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**A Re-Examination of Energy Intensity in the U.S. Manufacturing Sector***

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United States energy intensity, measured as primary energy consumption per dollar of real gross domestic product (GDP), fell approximately 49 percent from 1980 to 2013 (EIA, MER and BEA, NIPA). Research concerning the driving forces of improvements in energy intensity dates back to the late 1970s. This paper is comprised of two major analysis sections, which cover the 1998, 2002, 2006, and 2010 periods for the U.S. manufacturing sector. The first major analysis section decomposes movements in energy intensity into two factors: structural and efficiency change. The efficiency effect is the change in intensity resulting from efficiency changes within individual sectors. The structural effect is the change in energy intensity due to shifts in production between sectors. Contributions of this analysis section to the literature are: 1. It uses a newer U.S. data set than has been used in previous papers (Manufacturing Energy Consumption Survey [MECS]), which has data through 2010; 2. It provides results at both national and regional levels, whereas much of the literature focuses on the national level.

The second analysis section uses regression models to measure factors affecting energy intensity, where energy price is the primary variable of interest; previous studies have found significant correlations between energy prices and intensity. This section examines the 1998-to-2010 time period, while other studies in the literature explore less recent time periods. This analysis adds to the literature by employing regression analysis as only a few of the studies to-date implement econometric methods. Unlike previous econometric literature on the subject, the present study uses 3-digit North American Industrial Classification System (NAICS) level data for manufacturing industries at the national and regional levels. Also, in addition to accounting for within-industry variation via fixed-effects models, between-industry variation is accounted for via random-effects models.

One common method used to tease out the components of changes in energy intensity is index decomposition analysis (IDA). One advantage of IDA is that its data requirements are less stringent than other methods, such as structural decomposition analysis (SDA). This paper focuses on IDA. In the case of energy intensity, the components of changes in energy intensity are broken into two parts: 1. Efficiency change is the change in intensity resulting from efficiency changes within individual sectors. 2. Structural change is the change in energy intensity due to shifts in production between sectors. Even if efficiency of any individual sector has not changed, shifting production away from energy-intensive sectors results in lower energy intensity.

For literature reviews, see Liu and Ang (2007), as well as Ang and Zhang (2000). Studies estimating the causes of changes in energy intensity have been prevalent for several decades; Myers and Nakamura (1978) is cited in the literature as the earliest of these types of studies. Liu and Ang (2007) indicate the majority of U.S. studies found that both efficiency and structural change contribute to changes in energy intensity, with efficiency change having a larger impact in most studies.

Several studies have also used econometric analysis to study the decomposition of energy intensity. For instance, see Wing (2008); Wing and Eckaus (2004); Metcalf (2008); Bernstein, et al. (2003); Alghandoor, et al. (2008).

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**Data and Summary Statistics**

Data cover the 1998, 2002, 2006, and 2010 time periods. Descriptions of the variables used in the paper are provided in Table 1. Table 2 provides summary statistics of the national-level variables. Three different standard deviation measures are used: 1. Overall, 2. Between, and 3. Within. The Between measure only captures variation across NAICS codes, while the Within measure only captures variation within industries. The Overall measure encompasses both within and between variation. Each variable demonstrates substantially more between-industry variation than within-industry variation.

Regarding correlations between the levels of the national-level variables, energy price (EN_P) and energy intensity (EN_I) have a negative correlation (-0.68), indicating higher energy prices are associated with lower energy intensities. Another interesting relationship is the positive 0.53 correlation between EN_I and participation (Partic). Industries with higher participation rates in energy efficiency programs tend to have higher energy intensities than industries with lower participation; it is likely more attractive for industries that are more energy-intensive to enroll in such programs since they may have more to gain from improvements in efficiency than industries that have relatively low-energy intensities.

The industry breakout includes three-digit NAICS in the manufacturing sectors 311 through 339 (industries that are aggregated for the analysis include 311 and 312; 313 and 314; 315 and 316). The regional breakout occurs at a five-region level: National (U.S.), West, Midwest, South, and Northeast.

