Using Grey Model to Predict the Achievement of Policy Objectives

Transcription

1 Using Grey Model to Predict the Achievement of Policy Objectives Chiung-Wen Hsu, Pao-Long Chang Feng Chia University, Taichung, Taiwan Abstract--Owing to the pressures of decreasing CO 2 emissions and establishing a sustainable environment, many nations have set specific goals for conserving energy and reducing CO 2 emissions. Governments have implemented various policies to achieve these goals. The assessment of policies that can effectively lead to energy conservation and CO 2 reductions is becoming a critical issue. Hence, the aim of this paper is to develop an assessment model that can be used to predict the achievement of policy objectives. In this paper, first, a brief introduction of the background and the fundamentals of the grey model are presented. This is followed by a report on the application of the grey model to predict the achievement of Taiwan s subsidy policy. This paper uses data on Taiwan s solar water heater coverage area for the subsidized period ( ) to assess the achievement of the subsidy policy. Taiwan has set a policy objective of covering an area of 6 million m 2 by Considering Taiwan achievement from 1978 to 2009, representing a completion of 32%, the coverage is predicted to increase to 62% during the period from 2010 to Further, since China s coverage area for solar water heaters is the world s largest, this study also uses the grey model to predict its achievement of policy objectives to provide a comparison with reference to Taiwan. It is predicted that by 2020, China s achievement will reach 124% of its policy objectives. Compared to China s achievement, Taiwan s prediction shows that the current policy will fail to achieve its objectives. Therefore, early prediction may provide Taiwan s decision makers with a reference for an early response. I. INTRODUCTION In order to impede global climate change, many nations have considered the need for reducing CO 2 emissions and establishing an environment for sustainable development. Governments have set domestic energy conservation objectives and policies for achieving them. In Taiwan, CO 2 emission levels will reach 467 million tonnes by 2020 if energy conservation policies are not implemented. The government has set a goal of reducing this to the 2005 level of 257 million tonnes; thus, there must be a decrease of 210 million tonnes or 45% [1]. Therefore, the government has planned a variety of policies, measures, and programs to achieve this, and the achievement assessment of energy conservation has become an important issue. According to the statistics on energy use and CO 2 emissions published by the International Energy Agency and the Organisation for Economic Co-operation and Development (IEA/OECD) [2] in 2008, Taiwan emitted million tonnes of CO 2 in Its CO 2 emissions ranked 22nd among the listed nations and accounted for 0.96% of the world s total emissions. The per capita emission was tonnes, ranking 16th in the world [2]. Since Taiwan is an island, it has few energy reserves and its energy supply is almost entirely dependent on imports. For example, in 2009, Taiwan s own energy production accounted for 0.75% of the total energy supply, whereas its imports accounted for 99.25% [3]. Most of this was in the form of oil, coal, and natural gas. The extensive use of highly polluting energy sources such as coal and gas has led to Taiwan s high CO 2 emission levels. The implementation of appropriate policies is necessary to meet energy conservation and emission reduction objectives. Meanwhile, many nations have been setting desired objectives and promoting policies to achieve those objectives. Wu [4] compares the policy instruments of greenhouse gas reduction regulations among the EU, the UK, Japan, Korea, and Taiwan. On the basis of the IEA s policy instruments framework [5], the study divided the policy instruments into three categories: economic instruments, control instruments, and the policy process. The economic instruments include incentive and subsidy programs, taxation measures, total quantity control, and emissions trading mechanisms. Among these instruments adopted by the EU, the UK, Japan, and Korea, the study reveals that total quantity control and emissions trading are the most effective, followed by incentives and subsidies and taxation mechanisms, in that order. Taiwan s economic instruments include incentives and subsidies, funds for promoting energy conservation and reduction, energy taxes (in deliberation), and emissions trading. In Taiwan, greenhouse gas reduction due to emissions trading would be the most effective, but it is also the most difficult to implement. In contrast, incentive and subsidy mechanisms are the second most effective but the least difficult to implement. The budget and effectiveness of five different types of energy conservation technology employed