THE JOURNAL OF ENERGY

AND DEVELOPMENT

Amarendra Sharma and Cassondra Bruce,

“The Relationship between Energy and U.S. GDP:

A Multivariate Vector Error-Correction Model,”

Volume 38, Number 1

ADVANCE ONLINE COPY

Copyright 2013

THE RELATIONSHIP BETWEEN ENERGY AND U.S. GDP: A MULTIVARIATE VECTOR ERROR-

CORRECTION MODEL

Amarendra Sharma and Cassondra Bruce * Introduction

long-standing economic question is that of the relationship between energy consumption and the gross domestic product (GDP) growth rate. The goal

of this study is to expand the scope of previous studies conducted on the econ-­omy of the United States. While previous research has been conducted, the results are often inconclusive;; however, in several studies, when causality is found to be significant, it appears to run from energy consumption to GDP. The U.S. industrial revolution often is associated with great advancements not only in manufacturing but also in the new economy. Logically, a shift from hand-made products to machine-made products greatly boosted productivity, and higher standards of living soon followed. As entrepreneurs and inventors * Amarendra Sharma, Assistant Professor of economics at Elmira College (New York), holds Master’s and Ph.D. degrees in economics from the University of Cincinnati, as well as a Master’s in economics from the Delhi School of economics, and a B.A. with Honors in econom-ics from Ramjas College, University of Delhi, India. Dr. Sharma has previously taught various courses in economics at the Farmer School of Business, Miami University (Oxford, Ohio) and the Department of Economics, University of Cincinnati. The author also has held an academic position at the Queensland University of Technology, Australia. Dr. Sharma, whose areas of research specializations include applied econometrics, international trade theory, and industrial organization, has published articles in the subfields of Development Economics, Public Eco-nomics, and International Economics. His research has appeared in The Journal of Socio-Economics, Public Budgeting and Finance, Research in Applied Economics, International Journal of Economic Practices and Theories, and The Journal of International and Global Economic Studies. He also serves on the editorial board of the journal, Microeconomics and Macroeconomics. Cassondra Bruce is a Teaching Fellow in Economics; she is currently pursuing degrees in economics, business administration, and mathematics at Elmira College. Her expertise lies in the field of time series econometrics. The Journal of Energy and Development, Vol. 38, Nos. 1 and 2 Copyright 2013 by the International Research Center for Energy and Economic Development (ICEED). All rights reserved.

A

2 THE JOURNAL OF ENERGY AND DEVELOPMENT began to look toward machinery, a new need for energy soon ensued. This, however, became a cycle: with increasing availability of energy and power sources, innovations in production rose, which fed into new energy develop-­ments. This cycle can still be seen in today’s modern world. With each passing day and attention to the depletion of nonrenewable energy sources, there is a greater need for renewable energy. This search, however, also has given rise to new technological advancements. As such, the relationship and the direction of causality between energy consumption and economic growth are uncertain and quite important. Understanding this relationship can provide policy makers with vital information while trying to promote economic growth and energy conservation. Background Literature In past studies on the U.S. economy, researchers have come to several dif-­ferent conclusions about the relationship between energy consumption and GDP growth. Those relationships include: a uni-directional causation of energy consumption to economic growth, a bi-directional causation between energy consumption and GDP growth, and a uni-directional causation from GDP to energy consumption (see, for example, D. Stern, and B.-N. Huang et al.).1 J. Kraft and A. Kraft were the first to determine causality with gross national product Granger causing energy consumption.2 A. Akarca and T. Long, howev-­er, found these results to be spurious due to the non-stationarity of the data.3 They also did not find any causality between the two variables when a lag pe-­riod of two years was included. J. Kraft and A. Kraft’s conclusion was validat-­ed by S. Abosedra and H. Baghestani.4 They relied on U.S. data from 1947–1987 upon which they performed Granger causality tests. Other notable studies in the U.S. context that did not find any causal relationship between the two variables are E. Yu and B. Hwang, E. Yu and J. Choi, E. Yu and J. Jin, and B. Cheng.5 These later studies employed various advanced time-series economet-­ric techniques. While there have been many studies on the U.S. economy, there also has been much research on other developed and developing nations. As in the case of the research on the United States, when studying the effects of energy con-­sumption on economic growth for these countries, several relationships have been identified. The main cause of such differing relationships, particularly for the same country, is likely due to the differences in data, variables, years of study, and political or other such factors.6 D. Stern conducted a time-series, multivariate cointegration analysis on the relationship of energy for the U.S. economy.7 His study updated a previous analysis that was published seven years earlier. This first study tested GDP,

