Analysis of panel data

Panel data, also called pooling cross-section and time series data or longitudinal data, needs special estimation techniques. To make the presentation easier to understand, we choose the simple linear regression model with just use one independent variable. The extension to the general case of many independent variables is straightforward. The modified general model is (Ramanathan, 2002):

it it it it it

Y =α +β X + , (11) u where i = 1, 2, …, G, represent the G cross-sectional groups and t = 1, 2, …, n, represent time.

Because there are only Gn observations to estimate 2Gn the parameters, we need to impose some restrictions to reduce the number of unknown parameters. A popular approach to estimating models using models using panel is using dummy variables for each of the cross-section units called the fixed effects model. To illustrate, if G = 3, then we define three dummy variables for these three groups:

D1t which takes the value 1 when i = 1 and for all the time periods, and 0 otherwise;

D2t which takes the value 1 when i = 2 and for all the time periods, and 0 otherwise;

D3t which takes the value 1 when i = 3 and for all the time periods, and 0 otherwise.

The modified model is (for i = 1, 2, 3)

1 1 2 2 3 3 1

it t t t it i

Y =λD +λ D +λ D +β X + , (12) u In essence, we are assuming that the error variances in the equations are the same across the same across equations. If this is so, pooling gives more efficient estimates of the parameters because of the considerably increased number of observations.

The fixed effects model treated the dummy variable coefficients as fixed but unknown. In the random effects model (commonly known as the error component model), they are treated as random drawings from a common population with a fixed mean (call it θ). The modification is as follows:

1 and where θ is the fixed mean effect and εi is an unobservable time-invariant random effect, specific to the ith cross-section group, assumed to be independent of other ε’s with a zero mean and constant variance. The combined error term vit has two components (hence the name error component model), the group specific error (εi) and the overall error uit.

The various error terms are assumed to satisfy the following conditions:

2 2 The following results are easy to show:

2 2 2

( )_{it u}+ and Cov( , )_{it js} , for

Var v =σ σ_ε v v =σ_ε t s≠ . 3.2.5 Hausman test

Given a model and data in which fixed effects estimation would be appropriate, a Hausman test tests whether random effects estimation would be almost as good.

In a fixed-effects kind of case, the Hausman test is a test of H0: random effects would be consistent and efficient, versus H1: random effects would be inconsistent.

(Note that fixed effects would certainly be consistent.) The result of the test is a vector of dimension k (dim (b)) which will be distributed chi-square (k). So if the Hausman test statistic is large, one must use fixed effect estimation. If the statistic

is small, one may get away with random effects estimation. The statistic of Hausman test is as follows (Hausman and Tayor, 1982).

Given two estimators, mβ₀ and lβ₁ , where under the null hypothesis both estimators are consistent but only mβ₀ is asymptotically efficient and under the alternative hypothesis only lβ₁ is consistent, the statistic, m, is:

 l( ₁ l₀)  m q V= ′ −V −q,

where Vl₁ and V represent consistent estimates of the asymptotic covariance l₀ matrices of lβ₁ and mβ₀ , and l m

q=β β1− ₀ . The m-statistic is then distributed χ² with k degrees of freedom, where k is the rank of the matrix(V^l1−V^l0).

3.3 Analysis process

The growth of an economy’s output depends on capital formation as well as efficiency and productivity improvement. Labor and capital are two major inputs in production. When measuring an economy’s overall output, gross domestic product (GDP) is commonly used. While GDP (income) preferred to increase more, consumption of energy is preferred by an economy to be less and efficient. The question between change of GDP and consumption of energy is in an output and input relation: First, the increasing of GDP would be closely related to input consumption of energy directly because these resources are generally key input for production. In reverse, the supply of energy in an economy is at certain level and impossibly supply unlimited for GDP growth. An important point emerges upon this relation: How the energy is consumed in an economy and is the consumption efficient? The GDP growth goal and energy consumption level should be put together in order to set energy policy appropriately, the improvement and concerns to efficiency of energy consumption are key subjects to study and understand.

With respect to CO2 emissions for an economy, while GDP (income) is desirable, emissions (pollutions) are undesirable. The change in income and pollutions is a two-way relation: First, increasing income deteriorates the

environmental condition directly, because pollutions are generally by-products of a production process and are costly to dispose. Conversely, the growth of income is accompanied by the public increasing the demand for better environmental quality through driving forces such as control measures, technological progress, and the structure 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 GDP through a deduction of negative environmental and social impacts.

