Spatial Econometric Analysis of Urban and County-level Economic Growth Convergence in China

Abstract

Economic growth convergence, one of the classical assumption in regional economic growth, has been perplexing. There are many empirical studies trying to test if there is regional convergence in China. In this article, we bring new information of the finer spatial scale to the existing literature by using neoclassical convergence analysis, cross-sectional specifications, panel data models, and spatial econometric techniques to test the convergence hypothesis across 2,286 cities and counties in China. Empirical findings from cross-sectional data and spatial panel data show that significant absolute β and conditional β convergence are present in gross domestic product per capita after controlling for investment return rate, human capital, savings rate, population growth, technology advancement, capital depreciation rate, and initial technology level. We also find spatial agglomeration in urban and county economic growth is strong, and spatial effects are significant. Urban and county economic growth convergence rates for 1992–2010 show a gradually accelerated development trend. We present significant evidence that levels of investment, human capital, and initial technology impose significant facilitating effects on city and county economic growth, while savings and population growth have significant negative effects. And city and county economic growth differ in terms of convergence levels and influential factors.

Keywords

economic growth convergence urban and county economy spatial econometrics model China

Although after 200 years of theoretical and empirical development in regional economic growth, the differences in regional economic growth have not been well explained (Helpman 2009). In order to understand this mystery of economic growth, economists give analysis on regional economic disparity problems and the reasons from the theory and empirical aspects in different angles based on modern growth theory, mainly including neoclassical growth model and endogenous growth theory (Lucas 1988; Romer 1986; Solow 1956; Swan 1956). Since the 1990s, theoretical and empirical models of regional economic growth convergence established by Barro and Sala-i-Martin (1991, 1992, 2004) and Mankiw, Romer, and Weil (1992) played the crucial role in understanding regional economic growth inequality. Following the seminal work of economic growth convergence, the recent empirical literatures on regional economic growth have conducted a large quantity of empirical studies to test convergence hypothesis (Barro and Sala-I-Martin 2003). For the definitions of convergence, it includes different spatial–temporal scales and types such as σ convergence and β convergence, unconditional and conditional convergence, global and local or club convergence, growth rates and income-level convergence, and deterministic and stochastic convergence (Islam 2003). However, these studies mainly have been conducted in developed countries or economies, such as Europe (Quah 1996), the United States (Carlino and Mills 1996; Marjit and Mitra 1996), Japan (Nagayasu 2011), Canada (James and Krieckhaus 2008), Australia (Maxwell and Peter 1988), and so on. Unexceptionally, these theoretical and empirical studies have motivated increasingly downscaling research interests at the regional, provincial, prefectural, and county level (Budenya, Gebremdehin, and Schaeffer 2002; Bukenya et al. 2011; Drennan and Lobo 1999; Sala-I-Martin 1996). Meanwhile, these developments provide a path to explain regional economic growth of developed countries or economies. Although in the recent past few years, the research of regional economic growth convergence in developing countries have increasingly gotten a high note from the scholars (Das, Sinha, and Mitra 2010; Rivas 2007; Wei 1999). However, the related research with different spatial scales are inadequate, and differential convergence processes are poorly understood.

China, as the biggest developing country, has experienced a rapid economic development process since its reform and opening up (Fan and Sun 2008). But correspondingly, one of the most significant problems facing Chinese economic development is unbalanced regional development (Center Compilation and Translation Bureau 2011). Generally, in China, various factors such as location, resources, national development strategies, productive factors flows, and local government development strategies directly produce differing regional development paths (Wei and Liefner 2012). The effects of such differences can be intensified by a gradual increase mechanism of rewards, contributing to a significant Matthew effect (Fan and Sun 2008; Wei 2002). Yet, both domestic and international regional development patterns show that unbalanced regional development can cause serious social problems, reduce benefits of high growth, and further prevent future productive growth (Dupont 2007; Gardiner, Martin, and Tyler 2011; Petrakos and Saratsis 2000; Rey and Janikas 2005). Thus, theoretically, rapid economic growth of China, institutional transformation, and uneven development over the past thirty years can serve to extend and deepen our understanding of regional economic growth convergence for developing countries (Liao and Wei 2012; Wei 2007). Meanwhile, strategies for coordinating regional development and reducing differences between regions have been prioritized in China’s regional economic development plan at the government and policy level (Center Compilation and Translation Bureau 2011; Fan 1997; Xinhuanet 2006).

To effectively solve problems of unbalanced regional development, the first theoretical issue is to understand the degree of unbalanced development, the existence of convergence, the convergence rate, and influential factors at various scales. Further, we need to get the information about the changes in convergence rate over time and the factors that mitigate convergence and help overall regional growth. Once these factors are addressed, we can propose a remedy.

More specifically, this article aims to provide an empirical analysis for understanding the spatiotemporal dynamics of Chinese regional economic development and regional economic convergence and provide an empirically well-founded response to the following questions: are undeveloped regions growing faster, narrowing the development gap and its convergence speed? Are the empirical spatial econometrics methods used in convergence analyses appropriate? What are the differences in convergence in the administrative region unit of analysis (city and county)? What are the influences of functional economic regions on regional convergence? Which geographical unit is suitable to understand regional economic development in China (county and city vs. province vs. region)? In order to deepen our understanding for these issues, this article discusses Chinese economic growth convergence, verifies absolute β and conditional β convergence across both temporal and spatial dimensions, and examines specific convergence mechanisms at the urban and county levels. A data set for 2,286 units nationwide at the urban and county levels for 1992–2010 was used to examine regional economic convergence. Regarding application methodologies, spatial econometric models, and combined methods were applied to establish a spatial econometric system that focuses on spatial effects to reflect economic development differences in counties and cities. And a detailed comparative analysis of economic growth convergence across different time periods and different geographical units is conducted to explore implementation effects of regional economic policies and differences in urban and county economic growth.

The article is structured as follows: the second section presents a literature review, the third section describes the econometric analysis model and data sources, and the fourth section presents the results of the econometric analysis and explanations and provides a comprehensive discussion. The fifth section provides some conclusions.

Literature Review

Regional economic convergence studies of China have attracted considerable scholarly attention. The findings concerning the existence and speed of convergence that are examined over time are used as a tool to evaluate and test the effectiveness of regional development strategies and policies (Herrerias, Orts, and Tortosa-Ausina 2011). Numerous scholars believe that China has experienced regional economic convergence process. However, due to differences in research perspectives and data used, scholars have obtained inconsistent conclusions regarding the nature, degree, and speed of such convergence processes. Most studies have verified the existence of convergence at the regional and provincial level. Zhang (2001) verified the existence of convergence in the three regions of China (east, middle, and west) using a forty-plus-year time series data. Wang and Ge (2004) showed that while absolute β convergence does not exist in China, conditional β convergence does exist, concluding that differences between the eastern area and other areas are growing, while those between central and western regions are becoming less distinct. At the province level, Herrerias, Orts, and Tortosa-Ausina (2011) and Matsuki and Usami (2011) confirmed the existence of regional economic convergence in China. Other scholars applied a unit root test, unbalanced index, cross-sectional data model, and panel data model, further confirming the existence of β convergence in provinces (Yao and Zhang 2001a, 2001b). However, there is no consensus regarding convergence speed. Li, Liu, and Rebelo (1998) detected the estimated speed of conditional β convergence for twenty-nine provinces in China over the period 1978–1995, which is 4.74 percent over year. However, Chen and Fleisher (1996) found a significant trend of unconditional β convergence for twenty-five provinces over the period 1978–1993, at an annual convergence rate of 0.9 percent. Demurger (2001), examining twenty-four Chinese provinces between 1985 and 1998, found a significantly higher trend of unconditional β convergence, at an annual convergence rate of 13 percent to 21 percent.

However, there are many empirical studies that do not support the above-mentioned convergence hypothesis. In other words, these studies have not found economic convergence across Chinese regions and provinces (Liu 2006). Ma and Yu (2003) came to this conclusion, finding that regional differences have increased at a rate of between 1.2 percent and 2.1 percent. Wang (2004) also found that the Chinese economy as a whole has not exhibited the process of conditional convergence. These seemingly conflicting findings may show that, in regional economic development, there usually is a concomitance of regional economic convergence and divergence trends among different geographical unit (Petrakos, Kallioras, and Anagnostou 2011). It should be noted that these studies did not consider the endogenous growth effects.