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 3 energy use, capital, and labor inputs, addressing the relationship between ener-­gy use and economic growth;; however, he concluded that the relationship could not be identified with certainty. The newer study included data from1948 to 1994, on which D. Stern runs unit root tests for stationarity as well as Cobb-Douglas production functions to test one single equation, and Engle-Granger cointegrating regressions that correspond to several vector autoregression models. This single equation cointegration analysis showed that energy is a significant variable in understanding GDP growth;; likewise, the multivariate dynamic cointegration analysis supported the same conclusion. D. Stern also determined that GDP, capital, labor, and energy are cointegrated. The latter multivariate analysis also indicated that energy Granger causes GDP either uni-directionally or perhaps through a mutually causative relationship.”8 D. Stern ultimately concluded that energy was a limiting factor in economic growth and that energy supply shocks tended to result in a reduction in output.9 The research of B. Huang et al., which uses a dynamic panel data approach, suggests that there is a negative Granger causal relationship running from GDP to energy consumption for high-income nations, such as the United States.10 Their study is based on panel data of 82 countries from the year 1972 to 2002. Dividing the countries into four groups, low income, lower-middle income, upper-middle income, and high income, the researchers contribute detailed results. Using one equation for all 82 countries, the researchers conclude that there is a positive bi-directional feedback relationship between economic growth and energy consumption.11 Probing further, however, they determine that there is no causal relationship for low-income countries, a uni-directional positive causal relationship from economic growth to energy consumption for middle-income countries, and a negative, uni-directional, causal relationship from economic growth to energy consumption for high-income countries. As the United States is classified as high-income, it can be inferred that an in-­crease in GDP would cause a reduction in energy consumption. The research-­ers attribute this negative relationship to a conservative and environmentally friendly consumption policy.12 Another study on panel data for 25 Organization for Economic Cooperation and Development (OECD) countries (including the United States) for years 1981 to 2007 was conducted by A. Belke et al.13 Understanding the importance of knowing the relationship between energy consumption and economic growth, the researchers sought to make conclusive findings on the direction of causality by including the price of energy as a variable. From the analysis, it was determined that energy consumption is relatively price-inelastic, implying that energy is considered a necessity in today’s society. Also established is a long-run causal relationship in the energy demand equation, implying that global energy policies have a greater impact on energy consumption and eco-­nomic growth as opposed to national policies. Using unit root, cointegration,

4 THE JOURNAL OF ENERGY AND DEVELOPMENT and Granger causality tests, the analysis suggests that energy consumption and economic growth are bi-directionally related in the long run. As such, if energy or GDP increase, the other variable also will increase. A meta-analysis is a type of statistical analysis that addresses several studies collectively in hopes of identifying a trend or conclusion. C.-W. Song Zan and K. Chu-Chun investigated 30 manuscripts in three parts: economic development status, short run versus long run, and total energy consumption versus single electricity consumption.14 Analyzing the first topic of interest, the researchers conclude that the relationship between energy consumption and economic growth fluctuates. For instance, observing Turkey from 1950–2000 as a develop-­ing country and from 1970–2006 as a more developed nation, the same country represents differing relationships;; as such, the researchers conclude that a nation may yield different results based on its stage of development. Studying multivariate data, comprised of capital, labor, energy, and GDP for Korea from 1970–1999, it becomes evident that the time period—i.e., short run and long run—may have a significant effect on causality.15 The aforementioned study by W. Oh and K. Lee discovers that Korea’s long-run causal relationship between energy consumption and GDP is bi-directional, while its short-run rela-­tionship is uni-directional, running from energy consumption to GDP. In applica-­tion, this implies that it is crucial for policy makers to remember long-run impli-­cations, not just the short-run effects. The researchers also conclude that bi-directional causality exists between electricity consumption and economic growth based upon several studies in Korea.16 These researchers determine that for most developing countries, the causal relationship does not run from energy consumption to economic growth but, rather, the relationship varies with the degree of development. J. Payne conducted a similar survey of past studies, in which he determined that there is no general consensus on a causal relationship for energy consump-­tion and economic growth.17 Despite the lack of continuity for the global econo-­my, once breaking the studies into results, he was able to find that 29.2 percent of the studies yield a “neutrality hypothesis.” This neutrality hypothesis implies that there is an absence of Granger causality. J. Payne also discovered that 28.2 percent, 23.1 percent, and 19.5 percent of the studies suggested feedback, growth, and conservative hypotheses, respectively. As such, less than one in every four studies suggests that energy consumption Granger causes economic growth, and even fewer suggest that economic growth Granger causes energy consumption. K. Imran and M. Siddiqui conducted a study similar to the one being reported;; however, the two researchers analyzed panel data from the developing nations of Bangladesh, India, and Pakistan.18 The researchers first determined the order of integration, using unit root tests, and then tested for cointegration. Concluding that cointegration was present, a panel-based error-correction model was applied