As mentioned above, many studies criticize the commonly-used indicator of energy inefficiency - the energy intensity as a direct ratio of the energy input to GDP for measuring energy efficiency (e.g., Patterson, 1996; Renshaw, 1981). The ratio is only a partial-factor energy efficiency indicator since energy input is the only input-considered factor. Another argument is that this partial-factor ratio is inappropriate to analyze the impact of changing energy use over time (APERC, 2002). We compute the energy efficiency by a total-factor framework including labor and capital inputs. A total-factor efficiency indicator can provide more information and a more realistic comparative base to examine the de facto situation across economies. We then calculate IRT, IRTR, and TFIE through Equation (6) to (8) from the results of the CRS DEA model for energy input. The IRT, IRTR, and TFIE for energy are called energy-saving target (EST), energy-saving target ratio (ESTR), and total-factor energy efficiency (TFEE), respectively. We use the software DEAP 2.1, kindly provided by Coelli (1996), to solve the linear programming problems as specified in Equation (5) for computing the target inputs and outputs of each economy in each year.

An inefficient economy can reduce or save EST in energy use without reducing the real economic growth. ESTR represents each economy’s inefficiency level of energy consumption. Since the minimal value of EST is zero, the value of ESTR is between zero and unit. A zero ESTR value indicates an economy on the frontier

with the best total-factor energy efficiency up to one among the observed economies and means that no redundant or over-consumed energy use exists (the amount of target zero) in this economy. An inefficient economy with the value of ESTR larger than zero means otherwise that the energy should and could be saved at the same economic growth level. A higher ESTR implies higher energy inefficiency and a higher energy-saving amount.

With respect to CO2 emissions, we use CO2 emissions instead of energy consumption into the same framework including capital and labor inputs to calculate IRT, IRTR, and TFIE through Equation (6) to (8) for CO2 abatement. The IRT, IRTR, and TFIE for energy are called CO2 abatement target (CAT), CO2 abatement target ration (CATR), and total-factor CO2 abatement efficiency (TFCE), respectively. CAT represents that an inefficient economy can reduce the amount of CAT in CO2 emissions in the same real economic growth. Each economy’s inefficiency level of energy consumption is CATR. The greater CATR whose value is between zero and unit is, the more inefficiency and amount of CO2 abatement are.

A zero CATR value indicates an economy on the frontier with the best total-factor CO2 abatement efficiency up to one among the observed economies. An inefficient economy with the value of CATR larger than zero means otherwise should and could reduce CO2 emissions without reducing economic growth level.

Then we use Wilcoxon signed rank test to compare the total-factor indicator, which is constructed in this study, with the traditional partial-factor indicator.

Following the rising income, the center of weight in production and consumption shifts from primary to secondary and then to tertiary industry. In the process of a shift from primary to secondary industry with larger energy consumption, environment condition deteriorate, while the shift from secondary to tertiary industry causes alleviation of the negative impact on the environment with higher energy efficiency and less energy waste. With higher income, citizens become more aware of environmental quality and induce their governments to

introduce stricter regulations. Moreover, the investments necessary for environmental protection are only feasible with the financial resources made available by a certain level of income. Industrialization causes wastes of toxic chemical substances and heavy metals, on the one hand, and leads to larger energy consumption that results in increased emissions of air-pollutants and GHG, on the other hand. For finding out the relation between input-reducing target and income level and the relation between industrial structure and input-reducing efficiency, this study use panel data regression models to analyze. The results will show the relation among input reducing, income level, and industrial structure in APEC economies.

3.4 Data description

The analytical measures described in the preceding section are applied to a dataset of 17 APEC economies for the period 1991-2000. The APEC economies include Australia, Canada, Chile, China, Hong Kong, Indonesia, Japan, South Korea, Malaysia, Mexico, New Zealand, Peru, the Philippines, Singapore, Taiwan, Thailand, and the United States. Brunei Darussalam, Papua New Guinea, Russia, and Vietnam in APEC are not included due to a lack of data. Then 15 economies among the above 17 APEC economies are selected to do the panel data analysis, except South Korea and Singapore, since there is a limitation of data. The data of value-added percents of GDP by industry and service sectors for every economy are taken from World Development Indicators (World Bank, 2005).

To solve the data comparability problem, there are only two practical alternatives: the average rates of exchange and the purchasing power parity (PPP) as measured by OECD (Edvardsen and Førsund, 2003). Usually GDP measurements are commensurate with the exchange rate method. It is often argued in the literature that the PPP method of equivalent GDP should be used to obtain valid cross-national comparisons (Reister, 1987). This study chooses the PPP method to measure GDP.

There are three inputs and one output factor analyzed in this study. As for energy, the three inputs are capital stock, labor employment, and energy consumption. With respect to CO2 emissions, the three inputs are capital stock, labor employment, and CO2 emissions. The single output is all selected as real growth, gross domestic production (GDP) using purchasing power parties. It is expressed in 1995 US dollars. The data of GDP using purchasing power parties and the total energy consumption are from Energy Balances of OECD Economies (IEA, 2002a) and Energy Balances of Non-OECD Economies (IEA, 2002b). The data of CO2 emissions comes from Marland et al. (2005).