The correlations of the levels and first differences of the national-level variables tend to differ. Of particular interest is the weak (-0.13), although still negative, correlation between the first differences of EN_I and EN_P. Combined with the findings of the level correlations, this implies that while cross-section correlation between intensity and price is high, the correlation of changes within industries over time is much smaller. Another difference between the first difference and level correlations is the negative correlation between the first differences EN_I and Avgwage (-0.48), while the levels of the two variables have a positive correlation (0.48). Also of note is the weak negative correlation between the first differences of EN_I and Partic (-0.09)

Regional between variation tends to exceed within variation. Correlations between EN_P and EN_I are similar to the national figures, ranging from -0.47 to -0.66. Another finding of note is the relatively weak correlation between the first difference of EN_I and EN_P; the correlations range from -0.35 to +0.34.

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**Energy Decomposition Analysis [1]**

Divisia IDA is implemented to tease out the components of change in energy intensity: structural and efficiency change. Using the Multiplicative Log-Divisia Index, the relevant formulas for decomposing the movements in energy intensity between two time periods are shown in equations 1 through 4 (Choi and Ang, 2012):

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** (Eq. 1)**

**(Eq. 2)**

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** (Eq. 3)**

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**(Eq. 4)**

EI: Energy intensity index

R_{t}/R_{98}: Real Efficiency index (1998 is the base year)

S_{t}/S_{98}: Structural index (1998 is the base year)

S_{i,t}: Production share of sector i at time t

w_{i}: Weight for industry i

t: time period t

98: time period equals 1998

exp: exponential

Ln: natural logarithm

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Decomposition results are displayed in Table 3. At the national level, aggregate energy intensity declined 34.2 percent from 1998 to 2010. This was primarily driven by real efficiency, which improved 22.7 percent over the same period. The structural change index declined 14.9 percent over the same period. This implies real efficiency changes were responsible for 60 percent of the decline in aggregate intensity, while structural change was responsible for the remaining 40 percent. *(Note: Declines in the real efficiency index mean that the individual industries became more efficient, as opposed to less efficient.) *

Decomposition analysis was carried out in each of the four regions, in a manner similar to the National Level Decomposition (Table 3). In stark contrast to the national model, the Northeast, West and Midwest regions’ declines in aggregate intensity were driven more by structural change than efficiency; conversely, the South region’s intensity decline was driven more by efficiency change. More specifically, energy intensity in the West Region declined 57.7 percent from 1998 to 2010. The decomposition results imply 56 percent of this decline is ascribable to structural change. 84 percent of the 35.9 percent decline in South energy intensity is attributable to improvements in real efficiency. Conversely, 86 percent of the Midwest intensity decline of 14.2 percent is attributable to structural change. In the Northeast, the entire 33.8 percent decline in energy intensity is attributable to structural change.

**Table 3 Energy Intensity Decomposition Results**

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**Regression Analysis**

In addition to a decomposition analysis, a regression analysis is undertaken, which examines whether factors such as changes in energy prices are associated with changes in energy intensity over the 1998 to 2010 time period (with data for the years 1998, 2002, 2006, and 2010). The regression analysis is conducted at the national and regional levels.

Separate regression models are run at the national level and for each of the four regions. The fixed-effects model assumes common slope coefficients and intercepts that vary over industries. The industry specific effects are considered to be fixed.

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**(Eq. 5)**

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**(Eq. 6)**

EN_I: Energy intensity

i: Industry

t: Time period

x: time-varying covariates; these include the natural logarithms of the following variables: EN_P, Avgflsp; Avgwage; Empl. The level of Partic and a time trend are also included.

