Creating a Provincial Long-Term Growth Model for China using the Kohonen Algorithm

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1 Creating a Provincial Long-Term Growth Model for China using the Kohonen Algorithm Elpida Makriyannis, Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, U.K. Philip Treleaven, Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, U.K. ABSTRACT The capabilities of self-organising maps when applied to a long-term growth model of the Chinese provinces, are investigated in this work. The long-term growth indicator is created by taking into consideration the main growth areas in each of the provinces. Then the Kohonen algorithm is used to map the provinces according to the economic growth sectors that they have performed well in and make some predictions about the provincial growth. The algorithm s performance depends on the representational choices that are made, so the long-term growth indicator is designed in such a way that it gives as much information about each province s growth model as possible. Introduction This paper investigates the mechanisms behind clustering Chinese provinces in relation to long-term growth, using a Kohonen algorithm that will try to identify patterns and predict how each of the Chinese provinces grow and in which sectors. The Kohonen algorithm uses unsupervisedlearning to visualise and interpret large highdimensional data sets, like the Chinese provincial data sets. It also modifies the internal state of the network to model the features found in the training data. This is an approach to defend the idea that intelligent systems can be better than statistical methods in many different applications, including economic modelling. Good applications are needed to prove that computer algorithms can solve complicated real-world problems, so this application also tests the capabilities and limitations of selforganising maps. The capabilities of a Kohonen algorithm are investigated when it has to cluster large data sets with political and economic meaning for a whole country at a provincial level. On a larger scale, the result of this research can be used to help other countries understand how they

2 accomplished provincial growth in the past and how they can achieve and sustain future growth. Application looking for clustering algorithm. This application is searching for the clustering technique that will interpret it and represent it the best way possible. Comparing and selecting the most reliable and appropriate technique is often a difficult task. Not in this case though, due to the complexity of the data most clustering algorithms can not be used. The number of clusters is not known in advance, although an approximation can be assumed. We are dealing with large high-dimensional data sets and measurement problems can occur. In clustering techniques including K-means and Hierarchical Clustering techniques the number of clusters has to be known in advance, and also they don t always reach a global optimum. The Kohonen algorithm is better suited to this application because it maps high-dimensional data and it modifies the internal state of the network to suit the training data. It can also produce a hierarchical representation of the relations implicit in the primary data. Statistical methods are used for economic understanding and forecasting. These methods include factor analysis and principal component analysis, however they need precise information in advance about the structure of the economic model. The China Connection Due to its dual-track economy and its record in generating growth and improvements in productivity, the Chinese economy has been impressive over the past 20 years. China grows differently because its population density is tremendously different from anybody else s. It is not divided in historical, religious or racial groups that have been so important in the disintegration of the Soviet Union and Yugoslavia. China is populated overwhelmingly by those of the Han race and consists of 31 provinces that are divided into coastal and inland groups[6]. China is becoming more regionally integrated. Those who argue that regional fragmentation is likely believe that it will be the rich coastal regions that will break away. However, a look at the economically most successful province, Guangdong, suggests that it has become increasingly dependent on the rest of China, both as a source of raw materials and as a market for finished goods. What China is accomplishing slowly but steadily is bridging the gap between urban and rural development to increase productivity in the less endowed regions. Policies to bridge the gap include intensifying the construction of infrastructure and improving marketing conditions. Just as reform has led to China s greater integration into the world economy, the increasing marketisation of the domestic economy has led to increased internal economic integration[6].

