Among them, s2=i(Y-)2,=iY, Y represents the observation value of the i-th region. In this paper, the per capita GDP is the region n number, and w is the space weight matrix. The value range of I is -1矣/矣1. When I is close to 1, it means that there is a spatial positive correlation between the regions. When it is close to -1, it means that the space is negatively correlated. When it is close, there is no spatial correlation between the regions. It should be pointed out that, traditionally, the space weight matrix w mostly adopts a matrix based on the adjacency concept, but the idea that the non-adjacent regions do not have correlations is quite different from the reality. Considering the law of spatial correlation between general regions: the shorter the distance between different regions, the stronger the correlation between regions; as the distance between regions increases, the correlation between regions will gradually weaken. Therefore, in this study, we use the reciprocal of the linear distance between the provincial capitals of different provinces as the value of the elements in w.
From 1998 to 2009, the calculation and test value of Moran's/index with the distance reciprocal as the weight matrix element. The results in Table 1 show that for the vast regions of China, there is indeed a spatial correlation that varies regularly according to the distance between regions: as the distance between regions increases, the spatially related Moran's/index gradually declines. This means that there is a strong spatial positive correlation in different regions of China in a small bandwidth range, but as the bandwidth increases, the positive correlation becomes smaller, and when calculated with a bandwidth of more than 2,500 kilometers, Moran's/ The index changes from positive to negative. Of course, the accompanying probability P value at this time shows that there is no global spatial correlation. This feature runs through 12 years from 1998 to 2009.
From the time dimension, Table 1 shows that the spatial correlation between China's regions is gradually increasing over time. For example, according to the bandwidth of 0-500 km, the Moran's/index value in 1998 was 0.186, and increased to 0.294 in 2009; while the bandwidth of 02000 km, the Moran's/index value increased from 0.002 to 0.036. Other bandwidth ranges. It also shows the same features.
The /index measures the spatial correlation of the regions across China. The measurement results show that the global correlation becomes more and more intense over time. Next, we will examine from the local Moran's / index whether the number of regions with strong correlation with other regions is increasing over time. Anselm (1995) pointed out that the local distribution of spatial associations between regions may have an atypical situation that cannot be reflected by global indicators, and even the situation that local spatial correlation trends are opposite to the global trend, so it is necessary to use the spatial association bureau. Domain Indicators (LISA) to analyze the local characteristics of spatial associations. The local Moran's/index is the main indicator used to measure the local autocorrelation of regional space: where Zi=Yi-)Z=Y-)Fi, Y. indicates the observation value of the i-th and the first region, in this paper, the per capita GDPn For the number of regions, W is the space weight matrix. The index measures the degree of correlation between the i-th region and other surrounding areas: positive values ​​characterize the region's positive correlation with surrounding areas, ie regions with similar per capita income levels are clustered together; negative values ​​indicate presence with surrounding areas Negative correlations, where regions of varying per capita income levels are clustered together. The use of this indicator in conjunction with the Moran scatter plot gives a clearer picture of the local-related patterns and characteristics (Anselin, 1996).
Table 1 China's spatial autocorrelation Moran'sI index and its statistical test year distance in China's vast territory, the relationship between different regions often has different characteristics. The Moran scatter plots of per capita GDP in China and 1998 in 2009 and 2009 are given. It can be seen that the regions with atypical observations, that is, the regions in the second quadrant and the fourth quadrant, have changed greatly at the beginning and end of the period: in 1998, 11 regions belonged to atypical observations, and reached 2009. The number of such atypical observations fell to seven in the year. This trend indicates that over time, China's local spatial agglomeration characteristics are becoming more and more obvious, and regions with higher per capita GDP levels are surrounded by more regions with the same level of economic development; Areas with lower per capita GDP levels are surrounded by more regions with low levels of economic development, while those with high per capita income and low per capita income are reduced. 1 It has been seen from here that the spatial correlation of globality in different regions of China is closely related to the spatial correlation of locality. The geospatial effect of economic development must play a non-negligible role in regional economic development. Spatial Spillover of Economic Development In 1998, the region with a probability P value of less than 5% was only in Tianjin and Shanghai. In 2008, it increased to six regions including Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, and Guizhou. Due to space limitations, this paper does not list Moran's/index values ​​for local autocorrelation. Readers are required to request the author by email.
