Chapter 2 Methodology
In this chapter the data envelopment analysis (DEA) approach and Malmquist productivity index will be introduced to measure technical efficiency and productivity changes of decision making unit for the following empirical analysis.
2.1 Data Envelopment Analysis (DEA) Approach
DEA is known as a mathematical programming method for assessing the comparative efficiencies of a DMU1 (in this case, a region is counted as a DMU). DEA is a non-parametric method that allows for efficient measurement, without specifying either the production functional form or weights on different inputs and outputs. This methodology defines a non-parametric best practice frontier that can be used as a reference for efficiency measures. Comprehensive reviews of the development of efficiency measurement can be found in Lovell (1993). Assume that there are M inputs and N outputs for each of the K DMUs. For the pth DMU, its multiple inputs and outputs are presented by the column vectors xi and yj, respectively. The technical efficiency score ( ) of DMU p can be found by solving the following linear programming problem:
ηp
1 DMU is the abbreviation for a ‘decision-making unit.’
where ηp is the efficiency score; xi is the ith input; yj is the jth output of the production; and
λ
r is the weight of each observation. The above procedure constructs a piecewise linear approximation to the frontier by minimizing the quantities of the M inputs required to meet the output levels of the DMU p. The weightλ
r serves to form a convex combination of observed inputs and outputs. The efficiency score measures the maximal radial expansion of the outputs given the level of inputs. It is an output-orientated measurement of efficiency.ηp
Procedure (1) is also known as the CCR model, named after its authors, Charnes, Cooper, and Rhodes (1978), and it assumes that all production units are operating at their optimal scale of production. Banker, Charnes, and Cooper (1984) suggest an extension of the CRS model to account for variable returns to scale (VRS) situations. This model is called the BCC model, named after its authors. It can be obtained by adding one more constraint on process (1). This constraint essentially ensures that an inefficient DMU is only
‘benchmarked’ against DMUs of similar size. Under the assumption of constant returns to scale (CRS), the results from these two approaches are identical, whereas under variable returns to scale (VRS), the results could be different.
1
1
∑
== K
r
λ
r2.2 Malmquist Productivity Index
Productivity changes can be measured by the Malmquist productivity index, which takes panel data into account. This index was introduced by Caves et al. (1982) who name it the Malmquist productivity index. Sten Malmquist is the first person to construct quantity indices as ratios of distance functions. This method is applied by Färe et al. (1994) to analyze productivity growth of OECD countries, by considering labor and capital as inputs
and GDP as an output. Chang and Luh (2000) adopt the same method to analyze productivity growth of ten Asian economies. There may be several reasons for the popularity of the Malmquist productivity index. First, the index does not require information on cost or revenue shares to aggregate inputs and outputs, which means it is less data demanding. Second, compared with other productivity indices, the Malmquist index has the advantage of computational ease. And finally, further decomposition of total productivity can be achieved. The Malmquist index could generate output, such as efficiency change and technical change, which could assist in explaining the differences of growth pattern for different countries.
The efficiency measured from the above procedure is static in nature, as the performance of a production unit is evaluated in reference to the best practice in a given year. The shift of the frontier over time cannot be obtained from DEA. To account for dynamic shifts in the frontier, we use the Malmquist productivity index (MALM) developed by Färe et al. (1994).
This method is also capable of decomposing the productivity change into efficiency and technical changes, which are components of productivity change.
