THE MEASUREMENT OF HIERARCHICALLY SPATIAL INDUSTRIAL KNOWLEDGE SPILLOVER EFFECTS

Based on the “year–region–industry” three dimensional unbalanced industrial production panel data of Guangdong Province in China from 2005-2013, the relationship between knowledge spillovers and industrial structure is investigated by hierarchically spatial lagged with spatial autoregressive error (HSARAR) model. The empirical results indicate that the impacts of MAR, Jacobs, and Porter spillover on Guangdong's industry economic growth is positive and statistically significant. The industrial HSARAR model considers the hierarchical structure and spatial effect simultaneously, which has a better description on economic reality than the pooled model and SARAR model.


Introduction
Knowledge spillover is one of the important concepts to explain agglomeration, innovation and regional growth in endogenous growth theory, new economic geography and other theoretical economic branches. Knowledge spillover becomes the important factor that affects the regional growth and innovation. It has also become an entry point for explaining spatial interaction and is one of the important reasons for industrial agglomeration. Industrial agglomeration is also conducive to the overflow and innovation of knowledge. Knowledge spillover is considered to be a very important reason for the formation of long-term competitive advantage in the industry. From a large amount of literature, it can be seen that the knowledge spillover of a real estate industry plays a key role in the industrial and economic development of the local area and even neighboring areas, especially in the areas where high-tech industries are concentrated. In the empirical analysis Since the beginning of the 1990s, scientists have used different econometric models based on data from different countries and different period to examine the influence of three kinds of knowledge spillovers on the growth of the industry, see Glaeser et al. (1992), Henderson et al. (1995), Cainelli and Leoncini (1999), Cainell et al. (2001), Mihn (2004), Ejermo (2005), Zhang and Wu (2008), Martin et al. (2011), Drucker (2013), and Widodo et al. (2014). In actual economy, there are differences among industries in different regions. Due to the government policies, economic conditions, geographic locations and different economic operating characteristics among regions, which will have an impact on the knowledge spillover effect among industries. Kreft and de Leeuw (1998) and Goldstein (1998) concluded that a hierarchy consists of individuals or units nested within different levels. Cliff and Ord (1973) indicated that if the existence of a certain quality of a county in a country presented more or less similarity in the neighboring counties, then this phenomenon shows spatial correlation. In other words, one ought to consider the hierarchical structure and spatial correlation in economic data.
For the purpose of establishing spatial models to recognize the unobserved hierarchical effects and spatial correlation, Fingleton (2011, 2012) suggested the primitive structure of hierarchically spatial panel data models. Baltagi et al. (2014) applied the IV-2SLS method to estimate a hierarchically spatial lag (HSLAG) panel data model. While He and Lin (2015) extended the framework of Baltagi et al. (2014) to a SARAR model with both the spatially lagged dependent variable and the spatial autoregressive error, using MLE for estimation. Ye and Long (2016) derived the GMM-FGLS estimates for a hierarchically spatial autoregressive error (HSEAR) panel model. Then Fingleton et al. (2018) applied this approach to the house price of England. This article intends to use the HSARAR model to analyze the hierarchical effect, spatial correlation, and knowledge spillover effect.

The Theoretical Model and Variables
In terms of industrial knowledge spillover effect, numerous of researchers have been conducted according to different regions and period all over the world, they mainly focus on the issue that how knowledge spillover have an impact on industrial economic development (Lin and long, 2014). The existing literature, however, do not take account of the spatial effects and hierarchical structure among the data, causing estimation bias toward to knowledge spillover effect. GDP and its growth rate of Guangdong province are among the top ranks in China, contributing a large proportion to China's economic development. Figure 1 shows that, among 21 prefectures of Guangdong province, industry value added of 13 prefectures are lower than 15 billion Yuan, only 2 prefectures beyond 100 billion Yuan in 2005. In 2009, industry value added below 15 billion Yuan has fallen by 6 prefectures when compared to 2005, industry value added beyond 100 billion Yuan has increased to 4 prefectures. In 2013, industry value added 6 prefectures beyond 100 billion Yuan, only 1 prefecture below 15 billion Yuan. Nowadays, the scholars often use the onedimensional section or time series data, or two-dimensional balanced panel data, to investigate economic issues. However, the data they used is often "multidimensional", "incomplete" and "spatial correlated". Hence, this study employs HSARAR model and the "year-region-industry" three-dimensional unbalanced industrial production panel data set of Guangdong Province in  Considering the hierarchical structure and spatial effect of the data, we adopt Cobb-Douglas production function to discuss the impact of knowledge spillover on industrial economic development. The dependent variables are "t yeari region-j industry" of industry value added. The independent variables are technology, labor and capital inputs. 12 , ( 1, 2,..., ; 1, 2,..., ; 1, 2,..., ) Where y is industry value added, A is technology, L is labor inputs, and K is capital inputs. i Represents the i th region, j represents the j th industry, t represents the t th time period. To avoid dimensional effects, we take the logarithmic form of equation (1) and get 12 ln ln ln ln To decompose technology A , we have three spillover indicators: MAR spillover (specialized industry that focuses on a particular type of production can promote economic growth in that region). Jacobs spillover (diversification industrial structure in geographical proximity can promote industrial innovation and economic growth better than single industrial structure). Porter spillover (industry competition and the survival of the fittest promote the knowledge innovation and economic growth). They represent industry specialization, diversification and competitive spillover, and represented by SPEC, DIV and COMP. The theoretical model of industrial knowledge spillover effects can be obtained based on the hierarchically spatial lagged dependent variable and the spatial autoregressive error (HSARAR) model.
Where ijt y is the industry value added of the " t th time periodi th regionj th industry", to measure the industry development.  Table 1.  is the scalar spatial lag coefficient with 1   .  is the scalar spatial autoregressive error coefficient that captures the strengthen of spatial error correlation with 1   . ,