Although scholars have conducted numerous effective studies on Chinese regional economic growth convergence, such studies are often contradictory and limited in terms of spatial and scale effects. Investigations of economic growth convergence in China seldom consider spatial effects of regional economic development (Yu 2006) including spatial heterogeneity, spatial spillover, spatial dependence, and spatial scale (Rey and Janikas 2005). The nonspatial method, which primarily involves ordinary least squares (OLS) regression, is widely applied to evaluate economic growth convergence (Li and Wei 2010; Liao and Wei 2012; Wei and Fan 2000; Wei and Kim 2002). However, the standard analytical framework may disregard spatial dependence, which can cause estimation errors using the traditional OLS model or even render the estimation invalid. Ignoring spatial effects may lead to biased results partly because spatial effects greatly influence geographic processes (Yu and Wei 2008). Therefore, economists now use dummy variables to explain spatial effects, though this method may not reflect real geographic information. Several studies have attempted to address this limitation, using the spatial econometric model as the primary analytic framework. Hence, recently developed spatial econometric models provide a new tool for understanding the spatial effects of China’s regional economic convergence, effectively ameliorating unbalanced regional development.

Originally, spatial econometrics was developed based on the innovative work of Cliff and Ord (1972, 1981). Anselin (1988) and Elhorst (2003) introduced the spatial lag error term based on the traditional data model and incorporated spatial correlation into the econometric model. Elhorst (2010) systematically examined estimate methods of the spatial data model, gradually improving this model. In recent years, spatial econometrics has developed rapidly and a series of spatial econometric models were developed, such as spatial lag of X model, spatial autocorrelation (SAC) model, spatial Durbin model, spatial Durbin error model, general spatial model, spatial dynamic panel model, and dynamic space–time panel data model. However, so far the spatial autoregressive model (SAR) and spatial error model (SEM) are the most established and commonly used methods of econometric analysis. In data aspect, given scholarly doubts concerning the use of the cross-sectional data for analyzing economic growth, most scholars recommend using the panel data (Matsuki and Usami 2011; Tselios 2009). It is widely believed that the panel data model offers more information, a lower degree of collinearity and superior estimate efficiency (Tselios 2009). In practice, considerable spatial econometric research concerning regional economic convergence in developed countries or economies may provide useful reference for our study (Arbia and Paelinck 2003; Dall’erba and Le Gallo 2008; Rey and Montouri 1999; Tselios 2009).

Meanwhile, regional economic growth convergence in China is sensitive to geographic scale, as demonstrated by a host of studies (Li and Wei 2010; Wei 1999, 2002; Wei, Yu, and Chen 2011). However, most studies focus on a regional (Wei and Ma 1996; Yu and Wei 2003) and provincial (Fujita and Hu 2001; Yao and Zhang 2001a; Yu et al. 2011; Zhang and Fan 2004; Zhang and Zhang 2003) scales. The effects of functional economic regions were not comprehensively understood. For countries as large as China, regional economic growth convergence exists not only across regions and provinces but also within prefectures and counties (Liao and Wei 2012). Unlike sweeping, large-scale macroeconomic difference analyses conducted at the regional and province levels, studies on urban and county economic growth differences are more detailed and operational. Such studies offer information not only on macro spatial dimensions but also on patterns of local and regional spatial and temporal heterogeneity. Thus, studies on urban and county economic growth convergence can more tangibly guide intermediate microeconomic regional policies. Other studies of county level furtherly confirmed that the economic growth convergence process within the individual country have significant differences with various scales (Higgins, Levy, and Young 2006; Young, Higgins, and Levy 2008).

Data and Methodology

Estimation Model

Cross-sectional data models

The cross-sectional data model is the analytical method used in the classic β convergence model. For a relatively closed economy, its gradual increase occurs in a log linear manner (Barro and Sala-I-Martin 1991; Sala-I-Martin 1996):

\frac{1}{T - t} \cdot \log (\frac{y_{i T}}{y_{i t}}) = X_{i} * + \frac{1 - e^{- β (T - t)}}{T - t} \cdot \log (\frac{{\bar{y}}_{i}^{*}}{{\bar{y}}_{i t}}) + u_{i t},

where i is the basic economic unit, t and T represent the start and end of the period, respectively, T − t is the length of the observation period, y_it and y_iT represent production per capita or income levels at the start and end of the period, respectively, X_i* represents the growth rate of production per capita in a stable state, ${\bar{y}}_{i t}$ is the production level of each effective worker, ${\bar{y}}_{i}^{*}$ is the production-level per capita in a stable state, β represents the convergence rate, and u_it is the error item. Higher β values correspond with faster convergence to a stable state. If β is greater than 0, regional economic growth tends to converge, and if β is smaller than 0, regional economic growth tends to diverge.

For empirical purposes, it is often assumed that X_i* and ${\bar{y}}_{i}^{*}$ are constant. Consequently, equation (1) can be written as follows:

\frac{1}{T - t} \cdot \log (\frac{y_{i T}}{y_{i t}}) = B - \frac{1 - e^{- β (T - t)}}{T - t} \cdot \log y_{i t} + u_{i t}^{*} .

In this equation, B is a constant and $u_{i t}^{*}$ is the error value. β is only relevant to the level of production per capita at the start of the period and irrelevant to other parameters. Thus, the β measure calculated here denotes absolute convergence.

Per capita income growth is determined not only by the initial level but by a series of other factors as well.

\frac{1}{T - t} \cdot \log (\frac{y_{i T}}{y_{i t}}) = B - \frac{1 - e^{- β (T - t)}}{T - t} \cdot \log y_{i t} + ϕ X_{i t} + u_{i t}^{*} .

In this equation, ϕX_it is a series of influential factors of economic growth. This equation represents a conditional β convergence.

To simplify this equation, we improved the above-discussed traditional β convergence model. The basic model was illustrated as follows:

\ln (\frac{y_{i, t}}{y_{i, t 0}}) = α + β \ln (y_{i, t 0}) + u_{i, t} .

In this equation, y_i,t and y_i,t ₀ represent actual gross domestic product (GDP) per capita for cities and counties at the end and start of the period. If β < 0, β convergence exists, suggesting that the economic development of undeveloped cities and counties is faster than that of developed cities and counties and that undeveloped urban and county GDP may converge to that of developed cities and counties. Assuming that the specific convergence rate at this point is λ, if the convergence rate of β for a certain period must be given, then λ = −ln(β + 1)/T, with T as the time span.

To examine the nature of conditional convergence, we used the Solow economic growth model (Solow 1956), traditional Cobb–Douglas production function, and Mankiw-Romer-Weil (MRW) empirical model (Mankiw, Romer, and Weil 1992) to improve the traditional conditional β convergence model:

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t 0}}) = & α + β \ln (y_{i, t 0}) + β_{1} \ln K_{i, t} + β_{2} \ln H_{i, t} + β_{3} \ln S_{i, t} \\ + β_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) + β_{5} \ln A 0 + u_{i, t} . \end{array}

In this equation, α is an intercept term, β is the convergence estimated coefficient, β₁–β₅ is the influential factor coefficient of conditional convergence, K_i,t is the measurement index of the investment return rate and the average ratio of total investment in fixed assets and urban and county GDP for the same year was used. H_i,t is the measurement index of human capital, the average ratio of students enrolled in secondary school to the total population at the end of the year in cities and counties.¹ S_i,t is the savings rate. We used the average ratio of the residents’ deposit balance at the end of a year to the GDP of the same year to measure this variable. Variable n_i,t is the average change rate of total populations of cities and counties at the end of each year, g_i,t is the technology advancement variable, δ_i,t is the capital depreciation rate, and for variable n _i,t + g _i,t + δ_i,t, parameters g_i,t and δ_i,t are generally realized through assignment. We assumed that the two parameters are constant, referred to the processing model of the MRW analytical model, and set these two parameters as 0.02 and 0.03, respectively. A0 is the initial technology level, and we used preferential policies enjoyed in cities and counties to replace it. We used Demurger et al.’s (2002) method to quantify the qualitative problem. If a county or city has shared a preferential policy, it can be marked as 1. The value indicating preferential policies of each county or city can be calculated by aggregating all preferential policies. This method was also tested in our pervious study (Li and Fang 2014). Finally, u_i,t is the error term.