The data of labor and capital stock come from the Penn World Tables (Heston et al., 2002). Multiplying capital stock per worker by labor retrieves the capital stock. However, for China, Indonesia, Malaysia, and Singapore, the data on capital stock per worker are not available. They are calculated using the perpetual inventory method:

(1 ) 1

t t t

K = + −I δ K₋ , (15) where I denotes gross investment, which is estimated by first multiplying the real _t investment share by real GDP, at time t; and δ is the depreciation rate.

The choice of the rate of depreciation is problematic due to the difference between the developed economies and the developing ones. The perception is that developed economies can afford to update their equipment and apply new technology. Thus, the rate of depreciation of those economies may be greater than that of the developing ones. However, due to their backwardness and hence the leapfrogging effects, some developing economies may actually be able to adopt new technology faster than developed economies. Unless detailed data at the sector or firm level are available, it is difficult to derive a precise rate of depreciation (Wu, 2004). While the potential impact of the choice of the rate of depreciation is noted, due to data constraints this paper applies a unified rate of depreciation of 5%.

The units of real GDP, real capital, labor, energy consumption, and CO2

emissions are billions of US$, billions of US$, 10,000 people, millions tons of oil equivalent (Mtoe), and millions tons of carbon (Mt-C), respectively. Table 5 lists the average annual amounts and growth rates of real GDP, labor, real capital, energy consumption, and CO2 emissions for 17 APEC economies. The United States, China, and Japan are the first three having real GDP, labor, real capital, energy consumption, and CO2 emissions among APEC economies. China has the highest growth rate of real GDP (9.2%). However, the growth rates of energy consumption and CO2 emission, 1.1% and 0.9% respectively, in China are far less than average of those, 4.1% and 3.4%, among APEC economies. Singapore with the second highest economic growth rate only has the modest growth rates of energy consumption and CO2 emissions with the second highest growth rate of labor. The East Asian economies, with the exception of Japan, Indonesia, and the Philippines, indeed achieved high economic growth in the 1990s. In those economies, high economic growth rates matched the rapid expansion of capital stocks. On the other hand, the average labor growth was rather modest and quite even across all APEC economies.

Energy consumption and CO2 emissions growth rates also exhibited a similar pattern with real GDP growth rates. As Table 5 shows, the Southeast Asian economies, except Singapore, have the highest average annual growth rates in energy consumption and CO2 emissions. Among APEC economies, Hong Kong, the only one economy with negative growth rate of labor but the highest growth rate of real capital, has the highest average energy consumption growth rate (9.4%), Malaysia has the highest average CO2 emissions growth rate (7.1%), and Mexico has both the lowest growth rate (0.2%) in energy consumption and CO2 emissions.

We also can find that the energy consumption and CO2 emissions has very high correlation. That means that an economy consuming more energy emits more CO2.

Table 6 shows the percentages in total energy consumption and CO2 emissions of APEC economies. The United States is the largest energy-consuming and CO2

-emitting economy with almost half of the total energy consumption. For the other half of energy consumption, China, Japan, and Canada consume respectively around 20%, 11%, and 7% of the total energy consumption during the research period. The other 13 economies use only less than 13% of total energy consumption. The United States, China, and Japan, the largest three CO2-emitting economies, have about eighty percentages of the total CO2 emissions. During the ten years, the percentage in total energy consumption and CO2 emissions does not change drastically among APEC economies.

Table 5 Average annual amounts and growth rates of real GDP, real capital, labor, and energy consumption (1991-2000) Canada 707.86 2.9 1287.13 7.9 1500.7 1.2 126.45 1.9 121.54 1.8 Chile 112.04 5.8 155.5 13.3 551.45 2.0 11.2 5.6 13.11 5.9 China 3394.72 9.2 4122.14 14.7 73080.42 0.9 561.2 1.1 802.85 0.9 Hong Kong, China 138.49 3.2 226.59 15.5 329.07 -0.2 10.77 9.4 8.85 2.5 Indonesia 541.37 3.3 1033.7 7 7763.12 1.9 50.88 6.1 56.36 3.5 Japan 3079.92 1.1 7183.32 7.9 7963.75 0.3 326.69 1.4 309.39 0.8 South Korea 620.89 5.2 1304.9 12.7 1904.38 1.2 105.29 6.1 98.4 4.9 Malaysia 154.71 6.1 263.4 16.6 739.56 2.5 22.14 7.2 29.06 7.1 Mexico 723.02 3.1 958.6 9.6 3169.47 1.8 94.15 0.2 101.48 0.2 New Zealand 64.27 2.8 107.59 7.6 172.7 1.4 11.87 3.2 7.81 3.0 Peru 102.7 3.8 144.6 8.8 1005.13 4.3 7.59 3.6 6.77 3.2 Philippines 255.98 2.9 226.56 9.7 2791.67 2.5 14.57 6.2 17.34 5.5 Singapore 69.89 7.0 274.78 7.8 179.55 3.2 8.74 4.2 14.75 2.4 Taiwan 324.35 5.4 518.57 8.3 934.49 0.9 41.98 4.4 48.21 5.9 Thailand 341.43 3.5 748.04 13.6 3143.27 0.9 35.27 6.3 46.98 5.7 United States 7758.29 3.3 11191.59 10.1 13395.57 1.3 1400.83 1.4 1446.39 1.9 Average 1105.46 4.2 7030.42 1.6 1709.34 10.5 170.25 4.1 188.98 3.4 Notes: (1) Statistics in the ‘GDP,’ ‘Capital,’ ‘Labor,’ ‘Energy,’ and ‘CO2 Emissions’ columns are mean

