# Convergence Spatial Measurement of Economic Growth Based on Big Data

Authors: Jianglei Jin; Haowen Yan; Qianqian Zhao
Journal: Mobile Information Systems
 (2022)

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## Abstract

Economic growth has always been one of the hottest topics in economic research. Behind the rapid economic growth, the economic gap between regions is gradually widening, and the internal gap will have an impact on the overall coordination of economic growth. Research on the convergence of economic development and its causes has great strategic significance for narrowing the differences in raising economy among regions. In recent years, the impact of big data on economic analysis has become more and more obvious, and this fact has attracted the attention of the academic community. Big data are a new strategic resource and a tool for assessing economic trends. Adding big data technology to the research on the convergence raise of economics can predict the law of data changes, reduce data errors, optimize research results, and provide a more scientific basis for the coordinated development of regional economies. Based on big data theory and technology, this paper uses a spatial econometric model to empirically analyze the convergence of regional economic growth and its influencing factors. The experimental results show that the research on the convergence mechanism and spatial relationship of economic growth in the context of big data can improve the accuracy of the convergence analysis of economic growth to a certain extent. Through modeling analysis, the accuracy of economic convergence is improved by 4.1%. The utilization of big data in a trend of economic development makes the analysis results more reasonable and has greater reference value.


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## Body

## 1. Introduction

At the same time as rapid economic growth, and the economic development of various regions also show the obvious difference. In theory, the study of the convergence of economic growth can provide practical knowledge of economic development theory and development economics, helping to identify differences between economies. From the actual point of view, it is of great significance to implement practical and effective macroeconomic development policies, recognize the current situation of regional economic inequality, and find out the main reasons for the inequality problems in the region. Big data allow the collection, integration, classification, and processing of information on factors such as GDP, price levels, employment rates, household income, money, and the amount of credit. It can then provide strategic and economic means on the basis of certain development and regulation, which is of great significance to the study of economic convergence problems.Recently, technology has been improving, making the application of big data technology more and more widespread. A number of scientists have researched and analyzed big data technology and obtained good results. Zhang analyzed the concept and value orientation of the college education quality management system from the aspects of the establishment of a quality management system and the improvement of the service process, and constructed a college education quality management system based on big data. Finally, a systematic study is carried out on the evaluation of the quality management system of college education, which provides a certain reference for the development of college education [1]. Ni et al. used big data technology to carry out process optimization using case-based reasoning (CBR) approach. The results show that optimization results with different optimization objectives can be obtained using the CBR method and the solution time is less than 1 second [2]. The Pingping team proposed an employee incentive management model based on the background of big data [3]. Wang et al. proposed a new grid fault tracing method based on a big data platform [4]. Du and Zhao propose a mathematics web-based teaching technology, that is, based on the fusion of big data to build a teaching model that enables the adaptive allocation and integration of teaching resources [5]. Guo et al.’s team designed an EME portrait model based on big data. Studies have shown that portrait models are not only convenient for storage and retrieval, but also for transmission and expansion [6]. Yan and Wang propose an intelligent command system for road traffic through big data mining, which offers great practical value in addressing the complexity of transport systems [7]. The analysis of big data in these studies is more specific but does not involve the convergence of economic growth.The convergence of economic growth is an important part of regional economic development. The analysis and research on the convergence of economic growth being beneficial to the healthy development of the regional economy. Many teams have joined this research. Song et al. studied the “club convergence” of economic growth and used a dynamic panel threshold model to derive the nonlinear relationship between financial development and economic growth. The results show that the probability of convergence increases greatly. When the level is higher than the higher threshold, the positive effect of the level on the steady-state relative output will gradually weaken, and the marginal utility will decrease significantly [8]. Chakraborty calculated that public capital expenditure is positively related to economic growth through fiscal asymmetry based on the GMM model [9]. The Mei team modeled the variability of GDP per capita in each emerging and developing region, and then developed a combined energy efficiency and GDP per capita model. The study found that the growth of local per capita GDP reflects the trend of economic convergence, and the convergence degree of energy consumption is slightly lower than that of per capita GDP [10]. Ibrahim et al. performed regression analysis on regional economic growth convergence using a panel of fixed effects models (REM). The estimation results show that the analysis and management of the convergence of economic growth are beneficial to the rapid growth of the regional economy [11]. Godowsky applied descriptive statistics and multiple regression methods to study economic growth and business environment in EU countries in the context of economic convergence processes. Experiments show that the changes and upward trend of the entire EU business environment are gradually approaching the development of member economies [12]. The research on the convergence of economic growth has an important impact on regional economic development, but the traditional research methods can no longer meet the specific analysis requirements of economic convergence.The economic convergence index is used to construct a spatial weight table, and domain and regional factors are introduced into the economic growth convergence model. The real per capita GDP is used as the benchmark for measuring economic growth, and the per capita income and expenditure share are used as the benchmark for economic integration analysis. Through big data technology, the model of economic growth convergence mechanism and spatial correlation is constructed, and finally, the simulation model is concluded to improve the accuracy of economic growth convergence analysis to a certain extent. This also shows the convergence of economic growth makes the analysis results more accurate and reasonable and has greater reference value.


## 2. Statistical Analysis Based on Big Data

### 2.1. Big Data Technology

The network big data can be automatically recorded when the event occurs, and the investigation and collection of the data can be extracted directly through engineering methods [13]. Figure 1 is a diagram of a big data statistical model. It includes parallel processing techniques, database sharing, storage and programming, data mining, and cloud computing.Figure 1
Big data statistical model.


### 2.2. Statistical Analysis Framework of Big Data

Statistics is an important part of data processing. Due to the large statistical sample and the complex nature of the data, the statistical work is relatively heavy. Data mining is a kind of statistical model that processes, analyzes, and organically combines the relevant data by accurately processing the data in the state of big data, and then introducing the idea of statistics into data mining [14]. As shown in Figure 2, Hadoop provided a powerful and reliable analysis engine and shared memory for statistical tasks, including two key technologies, MapReduce and HDFS. MapReduce is responsible for data processing and analysis, and HDFS is responsible for shared data storage.Figure 2
The basic structure of data statistics.


### 2.3. Construction of Big Data Statistical Analysis Model

The statistical analysis system in the big data environment is based on batch data mining and adopts the method of regular data processing and analysis to update the model [15]. The key to system design is real-time retrieval, statistical analysis, data processing, and mass storage, and distribution of statistical data sources. The data collection, aggregation, and movement of Hadoop clusters, as well as the distributed storage of data, meet the demand for the diversity of statistical analysis, and task scheduling can manage and schedule jobs submitted by all users in a unified manner. The Hadoop-based computing model is shown in Figure 3, including cloud platform application layer, technology and interface layer, computer layer, file management layer, and physical top-level source code.Figure 3
A hierarchical statistical analysis model based on Hadoop.