Cross-sectional spatial econometric models

The SAR considers spatial and spatial spillover effects of surrounding spatial units on target units, producing an observed value for a single area i based on the observed value of a neighboring region (j ≠ i). Therefore, the SAR of absolute β and conditional β convergence for urban and county economic growth is set forth as follows:

\ln (\frac{y_{i, t}}{y_{i, t 0}}) = α + ρ \sum_{j = 1}^{N} w_{i j} \ln (\frac{y_{i, t}}{y_{i, t 0}}) + β \ln (y_{i, t 0}) + ∊_{i} ∊_{i} : N i d (0, σ^{2}) .

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t 0}}) = & α + ρ \sum_{j = 1}^{N} w_{i j} \ln (\frac{y_{i, t}}{y_{i, t 0}}) + β \ln (y_{i, t 0}) + β_{1} \ln K_{i, t} + β_{2} \ln H_{i, t} + β_{3} \ln S_{i, t} \\ + β_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) + β_{5} \ln A 0 + ∊_{i} ∊_{i} : N i d (0, σ^{2}) . \end{array}

In this equation, α is the intercept term, ρ represents the SAC coefficient, w_ij represents the spatial weight matrix, and ∊_i,t denotes the error item distribution.

When existing space interacts with the error item process, or when space covariance exists among errors from different regions, another spatial econometric model is used: SEM. In such cases, we set forth the SEM of absolute β and conditional β convergence of urban and county economic growth as follows:

\ln (\frac{y_{i, t}}{y_{i, t 0}}) = α + β \ln (y_{i, t 0}) + ∊_{i}, ∊_{i} = γ \sum_{j = 1}^{N} w_{i j} ∊_{i} + μ_{i}, μ_{i} : N i d (0, σ^{2}) .

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t 0}}) = & α + β \ln (y_{i, t 0}) + β_{1} \ln K_{i, t} + β_{2} \ln H_{i, t} + β_{3} \ln S_{i, t} + β_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) \\ + β_{5} \ln A 0 + ∊_{i}, ∊_{i} = γ \sum_{j = 1}^{N} w_{i j} ∊_{i} + μ_{i}, μ_{i} : N i d (0, σ^{2}) . \end{array}

In this equation, γ represents the space error coefficient.

Panel data models and spatial panel data models

To make the panel data analysis more efficient, combined with eliminating business cycles fluctuations and the delayed effects of institutional and human capital factors, we divided the 1992– 2010 period into the following three periods: 1992–2000, 2000–2005, and 2005–2010 (Badinger, Muller, and Tondl 2004; Bouayad-Agha and Vedrine 2010). To examine GDP per capita convergence, the following econometric model of absolute β convergence was used:

\ln (\frac{y_{i, t}}{y_{i, t - k}}) = α_{i} + β' \ln (y_{i, t - k}) + u_{i, t} .

In this equation, y_i,t and y_i,t−k represent real GDP per capita at the end of the period and during the previous k years, respectively, and β′ is the convergence coefficient. α changes to α _i (fixed coefficient), and thus equation (10) is the most traditional panel data model. Accordingly, the conditional β convergence model can be written as follows:

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t - k}}) = & α_{i} + β' \ln (y_{i, t - k}) + {β'}_{1} \ln K_{i, t} + {β'}_{2} \ln H_{i, t} + {β'}_{3} \ln S_{i, t} \\ + {β'}_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) + {β'}_{5} \ln A 0 + u_{i, t} . \end{array}

Anselin (1988) and Elhorst (2003) divided spatial panel data models into four types: fixed effects, random effects, fixed coefficient, and random coefficients. Most scholars use the fixed effects model. Thus, we apply the spatial panel model with fixed effects to examine the basic conditions of Chinese urban and county economic growth convergence. The SAR panel data model of absolute β and conditional β is thus adapted into the following:

\ln (\frac{y_{i, t}}{y_{i, t - k}}) = α_{i} + ρ \sum_{j = 1}^{N} w_{i j} \ln (\frac{y_{j, t}}{y_{j, t - k}}) + β' \ln (y_{i, t - k}) + u_{i} + ∊_{i, t} .

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t - k}}) & = α_{i} + ρ \sum_{j = 1}^{N} w_{i j} \ln (\frac{y_{j, t}}{y_{j, t - k}}) + β' \ln (y_{i, t - k}) + {β'}_{1} \ln K_{i, t} + {β'}_{2} \ln H_{i, t} \\ + {β'}_{3} \ln S_{i, t} + {β'}_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) + {β'}_{5} \ln A 0 + u_{i} + ∊_{i, t} . \end{array}

In this equation, w_ij is the spatial weight matrix. Because the panel data model is used, the spatial weight matrix should not be the N × N matrix but the (N × T) × (N × T) block matrix. y_j,t is the weighted average of the value observed spatially close to the observed value, u_i is the spatial special function item, and ε_i,t is the error distribution item.

The spatial error panel data model of absolute β and conditional β convergence of urban and county economic growth is set forth as follows:

\ln (\frac{y_{i, t}}{y_{i, t - k}}) = α_{i} + β' \ln (y_{i, t - k}) + u_{i} + φ_{i, t}, φ_{i, t} = γ \sum_{j = 1}^{N} w_{i j} φ_{i, t} + ∊_{i, t} .

\begin{array}{lr} \ln (\frac{y_{i, t}}{y_{i, t - k}}) & = α_{i} + β' \ln (y_{i, t - k}) + {β'}_{1} \ln K_{i, t} + {β'}_{2} \ln H_{i, t} + {β'}_{3} \ln S_{i, t} \\ + {β'}_{4} \ln (n_{i, t} + g_{i, t} + δ_{i, t}) + {β'}_{5} \ln A 0 + u_{i} + φ_{i, t}, φ_{i, t} = γ \sum_{j = 1}^{N} w_{i j} φ_{i, t} + ∊_{i, t} . \end{array}

In this equation, φ _i,t is the SAC error term and γ reflects spatial effects. However, unlike the spatial SAR panel model, the SAC error term reflects the degree to which unpredictable influential factors of urban and county economic convergence affect this phenomenon.

The above-mentioned spatial econometric models are usually estimated by maximum likelihood estimation (ML; Elhorst 2003, 2010). Common statistics include Lagrange multiplier (LM) err, LM lag, robust LM err, and robust LM lag. To examine spatial correlations, we tested the Moran’s I index. The testing equation is not explained in detail here.

Data and Preliminary Processing

There are three county-level administrative units in China: the county (“Xian” including autonomous counties, “Zizhixian”), the county-level city (“Xianjishi”), and the urban district (“Chengqu”). The county is an administrative unit. Generally, a county has relatively high ratios of agricultural output to GDP and rural population to total population. Therefore, the spatial spillover in a county is usually low, but there are exceptions, such as the top 100 counties of China located at the south of Jiangsu and the Pearl River Delta. The county-level city, which is of the same administrative level as a county, generally has a larger economic size, more downtown population, and higher urbanization and industrialization levels compared with a county. Hence, it has more spatial spillovers than a common county. There is remarkable difference between an urban district and a county. An urban district is usually an urban area in a prefecture-level city, which is a part of a city system. It focuses on urban functionality and the overall social and economic development of a city. In theory, an urban district is often a core component of a functional economic region.

However, in our opinion, an accurate distinguishing whether a county or city belonged to a functional economic region or not is difficult. It is because local and national functional economic regions, metropolitan regions, and urban agglomerations do not have clear and definite boundaries in China. And most functional economic regions are a mixture of both city and county and is continuous in space in China.

Data on counties (including autonomous counties) and county-level cities were primarily drawn from the China Regional Statistical Yearbook (2002–2011) and Social and Economic Statistical Yearbook of China’s County (City; 2000–2011). Data for 1992, 1995, and 1999 were primarily drawn from the 2000 Statistical Yearbook. Because the China Regional Statistical Yearbook (2002–2010) does not include urban district data, these data were primarily obtained from the China City Statistical Yearbook (1993–2011). Missing data for specific years and regions were supplemented using statistical yearbooks of various provinces (including districts and directly controlled municipalities; 1993–2011). Following basic data and data accessibility requirements, we constructed a socioeconomic database for Chinese cities (counties) for 1992–2010 that accounts for 2,286 urban and county units. Table 1 shows basic descriptive statistics for selected variables including GDP per capita, investment return rate (K_i,t ), human capital (H_i,t ), savings rate (S_i,t ), and n + g + δ.

Table 1.

Descriptive Statistics of the Selected Variables.

