The Analysis of Simultaneous Multi-Equations Model on the Relationship between Trade and Economic Growth in China

Since reform and opening up, foreign trade has played an important role in promoting the development of China's market economy. The thesis based on the theory of econometrics makes analysis of simultaneous multi-equations model on the relationship between foreign trade and economic growth in China by the data of 1978-2007, and concludes that export indeed played an important role in promoting economic growth, and the positive effect of export exceeds the negative effect of import; the negative effect of import on the economy can be offset through affecting consumption which impacts on economic growth positively; China's economy will have more space for development because of the discover in the thesis that domestic demand has almost the same effect in promoting economy as export.


Introduction
Over the past years, whether or not china's foreign trade promoting economic growth has been the focus of debate in economic area.As a result of different research methods, economists have different conclusions on this question.Chen Jiaqin (1999) said that the import plays a more important role in promoting the economic growth than export by making use of the methods of Elastic Analysis and Causal Analysis; Shen Chengxiang (1999) used the methods of Causal Test, ADF Unit Root Test and Cointegration Test, and found that there is a reversible causal relationship between export and economic growth but no long-term stable relations in China; Song Shaohua, Song Hongming (2001) made use of the methods of Causal Test, ADF Test and concluded that export promotes the economic growth in the short term, but it is invisible in the long term; Bao Qun, Xu Helian and Lai Mingyong (2003) recognized that different ways will lead to different conclusions and only the degree of dependence on foreign trade can reflect the relationship between economic growth and trade openness better than other variables by Correlation Analysis, Regression Analysis, Variable Regression Model.After further study, they found that economic growth depends mainly on the input of elements but not the trade openness.So many scholars above used different methods to prove their own point of view, but the author think that the study of the following issues are worth considering: 1.1 More scholars in the study of this issue, only considered the impact of import or export separately on the economy, but did not take full account of the impact of the two variables, the export and import, on economic growth together.
1.2 Previous studies only considered the impact of two variables, export and import, on economic growth without considering other variables, such as investment, consumption, government expenditure, and so on so forth.1.3 The studies above rarely noticed the lagging effect of the variables and only paid attention to the impact of the current variables on economy.

Model Specifications
We should consider some aspects researching the relations between foreign trade and economic growth as following: 2.1 The measure of foreign trade To this point, many economists at home and abroad used to make import or export or their difference as the measure of foreign trade.However, it is not comprehensive to consider these indicators separately due to import and export constituting one country's foreign trade together.Therefore, we should take into account the import and export at the same time while researching the impact of foreign trade on economic growth.

The measure of economic growth
There are many indicators to measure a country's economic growth, such as GDP, GNP and economic growth rate, and so on.Which one is more appropriate?The author decided to use GDP as the explained variable to measure economic growth because that the major countries in the world today are using GDP to measure their nations' economic growth, and GNP is lack of time series data relative to GDP.

The analysis of the factors
In this study, the total amount of exports and imports are considered to be the main factors.In addition, there are many other factors that affect economic growth according to economic theories.First of all, the consumption has played a significant role in economic growth, and Keynesian theory of consumption recognized that consumption can promote the production.Secondly, in the early period of classical economics, Adam Smith proposed a theory that the capital (investment) is the motivation of the economic growth.So, investment should be considered into the model.Finally, the Keynesian multiplier theory said that the government's spending could increase national income in number of times, so government spending should also be taken into account as the factors of the model.Therefore, this thesis makes "Import", "Export", "Consumer", "Investment" and "Government Expenditure" as explanatory variables of the model.

The design of the model's form
In this thesis, the theoretic gist of the model's design is based on the Keynesian National Income Accounting Identity: GDP = Consumption + Investment + Government Spending + Exports -Imports, but only a single equation model to explore the relationship between foreign trade and economic growth is not enough considering the probable two-way causal link existing in the variables.As a result, establishing simultaneous multi-equations model is a more appropriate choice.Here, the author assumed that the national income GDP as Y t, Consumption as C t, Investment as I t, Government Spending as G t, Exports as EX t, and Imports as IM t. .The establishment of simultaneous multi-equations model is as following: (1) Here, i and i (i =0, 1, 2) are the unknown parameters, and 1t and 2t are random disturbances representing the combined effects of those factors which affect the explained variables but not taken into the model.Endogenous variables are Y t , C t and I t , and endogenous variable number M = 3. Predetermined variables are G t , C t-1 and I t-1 , and its number K = 3. Note: the above simultaneous multi-equations accord with the conditions of the Two-Stage Least Squares, and the test is elided.

The collection of data
In this thesis, the relative data of china in 1978 -2007 are shown in the following Tables.
Insert Table 1 here

Model identification
In the simultaneous equations model, the first step is to judge the model's identification in order to obtain a reasonable estimate of the parameters.According to the simultaneous equations , , , we can conclude their standard forms are: The matrix (B, ) of their Standard forms is: Since the equation ( 4) is an identity, there is no need to judge its identification.The identification of equation ( 5) and ( 6) are as following: 4.1 Identification of the equation ( 5) First of all, use the order conditioning to judge.Make the number of endogenous variables as m 5, and m 5 = 2; make the number of predetermined variables as k 5 , and k 5 = 1.We know that K-k 5 = 2 and m 5 -1 = 1, so K-k 5 > m 5 -1.It showed that equation ( 5) may be over-identification.Secondly, use the rank conditioning to judge.We draw the second line and its non-zero coefficient which included serials 1,2,7,8 in (B, ) away and we could get: -1 1 -1 -1 0 It is clear that this matrix can form 9 non-zero second order (M-1 = 2) determinants, so we can conclude that equation ( 5) is over-identification referring to the judgment of its order conditioning.

Identification of the equation (6)
First of all, use the order conditioning to judge.Make the number of endogenous variables as m 6, and m 6 = 2; make the number of predetermined variables as k 6 , and k 6 = 1.We know that K-k 6 = 2 and m 6 -1 = 1, so K-k 6 > m 6 -1.It showed that equation ( 6) may be over-identification.Secondly, use the rank conditioning to judge.We draw the second line and its non-zero coefficient which included serials 1, 4, 9 in (B, ) away and we could get: - It is clear that this matrix can form 9 non-zero second order (M-1=2) determinants, so we can conclude that equation ( 6) is over-identification referring to the judgment of its order conditioning.

Model Estimation
From the part 4 we know that the model is over-identification, and it is appropriate to use the Two-Stage Least Squares (TSLS) to estimate the parameters.The estimation of equation ( 2) is as following: Insert Table 2 here According to the table we conclude the TSLS form of equation ( 2) is: The estimation of equation ( 3) is as following: Insert Table 3 here According to the table we conclude the TSLS form of equation ( 3) is: Instrument list: C GT CT(-1) IT(-1).
This proves that, to some extent, import and export impact on economic growth together rather than separately.This also proves that the Keynesian National Income Accounting Identity Y t = C t + I t + G t + EX t -IM t is right and the form of Y t = C t + I t + G t + NX t (NX t = EX t -IM t ) is wrong because their varying extents of effect.This is to say, import and export impact on economic growth together rather than net export.