For each time period t = 1,…, T, the Malmquist index is based on a distance function, which takes the form
Dt (Xt, Yt)=min﹛
δ
: (Xt, Yt /δ
)∈St﹜, (2)where
δ
determines the maximal feasible proportional expansion of output vector Yt for a given input vector Xt under production technology St at time period t. If and only if the input output combination (Xt, Yt) belongs to the technology set St, the distance function has a value less than or equal to one; that is, Dt (Xt, Yt)≤ 1. If Dt (Xt, Yt)=1, then the production is on the boundary of technology and the production is technically efficient.Caves et al. (1982) originally define the Malmquist index of productivity change between time period s (base year) and time period t (final year), relative to the technology level at time period s:
)
It provides a measurement of productivity change by comparing data (combination of input and output) of time period t with data of time period s using technology at time s as a reference. Similarly, the Malmquist index of productivity change relative to technology at time t can be defined as
Allowing for technical inefficiency, Färe et al. (1994) extend the above models and propose an output-oriented Malmquist index of productivity change from time period s to period t as a geometric mean of the two Malmquist productivity indices of (3) and (4). A CRS technology is assumed to measure the productivity change, and the MALM is expressed as outputs between the periods), then the productivity index signals no change when revealing MALM(⋅) 1. Equation (5) of productivity change can be rearranged by decomposing into two components, the efficiency change (EFFCH) and the technical change (TECHCH), which take the following forms:
=
)
The term EFFCH measures the changes in relative position of a production unit to the production frontier between time period s and t under CRS technology. Term TECHCH measures the shift in the frontier observed from the production unit’s input mix over the period.2 How much closer a region gets to the ‘regions’ frontier’ is called ‘catching up’, and is measured by EFFCH. How much the ‘regions’ frontier’ shifts at each region’s observed input mix is called ‘innovation’, shown by TECHCH. Improvements in productivity yield Malmquist indices and any components in the Malmquist index greater than unity. On the other hand, deterioration in performance over time is associated with a Malmquist index and any other components less than unity.
2.3 Coping with Undesirable Outputs
The growth of a nation’s (or a region’s) output depends on capital formation as well as efficiency and productivity improvement. Labor and capital are two major inputs in production. When measuring a nation’s (or a region’s) overall output, gross domestic product (GDP) is commonly used. For a nation/region, while GDP (income) is desirable, emissions (pollutions) are undesirable. The change of income and pollutions are two-way relations: First, the increasing of income deteriorates the environmental condition directly because pollutions are generally byproducts of a production process and are costly to dispose.
In reverse, the growth of income is accompanied by public increasing demand for better
2 In summary, the MALM is in the form: MALM=EFFCH×TECHCH.
environmental quality through driving forces such as the control measures, technological progress and the structural change of consumption. Desirable GDP and undesirable pollutions should be both taken into account in order to correct a nation’s output. This concept is called ‘green GDP.’ Green GDP is derived from the GDP through a deduction of negative environmental and social impacts.
Data envelopment analysis (DEA) measures the relative efficiency of decision making units (DMUs) with multiple performance factors which are grouped into outputs and inputs.
Once the efficient frontier is determined, inefficient DMUs can improve their performance to reach the efficient frontier by either increasing their current output levels or decreasing their current input levels. In conducting efficiency analysis, it is often assumed that all outputs are ‘good.’ However, such an assumption is not always justified, because outputs may be
‘bad.’ For example, if inefficiency exists in production processes where final products are manufactured with a production of wastes and pollutants, the outputs of wastes and pollutants are undesirable (bad) and should be reduced to improve the performance.
There are various alternatives for dealing with undesirable outputs in the DEA framework. The first is simply to ignore the undesirable outputs. The second is either to treat the undesirable outputs in terms of non-linear DEA model or to treat the undesirable ones as outputs and adjust the distance measurement in order to restrict the expansion of the undesirable outputs (Färe et al., 1989). The third is either to treat the undesirable output as inputs or to apply a monotone decreasing transformation (e.g.1 yb , represents the undesirable output proposed by Lovell et al., 1995).
yb
In this study, we treat pollutions as negative externalities which directly reduce output and productivity of capital and labor (López, 1994; Smulders, 1999; de Bruyn, 2000). In other words, the emission proxies used in our analysis are acted as by-product outputs or cost of loss, e.g. the health problem caused, the corrosion of industrial equipment due to polluted air, and other related social expenses. In the following analytical process, we will cope those
undesirable outputs by two alternatives: taking their reciprocals (applied in chapter 3) as well as taking them as input (applied in chapter 4). In other words, CO2 emissions are taken their reciprocals to measure a country’s productivity change. Soot, dust, and sulfur dioxide, the main components of Asian Brown Clouds, are considered as input terms to evaluate macroeconomic performance in terms of the regions in China with BCC and Malmquist models.