## 2.1. Big Data Technology

The network big data can be automatically recorded when the event occurs, and the investigation and collection of the data can be extracted directly through engineering methods [13]. Figure 1 is a diagram of a big data statistical model. It includes parallel processing techniques, database sharing, storage and programming, data mining, and cloud computing.Figure 1
Big data statistical model.


## 2.2. Statistical Analysis Framework of Big Data

Statistics is an important part of data processing. Due to the large statistical sample and the complex nature of the data, the statistical work is relatively heavy. Data mining is a kind of statistical model that processes, analyzes, and organically combines the relevant data by accurately processing the data in the state of big data, and then introducing the idea of statistics into data mining [14]. As shown in Figure 2, Hadoop provided a powerful and reliable analysis engine and shared memory for statistical tasks, including two key technologies, MapReduce and HDFS. MapReduce is responsible for data processing and analysis, and HDFS is responsible for shared data storage.Figure 2
The basic structure of data statistics.


## 2.3. Construction of Big Data Statistical Analysis Model

The statistical analysis system in the big data environment is based on batch data mining and adopts the method of regular data processing and analysis to update the model [15]. The key to system design is real-time retrieval, statistical analysis, data processing, and mass storage, and distribution of statistical data sources. The data collection, aggregation, and movement of Hadoop clusters, as well as the distributed storage of data, meet the demand for the diversity of statistical analysis, and task scheduling can manage and schedule jobs submitted by all users in a unified manner. The Hadoop-based computing model is shown in Figure 3, including cloud platform application layer, technology and interface layer, computer layer, file management layer, and physical top-level source code.Figure 3
A hierarchical statistical analysis model based on Hadoop.


## 3. Construction of a Spatial Econometric Model of Economic Growth Convergence

The theory of economic development is an important subject of economic research. The gap in economic development between countries or regions and its changing trend (the convergence of economic development) is one of the focuses that has received much attention [16]. Economic growth convergence refers to a state in which a country’s growth rate or per capita output is negatively correlated with its baseline level. That is, backward regions have higher economic growth rates than developed regions, which leads to a process in which the differences in the static indicators of each economic unit at the beginning of the period gradually disappear. The method of the spatial econometric model has been used in many fields, and the convergence of economic growth in different areas can be studied and analyzed by the method of spatial econometric model [17].


### 3.1. Economic Convergence

The concept of economic convergence comes from the concept of sequence convergence in mathematics. When∀ε>0, when n is large enough, if there are Xn−Xn−1<ε, the sequence Xn is said to be a convergent sequence. Eventually, it will converge and become constant over time, and the gaps between the different regions will shrink. Convergence is a data-related assumption that refers to the tendency of the standard deviation of real output per capita in different economies to decrease over time. When considering convergence phenomena, convergence can provide the most intuitive convergence information, mainly measured by the nondiscriminatory standard deviation [18]. The convergence type is as follows:(1)σt=1N−1∑i=1NlogYit−1N∑i=1NlogYit2,i=1,2,⋯,N;t=1,2,⋯,T,i represents the region, t represents the period. Yit represents the per capita output of the ith region in period t, σt. If there are σt+k=CσtCis a constant,andC<1 in epoch t+k, and then this region is said to have a k-order σ convergence [19].β convergence is a time series assumption that all regions will eventually reach the same per capita income or output over time [20]. β convergence is divided into two forms: absolute convergence β and conditional convergence β. The so-called absolute β convergence means that regions with similar basic characteristics such as technology, system, and culture have the same economic growth path and equilibrium state, and the regional economic growth rate is negatively correlated with the distance from the steady state. The so-called condition β convergence means that different economic regions have different technical, institutional, cultural, and other characteristics, and thus have different economic conditions, so there is no absolute convergence.The regression model with absolute convergenceβ is as follows:(2)1TlogYi,t0+TYi,t0=α+βlogYi,t0+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2,i represents the region, t0 is the beginning, and t0+T is the end. Yi,t0 and Yi,t0+T represent the per capita output at the beginning and end of the i-th region, respectively, εi,t0,t0+T represents the random error term. The distribution of εi,t in t0 and t0+T lags into an independent state distribution, σ changes with the change of technical conditions at the initial time t0, and β represents the convergence speed to be estimated.The Conditionβ convergent regression model is as follows:(3)1TlogYi,t0+TYi,t0=α+βlogYi,t0+φX+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2.Among them,X is the population growth rate, employment rate, degree of urbanization, degree of industrialization, transparency, government public expenditure, industrial structure, and other control variables, as well as several factors that may affect convergence. β indicates the conditional convergence rate to be measured.The connotation of club convergence theory is that the level of economic development, that is, countries or regions with similar economic basic conditions, will converge to the same local stable state. Club Convergence examines the convergence that exists between different systems within each economic bloc that has the same structural characteristics as human capital and market opening in its initial stages. For example, there is a phenomenon of club convergence in the three main regions of M country, east, middle, and west. For each prefecture-level city and urban area in area B, the regional dummy variables can be defined according to the city to converge the regression. The convergence model is as follows:(4)1TlogYi,t0+TYi,t0=α+βlogYi,t0+γD+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2.The description of each variable is similar to the previous model,γ is the coefficient vector of the dummy peripheral variable to be measured, and D denotes the subregion within the hypothesis domain. If the β value is negative, the area shows club convergence. According to the model comparison between club convergence and β convergence, it can be found that club convergence can be regarded as a form of absolute β convergence, which occurs in subdomains with the same stable state within the region, rather than in the entire economy.


### 3.2. Model Construction and Data Interpretation

Before the formal modeling, people first have a preliminary understanding of the overall economic operation of the B region of M country. Table1 gives the descriptive statistical indicator data of the total per capita income of area B. It can be seen from this table that in the past 20 years, the per capita income of district B has been greatly improved, the average value has increased by nearly 2 times, and the average annual growth rate is about 7.6%. From 1998 to the end of 2011, per capita income increased by 0.36 times, noting that the economic growth gap in the region is gradually widening, the standard deviation from 1998 to 2018 increased from 1257.13 to 3065.02.Table 1
Per capita income.
YearsMaximum valueMinimumStandard deviationMean199815311104931257.1312819.65201118167137591938.2415369.29201220966157812134.5717308.14201828228218103062.0225387.25Table2 gives the descriptive statistical indicator data of the total per capita expenditure in area B. It can be seen from the table that in the past 20 years, the per capita expenditure in district B has increased significantly, the average value has nearly tripled, and the average annual growth rate is about 5.8%. From 1998 to the end of 2011, per capita expenditure increased by 1.28 times.Table 2
Per capita expenditure.
YearsMaximum valueMinimumStandard deviationMean199849853096679.463886.13201176555378734.876057.48201289396347782.677614.3120181237110358846.2511492.5


#### 3.2.1.σ Convergence Index

σ convergence index refers to the fact that the dispersion of per capita income between regions tends to decrease over time. When the index tends to decline, there is economic convergence. The time series of changes in per capita GDP in region B from 1998 to 2018 is now plotted, as shown in Figure 4. The economic convergence of region B can be analyzed by directly observing the change in the coefficient of variation on the plot.Figure 4
Time series plot of log standard deviation per capita in region B.In the first stage (1998–2005), the instability of this stage gradually decreased over time, and the economic gap gradually narrowed. In the second stage (2005–2010), the coefficient of variation of this stage gradually increased with time, and the gap widened. In the third stage (2010–2012), the coefficient of variation of this stage showed a gradually decreasing trend with time. In the fourth stage (2012–2018), the coefficient of variation for this stage began to show an upward trend over time.


