*5.2. Model Estimation Results and Analysis*

The model we used is a system, and each equation does not contain endogenous explanatory variables. If we ignore the correlation between the disturbance terms of the different equations, the ordinary least squares estimate for each equation is consistent but not the most efficient. There is likely to be a period correlation between the residents' different expenditures, so it is efficient to use the Seemingly Unrelated Regression (SUR) to estimate the entire system at the same time. In addition, since the dependent variable of each equation is the proportion of "consumption expenditure/income," the sum is 1. In order to avoid over-recognition of the model estimation, one equation must be removed. Theoretically, randomly removing any one does not affect the result, and the parameters of the removed equation can be calculated through the constraints. But the purpose of this study is mainly to examine the impact of the income distribution changes on the consumption structure, and savings exists more as a tool variable, so choosing to remove the savings equation and its estimated results will not be given. For the parameter estimates, only the coefficient estimates of ln(*ξ*1/*y*1), ln(*ξ*2/*ξ*1) and ln(*y*2/*ξ*2) representing the income distribution change are given.

From the estimation results (Table 3), the model is well fitted, the Root Mean Square Error (RMSE) of each equation is small, and all R-square values are greater than 0.97. Furthermore, the correlation between the perturbations of the equations have also been tested by the Breusch-Pagan test, and the last line of Table 3 shows that the p-value of the "no-period correlation" is 0, so the original hypothesis of "the disturbance term is independent" can be rejected at a significance level of 1%. Therefore, the use of SUR for the systematic estimation can improve the estimation efficiency.


**Table 3.** The Estimation of the Impact of Income Distribution on the Consumption Structure.

Note: The t statistics are in parentheses. The symbols and thresholds are \* for p < 0.1, \*\* for p < 0.05, and \*\*\* for p < 0.01. "R-sq" represents R-squared statistics. (u1)–(u8) represent eight categories of goods: (u1) food, (u2) clothing, (u3) residence, (u4) household facilities, (u5) medical care, (u6) transportation and communications, (u7) entertainment and education, and (u8) other miscellaneous expenses and services.

For the period 2000–2004, the impact of the mean effect on clothing and residential consumption is not statistically significant. Among the consumption items that are significantly affected by the change in the mean of the income distribution, there is a positive impact on the consumption of food, medical care, transportation, entertainment, and education, and a negative impact on consumption of household equipment and miscellaneous services. We know that the demand for basic living expenses for food, clothing, and household equipment in China had been basically met by the year 2000 as a result of the rapid increase in the overall income level of the residents. According to the

data in the 2001 China Statistical Yearbook, by the end of 2000 the three sets of traditional home appliances, TV sets, washing machines, and refrigerators, had reached a high level of 116.56 units, 90.52 units, and 80.13 units per 100 urban residents. Therefore, during this period the proportion of household consumption expenditure on household equipment decreased with the increase of income, thereby reflecting the "Engel Law" trend. The positive effect of the mean change on food expenditure shows that the dietary structure of Chinese residents in this period was further optimized; people not only took "eat full" as a standard, more and more chose to pursue the "eat good" policy with an improvement in their food quality, and the proportion of spending on dining outside the home also increased. The trend with clothing expenditure is just between the middle of the two types of goods. The proportion of the expenditure on clothing is not sensitive to the growth of the income level, indicating that the residents' basic needs have been met, but the pursuit of quality has not yet been reflected. During this period, residents mainly focused on the three "core consumption" categories, which are health care, transportation and communications, and entertainment and education. This consumption structure represents a transition from a basic one to a development-centric one, but the enjoyment-centric consumption represented by the "other miscellaneous expenses and services" had not yet attracted the attention of the urban residents in the short term; they chose to reduce the basic type of consumption and transfer their focus onto the development-centric consumption.

China's income distribution is obviously right-sided, with the high-income groups growing rapidly, so the variance effect and residual effect mainly represent changes in the consumption choices of the high-income earners. The variance effect for the period 2000–2004 has a significant positive effect on the consumption of food, medical care, culture, and education, whereas it has a significant inhibitory effect on household facilities and miscellaneous services and has no significant effect on other items. This indicates that the high-income group will further increase their share of expenditure on food, medical care, and cultural education. As their income grows at a relatively faster pace, more income will be used to enjoy higher quality food and health care services and to receive better quality education, which may enhance their individual heterogeneity advantages and help them to stay in the forefront in terms of income distribution. However, the expenditures on household equipment, tourism, and other miscellaneous services have also been reduced, which may have been caused by a lack of innovation in the home appliance industry and the immaturity of the tertiary industry at that time.

The residual effect reflects the choice of the consumers with the most heterogeneous advantage, whose position in the income distribution levels was relatively higher. During 2000–2004 the residual effect had no significant effect on the other items except that there was a significant negative impact on the consumption of clothing and housing and a positive effect on the consumption of health care. As they are the group with the fastest growing income, they are most concerned about medical expenses and may even sacrifice some short-term clothing and residential consumption to meet their medical expenses. The difficult problem of seeing a doctor was always the focus of the society's attention in this period.