Chapter 3 The Asian Growth Experience
3.1 The Economic Growth and CO2 Emissions in Asia
A country’s macroeconomic policies generally have two objectives: creation of wealth and good living condition for its citizens. Gross domestic product (GDP) is commonly used in assessing a country’s wealth. However, it does not constitute a measure of welfare say for example without dealing with environmental issues adequately. There is necessity to calculate environmental degradation as a correction factor into our regular definition of economic growth (van Dieren, 1995). For the last three decades, Asia has emerged as one of the most important economic regions of the world. Since 1960, the economy of China, Hong Kong, Indonesia, South Korea, Malaysia, Singapore, Taiwan and Thailand together have grown more than twice as fast as the rest of Asia (Angel and Cylke, 2002). As Asia’s economic activities began to shift toward industry and manufacturing, there has been a dramatic increase in pollution in the region (World Bank, 1998). For instance, fast-developing Asia is now one of the major contributors to the global increase in carbon emissions (Hoffert et al., 1998; Siddiqi, 2000). In fact, the highest percentage rises came from the Asia-Pacific region, including India, China and the newly industrializing 'tiger' economies (Masood, 1997). Because emissions of carbon dioxide are generally acknowledged as a cause of ‘global warming,’ the United Nation has been trying to negotiate a global agreement to tackle carbon dioxide emissions. The Kyoto protocol in 1997 was an international milestone of this effort.
The conflict between economic priorities and environmental interests, for a long time, is at the national level since 1960s. However, as Mol (2003) states, there is an increasing clash of economic and environmental institutions, regimes and arrangements at international level
in recent decades. Studies for economic versus environmental issues is now in a transnational arena. For OECD members, the objective to pursue a balance between pro-development and pro-environment has received considerable attention. Lovell et al.
(1995) study the macroeconomic performance of 19 OECD countries by extended data envelopment analysis (DEA) approach, namely Global Efficiency Measure (GEM) for single period analysis. Japan is the only Asian country included in their sample. The study takes four services, real GDP per capita, a low rate of inflation, a low rate of unemployment, and a favorable trade balance as four outputs. When two environmental disamenities (carbon and nitrogen emissions) are included into the service list, the rankings change, while the relative scores of the European countries decline. According to the experience of the OECD countries, environmental indicators do seem to have crucial effects on a nation’s relative performance.
The aim of this chapter is to measure the macroeconomic performance of Asian countries by moderating unwanted externalities of economic growth using panel data over the period 1987-1996. In this study, performance is defined in light of a country’s ability to provide its citizens with both wealth and less polluted environments. We examine the overall performance of ten Asian economies including China, Japan, the East Asian Newly Industrialized Economies (the NIEs, including Hong Kong, Korea, Singapore, and Taiwan), and four countries of the Association of South East Asian Nations (the ASEAN-4, including Indonesia, Malaysia, Philippines and Thailand) by comparing their productivity change.
Based on the economic theory of production, productivity is generally defined in terms of the efficiency with which inputs (such as capital and labor) are transformed into outputs (such as gross domestic product, GDP) in the production process. The environmental disamenities are added and the analysis is repeated to see if the performance rankings change. The CO2
emissions are included as proxy of environmental impact.
3.2 Data of Asian Countries
The ten selected Asian countries are all APEC members, thus, we establish a data set of 19 Pacific Rim countries: Australia, Canada, Chile, China, Columbia, Hong Kong, Indonesia, Japan, Korea, Malaysia, Mexico, New Zealand, Papua New Guinea, Peru, the Philippines, Singapore, Taiwan, Thailand, and the United States during the period form 1987 to 1996.