by the Japanese government, namely, photovoltaic power, geothermal power, wind power, solar power systems, and high-efficiency gas turbines [6], were analyzed. The results revealed that solar power systems and high-efficiency gas turbines were the least expensive but the most effective. Milton and Kaufman [7] compared the energy conservation effectiveness of solar power, hydropower, wind power, and solar water heaters in different nations. The study shows that solar water heaters in India provided the highest energy conservation per unit cost. The solar energy industry is currently being promoted by various nations for energy conservation; within this industry, thermal conversion of solar water heaters is the most advanced technology. Owing to these highly developed products, many nations often provide subsidies for installing them, and the US and other major European and Asian countries have adopted various policies aimed at actively developing the solar energy industry. These include system 212

2 cost subsidies, tax exemptions, and investment in development, in addition to making building laws and regulations such as setting the proportion of a building s total energy that must come from solar power. Among these, the most commonly adopted policy is subsidies [8]. China, for example, adopts policies such as investment in R&D, setting building laws and regulations, and fixing targets for the number of solar water heaters. In order to achieve the policy objective of energy conservation, Taiwan s Ministry of Economic Affairs (MOEA) provided incentives and subsidies for installing solar water heaters, beginning in Following this, the annual installation area increased during the period from The subsidy program ended in June 1992, and it was discovered that the installation area had decreased. The subsidy was resumed in January 2000, and the installation area had once again increased. In order to improve results, the subsidy was again implemented and raised to 50% in January This demonstrates the importance of assessing the energy conservation and CO 2 emissions policies, including not just the assessment of implemented policies but also the degree of achievements toward objectives under the promoted policies. Policy assessment refers to using a systematic process to assess the operation of a policy or its results for the purpose of improving future policies [9]. It is primarily the combination of assessing the effectiveness and efficiency of a policy. In a broad sense, policy effectiveness refers to the anticipated and unanticipated results achieved by a policy [10]. Policy efficiency refers to the proportion between investment and benefit for a certain policy [11]. Quantitative methods for assessing policy effectiveness include the macroeconomic and microeconometric models and cost-benefit analysis. The macroeconomic model is used to assess the influence of policies on the economy and society. Because it is suitable for comprehensive empirical study of socioeconomic influence, it is not ideally suited for assessing the effectiveness of a specific energy conservation policy. In particular, the model requires data for a sufficiently long duration and cannot be used to assess the shorter-term impact of Taiwan s energy conservation policies in order to measure the degree of completion toward objectives. Microeconometric models are usually used to assess the effectiveness of subsidy-type public policies. To quantitatively assess a policy s intervention effect, this model gathers individual data and uses the econometric method to assess the economic benefit of public policies. In order to assess the policy benefit, a control group must be established for comparison. In addition, the complete time-series data before and after policy intervention are necessary for policy assessment. Therefore, it is difficult to use the method for assessing the shorter-term impact of energy conservation policies. For a cost-benefit analysis, all costs and benefits are converted into monetary value and classified as direct and indirect influences. Direct influences are directly caused by the policy and related to policy objectives. Indirect influences refer to effects other than the direct influences. Both have a tangible and intangible composition. The tangible portion can be quantified, usually with a monetary value, whereas the intangible portion includes spillover or external effects and is more difficult to measure. This paper aims to establish a model for assessing policies such that it can estimate the achievement of policy objectives before they are implemented. Thus, in this paper, the usefulness of the cost-benefit analysis with regard to assessment is limited. The grey theory was developed originally by Deng [12], and, in contrast to statistical methods, the potency of the original series in the time-series grey model has been proven to be more than four [13]. The