During 2005–2010 the mean effect had a significant negative effect on food, health care, and transportation, but the impact on the other categories of consumption was not significant. Therefore, compared with 2000–2004, the positive pull impact of the mean effect on the consumption rate disappeared, which perhaps just reflects the problem of the continuing decline of China's consumption rate with the mean effect reflecting the consumption dynamics of the main body of society. Fortunately, the variance and residual effects reflect some positive effects on individual markets, such as the variance effects on the expenditure on cultural and educational activities and miscellaneous services, and the residual effects on clothing and other services, even though their negative impacts on certain markets still exist. Based on the results, first, the second round of household food consumption has been completed, so the three effects of the income distribution are negative. Second, thanks to the deepening of the health care reform since 2005, which was defined as "The Year of Hospital Management" by the government, the medical expenses proportion of income has been reduced significantly. Finally, the trend of further escalation of the consumption structure is beginning to emerge, which shows that families with faster income growth tend to increase their spending on education and services. In addition, the attitudes towards apparel consumption have changed with people beginning to focus more on the quality and brand of clothing.

Considering the importance and centrality of real estate to China's economy, the issue of residential consumption will be discussed separately here. The results of Table 3 show that the mean effect of the two periods both had no significant effect on the residential consumption. The variance effect was not significant before 2004 but began to show a significant negative effect after 2004, while the residual effect reflects the negative impact on the consumption devoted to living expenses in the two periods. It is easy to understand why the mean effect is not significant, and this is because since 1998 the implementation of housing distribution monetization replaced the previous housing in-kind distribution. China's housing prices began to rise, especially in 2000–2010, which is known as the "Golden Decade" of the real estate market. Under the continued rising expectations, the housing bubble continued to expand, and according to the statistics of the Chinese Academy of Social Sciences in 2004, in Beijing and Shanghai the overall household debt ratio, which reached 155% and 122%, respectively, was higher than the ratio for European and American families. Therefore, with the investment attributes of the house becoming stronger, the residential market has gradually moved out of line with the income levels, and the mean effect has lost its role.

It is contrary to our intuition that the residual effect in the first period and the variance and residual effects in the second period have shown a negative impact on residential consumption, because most people would think that high-income people are characterized by residual and variance changes and should have increased their living expenses. To understand the statistical content of the Chinese Bureau of Statistics in respect of the consumption on living expenses, we find that most of the statistics use costs for the items including housing and decoration materials, rent, mortgage payments, daily energy consumption, and maintenance, but the expected income from that investment that should be taken into consideration is not included. For example, renovation costs that are incurred are included in the statistics reported, and generally Chinese families that are home owners choose to decorate the house they live in, but they do not decorate it for speculative reasons. Therefore, in the context of the increasing investment demand for houses, the complementarity between the usage cost and the housing expenditure is gradually weakened, and the substitution characteristics are gradually reflected. A few high-income families characterized by residual change chose speculative living expenses in 2001–2004, while in 2005–2010 the majority of high-income groups characterized by the variance effect were also involved, thereby strengthening the negative impacts of residual and variance effects on residential consumption.

In summary, the above model estimates are statistically significant, and they are consistent with the actual situation that prevailed in China over that time. The consumption effect of the income distribution in the two periods is obviously different. The mean effect is the theme during 2001–2004, and the change of the consumption structure from a survival mode to a development mode is the mainstream. However, the mean effect during 2005–2010 is no longer significant with the overall consumption being weak. Fortunately, in the individual markets, with regard to the high-income groups, the variance and residual effects reflect their positive side, which strengthened the individual market demand, and the consumption structure also shows signs of further escalation.

#### *5.3. Quantitative Counterfactual Estimation of the Effects*

The preceding analysis is qualitative, but as is customary in studies of the consumption structure, quantitative elastic analysis is still needed. However, after introducing the income distribution variables into the AIDS model, the economic meaning of the variables that this study is concerned with becomes difficult to define when performing elasticity analysis, especially the interpretation of the variance and residual terms. Therefore, we have decided to abandon the elasticity analysis and directly use the previous counterfactual analysis framework and the model's estimation results to

quantitatively measure the impact of the three factors of the income distribution on the consumption demand structure of the different commodities. We are then able to complete the interpretation of why China's household consumption rate continued to decline.

The essence of the simulation is based on the counterfactual sample constructed to predict the expenditure-income ratio for each category of goods. In the simulation process the coefficient estimates and variables in the sample other than the income factor remain unchanged. We are only assuming that the income distribution variables are changed according to the following three counterfactual cases. We still take two periods as an example, and the change in income is subject to Equation (7). Assuming that the income in the first period is *y*1, which we already know, *ui*<sup>2</sup> = *ui*2(*ξ*1, *ξ*2, *y*2) can be determined by model (14), whose coefficients have already been estimated. If, for example, we assume no change in the income distribution, then we get the predicted value *u*ˆ*i*2(*y*1, *y*1, *y*1), but if only the mean change occurs, its predicted value is *u*ˆ*i*2(*ξ*1, *ξ*1, *ξ*1), and so on. Finally, the following results are obtained:


By the above process, every two years' demand effects of the income distribution change on different commodities in each province are obtained.

