Two variables, production and price, are used to examine the current status of innovation in China. Both variables, calculated with GDP and CPI data published in the website of National Bureau of Statistics of China, are recognized as level variables and used for model estimation¹. The variables are normalized, with the values for 1995 adjusted to 100 for each province. Citing a lack of data, Tibet is excluded as an object of examination, therefore, 30 provinces are verified in total. To estimate the model for time-series data, such as VAR model, it is necessary to clarify the stationarity of data for estimation. Generally speaking, the reasons behind fluctuation in stationarity include both probabilistic and non-probabilistic factors. As for probabilistic factors, cases exist where the Data Generating Process (DGP) follow the process with probabilistic trend, such as unit root, which refers to a time-series process in which the mean value or variance deviates from the constant level. On the other hand, a non-probabilistic factor explains the process which follows with structural breaks. In the case that DGP follows a non-stationary process due to the probabilistic factor, the estimation result is suggested to become spurious regression. From the behavior of the data, both of the level variables are considered to have a higher order of integration than just one, which is unit root process, while first order differenced process is thought to be following unit root or long memory process. Furthermore, second order differenced process behaves as like stationary process around zero value. From the above, first order differenced variables of production and price are used for estimation. Before executing the estimation, it is necessary to confirm whether the variables are unit root process or long memory stationary process.

At first, the unit root tests are applied to both the production and price data for each province. Even if the data follows unit root process, the estimation results of their regression results are known not to be spurious regression when the regression is consistent with a cointegration relationship. In the case that first order differenced variables of both production and price follow stationary process, the spurious regression is not expected to occur, therefore, data will be used for estimation of VAR model. If the two variables are consistent with unit root process according to the statistical test and the relationship of regression is thought to display a cointegration relationship, the first order differenced processes are used for estimation. If only one variable follows unit root process, the same verification is executed for second order differenced processes.

After ensuring the stationarity of data, the AD-AS model explained in [2] is estimated. That model is based on the work proposed by [8] , and to which the long-run restriction for identification of [9] is introduced. The model is:

y s = E t − 1 ( y t ) + α ( p t − E t − 1 ( p t ) ) + ε t , ( α > 0 ) y t d + p t = E t − 1 ( y t ) + p t + η t y t d = y t s

Calculated by author.

y s denotes supply quantity, y d means demand quantity, p is price level, E t − 1 indicates the expectation value in t − 1 , and y is the equilibrium quantity, with α the parameter. E t − 1 value is constructed by information about past market status, therefore, the model is shown as below.

Calculated by author.

E t − 1 ( y t ) = A ( L ) y t ,   E t − 1 ( p t ) = A ( L ) p t

A ( L ) = [ a 11 ( L ) a 12 ( L ) a 21 ( L ) a 22 ( L ) ] can be expressed with lag operator L. This economy is described with reduced form VAR model as below.

[ y t p t ] = [ a 11 ( L ) a 12 ( L ) a 21 ( L ) a 22 ( L ) ] [ y t p t ] + [ e y t e p t ]

e y t and e p t are error terms of reduced form VAR model. C matrix is introduced, which expresses the relationship between the error term of reduced form and structural shock ε t and η t .

e t = C ϵ t [ e y t e p t ] = [ c 11 c 12 c 21 c 22 ] [ ε t η t ]

The model can be displayed as matrix form as below.

[ y t p t ] = [ E t − 1 y t E t − 1 p t ] + [ 1 1 + α α 1 + α − 1 1 + α 1 1 + α ] [ ε t η t ] = [ a 11 ( L ) a 12 ( L ) a 21 ( L ) a 22 ( L ) ] [ y t p t ] + [ 1 1 + α α 1 + α − 1 1 + α 1 1 + α ] [ ε t η t ]

Therefore, the coefficients of reduced form VAR and Structural VAR are shown below,

[ c 11 c 12 c 21 c 22 ] [ σ ε 2 σ ε η σ ε η σ η 2 ] [ c 11 c 21 c 12 c 22 ] = [ 1 1 + α α 1 + α − 1 1 + α 1 1 + α ] [ σ ε 2 σ ε η σ ε η σ η 2 ] [ 1 1 + α − 1 1 + α α 1 + α 1 1 + α ]

c 11 = α c 12 , c 11 = − c 21 , c 11 = c 22 can be derived.

