4894 22.5174 _

0.0002 0.1273

4 8 1.8404 43.5309 24.3494 0.0017 0.0840 0.0821

N&e: Significance levels of x2 statistics in italics. Sample period is 195 I -90.

Table 4. Likelihood ratio tests for lag length: first-differenced logarithmic model.

Alternative hypothesis H, : lag length =

Null hypothesis HO : lag length =

1 2 3

23.3236 0.1054

38.7263 18.5126 0.1921 0.2947

62.8332 45.1292 30.0648 0.0739 0.0549 0.0177

Nore: Significance levels of x2 statistics in italics. Sample period is 1952-90.

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data very well. Each F-statistic is a test of the joint significance of the two lagged values of the independent variable on the left, in the equation explaining the relevant dependent variable. The final column in the table lists the chi-square statistic for the joint significance of the lagged values of the independent variable at left in the equations explaining the other three variables. Clearly energy use is endogenous, its lagged values are insignificant in each of the other equations and jointly in the three equations. Under the assumptions of the model, we should accept the null hypothesis that energy does not Granger-cause economic growth. The lagged values of labour and capital are both highly significant in

Table 5. Akaike information criterion for four functional forms of the VARs.

Functional form Y A’(Y) In(y) A’(lu(y))

Lag length 2 1 2 1

Dependent variables

GDP 52.1416 52.2351 51.8705 52.1211 Capital 52.2566 52.3298 51.9519 52.4237 Labour 30.8343 31.0176 30.8420 31.3076 Energy 72.8335 72.9066 72.9107 73.0905

N&e: Sample period is 1949-90.

Energy and economic growth in the USA: D. I. Stern

explaining GDP. Under the assumptions of the model, we should accept the hypothesis that capital and labour both Granger-cause economic growth. GDP Granger-causes all three factors of production. This is in line with the standard theory of production and derived factor demand, and regarding energy, with some previous research results [ 1,4,36,69]. Changes in labour input, induce changes in energy use, but changes in capital input are insignificant in causing changes in energy consumption. Changes in labour and capital input are mutually Granger-causative.

The signs of the partial derivatives are the sign of the sum of the two lag coefficients if they are jointly significant and zero otherwise. All the derivatives have the expected sign. The derivatives of the factors of production with respect to GDP are all positive as expected from the theory of derived demand. The derivatives of the factors of production with respect to the factors of production, holding output constant, are negative or zero, consistent with substitution along an isoquant of a production function. Labour and capital are substitutes, as are labour and energy, but there is an asymmetric substitution relationship between energy and labour. An increase in labour ceteris paribus decreases energy use as expected but an increase in energy use does not cause labour use to decline again (the sign is negative but insignificant ). Capital and energy are neither substitutes nor complements. Some previous research [9,24, 321 has

Table 6. Vector autoregression with two lags of logarithms of variables 1949-90: Granger tests. __- -__

Dependent variables

GDP La bour Capital Energy All equations

Independent variables

GDP 5 1.2300 21.2323 22.8766 9.0908 35.9531 0.0000 O.IZE-05 0.6E-06 0.7163E-03 0.28E-05

dL/aGDP>O aK/aGDP>O ?E/aGDP>O

Labour 13.6457 14.8743 16.9992 15.8176 27.8717 0.48OE-04 0.24SE-04 0.84E-OS 0. I52E-04 0.993E-04

aGDPIaLi0 dKJdL co c?E/(?L <O

Capital 8.3956 9.3884 21.7103 2.2687 22.4532 O.II28E-02 0.59/9E-03 O.IOE-05 0.1193 O.I002E-02

aGDPldKi0 aLlaK ~0 AEJdK =0

Energy 0.5850 0.0333 0.0131 46.9532 5.2760 0.5628 0.9673 0.9870 0.0000 0.5089

aGDP/aE=O aLjaE=o dK/dE = 0

R2 0.9978 0.9954 0.9992 0.9927 _

Q(18) 13.1392 10.3116 15.4836 22.1837 _ 0.7832 0.9213 0.6285 0.2239

Note: Significance levels in italics. For the within equations restrictions the test statistic is F. For the cross-equations restrictions the test statistic is x2. Signs ofpartial derivatives are the sign of the sum of the coefficients of the two lags if they are jointly significant and zero otherwise.

