A multivariate cointegration analysis of the role of energy in the US macroeconomy

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1 Ž. Energy Economics A multivariate cointegration analysis of the role of energy in the US macroeconomy David I. Stern Centre for Resource and En ironmental Studies, Australian National Uni ersity, Canberra, ACT 0200, Australia Abstract This paper extends my previous analysis of the causal relationship of GDP and energy use in the USA in the post-war period. A majority of the relevant variables are integrated justifying a cointegration analysis. The results show that cointegration does occur and that energy input cannot be excluded from the cointegration space. The results are plausible in terms of macroeconomic dynamics. The results are similar to my previous Granger causality results and contradict claims in the literature Ž based on bivariate models. that there is no cointegration between energy and output Elsevier Science B.V. All rights reserved. JEL classification: Q41 Keywords: Energy; GDP; Cointegration; United States 1. Introduction Stern Ž addressed the debate among economists and energy analysts regarding the role of energy in the US macroeconomy. Several analysts ŽKraft and Kraft, 1978; Akarca and Long, 1980; Yu and Hwang, 1984; Abosedra and Baghestani, have used Granger Ž or Sims Ž tests to test whether energy use causes economic growth or whether energy use is determined by the level of output. The results are generally inconclusive. Where significant results were Tel.: ; fax: Ž. address: dstern@cres.anu.edu.au D.I. Stern $ - see front matter 2000 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 268 D.I. Stern Energy Economics obtained they indicate that causality runs from output to energy use. Erol and Yu Ž found some indications of a causal relationship between energy and output in a number of industrialised countries with the most significant relationship being for Japanese data between 1950 and However, when the sample was restricted to the relationship was no longer significant. Yu and Choi Ž also found a causal relationship running from energy to GDP in the Philippines economy, and causality from GDP to energy in the economy of South Korea. In the latter economy, causality from energy to GDP is significant only at the 10% level. Ammah-Tagoe Ž found causality from GDP to energy use in Ghana. My previous study Ž Stern, tested for Granger causality in a multivariate setting using a vector autoregression Ž VAR. model of GDP, energy use, capital, and labour inputs. I also used a quality-adjusted index of energy input in place of gross energy use. The multivariate methodology is important because changes in energy use are frequently countered by the substitution of other factors of production, resulting in an insignificant overall impact on output. Weighting energy use for changes in the composition of energy input is important because a large part of the growth effects of energy are due to substitution of higher quality energy sources such as electricity for lower quality energy sources such as coal ŽJorgenson, 1984; Hall et al., 1986; Kaufmann, When both these innovations are employed, energy is found to Granger cause GDP. These results are supported by Hamilton Ž and Burbridge and Harrison Ž 1984., who found that changes in oil prices Granger-cause changes in GNP and unemployment in VAR models whereas oil prices are exogenous to the system. More recently, Moroney Ž presented a theoretical and empirical analysis that counters the argument of Perry Ž 1977., Solow Ž 1978., Denison Ž 1979, 1985., and others, that because energy costs are only a small proportion of GDP, energy use is unlikely to be a very important factor in changing the rate of economic growth. Moroney Ž uses a labour-intensive form of a production function with capital embodied technological change to investigate the effects of changes in capital and energy used per unit of labour on labour productivity. The estimates of the output elasticities are similar for both the latter variables. Furthermore, a breakdown of the sources of growth shows that in the period changes in energy used per unit of labour contributed an annual average 1.17 percentage points to economic growth, while from 1974 to 1984 declines in energy use reduced growth by an annual average of 0.5 percentage points. Yu and Jin Ž were the first to test whether energy and output cointegrate. They found that no such relationship exists between energy use and either employment or an index of industrial production. However, the lack of a long-run equilibrium relationship between gross energy use and output alone does not necessarily imply that there is no relation between the variables. Few analysts believe that capital, labour, and technical change play no significant role in determining output. If these variables are integrated, then there will be no cointegration between energy and output whether there is a relationship between the latter two variables or not. Also, decreasing energy intensity, due to increased