Variable	Year	Mean	Median	Maximum	Minimum	Standard deviation	Observations
GDP per capita	1992	1,787.94	1,358.46	18,428.76	125.23	1,467.90	2,286
	2000	6,022.24	4,203.07	133,304.60	254.76	6,415.93	2,286
	2010	26,099.59	18,150.50	368,704.00	967.34	26,349.66	2,286
K_i,t	1992	10.67	5.72	264.03	0.12	14.23	2,286
	2000	15.34	9.29	306.49	0.68	18.14	2,286
	2010	70.04	59.21	3,754.89	0.49	88.36	2,286
H_i,t	1992	5.15	5.19	20.24	0.01	1.89	2,286
	2000	5.72	5.81	12.28	0.01	1.78	2,286
	2010	5.58	5.41	25.25	0.01	1.62	2,286
S_i,t	1992	41.83	38.52	210.37	0.12	21.27	2,286
	2000	57.98	52.52	263.90	2.54	30.10	2,286
	2010	65.43	57.34	4,784.97	1.49	105.10	2,286
n+g+δ	1992	1.03	1.03	2.50	0.48	0.07	2,286
	2000	1.07	1.06	6.56	0.38	0.21	2,286
	2010	1.08	1.05	11.94	0.78	0.35	2,286

Note: GDP = gross domestic product.

Spatial data were primarily drawn from the National Fundamental Geographic Information System of China (http://ngcc.sbsm.gov.cn), and data were provided by the National Science and Technology Basic Conditions Platform Construction Project Data-Sharing Network of Earth System Science (www.geodata.cn). Data were stored as shp. files, and ArcGIS 10.0 was used as the work platform. Due to continuous changes in administrative divisions, we needed to adjust county-level administrative units (cities and counties). To ensure consistency between cities and counties over several years, a backtracking method, in which administrative division codes were reviewed from the final year to the first year, was applied. As regions changed constantly over the years, and especially among prefecture-level cities, county-level cities, and counties, such changes were more frequent. To ensure regional continuity overtime and to render the data order consistent with basic characteristics of panel data, we compared regional characteristics for each year and adjusted regions that experienced changes. Because GDP is a current price measure that must be deflated and to improve the accuracy of data and demonstrate diversity, we deflated the urban and county GDP index for all of the studied years to the level recorded in 1992. Figure 1 shows an overall spatial distribution for GDP per capita of 2,286 cities and counties between 1992 and 2010.

Figure 1.

Spatial distribution of gross domestic product (GDP) per capita for 2,286 cities and counties between 1992 and 2010, in China.

Basic spatial weight matrix calculation data included latitude and longitude coordinates for the central points of counties and cities listed on a nationwide county map provided by the National Fundamental Geographic Information System. Coordinate information extraction and application was realized through ArcGIS 10.0. We used the Matlab 2012a platform to convert coordinate information into a spatial weight matrix via xy2cont coding (http://www.spatial-econometrics.com/), finally obtaining a 2,286 × 2,286 adjacency matrix.

Results and Discussion

Traditional β convergence testing focuses on the temporal rather than spatial analysis. We estimate dynamic changes at temporal and spatial scales of convergence in Chinese urban and county economic growth using the spatial cross-section and spatial panel data models. The sample analysis focuses on β convergence characteristics at the city and county scales for 1992–2010. This analysis examined the applicability of neoclassical convergence theories and analytical frameworks by comparing the classic convergence model to the spatial econometric model. To examine these dynamics at the temporal level, we divided 1992–2010 period into the following three periods: 1992–2000, 2000–2005, and 2005–2010. This was carried out to examine whether the Western Development Strategy, the Revitalize the Old Northeast Industrial Bases Plan, the Rise of Central China Plan (RCCP), and other national strategies intensively approved in recent years reduced regional differences (for a detailed description see Appendix). In addition, despite identifying common features, differences in economic development between cities and counties were specifically focused on a comparative analysis of urban and county economies. The analysis described below was conducted in three parts: whole sample, three periods, and differences between urban and county economies.

β Convergence Analysis for the Total Sample

Table 2 presents the results of the specification tests of cross-sectional OLS regression model as well as the SAR and SEM. Data for 2,286 urban and county units for 1992–2010 and cross-sectional data regression results show that absolute β convergence has been present in urban and county economic growth across China. We also found significant spatial effects for the entire sample analysis, and Moran’s I coefficient was found to be significantly greater than 0 (0.5571, p < .01). Therefore, we reject the null hypothesis of SAC, suggesting the importance of spatial interaction effects, geographic location, and spatial proximity to regional economic growth. The traditional neoclassic economic analytical framework states that economies are closed and accordingly ignores effects of location on economic growth. Such a claim cannot be upheld. Restrictions on trade and element flow barely exist within regions. Using the OLS framework to study convergence may generate estimate errors or invalid results. To address this problem, we applied spatial econometric analysis methods, of which SAR and SEM methods are the most established. For comparison purposes, we provide the analysis results of the classic convergence analytical framework (model 1). The results of OLS model show a convergence rate of 0.95 percent and an adjusted R ² of only .0240, and economically underdeveloped areas could reach half the development of developed areas in 73.16 years.

Table 2.

Regression Results of the Absolute β Convergence Cross-sectional Data, Panel Data and Spatial Panel Data Analysis for the Total Sample.

	Cross-sectional data models			Panel data and spatial panel data models
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	OLS	SAR (ML)	SEM (ML)	Pooled OLS	SAR no fixed (ML)	SAR spatial fixed (ML)	SEM no fixed (ML)	SEM spatial fixed (ML)
α	3.5398*** (28.4456)	1.8225*** (10.8819)	4.2747*** (24.4119)	1.0215*** (35.9064)	0.6318*** (12.7653)		1.5130*** (33.1188)
ln(y_i,t ₀)	−0.1568*** (−7.5867)	−0.1321*** (−8.7986)	−0.2307*** (−9.9806)	−0.0603*** (−17.7848)	−0.0485*** (−14.5380)	−0.1047*** (−42.4392)	−0.1192*** (−22.2483)	−0.8500*** (−90.1315)
ρ		0.6680*** (16.2798)			0.5610*** (9.7796)	0.5230*** (10.2731)
γ			0.6860*** (27.8797)				0.6000*** (57.6355)	0.9170*** (297.7349)
${\bar{R}}^{2}$	0.0240	0.0602	0.3953	0.0269	0.2653	0.3423	0.2949	0.6205
σ²		0.1710		0.1322	0.0998	0.1778	0.0958	0.0516
λ	0.0095	0.0079	0.0146	0.0155	0.0124	0.0276	0.0317	0.4742
Half-life (year)	73.1635	88.0279	47.5717	44.5945	55.7572	25.0732	21.8367	1.4617
Moran’s I	0.5571*** (45.8480)			0.3543*** (65.1273)
LM lag	2,093.1366***				3,910.2819***	3,635.6029***
LM err	3,664.7043***						4,334.2460***	2,646.1945***
R-LM lag	188.6612***				240.5478***	4,741.9894***
R-LM err	1,760.2289***						564.5119***	3,752.5810***
Log likelihood		−546.2504	−506.6607	−2,671.6000	−3,411.9980	−2,726.1208	−3,240.6366	−619.8592
Observations	2,286	2,286	2,286	2,286	2,286	2,286	2,286	2,286

Note: T values are given in parentheses. SAR = spatial autoregressive model; SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares; LM = Lagrange multiplier.

***Significant at 1 percent confident level.

The estimation results of the SAR and SEM show that the elasticity coefficient is statistically significant, which indicates the existence of convergence. In empirical analysis, determining whether SAR model or SEM model is more appropriate is a critical issue (Elhorst 2014). Elhorst (2014) suggests that SAR and SEM application first involved LM lag and LM err tests of the spatial econometric model. If neither rejects the null hypothesis, stick with the OLS results (Anselin 2004). If the testing results for both were significant, the robust LM err and robust LM lag were conducted. Typically, only one of them will be significant, or one will be orders of magnitude more significant than the other (Anselin 2004). In that case, the decision is simple: estimate the spatial regression model matching the (most) significant statistic. In the rare instance when both would be highly significant, go with the model with the largest value for the test statistic (Anselin 2004). Here the test results show that the SEM model (model 3) is superior to the SAR model based on the values of LM tests. Thus, overall, SEM is the most reasonable choice. Based on the analysis results, adjusted R ² apparently increased and γ values are higher than 0.6, suggesting significant spatial effects. Considering the significant increase in the convergence rate after spatial effects were evaluated, the annual convergence rate is 1.46 percent and the half-life decreased to 47.57 years. Therefore, both classic convergence and spatial econometric models show that China’s urban and county economic growth has presented significant absolute β convergence from 1992 to 2010, though the convergence rate was found to be lower than the 2 percent level (Barro and Sala-I-Martin 1992, for the US states, a recognized convergence rate) in similar studies (Xu and Li 2004; Cai, Wang, and Du 2002, for China’s cities). However, Hong, Hu, and Li (2010) also found a lower convergence speed (1.4 percent).