In 1998 and 009, the Moran scatter plot effect of per capita GDP in various regions of China was more of a local spatial spillover. Then, how does this local spatial spillover effect play a major role in the economic development of China? This requires further empirical analysis through rigorous quantitative analysis.
Third, the model of spatial spillover effect is set in real life. The economic growth and economic development of countries or regions in the world vary greatly. Exploring the reasons, externalities have a very large impact on economic growth or development. The classical growth theory believes that the growth of a region is mainly caused by the growth of its capital, labor and other factors, while the new growth theory believes that the economic development of a certain region benefits from the implied technology of fixed capital investment into 1986), or Benefit from the accumulation of human capital in the form of “dry middle school†(Lucas, 1988). In recent years, the new geo-economics has described the mechanism of polarization of economic growth in different regions from the perspective of the cumulative cycle of supply and demand. It is called “the spatial externality of large geographical concentration†(Fuitaetal., 1999). ; FuitaandThisse, 2002). They use space distance as a weight to aggregate the gross domestic product of all surrounding areas to measure the potential demand for products and services produced in a region, and use it as a market potential to examine the impact on regional wage levels. Redding Venables (2004) and Redding (2005) directly extended this idea to the study of the factors affecting regional GDP per capita. Based on the research of cross-country data, they found that market potential is in explaining the difference in GDP per capita between countries. Significant role. Crozet (2005) also used empirical data from panel data in Europe to find that market potential in a region has a significant positive impact on the growth rate of GDP per capita. Although the reasoning process is not the same, most studies express the influence mechanism of spatial externalities on regional per capita income as a simple model of the following form: 1 (3) is the classic wage equation in the so-called New Economic Geography model (Fuitaetal. , 1999), which shows that the labor price in a certain region under market equilibrium is a function of the products of the region entering the markets of other regions. (X factory. The so-called r-region Krugman sense of market potential, which is the consumption expenditure of each region. Weighted sum, the weight is a combination of trade costs related to the distance between regions and the regional market price index. When wages are regarded as the income of the unit worker or the output created by the unit worker, (3) indicates a region The market potential has important implications for its economic development. Krugman's market potential theory reveals the mechanism of regional spillover effects on regional economic development: when a region's economic development level is high, its economic aggregate size tends to be larger. , the speed of development is also faster, so the region sees the surrounding area The demand for products is large, which means that the economic development of the region has a strong driving effect on its surrounding areas. Taking MPr as the market potential of the region, that is, the potential development effects of economic development in other regions may be used in the region. The per capita income substitution (3) of wages can be related to the relationship between the per capita income level of a certain region and the spillover effect of regional economic development: where Y=1/. introduces the time dimension t, and (4) can be further written as the form of growth rate. The formula (5) indicates that the growth of per capita income in a region is directly dependent on the market potential of the region, and the market potential of the region is mainly related to the economic development level and price of the surrounding region and the market distance between the region and its surrounding areas. It is regarded as a direct spillover effect of economic development in the surrounding areas on the region.
According to the above theoretical model, the per capita GDP represents the per capita income of the region, and the regional economic development characterized by GDP per capita is affected by the market potential of the region or by the economic development of other regions. In addition, according to classical growth theory and new growth theory, we introduce capital, labor, and human capital into the econometric model to examine the impact of major input factors on regional economic development. Taking into account China's national conditions, we also introduce the distance from each region to the nearest coastal port to represent the factors affecting the overseas markets of each region. Based on this, the basic econometric model of regional economic development is as follows: Among them, subscript r represents the region and representative year, Yrt represents the per capita GDP of the region r; trt represents per capita fixed asset investment, including domestic Investment, including foreign investment; DKLrt = KLrt-KLr, 1 is the change of human capital, KLrt is the proportion of the population with a college education or above in the t-year of the region r; DLrt=Lrt-Lr, 1 is the labor input Change, Lrt is the ratio of the labor population to the total population in the t-year of the region. Drt is the distance between the provincial capitals of the provinces and the nearest coastal ports.
IV. Spatial Spillover Effect of Economic Development in China In order to compare and analyze the influencing factors of economic development in 31 provinces and autonomous regions in China, especially to examine the spatial spillover effects of regional economic development, we use the (6) formula as the econometric model. Conduct an empirical analysis.