3 China is currently managing two transitions: on an international level, from a centrallyplanned to a market-oriented economy and on a provincial level, from a rural and agricultural to an urban and industrialised country. Economists are cautious with their predictions for China s future due to China s transitional period, the Hong Kong and Macao handovers in the recent years and its planned entry in the World Trade Organisation(WTO) in 2002 as a developing country. However, Nicholas Lardy[6], a reputable economist, gives a good theoretical model of China s economy and trade in the past and the future. Peter Verburg[14], an expert in applied geography in China, has produced a very useful tool that models the agricultural sector in China s interior. Making noisy data sing Chinese data tends to be noisy and incomplete. The sections that follow explain how this research pre-processed the data in order to deal with incomplete panels, measurement and representation. Nature of the data The empirical work for this research employs continuous-valued 3D panel data on 29 provinces, and 8 economic sectors, over the period 1978 to The 29 provinces are Anhui, Beijing, Fujian, Guangxi, Guizhou, Gansu, Guangdong, Hainan, Henan, Hebei, Heilongjiang, Hunan, Hubei, Inner Mongolia, Jilin, Jiangxi, Jiangsu, Liaoning, Ningxia, Shanghai, Shangdong, Shanxi, Shaanxi, Sichuan, Tianjin, Xingjiang, Yunnan, Zhejiang. The sectors are agriculture, industry, energy, population, communications, construction, income, and employment. The data sets are obtained from the Statistical Yearbook of China which covers the period 1981 to 1998 for country figures, and from the Provincial Statistical Yearbooks for 1978 to 1998 for provincial figures. The Facts and Figures Book is also consulted for years 1978 to The China Energy Yearbook( , ) is used because it provides more accurate energy data. The long-term economic growth measure is constructed considering three determinants, the accumulation of capital, population growth, and technological progress. The accumulation of capital is an important element of growth because it encompasses physical capital (machines, manufacturing) as well as human capital (quality of labour, labour force). Growth though, cannot go on forever just by adding to the capital stock. Population growth can sustain growth in the level of output but not in the levels of product and income per capita and so technological progress plays a crucial role for sustaining growth in the long run. It is clear that more sectors could be added when defining such a broad measure as long-term economic growth, however consistent data was not available and would present measurement problems. The following adjustments were made: Tibet and Qinghai had to be excluded from the sample due to the

4 insignificance of the data in almost every sector. Coal and Oil production were combined into a single energy sector as an aggregate of energy production because they are the two largest components of energy production and adding other minor energy components (natural gas and hydro-power) would create measurement problems. Income here represents disposable income that consists of final consumption plus total savings. Incomplete Panel Data Incomplete observations can be recovered by creating functions that help us obtain an accurate estimate of the missing data. The Gourieroux-Monfort(G-M) method,[13], is used to obtain good approximations of missing values. The main structure of the G- M method is used here, and the equations derived are shown below. The first equation is for data that is only missing up to three values from the two decades examined. The missing values are obtained from the following equation: Q it = a + by it + e t Eq 1 where y it is the log sector of i for year t. The second equation is for data that is missing more than three values for the two decades examined. The way these values are recovered is significant in order to retain crucial information: Q it = a + by it +CQ jt Eq 2 where Q jt is the province or average of similar-valued provinces. Scaling and Smoothing Using data that makes sense to the analyst and to the system that it is applied to, is essential. The way that data is prepared plays a crucial role in how good the results are going to be. The data is scaled, taking growth rates of each province for each sector. In order to obtain a balanced data set, 3-year moving averages are used. The reason for using moving averages is that the minimum information about the data is lost. This way only the first and last year of the data set are lost and there is still the advantage of the smoothened average values[14]. A radar diagram that shows the position of each province after scaling is shown below. Sichuan Shaanxi Shanxi Shangdong Tianjin Shanghai Xinjiang Ningxia Growth for Chinese provinces from 1978 to 1998 Anhui Zhejiang Yunnan Liaoning Jiangsu Jiangxi Two-way analysis of variance Beijing Fujian Hubei Inner Mongolia Guangxi Guizhou Hunan Gansu Guangdong Hainan Henan Heilongjiang Given that we have 3D panel data, in time, provinces and sectors, we can decompose the total variance of growth levels in year t, into the sum of the variance across sectors, the variance across provinces and a residual term. Consider the unweighted average Jilin