Table 2 also shows regression results based on the panel data model and the spatial panel data models. Sample panel data were processed in three periods, following methods recommended in several studies of this type (Badinger, Muller, and Tondl 2004; Bouayad-Agha and Vedrine 2010). Compared to the cross-sectional data regression results, though the overall convergence rate increased, other variables did not undergo any significant changes. These results also indicate the existence of absolute convergence. Through a comparison of test parameters, we found the SAR spatial fixed effects model (model 6) to be the most appropriate. Results for this model indicate that lagging cities and counties caught up with developed cities and counties at a rate of 2.76 percent each year. These results were 77.86 percent higher than those of the pooled OLS, and the half-life also declined to 25.07 years, suggesting that spatial interactions play an extremely key role in regional economic development. Economic interaction and trade within Chinese cities and counties is relatively frequent, and spatial spillovers (including technology, knowledge, industry, growth, etc.) may occur quite quickly. Some regions may even generate high-high or low-low concentration clusters. Some regions have also relied on preexisting conditions and advantages, experiencing fairly rapid economic development, concurrently facilitating economic development in neighboring cities and counties via spatial spillover processes. This form of spatial development is an inevitable product of spatial externality.

While the above-discussed empirical analysis suggests the existence of unconditional β convergence, it is still necessary to estimate whether conditional β convergence exists and to further identify influential factors of urban and county economic growth. Cross-sectional data regression results show that conditional β convergence is present in Chinese urban and county economic development (Table 3). Similar to the previously discussed model choice method, we found the SEM model (model 3) to be the most appropriate model. Regression results show that, conditional to absolute β convergence, goodness of fit and convergence rate values increased. Such results indicate that influential factors selected have certain effects on urban and county economic growth. Stimulation effects on investment on economic growth were as expected, with all models showing significant positive effects. The high investment development model is once again confirmed for the period following the reform and opening-up policy at the urban and county economic development levels in China. Compared to investment effects, stimulating effects of human capital appear to be more significant. Results also show restrictive citizen savings effects on economic development, suggesting that high saving rates among Chinese residents do not have a positive effect on GDP per capita growth. This may be attributable to the fact that China’s high savings rate does not translate into investment ability and instead reinforces low investment efficiency (Cristadoro and Marconi 2012; Horioka and Wan 2007). Multiplier effects have not played their role, and savings capital is deposited in banks (Kuijs 2005; Xu, Yang, and Ma 2016). Population growth also restricts urban and county economic growth. Such results are consistent with those of similar studies (Lau 2010). In fact, population growth has two major effects. Labor force expansion benefits economic growth while also limiting per capita benefits, thus restricting economic growth. This indicates that Chinese urban and county economic growth evolved gradually, relying less and less on labor benefits. However, the population growth also exhibited a welfare-consuming characteristic (i.e., population growth leads to a decrease in average welfare level, and the society needs to support a growing aging population). In addition, initial technology levels also had significant facilitating effects on economic growth in cities and counties, suggesting that initial technology levels and technological development inertia play a critical role in regional economic development.

Table 3.

Regression Results of the Conditional β Convergence Cross-sectional Data, Panel Data and Spatial Panel Data Analysis for the Total Sample.

	Cross-sectional data models			Panel data and spatial panel data models
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	OLS	SAR (ML)	SEM (ML)	Pooled OLS	SAR no fixed (ML)	SAR spatial fixed (ML)	SEM no fixed (ML)
α	4.7590*** (32.9746)	2.8341*** (8.5742)	5.2513*** (5.3607)	0.6352*** (21.1687)	0.4672*** (20.0071)		1.3081*** (29.2612)
ln(y_i,t ₀)	−0.3308*** (−14.7780)	−0.2368*** (−28.4530)	−0.3712*** (−4.9408)	−0.0711*** (−20.0487)	−0.0589*** (−21.3395)	−0.1177*** (−30.5086)	−0.1265*** (−27.8273)
lnK_i,t	0.1417*** (6.9531)	0.1025*** (30.8134)	0.091723** (2.2242)	0.0774*** (27.8448)	0.0441*** (20.1960)	0.0600*** (20.5811)	0.0361*** (12.5768)
lnH_i,t	0.3589*** (15.9868)	0.3867*** (14.9380)	0.5535*** (14.1529)	0.0649*** (9.3458)	0.0327*** (6.0671)	0.1006*** (12.0548)	0.0325*** (4.4184)
lnS_i,t	−0.3411*** (−15.4437)	−0.2676*** (−54.1523)	−0.3209*** (−4.5277)	−0.0252*** (−4.8637)	−0.0171*** (−4.2174)	−0.0240*** (−4.2485)	−0.0386*** (−7.4730)
ln(n_i,t +g_i _,t+δ _i _,t)	−0.0678*** (−3.4660)	−1.6234*** (−4.7223)	−0.7634 (−1.3688)	−0.3231*** (−5.0811)	−0.2855*** (−5.7938)	−0.2162*** (−4.3624)	−0.2049*** (−4.4086)
lnA0	0.2705*** (12.5356)	0.0562*** (22.4490)	0.0715*** (4.6055)	0.0192*** (10.8420)	0.0149*** (10.8439)	0.0789*** (18.5640)	0.0245*** (12.1621)
ρ		0.5980*** (26.1832)			0.6740*** (87.2200)	0.6350*** (77.9968)
γ			0.6870*** (5.5902)				0.7360*** (91.5470)
${\bar{R}}^{2}$	0.1960	0.1277	0.4937	0.0748	0.4453	0.4403	0.4761
σ²		0.1540	0.1370	0.0865	0.0518	0.0418	0.0489
λ	0.0223	0.0150	0.0258	0.0184	0.0152	0.0313	0.0338
Half-life (year)	31.0568	46.1696	26.8908	37.5736	45.7093	22.1510	20.5042
Moran’s I	0.5712*** (47.0070)			0.4668*** (85.8653)
LM lag	3,736.5680***				7,415.7017***	6,196.7732***
LM err	2,200.3740***						7,348.2661***
R-LM lag	1,755.2066***				165.4122***	141.5637***
R-LM err	219.0127***						97.9767***
Log likelihood		−373.0959	−301.4117	−2,227.1000	132.8539	1,433.2432	317.3950
Observations	2,286	2,286	2,286	2,286	2,286	2,286	2,286

Note: T values are given in parentheses. SAR = spatial autoregressive model; SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares; LM = Lagrange multiplier.

**Significant at 5 percent confident level.

***Significant at 1 percent confident level.

The regression results of panel data and cross-sectional data were similar, as only the size of parameters changed. Related parameter test results show that the SAR spatial fixed effects model (model 6) is the optimal model (Table 3). Convergence rates for Chinese urban and county economic growth indicated by cross-sectional and panel data fell within the same range, demonstrating that regression results are relatively stable. Compared with absolute β convergence, we found that, after controlling for fixed investment, human capital, savings, population growth, and initial technology levels, Chinese urban and county economic growth convergence rates increased. In order to investigate the endogenous growth effects of these factors, we employed the Durbin–Wu–Hausman test (Wooldridge 2010) for each explanatory variable of our model. The test results indicate that there is no evidence of endogenous explanatory variables in our model. Nonetheless, endogeneity effects seem to be potentially important in our article and thus need to be recognized. Panel data regression results indicate a convergence rate of 3.13 percent and a half-life accordingly reduced to 22.15 years. However, these results are significantly higher than those of previous studies on economic growth at the provincial level (Chen and Fleisher 1996; Ding and Haynes 2006; Gundlach 1997; Lei and Yao 2008).