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shown that energy and capital are complements in the manufacturing sector and in the macroeconomy. The partial derivatives of GDP with respect to the factors of production are negative. This is as lagged values of output are held constant. So a rise in the use of a factor holding output constant means a fall in factor productivity. The result is a fall of GDP in the next period. Vice versa, increasing factor productivity, ie less factors used per constant unit of output causes economic growth. Improvements in energy efficiency do not, however, cause economic growth.

This information can be used to explain the results of bivariate Granger tests that I carried out on the same data set (see Table 7) and illustrate the advantages of the VAR methodology. Neither causation from energy to GDP or from GDP to energy can be supported by the F tests. In the VAR model the full effect of a change in GDP is transmitted to energy use by the following differential :

dE t?E aE aL -= ----AGDP+-- AGDP dGDP aGDP aL aGDP

aE aK ___ AGDP

+ i% i3GDP

The results of the VAR (Table 6) show that aE/aK is equal to zero and therefore the third term on the RHS is equal to zero. The first term on the RHS is positive and the second term on the RHS is negative.

Table 7. Bivariate Changer test: two lags of logarithms of variables 1949-90.

Independent variables

GDP

Energy

Q(lU

Dependent variables

GDP Energy

209.8780 0.342 1 0.0000 0.7125

0.8328 60.7968 0.4428 0.0000

0.9952 0.9865

7.0783 8.6866 0.9894 0.9666

Note: Significance levels in italics.

If those terms are of similar magnitude dE/dGDP will be near zero. In the VAR model labour is held constant and the effect of GDP on energy use is the first term alone. In the bivariate model labour is not held constant and the effect of GDP on energy is the sum of both terms resulting in an insignificant effect.

Discussion of results

Though these tests appear fairly conclusive in their support of the simple neoclassical model of production and growth and their rejection of the simple biophysical model of production and growth, I argue that the estimators are biased and that the statistical tests based on them are therefore potentially misleading. The sources of potential bias fall into three formal categories : errors of measurement of variables, omitted variables and inappropriate functional form. In the remainder of this paper, I concentrate on the first of these, and in particular, measurement of the energy input to economic production. I test for biases of these types by carrying out a test for time-varying regression coefficients. In the version of Breusch and Pagan’s [l l] test used by Slade [54], u,~/s,~ is regressed on the time trend and the square of the time trend, where u are the regression residuals and sU2 their variance. The chi-squared statistic is equal to one half of the explained sum of squares in the subsidiary regression. The statistics are presented in Table 8. In the GDP equation the null hypothesis of no parameter variation can be rejected at the 10% level. In the labour equation the null hypothesis is rejected at the 1% level.

The largest errors of measurement may relate to the energy input. Whereas the labour and capital input variables only include factors that are actually being employed to produce GDP, that is I excluded residential capital, and non-workers, the energy input includes a large volume of energy used in final consumption and not as an intermediate factor in the production of GDP. How one should view this energy use from a production theory perspective is debatable. From a biophysical perspective energy can only add value if it is used to do work. That is, fuels used in

Table 8. Breuscb-Pagan test for random coefficient variation.

Model

Gross energy VAR Quality weighted Energy VAR

Equation GDP

5.4379 0.06594 2.0726 0.3548

Labour Capital Energy

9.8614 1.8608 5.3462 0.007222 0.3944 0.1481 0.88189 0.9782 0.5320 0.6434 0.6132 0.7664

Note: Significance levels of x2 statistics in italics. Sample period is 1951-90.

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Energy and economic growth in the USA: D. I. Stern

final consumption cannot add value in the fuel- production and marketing sectors. The energy in

question is used in the production of non-marketed services such as car trips, residential heating etc which use a non-marketed labour input, and consumer durables and residential capital as a capital input, but these outputs are not included in GDP. It would appear that for the sake of consistency we should remove this energy use from the energy input. Unfortunately this ‘unproductive’ energy is not a fixed proportion of total energy use and there are no

available data for energy used in final consumption as opposed to production. Of course, some biophysical economists [25] argue that all energy used in final consumption is used in ‘supporting’ the labour input. Then, for consistency, we should include residential capital and consumer durables in the capital input. Also indirect energy embodied in imports is not