Another common panel data model is the random-effects model. Contrary to the fixed-effects model, the random-effects model assumes the are random. Its equation is:

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**(Eq. 7)**

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**(Eq. 8)**

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**(Eq. 9)**

A potential major advantage of the fixed-effects estimator is its consistency when the industry-specific effects are correlated with the time-varying covariates (assuming the time-varying covariates are uncorrelated with the right-hand portion of the composite error term); conversely, the random-effects estimator is inconsistent if individual specific effects are correlated with the time-varying covariates. A Hausman test can be used to test which model is theoretically preferred. A disadvantage of the fixed-effects model is that it only measures variation within industries; as the data in Table 2 show, the majority of the variation in the variables occurred between industries, so the fixed-effects model may result in less precise estimates. When covariates do not display significant variation over time, implementation of the random-effects model may be required to discover anything about the dependent variable’s relationship with the covariates (Wooldridge 2002).

The national and regional[2] level regression results are displayed in Table 4 (Fixed Effects) and Table 5 (Random Effects). The national-level model finds a negative association between energy prices and energy intensity; conversely, the fixed-effects models does not find a significant negative association, implying that price changes within industries did not significantly affect energy intensity in these industries over the 1998 to 2010 period. This is consistent with the low correlation between the first differences of EN_I and EN_P, as well as their low degree of within-industry variation relative to between-industry variation (Table 2).

The fixed-effects model finds most covariates to be insignificant at the national level, with the exception that changes in average wage are significantly (negatively) associated with changes in energy intensity. One plausible explanation for the lack of significance in the other covariates in the fixed-effects models is that all variables displayed a small amount of variation within industries relative to the amount of variation between industries. The fixed-effects model has a high R-squared (0.973) when accounting for industry-specific effects (the industry dummy variables), but a low R-squared (0.304) when only accounting for the effects of the within-industry variation.

The National-level random-effects model finds:

- Industries with higher levels of employment tend to have lower energy intensities
- Industries with higher average wages tend to have higher intensities.
- Significant negative time trend for energy intensity, even after accounting for the other covariates.

In the regional analysis, the fixed-effects models all find a negative coefficient for Ln_Avgwage, and three of these are found to be significant (West, South and Northeast regions). Other than Ln_Avgwage, no variable is found to be significant in at least two regions. This may be ascribable to factors such as large standard errors resulting from the combination of small within-industry variation and omitting between-industry variation, measurement error, omitted variable bias (not all variables in the national model were available at the regional model), and missing data for certain regions/industries. As far as random-effects models, only the South region has a significant negative coefficient for the natural logarithm of energy price (Ln_EN_P), while two other regions find a negative coefficient, but are not statistically significant.

The majority of regional random-effects models find a significant positive coefficient for the log of average wage (Ln_Avgwage). All of the random-effects regional models estimate a significant negative coefficient for the natural logarithm of employment (Ln_Empl) and display a significant negative time trend in energy intensity. Hausman tests for the National model and West region fail to reject the null hypothesis at the 95% level, (p-values = 0.129 and 0.169, respectively); this implies the random-effects model is preferred to the fixed-effects model for these regions. For the South, Midwest, and Northeast regions, the Hausman test results imply the fixed-effects model is preferred to the random-effects model.

**Table 4. Fixed Effects Regression Results [3]**

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**Table 5. Random Effects Regression Results**

**Conclusion**

This study implemented decomposition and regression analysis to examine the energy intensity of the U.S. manufacturing sector over the 1998 to 2010 period; energy intensity in the manufacturing sector declined 34 percent during this time. The decomposition analysis separated changes in intensity into efficiency changes and structural changes, while the regression analysis examined the association between intensity with other variables, where the energy price was the key variable of interest.

Conclusions drawn from the energy intensity decomposition vary, depending on whether a national or regional scheme was used. The national analysis found that 60 percent of the decline in intensity from 1998 to 2010 was due to efficiency, with the remainder due to structural change. The regional analyses found structural change as the main driver in intensity in three of the four regions. The structural change component’s dominance in these regions implies that factors such as international competition from countries with competitive advantages, such as lower wage rates, may have played a substantial effect. This further implies that policies which increase costs could weaken the ability of the U.S. to retain manufacturing facilities.

One policy implication of the energy decomposition analysis is that improvements in energy intensity should not be assumed to come solely from efficiency improvements—structural change can have a large effect as well. It is important to attempt to understand what may drive efficiency improvements and structural change.

