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Date: 20 10/ May 27th, 2008
Multi-factor analysis of China's urban GDP change in 2006
Based on the multi-factor analysis of the GDP of cities in the same period, this paper establishes a multiple linear regression model with the GDP of cities in the same period as the explained variable and other quantifiable cross-sectional data as the explained variable, so as to quantitatively analyze the GDP of cities in the same period.
Keywords: GDPY (100 million yuan) multi-factor analysis model econometric test
I. Introduction
Gross domestic product (GDP) refers to the final result of production activities of all permanent units in a country (or region) in a certain period of time. From the perspective of value form, it is the difference between the value of all goods and services produced by all permanent units in a certain period and the value of all non-fixed assets invested in the middle of the same period, that is, the sum of the added value of all permanent units. While creating GDP, it is also divided by the corresponding production factors, mainly reflected in labor remuneration and profits. In modern society, the government should take away part of GDP in the form of tax. This paper mainly studies the influence of L (10,000 people) and total capital formation K (100 million yuan) on the GDP of cities in the same period after excluding the price influencing factor, namely the retail price index P (last year = 100).
Second, literature review
Note: The data of urban GDP in the same period of 2006 comes from China Statistical Yearbook 2007;
In 2006, the data of L (employment of ten thousand people) came from China Statistical Yearbook 2007.
The data of total capital formation K (100 million yuan) in 2006 comes from China Statistical Yearbook 2007, which is calculated at 2006 prices.
In 2006, the data of commodity retail price index P (last year = 100) came from China Statistical Yearbook 2007;
Third, the purpose of the study
By studying the GDP of each city in the same period, a multiple linear regression model is established with the GDP of each city in the same period as the explained variable and other quantifiable cross-sectional data as the explained variable, so as to quantitatively analyze the GDP of each city in the same period. Master the methods of establishing multiple regression models and comparing and screening models.
Fourth, the experimental content
According to the theory of production function, the basic form of production function is: L and K are labor and capital invested in the process of GDP output, respectively. This paper does not consider the influence of time variable, that is, technological progress. The above table lists the relevant statistical data of GDP of cities in China in 2006; Among them, the output y is the GDP (comparable price) of each city in the same period, and L and K are the number of employees at the end of 2006 and the total capital formation (comparable price) of each region respectively.
5. Establish the model and estimate, test and correct the parameters of the model.
(a) We first establish the relationship model between Y 1 and l:
Among them, y 1- actual GDP of each city in the same period (100 million yuan)
L —— Number of employees at the end of 2006 (ten thousand)
Parameter estimation of the model and its economic significance and test of statistical inference
Using EVIEWS software, after regression analysis, the scatter plot of Y 1 and l is as follows:
Using EVIEWS software and OLS method, it is estimated that:
Dependent variable: Y 1
Methods: Least square method.
Date: 05/27/ 10 Time: 14:45
Sample: 1 36
Comments included: 3 1
Variable coefficient standard. Error t- statistics problem.
c- 1647.264 5 17.2 169-3. 18486 1 0.0034
l 14.994 17 0.7 12549 2 1.04299 0.0000
R squared 0.938534 average dependent variable 7387.979
Adjusted R-squared 0.9364 15 standard deviation dependent risk value 6367. 139.
Standard deviation of regression 1605.545 information standard of red pool 17.66266
The sum of squares of resid is 747555 13 Schwartz criterion 17 5653867.
Logarithmic likelihood -27 1.77 12 F- statistic 442.8073
Durbin-Watson statistics 1.503388 probability (f statistics) 0.000000.
It can be seen that the t value of L is significant and the coefficient accords with economic significance. Economically speaking, every additional unit of labor force can increase the real GDP by 14+38+0, which can be achieved under certain conditions. In addition, the revised determinable coefficient is 0.9364 15, and the F value is 442.8073, which obviously passes the F test. And the p test value of l is 0, less than 0.05, so it passes the p test.
(2) Establish the relationship model between Y 1 and K 1;
Among them, y 1- actual GDP of each city in the same period (100 million yuan)
K1-total capital formation (actual investment) by region (100 million yuan)
Parameter estimation of the model and its economic significance and test of statistical inference
Using EVIEWS software, after regression analysis, Y 1 and K 1 scatter plots are as follows:
Using EVIEWS software and OLS method, it is estimated that:
Dependent variable: Y 1
Methods: Least square method.
Date: 05/2710 Time: 17: 16
Sample: 1 36
Comments included: 3 1
Variable coefficient standard. Error t- statistics problem.
393.0357 - 1.793873 0.0833
k 1 24 1 106 0.08675 1 25.83385 0.0000
R squared 0.958357 average dependent variable 7387.979
The adjusted R-squared value is 0.95692 1 standard deviation dependent risk value 6367. 139.
Standard deviation of regression 132 1.537 information standard of red pool 17.27332
Sum of squares of residuals 50647333 Schwartz criterion 17.36583
Logarithmic likelihood -265.7364 F- statistics 667.3880
Durbin-Watson statistics 1.6979 10 probability (f statistics) 0.000000.