#### 3.2.2.β Convergence Trend

Convergence trend refers to a trend in which the initial development level of a country or region is inversely proportional to the development speed. In addition to the coefficient of variation, graphs of economic growth rates and output levels can also be used to roughly describe the convergence trend of economic convergence [21]. Figure 5 shows that the trend line shows a downward trend, and the economic growth rate of area B is negatively correlated with the initial output level, showing a convergence trend. The slope of the trend line can be approximated as the convergence force of convergence.Figure 5
Scatter plot of economic growth rate and initial output level.The model is constructed based on the related concepts of economic convergence. The convergence mainly examines the changes in the level of economic development between different economic systems over time [22]. If the standard deviation tends to decrease, it means that the economic growth of each region is converging. On the contrary, it shows that the economic growth of different regions is different. The types of tests introduced in convergence concepts are used below. The definition of Equation (1) can be obtained by constructing a regression model, namely, yit=logYit. The logarithmic form of the per capita GDP of each region in the tth period is y¯t=1/N∑i=1NlogYit, and the unbiased estimate of the variance of the random error term εit after regression is σt2. The regression model is as follows:(5)yit=y¯t+εit,εit∼iid,N0,σt2.Among them,yit and y¯t are as defined in parentheses above, and the area is i=1,2,⋯,N; time is t=1,2,⋯,T. For this regression model, since this regression model assumes a standard normal distribution, the regions are independent of each other at the same time t, and the regions are considered as independent individuals, there is no spatial correlation between regions, these are all true. After constant regression of Equation (5), a random error term is generated. The unbiased variance estimator is as follows:(6)St2=∑i=1Ne2/itN−1.Among them, the residual termeit=yit−y¯t is obtained according to equation (1), that is, the mean square error σt in the result obtained by performing Stata regression on the model. Using the data from each region to perform a temporal regression and calculate a set of values σt, the time series of design values σt are shown in Figure 6, in which the difference in economic growth in region B shows obvious volatility. Overall, the variance patterns roughly matched the variance trends of the variance coefficients from descriptive statistics studies, which also suggested that the variance coefficients could be measured and converged to describe economic disparities between regions.Figure 6
Time series plot of log standard deviation per capita in region B.


#### 3.2.3.β Convergence Model

The convergence model is similar to the analysis of convergence, before the introduction of the spatial matrix, the convergence modeling of the regional spatial correlation is not considered. Absolute convergence phenomena in region B are analyzed using equations that define the concept of convergence. The regression model used for absolute convergence is as follows:(7)130logY⌢i,2018Yi,1998=α+βlogYi,1998+εi.1978,2018.Using Stata software to perform regression analysis on this equation, the regression equation obtained is as follows:(8)130logY⌢i,2018Yi,1998=0.286−0.022logYi,1998,0.0070.038,−3.04∗∗∗7.52∗∗∗,R2=0.352,Fstatistics=9.25∗∗∗,Prob>F=0.007,Sample size=19.The value in parentheses in the first row below the equation is the standard deviation of the regression coefficient, and the second row is the statistict, ∗∗∗ which means significant at the 1% confidence level. This shows that the regression result, the statistic F is significant at the 1% confidence level. The regression equation is established, and the value of the regression coefficient is very important to the confidence.Starting from the turning point in 2003, we compare and analyze the convergence situation before and after 2003. The regression model used for absolute convergence from 2003 to 2018 is as follows:(9)115logYi,2018Yi,2003=α+βlogYi,2003+εi,2003,2018.Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(10)115logYi,2018Yi,2003=0.203−0.037logYi,2003,0.0330.01,6.18∗∗∗−3.86∗∗∗,R2=0.235,FStatistics=14.91∗∗∗,Prob>F=0.0013,Sample size=19.At this time, the equation is still significant, but the value ofβ increases significantly, and the convergence speed is accelerated. The regression model used for the absolute β convergence for 1998–2003 is as:Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(11)115logY^i,2003Yi,1998=0.118−0.021logYi,1998,0.0180.008,6.65∗∗∗−3.86∗∗∗,R2=0.264,FStatistics=7.05∗∗∗,Prob>F=0.0167,Sample size=19.The currentβ convergence rate is about 2.1% per year. Based on the availability and reliability of the data to analyze the conditional convergence, take 2003 as the data starting point, and carry out the convergence regression according to the degree of industrialization and the explanatory variables that affect the degree of convergence. The regression model is used as:(12)115logYi,2008Yi,1993=α+βlogYi,2003+γ1Ri,pop+γ2Ri,i+γ3Ri,g+γ4ISi+γ5IOi+εi,2003,2018.Ri,pop represents the natural growth rate of population in district i, and γ1 is the measure of the impact of population on economic development. Ri,i represents the percentage of investment in the region, γ2 is the measure of the impact of investment on economic development, Ri,g is the level of government spending in region i, γ3 is the impact of government behavior on economic development, and IS is the level of industrialization in region i. γ4 is measured by the proportion of the secondary and tertiary industries in economic development in the industrial structure, IO is the degree of international openness, and γ5 is the impact of the degree of openness on economic growth.Running the sample data to estimate the model. Finally, it is found that only investment and the degree of opening to the outside world have an impact on economic growth, while the three factors of population growth rate, government public expenditure rate, and industrial structure are not significant. The population growth rate is 0.5, theP rate is 0.28, the public expenditure rate is 0.057, the P rate is 0.763, the industrial structure rate is 0.038, and the P rate is 0.245. So the final estimated regression equation is as follows:(13)115logYi,2018Yi,2003=0.236−0.0413logYi,2003+0.0397Ri,i+0.008IOi,0.0480.0150.0210.0034,4.9∗∗∗−2.73∗∗1.9∗2.41∗∗R2=0.449,FStatistics=7.73∗∗∗Prob>F=0.0024,Samplesize=19.The first line is the standard deviation of the estimated factor, and the second line is the statisticalt, ∗∗∗which means significant at the 10% confidence level, ∗∗means significant at the 5% confidence level, and ∗means significant at the 1% confidence level. Compared with absolute convergence, the convergence speed is significantly faster.