The economic and demographic data used in this study are from the 1999-2010 China Statistical Yearbook. The distance between provincial capital cities and the distance between provincial capitals and the nearest coastal ports are based on the National Basic Geographic Information System published by the State Bureau of Surveying and Mapping. The 1:4 million Chinese terrain database is obtained by using the Euclidean linear distance.
Each study focused on the spillover effects between regions in China's regional economic development. It is characterized by the market potential.
We use the most common market potential function method proposed by Harris (1954) to measure the market potential of each region: GDPs, which is the GDP of the region in the t-year, and d is the Euclidean distance between the region r and the provincial capital of the region. This method simply depicts the market potential of the region r, which is the weighted sum of the economic development level of other regions, and the weight is the reciprocal of the distance from other regions in the region. This approach suggests that the spillover effects of economic development in other regions on the region are diminished as the distance between regions increases.
Finally, it should be pointed out that the GDP data of each region has been reduced by the GDP deflator. Similarly, the fixed asset investment data has also been reduced according to the fixed asset investment price index of each region, so their changes do not include price changes. influences.
(II) Model Estimation Our research uses 11 years of relevant data from 31 provinces and regions in mainland China. Therefore, it has typical panel data characteristics and needs to use the paneldata method for metrological analysis. In panel data analysis, two types of non-observing effect individual effects and time effects must be controlled. Therefore, we set the (6) random error term to the form of =4+table+.
However, as with many other methods of econometric analysis, the estimation of equation (6) depends on whether the random error term in the model satisfies the classical Gauss hypothesis. If satisfied, the usual method of estimating the panel data model yields an unbiased and consistent estimate. Here, the aspect needs to consider whether the A representing the individual effect and the time effect representing the time are related to the explanatory variables in the model, thereby determining whether the panel data model is estimated by using a fixed effect or a random effect; another aspect needs to consider the random error term urt Has a distribution pattern. In the discussion of the second part, we have already seen that there is a certain degree of spatial dependence between different regions of China. Therefore, it is necessary to introduce this geospatial dependence information into the model in order to obtain a more credible estimate. result. In the setting of our model, the variable of market potential has been used to characterize the spatial dependence of a region on other regions.
However, we know that the dependence of other regions on other regions is quite complicated. Only one indicator of market potential may not fully grasp all the influencing factors. Other spatially relevant factors that may affect regional economic growth will enter. In the error term of the model, this will likely result in a strong spatial correlation of the random error term of the model. Therefore, we classify (6) as the spatial error model to estimate: where is the column vector composed of ln/Fm), x is a matrix, and the columns of the matrix are respectively ln(MPrt/ Finance) nUyKm), /, /, must be the column vector of the element. ", 5, is a random column vector that characterizes individual effects and time effects, u, and e, both are column vectors with elements of urt and ert. We call (8) the spatial error panel data model (spatial error panel data model). A is a parameter that reveals the spatial correlation strength between regression residuals in the spatial error model. (8) W is the spatial autocorrelation weight matrix, which is generated in the same way as the weight matrix W in the aforementioned Mornn'I index. Spatial error model It is no longer suitable for estimation by the OLS method. Generally, the maximum likelihood method (ML) is used for estimation to obtain a reliable parameter estimation value.
Our metrology analysis uses R software and Matlab software in combination. 1 Because the purpose of this study is to examine the spatial spillover effects of economic growth in China, and a direct manifestation of this effect is the regional market potential. At the same time, spatial correlation analysis has found that China's regional economic development is spatially related, so it is necessary to use spatial econometric models for estimation. Of course, because it is a panel data model, the choice of estimation method is extremely important, and it needs to be selected in the fixed effect estimation and random effect estimation methods. For comparison, we first estimate the basic panel data model (6) that does not consider spatial correlation, and select it in the fixed effect and random effect estimation method by Hausman test. At the same time, it also passes the Wooldridge sequence correlation test and Baltagi. Sequence correlation tests to verify the time effect of the basic panel data model. Model 1 and Model 2 in Table 2 give the corresponding estimation results.
