**2. Review of Literature**

There are many explanations for the root causes of China's insufficient domestic demand, and one of these is the mainstream view that says the problem can be attributed to the Chinese residents' high and rising savings. The research [11–13] on this explanation suggests that China's economic structure is in rapid change, and the urban and rural social security system is not perfect, so there is uncertainty about personal future income and expenditure thereby causing residents to require precautionary savings. But Aziz and Cui [14] suggest that the increase in saving alone explains only a small fraction of the decline in the consumption share; in their view a much larger cause of the problem has been the role of the declining share of household income in the national income.

Another popular view is that the insufficient domestic demand is due to the increasing income disparity between residents, which is actually more a reference to foreign scholars' related research [15,16]. For example, based on a cointegration and error correction model, Chen [17] found that the urban Gini coefficient, rural Gini coefficient, and urban and rural income ratio are all Granger reasons for the decline in the consumption rate. Zhang and Chen [18] used the Theil index to discuss the relationship between income distribution and expanding domestic demand, and they believe that the widening income gap is the fundamental factor hindering China's expansion of domestic demand and the transformation of economic growth. However, Zhu et al. [19] pointed out that this view is based solely on the measurement results and lacks sufficient theoretical support, which still needs further discussion. In recent years some empirical results have also come to the opposite conclusion: Li [20] studied the relationship between the income gap and consumption demand of urban residents in China and found that the widening income gap could not be the main cause of the inadequate domestic demand; Qiao and Kong [21] argued that the impact of the income gap on the consumption propensity is related to the level of economic development; Su and Sun [22], by depicting the "U" non-linear characteristics of Chinese residents' consumption demand with income changes, further argued that the income gap may not be the main reason for the insufficient domestic demand. From the current empirical results, this view reflects a certain degree of controversy.

Theoretically, the view of the income distribution affecting consumption is derived from Keynes [23], who proposed the rule of the "marginal propensity to decline." If a social income distribution gap widens, income will be concentrated in the hands of a small number of people, and the marginal propensity to consume will lead to a decline in consumer demand. However, this hypothesis focuses on short-term analysis and does not give sufficient attention to the long-term relationship between income distribution and consumption demand. In response to this deficiency, Modigliani proposed a life-cycle hypothesis [24], which argues that consumption depends on the permanent income not the current income. In the generalized life cycle hypothesis, he also believes that a widening income gap will lead to a lack of consumer demand through the bequest effect. Post-Keynesians believe that income distribution is a determinant of consumer demand. They have established a persuasive theoretical model [25,26] trying to reveal the relationship between income distribution and consumer demand, and the conclusion is that a widening income gap leads to insufficient demand.

In fact, these theories do not show a clear relationship between income distribution or the income gap and social aggregate demand, because they have all adopted a simplified way of using "the representative agent" to deal with the problem of aggregation, that is, the transition from the individual level to macro data. Stokes [27] confirms that the form and coefficient of the macroscopic consumption function depend not only on the form and coefficient of the microscopic function but also depend on the characteristics of the social income distribution. Campbell and Mankiw [28] then broke this homogeneity constraint and put forward the "*λ* hypothesis." This hypothesis holds that a class of consumers in society chooses to consume based on their permanent income, whereas the other consumers base their consumption on their current income. If you choose to spend based on your permanent income, the widening income gap will result in a reduction in consumption through bequests; if the current income is arranged to be consumed, the widening income gap will result in a reduction in consumption through a reduction in the consumption propensity.

In addition to the above two points of view, there are still aspects related to the population age structure and infrastructure that need to be considered [29,30], and it clear that there is no perfect explanation for the issue of insufficient domestic demand. Although there is little doubt that these factors could be important in explaining the insufficient domestic demand, it is less convincing that these are the main reasons because of the incompetence facing the phenomenon of the strong demand in a single market.

