*5.1. Change in Energy Intensity of Industries*

First, we analyze how energy intensity has evolved in US manufacturing for over the five decades. We concentrate on the top and bottom 10% of the industries in terms of their energy intensity. More specifically, we calculate the 10th and 90th percentile of energy intensity in the 1960s, then we consider industries whose energy intensity is smaller than the 10th percentile and larger than the 90th percentile in the 1960s. Of these industries, we consider only those for which data are available for a period of at least 4 years. Then we repeat this exercise for the other four decades. Table 1 gives a summary statistics of the energy intensity for all industries for the period 1958–2011 as well as by decade and by energy intensity. As we can see, there are industries for which the energy use is negligible. However, some industries consume quite a lot of energy in the production process. All parts of the distribution were increasing up to the 1990s and then started declining.


**Table 1.** Descriptive statistics of energy intensity by decade and by the intensity of energy use.

It can be seen that in each decade, the 10th and 90th percentiles are specific for the decade. The industries that satisfy the above procedure are shown in Figures 1 and 2. The red decade-specific horizontal lines show 10th and 90th percentiles for low and high energy-intensive industries, respectively. The bold green solid line shows the mean of energy intensity for these industries.

One conclusion that we can draw from Figures 1 and 2 and Table 1 is that the energy intensity has a shape that is closer to a parabola than a flat line. Whether we are looking at the 10th or the 90th percentile, the energy intensity has been increasing from 1960s through the 1980s and then started to fall in the 1990s and then stalled through the 2000s. One possible explanations can be that energy was abundant and relatively cheap up until 1990s when manufacturers started to consider better and more energy-saving technologies.

**Figure 1.** Energy intensity of industries. Shown are industries whose energy intensity are lower than the 10th percentile in a respective decade. Notes: Horizontal red lines show the 10th percentile of energy intensity in a respective decade. The bold green solid line shows the mean of energy intensity for industries whose energy intensity are lower than the 10th percentile in a respective decade.

**Figure 2.** Energy intensity of industries. Shown are industries whose energy intensity exceeds the 90th percentile in a respective decade. Notes: Horizontal red lines show the 90th percentile of energy intensity in a respective decade. The bold green solid line shows the mean of energy intensity for industries whose energy intensity exceeds the 90th percentile in a respective decade.

#### *5.2. Energy Use Efficiency*

In this section, we present the results from three models that are presented in Equations (3), (8) and (10). In all three models, the transient inefficiency is modeled to follow either linear or quadratic trend, that is *σuit* is a function of time in (14). Further, in all three models, we used a translog (log quadratic) specification for the underlying technology. The first model considers energy use inefficiency via an input distance function (IDF). Since inefficiency is radial in the IDF formulation in (3), the energy use efficiency is the same as the efficiency in the use of all other inputs. In the latter two models, inefficiency comes from energy use alone. The difference is that in (10), output can be endogenous, and manufacturing firms are assumed to be profit-maximizing.

The results from models 1, 2, and 3 by decade are presented in Tables 2–4. We observe that in all these models, with an exception of the model 3 for the 1990s, all 4 components are statistically significant and thus use of the [11] model is justified. So, the conclusion about appropriateness of using the 4-component model is in line with [33,34]. This means that models that account for only two components such as [41–43], or three components such as [21] or [18–20] are misspecified and likely to produce wrong results on efficiency. For the 1990s, model 3 could have been estimated using [20] approach.


**2.**Model 1 as in Equation (3). Dependent variable is−log*E*.*z*-values in parentheses.

**Table**


Model 2 as in Equation (8). Dependent variable is log *E*. *z*-values in parentheses.

**Table 3.**