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 5 to determine short-run and long-run causality and a Granger causality test was run. These statistical techniques determined that energy consumption Granger caused GDP in the long run, but not in short run, and that no causal relationship between GDP and energy consumption existed in the short run.19 The researchers went on to suggest that there would be an increase in output, given a continuous use of energy. Using similar methodology, A. Aqeel and M. Butt determine that for the de-­veloping nation of Pakistan GDP Granger causes total energy consumption and petroleum consumption, while GDP has no Granger causal relationship with gas consumption, electricity consumption Granger causes GDP, and energy con-­sumption Granger causes employment.20 Also closely following the same meth-­odology, U. Soytas and R. Sari determine the causal relationship between energy consumption and GDP for 16 countries.21 Finding the data to be stationary after taking the first difference for all nations, the researchers use a vector error-correction model for Granger causality. For Turkey, France, Germany, and Japan, energy consumption Granger causes GDP. In Argentina, there is bi-directional causality. In Italy and Korea, the researchers find GDP to Granger cause energy consumption. A summary of studies in the U.S. context is provided in table 1.

Table 1

SUMMARY OF ENERGY CONSUMPTION AND ECONOMIC GROWTH STUDEIS FOR THE UNITED STATESa

Authors (Year) Period Country Methodology Results

D. Stern (2000) 1948–1994 United States Co-integration,

Causality EC GDP N. Bowden and J.

Payne (2009) 1949–2006 United States Causality EC GDP J. Kraft and A.

Kraft (1985) 1947–1979 United States Bivar. Sims Cau-

sality Growth EC U. Erol and E. Yu

(1987) 1973–1984 United States Bivar. Granger

Test EC ≈ Growth E. Yu and J. Jin

(1992) United States Bivar. Granger

Test EC ≈ Growth

U. Soytas and R. Sari (2003) 1950–1992

Canada, United States, and Unit-

ed Kingdom Bivar. VECM EC Growth A. Akarca and T.

Long (1980) 1973–1979 United States EC ≈ Growth a EC = energy consumption; GPD = gross domestic product; bivar. = bivariate; and VECM = vector error-correction model. Sources: D. Stern, “A Multivariate Cointegration Analysis of the Role of Energy in the US Mac-roeconomy,” Energy Economics, vol. 22, no. 2 (2000), pp. 267–83; N. Bowden and J. Payne, “The

6 THE JOURNAL OF ENERGY AND DEVELOPMENT Causal Relationship between U.S. Energy Consumption and Real Output: A Disaggregated Analy-sis,” Journal of Policy Modeling, vol. 31, no. 2 (2009), pp. 180–8; J. Kraft and A. Kraft, “On the Relationship between Energy and GNP,” The Journal of Energy and Development, vol. 3, no. 2 (spring 1978), pp. 401–3; U. Erol and E. S. H. Yu, “On the Causal Relationship between Energy and Income for Industrialized Countries,” The Journal of Energy and Development, vol. 13, no. 1 (au-tumn 1988), pp. 113–22; E. S. H. Yu and J. C. Jin, “Cointegration Tests of Energy Consumption, Income, and Employment,” Resources and Energy, vol. 14, no. 3 (1992), 259–66; U. Soytas and R. Sari, “Energy Consumption and GDP: Causality Relationship in G-7 Countries and Emerging Mar-kets,” Energy Economics, vol. 25, no. 1 (2003), pp. 33–7; and A. T. Akarca and T. V. Long, “On the Relationship between Energy and GNP: A Reexamination,” The Journal of Energy and Development, vol. 5, no. 2 (spring 1980), pp. 326–31. Data, Methodology, and Results Previous studies have chosen to include only the variables of interest, represent-­ing energy consumption and economic growth;; however, in this study we will examine both bivariate and multivariate models. The multivariate models will include non-agricultural labor hours and net domestic investments in addition to real GDP and two measures of energy consumption. These variables have been obtained from the Bureaus of Labor Statistics and of Economic Analysis and the U.S. Energy Information Administration.22 The multivariate model is advanta-­geous over the bivariate model in the sense that it allows us to see how other, more specific, macroeconomic indicators affect economic growth and energy consump-­tion. The summary statistics of all variables used in this study are given in table 2.