The long-run restriction for identification is displayed below.

[ I − A ( 1 ) ] y t = e t y t = [ I − A ( 1 ) ] − 1 e t

The cumulative impulse response functions are expressed with matrix C ,

y t = [ I − A ( 1 ) ] − 1 C e t = [ 1 − a 11 ( 1 ) − a 12 ( 1 ) − a 21 ( 1 ) 1 − a 22 ( 1 ) ] − 1 [ c 11 ε t + c 12 η t c 21 ε t + c 22 η t ] = a 12 ( 1 ) a 21 ( 1 ) [ 1 − a 11 ( 1 ) ] [ 1 − a 22 ( 1 ) ] [ 1 − a 22 ( 1 ) a 12 ( 1 ) a 21 ( 1 ) 1 − a 11 ( 1 ) ] [ c 11 ε t + c 12 η t c 21 ε t + c 22 η t ]

and the above relationship can be reduced. Suppose B = a 12 ( 1 ) a 21 ( 1 ) [ 1 − a 11 ( 1 ) ] [ 1 − a 22 ( 1 ) ] , and the response of production for AD shock,

which is the object of long-run restriction for identification, is shown as,

y t = B [ 1 − a 22 ( 1 ) ] ( c 11 ε t + c 12 η ) + B a 12 ( 1 ) ( c 21 ε t + c 22 η t ) = B [ ( 1 − a 12 ( 1 ) ) c 12 + a 12 ( 1 ) c 22 ] η t + B [ ( 1 − a 22 ( 1 ) ) c 11 + a 12 ( 1 ) c 21 ] ε t

then the neutrality of production to AD shock is B [ ( 1 − a 12 ( 1 ) ) c 12 + a 12 ( 1 ) c 22 ] = 0 .

[2] ’s model allows for not only the correlation between structural shocks, but also the causality relationship of structural shock as shown below.

η t = ρ ε t + ν t

This assumes the causality from AS shock to AD shock. ν t ∼ N ( 0 , σ ν 2 ) denotes the white noise, which does not correlate with ε t . This equation is written in matrix form as below.

[ ε t η t ] = [ ε t ρ ε t + ν t ] = [ 1 0 ρ 1 ] [ ε t ν t ]

The values of variance-covariance matrix of error terms of reduced form VAR lead,

E ( e t e ′ t ) = [ 1 1 + α α 1 + α − 1 1 + α 1 1 + α ] [ 1 0 ρ 1 ] [ σ ε 2 0 0 σ ν 2 ] [ 1 ρ 0 1 ] [ 1 1 + α − 1 1 + α α 1 + α 1 1 + α ]

furthermore, the strength of causality of AS shock to AD shock can be expressed with ρ coefficient. Since the coefficient of first order difference variables model and second order differenced variables model are the same because of the model structure, the causality coefficients ρ are indiscriminately verified for all provinces.

With Tibet excluded from verification, the stationarity of data was examined for 30 provinces. The behaviors of all first order differenced variables are recognized as the processes with non-zero intercepts, which are consistent with non-zero real GDP growth or inflation rates. Given the possibility of non-zero constant terms, [10] ’s unit root test was executed, with the results of statistical testing shown in Table 3. The table shows the null hypothesis that “process is unit root process” is rejected in 18 provinces for both variables. Liaoning province showed the null hypothesis is rejected for neither variable, therefore, VAR residuals are tested using the 5% critical point outlined in [11] ’s unit root. For the remaining provinces, second order differenced variables were tested. The behavior of second order differenced data is considered to follow stationary process around zero, therefore, the Augmented Dickey Fuller test was applied. As results of the statistical tests show, to estimate the model, first order differenced variables were used for 19 provinces, while second order differenced variables were applied to 11 provinces.

According to Table 4, most of the ρ coefficients show high causality, with the exception of Hebei, Zhejiang and Ningxia, where causality is lower. The

1 denotes that the null hypothesis is rejected at 5 % significant level, 0 denotes otherwise.

provinces, of which the value of causality coefficients ρ are ranked in the top 25%, are Heilongjiang, Anhui, Hubei, Hunan, Chongqing, Sichuan, Guizhou and Yunnan. We learn that AS shock causes strong AD shock, and, technical improvement or introduction of new production methods leads to potential market demand. As a result, AS shock expanded production quantity more than it did in cases without the causality effect.