5 growth measure jt averaging over the sectors for each province jt =Σ i y ijt /I where I is total number of sectors, and the unweighted average growth y ijt, averaging over the provinces for each sector jt = Σ j y ijt / J where J is total number of provinces. For y ijt = q ijt g ijt where q ijt is output and g ijt is growth. Then long-term growth in sectors i, province j and year t, y ijt can be written as: y ijt = it + jt + ε ijt Eq 3 The Design Objectives An SOM can cluster at a multidimensional level and it can also modify the network s internal state to form its own classification of the training data sets. The Chinese provincial data has three dimensions, which increases the complexity of the processing. This is also the reason why economists analyse one economic sector at a time and not in parallel, like this research is trying to accomplish. The objective is to design the economic input data in such a way that it clusters provinces according to individual growth and development in the different sectors and predicts the future of each province s growth. Model of the Provincial Long-term Growth The growth model is constructed to answer the following question How will China grow at a provincial level?. It has to include all provinces, take into consideration the main sectors that each of these provinces is growing in, and explain the long-term economic growth indicator for each province s growth performance. Although there are studies focusing on China, [4],[6],[14] there is not any model defining and explaining the long-term economic growth indicator for all the Chinese provinces. The long-term economic growth measure is constructed considering three determinants, the accumulation of capital, population growth, and technological progress. These three determinants include some of the main sectors that are used in this model, namely agriculture, industry, energy, population, communications, construction, income, and employment. GDP is also used as the total growth measure. Information about the sectors is updated annually and the growth in these sectors is observed for two decades, 1978 to 1987 and 1988 to The reason behind this is that 1979 was the year that China started its economic reform and introduced its open door policy. In order to get a good sample of the way in which the Chinese provinces are growing and what affects them, at least two decades are needed. Experimenting with the Kohonen Algorithm After pre-processing, all the provinces now possess data for all their attributes. There are 8 attributes, in this work, and they constitute the pattern vector that acts as a set of signal values at the inputs of the network. A column gives a schematic description of each of the provinces. For the initial tests the number of nodes used are proportional to the number of Chinese provinces. They are selected and arranged on a 6x6 square grid, i.e. 36 nodes[12]. The method to derive the exact number of input nodes is spread encoding. The input data is split into a

6 number of bins, then each value is assigned to one of the bins proportional too the distance between them. The Euclidean distance is used as a similarity measure. The input data is then organised into nodes. The weights between the nodes are given large values to start with so that no useful information is lost. Each neighbourhood has to be tested on its own and as a whole. The experiments are prepared using the first 10 years of growth data to train the network and then the next 10 to interpret how the system classifies new information and if there are any meaningful economic and political predictions. The outputs of the Kohonen network have to be explained and converted to significant political and economic comments on China s provincial growth. Conclusions Due to the originality of this research it would be easy to make wrong assumptions about how to process the data so that it makes sense to the algorithm, and also how many nodes the network should have. The limitations were mostly in the data set, the provincial data was all in Chinese and each province had a different way of classifying and naming the sectors, which made it difficult to get the correct data. The application designed here, is used for analysing Kohonen algorithms and expanding their range of applications. The long-term growth indicator is designed in such a way that it gives as much information about each province s growth model as possible. Statistical analysis is used to design the economic growth model. Bibliography [1] Deidda, L. (1997), A theoretical story about the inter-regional trade in financial services, SOAS Economic Digest, June 1997, Issue 1, No.2. [2] Everitt, B. (1993), Cluster Analysis, Edward Arnold, 3 rd ed. [3] Green,P., Frank, R.E., Robinson P.J.(1967), Cluster Analysis in Test Market Selection, Management Science, vol 13, no8, April [4] Hendrischke, H., Chongyi, F.(1999), The political economy of China s provinces: comparative and competitive advantage, Routledge, New York. [5] Kohonen, T. (1995), Self-organising Maps, Springer Series in Information Sciences, Springer, Berlin, 2 nd ed. [6] Lardy, N. (1994), China in the World Economy, Institute for International Economics, Washington D.C. [7] Matyas, L. and Sevestre, P. (1996), The Econometrics of Panel Data: A handbook of the theory with applications, Matyas, 2 nd ed. [8] Mitchell, T. (1997), Machine Learning, McGraw Hill International Editions.

7 [9] Paton, R. (1994), Computing with Biological Metaphors, Ed. Paton, Chapman and Hall. [10] Statistical Publishing House, Beijing. Statistical Yearbook of China( ), China Statistical Bureau. [11] Energy Statistical Yearbook of China( ), China Statistical Bureau. [12] Swingler, K. (1996), Applying Neural Networks: A practical guide, Academic Press. [13] Tybout, J.(1992), Making noisy data sing: Estimating production technologies in developing countries, Journal of Econometrics, vol 53, p [14] Verburg, P. (1997), PhD Thesis: Exploring the spatial and temporal dynamics of land use, Wageningen University, The Netherlands.