grey theory can deal with systems that are characterized by poor information and/or for which information is lacking. The grey system theory is a useful method for short-term prediction [14]. The fields covered by the grey theory include systems analysis, data processing, modeling, prediction, decision making, and control [15]. This theory has been broadly applied in various business and management research fields [16 21]. The theory is most suitable for predictions with a small sample or uncertain data [13]. It makes all random variables grey quantities within a certain range and organizes the original unorganized series of these grey quantities into more organized generate variables. A relatively small number is sufficient for prediction in the grey model [14]. That is, given a small sample, grey prediction has a high degree of precision, and its margin of error is less than that of other models [13]. Therefore, the grey prediction model is suitable to assess the achievement of energy conservation policy objectives, and this study uses this model to establish a model for predicting the achievement of such policies. II. GREY PREDICTION MODEL This paper uses the first-order linear model of grey prediction, or GM (1,1), to assess the achievement of policy objectives. The establishment of the GM (1,1) model consists of five steps: Step 1: Organize the annual solar water heater coverage area data into a nonnegative original sequence X. X = (X (1), X (2),, X (n)) (1) Step 2: Apply the original sequence to establish an accumulated-generation sequence X (1). X (1) = ( X (1) (1), X (1) (2),, X (1) (n)) 1 2 n = ( X (, X (,, X ( ) (2) t1 t1 Step 3: Establish the GM (1,1) model. X ( + az (1) ( = b, (3) t = 2, 3,, n, Z (1) ( = αx (1) (+(1 α)x (1) (t 1). Here, a and b are parameters to be estimated, α is the horizontal-adjusting factor, and 0 < α < 1. Because the data structure of the solar water heater coverage area is t1 213

3 not special, this study sets α at a general value of 0.5. The solution of (3) can be expressed as b b X ˆ ( 1) ( 0 at ( t 1) ( X ) (1) ) e (4) a a Step 4: Use the GM (1,1) model to create a matrix and the estimates of a and b. X ( + az (1) ( = b, t = 2, 3,, n, is Y = B, where (1) X (2) Z (2) 1 (1) X (3), Y Z (3) 1, a B b. (1) X ( n) Z ( n) 1 Using the ordinary least-square method, the estimation of parameters â and bˆ is given by ˆ aˆ T 1 T ( B B) B Y bˆ (5) Step 5: Make predictions through inverse accumulatedgeneration operation. Substitute the parameter values of â and bˆ obtained from step 4 into equation (4) in order to obtain ˆ (1) X ( t 1). Series X (1) is the original series X produced through the one-time accumulated generation. Therefore, before the prediction begins, X (1) (t + 1), obtained through prediction, must undergo an inverse accumulated-generation restoration to become ˆ X ( t 1). The inverse generated series is ˆ ˆ (1) ( 1) ( 1) ˆ (1 X t X t X ) (. (6) After establishing the model, we must go through another step to review the difference between the predicted and actual values. The equation below shows the residual and mean residual errors for the grey prediction model: Error = x( xˆ( (7) x(. n Average error = 1 x( xˆ( (8) n t 1 x( This average error has been defined as the mean absolute percentage error (MAPE), and it represents the strengths and weaknesses of the prediction model. The MAPE assessment criteria according to Lewis s standard [22] are shown in Table 1. TABLE 1: MAPE ASSESSMENT CRITERIA MAPE (%) Prediction Effectiveness Less than 10 Very good Good Ideal Over 50 Inaccurate III. TAIWAN S SOLAR WATER HEATERS A. Background of the Subsidy Policy Taiwan s geographical position is north latitude degrees and east longitude degrees, in the subtropical zone. The northern and central areas receive on average about 1,500 hours of sunlight in a year, and the south receives 2,000 2,500 hours of sunlight [23]. The average radiant heat intensity is 716 1,027 kcal/day-m 2. Therefore, Taiwan s geography is conducive to the installation of solar water heaters. Taiwan can install solar water heaters in a maximum of 3.52 million households, and assuming an area of 5 m 2 per household, the maximum area would be million m 2 [24]. Taiwan has a policy objective of promoting solar water heaters covering an area of 6 million m 2 by 2020 [25], and hopes to achieve about one-third of the target. After the first energy crisis in 1973, Taiwanese companies began importing and selling solar water heaters for domestic use. However, the area of installation was low, so in 1986 the MOEA started the Solar Water Heater System Promotion and Incentive Program. The subsidy policy lasted six and a half years, but was not implemented for seven and a half years thereafter that is, from July 1992 until the end of In May 1998, during the National Energy Conference s New Energy and Clean Conservation Energy Research and Development Program, incentives