included in the energy estimates [57]. The US economy can improve its energy efficiency by transferring energy-intensive operations abroad and concentrating low energy operations in the USA. The Office of Technology Assessment [57] estimates that this embodied energy in imports was equal to about 7 quadrillion Btu in 1985 or around 9% of total energy consumption. With the fluctuating trade balances of the 1980s this became a major item in determining energy use. Because this imported indirect energy is partly used directly in final consumption goods, for both domestic and export consumption, and partly incorporated into the embodied energy of domestically produced goods, for both domestic and export consumption, we would have to redefine output as domestic absorption plus exports, or GDP plus imports. There are other well known problems in the definition of GDP. For example if the services provided by fuels used in consumption were included in some measure of social welfare then the first problem mentioned above would not be an issue. The basic problem is that available energy data are not consistent with the national accounts. Measuring the net capital stock is of course another contentious issue as assumptions must be invoked in aggregation and in the estimation of depreciation.

This leads us on to the next issue, the changing quality of the factor inputs. The quality of the energy input depends on the changing mix of fuels and other energy resources that make up energy use. Some biophysical analysts have explained a large part of the changes in energy intensity in the US economy in terms of changing fuel mix [ 161. For example, as electricity is approximately ten times as expensive as coal per Btu, it is reasonable to assume that a Btu of electricity is much more productive, or economically useful than coal is [7, 561. Labour quality or the

quality of human capital has recently become a central issue in growth theory [6, 38, 41, 451. It is more difficult to measure accurately than energy quality is, especially as it is difficult to disaggregate labour into uniform quality classes. Capital should be less problematic than either energy or labour, as the value of the capital stock should express the discounted sum of its productive services. Thus a more technically sophisticated and therefore more productive piece of equipment should be more expensive than a less sophisticated device. This embodiment of technical change in capital accumulation is one of the major difficulties with the traditional approach to creating a breakdown of the sources of growth [ 5 11. However, there may be problems over time in the choice of deflators. A particularly controversial case is the choice of deflator for computer equipment where, in recent years, extremely rapid advances have been

made in the computing power available per nominal dollar [ 571.

The effect of fuel mix and final energy use on economic growth

As a first step in improving the measurement of factor input, I adjusted the energy input for changes in the mix of fuels and for energy used in the production of electricity. Quality weighted final energy use, net of losses in electricity generation, is likely to be a superior measure of the energy input to economic activity as it will reflect better the productivity of the uses to which energy is put. Turvey and Nobay [ 561 weighted the fuels in aggregate energy use by their prices relative to a numeraire fuel, to approximate the variations in quality between different fuels. This type of index is very sensitive to the choice of numeraire. As fuels are not perfect substitutes a rise in the price of one fuel relative to output will not be matched by equal changes in the prices of the other fuels relative to output. For example the rise in oil prices in 1979980 causes an aggregate energy index using an oil numeraire to fall dramatically. An index using a coal numeraire shows a large fall in 1968-74 not indicated by the oil based index. For this reason Berndt [7] proposed using a discrete approximation to the Divisia Index. Diewert [21] showed that this index is an exact index number representation of the linear homo- geneous translog production function, where fuels are homothetically weakly separable as a group from the other factors of production. Though the index does not restrict the elasticities of substitution between fuels, it does assume that the substitution possibilities among all fuel types and output are equal. The formula for constructing the discrete Divisia index E* is:

ENERGY ECONOMICS April 1993 145

Energy and economic growth in the USA: D. I. Stern

InET-InET_,= i

i=l ((

P,$if pit- lEit- 1 +-n

2 ~ PitEi* 2 C Pi,_lEi,-l >

i=l i=l

X (In Ei, - In Ei,-1) >

(10)

where P are the prices of the n fuels i, and E are the quantities of Btu for each fuel in final energy use. The fuel types are oil, natural gas, coal, electricity, biomass and ‘other’. The prices used were the price of Fuel Oil No 2, of natural gas to industrial consumers, of coal to industrial users, and of electricity to all users. I assumed that biomass and the ‘other’ category had a price equal to 60% of the coal price. The Divisia index

1.2Et17 T ,

6E+16

‘lE+16

2E+16 4

of final energy use is plotted against gross energy use in Figure 2 and against GDP in Figure 3.