The estimation results of Model 1 and Model 2 in Table 2 show that both fixed-effect OLS estimation and random-effect GLS estimation show that capital investment and labor input growth are indispensable elements of China's regional economic growth, and they have all passed. Statistical test at 1% significance level, but the impact of human capital changes has not passed the test of 10% significance level; the greater the distance from coastal ports in China, the higher the transportation cost to enter overseas markets, so The negative impact effect, but the GLS estimate of the random effect shows that the strength of this negative impact is almost negligible; of course, the fixed effect ML estimate does not have this one.
The regional market potential that we are concerned with, or the direct spatial spillover effect between regions, shows a significant positive impact relationship in both estimates, which is completely consistent with the theoretical analysis, and from the estimation results, this market potential changes. The elasticity value has exceeded the elasticity of fixed asset investment.
Table 2 Analysis of China's regional economic growth factors Basic panel data model Spatial error panel Data model Model type/estimation method Model 1: Fixed effect model 2: Random effect model 3: Fixed effect model 4: Fixed effect LSDV estimation ttS estimated ML estimated constant term Whether muscle n contains a time dummy variable or whether there is a time effect of the adjusted R2 test: whether to select a random effect model Note: 1. In "whether there is a test of time effect", Wooldridge'stest and Baltagi'stest are used respectively To test whether there is sequence correlation between the residuals of the fixed effect model and the random effect model, the original hypothesis is “there is no sequence correlationâ€. In the test of “whether to choose the random effect modelâ€, Hausmantest is used to test whether the random effect model is more than the fixed effect. The model is more appropriate, the original hypothesis is "there is no significant difference between the two"
2. The data in the parentheses in the table is the accompanying probability P value of the corresponding estimator, ", and respectively indicate significant at the significance level of 1%, 5%, and 10%, the same below.
Of course, from the perspective of measurement test, both estimates of the basic panel data model show that there is no unobserved time effect, and the Woolridge sequence correlation test value of the fixed effect OLS estimate; x2(1)=0.010, random effect The GLS estimated Baltagi sequence correlation test is z = 0.029, both of which do not reject the assumption that there is no time effect at the 10% significance level; on the other hand, as the test shows further, 2(4) = 16.60, At the 1% significance level, the assumption that the fixed effect and the random effect estimate are not different is rejected. Therefore, the estimation method of the fixed effect model is relatively better.
If the model setting does not take into account the interaction between the various regions in the regional economic development process, the analysis will stop here. However, as discussed in the second part, it has been found that 31 provinces in China have obvious autocorrelation, that is, there are clusters in geographical locations, and over time, the characteristics of such clusters become more and more significant, indicating that there are different regions. There is a spillover effect of economic development. Although we describe the spillover effect between regions by introducing market potential variables, if the market potential variable cannot contain all the factors of spatial spillover, then those factors that are not introduced and have spatial correlation will enter. The random error term of the model. At this time, the traditional panel data model (paneldatamodel) and the traditional estimation method will no longer be applicable, and the spatial error panel data model of spatial correlation needs to be introduced and estimated by space technology.
Model 3 and Model 4 of Table 2 are estimates obtained by the fixed-effect ML estimation method for the spatial error panel data model (8). Since the basic panel data model test found no time effect, model 3 did not consider the time effect. Of course, for comparison, we also introduce a time dummy variable in Model 4, and its estimation can improve the robustness of Test Model 3. The estimation results show that even compared with the traditional panel data fixed effect model (model 1), the spatial error model not only has a larger adjusted R2, but also the corresponding log likelihood function value increases. At the same time, the parameter A characterizing the spatial error effect also passed the test at the 5% significance level, indicating that the spatial error model for introducing spatial correlation between regions is more correct. From the results of model estimations that contain time dummy variables and time-deficient variables, on the one hand, after introducing time dummy variables, it is still found that there is no significant time effect. On the other hand, the significance of other variables has not changed, and each The variation of the variable parameter estimation results is not large, indicating that the setting of the spatial error model without time effect is robust. To this end, we choose panel data space error model 3 as the final model to further analyze the spatial spillover effects of economic growth in China.