### 3.3. Spatial Econometric Model

Spatial econometric models are mainly divided into two types: spatial lag model and spatial error model. Both of these models are based on the introduction of the spatial weight table to modify the basic model [23]. The spatial lag model is suitable for the behavior of adjacent areas, which affects the behavior of other areas in the whole area, and the spatial error model is suitable for the impact of uncertainty shocks on local economic variables in adjacent areas. The estimation of the spatial model adopts the maximum likelihood estimation method and the generalized least squares method.


#### 3.3.1. Spatial Lag Model

In order forσ to converge, after introducing the constant regression (1) into the spatial table, the spatial lag model is as follows:(14)yt=αtI+λtWyt+εt.Among them,yt=y1t,y2t,⋯,yNt, is the vector model, αt and λt are constants, W is spatial weight table, and λt is weight factor. Write the vector model in the form of a component model:(15)yit=αt+λtWiyt+εit=αt+λt∑i≠j,j=1Nwijyjt+εit.Wi is a vector with i rows, Wij is a value with i rows and j columns. In this way, the establishment αt+λt∑i≠j,j=1Nwij,yjt of the area balance is not only related to t, but also to the area i. For absolute β convergence, after substituting equation (2) into the spatial weight table, the spatial delay model is as follows:(16)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+λW1TlogYi,t0N×1+εt0,t0+T.This is again a vector equation, with a column vector of local growth rates on the left, which is a unit vector, and a table of coefficients and spatial weights to be estimated. Writing the equation in terms of components, it can be got:(17)1TlogYi,t0+TYi,t0=α+βlogYi,t0+λ∑i≠j,j=1Nwij1TlogYj,t0+εi,t0,t0+T.It can be seen from this equation that the economic growth rate of thei th region is not only related to time T and the initial level logYi,t, but also to the growth rate of the j th region, so the spatial lag model can test the spatial diffusion of this region.For conditionβ convergence, a series of variables are introduced on the basis of the absolute convergence model to constitute the regression model.


#### 3.3.2. Spatial Error Model

Spatial error models fall into two categories: spatial error autocorrelation models and overlapping moving average error models. The spatial error autocorrelation model is as follows:(18)y=Xβ+εε=λWε+u⇒y=Xβ+I−λW−1uu∼iid,N0,σ2.Among them,λ spatial error is the autocorrelation coefficient and Wε is the lag spatial error term. The moving average spatial error model is as follows:(19)y=Xβ+εε=u−θWu⇒y=Xβ+I−θWu,u∼iid,N0,σ2.θ is the moving average error rate for spatial error, and Wu is the concept of spatial delay error.Forσ converging, the constant regression (1) are identical in model form, so only the moving average model needs to be considered in the comparative analysis.(20)y=αI+I−θWu,u∼iid,N0,σ2.For absoluteβ convergence, the equation for the spatial error autocorrelation model is as follows:(21)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+I−λW−1u.This is a vector equation withu representing a column of random error terms in N regions and λ representing the power of the spatial relationship between the regression residuals.The conditionβ convergence model goes on to introduce additional variables on top of the absolute convergence model. The abovementioned describes the form of the spatial econometric model and introduces the tests of two pairs of models. Before proceeding with the spatial modeling analysis, the spatial correlation is first checked.(22)Moran,sI=∑i=1N∑j=1NwijYi−Y¯Yi−YS2∑i=1N∑j=1Nwij.Among them,S2=∑i=1NYi−Y¯2/N,Y¯=∑i=1NYi/N, is the observed value of a variable in the Yi th region; Wij is the value of the element in the W th row and j th column.


## 3.1. Economic Convergence

The concept of economic convergence comes from the concept of sequence convergence in mathematics. When∀ε>0, when n is large enough, if there are Xn−Xn−1<ε, the sequence Xn is said to be a convergent sequence. Eventually, it will converge and become constant over time, and the gaps between the different regions will shrink. Convergence is a data-related assumption that refers to the tendency of the standard deviation of real output per capita in different economies to decrease over time. When considering convergence phenomena, convergence can provide the most intuitive convergence information, mainly measured by the nondiscriminatory standard deviation [18]. The convergence type is as follows:(1)σt=1N−1∑i=1NlogYit−1N∑i=1NlogYit2,i=1,2,⋯,N;t=1,2,⋯,T,i represents the region, t represents the period. Yit represents the per capita output of the ith region in period t, σt. If there are σt+k=CσtCis a constant,andC<1 in epoch t+k, and then this region is said to have a k-order σ convergence [19].β convergence is a time series assumption that all regions will eventually reach the same per capita income or output over time [20]. β convergence is divided into two forms: absolute convergence β and conditional convergence β. The so-called absolute β convergence means that regions with similar basic characteristics such as technology, system, and culture have the same economic growth path and equilibrium state, and the regional economic growth rate is negatively correlated with the distance from the steady state. The so-called condition β convergence means that different economic regions have different technical, institutional, cultural, and other characteristics, and thus have different economic conditions, so there is no absolute convergence.The regression model with absolute convergenceβ is as follows:(2)1TlogYi,t0+TYi,t0=α+βlogYi,t0+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2,i represents the region, t0 is the beginning, and t0+T is the end. Yi,t0 and Yi,t0+T represent the per capita output at the beginning and end of the i-th region, respectively, εi,t0,t0+T represents the random error term. The distribution of εi,t in t0 and t0+T lags into an independent state distribution, σ changes with the change of technical conditions at the initial time t0, and β represents the convergence speed to be estimated.The Conditionβ convergent regression model is as follows:(3)1TlogYi,t0+TYi,t0=α+βlogYi,t0+φX+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2.Among them,X is the population growth rate, employment rate, degree of urbanization, degree of industrialization, transparency, government public expenditure, industrial structure, and other control variables, as well as several factors that may affect convergence. β indicates the conditional convergence rate to be measured.The connotation of club convergence theory is that the level of economic development, that is, countries or regions with similar economic basic conditions, will converge to the same local stable state. Club Convergence examines the convergence that exists between different systems within each economic bloc that has the same structural characteristics as human capital and market opening in its initial stages. For example, there is a phenomenon of club convergence in the three main regions of M country, east, middle, and west. For each prefecture-level city and urban area in area B, the regional dummy variables can be defined according to the city to converge the regression. The convergence model is as follows:(4)1TlogYi,t0+TYi,t0=α+βlogYi,t0+γD+εi,t0,t0+T,εi,t0,t0+T∼iid,N0,σt2.The description of each variable is similar to the previous model,γ is the coefficient vector of the dummy peripheral variable to be measured, and D denotes the subregion within the hypothesis domain. If the β value is negative, the area shows club convergence. According to the model comparison between club convergence and β convergence, it can be found that club convergence can be regarded as a form of absolute β convergence, which occurs in subdomains with the same stable state within the region, rather than in the entire economy.