We then construct a world frontier based on the data from our country sample. Each country is compared to that frontier. In the analysis without environmental impacts, there are two inputs and one output. We take capital formation and labor force as two inputs and GDP per capita as the only output for a specific country. The data of our multiple comparisons are from Penn World Table Version 6.1 provided by Center for International Comparisons at the University of Pennsylvania (CICUP, 2002). Although capital formation and labor force are not directly available from the data set, simple calculation can be applied. The capital formation is retrieved from the product of real GDP per capita and investment share of real GDP per capita, while the labor force is calculated by dividing real GDP per capita with real GDP per worker. In addition to those two inputs and one output, Table 3.1 transformed CO2
emissions are added into the model. The data of per capita CO2 emissions (metric tons of carbon) is from Carbon Dioxide Information Analysis Center (Marland et al., 2003). The data after 1996 are not included due to the lack of data for certain countries.
Macroeconomic performance is evaluated in terms of the ability of a country to maximize the desirable output GDP while minimizing the CO2 emissions. The value of monetary inputs and outputs such as GDP per capita and capital formation are in 1996 international prices. Summary statistics of these inputs and outputs are shown in Table 3.1.
The software Deap 2.1 (Coelli, 1996) is applied to solve the linear programming problems.
Table 3.1 Summary Statistics of Inputs and Outputs
Output data Input data
Country GDP CO2 Capital Labor
East Asian economies
Mean 2014.40 0.63 423.77 0.6022
China
Std. dev. 603.46 0.07 155.19 0.0047
Mean 20248.31 2.35 6802.04 0.6325
Japan
Std. dev. 2920.71 0.16 901.47 0.0017
NIEs
Mean 20858.23 1.36 5299.07 0.5834
Hong Kong
Std. dev. 3995.09 0.12 1537.09 0.0661
Mean 10300.18 1.77 4033.09 0.4154
Korea
Std. dev. 2634.26 0.41 1254.83 0.0020
Mean 17454.96 3.73 7446.65 0.5241
Singapore
Std. dev. 4731.45 0.57 1969.56 0.0443
Mean 11246.89 1.86 2287.07 0.4369
Taiwan
Std. dev. 2726.79 0.34 699.03 0.0019
ASEAN-4
Mean 2811.29 0.26 554.93 0.3915
Indonesia
Std. dev. 670.49 0.06 185.22 0.0025
Mean 6357.23 1.07 1803.68 0.3727
Malaysia
Std. dev. 1669.54 0.34 804.68 0.0281
Mean 2663.87 0.21 402.95 0.3823
Philippines
Std. dev. 263.94 0.03 69.87 0.0149
Mean 4908.42 0.58 1931.65 0.5286
Thailand
Std. dev. 1420.45 0.21 714.98 0.0026
Other APEC economies Industrialized
Mean 18754.64 4.27 4434.83 0.4825
Australia
Std. dev. 2468.40 0.22 598.39 0.0080
Mean 20082.99 4.13 5034.40 0.5042
Canada
Std. dev. 1804.36 0.10 366.15 0.0045
Mean 14790.74 2.01 3116.88 0.4596
New Zealand
Std. dev. 1710.69 0.08 609.79 0.0104
Mean 24241.51 5.30 4942.76 0.4975
USA
Std. dev. 3166.75 0.12 737.36 0.0072 Developing
Mean 6388.21 0.72 1283.88 0.3737
Chile
Std. dev. 1640.98 0.13 516.38 0.0107
Mean 4541.05 0.46 574.91 0.3895
Columbia
Std. dev. 639.61 0.03 181.77 0.0618
Mean 6683.87 1.04 1194.36 0.3410
Mexico
3.3 Results of Productivity Change
Using the method in section 2.1, the average cumulative changes of ten Asian economies’ productivity without/with CO2 emissions are shown in Figure 3.1, with the year 1987 as the reference year. The overall productivity growth without/with emissions are rising. The trends go up steadily from 1990 to the end of the sample period. The productivity growth with CO2 emissions is below that without CO2 emissions every year except in 1989. It is to be noted that the gap between these two trends seems to be widening each year. In 1996, the difference almost mounts to six percent. This phenomenon is a contrast with the productivity patterns of the industrialized APEC countries in our sample.
Figure 3.2 shows the average cumulative productivity without/with CO2 emissions changes of Australia, Canada, New Zealand and the USA. The two lines of industrialized APEC countries are almost identical, indicating a relatively stable performance without/with including environmental factors comparing with the East Asian experience. Therefore, the productivity of fast developing Asian economies is not as high as reported after considering other non-economic variables. This result is consistent with the estimation that the rapid growth of Asian economies might take a toll on the environment.