β Convergence Analysis over Different Time Periods

Table 4 presents cross-sectional data regression results for absolute β convergence over three periods. Panel data regression results for each period are not presented because, in testing across multiple periods, we found that spatial panel data regression analyses are not applicable to short-term yearly analyses. However, cross-sectional data regression results show overall trends (previous analyses show that SEM model is the optimal model, and thus we only list OLS and SEM regression results here). Cross-sectional data regression results for the three periods once again show that absolute β convergence was present in Chinese urban and county economic growth from 1992 to 2010. A comparison of convergence coefficients for the three periods shows that the 2005–2010 absolute β convergence rate of 3.44 percent was the highest, with the second highest convergence rate of 2.21 percent also occurring in this period. The lowest convergence rate of 2.06 percent was recorded in the period from 1992 to 2000. This accelerating convergence process indicates that national strategies implemented in China after 2000 played major role in reducing regional differences, and these strategies especially generated catch-up opportunities for the central and west regions. With national attention dedicated to regional differences, national strategies were frequently developed and relative policy advantages at the urban and county levels continuously emerged and converged, suggesting that growing policy support for underdeveloped areas of central and western China has had an effect. However, this finding may be contrary to the study of Ho and Li, they do not find any obvious evidence for the implementation effect of the Western Development Strategy in helping the western China out of their current poor economic status (Ho and Li 2008).

Table 4.

Regression Results of the Absolute β Convergence for the Three-subperiod Panel Data Analysis.

	1992–2000 year		2000–2005 year		2005–2010 year
	(1)	(2)	(3)	(4)	(5)	(6)
	OLS	SEM (ML)	OLS	SEM (ML)	OLS	SEM (ML)
α	1.3815*** (13.6332)	2.1684*** (26.8036)	1.2785*** (15.6374)	1.5090*** (13.8466)	1.8145*** (23.2215)	2.2652*** (40.5689)
ln(y_i,t ₀)	−0.0433*** (−3.1186)	−0.1516*** (−14.6945)	−0.0772*** (−7.9671)	−0.1045*** (−8.1942)	−0.1083*** (−12.5746)	−0.1582*** (−25.0734)
${\bar{R}}^{2}$	0.0040	0.2808	0.0270	0.1970	0.0640	0.2092
σ²		0.1267		0.0970		0.0837
λ	0.0055	0.0206	0.0161	0.0221	0.0229	0.0344
Half-life (year)	125.2711	33.7292	43.1369	31.4002	30.2353	20.1247
Log likelihood		−181.2670		159.3595		330.0996
Observations	2,286	2,286	2,286	2,286	2,286	2,286

Note: T values are given in parentheses. SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares.

***Significant at 1 percent confident level.

Regression results of period conditional β convergence reflect our expectations. The only difference found involved the degree of economic growth effects between different periods, with differences found between conditional and absolute convergence rates (Table 5). According to the SEM model, the convergence rate for 1992–2010 shows a gradually accelerated development trend. Regarding influential factors of economic growth, OLS and SEM model results vary, though effect codes are consistent. Without considering spatial effects, investment stimulation effects on economic growth showed a gradual increasing trend, but this trend was not obvious when considering spatial effects. Effects of human capital on economic development show a dynamic changing trend: from 1992 to 2000, human capital had a strong positive effect and such effects gradually decrease from 2000 to 2005 and gradually increase from 2005 to 2010. This indicates that China’s investment policy prefers physical capital to human capital in the period of 2000–2005. Savings trends followed a similar pattern, though the direction of effects differed. Population growth had a strong effect. Its restrictive effects on economic growth (a high population growth rate leads to a low economic growth) were strongest from 2000 to 2005 and may have been the primary cause of convergence rate decline from 2000 to 2005. Initial technology-level effects on economic growth showed a decreasing trend from 1992 to 2010, suggesting that knowledge and technology spillovers and the spread of the “learning by doing” development model² reduced variations in initial technology levels.

Table 5.

Regression Results of the Conditional β Convergence Cross-sectional Data Analysis for the Total Sample.

	1992–2000 year		2000–2005 year		2005–2010 year
	(1)	(2)	(3)	(4)	(5)	(6)
	OLS	SEM (ML)	OLS	SEM (ML)	OLS	SEM (ML)
α	2.6972*** (24.6243)	3.1271*** (4.0478)	1.5672*** (14.0710)	1.7882*** (20.4958)	2.1861*** (18.5535)	2.7446*** (36.1193)
ln(y_i,t ₀)	−0.2043*** (−13.8697)	−0.2793*** (−4.3492)	−0.1117*** (−9.0492)	−0.1945*** (−17.3745)	−0.1372*** (−13.0573)	−0.2059*** (−23.9153)
lnK_i,t	0.0059 (0.7386)	0.0203*** (2.5645)	0.0373*** (3.6667)	0.0499*** (4.4774)	0.0470** (3.6474)	0.0251*** (3.0044)
lnH_i,t	0.2928*** (16.7090)	0.2853*** (14.5368)	0.0917*** (4.5046)	0.0979*** (4.1287)	0.1229*** (5.2636)	0.1677*** (6.7823)
lnS_i,t	−0.1625*** (−10.2278)	−0.1433*** (−1.9764)	−0.0458*** (−2.8479)	−0.0581*** (−3.9150)	−0.1219*** (−9.2041)	−0.1200*** (−9.6026)
ln(n_i,t +g_i _,t+δ _i,t )	−2.1427*** (−7.2141)	−1.6133 *** (−6.2461)	−2.1485*** (−7.7416)	−1.8150*** (−7.2504)	−0.8896*** (−2.6930)	−0.2432 (−0.8146)
lnA0	0.0946*** (17.3638)	0.0911*** (20.1399)	0.0250*** (5.0714)	0.0277*** (4.9143)	0.0133*** (3.2673)	0.0233*** (5.0666)
γ		0.5540*** (3.7747)		0.4870*** (20.6520)		0.4950*** (32.2621)
${\bar{R}}^{2}$	0.2210	0.3896	0.0690	0.2292	0.1030	0.2409
σ²		0.1073		0.0929		0.0802
λ	0.0286	0.0409	0.0237	0.0433	0.0295	0.0461
Half-life (year)	24.2642	16.9302	29.2601	16.0234	23.4850	15.0327
Log likelihood		27.1152		210.5075		375.7716
Observations	2,286	2,286	2,286	2,286	2,286	2,286

Note: T values are given in parentheses. SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares.

**Significant at 5 percent confident level.

***Significant at 1 percent confident level.

Comparative Analysis of Urban and County Urban β Convergence

As discussed above, Chinese urban and county economic development trends follow different models, and thus, we conduct a comparative analysis to identify the differences in urban and county economic growth convergence and formation mechanisms behind such differences. Cross-sectional data regression results indicate that the economic growth convergence rate of city is significantly higher than that of county economic growth and the half-life of the former is approximately ten years shorter (Table 6). The SEM model (models 3 and 6) is optimal for this purpose. Compared to regression results for the whole sample, the city economic growth convergence rate is significantly higher than the national average, suggesting that urban economic development played a major role in facilitating regional economic convergence and served as the engine for regional economic catch-up. Unlike county economies, city economy free-riding effects have influenced individuals, materials, capital, and technologies in cities, further optimizing advantages to maximize effects. The advantages of traditional agriculture-oriented county economies cannot compare those of urban industrial development. The convergence rate of county economic growth is basically consistent with that of the whole sample. Though county economies form much of the sample, the overall county economy growth rate and industrial development lag represent more nuanced processes.

Table 6.

Regression Results of the Absolute β Convergence Cross-sectional Data Analysis of City- and County-level Economic Growth for the Whole Sample.

	Urban economy			County economy
	(1)	(2)	(3)	(4)	(5)	(6)
	OLS	SAR (ML)	SEM (ML)	OLS	SAR (ML)	SEM (ML)
α	4.2280*** (16.3870)	3.0750*** (20.2144)	5.1597*** (77.4530)	4.0640*** (24.5900)	2.0052*** (7.5593)	4.3726*** (18.8031)
ln(y_i,t ₀)	−0.2330*** (−6.0810)	−0.2341*** (−6.5973)	−0.3222*** (−30.6160)	−0.2180*** (−9.0410)	−0.1606*** (−6.8634)	−0.2541*** (−7.9973)
ρ		0.5270*** (10.6054)			0.6630*** (12.1838)
γ			0.5600*** (17.2482)			0.6820*** (23.5576)
${\bar{R}}^{2}$	0.0530	0.0423	0.2642	0.0470	0.0019	0.4058
σ²		0.1791	0.1690		0.1745	0.1696
λ	0.0147	0.0148	0.0216	0.0137	0.0097	0.0163
Half-life (year)	47.0340	46.7773	32.0843	50.7386	71.2738	42.5676
Moran’s I	0.5357*** (23.4307)			0.5642*** (39.2981)
LM lag	992.2905***			2,657.3916***
LM err	540.8072***			1,535.2456***
R-LM lag	495.4815***			1,274.9063***
R-LM err	43.9982***			152.7603***
Log likelihood		−156.3224	−140.2257		−406.9266	−389.0524
Observations	647	647	647	1,639	1,639	1,639

Note: T values are given in parentheses. SAR = spatial autoregressive model; SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares; LM = Lagrange multiplier.