The changes in AS shock are shown in Figure 1. Changes are expressed as minimum points, maximum points, quartile points and medians, and indicates that the changes in AS shock of each province display the same trend. Except for the drastic decline in Liaoning province in 2016, changes in AS shock fluctuate across a narrow range, and all provinces were severely impacted by the Global Recession of 2009.

The geometrical distribution of ρ is shown in Figure 2. Except for Heilongjiang, the provinces whose ρ values rank in the upper quartile are concentrated in inland China. On the other hand, the provinces with ρ values ranked in the bottom 25% represent a portion of the Jing-Jin-Ji economic area or advanced economy area, such as Beijing, Hebei, Zhejiang and Guangdong. The definition of innovation applied to this study is concerned with the relationship between the supply side and market systems, and not whether the target area has high aggregate demand. Therefore, the AS shocks do not correspond to short-term economic growth, and ρ values show whether the catalyst of innovation in a province is AS shock accompanied with AD shock, which results in to technological improvement or the introduction of new production methods in response to potential requirements within the market.

Although the estimated values of ρ , see Figure 1, suggest a geometrical concentration, it does not necessarily correspond to the country’s wide-area development policies, such as China Western Development or Rise of Central China. Instead, provincial domestic factors may be a more likely reason.

To confirm the robustness of the results, the same estimation is executed with Retail Price Index (RPI as follow) of China, shown in Table 5. Similar results are shown with RPI data for Price variables as CPI data. 5 of the 8 provinces show both results as −1 (denotes that the value is less than lower 25%), and 7 of the 8

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provinces show both results as 1 (denotes that the value is higher than upper 25%). Furthermore the geometric concentrations of Inland area of China (Chongqing, Sichuan, Guizhou, Hubei, Anhui, and Yunnan) is shown in the estimation results with RPI data.

This paper defines innovation as not only the discovery of imaginative technology, but also the improvement of the supply side in a broader sense. Most importantly, this definition states that improvement is consistent with the market requirements. This innovation is conformable with the definition pointed out in existing literature; in fact, some cases highlight achievements in innovation which occurred in response to potential requirements of market, such as shared bicycle industry and online payments. As results show from verification of the

When ρ value is higher than upper 25 %, the value is 1, and less than lower 25 %, the value is −1.

degree of innovation in each province using AD-AS model, although Heilongjiang province can be considered as a single innovative province, other more innovative provinces are concentrated in a region of inland China. In these provinces, positive AS shock brings an expansion of aggregate demand to the market and contributes to economic growth. Furthermore, it is shown that advanced economic areas are not required to achieve innovation. The above description does not contradict the definition of innovation offered in this paper. In an area where explicit aggregate demand exists, the motivation to explore potential demand is possibly less on the supply side.

Considering the geometric distribution of estimated values of ρ coefficient, interaction effects might exist among province, because some high values provinces are concentrated, while other lower values provinces are adjacent, such as Hebei, Beijing and Shandong, or Zhejiang, Fujian and Guangdong. It is considered that innovation is not specific to each province and that contributing factors may include interaction effects between neighboring provinces, or the possibility of AS shock spreading from one province to adjacent provinces. Although the distribution shows geometric characteristics, it does not correspond with the country’s wide-area development policies, such as China Western Development or Rise of Central China. Therefore, it is probable that the high ρ values reflect not only Central Government policy, but also improvement in the supply side stimulated by provincial government policy, and the economic activities of the private sector.

The effects of interaction will be further investigated in future research. In closing, though the methodology outlined in this paper is used to clarify innovation and the resulting economic growth in China, it can be applied to any other nation or economy that intends to investigate the degree of achievement of innovation corresponding to its market requirements. With the use of only two basic data, such as production and price, this method is considered to be highly feasible.

The author declares no conflicts of interest regarding the publication of this paper.

Minamikawa, T. (2019) A Study of the Distribution between Each Province about China Style Innovation. Theoretical Economics Letters, 9, 1316-1329. https://doi.org/10.4236/tel.2019.95085