It can be seen that the t value of K 1 is significant, and the coefficient accords with economic significance. Economically speaking, each additional unit of capital can increase the real GDP by 2.241106, which can be realized under certain conditions. In addition, the revised determinable coefficient is 0.95692 1, and the F value is 667.3880, which obviously passes the F test. The p test value of K 1 is 0, which is less than 0.05, so it passed the p test.
By comparing the absolute coefficient, adjusted determinable coefficient, T test, F test and P value test of the two models, it is obvious that the relationship model of Y 1 and K 1 is better than that of Y 1 and L, so the relationship model of Y 1 and K 1 is better than that of L.
(3) Establish the binary relation models of Y 1 and K 1 and L.
Among them, y 1- actual GDP of each city in the same period (100 million yuan)
K1-total capital formation (actual investment) by region (100 million yuan)
L —— Number of employees at the end of 2006 (ten thousand)
Using EVIEWS software, OLS method is used to estimate.
Dependent variable: Y 1
Methods: Least square method.
Date: 05/2710 Time: 17:23
Sample: 1 36
Comments included: 3 1
Variable coefficient standard. Error t- statistics problem.
c- 1369.643 303.22 18-4.5 16968 0.000 1
k 1 1.336796 0. 176 104 7.590936 0.0000
l 6.522268 1. 190606 5.478 107 0.0000
The square value of R is 0.979900, and the average dependent variable is 7387.979.
Adjusted R squared 0.978464 standard deviation dependent risk value 6367. 139
The standard deviation of regression is 934.3899 16.60943.
Sum of squares of residuals 24446367 Schwartz criterion 16.74820
Logarithmic likelihood -254.4462 F- statistic 682.5040
Durbin-Watson statistics 1.633 165 probability (f statistics) 0.000000.
It can be seen that the t values of K 1 and l are significant, and the coefficients are in line with economic significance. In the economic sense, every unit of capital increase can make the real GDP increase correspondingly. In addition, the revised determinable coefficient is 0.978464, and the F value is 682.5040, which obviously passes the F test. And the p test values of K 1 and l are both 0, both less than 0.05, so they passed the p test.
By comparing the absolute coefficient, adjusted determinable coefficient, T test, F test and P value test of the two models, it can be clearly seen that the relationship models of Y 1 and K 1 and L are better than those of Y 1 and K 1. Therefore, the establishment of binary relationship model is more in line with the actual economic situation.
(4) Establish a nonlinear regression model-C-D production function.
The C-D production function is: For this nonlinear function, the following two methods can be used to establish the model.
Mode 1: Convert to linear model for estimation;
At the same time, take the logarithm of both ends of the model and get:
Type the following commands in turn in the command window of EViews software:
GENR LNY 1=log(Y 1)
GENR·LNL = logarithm (l)
GENR LNK 1=log(K 1)
LNL LNK 1
The estimated results are shown in the figure.
Dependent variable: LNY 1
Methods: Least square method.
Date: 05/2710 Time: 17:29
Sample: 1 36
Comments included: 3 1
Variable coefficient standard. Error t- statistics problem.
c 0.242345 0. 198 180 1.222853 0.23 16
lnk 1 0.66500 0.082707 8.058538 0.0000
LNL 0.493322 0.088 128 5.597775 0.0000
R-squared 0.988755, average dependent variable 8.50486
The adjusted R-squared value is 0.98795 1 standard deviation dependent risk value 1.037058.
The standard deviation of regression is 0. 1 13834 information standard of red pool-1.4 16379.
The sum of residual squares is 0.36283 1 Schwartz criterion-1.277606.
Logarithmic likelihood 24.95388 F- statistic 1230.946
Durbin-Watson statistics 1.295 173 probability (f statistics) 0.000000.
It can be seen that the t values of K 1 and l are significant, and the coefficients are in line with economic significance. In the economic sense, every unit of capital increase can make the real GDP increase correspondingly. In addition, the revised determinable coefficient is 0.98795 1 and the f value is 1230.946, which obviously passes the f test. And the p test values of K 1 and l are both 0, both less than 0.05, so they passed the p test.
By comparing the above model's determinable coefficient, adjusted determinable coefficient and F test, it can be clearly seen that the model is optimal. Therefore, this model is chosen as the optimal multivariate linear regression model with GDP of each city as the explained variable and other quantifiable cross-sectional data as the explained variable.
Abstract of intransitive verbs
To sum up, the cross-sectional data fitting model successfully reflects the quantitative relationship between GDPY 1 and the number of employees L (10,000 people) and the total capital formation K 1 (100 million yuan) after excluding price factors, and is a successful model. It can be seen from the model that the GDPY 1 of each city in the same period has a very close relationship with the number of employees L (10,000) and the total capital formation of each region after excluding price factors, that is, the retail price index P (last year = 100) is closely consistent with Cobb-Douglas (C-D) production function, which verifies that.
References:
1, National Economic Accounting -2007 National Statistical Yearbook
2. Price Index -2007 National Statistical Yearbook
3. Xu Xianchun's Accounting for China's Gross Domestic Product,