The establishment of consumption function is based on the proportional relationship between personal consumption and income, and the research on consumption mainly focuses on consumption function. Since Keynes, it has been an important proposition of macroeconomics to find the form of consumption function that accurately describes consumer behavior, including Keynes's absolute income hypothesis, Dusenbury's relative income hypothesis, Modilian's life cycle consumption theory and Friedman's permanent income hypothesis. Hall introduced rational expectation factors into life cycle and permanent income hypothesis, which made consumption function have modern form. The similarity between them lies in using income tools to explain the changes in consumption. The difference is that Keynes's pioneering contribution directly overturns Say's law, which makes it possible to explain the existence of involuntary unemployment and to eliminate involuntary unemployment and economic depression through fiscal and monetary policies. China's economic reform is not long, and the gradual reform of "crossing the river by feeling the stones" obviously has the characteristics of China. The dual-track system makes the market track and the planned track coexist for a long time, the market economy is not developed, and consumers do not have enough time to form consumption behavior under the complete market decision. The relative closeness of the countryside has created the characteristics of self-sufficient small-scale peasant economy, and its consumption behavior is deeply influenced by traditional Confucian culture, which is different from urban residents and western residents. As far as the external environment (budget constraints, liquidity constraints, etc.) is concerned, these neoclassical consumption functions are not universal to farmers in China. ) and intrinsic motivation (rational subject, utility maximization, etc. ), various theoretical hypotheses about farmers' consumption behavior need to be further tested. Therefore, in addition to consumption function, multivariate statistical methods are more and more widely used in the field of consumption research. Based on partial correlation analysis, this paper establishes a typical correlation model of farmers' consumption-income in China, explains consumption expenditure with income variables, quantitatively judges the correlation and function of each variable, and analyzes the structural characteristics of farmers' consumption-income Two. Index selection and sample data Keynes believes that "there is a basic psychological law that we can determine whether we proceed from transcendental human nature or from specific facts in experience." Generally speaking, when income increases, people will increase their consumption, but the increase in consumption is not as big as the increase in income ... "(1) A lot of theoretical and empirical research on consumption function in the past did not damage Keynes's central point: that is, consumption (and savings) is affected by current income rather than independent of current income. This paper still takes Keynes's hypothesis as the basic basis for variable selection. However, the sample data is cross-sectional data, because it is not appropriate to apply the information of income difference in the same period to income changes in different periods, and there will be two problems: (1) the total amount problem: only when the marginal consumption tendency of income families is very close, the total amount problem can be ignored; (2) Even if the total amount problem is not considered, the income difference of cross-sectional household budget data is applied to the change of time series income, and the problem is even greater. ② From the econometric point of view, the time series data has series correlation and non-stationarity, and the cross-sectional data of the same population can not only ensure the homogeneity of the data, but also overcome the above defects. Based on the above reasons, four indicators reflecting the source of net income are selected as the "influence group": x1-wage income, x2-net income of family business, x3-property income and x4-transfer income; Eight indicators reflecting household consumption expenditure are regarded as "expenditure groups": y1-food, y2-clothing, y3-residence, y4-household equipment and services, y5-medical care, y6-transportation and communication, y7-cultural, educational and entertainment supplies and services, and y8-other goods and services. Specifically, the inter-provincial cross-sectional data of Chinese mainland in 2002 are taken as samples (that is, Chinese mainland 3 1 province and city, excluding Hong Kong, Macao and Taiwan), and the samples are all from the China Statistical Yearbook in 2003. 3. Establishing a model (I) Partial correlation analysis Partial correlation coefficient is an index to measure the linear correlation degree of two variables in multiple variables under the control of other variables, which is essentially the correlation between the remaining deviations in the control variables. In the case of multivariable, he removed the factor that the variable changes with other variables, which may be very different from the simple correlation coefficient in value, or even opposite in sign, but it is more reliable to describe the internal relationship between two economic variables with partial correlation coefficient. According to the sample data, the one-to-one partial correlation coefficient between two groups of variables X and Y is calculated as follows. Table 1 partial correlation coefficient analysis table y1y2y3y4y5y6y7y8x10.14640.4820 * * * 0.0599 * *-0.1358-0. 0. 1975-0.3747 * * 0. 