3 D.I. Stern Energy Economics energy efficiency, shifts in the composition of the energy input, and structural change in the economy, mean that energy and output will drift apart. Similar comments apply to the bivariate energy employment relationship. Furthermore, the insensitivity of the test may be compounded by using total energy in the economy as a whole but measuring output as industrial output alone. Masih and Masih Ž find cointegration between energy and GDP in India, Pakistan, and Indonesia, but no cointegration in Malaysia, Singapore, or the Philippines. Granger causality runs from energy to GDP in India but in the opposite direction in the other two countries. Ohanian Ž and Toda and Phillips Ž showed that the distribution of the test statistic for block exogeneity in a VAR with non-stationary variables is not the standard 2 distribution. This means that the significance levels reported in previous studies of the Granger-causality relationship between energy and GDP may be incorrect, as both variables are generally integrated series. If there is no cointegration between the variables then the causality test should be carried out on a VAR in differenced data, while if there is cointegration, standard 2 distributions apply when the cointegrating restrictions are imposed. Thus, testing for cointegration is a necessary prerequisite to causality testing. It seems that if a multivariate approach helps in uncovering the Granger causality relations between energy and GDP a multivariate approach should be used to investigate the cointegration relations among the variables. In this paper, I investigate the time series properties of GDP, quality weighted energy, labour, and capital series, estimate some simple static single equation production functions, and estimate three versions of a dynamic cointegration model using the Johansen methodology. The methods are outlined in Section 2 of the paper, which is followed by the results and finally some conclusions. 2. Methodology 2.1. General The basic model is a four equation VAR on annual data for US GDP, energy input, capital input, and labour input, between 1948 and The general form of the VAR is: 1t rt t fž x. fž x. u Ž 1. rt t 1 t r t 1 t r fž x. 1,t, lnž GDP.,..., lnž GDP., lnž K.,..., lnž K., Ž. Ž. Ž. Ž. Ž. ln L,..., ln L,lnE,..., ln E 2 t 1 t r t 1 t r where GDP is gross domestic product, K is capital input, L is labour input, and E is energy input. r is the number of lags, is a ŽŽ 4 r matrix of regression coefficients, and ut is a 4 1 random error vector. The time trend is intended to

4 270 D.I. Stern Energy Economics capture the effects of exogenous technical change. The optimum lag length r was chosen using the Hannan Quinn Information Criterion. The maximum lag length considered is four. Energy input is measured by a quality-adjusted index of final energy use. This quality-adjusted index is created using Divisia aggregation Žsee Appendix A for details Tests for integration The variables in Eq. Ž. 2 may be integrated. I test this hypothesis using four unit root tests. The Dickey Fuller Ž Dickey and Fuller, 1979, and Phillips Perron Ž Phillips and Perron, tests are the same but use different approaches to cope with serial correlation in the data. For both tests, the null-hypothesis is that the series has a stochastic trend. The model for the Dickey Fuller test is: p Ý y t y y Ž 3. t t 1 i t i t i 1 where y is the variable under investigation and t is a random error term. The number of lags p is chosen using the Akaike Information Criterion Ž Akaike, The maximum lag length considered is four. The lagged variables provide a correction for possible serial correlation. The null hypothesis is given by 0. This is tested using the t-statistic Ž in Table 1. which has a non-standard distribution. The alternative hypothesis is that the process is stationary around the deterministic trend. A further battery of tests looks at other alternatives including levels stationarity. In the model above Ž Model 1 in Table 1. the test is a t-test on the parameter given that 0, and tests 0 given that 0. The statistics 2 and 3 are F-type statistics. 2 evaluates the joint restriction 0 while 3 evaluates the joint restriction 0. Model 2 in Table 1 is the same as Eq. Ž. 3 but without the deterministic time trend. If the data do not contain a deterministic trend then this model should provide a more powerful test of the Table 1 Dickey Fuller statistics a Variables Lags Model 1 Model 2 Model lqe lqk lql lgdp ,, 0 1 0, 0 given given a Figures in bold indicate that the statistic is significant at the 5% level.

