Cointegration relationship of residents' consumption level

The consumption level of residents is greatly influenced by the overall economic situation. Gross domestic product (GDP) is an overall economic indicator used to measure a country's total income. During the period of economic expansion, residents' income is stable, GDP is also high, and residents' consumption expenditure is high and consumption level is high. On the other hand, when the economy shrinks, the income drops, the GDP is also low, the expenditure for consumption is less, and the consumption level drops accordingly. Since the reform and opening up, Shanghai's GDP has been increasing and people's material living standards have been improving. This paper will discuss whether there is a long-term and stable relationship between Shanghai's GDP and residents' consumption level from the perspective of cointegration.

The concept of cointegration was put forward by Engle—Grange in 1980s, and later developed into cointegration theory and error correction model (ECM) by many econometrics. Cointegration theory holds that some linear combination of two or more nonstationary time series may be stable. From the understanding of economic theory, it shows that these economic variables have a long-term equilibrium relationship. Understanding the long-term equilibrium relationship of economic variables is of great practical significance for mastering economic laws and formulating economic policies. Co-integration theory overcomes the shortcoming that the traditional econometric model relies on the stationarity of the data after the difference, resulting in the loss of long-term change trend information, which makes the model integrate the short-term dynamic fluctuation and long-term stable equilibrium of the system at the same time, and provides a powerful tool for economic analysis and prediction. Co-integration theory has aroused extensive interest in academic circles and has been widely used in economic modeling. The application of cointegration theory in China's economic field mainly focuses on the following aspects: cointegration analysis of income and consumption, cointegration relationship between commodity futures prices and spot prices, cointegration analysis of interest rates and exchange rates, cointegration analysis of money demand function, and so on.

The emergence of cointegration is a challenge to traditional linear regression, and its application in consumption function marks that consumption function has entered a new stage. A basic idea of cointegration used in this paper is: although there are random trend items in income and consumption time series, are their trends the same, so as to maintain a long-term equilibrium relationship? The equilibrium here is a statistical equilibrium, not an economic equilibrium. Explain that there is a long-term relationship between income and consumption. Although this relationship will be destroyed in the short term, the deviation from the long-term relationship is stable. This is the core of this paper's analysis of the internal relationship between income and consumption.

I. Overview of the study

Economists understand and describe the consumption function from different angles and form five common basic consumption functions:

The long-term consumption function C=kY of ⒈S.Kuznets.

⒉A。 Smith's short-term consumption function c = a+by+Δ t is basically the absolute income level. Add qualitative trend items. If the time t is taken as the parameter, the linear consumption function can be obtained according to the cross-section data. Then, taking t as the index, a family of consumption functions is obtained. Its significance lies in the different linear relationship between consumption and income at different time points.

⒊J。 S. Duesenberry's short-term consumption function based on relative income level.

4. Modigliani's lifetime income consumption function introduces the concept of savings stock W in addition to income.

Discuss ⒌ Friedman's durable income consumption function with stochastic process language.

Although several theories have different emphases, they all boil down to one fact: in the long run, income linearly (proportionally) determines consumption. However, the above discussion lacks logical argumentation in a strict statistical sense. Co-integration analysis, which has appeared since 1980s, has taken a big step forward in methodology, thus bringing the research on the relationship between income and consumption into a new field.

Cang of Shandong University summed up the study of China's consumption function in the book Analysis of China's Consumption Function, and listed functions, functions, Qin Duo functions, Li Yining functions, Zhang functions and Li Zinai functions. The difference between these functions and simple linear consumption functions is that the lag variables of consumption c and income y are added, namely:

Ct =α+β0Yt+β 1Yt- 1+γCt- 1+εt

In fact, all of them can be unified as the VAR model of (Yt, Ct)τ. Cang studied the consumer behavior and consumption function before 1978 and after 1978. In particular, he put forward the research method of establishing consumption function in towns and rural areas respectively.