Table 2 SUMMARY STATISTICS

Variable Obser-vations Mean

Standard Deviation Minimum Maximum

Total energy 56 7.60x107 1.88x107 4.02x107 1.01x108 Fossil fuel 56 6.70x107 1.45x107 3.74x107 8.63x107 Labor 56 99,190.57 28,580.23 55,722 143,952 GDP 56 4,946.49 4,514.57 414.7 14,526.5 Net investment 56 729.16 645.52 63.5 2,178.5 Establishing the direction of causality between real GDP and the two measures of energy consumption, namely, total energy consumption and fossil fuel con-­sumption, involves three steps. In the first step of the analysis, we employ two standard unit root tests, namely, the augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test, to deter-­mine the order of integration for each variable in our study.23 Testing for stationari-­ty ensures that our regression results are not spurious. Additionally, cointegration requires that the variables are integrated of the same order. Testing each variable in the levels form allows us to determine the degree of integration.

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 7 The ADF test makes a parametric correction for higher-order autocorrelation by including the lagged differences of the dependent variable as explanatory variables. The following regression is used for the ADF test: 𝑦 = 𝛽′𝑥 + 𝛼𝑦 + ∑ 𝜃 ∆𝑦 + 𝜀 (1)

where xt is a vector of deterministic terms (constant, trend, etc.). The k lagged difference terms, Δyt−j, are used to approximate the autoregressive moving-average (ARMA) structure of the errors, and the value of k is set such that the error εt is serially uncorrelated. The error term also is assumed to be homoske-­dastic. The Phillips-Perron (PP) unit root test differs from the ADF test primarily in terms of its treatment of error-specific serial correlation and hetereskedasticity. In particular, the PP test ignores any serial correlation in the test regression, whereas the ADF test tries to mimic the ARMA structure of the error terms through parametric autoregression, The test regression for the PP test is: ∆𝑦 = 𝛽′𝑀 + 𝜋𝑦 + 𝑢 (2)

where ut is )0(I and may be heteroskedastic. The PP test corrects for any serial correlation and heteroskedasticity in the error ut by directly modifying the test statistics. One advantage of the PP test over the ADF test is that it is robust to general forms of heteroskedasticity in the error term ut. The above descriptions of ADF and PP tests are borrowed from A. Sharma.24 The second step of analysis consists of cointegration test, which may be tested by using either the Engle-Granger or the Johansen- Juselius procedure.25 We opt for the Johansen-Juselius test since it has been shown to have superior properties to the Engle-Granger two-step procedure.26 The Johansen-Juselius cointegration test allows us to compare trace statistics to a critical value. If the trace statistic is greater than the critical value, then we can reject the null hypothesis of at most ‘r’ cointegrating relationships among the specified variables. This allows us to determine cointegration among the variables. While cointegration can establish causal relationship, it cannot tell us the direction of causality, so we must use the Granger causality test. In the third step of the analysis we consider the Granger causality test, which crucially depends on the degree of integration of variables. If all variables are stationary in the levels or I(0), then the standard Granger causality test can be applied. But if they are I(1), then the Granger causality test can be implemented within a vector error-correction model.27

8 THE JOURNAL OF ENERGY AND DEVELOPMENT Unit Root Tests: The results of the augmented Dickey-Fuller and Phillips-Perron tests on the series in levels are provided in table 3;; table 4 displays the results of these unit root tests performed on the series after first differencing.

Table 3 UNIT ROOT TESTS IN LEVELSa

a GPD = gross domestic product; lag lengths are provided in the parentheses and have been selected by the Akaike’s Information Criterion (AIC). According to the results in table 3, we cannot reject the null hypothesis of unit root for any variable in the levels using the augmented Dickey-Fuller and Phillips-Perron tests. However, when we first difference these variables and then perform the two tests again, we are able to reject the null hypothesis of unit root in each case. Thus, we conclude that the variables are integrated of first order or I(1). Cointegration: First we present the Johansen’s cointegration test results for the bivariate cases and thereafter the multivariate cases. Tables 5 and 6 display the results of the bivariate cases. The optimal lag lengths have been determined by the Akaike Information Criterion and in both cases it is 4. The null hypothesis is that there are at most ‘r’ cointegrating relationships among the specified variables. For real GDP and energy consumption we cannot reject the null hypothesis that there is at most one cointegrating relationship. Similarly, we cannot reject the null hy-­pothesis of at most one cointegrating relationship between real GDP and fossil fuel consumption. Thus, we conclude that these variables are cointegrated.