5 D.I. Stern Energy Economics unit root hypothesis.,, and 1 correspond to the statistics,, and 3 in Model 1. Model 3 excludes both the constant and time trend from Eq. Ž. 3. The only relevant test statistic is, at-test for 0. I do these tests in the order suggested by Dolado et al. Ž The Phillips Perron test uses the same models as the Dickey Fuller tests, but uses a non-parametric correction, due to Newey and West Ž 1987., to cope with potential serial correlation. I chose the lag truncation for this non-parametric correction using an automated bandwidth estimator employing the Bartlett kernel Ž Andrews, The test statistics for both the Dickey Fuller and Phillips Perron tests have the same distributions. Critical levels are reproduced in Hamilton Ž and Enders Ž The model used in the Schmidt Phillips test Ž Schmidt and Phillips, is given by: Ž. y S 4 t t 1 t t 1 T S y y Ý y Ž 5. t t 1 t T t 1 where T is the number of observations, and t is a random error term. First the residual S is computed using Eq. Ž. 5 and then the regression in Eq. Ž. t 4 is estimated. The test statistic is again a t-test on. The null is again the presence of a stochastic trend, while the alternative is trend stationarity. Critical values for the test statistic are presented in Schmidt and Phillips Ž I use the same correction for serial correlation as for the Phillips Perron test. The Kwiatowski et al. Ž test Ž KPSS. differs from the other three tests in that the null hypothesis postulates that the series is stationary and the alternative hypothesis is the presence of a stochastic trend. A second version has a null of trend stationarity. The test statistic is a Lagrange Multiplier statistic, which is calculated as the square of the sum of residuals divided by the estimated error variance from a regression of the variable in question on either a constant or a constant and a trend. I again use the Andrews Newey-West procedure to correct for serial correlation Cointegration analysis On condition that at least some of the variables are integrated, the VAR model Ž.Ž. 1, 2 can be estimated subject to cointegrating restrictions. Maximum likelihood estimation is carried out using the Johansen procedure ŽJohansen, 1988; Johansen and Juselius, Practical and theoretical background is given by Hamilton Ž 1994., Enders Ž and Hansen and Juselius Ž Based on my previous Granger causality results Ž Stern, it should not be possible to exclude energy from the cointegration space. Neither should it be possible to exclude the relevant cointegration residual from the GDP equation.

6 272 D.I. Stern Energy Economics Table 2 Phillips Perron tests a Variables Lags Model 1 Model 2 Model lqe lqk lql lgdp ,, 0 1 0, 0 given given 0 2 y 0 a Figures in bold indicate that the statistic is significant at the 5% level. These are the two most important hypotheses to be tested in the cointegration analysis. Some initial specification testing is also carried out with single equation Cobb Douglas production functions estimated using ordinary least squares. These are the Engle Granger cointegrating regressions corresponding to the vector autoregression model in logarithms. 3. Results 3.1. Tests for integration The Dickey Fuller test suite Ž Table 1. provides mixed evidence on the order of integration. Looking at the statistics for model 1 for energy, capital, and GDP, we can accept the hypothesis that the series contain a unit root Ž. and that there is neither a constant Ž,. nor a deterministic time trend Ž. 3 in the process. But the test for a drift term is not very powerful in the presence of the deterministic trend in the regression as shown by the fact that the joint restriction 0 is rejected. The Dolado et al. Ž algorithm suggests estimation of model 2, Table 3 Schmidt Phillips tests a Variable Lags Z lqe lqk lql lgdp a The null is non-stationarity. is the t statistic described in the text while Z is corrected for serial correlation. Critical value at 5% significance level is 3.11 and at the 1% significance level is 3.73.

7 Table 4 Kwiatowski Phillips Schmidt Shin tests a D.I. Stern Energy Economics Variable Lags Lags lqe lqk lqh lgdp a The null is stationarity. is the test statistic against levels stationarity, is the test statistic against trend stationarity. Figures in bold indicate that the statistic is significant at the 5% level. which excludes the deterministic time trend a priori. The test suggests that the energy and capital series are levels stationary with a significant constant Žas shown by and. 1. The 5% significance level for is This result is suspect because both these series are strongly trending. For GDP indicates that the data have a unit root while 1 rejects restriction of the constant to zero. This series is more clearly a random walk with drift. For labour, the tests for model 1 reject the unit root hypothesis and suggest the inclusion of a linear time trend. According to this test labour is trend stationary. The Phillips Perron test Ž Table 2. indicates that capital, labour, and GDP are integrated. The statistic is significant at the 5% level for the energy input variable, which would indicate that the series is level stationary. Given that the variable has a strong trend up until 1973 this result is anomalous. The Schmidt Phillips test results Ž Table 3. indicate the acceptance of the unit root hypothesis for energy, capital, and GDP at the 5% significance level, but at the 1% significance level all variables, including labour, are found to be integrated. The KPSS test Ž Table 4. shows that all the variables with the exception of labour input are integrated with drift when compared to a trend stationary specification. Labour input is trend stationary. In conclusion, the univariate tests seem to show that energy, capital, and GDP are integrated variables while labour is more likely to be trend stationary Single equation specification and cointegration tests Table 5 presents estimates of four different Cobb Douglas aggregate production functions. These are static cointegrating Ž or spurious. regressions, which correspond to the long-run relation in the vector autoregression model in logarithms presented below. The Cobb Douglas production function unrealistically imposes a unitary elasticity of substitution between all factors of production. This restriction is justifiable because: more flexible functional forms, such as the translog, are difficult to estimate in the VAR context with the available length of time series; and accurate single equation static estimates of flexible functional forms are also very difficult to obtain due to multicollinearity. Model A is a production function with an exogenous technical change trend. While the Durbin Watson statistic