In order to set up the VAR on the logarithms of GDP, capital, labour and quality weighted final energy use, the log-likelihood tests for lag length had to be repeated. These are presented in Table 9. The single lag structure is rejected in all tests. Setting the significance level at 5%, the two period lag length is rejected in the test against the four period lag length but not against the three period lag. The three period lag is rejected in the test against the four period lag length. Setting the sample period at 1952-90 results in the acceptance of the four period lag at the 6% level in tests against the two, three, and five period lags. AIC statistics and time-varying parameter tests (not

400 -

350 --

300 --

260 ~~

;

f - 200 --

c” -u

E 160 --

II,.,1 ,,,/“\\,_;- ‘- 1’ ;;I

100

50 1

Figure 2. USA : gross energy use and quality weighted final energy use.

Table 9. Likelihood ratio tests for lag length: logarithmic model with quality weighted final energy use.

Alternative hypothesis H, : lag length =

Null hypothesis HO : lag length =

56.44610 _

O.ZIOOE-05

72.84676 23.68350 0.5060604 0.9665&01

92.54139 50.66158 O.l195E-03 O.I923E-01

30.48614 O.l564E-01

No/e: Significance levels of x2 statistics in italics. Sample period is 1951-90.

146 ENERGY ECONOMICS April 1993

Energy and economic growth in the USA: D. I. Stern

Table 10. Vector autoregression with four lags of logarithms of variables 1951-90: Granger tests.

Dependent variables

GDP Labour Capital Energy All equations

Independent variables

GDP 15.3349 4.3061 5.0102 0.8458 21.8062 0.3E-05 0.9569E-02 0.47/4E-02 0.5106 0.3975E-01

SL/SGDP>O dK/dGDP>O SEjsGDP=O

Labour 5.8248 1.9683 3.9339 2.2098 21.3373 0.2175E-02 0.1332 0.2694E-01 0.996OE-01 0.4565E-01

SGDPIliL<O c7K/dL <O dE/dL <0

Capital 4.2670 3.2063 3.9339 1.3607 21.7571 0.9965E-02 0.313IE-01 O.l414E-01 0.2783 0.4033E-01

SGDPIbK <CO dL/SK <O SEjc?K =0

Energy 3.1902 1.5613 1.7851 22.4114 30.6852 0.3188E-01 0.2182 0.1662 O.lE-06 0.22OOE-02

dGDPf?E<O SLjc?E=O aKjaE=O

R2 0.9982 0.9952 0.9992 0.9961 _

Q(l8) 14.4931 13.0788 14.4280 13.5584 _ 0.6964 0.7869 0.7008 0.7574

Note: Significance levels in italics. For the within equations restrictions the test statistic is F. For the cross-equation restrictions the test statistic is 1’. Signs of partial derivatives are the sign ofthe sum of the coefficients of the four lags ifthey are jointly significant and zero otherwise.

Table 11. Bivariate Granger test : four lags of logarithms of variables 1951-90.

Dependent variables

Independent variables

GDP

Energy

rz=

Q(f8)

GDP Energy

106.5578 0.7154 0.0000 0.5878

0.9657 76.9516 0.4402 0.0000

0.995 1 0.9937

6.8654 6.9940 0.9912 0.9902

Note: Significance levels in italics.

reported) showed that as in the case of the gross energy model the best fitting model was the undifferenced logarithms model.

Table 10 presents the results for the four period lag logarithmic model. The most important difference in the results is the significance of the lagged values of energy in explaining GDP. Not only are lagged values of energy significant in the GDP equation, but they are jointly significant in the GDP, capital and labour equations at a 0.22% level of significance. Also the joint cross-equation significance level of the lagged values of energy is much greater than that of capital, labour, or GDP which have significance levels between 3.975% and 4.565%. One problem with these results is, however, that lagged values of GDP are not

ENERGY ECONOMICS April 1993 147

significant in explaining the level of energy use, contradicting the theory of derived demand, though the sign of the relationship is correct. Alternatively, one can view this result as evidence that energy is the only ‘primary’ factor of production. However, this result is sensitive to the sample period used. Removing the last few years from the sample results in a significant statistic. Otherwise the results do not differ from those obtained for the gross energy use model. This result is partially due to the changed definition of the energy input but also partially due to the longer lag length employed. If a four-period lag is used on the gross energy model the coefficients of energy use are jointly significant in the three equations at a significance level of 7%, which is rather higher than that obtained using the two lag structure. The four period structure would be accepted at the 9% significance level in a test against the two lag model. However, even when using a four period lag length gross energy is not significant in the GDP equation alone.