Level Augmented-Dickey Fuller Phillips-Perron With no constant and no time trend

Energy 2.204 (1) 2.928 (1) Fossil 1.093 (4) 1.881 (4) Real GDP 2.790 (3) 8.922 (3) Labor 2.255 (3) 4.618 (3) Investment 3.492 (4) 1.160 (4)

With a constant and no time trend Energy −1.652 (1) −1.857 (1) Fossil −2.192 (4) −2.050 (4) Real GDP 3.352 (3) 5.146 (3) Labor −0.962 (3) −0.846 (3) Investment 2.116 (4) −0.273 (4)

With a constant and a time trend Energy −1.615 (1) −1.247 (1) Fossil −2.061 (4) −1.413 (4) Real GDP 0.671 (3) −1.019 (3) Labor −1.706 (3) −1.653 (3) Investment −1.379 (4) −2.339 (4)

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 9

Table 4 UNIT ROOT TESTS AFTER FIRST DIFFERENINGa

First Differenced Augmented-Dickey Fuller Phillips-Perron With no constant and no time trend

Energy −3.808 (1)*** −4.639 (1)*** Fossil −2.312 (3)** −4.871 (3)*** Real GDP −1.237 (1) −1.470 (1) Labor −1.864 (2)* −3.069 (2)*** Investment −3.587 (3)*** −5.387 (3)***

With a constant and no time trend Energy −5.111 (1)*** −5.656 (1)*** Fossil −2.832 (3)* −5.411 (3)*** Real GDP −2.540 (1)* −3.084 (1)** Labor −3.959 (2)*** −4.518 (2)*** Investment −5.027 (3)*** −5.622 (3)***

With a constant and a time trend Energy −5.451 (1)*** −5.816 (1)*** Fossil −3.243 (3)* −5.564 (3)*** Real GDP −6.180 (1)*** −5.363 (1)*** Labor −3.846 (2)** −4.518 (2)*** Investment −6.100 (3)*** −5.572 (3)***

a GDP = gross domestic product;***significant at 1-percent level; **significant at 5-percent level; *significant at 10-percent level; lag lengths are provided in the parentheses and have been selected by the Akaike’s Information Criterion (AIC);; z(t) test statistics for Phillips-Perron.

Table 5 JOHANSEN’S TEST FOR COINTEGRATION VARIABLES:

GDP AND TOTAL ENERGY CONSUMPTIONa

Maximum Rank Trace Statistic 5-Percent Critical Value 0 29.3989 15.41 1 1.7417* 3.76

a GDP = gross domestic consumption; * indicates the maximum number of cointegrating rela-tionships (4 lags according to the Akaike Information Criterion).

Table 6 JOHANSEN’S TEST FOR COINTEGRATION VARIABLES:

GDP AND FOSSIL FUEL CONSUMPTIONa

Maximum Rank Trace Statistic 5-Percent Critical Value 0 28.3053 15.41 1 3.0638* 3.76

a GDP = gross domestic consumption; * indicates the maximum number of cointegrating rela-tionships (4 lags according to the Akaike Information Criterion).

10 THE JOURNAL OF ENERGY AND DEVELOPMENT

Table 7 JOHANSEN’S TEST FOR COINTEGRATION VARIABLES:

GDP, TOTAL ENERGY CONSUMPTION, LABOR AND INVESTMENTa

Maximum Rank Trace Statistic 5-Percent Critical Value 0 79.1668 47.21 1 19.5996* 29.68 2 7.8336 3.76

a GDP = gross domestic consumption; * indicates the maximum number of cointegrating rela-tionships (3 lags according to the Akaike Information Criterion).

Table 8 JOHANSEN’S TEST FOR COINTEGRATION VARIABLES:

GDP, FOSSIL FUEL CONSUMPTION, LABOR AND INVESTMENTa

Maximum Rank Trace Statistic 5-Percent Critical Value 0 52.9380 47.21 1 24.1510* 29.68 2 8.2546 15.41

a GDP = gross domestic consumption; * indicates the maximum number of cointegrating rela-tionships (4 lags according to the Akaike Information Criterion). Table 7 and 8 present the results of the multivarite cases where we have added labor hours and net investment to the bivariate cases. When we consider cointe-­gration among real GDP, energy consumption, labor hours, and net investment, the null hypothesis of at most one cointegrating relationship cannot be rejected at the 5-percent level. Similarly, we cannot reject the null hypothesis of at most one cointegrating relationship among real GDP, fossil fuel consumption, labor hours, and net investment at the 5-percent level. In the light of this evidence, we con-­clude that these variables are cointegrated. Granger Causality: It is well known that if the variables are integrated of the first order, a vector error-correction model (VECM) is a better representation of the data than a vector autoregression (VAR) model. Since we have already estab-­lished cointegration among variables, this means that there exists a causal rela-­tionship. However, cointegration does not reveal the direction of causality. In order to determine the direction of causality, we have to resort to a VECM. One advantage of VECM over VAR is that it establishes both short- and long-run causality. Thus, the next step is to apply the Granger causality test. Granger cau-­sality is a two-step procedure. The first step involves obtaining the residuals from the long-run equation. In the second step the residuals are used as an ex-­planatory variable in the error-correction model. Thus, we estimate the following error-correction models.

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 11 Bivariate Cases: ∆𝐺𝐷𝑃 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 + 𝑢 , (3)

∆𝐸𝑛𝑒𝑟𝑔𝑦 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 + 𝑢 , (4)

∆𝐺𝐷𝑃 = 𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 + 𝑢 , (5)

∆𝑓𝑜𝑠𝑠𝑖𝑙 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 + 𝑢 , (6)

Multivariate Cases: ∆𝐺𝐷𝑃 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (7)

∆𝐸𝑛𝑒𝑟𝑔𝑦 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (8)

∆𝐿𝑎𝑏𝑜𝑟 =𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (9)

12 THE JOURNAL OF ENERGY AND DEVELOPMENT ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 =

𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝐸𝑛𝑒𝑟𝑔𝑦 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (10)

∆𝐺𝐷𝑃 =

𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (11)

∆𝑓𝑜𝑠𝑠𝑖𝑙 =

𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (12)

∆𝐿𝑎𝑏𝑜𝑟 =

𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (13)

∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 =

𝛼 + 𝜆 𝐸𝐶𝑇 + ∑ 𝛽 , ∆𝐺𝐷𝑃 + ∑ 𝛽 , ∆𝑓𝑜𝑠𝑠𝑖𝑙 +∑ 𝛽 , ∆𝐿𝑎𝑏𝑜𝑟 + ∑ 𝛽 , ∆𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑢 , (14)

Equations (3) through (6) represent the bivariate cases, whereas, equations (7) through (14) represent the multivariate cases. The term ECT in all equations represents the error term. If the coefficient of the error-correction term is statisti-­cally significant, then we can conclude that there is a long-term causal relation-­ship among the variables. In order to establish the short-term Granger causality, we need to use the F-test. If the coefficients of energy in equation (3) are jointly significant and the coefficients of GDP in equation (4) are jointly insignificant, then we can conclude that energy causes GDP. Analogously, if the coefficients of energy in equation (3) are jointly insignificant and the coefficients of GDP in equation (4) are jointly significant, then we can conclude that GDP Granger causes energy. And, if both of them are jointly significant, then there is bi-

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 13 directional causality. If none of them are jointly significant, then we can con-­clude that there is no short-term causality between the variables. The estimates of these equations are presented in tables 9 and 10. Vector Error-Correction Model: The estimate of equation (3) is presented in column 1 of table 9. The F-test suggests that energy consumption does not Granger cause GDP. GDP, however, does Granger cause energy consumption according to the estimate of equation (4) presented in column 2 of table 9. We have a similar conclusion based on the estimates of equations (5) and (6) pre-­sented in columns 3 and 4 of table 9, respectively. The estimates suggest a uni-directional causality from GDP to fossil fuel consumption.

Table 9 BIVARIATE VECTOR ERROR-CORRECTION MODEL RESULTSa

D_GDP

(I) D_ENERGY

(II) D_GDP

(III) D_FOSSIL

(IV)

D_ECT_1 −0.0033295 (0.0133421)

−0.0234344 (0.0324023)

0.0010795 (0.0123181)

−0.0427002 (0.0367732)

D_GDP_1 0.7816533*** (0.2399639)

103.7965 (2574.887)

0.7955076*** (0.2379972)

680.2597 (2520.167)

D_GDP_2 −0.4729458 (0.3789246)

−6957.154* (4029.324)

−0.4732305 (0.3759056)

−7842.918* (3941.521)

D_GDP_3 0.4261752 (0.275278)

3639.78 (2858.875)

0.3920799 (0.2817526)