percentage rates of growth. (2) The base year for real GDP and real capital is 1995. (3) Source:

Penn World Tables, IEA Statistics 2002 Edition, Marland et al. (2005).

A correlation matrix is given in Table 7 that shows a high correlation exists between input and output factors selected for this analysis among APEC economies.

As shown in Table 7, all inputs have positive correlation coefficients with the output.

That is, all inputs satisfy the isotonicity property with the output. Labor employment, capital stock, energy consumption, and CO2 emissions do actually correlate to GDP performance in this analysis model. The correlation coefficients between energy input and GDP output and CO2 emissions and GDP are calculated as 0.98 and 0.97, respectively, which are statistical significant. The relation reveals that the more energy is consumed, the more GDP is generated. The more GDP is generated, the more CO2 is emitted. However, energy efficiency and CO2 abatement efficiency need to be analyzed in this study in order to learn individual efficiency scores for all APEC economies.

Table 6 Percentage in total energy consumption and CO2 emissions of APEC economies in 1991, 1995, and 2000 Note: The unit is percentage.

Table 7 Correlation Coefficients between inputs and the output for APEC economies Real Capital

Stock Labor Energy

Consumption CO2 Emission

Real GDP 0.95 0.46 0.98 0.97

Chapter 4 Empirical Analysis

4.1 Energy-saving targets for APEC economies

Each economy’s ESTR is also calculated. Table 8 reports the summary of ESTR based on Equation (7) for each economy. Table 9 shows EST for each APEC economies. Table 10 presents the per capita EST for each economy. Several interesting observations are summarized as follows.

Table 8 Summary of ESTR for each APEC economy (1991-2000)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Australia 10.81 10.73 12.69 14.61 13.18 10.76 8.45 5.12 4.25 6.45 Note: (1) The unit is percentage. (2) Scores with a gray background are those reached at the best

efficiency with zero score.

1. The ESTR score generally decreases for the APEC economies during the period considered. As seen in Table 8, the APEC economies, except Canada and New Zealand, have become more efficient in energy efficiency and energy-saving efficiency over time. In the late 1990s, they improved their energy efficiency

and were closer to the frontier than in the beginning. We separate the samples into developed and developing groups: developed economies included Australia, Canada, Hong Kong, Japan, New Zealand, Singapore, and the United Sates. The other economies belong to the developing group. Since developed economies could afford to update equipment and apply new technologies, they have lower ESTR scores than those in the developing group.

2. The ESTR scores of all the Asian economies but four (Hong Kong, Japan, Singapore, and Taiwan) are higher than the average scores during the research period. Neither any of the Central nor the South American economies are efficient EST economies. Their ESTRs are much lower than the Asian economies under a similar growth level.

3. China has the largest EST with almost half the amount of its current usage even as it owns the highest development growth rate from 1991 to 2000. China can save around 50% of the amount of its current energy consumption by improving technology efficiency without reducing the high production level. As seen in Table 9, the EST of China in 2000 is 273.67 Mtoe by 65% of the total APEC’s EST. China plays a key role in energy saving and environmental protection in the association of APEC economies. However, the ESTR score decreased from 83% in 1991 down to 50% in 2000. An improvement in energy efficiency and technical and structural changes has been identified as the main factor that caused the fall in ESTR in China (Crompton and Wu, 2005).

4. Hong Kong, the Philippines, and the United States have the ‘best practice’

among APEC economies and have the complete know-how of production function. They have the lowest ESTR rankings with zero over the 1990s among APEC economies. Chile, Mexico, and Taiwan significantly improved their energy efficiency in the last 7 years of the 1990s. Mexico and Taiwan possess an ESTR value of zero in the latter three years of the research period. Chile’s ESTR scores are at zero from 1995 to 1996 and 1998, but then increase slightly