1 1240.0228-0.07520.5352 * * * X3-0.2572-0.002220.046545438+060.3776 * * 0.4605 * * *-0.4 120 * * -0.28095 The overall correlation level in the above table is not high, mainly because there are many variables that make the control factors in the partial correlation process a little more, and there will be complicated relationships between the control factors, so the significance level can be appropriately reduced, which just verifies the limitations of the application of consumption function to farmers' consumption in China. It can be seen that farmers' wage income has a strong correlation with clothing, culture, education, entertainment supplies and services, property income and medical care expenditure, transfer income and household equipment and services expenditure. Other goods and services that are not included also play an important role, which shows that besides the seven categories of consumption expenditure, there are other important expenditure variables that are highly related to income level. (II) Establishment of canonical correlation model The canonical correlation model reveals the relationship between two groups of multivariate variables, that is, the first canonical variable is put forward in the two groups of variables, and the maximum correlation coefficient of the two canonical variables is r 1, which is called the first group of canonical variables; Then, the second typical variable is put forward in each group of variables, so that the correlation component r2 they reflect is second only to r 1 ... and so on, until the correlation coefficient rp of the last group of typical variables reaches the minimum, which is called the last group of typical variables. It transforms the correlation between the original two groups of variables into the correlation between several typical variables proposed in each group, and simplifies the analysis by reducing the number of variables, so it is widely used. Usually, the less logarithm of typical variables, the easier it is to explain, which is mainly judged by the significance test of typical correlation coefficient. According to the sample data, the typical correlation coefficients of x and y variables are obtained, and the test is as follows. Table 2 Typical correlation coefficient and its error serial number Typical correlation coefficient (r)r2 standard error characteristic value10.98220.96480.006527.306220.3300.69995664 R2 data show that 96.48%, 69.39% and 58.29% in the "expenditure group". Table 3 Significance of the critical value of freedom () calculated in the canonical correlation coefficient test table132140.976645.91* * 22159.758332.67 * * 3123. Considering the comparability of original variables, the canonical correlation model is established by using standardized canonical correlation coefficient as follows. Canonical correlation model. Canonical correlation model 123 (III) Canonical correlation analysis According to the importance and coefficient of typical variables, it can be seen from the established canonical correlation model that the degree of Chinese farmers' consumption expenditure affected by changes in income factors can be comprehensively described by three pairs of canonical correlation variables. The first pair of typical variables separates household equipment and services, other goods and services from other types of expenditures (typical load is 0.3398 and 0.3937 respectively), and has the greatest correlation with wage income (corresponding typical load is 0.6530). The second pair of typical variables separates other goods and services from culture, education, entertainment goods and services and medical care (typical loads are 1.7973,-1.4 1 19 and1.0/kloc-respectively. The third pair of typical variables mainly separates the expenditure on household equipment, services and clothing from other expenditures (typical loads are 3.88 16 and-1.0975 respectively), and the most relevant ones are wage income and transfer income (typical loads are-1.4338 and1. Conclusions and Suggestions (1) The rural consumption structure in China is in transition, and the rural infrastructure construction should be accelerated. From the typical correlation model of farmers' living consumption expenditure and net income, the expenditure on household equipment and services, including color TV sets, refrigerators and washing machines, is most closely related to farmers' wage income, indicating that farmers' wage income (labor remuneration) is mainly used to buy household equipment and services. According to Maslow's hierarchy of needs theory, the close relationship between household equipment and service expenditure and wage income shows that rural areas in China are gradually entering a well-off society, farmers' demand for major durable consumer goods (including color TV sets, refrigerators and washing machines) is increasing, and the overall consumption structure in rural areas is in a transitional stage. Lin Yifu believes that "it is not the income level that restricts rural residents' willingness to consume, but the lack of infrastructure", and "it is the right policy choice to fundamentally alleviate the widespread overcapacity problem in China's current national economy and accelerate the construction of rural infrastructure". Therefore, the important task of building a well-off society in rural areas is to adjust the structure of rural public expenditure, increase investment in infrastructure construction and rural industrial products, optimize the structure of farmers' living consumption expenditure, and improve the overall consumption level in rural areas. (2) With the increase of farmers' "exogenous" consumption, the construction of rural social security system should be accelerated. Higher-level expenditures such as culture, education, entertainment goods and services, and medical care in farmers' living expenses have a strong correlation with farmers' wage income (labor remuneration) and property income (capital gains). A lot of actual disposable