***Significant at 1 percent confident level.

The panel data regression results reflect similar patterns (Table 7). The panel data regression indicates that the expected economic growth convergence speed of a city is approximately twice of that of a county. However, according to comprehensive estimate parameter and model regression results, the SAR spatial fixed model (models 3 and 7) is the optimal model. After adjusting spatial effects, the SAR spatial fixed panel data model shows that convergence rate differences decreased, though city economic convergence was still faster than that experienced in counties. In addition, the SAC of city economic growth is slightly lower than that of counties. Such results are attributable to the larger number of county economy units examined and to natural proximity. Even though city economy free-riding effects are important, spatial proximity is another important factor that cannot be ignored. A comparison with regression results for the entire panel data sample shows that urban and county convergence levels fell within the same range as the full sample, suggesting model stability.

Table 7.

Regression Results of the Absolute β Convergence Panel Data Analysis of City- and County-level Economic Growth for the Whole Sample.

	Urban economy				County economy
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Pooled OLS	SAR no fixed (ML)	SAR spatial fixed (ML)	SEM no fixed (ML)	Pooled OLS	SAR no fixed (ML)	SAR spatial fixed (ML)	SEM no fixed (ML)
α	1.4725 *** (27.8630)	0.7884*** (15.8765)		1.5658*** (16.3844)	0.9948*** (27.0415)	0.6653*** (20.0437)		1.8151*** (26.5416)
ln(y_i _,t0)	−0.1054*** (−17.8895)	−0.0637*** (−12.2989)	−0.1159*** (−18.6108)	−0.1159*** (−11.2506)	−0.0594*** (−13.1572)	−0.0532*** (−13.4281)	−0.0979*** (−21.6273)	−0.0841*** (−18.2186)
ρ		0.5860*** (34.4053)	0.5380*** (31.3898)			0.5440*** (46.7233)	0.5270*** (12.1597)
γ				0.6090*** (11.0480)				0.5120*** (49.6907)
${\bar{R}}^{2}$	0.0898	0.3528	0.3033	0.3699	0.0206	0.2538	0.1579	0.1385
σ²	0.1047	0.0744	0.0641	0.0725	0.1411	0.1074	0.0970	0.1196
λ	0.0278	0.0165	0.0308	0.0308	0.0153	0.0137	0.0258	0.0220
Half-life (year)	24.8934	42.1242	22.5075	22.5075	45.2761	50.7174	26.9105	31.5612
Moran’s I	0.3614*** (35.1858)				0.5313*** (82.5840)
LM lag		1,210.7473***	1,385.6183***			6,745.5653***	6,515.6856***
LM err				1,230.5972***				6,306.2050***
R-LM lag		183.1308***	699.0168***			347.4098***	825.8196***
R-LM err				202.9807***				208.0496***
Log likelihood	−939.6359	−502.2943	−240.2642	−470.4034	−3,601.7000	−2,730.6623	−2,295.1845	−3,136.6033
Observations	647	647	647	647	1,639	1,639	1,639	1,639

Note: T values are given in parentheses. SAR = spatial autoregressive model; SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares; LM = Lagrange multiplier.

***Significant at 1 percent confident level.

Urban and county conditional β convergences are examined and economic growth factors in counties and cities are compared. A comparison between cross-sectional data and panel data model regression results shows that the former reflects the reality more closely due to the latter has biased error. We found that, for the results of panel data model, the regression coefficients β values are extremely low, and the R ² of the partly models were less than 0. Hence, only cross-sectional data regression results were used for our analysis (Table 8). According to comprehensive estimate parameter and model regression results, the SAR model (models 2 and 5) is the optimal model. After controlling various influential factors, both regression model and convergence rate goodness of fit increased. The results show that investment had stronger stimulating effects on city economic growth than on county economic growth, suggesting that fixed asset investment is a primary factor behind city economic growth. Compared to cities, driving effects of investment are relatively weak at the county, and some model parameters did not even pass the significance test. Contrary to our expectations, human capital effects on city economic growth are less significant than those at the county level. The average percentages of students enrolled in secondary school out of the total population at the end of each year were used to calculate human capital levels. This, to a certain extent, could not reflect human capital benefits to cities and most likely weakened the driving effects of human capital on city economic growth. It also indicates that county economic growth relies heavily on low human capital, and increasing human capital is thus a central task for increasing county economic growth. Resident savings have less negative effects on city economic growth than on county economic growth, suggesting that the benefits of converting resident savings into investments are more central to urban economic development and that the probability of capital precipitation is lower. Overall, negative effects of population growth are stronger at the county level, suggesting that the relationship between population size increase and benefit decrease is more significant at the county scale. Initial technology-level effects were found to be highly significant at both the urban and county levels. Overall, stimulating effects of initial technology levels on urban economic growth are slightly more significant. These results show that initial technology levels (indicated by the preferential policies of a city or a county) rooted in favorable policies play a critical role in urban and county economic growth. This framework laid the foundation for urban economic growth, suggesting that regional development policies (including the Western Development Strategy, the Revitalize the Old Northeast Industrial Bases Plan, and the RCCP) have had a significant effect.

Table 8.

Regression Results of the Conditional β Convergence Cross-sectional Data Analysis of City-and County- level Economic Growth for the Whole Sample.

	Urban economy			County economy
	(1)	(2)	(3)	(4)	(5)	(6)
	OLS	SAR (ML)	SEM (ML)	OLS	SAR (ML)	SEM (ML)
α	5.4940*** (17.3390)	2.7708*** (6.1755)	4.2322*** (23.2441)	5.8130*** (27.7560)	3.0828*** (28.7085)	5.4227*** (71.6230)
ln(y_i,t ₀)	−0.3840*** (−9.8500)	−0.3775*** (−4.8680)	−0.5049*** (−14.9119)	−0.3380*** (−14.1590)	−0.3136*** (−18.6553)	−0.4721*** (−18.9129)
lnK_i,t	0.2200*** (5.3880)	0.1343*** (4.1935)	0.1628*** (5.6994)	0.0690*** (3.0130)	0.0304** (2.1699)	−0.0262 (−1.5218)
lnH_i,t	0.1350*** (3.8530)	0.2035*** (0.7230)	0.3601*** (4.2409)	0.3810*** (14.2270)	0.2280*** (7.9467)	0.3964*** (11.4317)
lnS_i,t	−0.3190*** (−8.1430)	−0.2130*** (−2.0765)	−0.2015*** (−5.0300)	−0.3950*** (−15.3930)	−0.3557*** (−17.6066)	−0.4046*** (−16.9487)
ln(n_i,t +g_i,t +δ _i,t )	−0.0730*** (−1.9310)	−0.4254*** (−0.5580)	−0.3065 (−0.4767)	−0.1340*** (−5.8980)	−2.5236*** (−4.4410)	−0.2591 (−0.3175)
lnA0	0.3530*** (9.1430)	0.4758*** (2.7014)	0.5337*** (11.2048)	0.1250*** (5.4160)	0.3893*** (15.4015)	0.5117*** (18.1334)
ρ		0.4220* (1.7564)			0.5500*** (31.1653)
γ			0.5640*** (24.7477)			0.7070*** (39.8426)
${\bar{R}}^{2}$	0.2400	0.1679	0.4115	0.2200	0.2643	0.5901
σ²		0.1492	0.1341		0.1362	0.1166
λ	0.0269	0.0263	0.0391	0.0229	0.0209	0.0355
Half-life (year)	25.7512	26.3226	17.7456	30.2472	33.1630	19.5299
Moran’s I	0.6097*** (26.6666)			0.5810*** (40.4659)
LM lag	1,176.5469***			2,871.4157***
LM err	700.5632***			1,627.9020***
R-LM lag	555.2766***			1,423.9223***
R-LM err	79.2929***			180.4087***
Log likelihood		−89.8698	−65.8231		−175.0020	−91.3218
Observations	647	647	647	1,639	1,639	1,639

Note: T values are given in parentheses. SAR = spatial autoregressive model; SEM = spatial error model; ML = maximum likelihood; OLS = ordinary least squares; LM = Lagrange multiplier.

