**1. Introduction**

According to the U.S. Energy Information Administration, manufacturing industries in the US consume about a third of total energy consumed (see also [1]). (https://www.eia.gov/consumption/) The analysis of energy demand for manufacturing has therefore important implications for energy policy, where energy efficiency and savings is an important agenda (see, e.g., [2]). Additionally, improving energy use efficiency seems to be a natural way to mitigate climate change (see, e.g., [3]). If manufacturing industries are not efficient, it puts strains on the whole economy in general and energy producers and distributors in particular. This is especially true for the energy-intensive industries where energy consumption relative to its output is large.

For a long time, a lot of effort has been made to develop energy-efficient technologies, not only to lessen environmental damage but also to bring down the monetary cost of production. However, Refernece [4] identify and discuss the wide-spread "energy-paradox", whereby energy-efficient technologies, that would have paid-off, are in reality not adopted. The authors of [5] find that the adoption of energy-efficient technologies may be boosted by involving managers, who are in a position close to operations. The existence of the "energy-paradox" may indicate that the industry remains inefficient. Indeed, [6] find that the mean plant-level efficiency in the United States over the time-period 1987–2012 ranges from 33% to 86% for plants in various manufacturing industries.

Such huge inefficiencies are a matter of concern. Enormous financial savings could have been achieved if manufacturing firms were more efficient. The performance of manufacturing in terms of energy use is heterogeneous both in time and cross-sectional dimensions. One common factor influencing energy consumption is the price of energy. The authors of [7] confirm that the biggest determinant of energy intensity is the price of electricity. The cross-sectional variation is further determined by technology, i.e., some industries require more energy than others. The time variation has many determinants. Most important is probably the change in macroeconomic conditions. The beginning of the 1970s was marked by the oil prices, which had a detrimental effect on costs related to energy in manufacturing. It was an expectation that there should have been a surge in adopting the new energy-saving technologies which would eventually improve energy efficiencies. However, [8] finds that the energy consumption did not rebound quickly implying that the response to a decline in real energy prices was slow.

In this paper, we investigate the energy use efficiency of US manufacturing from 1958 to 2011. More specifically, we conduct an analysis at an aggregated level, where the unit of observation is defined as NBER 6-digit NAICS (see [9]). We split the whole time period into five decades and assume a decade-specific technology. We define energy intensity as energy demand per measure of economic activity (see, e.g., [10]). In each decade, we consider 10 percent the most and least energy-intensive industries. Further, following [11], we decompose overall inefficiency into persistent or structural and transient inefficiencies. This has an advantage over for example [3] or [6] since we can identify if efficiency can be improved with relatively small effort, or structural approach is required. We find a significant drop in energy use efficiency in the 1970s, which has probably been caused by the oil crisis. The return to the pre-1970s levels was reached only in the 2000s, which is in agreement with slow rebound estimates of energy consumption (see, e.g., [8]). Remarkably, such low levels of overall energy use efficiency owing to very low levels of structural inefficiency that cannot be managed with ease. This finding goes in unison with the "energy-paradox" (see [4]). Finally, higher energy-intensive industries are characterized by lower levels of energy use efficiency than low-intensive counterparts.

The paper is organized as follows. Section 3 introduces models that are used to measure energy use efficiency and 4-component stochastic frontier model that accounts for heterogeneity and splits overall inefficiency into persistent and transient components. Section 4 describes data and variable construction. Empirical results are presented and discussed in Section 5. Section 6 concludes.

#### **2. Literature Review**

Analysis of the energy use efficiency is interesting from both academic and business perspective. More efficient use, especially by energy-intensive industries, would result in lower demand for energy as well as output (see, e.g., [12]). Examining efficiency estimates could also complement accounting for rebound effects ([13]) when making energy consumption forecasts. Energy subsidies could also be inappropriately targeted to support highly inefficient producers if inefficiency measurement is improper (see, e.g., [14]). Here we provide a brief review of methods used in measuring energy and technical or cost efficiency.

Depending on the available data, measurement of technical efficiency can be done by using either stochastic frontier (SF) methods (see [15]) or data envelopment analysis (DEA) approach (see [16]). For a cross-sectional data with fewer observations, one can opt for DEA to estimate the benchmark and then measure inefficiency as a deviation from the benchmark. SF in contrast defines the benchmark accommodating stochastic noise and decomposes the composed error (sum of noise and inefficiency) into inefficiency and statistical noise. The noise can be both positive and negative and can be seen as positive and negative shocks to the production process. In the panel-data context, there are different possibilities to decompose the composed error term. One way is to allow inefficiency to be persistent and hence time-invariant. This approach is referred to as the first-generation panel-data SF modeling. The second-generation SF models assume that the inefficiency is time-varying. The first and second-generation models assume an error term (the deviation from the frontier) that has two

components. Applying DEA to a panel data would be comparable to a second-generation SF model, which would produce time-varying efficiency estimates without accounting for possible noise. The third-generation SF model considers an error term with three components. The two components are time and firm-specific, i.e., statistical noise and time-varying inefficiency. The third component is time constant. The authors of [17–20] propose to treat it as time-invariant inefficiency. The authors of [21] assume it is an individual effect or firm heterogeneity. Thus, Kumbhakar and co-authors model two types of inefficiency (persistent and transient) ignoring heterogeneity, while Greene models transient inefficiency and heterogeneity ignoring persistent inefficiency. The fourth-generation class of SF models is originally introduced by [22] and accounts for both types of inefficiency as well as heterogeneity. Incidentally, the fourth-generation SF models are also known as the 4-component SF models.

Traditionally, energy efficiency measurement is contemplated in terms of energy intensity. However, it is argued that other measures should also be considered, for example DEA ([23]). This was one of the first studies to consider the production theory framework as a base for energy efficiency measurement. The authors of [23] employ DEA for the manufacturing sector constructed by the U.S. Bureau of Labor Statistics (BLS). She finds quite high efficiency scores for aggregate manufacturing for the 1970–2001 time period. Recall, however, that DEA does not account for heterogeneity or persistent efficiency akin to the second generation SF models, which can be seen as a disadvantage of using DEA. Furthermore, she finds higher efficiency scores towards the end of the sample. But because she used an intertemporal frontier approach, she could not distinguish whether this is attributed to technical progress or not. This can be viewed as the second disadvantage of using DEA when panel data are available. Many other studies have used DEA to analyze energy efficiency. The authors of [24], for example, investigate the energy efficiency of the Indian manufacturing sector for the 1998–2004 time period. The authors of [25] apply DEA to measure economy-wide energy efficiency using aggregated data on the OECD countries. The authors of [26] investigate energy use efficiency of canola production in Iran. See the review of [27] for other studies that employ DEA.

SFA has also been used to measure energy efficiency and efficiency in the energy sector. The authors of [28,29] were the first to advocate using SFA to estimate efficiency in manufacturing sectors. However, he did not go beyond a cross-sectional analysis. The authors of [30] use the second-generation SF model to measure energy efficiency of different states in the US residential sector. The authors of [31] investigate energy efficiency in the automotive manufacturing sector using plant-level data. The authors again use the second generation model. The authors of [32] are the first to use the third generation SF model to analyze the efficiency of the Swiss electricity distribution sector. The authors of [33] used the fourth-generation model to aggregate frontier energy demand model and estimate economy-wide persistent and transient energy efficiency in the US. The authors confirm the findings and arguments of [23] that energy intensity is not a good indicator of energy efficiency. The authors of [33] as well as [34] emphasize the importance of accounting for heterogeneity as well as estimating two types of inefficiency. This is the approach, which we apply for the first time to this type of data using three different models. Our models are described in the next section.
