The most famous research on the relationship between environmental pollution and economic growth is the “environmental Kuznets curve” (EKC), which uses economic growth as an explanatory variable and uses environmental pollution as an explanatory variable. The economic growth is depicted on the horizontal axis, and the environmental pollution is depicted on the vertical axis. Finally, the economic growth and environmental pollution are found like “Inverted U” curve. On this basis, Grossman [6] proved the relationship between environmental quality and per capita GDP, and pointed out that “environmental pollution in relatively will increase with the increase of per capita GDP when the income level is low, but with the development of GDP, the pollution will be less”. After that, scholars at home and abroad made further researches. Schmalensee et al. [7] uses piecewise linear function to study the relationship between the emission of CO₂ and the per capita GDP between 141 countries during the period of 1950 to 1990, and proves the existence of EKC. Millimet [8] uses application semi parametric model to study the relationship between the emission of nitrogen dioxide and sulfur dioxide in various states of the United States and the GDP of each state, as well as proving the existence of EKC. Lau [9] uses an empirical study on the relationship between 1970-2010 CO₂ emissions from Malaysia and economic growth, and validates the existence of the inverted U-type environmental Cruz Nez curve. Gio-Vanis [10] uses the fixed effect, the dynamic panel and the two variable Logit model to make an empirical study on the relationship between air pollution and family income in Britain from 1991 to 2009. The results show that the hypothesis of the inverted U curve is proved by other models other than the fixed effect model.

All in all, the above scholars’ research shows that developing cause environmental pollution. And we know that the cost of environmental pollution is very serious, and one of them is the impact on our well-being. The economic research thought of humanism encourages us to consider subjective perception, and happiness is the main index to measure human subjective dynamic. Research on the relationship between happiness and environmental pollution is rising. Air pollution affects the decline of happiness mainly through the following three conduction paths. First, air pollution causes the decline of human immunity, increases the sensitivity of the pathogen to the pathogen, and thus increases the incidence of disease, which affects the well-being index of people through the transmission mechanism for the health of the people. Secondly, air pollution increases the adverse degree to the living of the residents from the higher level. It affects the quality of life of the residents. Air pollution causes frequent fog and haze, which leads to restricted road operation and obstructed air operation; air pollution also leads to lower atmospheric visibility, which leads to frequent traffic accidents, and then affects the residents’ living and welfare index. Finally, air pollution also accelerated the depreciation of fixed assets, such as the frequent occurrence of acid rain events, which accelerated the depreciation of the buildings, resulting in serious losses to the national property, and thus affected the well-being index of the residents.

Sustained economic growth brings environmental pollution, since twenty-first Century. Foreign scholars have attached great importance to the study of happiness economics. Welsch [11] put SO₂ and NO₂ as a measurement of air quality index, in 2006, using the panel data of 54 European countries, excluding the unobserved heterogeneity in the study. Then he came up with a saying. The results show that the air pollution is the cause of the different level of national happiness. Juncal [12] studied the relationship between Spain’s air pollution, climate conditions and the happiness of Spanish residents. The results showed that in different zones, air pollution had different influence on Residents’ happiness, but it had a significant impact on the whole. Based on the data from ESS (European Social Survey), Ferreira [13] used sulfur dioxide as the main index of air pollution, and discussed the negative correlation between air pollution and European residents’ happiness. Menz [14] firstly discussed the relationship between air pollution and well-being of the developing countries. He used unbalanced panel data of 48 developing countries which are in Europe, Asia and South America between 1990 and 2006. Then he found that there was a negative correlation between air pollution and subjective well-being. Domestic research on air pollution and residents’ happiness started relatively late. Huang Yongming studied the relationship between environmental pollution and residents’ happiness in different provinces and cities in China, and found that the influence of work and living environment on happiness is different between regions. Zheng Junjun, Liu Can, Li Chengzhi etc. use the ordered logit model to analyze the influence of environmental pollution factors to happiness, and discuss those problems between different age groups, region groups. The results show that there is no difference between different groups when we discuss the impact of environmental pollution on the happiness [15] . So it is not difficult to see that there is an inherent link between the subjective well-being and the air pollution. However, the current research on happiness in China is mainly focused on the impact of income inequality on happiness [16] , to explore the impact of inflation on residents’ happiness [17] , to explore the relationship between public expenditure and happiness [18] , but pays less attention on the impact of air pollution to the well-being of residents.

To sum up, the shortcomings of the above research are as follows: first, few scholars have studied the difference between groups of air pollution and residents’ happiness; secondly, there are less articles which discuss the residents’ willingness to pay for environmental pollution.