The results of the random effects national model are mixed, in regards to whether industries with higher prices tend to be more efficient; however, the fixed-effects model did not find a significant price effect, implying that price changes within industries did not significantly affect energy intensity in these industries. Contrary to the national model, the majority of the regional random-effects models do not find a significant association between energy prices and intensity; only one of the regional fixed-effects model found a significant association between prices and intensity.

For the regression analysis, the stronger findings of the random-effects relative to the fixed-effects models, is likely attributable to the relative lack of variation within industries over time. One policy implication of the regression analyses is that while there is evidence in two of the regions that firms with higher costs tend to have lower intensities, there is less evidence that increases average energy price over time lead industries to improve their intensities. This begs the question of whether policies that encourage efficiency improvements that result in increased costs lead to U.S. industries becoming more efficient or whether these policies result in companies relocating their manufacturing facilities to other countries, with less costly policies.

**References**

Alghandoor, A., Phelan, P., Villalobos, R., Phelan, B. (2008). “U.S. manufacturing aggregate energy intensity decomposition: The application of multivariate regression analysis.” *International Journal of Energy Research* 32: 91-106.

Ang, B., Zhang, F. (2000). “A survey of index decomposition analysis in energy and environmental studies.” *Energy *25: 1149-1176.

Bernstein, M., Fonkych, K., Loeb, S., Loughran, D. (2003). “State-level changes in energy intensity and their national implications.” RAND Corporation. Appendix B. Santa Monica, CA.

Bureau of Economic Analysis (BEA), National Income and Product Account (NIPA) Table 1.1.6, Real Gross Domestic Product, Chained Dollars.

Choi, K., Ang, B. (2012). “Attribution of changes in Divisia real energy intensity index—An extension to index decomposition analysis.” *Energy Economics* 34: 171-176.

Energy Information Administration (EIA). “International Energy Statistics. Energy Intensity - Total Primary Energy Consumption per Dollar of GDP (Btu per Year 2005 U.S. Dollars (Market Exchange Rates)).”

EIA Manufacturing Energy Consumption Survey. 1998, 2002, 2006, and 2010 editions.

EIA Monthly Energy Review (MER), Table 1.3, Primary Energy Consumption by Source.

Liu, N., Ang, B. (2007). “Factors shaping aggregate energy intensity trend for industry: Energy intensity versus product mix.” *Energy Economics* 29: 609-635.

Metcalf, G. (2008). “An empirical analysis of energy intensity and its determinants at the state level.” *The Energy Journal *29(3): 1-26.

Myers, J., Nakamura, L. (1978). “Saving Energy in Manufacturing.” Cambridge, MA: Ballinger.

Wing, I., Eckaus, R. (2004). “Explaining long-run changes in the energy intensity of the U.S. economy.” MIT. Report No. 116. Cambridge, MA.

Wing, I. (2008). “Explaining the declining energy intensity of the U.S. economy.” *Resource and Energy Economics* 30: 21-49.

Wooldridge, J. (2002). Econometric Analysis of Cross Section and Panel Data. Cambridge: The MIT Press.

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**Note:**

*** **This paper is an update of a presentation by its authors at the 31^{st} USAEE/IAEE North American Conference in Austin, TX (2012).

[1] Due to lack of data, industries 313_314 and 315_316 are excluded from the regional analysis (except the South region, which had sufficient data for industry 313_314). Additionally, the West and Northeast regions do not have sufficient data for industry 331, while the Northeast region lacks sufficient data for industry 333, and the West region lacks sufficient data for industry 323.

[2] Due to lack of data, industries 313_314 and 315_316 are excluded from the regional analysis (except the South region, which had sufficient data for industry 313_314). Additionally, the West and Northeast regions do not have sufficient data for industry 331, while the Northeast region lacks sufficient data for industry 333, and the West region lacks sufficient data for industry 323.

[3] Overall employment is included in place of average employment due to multicollinearity—average employment is very highly correlated with both Avgflsp (correlation coefficient = 0.74) and Avgwage (correlation coefficient = 0.47).