8 274 Table 5 Single equation models a Variable Coefficient t Statistic Variable Coefficient t Statistic Model A Model C Time trend, unrestricted returns to scale No time trend, unrestricted returns to scale Constant Constant LQE LQE LQK LQK LQL LQL TREND Durbin Watson Durbin Watson Dickey Fuller Dickey Fuller RSS RSS Model B Model D Time trend, constant returns to scale No time trend, constant returns to scale F Ž F Ž ,42 1,43 Constant Constant LQE LQE LQK LQK LQL LQL TREND D.I. Stern Energy Economics 22 ( 2000 ) Durbin Watson Durbin Watson Dickey Fuller Dickey Fuller RSS RSS a RSS is the residual sum of squares. Critical values for the Dickey Fuller test: 10% 3.84, 5% 4.16, 1% 4.65.

9 D.I. Stern Energy Economics indicates that there is cointegration Ž Engle and Granger, 1987., the coefficient on capital input is insignificant and has the wrong sign. The Dickey Fuller cointegration statistic is only just significant at the 10% level. Model B imposes a restriction so that GDP exhibits constant returns to scale in capital and labour. This restriction can just be accepted at the 5% level. Now all the coefficients are significant. The Dickey Fuller statistic shows that we can reject the non-cointegration hypothesis at a higher level of significance. The estimated rate of technical change is lower than before. As the coefficient of energy is significant and positive, we find that there are increasing returns in terms of GDP when energy and the two primary inputs are all increased. Some of this effect is absorbed by the time trend in the unrestricted model. Model C is a Cobb Douglas function without a time trend and with unrestricted returns to scale. All the input coefficients have the expected sign and are significant. There are increasing returns to scale to both capital and labour alone and to all three inputs. There is cointegration. Model D imposes constant returns to primary inputs on Model C. This restriction is, however, easily rejected and the equation no longer cointegrates. Though the time trend is significant in models A and B, model C has a better fit to the data than model B. Models B and C have the best cointegration properties. These results show that the system can be represented as either one with constant returns in capital and labour and exogenous technical change or as an unrestricted increasing returns specification with no exogenous technical change. The latter model can be estimated using the CATS package Ž Hansen and Juselius, while the constant returns to scale restriction cannot be implemented in that package. 1 Also the increasing returns approach is more compatible with the idea of endogenous technical change. However, models with time trends are also estimated in the multivariate analysis Multi ariate cointegration analysis The optimal lag length is selected using the information criteria in Table 6. These statistics refer to a model with a constant restricted to the cointegration space and no time trends. According to the Hannan Quinn criterion the optimal lag length is two lags. The Schwartz criterion favours only one lag. I choose two lags because this allows for short-run dynamics in the vector error correction model and the residual properties of the two lag models are also very adequate compared to the other models. This was assessed using the array of serial correlation, ARCH and normality statistics provided by the CATS program. 2 Table 1 The constant returns restriction could be implemented by estimating a VAR in terms of the variables lnž GDP L.,lnŽ K L,. and ln E. 2 These tests are: Lagrange multiplier tests for first order and fourth order multivariate serial correlation, the Ljung Box multivariate autocorrelation test, a multivariate normality test, and univariate tests for skewness, kurtosis, ARCHŽ. 2, and normality for each individual residual series. The results were generally adequate for all models though somewhat better for the two lag model than for the one lag model.