## 3.2. Model Construction and Data Interpretation

Before the formal modeling, people first have a preliminary understanding of the overall economic operation of the B region of M country. Table1 gives the descriptive statistical indicator data of the total per capita income of area B. It can be seen from this table that in the past 20 years, the per capita income of district B has been greatly improved, the average value has increased by nearly 2 times, and the average annual growth rate is about 7.6%. From 1998 to the end of 2011, per capita income increased by 0.36 times, noting that the economic growth gap in the region is gradually widening, the standard deviation from 1998 to 2018 increased from 1257.13 to 3065.02.Table 1
Per capita income.
YearsMaximum valueMinimumStandard deviationMean199815311104931257.1312819.65201118167137591938.2415369.29201220966157812134.5717308.14201828228218103062.0225387.25Table2 gives the descriptive statistical indicator data of the total per capita expenditure in area B. It can be seen from the table that in the past 20 years, the per capita expenditure in district B has increased significantly, the average value has nearly tripled, and the average annual growth rate is about 5.8%. From 1998 to the end of 2011, per capita expenditure increased by 1.28 times.Table 2
Per capita expenditure.
YearsMaximum valueMinimumStandard deviationMean199849853096679.463886.13201176555378734.876057.48201289396347782.677614.3120181237110358846.2511492.5


### 3.2.1.σ Convergence Index

σ convergence index refers to the fact that the dispersion of per capita income between regions tends to decrease over time. When the index tends to decline, there is economic convergence. The time series of changes in per capita GDP in region B from 1998 to 2018 is now plotted, as shown in Figure 4. The economic convergence of region B can be analyzed by directly observing the change in the coefficient of variation on the plot.Figure 4
Time series plot of log standard deviation per capita in region B.In the first stage (1998–2005), the instability of this stage gradually decreased over time, and the economic gap gradually narrowed. In the second stage (2005–2010), the coefficient of variation of this stage gradually increased with time, and the gap widened. In the third stage (2010–2012), the coefficient of variation of this stage showed a gradually decreasing trend with time. In the fourth stage (2012–2018), the coefficient of variation for this stage began to show an upward trend over time.


### 3.2.2.β Convergence Trend

Convergence trend refers to a trend in which the initial development level of a country or region is inversely proportional to the development speed. In addition to the coefficient of variation, graphs of economic growth rates and output levels can also be used to roughly describe the convergence trend of economic convergence [21]. Figure 5 shows that the trend line shows a downward trend, and the economic growth rate of area B is negatively correlated with the initial output level, showing a convergence trend. The slope of the trend line can be approximated as the convergence force of convergence.Figure 5
Scatter plot of economic growth rate and initial output level.The model is constructed based on the related concepts of economic convergence. The convergence mainly examines the changes in the level of economic development between different economic systems over time [22]. If the standard deviation tends to decrease, it means that the economic growth of each region is converging. On the contrary, it shows that the economic growth of different regions is different. The types of tests introduced in convergence concepts are used below. The definition of Equation (1) can be obtained by constructing a regression model, namely, yit=logYit. The logarithmic form of the per capita GDP of each region in the tth period is y¯t=1/N∑i=1NlogYit, and the unbiased estimate of the variance of the random error term εit after regression is σt2. The regression model is as follows:(5)yit=y¯t+εit,εit∼iid,N0,σt2.Among them,yit and y¯t are as defined in parentheses above, and the area is i=1,2,⋯,N; time is t=1,2,⋯,T. For this regression model, since this regression model assumes a standard normal distribution, the regions are independent of each other at the same time t, and the regions are considered as independent individuals, there is no spatial correlation between regions, these are all true. After constant regression of Equation (5), a random error term is generated. The unbiased variance estimator is as follows:(6)St2=∑i=1Ne2/itN−1.Among them, the residual termeit=yit−y¯t is obtained according to equation (1), that is, the mean square error σt in the result obtained by performing Stata regression on the model. Using the data from each region to perform a temporal regression and calculate a set of values σt, the time series of design values σt are shown in Figure 6, in which the difference in economic growth in region B shows obvious volatility. Overall, the variance patterns roughly matched the variance trends of the variance coefficients from descriptive statistics studies, which also suggested that the variance coefficients could be measured and converged to describe economic disparities between regions.Figure 6
Time series plot of log standard deviation per capita in region B.


### 3.2.3.β Convergence Model

The convergence model is similar to the analysis of convergence, before the introduction of the spatial matrix, the convergence modeling of the regional spatial correlation is not considered. Absolute convergence phenomena in region B are analyzed using equations that define the concept of convergence. The regression model used for absolute convergence is as follows:(7)130logY⌢i,2018Yi,1998=α+βlogYi,1998+εi.1978,2018.Using Stata software to perform regression analysis on this equation, the regression equation obtained is as follows:(8)130logY⌢i,2018Yi,1998=0.286−0.022logYi,1998,0.0070.038,−3.04∗∗∗7.52∗∗∗,R2=0.352,Fstatistics=9.25∗∗∗,Prob>F=0.007,Sample size=19.The value in parentheses in the first row below the equation is the standard deviation of the regression coefficient, and the second row is the statistict, ∗∗∗ which means significant at the 1% confidence level. This shows that the regression result, the statistic F is significant at the 1% confidence level. The regression equation is established, and the value of the regression coefficient is very important to the confidence.Starting from the turning point in 2003, we compare and analyze the convergence situation before and after 2003. The regression model used for absolute convergence from 2003 to 2018 is as follows:(9)115logYi,2018Yi,2003=α+βlogYi,2003+εi,2003,2018.Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(10)115logYi,2018Yi,2003=0.203−0.037logYi,2003,0.0330.01,6.18∗∗∗−3.86∗∗∗,R2=0.235,FStatistics=14.91∗∗∗,Prob>F=0.0013,Sample size=19.At this time, the equation is still significant, but the value ofβ increases significantly, and the convergence speed is accelerated. The regression model used for the absolute β convergence for 1998–2003 is as:Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(11)115logY^i,2003Yi,1998=0.118−0.021logYi,1998,0.0180.008,6.65∗∗∗−3.86∗∗∗,R2=0.264,FStatistics=7.05∗∗∗,Prob>F=0.0167,Sample size=19.The currentβ convergence rate is about 2.1% per year. Based on the availability and reliability of the data to analyze the conditional convergence, take 2003 as the data starting point, and carry out the convergence regression according to the degree of industrialization and the explanatory variables that affect the degree of convergence. The regression model is used as:(12)115logYi,2008Yi,1993=α+βlogYi,2003+γ1Ri,pop+γ2Ri,i+γ3Ri,g+γ4ISi+γ5IOi+εi,2003,2018.Ri,pop represents the natural growth rate of population in district i, and γ1 is the measure of the impact of population on economic development. Ri,i represents the percentage of investment in the region, γ2 is the measure of the impact of investment on economic development, Ri,g is the level of government spending in region i, γ3 is the impact of government behavior on economic development, and IS is the level of industrialization in region i. γ4 is measured by the proportion of the secondary and tertiary industries in economic development in the industrial structure, IO is the degree of international openness, and γ5 is the impact of the degree of openness on economic growth.Running the sample data to estimate the model. Finally, it is found that only investment and the degree of opening to the outside world have an impact on economic growth, while the three factors of population growth rate, government public expenditure rate, and industrial structure are not significant. The population growth rate is 0.5, theP rate is 0.28, the public expenditure rate is 0.057, the P rate is 0.763, the industrial structure rate is 0.038, and the P rate is 0.245. So the final estimated regression equation is as follows:(13)115logYi,2018Yi,2003=0.236−0.0413logYi,2003+0.0397Ri,i+0.008IOi,0.0480.0150.0210.0034,4.9∗∗∗−2.73∗∗1.9∗2.41∗∗R2=0.449,FStatistics=7.73∗∗∗Prob>F=0.0024,Samplesize=19.The first line is the standard deviation of the estimated factor, and the second line is the statisticalt, ∗∗∗which means significant at the 10% confidence level, ∗∗means significant at the 5% confidence level, and ∗means significant at the 1% confidence level. Compared with absolute convergence, the convergence speed is significantly faster.