income is used for these high-level consumption. Obviously, the actual income level of farmers in China has not reached this demand level, and Maslow's law of demand level has obviously been seriously distorted. As can be seen from the model, the typical load of cultural, educational, recreational goods and services expenditure and wage income is negative at the same time, in fact, there is a positive correlation. The direct consequence of the decrease in wage income is that farmers' spending on culture, education, entertainment goods and services has decreased rapidly. The only explanation of Maslow's distorted hierarchy of needs theory is that the consumption of farmers in China is involuntary and exogenous, and it is a compulsory consumption imposed by the external environment. In fact, due to the influence of institutional changes (especially the reform of education system), the education cost borne by farmers is increasing, which mainly comes from the increase of tuition fees and other education expenditures. Of the 654.38+0.9 billion students receiving compulsory education in China, 70% are in rural areas, and most of these education funds (98%) are borne by county and township governments (28%) and farmers themselves (70%). Not to mention higher education. In many areas, children's admission to universities has turned from a happy event to a tragedy. Farmers have to cut other expenses to meet their children's school needs, which forces Maslow's law of demand to be distorted. In addition, after the disintegration of the traditional rural public health care system in the planned economy era, farmers' health care expenditure was mainly borne by themselves, which was reflected in the rapid increase of farmers' health care expenditure, and the increased wages and property income of farmers were mainly used for medical expenses. High medical expenses often make farmers fall into the strange circle of "getting rid of poverty-returning to poverty" and "minor illness, etc." Suffering from a serious illness and waiting for a serious illness has become one of the strange situations in rural areas. The negative effect of compulsory institutional change on the increase of farmers' consumption expenditure is gradually emerging, and medical expenditure is negatively correlated with income. The dilemma of farmers' "no money and no debt due to illness" has been reflected in the model. To build a well-off society in rural areas in an all-round way and coordinate urban and rural economic development, we should speed up the construction of a social security system including rural medical and educational support systems. After SARS, the medical and health system in rural areas is being strengthened, but the construction of education support system needs to be strengthened urgently. There is an urgent need to build an education support system for rural areas, especially the middle and low income classes in rural areas, otherwise the rural areas will really become the situation described by Li Changping as "the peasants are miserable, the rural areas are poor and agriculture is dangerous". (3) The share of food expenditure is declining, but the overall consumption in rural areas is still low. The r2 of the third group of typical related variables is not high, and the explanatory power of the "influence group" is not very strong, which shows that the consumption expenditure of this group is greatly influenced by factors other than income level. However, it can still be seen that the importance of food expenditure is declining, which is consistent with the continuous decline of Engel coefficient of rural residents since the reform and opening up. However, the status of basic living expenses such as housing and clothing is still outstanding, and the typical load of some income types is negative, which once again shows that although the overall consumption structure of farmers in China is in the transition stage and the consumption structure is constantly improving, it has not fundamentally changed because of the low level and uncertainty of income (mainly manifested in the low net income of family business and the unstable wage income, resulting in its typical load less than 0). This fully shows that the work of increasing farmers' income and stimulating rural consumption still has a long way to go. In short, as far as the consumption of farmers in China is concerned, there is a strong motivation to save for housing, education and medical care, among which education accounts for the largest proportion. Because these motives have nothing to do with interest, lowering the savings interest rate and collecting interest tax will not have any impact on farmers' consumption, which has been strongly proved by the central bank's previous interest rate cuts. The fundamental reason is that farmers' income level is too low and "exogenous" expenditure is too high. Under such double pressure, farmers have a strong motivation to save for education and medical care. They usually increase their income in disguise by scrimping and saving, thus limiting their current consumption. Therefore, on the one hand, the fundamental way to solve the problem still lies in improving farmers' income level and promoting farmers' income; On the other hand, it is necessary to establish an education support system and a medical care system for rural areas, especially low-and middle-income groups, improve the rural social security system by increasing government investment to provide low-interest and discounted education credit, and correct those "mandatory" consumption expenditures brought about by institutional changes, especially in those economically underdeveloped areas. The reform of land circulation system should be cautious, and land undoubtedly provides natural protection for local farmers, so we should not act rashly.