Therefore, China's domestic demand problem is not just a matter of level, but it is also a structural problem. There are many explanations for it, but, as we all know, the dramatic changes in the income distribution have been one of the most significant social characteristics in China [31], and the impact of income distribution is very important to consumption. Therefore, the idea of analyzing the impact of changes in income distribution on the evolution of consumption structure arose. Fitting income distribution is a traditional economic problem, especially in the field of labor economics. Recently, scholars have paid more attention to the decomposition of income distribution changes in order to dig deeper information of income changes. Using counterfactual analysis the income distribution can be decomposed into three parts: the mean change, variance change, and residual (skewness, kurtosis, and other high-order moments) change [32,33]. This study will also use this method to decompose the income distribution of Chinese residents. The counterfactual method was first proposed by Fogel [34]. He used it to measure the contribution of the railway to the economic growth of the United States in the 19th century, refuting the mainstream view that the large-scale railway investment was the main reason for the rapid growth of the US economy at that time. Today it is still widely used in the impact assessment of events or policies [35].

Although it is a new attempt to explain the demand of urban residents in China from the perspective of the income distribution change, the existing research on the consumption structure has laid a solid foundation for the work in this study. The study of consumption structure began in the 1950s. Subsequently, different models have been proposed one after another. The more famous models are the linear expenditure system (LES) proposed by Stone [36], the extended linear expenditure system (ELES) model proposed by Lluch [37], and the approximate ideal demand system (AIDS) model proposed by Deaton [38]. Among them, AIDS model is the most widely used. Based on this model, Ray [39] used household expenditure survey data to analyze the consumption structure of Indian residents, while Blanciforti and Green [40], Chesher and Rees [41] studied the food consumption situation of American and British residents respectively. Filippini [42] measured the various elasticities of Swiss household consumption. However, there is a non-linear relationship between the share of commodity expenditure and the price and expenditure in the AIDS benchmark model. Therefore, only the non-linear method can be used in the estimation, which makes the actual estimation not very convenient. Deaton [38] proposed that when the prices of various consumer goods have strong multi-collinearity, they can be approximated by linear relationship (LA-AIDS). Subsequently, the expansion of AIDS has gradually enriched, such as inverse AIDS, quadratic AIDS, two-stage linear expenditure system-approximate ideal demand system LES-AIDS, etc [43–48].

In addition, more and more scholars begin to add some other variables to traditional AIDS or LA-AIDS models, such as demographic characteristics, seasonal variables, time trend variables, structural change paths, and other external disturbances, to characterize the impact of these factors on budget share and consumption structure [40,49]. These studies make the AIDS model more perfect and convenient. Therefore, this paper also chooses AIDS model as the basic model to integrate the factors of income distribution changes.

However, numerous existing AIDS models are all based on the assumption that the expenditure is equal to the income; the expenditure is allocated among the different commodities, and then the expenditure structure is used to approximate the demand structure. Foreign economic development tends to be stable, because the residents' income is already at a high level, and the credit and social security systems are perfect. In these circumstances the residents have the courage to advance their consumption, and the expenditure structure can then better reflect the demand structure.

China's economy is operating at a rapid speed, the residents' income changes violently, and the rapid and significant change in income of hundreds of millions of people has a strong impact on consumer demand, which is rarely encountered in the development of other countries. Coupled with the lack of social security and the consumption habit of "base one's expenditures upon one's income" and other reasons, a considerable part of the residents' income is saved, so their expenditure is not equal to their income, and then the expenditure and demand structures are inconsistent. Therefore, to study China's consumption structure problem, following the existing foreign models will require some deviations.

In order to achieve the research objectives, this study will make two improvements to the AIDS model. One of these is to relax the hypothesis that the expenditure is equal to the income through the introduction of income items in the model to make it more in line with the concept of consumption of China's residents. The second improvement to the AIDS model is based on counterfactual analysis, whereby the three dynamic features of the income distribution change are introduced into the model.