## 3.2.1.σ Convergence Index

σ convergence index refers to the fact that the dispersion of per capita income between regions tends to decrease over time. When the index tends to decline, there is economic convergence. The time series of changes in per capita GDP in region B from 1998 to 2018 is now plotted, as shown in Figure 4. The economic convergence of region B can be analyzed by directly observing the change in the coefficient of variation on the plot.Figure 4
Time series plot of log standard deviation per capita in region B.In the first stage (1998–2005), the instability of this stage gradually decreased over time, and the economic gap gradually narrowed. In the second stage (2005–2010), the coefficient of variation of this stage gradually increased with time, and the gap widened. In the third stage (2010–2012), the coefficient of variation of this stage showed a gradually decreasing trend with time. In the fourth stage (2012–2018), the coefficient of variation for this stage began to show an upward trend over time.


## 3.2.2.β Convergence Trend

Convergence trend refers to a trend in which the initial development level of a country or region is inversely proportional to the development speed. In addition to the coefficient of variation, graphs of economic growth rates and output levels can also be used to roughly describe the convergence trend of economic convergence [21]. Figure 5 shows that the trend line shows a downward trend, and the economic growth rate of area B is negatively correlated with the initial output level, showing a convergence trend. The slope of the trend line can be approximated as the convergence force of convergence.Figure 5
Scatter plot of economic growth rate and initial output level.The model is constructed based on the related concepts of economic convergence. The convergence mainly examines the changes in the level of economic development between different economic systems over time [22]. If the standard deviation tends to decrease, it means that the economic growth of each region is converging. On the contrary, it shows that the economic growth of different regions is different. The types of tests introduced in convergence concepts are used below. The definition of Equation (1) can be obtained by constructing a regression model, namely, yit=logYit. The logarithmic form of the per capita GDP of each region in the tth period is y¯t=1/N∑i=1NlogYit, and the unbiased estimate of the variance of the random error term εit after regression is σt2. The regression model is as follows:(5)yit=y¯t+εit,εit∼iid,N0,σt2.Among them,yit and y¯t are as defined in parentheses above, and the area is i=1,2,⋯,N; time is t=1,2,⋯,T. For this regression model, since this regression model assumes a standard normal distribution, the regions are independent of each other at the same time t, and the regions are considered as independent individuals, there is no spatial correlation between regions, these are all true. After constant regression of Equation (5), a random error term is generated. The unbiased variance estimator is as follows:(6)St2=∑i=1Ne2/itN−1.Among them, the residual termeit=yit−y¯t is obtained according to equation (1), that is, the mean square error σt in the result obtained by performing Stata regression on the model. Using the data from each region to perform a temporal regression and calculate a set of values σt, the time series of design values σt are shown in Figure 6, in which the difference in economic growth in region B shows obvious volatility. Overall, the variance patterns roughly matched the variance trends of the variance coefficients from descriptive statistics studies, which also suggested that the variance coefficients could be measured and converged to describe economic disparities between regions.Figure 6
Time series plot of log standard deviation per capita in region B.


## 3.2.3.β Convergence Model

The convergence model is similar to the analysis of convergence, before the introduction of the spatial matrix, the convergence modeling of the regional spatial correlation is not considered. Absolute convergence phenomena in region B are analyzed using equations that define the concept of convergence. The regression model used for absolute convergence is as follows:(7)130logY⌢i,2018Yi,1998=α+βlogYi,1998+εi.1978,2018.Using Stata software to perform regression analysis on this equation, the regression equation obtained is as follows:(8)130logY⌢i,2018Yi,1998=0.286−0.022logYi,1998,0.0070.038,−3.04∗∗∗7.52∗∗∗,R2=0.352,Fstatistics=9.25∗∗∗,Prob>F=0.007,Sample size=19.The value in parentheses in the first row below the equation is the standard deviation of the regression coefficient, and the second row is the statistict, ∗∗∗ which means significant at the 1% confidence level. This shows that the regression result, the statistic F is significant at the 1% confidence level. The regression equation is established, and the value of the regression coefficient is very important to the confidence.Starting from the turning point in 2003, we compare and analyze the convergence situation before and after 2003. The regression model used for absolute convergence from 2003 to 2018 is as follows:(9)115logYi,2018Yi,2003=α+βlogYi,2003+εi,2003,2018.Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(10)115logYi,2018Yi,2003=0.203−0.037logYi,2003,0.0330.01,6.18∗∗∗−3.86∗∗∗,R2=0.235,FStatistics=14.91∗∗∗,Prob>F=0.0013,Sample size=19.At this time, the equation is still significant, but the value ofβ increases significantly, and the convergence speed is accelerated. The regression model used for the absolute β convergence for 1998–2003 is as:Using the software to perform regression analysis on this equation, the regression equation obtained is as follows:(11)115logY^i,2003Yi,1998=0.118−0.021logYi,1998,0.0180.008,6.65∗∗∗−3.86∗∗∗,R2=0.264,FStatistics=7.05∗∗∗,Prob>F=0.0167,Sample size=19.The currentβ convergence rate is about 2.1% per year. Based on the availability and reliability of the data to analyze the conditional convergence, take 2003 as the data starting point, and carry out the convergence regression according to the degree of industrialization and the explanatory variables that affect the degree of convergence. The regression model is used as:(12)115logYi,2008Yi,1993=α+βlogYi,2003+γ1Ri,pop+γ2Ri,i+γ3Ri,g+γ4ISi+γ5IOi+εi,2003,2018.Ri,pop represents the natural growth rate of population in district i, and γ1 is the measure of the impact of population on economic development. Ri,i represents the percentage of investment in the region, γ2 is the measure of the impact of investment on economic development, Ri,g is the level of government spending in region i, γ3 is the impact of government behavior on economic development, and IS is the level of industrialization in region i. γ4 is measured by the proportion of the secondary and tertiary industries in economic development in the industrial structure, IO is the degree of international openness, and γ5 is the impact of the degree of openness on economic growth.Running the sample data to estimate the model. Finally, it is found that only investment and the degree of opening to the outside world have an impact on economic growth, while the three factors of population growth rate, government public expenditure rate, and industrial structure are not significant. The population growth rate is 0.5, theP rate is 0.28, the public expenditure rate is 0.057, the P rate is 0.763, the industrial structure rate is 0.038, and the P rate is 0.245. So the final estimated regression equation is as follows:(13)115logYi,2018Yi,2003=0.236−0.0413logYi,2003+0.0397Ri,i+0.008IOi,0.0480.0150.0210.0034,4.9∗∗∗−2.73∗∗1.9∗2.41∗∗R2=0.449,FStatistics=7.73∗∗∗Prob>F=0.0024,Samplesize=19.The first line is the standard deviation of the estimated factor, and the second line is the statisticalt, ∗∗∗which means significant at the 10% confidence level, ∗∗means significant at the 5% confidence level, and ∗means significant at the 1% confidence level. Compared with absolute convergence, the convergence speed is significantly faster.