4124.411 (2848.926)

D_ENERGY_1 −0.0000179 (0.000016)

0.1916193 (0.170324)

D_FOSSIL_1 −0.0000179 (0.0000158)

0.2281081 (0.1658861)

INTERCEPT 99.47581** (51.1213)

1794038*** (508484)

101.4808* (51.12278)

1531406*** (480548)

F-TEST

Energy F(1,46) =1.26

Prob >F = 0.2684

GDP F(3, 46) =3.34

Prob > F = 0.0272

Fossil F(1,46)=1.28

Prob >F = 0.2633

GDP F(3, 46) =3.47

Prob > F = 0.0236

a ***significant at 1-percent level; **significant at 5-percent level; and *significant at 10-percent level.

Table 10 presents the estimates of equations (7) through (10). We conclude, on the basis of these estimates, that GDP Granger causes total energy consump-­tion. These estimates also suggest that there is a bi-directional causality between GDP and net investments, a uni-directional causality between net investments and labor where the direction of causality runs from net investments to labor, and net investments causing energy consumption. GDP also causes labor.

14 THE JOURNAL OF ENERGY AND DEVELOPMENT

Table 10 MULTIVARIATE VECTOR ERROR-CORRECTION MODEL RESULTS: VARIABLES USED

ARE GROSS DOMESTIC PRODUCT (GDP), ENERGY, LABOR AND INVESTMENTa

D_GDP

(I) D_ENERGY

(II) D_LABOR

(III) D_INVEST

(IV)

D_ECT_1 −0.002374 (0.0493547)

−0.0703519 (0.0611746)

0.0327966 (0.0453719)

−0.2492202 (0.2289021)

D_GDP_1 −.2688196 (0.6177538)

−6895.777 (7703.413)

−2.692694 (5.428733)

−0.2090096 (0.4046228)

D_GDP_2 −1.561974** (0.5823305)

−20168.35*** (7299.875)

−17.52482*** (5.133905)

−1.342213*** (0.3649022)

D_GDP_3 2.766068*** (0.5830984)

22308.42*** (7311.116)

17.77786*** (5.201374)

1.55195*** (0.397142)

D_ENERGY_1 6.24e-06 (0.0000166)

0.4722935** (0.1996913)

0.0002091 (0.0001419)

2.74e-06 (9.90e-06)

D_LABOR_1 −0.0304088 (0.0299265)

-447.8354 (366.3928)

−0.0118229 (0.2600821)

−0.0232125 (0.0184472)

D_LABOR_2 −0.0053752 (0.0264647)

−262.8837 (327.6772)

−0.2322663 (0.2310994)

−0.0120906 (0.0164401)

D_LABOR_3 .045062* (.0261611)

142.3909 (327.5039)

.1800196 (.2315501)

.0229906 (.0173542)

D_INVEST_1 1.622981* (0.9170368)

9138.764 (11402.24)

10.03534 (8.042118)

1.004315* (0.5718396)

D_INVEST_2 2.774423*** (0.7989367)

32762.92*** (10024.61)

26.16777*** (7.053169)

2.129864*** (.5044649)

D_INVEST_3 −3.497289*** (.6880476)

−17510.2** (8587.262)

−13.87852** (6.197868)

−1.882364*** (0.5302154)

D_INVEST_4 −0.5168192 (0.4208082)

−2991.618 (5227.875)

−4.686093 (3.689598)

−0.2920198 (0.2801936)

INTERCEPT 26.04808 (67.01391)

2249603*** (807445.4)

1677.744*** (581.0392)

36.45782 (40.63718)

F-TEST

Energy F(1, 38) = 0.14

Prob > F= 0.7096 Labor

F(3, 38) =1.53 Prob > F= 0.2233

Investment F(3, 38) =8.92

Prob > F= 0.0001

Labor F(3, 38) = 1.09

Prob > F= 0.3653 Invest

F(3,38) = 3.76 Prob >F = 0.0186

GDP F(3, 38) =4.66

Prob > = 0.0072

GDP F(3, 38) = 5.55

Prob >F= 0.0029 Energy

F(1,38) = 2.17 Prob > F= 0.1487

Invest F(3, 38) = 5.10

Prob > F= 0.0046

Energy F(1, 38) = 0.08 Prob>F=0.7835

GDP F(3, 38) = 6.54 Prob>F=0.0011

Labor F(3,38) =1.51

Prob>F=0.2265 a ***significant at 1-percent level; **significant at 5-percent level; and *significant at 10-percent level. In table 11 we present the estimates of equations (11) through (14). These results are very similar to the previous cases. On the basis of these estimates, we conclude that GDP Granger causes fossil fuel consumption. We also conclude

ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 15 that there is a bi-directional causality between GDP and net investments, a uni-directional causality between net investments and labor, where the direction of causality runs from net investments to labor and net investments causing fossil fuel consumption. Additionally, GDP Granger causes labor. Conclusions In this paper we examine the relationship between energy consumption and real GDP in the United States. We employ a multivariate vector error-correction model to determine causality, which in itself is an improvement over the previ-­ous studies. Using Johansen’s multivariate cointegration procedure, we find that the variables are cointegrated. The multivariate VECM suggests that there is a uni-directional causality running from real GDP to total energy and fossil fuel consumption, implying a change in GDP is the driving force behind the changes in energy consumption, and not the other way around. This study provides vital information to the policy makers who design policies to conserve energy and promote economic growth. NOTES 1 David. I. Stern, “A Multivariate Cointegration Analysis of the Role of Energy in the US Macroeconomy,” Energy Economics, vol. 22, no. 2 (2000), pp. 267–83, and Bwo-Nung Huang, M. J. Hwang, and C. W. Yang, “Causal Relationship between Energy Consumption and GDP Growth Revised: A Dynamic Panel Data Approach,” Ecological Economics, vol. 67, no. 1 (2008), pp. 41–54. 2 John Kraft and Arthur Kraft, “On the Relationship between Energy and GNP,” The Journal of Energy and Development, vol. 3, no. 2 (spring 1978), pp. 401–3. 3 A. T. Akarca and T. V. Long, “On the Relationship between Energy and GNP: A Reexamina-tion,” The Journal of Energy and Development, vol. 5, no. 2 (spring 1980), pp. 326–31. 4 S. Abosedra and H. Baghestani, “New Evidence on the Causal Relationship between United States Energy Consumption and Gross National Product,” The Journal of Energy and Develop-ment, vol. 14, no. 2 (spring 1989), pp. 285–92. 5 E. S. H. Yu and B. K. Hwang, “The Relationship between Energy and GNP: Further Results,” Energy Economics, vol. 6, no. 3 (1984), pp. 186–90; E. S. H. Yu and J. Y. Choi, “The Causal Relationship between Energy and GNP: An International Comparison,” The Journal of Energy and Development, vol. 10, no. 2 (spring 1985), pp. 249–72; E. S. H. Yu and Jang C. Jin, “Cointegration Tests of Energy Consumption, Income, and Employment,” Resources and Energy, vol. 14, no. 3 (1992), 259–66; and B. S. Cheng, “An Investigation of Cointegration and Causality between Ener-gy Consumption and Economic Growth,” The Journal of Energy and Development, vol. 21, no. 1 (autumn 1995), pp. 73–84.

16 THE JOURNAL OF ENERGY AND DEVELOPMENT 6 Chiou-Wei Song Zan and Ko Chu-Chun, “A Meta-Analysis of the Relationships between Energy Consumption and Economic Growth,” Proceedings of the 14th Conference on Interdisci-plinary and Multifunctional Business and Management, Taiwan, June 25, 2011, pp. 528–45. 7 David. I. Stern, op. cit. 8 Ibid. 9 Ibid.

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ENERGY CONSUMPTION AND U.S. ECONOMIC GROWTH 17 pp. 427–31, and P. C. B. Phillips and P. Perron, “Testing For Unit Root in Time Series Regres-sion,” Biometrika, vol. 75, no. 2 (1988), pp. 335–46. 24 A. Sharma, “The Long Run Determinants of the U.S. Trade Balance: A Reexamination Using Bi & Multivariate Cointegration Approach,” Research in Applied Economics, vol. 4, no. 1 (March 2012), pp. 16–32. 25 R. Engle and C. Granger, “Cointegration and Error Correction: Representation, Estimation and Testing,” Econometrica, vol. 55, no. 2 (1987), pp. 251–76, and S. Johansen and K. Juselius, “Maximum Likelihood Estimation and Inference on Cointegration with Applications to the De-mand for Money,” Oxford Bulletin of Statistics, vol. 52, no. 2 (1999), pp. 169–210. 26 J. Gonzales, “Five Alternative Methods of Estimating Long-Run Equilibrium Relationships,” Journal of Econometrics, vol. 60, nos. 1–2 (1994), pp. 203–33. 27 Walter Enders, Applied Econometric Time Series (New York: John Wiley & Sons, 2010).