were proposed for solar water heater systems once again in response to a decline in the installation of solar water heaters. The MOEA believed that the earlier incentives had laid the groundwork for the domestic solar energy industry. Meanwhile, the increased rate of solar water heater installation during the incentive period was proof of the program s success. Therefore, the MOEA implemented the second wave of subsidies in B. The Solar Water Heater Subsidy Policy The variations in coverage area reflect the influence of subsidy policies. Before 1986, solar water heaters covered an area of less than 10,000 m 2 ; after the subsidies were implemented, from 1988 to 1991, the annual area covered increased to 60,000 m 2. In 1992, this figure increased to over 80,000 m 2. However, after the subsidies were stopped, the annual area covered gradually declined to less than 60,000 m 2. When subsidies were resumed in 2000, the annual area covered gradually rose from 55,000 to 117,200 m 2 in 2007 [8]. In sum, the total area covered from 1986, when subsidies began, to the end of 2009 reached 1.9 million m 2 or 32% of the objective for 2020 set by the government. From 1986 to June 1992, the government implemented the first phase of the Solar Water Heater System Promotion and Incentive Program and began subsidizing different types of solar heat collectors such as cover-type panels, vacuum tubes, and coverless heat collectors. Subsidies were calculated on the basis of how much area the collectors covered. The most commonly installed type was the cover-type panel heaters, accounting for over 93% of the national total [26]. They were subsidized at NT$2,000 per m 2 from 1986 to 1989; from 214

4 1990 to June 1992, the subsidy was NT$1,000 per m 2. During the second wave of subsidies, the cover-type panel heaters were subsidized at NT$1,500 per m 2 from By 2009, global CO 2 reduction and energy conservation became an important issue, and in January, subsidies were raised again to NT$2,250 per m 2 for the cover-type panel heaters. The average household received NT$8,000 12,000 in subsidies, totaling about 15% of the cost of installation. C. Data on the Solar Water Heater Coverage Area The data for this study were sourced from the Industrial Technology Research Institute (ITRI) surveys on the area covered by Taiwan s solar water heaters as well as government announcements about solar water heater subsidy policies. The data period is from , when the subsidy was in force. Table 2 shows the data of annual coverage area for solar water heaters. TABLE 2: SOLAR WATER HEATER COVERAGE AREA Year Coverage Area (m 2 ) , , , , , , , , ,000 IV. PREDICTION OF SOLAR WATER HEATER COVERAGE IN TAIWAN According to the GM (1,1) grey prediction model and the solar water heater coverage area data for , the primitive sequence X is X = (75500, 78300, 89000, , , , , , ). From equation (2), the first-order accumulated-generation sequence X (1) is obtained as follows: X (1) = (75500, , , , , , , , ). Additionally, matrix B and vector Y are given by 114, , , , , , ,600 1 B 112,400 Y 527, , , , , , , ,000 From equation (5), we obtain the values of â andbˆ : ˆ aˆ ˆ b 87, We substitute the values of â and bˆ into equation (4) to compute the predicted annual coverage area, as shown below: ( t 1) ( X 87, (1) ) e ˆ (1) t X 87, ) (9) Therefore, substituting t = 1,, 8 into equations (9) and (6), the coverage area from is ˆX, which is, respectively, ˆX = (92416, 96469, , , , , , ). The residual and average residual errors can be obtained by substituting the actual and predicted coverage area values into equations (7) and (8); X ˆ ( 1) ( t 1) and X (t + l) for t = l,, 8. Table 3 shows that the model s average residual error is 8.39%, the maximum residual error is 18.03%, and the minimum residual error is 0.37%. These statistics confirm the efficiency of the proposed prediction model [22]. TABLE 3: GREY PREDICTION MODEL FOR SOLAR WATER HEATER COVERAGE AREA (M 2 ), Year t-value Actual Coverage (m 2 ) Predicted Coverage (m 2 ) Residual Error (%) Average Residual Error (%) ,500 75, ,300 92, ,000 96, , , , , , , , , , , , ,

5 Using the grey prediction model established on the basis of the subsidized period from , given t = 9,, 19, one can predict the solar water heater coverage area for the period Combining the actual and model prediction values for the period in Table 3, we can show the actual and predicted coverage area for this period, as shown in Figure 1. As shown in Table 4, this study uses the grey prediction model to predict the annual coverage area from 2010 to Given that the current subsidies will continue until 2020, it is predicted that the coverage area will increase by 1,792,237 m 2. In addition, Table 4 shows the annual and total energy conserved and CO 2 emission reduced. Given that the heaters have a minimum work life of 10 years, the study hypothesizes that their efficiency will not