In this paper, we measure total-factor energy efficiency (TFEE) by 11 industries in 14 developed countries for the period 1995-2005 by using the data envelopment analysis (DEA) approach. TFEE is defined as the ratio of the target energy input suggested by the DEA to the actual energy inputs.
2. Methods and Data
DEA is known as a linear programming method for assessing the comparative efficiencies of a decision making unit (DMU) such as country, firm, and other organization. There are K inputs and M outputs for each of these N DMUs. The envelopment of the i-th DMU can be derived from the following linear programming problem:
Min θ, λ θ
s.t. -yi +Yλ ≥0,
-θxi +Xλ ≥0,
eλ=1,
λ≥0,
where θ is a scalar representing the efficiency score for the i-th DMU; e is an Nx1 vector of ones; λ is an Nx1 vector of constants; yi is an M´1 output vector of DMU i; Y is an MxN output matrix constituted by all output vectors of these N DMUs; xi is a Kx1 input vector of DMU I; and X is a KxN input matrix constituted by all input vectors of these N DMUs. The efficiency score will satisfy 0 ≤ θ ≤ 1. If θ = 1, DMU i operates on the frontier and hence it is technically efficient. In order to control the annual environment, all the efficiency scores and input targets for DMU i in year t are found by comparing to efficiency frontier in year t; that is, only the observations in the same year are used in a DEA model.
Target Energy Input(i, j, t) is defined as
Actual Energy Input(i, j, t) - (Radial Adjustment(i, j, t)+ Slack Adjustment(i, j, t) ),
where (i, j, t) refers to each value in j-th industry the in country i at the t-th year. Radial adjustment is given by (1-θ)x(i, j, t) and slack one is defined as the amount which could be reduced by non-radial way. The total-factor energy efficiency (TFEE) index is introduced defined as
TFEE(i, j, t) =Target Energy Input(i, j, t)/Actual Energy Input(i, j, t).
This model employs four inputs: labor, capital stock, and intermediate inputs without energy, and energy. Value added is the sole output. Economic data are taken from EU-KLEMS 2008. Using purchasing power parties (PPP), they are expressed in 1995 euro. Data on energy consumption are taken from Energy Balances of OECD Countries (IEA).
3. Empirical Results
The most inefficient industry is metal which has an average TFEE of 40.6%. Australia is the most inefficient country with the lowest weighted TFEE except for 1996 and 1998. The most efficient countries are United States from 1995 to 1998, Denmark from 1999 to 2002, and Netherlands from 2003 to 2005. The number of inefficient industries decreases over time, implying larger spaces for most industries across countries to improve their energy efficiency as time goes by.