10 276 D.I. Stern Energy Economics Table 6 Selection of lag length Number of lags Log likelihood Schwartz Hannan Quinn function criterion criterion Table 7 Joint selection of deterministic components and cointegration rank a Cointegration Constant in Unrestricted Trend in rank cointegration constant cointegration space space Ž Ž Ž Ž Ž Ž Ž Ž Ž a The first figure is the Johansen trace cointegration statistic. Figures in parentheses are the 90% critical values of the trace cointegration statistic. 7 reports the Johansen trace cointegration test statistics and 90% critical values for cointegration ranks of 1, 2, and 3 as there are four equations a rank of 4 would imply that the model was stationary and different deterministic specifications. These results are for two lags. Restriction of the cointegration rank to one is rejected. Any model of rank 2 is acceptable. As a consequence I estimate all three rank 2 models. Table 8 presents the results for the model with the constant restricted to the cointegration space which is equivalent to the static Model C described above. On the basis of the values of the parameters the second cointegrating vector is clearly a production function. Because of this I have not tested identifying restrictions of the vectors as this would imply setting at least one of the coefficients in this equation to zero. The exclusion test statistics suggest that the relation could, however, be identified by excluding capital. The most important result from the point of view of this paper is that energy cannot be excluded from this cointegrating relation. Energy is, however, the only variable that can be considered weakly exogenous. As shown by the t statistics for alpha the second cointegrating vector loads strongly into the GDP equation. There is, therefore, Granger causality from energy to GDP. The first cointegrating vector loads strongly into the GDP and

11 Table 8 Constant in cointegration space model D.I. Stern Energy Economics lgdp lqe lqk lql Constant First cointegrating vector Second cointegrating vector 1 Ž test statistic for exclusion from cointegration space Ž 5% critical level test statistic for weak exogeneity Ž 5% critical level First column of alpha Žt stats in parentheses. Ž Ž Ž Ž Second column of alpha Žt stats in parentheses. Ž Ž Ž Ž labour equations. I have therefore normalised it on labour. It could possibly be interpreted as a labour supply function. I investigate this hypothesis by plotting in Fig. 1 the percentage changes in the long-run equilibrium values of labour predicted by the two cointegrating relations. Actual labour use closely follows the predicted value from the first cointegrating vector, albeit with a smaller variance. The predicted value from the production function the second cointegrating vector moves in the opposite direction to actual labour use or rather labour use responds with a lag to changes in labour demand. From Table 8 we can see that, in the long-run, disequilibrium between labour demand and supply closes at 14% Ž per year. This fits the stylised fact that declines in unemployment tend to lag GDP growth. However, labour use tends to accelerate further in response to disequilibrium in the first cointegrating relation. This is a labour discouragement encouragement accelerator. In recessions labour use is below long-run equilibrium but more workers are discouraged from searching. In booms more labour enters the work-force when labour supply is above equilibrium. GDP obviously responds positively to this labour oversupply. The alpha coefficient that loads the production function relation into the GDP equation is also positive. When GDP is above its long-run equilibrium it tends to accelerate further and vice versa. As can be seen in Fig. 2, GDP is normally below equilibrium during booms and above equilibrium in recessions. Table 9 shows the results that occur when the constant is unrestricted. These differ somewhat from the results for the model with constant restricted to the cointegration space and the model, described below, which includes a linear trend in the cointegration space. In the production function the returns to scale are similar to the restricted model in Table 8 but the role of capital is smaller. As in the other models, capital can be excluded from the cointegration space. However, none of the variables can be treated as weakly exogenous. The sign of GDP in the second cointegrating vector is different to that in the other two models. Also the

12 278 D.I. Stern Energy Economics Fig. 1. Predicted percentage changes in equilibrium values for labor input. first cointegrating vector loads into the capital equation. So perhaps in this case the first cointegrating relation can be interpreted as a capital accelerator function rather than as a labour demand function. Accordingly I have normalised the vector on capital. The sign of the relevant alpha coefficient is negative when there is over-accumulation of capital there is a regression to equilibrium. Plots of the two cointegrating relations Ž not shown. show that required capital from the production function relation is countercyclical, rising sharply in recessions and vice versa. Equilibrium capital from the first cointegrating relation moves with the economic cycle.