Zhang Ping, Institute of Economics, Chinese Academy of Social Sciences, established the total consumption function (year) of urban and rural residents from 198 1 to 1994 by traditional linear regression method, and the annual consumption function of cities from 198 1 994. All three functions are in the form of forward-looking consumption function proposed by Li Zinai 1992:

Ct=α+β0YtγCt- 1+εt

Zhang Ping used disposable income as an explanatory variable in the function, and put forward a flexible method under the condition that disposable income is vacant in China's current national economic accounting system. In the institutional explanation of consumption-income behavior, Zhang Ping analyzed the institutional characteristics of 1979, 1979~ 1988 and before 1990s, respectively, in order to explain the different types of rationality of consumption behavior.

Zhao Ziqi published "Co-integration Theory in Contemporary Econometrics" in Statistical Research, summed up the concept and test method of co-integration, and applied it to the study of the relationship between consumption and income in Tianjin. He used the data from 1950 to 1990 * * 4 1 to establish the co-integration relationship between them.

At present, the relationship between macro-consumption theory in economic research reflects the reality that with the deepening of China's economic system reform, the gradual establishment of socialist market economy, the improvement of people's income level and consumption level, especially after the founding of the People's Republic of China, the long-standing seller's market determined by supply has changed to buyer's market, and the influence of consumer demand on macro-economic operation, macro-economic policy formulation and implementation, and government behavior has become more and more obvious. Whether based on academic significance or practical significance, it is more and more important to study the macro-consumption theory with China characteristics.

Second, empirical analysis and results

data processing

The data used for analysis are all from the relevant period of Shanghai Statistical Yearbook, and the sample data is 1978 to 2004. The consumer price index is used to convert the gross domestic product (GDP) and the consumer level into the value 1978 calculated at constant prices, and then the natural logarithm value of each variable is taken to eliminate its changing trend.

Figure 1 Source: Shanghai Statistical Yearbook

As can be seen from figure 1, lng and Inc have a growing trend, and the changing direction is relatively consistent.

Unit root test of data.

According to the definition of cointegration, only when the sequences of two variables are in the same order can we consider whether there is a cointegration relationship. We test the variables with ADF and PP respectively (all the tests in this paper are done with Eviews3. 1 software), and the test results are shown in table 1.

13. Cointegration test of variables

The significance of cointegration lies in revealing whether there is a long-term stable equilibrium relationship between variables. Economic variables that meet the requirements of co-integration cannot be separated too far from each other. One impact can only make them deviate from the equilibrium position in a short time, and will automatically return to the equilibrium position in a long time. Engle Langer( 1987) two-step method is usually used to test the cointegration relationship between two variables, but it is not convenient to test the cointegration relationship between multiple variables. Johansen( 1988) and Juselius( 1990) put forward a test method with vector autoregression, which is usually called Johansen test. It can be used to test multiple variables and find out several cointegration relationships between them. We can do two-step cointegration test on the data of two variables. Since the binary sequences 1nc and 1ng are both second-order simple integers with the same shaping order, we can consider whether there is a cointegration relationship between them. Because δ 1NC ~ I (1) and δ ing ~ I (1), the co-integration regression model is:

δLNC =α+βδLNG+ε

The equation of each parameter is estimated by least square method;

δLNC = 0.056870+0.505647δLNG+ε

(4.5622) (3.033)

R2 = 0.285702 F = 9. 199463 DW = 1.5686 1 1

We carry out ADF unit root test on the residual sequence ε, and get the statistical value of -3. 1605 14, which is less than the critical value when the significance level is 0.05-2.9969. It can be considered that the estimated residual sequence ε is a stationary sequence, indicating that there is a co-integration relationship between the sequence LNC and LNG. Therefore, we can draw a conclusion that there is a long-term and stable relationship between Shanghai's GDP and residents' consumption level, and they show the same changing relationship.

Causality test of variables.

The results of cointegration test tell us whether there is a long-term equilibrium relationship between variables, but whether this relationship constitutes a causal relationship needs further verification. Granger's causality test (1969) can solve this kind of problem. According to the Akachi Information Criterion (AIC), we determine that the lag order of each variable is 2, and the causality test of each variable is shown in Table 2.