The estimation results in Table 2 show that the estimation results of the market potential parameters of the spatial error panel data model 3 are basically the same as those of the basic panel data model 1, both of which are around 0.47, indicating that the direct spatial spillover effect represented by the regional market potential is close. In the past 10 years, economic growth in various regions of China has played a larger role: for every 1% increase in market potential, the regional economic growth rate will increase by 0.47 percentage points. From the perspective of elasticity, the effect of market potential expansion has exceeded the effect of fixed asset investment growth. The latter's elasticity value is only 0.13.2, which is completely consistent with the expectations of new economic geography, that is, one region has entered other large scales. Good opportunities in the market, the externalities generated by the correlation effect will lead to higher growth levels in the region (Crozet and Koemg, 2005). Moreover, the spatial error model also shows the results that cannot be found in the basic panel data model: the economic growth in China is also closely related to the random impact of the surrounding provincial economic growth, revealing the spatial correlation strength between regression residuals. The significant non-zero parameter A indicates that other factors affecting regional economic growth will also have a diffusion effect on economic growth in the surrounding areas, which we call indirect spatial spillover effects. In short, from the perspective of this direct and indirect spatial spillover effect, since the beginning of the 21st century, the spatial spillover effect between regions has played an important role in the economic development of China.
Of course, the estimation results of the spatial error panel data model also show that the classical growth theory is still applicable to the interpretation of China's economic growth phenomenon, that is, fixed asset investment and labor increase will promote economic growth in China, the result and basic panel The estimation results of the data model are similar; however, the difference from the basic panel data model estimates is that the spatial error model indicates that human capital has a significant positive effect on the economic growth of China, and the estimated value of human capital parameters reaches 0. 176. Passing the statistical test at the 10% significance level means that for every 1% increase in the proportion of people with a college education or above who are over 6 years old, the economic growth rate in China will increase by 0.176%. This estimate shows that since the beginning of the 21st century The growth of human capital in the economic development of various regions in China has also played a positive role in promoting. However, this effect has not been detected in the traditional panel data model. It shows once again that the traditional model that does not consider spatial correlation is biased in the model setting, which also brings the bias of the estimation results.
The results listed in Table 2 are the results of Global estimates and are the average of economic development in 31 provinces and autonomous regions in China.
As mentioned above, the spatial spillover effect of regional economic development that we are concerned about is likely to have a greater relationship with the spatial distance between different regions: the closer the distance, the more spatial spillover effects should be. Therefore, when we set the market potential variable of a certain region, we use the reciprocal of the distance between the regions as the weight to obtain the weighted average of the GDP of other regions. In order to further investigate the spatial spillover effect of spatial distance between regions on regional economic development, we will carry out spatial panel data analysis according to the extent of the linear distance between provincial and provincial capital cities.
Table 3 is the result of estimating the panel data space error model without time dummy variable by the fixed-effect ML method. Due to space limitations, the estimated value of the time dummy variable and the corresponding accompanying probability value are not specifically listed in the article. Interested readers can request it from the author.
Since the two methods of setting labor input and human capital in the model are different from the fixed variables input and market potential, the parameter estimation results between them cannot be directly compared.
The market potential indicators are calculated according to the range of linear distance between provincial and provincial capital cities. The data in the table shows that the estimated value of the market potential parameter decreases with the increase of the spatial distance between regions: when the linear distance between provincial capital cities is less than 1000 km, the market potential has the greatest influence on regional economic development. Estimated value is as high as 0. 399; and when the linear distance between provincial capital cities is between 2,500 and 3,000 km, the estimated market potential parameter is reduced to 0. 275. When the linear distance between provincial capitals exceeds 3000 In the case of kilometers, the parameter estimate is 0.076, but from the accompanying probability, it is not even passed the test of 10% significance level. This means that the economic growth of a certain region no longer has a substantial direct spillover effect on the area 3,000 kilometers away from it, or there is no direct spatial spillover effect in the provincial interval with a distance of more than 3,000 kilometers. Different from the direct spatial spillover effect between the regions characterized by market potential, the A value of the indirect influence between regions represented by the random error term does not decrease with the increase of the inter-regional spatial distance, and they all pass 1%. Statistical tests at the level of significance mean that economic growth in various regions of China also indirectly affects economic growth in other regions through random error effects, and this indirect spillover effect is not affected by the spatial distance between regions.