Estimation Results of the HSARAR Model
The pooled regression model and SARAR panel data model in our empirical research are used to compare to HSARAR model. In terms of pooled regression model, the variable value will be marked "null" when there is no corresponding industry, and we employ OLS to estimate the parameters. For SARAR model, we use the GMM estimators for the spatial autoregressive error coefficient and standard deviation of the error term, then the regression parameters are estimated by IV estimation. With regard to HSARAR model, we use GMM estimation to estimate the spatial autoregressive error coefficient and standard deviation of the error term, then the regression parameters are estimated by FGLS estimation. All the calculations are running in GAUSS 15.0. The results are stated in Table 2.  1889 Note: *** is significant at 1% confidence level, ** is significant at 5% confidence level, * is significant at 10% confidence level. The pooled regression model empirical results imply that labor input, capital input, and knowledge spillover effect can promote economic growth. The OLS estimators support that the capital input elasticity (0.8188) is larger than labor input elasticity (0.1767), which suggests that Guangdong industrial development is mainly based on the capital input. However, the result is not in accordance with the facts reflected in Guangdong's economy. The parameter of ln DIV is not significant, which reveals that diversification industrial structure cannot promote economic growth. The other parameters are significant at 1% level. The parameter of spillover elasticity of specialization and competition are 0.0110 and 0.0122, respectively. The results show that industrial specialization and competition have minimum impact on industry value added, which is contrary to Guangdong province's technology-intensive characteristics. The pooled regression model simply conduct regression on the nine-year Guangdong province data, variance inflation factor (VIF) of core variables, LnL and LnK, are greater than 10, indicating a serious multicollinearity. Besides, the pooled regression model ignores the time span, hierarchical characteristics, and spatial spillover of data, resulting in over-fitting and unrealistic OLS estimation, and leading to the distortion of regression results.
SARAR and HSARAR models showed that all of them took time span and spatial effect into account, all the parameters were significant at 1%. Labor input elasticity were 0.4233 and 0.3977, respectively. Capital input elasticity were 0.5932 and 0.6051, respectively. MAR spillover elasticity were 0.1191 and 0.1099, respectively. Jacobs spillover elasticity were 0.0268 and 0.0216, respectively. Porter spillover elasticity were 0.0268 and 0.0246, respectively. Different from the pooled regression model, the results suggested that all variables in our empirical research can boost industry value added. They supported that MAR spillover, Jacobs spillover, Porter spillover were positive with industry value added, which was consistent with the expected economic meaning of Table 1. Labor input elasticity and three kinds of knowledge spillover elasticity were bigger, capital input elasticity was smaller than the results of the pooled regression model. It revealed that labor input and the knowledge spillovers could also promote industry value added when the models considered data spatial correlation. The inter-regional factors of labor input, capital input, industrial specialization, diversification, and competition spillover were reflected by SARAR and HSARAR models.
To assess the spatial correlation, the results indicated there were positive and statistically significant spatial lag of the prefectural industry value added and spatial error autocorrelation of the error term. The spatial lag coefficients  of SEARAR and HSARAR model were 0.1396 and 0.1568, while the spatial autoregressive error coefficients  were 0.2418 and 0.2224, respectively.
HSARAR model had considered spatial correlation and hierarchical structure of the data and obtained the greater value of  and the smaller value of  than SARAR model.

Conclusions
The empirical research of industrial knowledge spillover effect of Guangdong province, which was based on HSARAR model, confirmed that labor input, capital input, industrial specialization, diversification, and competition spillover could promote industrial development, and strong industry spatial correlation also existed. When the data contained the hierarchical structure and spatial correlation, compared to SARAR model, HSARAR model could recognize the regional difference and amend industrial difference. It is of interest to consider the geographic coordinate and spatial moving average error simultaneously for further research.