13 D.I. Stern Energy Economics Fig. 2. Predicted percentage changes in equilibrium values for GDP. Table 10 shows the results that occur when a linear trend is included in the cointegration space. The coefficient signs are the same as in the model with the constant restricted to the cointegration space. The time trend in the production function is 0.9% which is very close to the 1.0% rate estimated in the static model in Table 5 Ž Model A.. However, the output elasticity estimates are superior in this dynamic model in that they all have the correct sign but there are actually decreasing returns to capital and labour and roughly constant returns Ž to all three factors of production. The negative trend coefficient in the first cointegrating vector indicates that labour supply tends to decline when holding the other inputs constant. This expresses stylised facts such as increased use of capital per worker and the tendency to a shorter working week over time. Again capital can be excluded from the cointegration space but energy is not weakly exogenous. Both cointegrating vectors now have a significant effect on energy use. So, in this model there is more a case of mutual causality between energy and GDP as in Stern Ž The signs of all the alpha coefficients are similar but much larger than in

14 280 D.I. Stern Energy Economics Table 9 Unrestricted constant model lgdp lqe lqk lql First cointegrating vector Second cointegrating vector test statistic for exclusion from cointegration space Ž 5% critical level test statistic for weak exogeneity Ž 5% critical level First column of alpha Žt stats in parentheses. Ž Ž Ž Ž Second column of alpha Žt stats in parentheses. Ž Ž Ž Ž the more restricted models. The patterns of the cointegrating relations are somewhat different than in the previous examples but still the effects on each of the variables of the two CVs move in opposite directions cyclical and countercyclical. 4. Conclusions Both the single equation static cointegration analysis and the multivariate dynamic cointegration analysis show that energy is significant in explaining GDP. They also show that there is cointegration in a relationship including GDP, capital, labour, and energy. This result contradicts the bivariate analysis of Yu and Jin Ž for the United States. Masih and Masih Ž found cointegration between energy and GDP in three of the six Asian countries that they investigated, but only Table 10 Trend in cointegration space model lgdp lqe lqk lql Trend First cointegrating vector Second cointegrating vector test statistic for exclusion from cointegration space Ž 5% critical level test statistic for weak exogeneity Ž 5% critical level First column of alpha Žt stats in parentheses. Ž Ž Ž Ž Second column of alpha Žt stats in parentheses. Ž Ž Ž Ž

15 D.I. Stern Energy Economics in India did they find cointegration together with causality running from energy to GDP. This study differs from those two by including capital and labour variables and using a quality weighted index of energy input. The multivariate analysis shows that energy Granger causes GDP either unidirectionally as indicated by the first of the three models investigated or possibly through a mutually causative relationship as indicated by the latter two models examined. These results support the conclusions of Stern Ž regarding Granger causality between energy and GDP. The results presented in this paper, strengthen my previous conclusions that energy is a limiting factor in economic growth. Shocks to energy supply will tend to reduce output. Acknowledgements I thank Robert Kaufmann and an anonymous referee for many useful comments. Appendix A. Data sources and construction Detailed sources of data are described in Stern Ž That database was updated to 1994 Ž from and all prices based on 1987 constant dollars. The following additional changes or improvements were made: Labour is measured in terms of hours worked by full-time and part-time employees in domestic industries. Capital is measured as the aggregate value of the non-residential private and government net capital stock in constant 1987 dollars. The capital series were updated from 1993 to 1994 using data on investment in Energy is measured as a Divisia index of the energy content Ž BTU. of the final use of coal, natural gas, petroleum, electric power, and biofuels. These categories reflect changes that the Energy Information Administration has made in the way it reports energy data since The major change is expanded reporting of non-utility production of electricity and renewable energy sources. Final use of the fossil fuels is calculated as the primary inputs minus the amounts used in generation by electric utilities. Use of fossil fuels by non-utility electricity producers are considered as final use. This is so as to avoid a break in the data in 1989 when non-utility coverage is expanded. All use of biofuels by non-utilities is considered as final use consumption by utilities is subtracted. All geothermal, solar, and wind power is included in terms of electricity produced regardless of whether it is produced by utilities or non-utilities. Fossil fuel prices for the aggregation were improved by using the expenditure data reported in the Annual Energy Re iew ŽUS Department of Energy, Energy Information Administration, 1992, to produce better estimates of actual final use fuel prices for oil, natural gas, and coal.

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