This paper mainly uses the AQI (air quality index) as a measurement of the degree of the air pollution index, the datas of AQI in various provinces and cities comes from the environmental protection of People’s Republic of China, The National Statistical of China (2013), the announcement that are came up with Chinese Ministry of environmental protection.

The index of happiness refers to the relevant indicators to measure the specific satisfaction of residents. The data on happiness of Chinese residents in this article mainly comes from the Chinese General Social Survey (CGSS). It is the official authoritative data that is recognized throughout the country at present. The happiness about Chinese residents in CGSS (2013) is: in general, do you think your life is happy? (A36). There are five kinds of answers: “very unhappy”, “less happy”, “not happy or unhappy”, “more happy” and “very happy”. According to the previous study, this paper will assign it to 1-5. And the following results are shown in Table 1.

The selection of other variables mainly includes the selection of individual characteristic variables and the selection of social characteristic variables. Selecting the individual characteristic variables includes 13 indicators which are as follows: gender, age, city, political affiliation, marital status, religion, nationality, physical and mental health, health status, annual household income, social trust, social integrity, and social justice. Social characteristics variables choose mainly per capital GDP in various provinces and cities. Principles and methods are shown in the CGSS (2013).

And this article put them all in Table 2. We can see from Table 2, which shows the average index of Chinese residents. Data sources use STATA to compile the national statistical yearbook. Happiness is about 3.16, which is more than the middle value. AQI index of the average city is 80.19, AQI index showed a rising trend from the view of social trust, social integrity, social equity, the assignment in the middle level. The detail of Table 2 can be seen from Table 3.

This paper uses model which is put by Di Tella, in order to estimate the impact of air pollution on the well-being of the residents. The model is like this:

H i j = β p o l l u t i o n j + λ ln I n c o m e i j + θ X i + χ Y j + μ i j .

Among them, H_ij represents the happiness level of resident I in the area. J. pollution_i indicates the air pollution level of the city J. As we mentioned before, we use the AQI index of every city as a measurement index, λlnIncome_ij represents the logarithm of household income. X_i is a set of individual characteristic variables, which mainly include the age, political outlook, marital status, and individual character variables of the individual I. Y_j is mainly expressed as the city characteristic variables of the J, which mainly includes the per capita GDP of various provinces and cities. Because happiness is an ordinal discrete variable that can be ordered from 1 to 5, the ordinary OLS regression analysis is not applicable. Therefore, this paper uses Ordered Probit model to analyze.

Air pollution is a kind of social public goods, and there is a certain difficulty in pricing it. This paper mainly uses the “subjective well-being” method to evaluate, mainly through the measurement of more or less pollution to measure positive or negative effect on subjective well-being, and the positive effect of income increasing to happiness, so that to calculate the residents’ willingness to pay for environmental goods. On the basis of previous research, this paper assumes that the happiness can only be affected by the air pollution and the income level of residents can be liked as this: H = F (M, Q). H represents the subjective well-being of the residents, and M represents income and Q represents environmental pollution. Based on the above hypothesis, we can easily estimate the residents’ willingness to pay for air pollution. The principle is to regard all people as rational brokers. The hypothesis of utility maximization is that the marginal utility of air pollution reduction is equal to the marginal utility brought by income increase. Just as: dH = 0, the following formula can be obtained:

M V = − d M d Q = ∂ F / ∂ Q ∂ F / ∂ M

The above formula shows that once we get the marginal replacement rate of income and air pollution, we can measure the happiness cost of air pollution. According to the following formula, we can calculate the residents’ willingness to pay air pollution,

W T B = − Y ∂ M ∂ Q = − Y α β

where α and β present the of air pollution and the marginal utility of the affection between well-being and happiness. WTB represents the money that the residents can be able to pay while reducing air pollution. For this reason, we should first consider the calculation of marginal utility. By using the above method and ordered Probit model, we can come up with Table 5.

From Table 6, we can draw the average level of happiness is 3.76, close to the 4, so this paper use the happiness index of 4 to calculate the willingness to pay. The marginal utility of air pollution is −0.0005; the marginal effect of income is 0.0113; the average willingness to pay for pollution is 49,020 per person. According to the above formula, we can conclude that the willingness to pay for air pollution: WTB = 0.0005/0.0113 × 49020 = 2169.03. This shows that when we image to keep the level of happiness stay in the same situation, each person is willing to pay 2169.03yuan per year to relieve air pollution.