Table 3: Analysis of economic growth factors in China: According to the distance range, the distance between the provinces and provinces is linear. 5 Conclusions and revelations Over the past 30 years, with the deepening of China's reform and opening up, market segmentation between different regions has been eliminated, products and factors. The free flow between different regions not only improves the efficiency of resource allocation, but also expands the market space of each province; the economic development of each region depends not only on the growth of capital, labor and human capital investment in the region, but also to a large extent. It is also affected by the scale of market demand created by the economic development of its neighboring regions, that is, the expansion of market potential. Therefore, the development of China's regional economy must be analyzed from the perspective of new economic geography to be more comprehensive and in-depth. The spatial spillover effect between regions represented by regional market potential has become the main topic of this study.
Firstly, this paper uses exploratory spatial data analysis tools to study the spatial distribution pattern and characteristics of per capita GDP in China's provinces and regions from 1998 to 2009. The results show that, on the one hand, there is a positive spatial autocorrelation across the whole domain, and this correlation also exhibits a regular variation in the spatial distance between regions, that is, as the spatial distance of the region increases, the spatial correlation The intensity tends to decrease; at the same time, from the time dimension, the positive spatial autocorrelation of the whole domain is strengthening over time. On the other hand, from the perspective of regional localization, the number of regions significantly associated with neighboring provinces in various provinces has increased over time.
Secondly, this paper reveals how the economic growth in China is affected by the economic development of its surrounding regions through a new economic geography model that characterizes the market potential's impact on regional economic development. Here we regard the market potential as a direct measure of the spatial spillover effect of regional economic development, and incorporate the material capital investment and human capital investment of classical growth theory and new growth theory into a unified measurement model framework, using near The panel data of 31 provinces and regions for more than 10 years have analyzed the factors of economic growth in China. The econometric analysis found that the growth mechanism reflected by the classical growth model and the new growth theory still determines the fundamentals of China's regional economic growth. The economic growth of each region is still inseparable from the accumulation of local factors; on the other hand, when we control After the influence of factor inputs, it was found that the market potential of each region has a very significant positive impact on its economic growth. In other words, the spillover effect of inter-regional economic development has significantly affected China's economic growth since the late 1990s. This factor has even more elasticity than the elasticity of fixed-asset investment. At the same time, the spatial error model we have adopted further shows that the economic development in China is also closely related to the random impact of economic growth around the province, that is, other factors affecting regional economic growth will also affect the surrounding areas. Economic growth has an indirect diffusion effect. Therefore, a direct policy inspiration is to further eliminate market barriers in different provinces and accelerate the process of China's global market integration, so as to open up more room for space spillover effects of regional economic growth, which should be the future regional economic development of China. Issues that are considered in policy development.
Third, another important issue that the Institute is concerned about is that “the spatial spillover effect between regions will indeed decrease as the spatial distance increases.†We calculate the range of linear distances between provincial capital cities. After the market potential indicators, the quantitative analysis of China's regional economic growth factors was conducted again. The results show that the spatial spillover effect of per capita GDP growth in China does decrease with the increase of spatial distance between regions. This study once again clearly validates the famous first law of geography, that is, everything is related. Things that are closer are always more relevant than things that are farther away (Tobler, 1979). Therefore, one policy inspiration here is that the government should encourage economic activities and the spatial agglomeration of the population, that is, it can consider adapting to the current regional cross-regional agglomeration trend, and transfer part of the western population to the southeastern coastal areas, where several A world-class large-scale metropolitan area will give full play to the fruits of economic development while giving full play to the economic agglomeration effect and diffusion effect, while driving the faster growth of the central and western regions.
Finally, due to the different ways of setting model variables, the results of human capital, labor input and market potential, and capital investment can not be directly compared, but the results show that fixed asset investment and labor input are still the most economic growth in China. An important source of power, China is still inseparable from physical capital and labor input to promote regional economic growth. Of course, the greater potential of human capital and the spatial spillover effect between regions also reveals two major points for promoting economic growth in China in the future: First, further increase human capital investment, and promote high-quality population to occupy the total population of the region as soon as possible. The proportion should be given to give full play to the important role human capital plays in regional economic growth in the middle and late stages of industrialization in China; the second is to further eliminate market barriers in different provinces and accelerate the construction of a global integrated market to give full play to regional economic development. Space overflow effect. These two points are extremely important in the context of China's future economic growth pattern shift, and the demographic dividend, especially the labor dividend, is gradually weakening.
(Finish)
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