0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 year
MALM without
with
Figure 3.1 Cumulative Change in the MALM without/with CO2 Emissions for Ten Asian Countries
0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 year
MALM without
with
Figure 3.2 Cumulative Change in the MALM without/with CO2 Emissions for Industrialized APEC
Countries
Further comparisons taking into account CO2 emissions among countries are displayed in Tables 3.2. On the left half side of Table 3.2, the average Malmquist index without CO2
emissions of the total sample is 1.007, with 7 Asian countries’ indices exceeding unity implying that they have positive production growth. Singapore has the highest productivity growth, followed by China, Japan and the NIEs. The productivity growth of ASEAN-4, except Thailand, shows deterioration. We then repeat the computation again by adding transformed CO2 emissions as environmental proxies. On the right half side of Table 3.2 is the average Malmquist index with CO2 emissions with total sample mean of 1.004. Not only the average Malmquist index is lower than that without CO2 emissions, so are efficiency change and technical change indices. Among the East Asian economies, while the Malmquist indices of China, Japan and the NIEs still perform positive, that of all ASEAN-4 countries declines. Singapore is the best performer without or with the environmental factors. Between our experiments without/with CO2 emissions, it is clear from Table 3.3 that the ranking based on the 10-year average growth performance remain average unchanged, except Indonesia and Thailand, whose ranking regress rather significant compared with other countries’ after taking environmental factors into account. Among the ten Asian economies, those countries with per capita GDP exceeding 10,000 US dollars, such as Singapore, Japan and Hong Kong, generally rank higher no matter whether environmental factor is considered or not.
Lovell et al. (1995) shows that the inclusion of two environmental indicators drastically changes the ranking, reflecting that the environment is a decisive variable when assessing a country’s relative performance for OECD countries. Whether environmental factors are unimportant to a comparison of Asian economies because of average unchanged productivity ranking deserves further study. The ‘Environmental Kuznets Curve’ provides a way to explain this phenomenon. The countries with lower per capita GDP are on the increasing stage of per output pollution. On the contrary, countries with higher per capita GDP report a
decrease in the per output pollution. It could therefore be stated that better environmental performance has been accompanied with economic achievement for richer countries.
Table 3.2 Decomposition of Malmquist Productivity Index without/with CO2 Emissions
Average annual changes without CO2 Average annual changes with CO2
Country
China 1.006 1.020 0.987 1.000 1.020 0.981
Japan 1.037 1.004 1.033 1.043 1.008 1.035
NIEs
Hong Kong 1.034 1.015 1.019 1.052 1.025 1.026
Korea 1.031 1.005 1.026 1.036 1.011 1.025
Singapore 1.075 1.031 1.042 1.068 1.028 1.039
Taiwan 1.002 1.007 0.995 1.002 1.007 0.995
ASEAN-4
Indonesia 0.998 1.011 0.987 0.973 0.993 0.979
Malaysia 0.980 0.985 0.995 0.984 0.986 0.998
Philippines 0.980 1.001 0.980 0.949 0.981 0.968
Thailand 1.005 1.007 0.998 0.983 0.987 0.996
Other APEC economies
Industrialized
Australia 1.019 1.007 1.012 1.019 1.007 1.012
Canada 1.019 1.006 1.013 1.018 1.005 1.013
New Zealand 0.997 0.997 1.000 0.997 0.997 1.000
USA 1.022 1.000 1.022 1.022 1.000 1.022
Developing
Chile 0.992 0.996 0.996 0.993 0.994 0.999
Columbia 0.989 1.000 0.989 0.985 1.000 0.985
Mexico 0.991 1.000 0.991 0.992 1.000 0.992
Papua N. Guinea 0.984 1.000 0.984 0.979 1.000 0.979
Peru 0.979 0.995 0.984 0.983 0.981 1.002
Mean 1.007 1.005 1.003 1.004 1.001 1.002
Note: All Malmquist index averages are geometric means.