*Significant at 10 percent confident level.

**Significant at 5 percent confident level.

***Significant at 1 percent confident level.

Comparative Analysis of Different Scales

Table 9 compares the convergence type and speed from our study with a number of recent regional economic growth convergence studies for China. The result of this comparative analysis between our findings and some previous studies demonstrates that our results are consistent with some past studies. Yet there was significant difference among different spatial scales in convergence speed, especially provincial and city or county level. The convergence speed of this study is a little faster than some previous studies. And our finding agrees with Xu and Li (2004) at the city level. So it can be used to deduce that county and city scale is a better position to understand regional economic growth in China. One possible reason is that in China the most of regional development policies are directly enacted on the urban or county scales. In addition, the targeted areas of these preferential policies are highly relevant to corresponding cities or counties, such as national-level new development areas and development area approved by the State Council of China (Jones, Li, and Owen 2003). Hence, evaluating the implementation effects of these regional development policies at the city and county level is appropriate.

Table 9.

Comparison of Convergence of Different Scale Studies for China.

Study	Sample	Dependent variable	Study period	Convergence type	Implied λ	Methods
Lei and Yao (2008)	Thirty provinces, Hong Kong and Macau	GDP per capita	1961–1977	Absolute β	0.5%	Cross-sectional
			1978–2002	Absolute β	1.6%	Cross-sectional
			1961–2002	Absolute β	1.2%	Cross-sectional
			1963–1977	Absolute β	0.68%	Panel data
			1978–2002	Absolute β	0.49%	Panel data
			1963–2002	Absolute β	0.1%	Panel data
Chen and Fleisher (1996)	Twenty-five provinces	GDP per capita	1978–1993	Conditional β	1.6%	Panel data, OLS
Gundlach (1997)	Twenty-nine provinces	Output per worker	1979–1989	Absolute β	2.2%	Cross-sectional
Raiser (1998)	Twenty-nine provinces	GDP per capita	1978–1992	Conditional β	3.69%	Cross-sectional
Li, Liu, and Rebelo (1998)	Twenty-nine provinces	GDP per capita	1978–1995	Conditional β	4.74%	Cross-sectional
Weeks and Yao (2003)	Twenty-eight provinces	GDP per capita	1978–1997	Conditional β	2.23%	System GMM
Ding and Haynes (2006)	Twenty-nine provinces	GDP per capita	1986–2002	Conditional β	1.1–1.6%	System GMM
Yao and Zhang (2001b)	Thirty provinces	GDP per capita	1978–1995	Conditional β	0.9%	Cross-sectional
Cai, Wang, and Du (2002)	Twenty-nine provinces	GDP per capita	1978–1998	Conditional β	3.3%	Cross-sectional
Xu and Li (2004)	216 Cities	GDP per capita	1989–1999	Absolute β	1.55%	Cross-sectional
	Eastern cities		1989–1999	Absolute β	3.89%	Panel data
	Provincial capital cities		1989–1999	Absolute β	4.16%	Panel data
	Coastal cities		1989–1999	Absolute β	4.07%	Panel data
	Other cities		1989–1999	Absolute β	5.24%	Panel data
Hong, Hu, and Li (2010)	240 Cities	GDP per capita	1990–2007	Absolute β	1.4%	Generalized spatial autoregressive model
The results of this article	2,286 Counties	GDP per capita	1992–2010	Absolute β	2.67%	Spatial panel data
			1992–2010	Conditional β	3.13%	Spatial panel data
			1992–2000	Conditional β	4.09%	Cross-sectional
			2000–2005	Conditional β	3.03%	Cross-sectional
			2005–2010	Conditional β	4.61%	Cross-sectional
	647 Cities		1992–2010	Conditional β	3.78–3.91%	Cross-sectional
	1,639 Counties		1992–2010	Conditional β	3.81–4.41%	Cross-sectional

Note: GDP = gross domestic product; OLS = ordinary least squares; GMM = generalized method of moments.

From the perspective of methodology, this study is primarily concerned with the integration of statistical data and geographic information system (GIS) data as well as GIS techniques and spatial economics in exploring the convergence type and speed of regional economic growth at the county and city level. Cross-sectional data models and spatial panel data models have been developed to identify the existence of convergence of regional development. The empirical study demonstrates that these rigorous GIS techniques and spatial economics models are superior to conventional OLS models and are appropriate tools for understanding regional development issues at the county and city level. Ignoring spatial effects might and often does lead to biased results because spatial effects are important to geographic processes (Yu and Wei 2008). Thus, the application of these spatial economics models and techniques has significant potential for future studies.

Conclusions

This study examines patterns of economic growth convergence in 2,286 cities and counties in China. China’s regional economies have experienced significant development since reform and opening up was implemented, and especially since the 1992 market economy system was formed and implemented, though difference in regional economic growth cannot be ignored. And much of this measuring difference is likely due to variable endogenous growth factors. Most previous studies have focused on China’s three largest regions and on provincial variations. Studies focusing on the urban and county scales are rare, and studies that examine regional convergence at the urban and county level are still even more scarce. It is necessary to study China’s regional economic convergence at the urban and county scales.

We used the neoclassical convergence model, panel data model, and spatial econometric models to a conduct comparative analysis. We emphasized the control of spatial effects in urban and county economic growth convergence. Following this econometric analytical framework and analysis, we drew different conclusions from those of previous studies. We found absolute and conditional β convergence in urban and county economic growth. The spatial panel data regression results showed that the absolute β convergence rate has fallen to 2.67 percent and that the half-life cycle has fallen to 25.07 years. The conditional convergence rate reached approximately 3.13 percent and the half-life cycle period accordingly reduced to 22.15 years. We also found that spatial effects, geographic location, and spatial proximity significant affected regional economic growth. Using the OLS model framework to examine these effects may lead to estimation errors or invalid estimates. Meanwhile, the spatial effects can be used to conclude that county and city scale is more suitable than other spatial scales to understand regional economic growth in China.

In terms of influential factors of economic growth, investments have had significant positive stimulating effects, though stimulating effects of human capital appear more significant. Multiplier effects of human capital comprehensive increases on economic growth are becoming increasingly more significant. Resident savings had a negative impact on regional economic growth. Thus, the high saving rate of China does not lead to effective investments; investment efficiency is low, and savings capital is deposited in banks. Population growth levels have restrictive effects on urban and county economic growth. China’s urban and county economic growth is gradually becoming less reliant on labor benefits, and population growth is exhibiting a more welfare-consuming characteristic as a growing aging population needs to be supported. Initial technology levels have significant facilitative effects on urban and county economic growth.

Our convergence analysis of the three periods shows that national strategies implemented in China after 2000 played major role in reducing regional differences. National policy support for lagging central and western regions has had an effect. The convergence rate from 1992 to 2010 showed a gradually accelerated development trend. Influential factors of economic growth during three periods varied greatly, and fixed temporal effects generated significantly different results.

Comparative analysis results of urban and county economic growth show that urban economic development played a central role in facilitating regional economic convergence and spurred regional economic catch-up. This implied that county economic development, by contrast, played a minor role. Regarding influential factors of urban and county economic growth, stimulating effects of investment on urban economic growth were stronger. County economic growth relies heavily on low human capital levels. Resident savings are converted into investment more efficiently in the process of urban economic development, and probabilities of capital precipitation are lower. The relationship between population size increases and benefit decreases is more significant at the county level. Finally, urban adherence to regional development policies has laid the foundation for urban economic growth.

Based on these conclusions, continual policy support for underdeveloped cities and counties in central and western China, and especially increases in investment levels and efficiency, human capital qualification, savings conversion ratios, efficient population growth control, and uses of knowledge and technology spillovers from developed regions, are effective mechanisms for mitigating gaps in regional, urban, and county economy under the situation of China’s overall economic growth.

Footnotes

Appendix

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Natural Science Foundation of China (NSFC) (41590842, 41501175 and 71433008).

Notes

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