decrease over a 10-year span. As each square meter of solar heater coverage area reduces 186 kg of CO 2 emissions [27], the estimated total reduction is million tonnes of CO 2. From the perspective of energy conservation, each square meter saves the equivalent of 66 liters of oil [27] for an estimated total of million liters. Taiwan has set a policy objective of a 6 million m 2 solar water heater coverage area by From 1978 to 2009, this figure reached 1,924,800 m 2, representing 32% completion by It is predicted that from 2010 to 2020, the total coverage area will reach 1,792,237 m 2, raising the level of completion to 62%. This prediction shows that the current subsidies will fail to achieve the policy objectives, and therefore, early prediction may provide decision makers with a reference for an early response. m2 250, ,000 predicted value for subsidy policy actual value for subsidy policy 150, ,000 50, Year Figure 1: Coverage Area for Solar Water Heaters in Taiwan Year TABLE 4: COVERAGE AREA FOR SOLAR WATER HEATER SUBSIDIES, Predicted Value for the Subsidy Policy (m 2 ) CO 2 Reduction Effectiveness (tonnes) Energy Conservation Effectiveness (1,000 liters of oil) ,267 24,230 8, ,978 49,522 17, ,940 75,923 26, , ,481 36, , ,248 46, , ,275 57, , ,620 68, , ,339 80, , ,492 92, , , , , , ,288 Total 1,792,237 1,857, ,

6 V. PREDICTION OF SOLAR WATER HEATER COVERAGE IN CHINA Since China s coverage area for solar water heaters is the world s largest [8,28], this study also uses the grey model to predict its achievement of policy objectives for a comparison with reference to Taiwan. The data are sourced from the Energy Research Institute National Development and Reform Commission [29 31]. The grey prediction model established for the period shows that the estimation of a, b is a ˆ Table 5 shows the actual coverage area ˆ b 1, for , the coverage area predicted by the model, and the residual and average residual errors. It also shows that the model s mean residual error is 4.77%, the maximum residual error is 9.24%, and the minimum residual error is 1.41%. The statistics above show the efficiency of the prediction model. Using the grey prediction model established for the period, given t = 7,, 16, one can predict the solar water heater coverage area for the period Combining the actual and model prediction values for the period in Table 5, we can show the actual and predicted coverage area for the period, as shown in Figure 2. This study uses the grey prediction model to predict the annual coverage area from 2011 to China has set a policy objective of a 300 million m 2 coverage area by They could reach 168 million m 2, representing 56% completion, by It is predicted that by 2020, the total coverage area will reach million m 2, taking the completion level to 124%. This prediction shows that at the current level of coverage, China will achieve its policy objectives. TABLE 5: GREY PREDICTION MODEL FOR CHINA S SOLAR WATER HEATER COVERAGE AREA (10,000 M 2 ), Year t-value Actual Coverage (m 2 ; in Predicted Coverage (m 2 ; in Residual Error (%) Average Residual 10,000s) 10,000s) Error (%) ,000 1, ,500 1, ,500 1, ,800 1, ,700 1, ,000 2, ,300 2, Figure 2: Coverage Area in China 217

7 VI. CONCLUSION This paper uses Taiwan s solar water heater coverage area to predict the achievement of policy objectives. It uses the data from the period. Taiwan has set a policy objective of a 6 million m 2 coverage area by It is predicted that by 2020, its achievement level will reach 62%. In comparison, China is predicted to achieve a level of 124% by Compared to China s achievement of policy objectives, Taiwan s prediction shows that at the current level, the country will fail to achieve its policy objectives. Early prediction may provide Taiwan s decision makers with a reference for an early response. The study used the grey prediction model to assess the achievement of the energy conservation and CO 2 reduction policy objectives. It focused on solar water heaters in Taiwan. Testing and verification by the grey prediction model revealed that the GM (1,1) prediction model can make accurate predictions to assess the achievement of policy objectives. The model also used an actual case to show that policy assessment should reflect results in a short period in order to help decision makers implement adjustments. The grey prediction model is suitable for understanding short-term policy assessment, but it requires actual data for five periods (five years) to establish a prediction model. Simulating data for five periods with the help of experts or through other methods of prediction should be considered in the future to deal with the insufficiencies resulting from the lack of data at the beginning of policy implementation. ACKNOWLEDGEMENT The authors appreciate the financial support from the National Science Council of Taiwan (NSC P ). 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