## 3.3. Spatial Econometric Model

Spatial econometric models are mainly divided into two types: spatial lag model and spatial error model. Both of these models are based on the introduction of the spatial weight table to modify the basic model [23]. The spatial lag model is suitable for the behavior of adjacent areas, which affects the behavior of other areas in the whole area, and the spatial error model is suitable for the impact of uncertainty shocks on local economic variables in adjacent areas. The estimation of the spatial model adopts the maximum likelihood estimation method and the generalized least squares method.


### 3.3.1. Spatial Lag Model

In order forσ to converge, after introducing the constant regression (1) into the spatial table, the spatial lag model is as follows:(14)yt=αtI+λtWyt+εt.Among them,yt=y1t,y2t,⋯,yNt, is the vector model, αt and λt are constants, W is spatial weight table, and λt is weight factor. Write the vector model in the form of a component model:(15)yit=αt+λtWiyt+εit=αt+λt∑i≠j,j=1Nwijyjt+εit.Wi is a vector with i rows, Wij is a value with i rows and j columns. In this way, the establishment αt+λt∑i≠j,j=1Nwij,yjt of the area balance is not only related to t, but also to the area i. For absolute β convergence, after substituting equation (2) into the spatial weight table, the spatial delay model is as follows:(16)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+λW1TlogYi,t0N×1+εt0,t0+T.This is again a vector equation, with a column vector of local growth rates on the left, which is a unit vector, and a table of coefficients and spatial weights to be estimated. Writing the equation in terms of components, it can be got:(17)1TlogYi,t0+TYi,t0=α+βlogYi,t0+λ∑i≠j,j=1Nwij1TlogYj,t0+εi,t0,t0+T.It can be seen from this equation that the economic growth rate of thei th region is not only related to time T and the initial level logYi,t, but also to the growth rate of the j th region, so the spatial lag model can test the spatial diffusion of this region.For conditionβ convergence, a series of variables are introduced on the basis of the absolute convergence model to constitute the regression model.


### 3.3.2. Spatial Error Model

Spatial error models fall into two categories: spatial error autocorrelation models and overlapping moving average error models. The spatial error autocorrelation model is as follows:(18)y=Xβ+εε=λWε+u⇒y=Xβ+I−λW−1uu∼iid,N0,σ2.Among them,λ spatial error is the autocorrelation coefficient and Wε is the lag spatial error term. The moving average spatial error model is as follows:(19)y=Xβ+εε=u−θWu⇒y=Xβ+I−θWu,u∼iid,N0,σ2.θ is the moving average error rate for spatial error, and Wu is the concept of spatial delay error.Forσ converging, the constant regression (1) are identical in model form, so only the moving average model needs to be considered in the comparative analysis.(20)y=αI+I−θWu,u∼iid,N0,σ2.For absoluteβ convergence, the equation for the spatial error autocorrelation model is as follows:(21)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+I−λW−1u.This is a vector equation withu representing a column of random error terms in N regions and λ representing the power of the spatial relationship between the regression residuals.The conditionβ convergence model goes on to introduce additional variables on top of the absolute convergence model. The abovementioned describes the form of the spatial econometric model and introduces the tests of two pairs of models. Before proceeding with the spatial modeling analysis, the spatial correlation is first checked.(22)Moran,sI=∑i=1N∑j=1NwijYi−Y¯Yi−YS2∑i=1N∑j=1Nwij.Among them,S2=∑i=1NYi−Y¯2/N,Y¯=∑i=1NYi/N, is the observed value of a variable in the Yi th region; Wij is the value of the element in the W th row and j th column.


## 3.3.1. Spatial Lag Model

In order forσ to converge, after introducing the constant regression (1) into the spatial table, the spatial lag model is as follows:(14)yt=αtI+λtWyt+εt.Among them,yt=y1t,y2t,⋯,yNt, is the vector model, αt and λt are constants, W is spatial weight table, and λt is weight factor. Write the vector model in the form of a component model:(15)yit=αt+λtWiyt+εit=αt+λt∑i≠j,j=1Nwijyjt+εit.Wi is a vector with i rows, Wij is a value with i rows and j columns. In this way, the establishment αt+λt∑i≠j,j=1Nwij,yjt of the area balance is not only related to t, but also to the area i. For absolute β convergence, after substituting equation (2) into the spatial weight table, the spatial delay model is as follows:(16)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+λW1TlogYi,t0N×1+εt0,t0+T.This is again a vector equation, with a column vector of local growth rates on the left, which is a unit vector, and a table of coefficients and spatial weights to be estimated. Writing the equation in terms of components, it can be got:(17)1TlogYi,t0+TYi,t0=α+βlogYi,t0+λ∑i≠j,j=1Nwij1TlogYj,t0+εi,t0,t0+T.It can be seen from this equation that the economic growth rate of thei th region is not only related to time T and the initial level logYi,t, but also to the growth rate of the j th region, so the spatial lag model can test the spatial diffusion of this region.For conditionβ convergence, a series of variables are introduced on the basis of the absolute convergence model to constitute the regression model.