The Lagrange multiplier statistics for coefficient variation demonstrate that this model is better specified than the gross energy model (Table 8). The null hypothesis of no parameter variation can be accepted for each equation. Bivariate Granger tests (Table 11) were still insignificant using the adjusted definition of energy use. Therefore neither the use of the VAR methodology nor the Divisia index of quality weighted final energy is alone sufficient to yield a significant result in the Granger test.

Energy and economic growth in the USA: D. I. Stern

Conclusions

I believe that the methods used in this paper represent a significant advance on the methods used in previous studies of the causal relationship between energy use and economic growth. First, in expanding the model within which hypotheses are tested to include the two major conventional neoclassical factors of production, and second in measuring the energy input to the economic system more accurately by weighting individual energy types by their relative qualities. The first development allows the estimation of the marginal effect of a change in the use of a factor of production on economic growth net of its effects on the use of other factors whether in substitution or complemen- tarity relationships, that either counteract, or accentuate, the direct effect. As the empirical results show, both innovations are necessary to reject the hypothesis that energy use does not cause economic growth.

of this research would be that raising taxes on energy or adopting other policies that cut energy use without specifying the ways in which energy use should be reduced, would reduce the rate of economic growth and, if severe enough, reduce the level of output.

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Energy, and economic growth in the USA : D. I. Stern

Energy and economic growth in the USA: D. I. Stern

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Appendix Energy input

The Annual Energy Review 1990 [66] was used to obtain estimates of the following categories of energy consumption in Btu between 1949 and 1990: coal, natural gas, petroleum, nuclear electric power, hydroelectric power, geothermal power and a further category referred to as ‘other’ by the EIA. The latter category ‘includes net imports of coal coke and electricity produced from wood, waste, wind, photovoltaic, and solar thermal sources connected to electric utility distribution systems’ [ 661. Estimates of coal, natural gas, petroleum and hydroelectric power use for 1947 and 1948 were drawn from Historical Statistics of the United States [SS]. To the sum of these categories were added estimates of wood energy use, energy produced from waste and energy produced from alcohol. I also estimated the quantity of wood used to generate electricity by electric utilities and subtracted it from the ‘other category’. I had no data available on waste used to generate electricity by electric utilities, so that the estimates for waste energy and ‘other’ result in some amount of double counting.

Total US wood energy use was taken from three Energy Information Administration sources [64, 65, 661. I used exponential growth rate interpolation to obtain an estimate ofwood energy consumption in 1988 at 2457.8 x lOi Btu.

Estimates of US biofuels consumption 1990 [67] provides estimates of energy produced from waste and energy from alcohol at various intervals from 1981. I used the exponential growth rate method to interpolate values and used the growth rate in the earliest period to extrapolate back to 1947 (when the quantities were effectively zero). The same source provides estimates of electricity generated from wood at five year intervals from 1949. The exponential growth rate interpolation method was used to estimate internodal values. I computed estimates of final energy use in each of these fuel categories by subtracting data on energy use in electricity generation by fuel type from the gross energy figures. Data on energy used in electricity generation were taken from the same sources as the gross energy data. I used the same definitions for waste, alcohol, and ‘other’ in the

150 ENERGY ECONOMICS April 1993

final energy use data as in the gross energy use data due again to lack of data on electricity generation using these

fuel types.

Capital input The net fixed private non-residential and government capital stock in 1987 prices is from the Survey of Current Business [63]. The unemployment rate is from the Statistical Abstract of the United States [ 591 and the Federal Reserve Bulletin [ 221.

Labour input

Full time equivalent employees from National Income and Product Accounts 1929-1982 [61], and updated to 1990 from the Survey of Current Business [60]

Gross domestic product

Gross domestic product in 1982 prices is from National Income and Product Accounts 192991982 [61], and updated from the Survey of Current Business [60].

Energy prices

All energy prices for 1949-90 are from Annual Energy Reuiew [66]. Data for 1947 and 1948 are from Historical Statistics of the United States [ 581. The nominal prices were deflated by the GDP deflator from National Income and Product Accounts 192991982 [61], and updated from Survey of Current Business [ 601.

Acknowledgements

A version of this paper was presented at the 2nd meeting of the International Society for Ecological Economics in Stockholm, August 1992. The author thanks participants in that meeting and Robert Kaufmann for their criticism of that version of the paper.