## 3.3.2. Spatial Error Model

Spatial error models fall into two categories: spatial error autocorrelation models and overlapping moving average error models. The spatial error autocorrelation model is as follows:(18)y=Xβ+εε=λWε+u⇒y=Xβ+I−λW−1uu∼iid,N0,σ2.Among them,λ spatial error is the autocorrelation coefficient and Wε is the lag spatial error term. The moving average spatial error model is as follows:(19)y=Xβ+εε=u−θWu⇒y=Xβ+I−θWu,u∼iid,N0,σ2.θ is the moving average error rate for spatial error, and Wu is the concept of spatial delay error.Forσ converging, the constant regression (1) are identical in model form, so only the moving average model needs to be considered in the comparative analysis.(20)y=αI+I−θWu,u∼iid,N0,σ2.For absoluteβ convergence, the equation for the spatial error autocorrelation model is as follows:(21)1TlogYi,t0+TYi,t0N×1=αI+βlogYi,t0N×1+I−λW−1u.This is a vector equation withu representing a column of random error terms in N regions and λ representing the power of the spatial relationship between the regression residuals.The conditionβ convergence model goes on to introduce additional variables on top of the absolute convergence model. The abovementioned describes the form of the spatial econometric model and introduces the tests of two pairs of models. Before proceeding with the spatial modeling analysis, the spatial correlation is first checked.(22)Moran,sI=∑i=1N∑j=1NwijYi−Y¯Yi−YS2∑i=1N∑j=1Nwij.Among them,S2=∑i=1NYi−Y¯2/N,Y¯=∑i=1NYi/N, is the observed value of a variable in the Yi th region; Wij is the value of the element in the W th row and j th column.


## 4. Convergence of Economic Growth Results

As can be seen from the abovementioned, as far as the GDP of each region in country M is concerned, there is a spatial correlation between adjacent regions. Figures7 and 8 are Moran scatter plots of M country GDP in 2010 and 2015.Figure 7
Moran scatter plot of GDP in 2010.Figure 8
Moran scatter plot of GDP in 2015.Scatter plots exhibit the common characteristic of positive spatiality. Most of the country M falls into the first and third quadrants, showing a spatial relationship. In the third quadrant more than in the first quadrant, mostly low-aggregation type. The fourth quadrant represents the high and low agglomeration area, and the two quadrants are in a negative spatial relationship.


### 4.1.σ Analysis of Convergence Results

As shown in Figure9, the per capita GDP of area B fluctuates greatly, but the overall trend is a slight downward trend, indicating that the economic development of area B tends to converge.Figure 9
Coefficient of variation of GDP per capita in area B.


### 4.2. Absolute 55 Convergence Analysis Results

Regression analysis was performed using the OLS model. From Table3 the regression coefficient between the average GDP growth rate in region B and the baseline level of per capita GDP is negative. If P=0.000 is at a significant level, through the significance test, the economic growth of area B has a global correlation convergence under the spatial interaction.Table 3
OLS model parameter estimation results.
Estimated resultsCoefficientPvalueModel checkingPvalueα0.265540.000000Jarque-Bera0.14637β−0.018150.000000Breu‒Pagan0.00039AdjustmentR20.368724—Koenker‒Basett0.00738LJK103.6845—White0.00651AIC−289.257—LM (lag)0.478465SC−263.348—LM (Lerro)0.91724As can be seen from Figure10, the global Moran index of per capita GDP in region B is positive. Except for the three years of 2006, 2007, and 2008, the Moran index value in other years did not change much. And all passed the significance test at the significance level of 0.05. It shows that the distribution of per capita GDP in region B has a long-term spatial dependence.Figure 10
Global Moran index of GDP per capita in region B.As can be seen from Figure10, the Moran index of per capita GDP in region B is always positive. Except for 2006, 2007, and 2008, the Moran index values in other years did not change much, and the significance level was 0.05. The test showed that the distribution of per capita GDP showed long-term spatial dependence.The comparison of the accuracy results of the spatial econometric analysis model based on big data and other analysis models is shown in Figure11.Figure 11
Spatial econometric model comparison.Figure11 shows the results of the convergence of economic growth in region B from 1998 to 2018 based on the spatial econometric model under big data and the general model. It can be seen from the spatial econometric model based on big data and the general analysis model are roughly the same, but slightly higher. This shows that the introduction of big data has significantly enhanced the accuracy of economic convergence analysis, and the accuracy has increased by 4.1%.


## 4.1.σ Analysis of Convergence Results

As shown in Figure9, the per capita GDP of area B fluctuates greatly, but the overall trend is a slight downward trend, indicating that the economic development of area B tends to converge.Figure 9
Coefficient of variation of GDP per capita in area B.


## 4.2. Absolute 55 Convergence Analysis Results

Regression analysis was performed using the OLS model. From Table3 the regression coefficient between the average GDP growth rate in region B and the baseline level of per capita GDP is negative. If P=0.000 is at a significant level, through the significance test, the economic growth of area B has a global correlation convergence under the spatial interaction.Table 3
OLS model parameter estimation results.
Estimated resultsCoefficientPvalueModel checkingPvalueα0.265540.000000Jarque-Bera0.14637β−0.018150.000000Breu‒Pagan0.00039AdjustmentR20.368724—Koenker‒Basett0.00738LJK103.6845—White0.00651AIC−289.257—LM (lag)0.478465SC−263.348—LM (Lerro)0.91724As can be seen from Figure10, the global Moran index of per capita GDP in region B is positive. Except for the three years of 2006, 2007, and 2008, the Moran index value in other years did not change much. And all passed the significance test at the significance level of 0.05. It shows that the distribution of per capita GDP in region B has a long-term spatial dependence.Figure 10
Global Moran index of GDP per capita in region B.As can be seen from Figure10, the Moran index of per capita GDP in region B is always positive. Except for 2006, 2007, and 2008, the Moran index values in other years did not change much, and the significance level was 0.05. The test showed that the distribution of per capita GDP showed long-term spatial dependence.The comparison of the accuracy results of the spatial econometric analysis model based on big data and other analysis models is shown in Figure11.Figure 11
Spatial econometric model comparison.Figure11 shows the results of the convergence of economic growth in region B from 1998 to 2018 based on the spatial econometric model under big data and the general model. It can be seen from the spatial econometric model based on big data and the general analysis model are roughly the same, but slightly higher. This shows that the introduction of big data has significantly enhanced the accuracy of economic convergence analysis, and the accuracy has increased by 4.1%.


## 5. Conclusions

Based on big data, this paper uses a spatial econometric model to test and analyze the convergence mechanism of economic growth. The economic convergence index is used to construct the spatial weight table, the spatial and geographical factors are introduced into the economic growth convergence model, the real GDP per capita is used as the indicator to measure economic growth, and the per capita income and expenditure ratio is used as the factor of economic convergence. Studies have shown that considering the correlation between regions, especially the correlation between economies, the differences between regions have been significantly reduced. There areσ convergence and periodic fluctuations between regions, but the general trend is still convergent. As big data’s revolutionary impact on economic analysis grows, so too had economic policymakers and academia. When studying the convergence of economic growth, the addition of big data technology can predict the change law of data, thereby reducing data errors, optimizing research results, and providing a stronger scientific basis for the development of a coordinated regional economy.



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*Source: 6230817-2022-09-07.xml*