The estimated results for each effect by the year group are given in Figure 4, which is obtained by averaging the provincial data. The results show that the mean effect is the largest effect in all kinds of consumption and from it the size and direction of the total effect is basically determined, but its role is to reduce the consumption rate in a comprehensive view. For home equipment the mean effect is changed from a negative effect before 2004 to a positive effect after 2004, but the positive effect is very small. As the industry has been in a very mature stage, most of the consumption is to meet the needs of family equipment updates, so there is little room for further improvement in the proportion of the expenditure in the future. The impact of the mean effect on miscellaneous consumption and service items is developing in a positive direction, and there is a potential for further improvement, but it is still in a negative stage in the figure. The mean effect on the consumption of clothing has always reflected the inhibitory effect, and the effects of the mean on the other five categories all change from positive to negative and show a downward trend.

The variance effect and the residual effect are relatively small, so in order to show the results more clearly, Table 4 gives the yearly average of the effects of the two phases. Among the three effects, the residual effect is the smallest, and has a certain individual randomness, so no further analysis is warranted. For the variance effect the expansion of the income variance had a negative effect on consumption before 2004. This was mainly because it hindered the upgrading of the consumption structure of the medical, transportation, and cultural and educational consumption, but at the same time it played a positive role in the clothing, living, and home equipment categories, especially in service consumption, which represents the main direction for the further upgrading of the consumption structure. In the second stage the promotion effect of the variance on the food, living, and medical care categories was a rare bright spot when the mean effect was almost entirely negative. On the whole, the effect of the variance was much smaller than that of the mean and did not affect the overall trend of the total effect, but the variance of the income distribution still had a positive effect on the individual markets.

**Figure 4.** Counterfactual Decomposition of the Income Distribution's Consumption Effects.


**Table 4.** Annual Average Estimate of the Income Distribution's Consumption Effects.

Note: The numerical values in brackets indicate the percentage of contributions corresponding to each effect; the total effect is 100.

#### *5.4. Discussion on China's Insufficient Domestic Demand*

The impacts of the changes in the income distribution on the consumption structure have been adequately analyzed. On this basis, this section discusses the problem of insufficient domestic demand in China. It is easy to judge from the previous analysis that the main reason for the decline in the consumption rate may not be the expansion of the income gap, it is likely to be caused by the recession of the incentive effect on the consumption demand made by the increasing income level. In other words, the mean effect of the income distribution change has not been fully released in the markets. Therefore, we now discuss why the mean effect is weakened.

Based on the previous results, we further summarize the influence direction of the mean and variance effects on a fixed commodity when the different groups from high to low income levels pass through a fixed commodity market (Table 5). For simplicity, assume that there are only low, medium, and high income groups, the income distribution changes as shown in Figure 2, both the income mean and the variance increase, and there are the following four cases:



**Table 5.** The Influence Direction of the Mean and Variance Effects on a Fixed Commodity.

Note: The symbol "+" indicates a positive effect, and "−" indicates a negative effect.

We use the summary in Table 5, combined with the information in Figure 4 and Table 4, to help us give the reasons below for the diminishing mean effect.

First, it can be seen from Table 4 that many of the expenditure items are in Case 3 and Case 4 in Table 5; that is, most commodities are no longer the core consumer choice of the middle and above income families, and their market demand has begun to decline. This reflects the irrationality of the supply-side structure, whereby there is an excess supply of low-end products but a shortage caused by the targeted consumption that cannot be met in a timely manner. Therefore, the mean effect is weakened and the market demand cannot be fully released.

Second, the rapid rise in house prices after 2000 may have inhibited the release of the mean effect. Campbell and Cocco [53] believed that housing prices may make some residents "save for buying a house" and thereby reduce their consumption. Figure 4 shows that the effect of the variance on the living consumption is positive and has a tendency to strengthen. Table 4 further confirms this result. At the same time the mean effect on the living consumption is changed from positive to negative, but it should be noted that this is not the corresponding case 3 in Table 5, which reflects the plight that the middle-income people face when entering the housing market. After the reform of the real estate market in 1998, the increase in the mean and variance of the income in the first stage played a catalytic role in helping high-income families to own one house, and the real estate market soon became overheated. Due to the speculative properties of housing, some high-income people changed from being consumers to becoming speculators, which led to the emergence of a real estate bubble. In this environment house prices are rising at a speed far faster than the improving speed of the average income, and the threshold of residential consumption continues to increase. Middle-income families are trapped in residential consumption, which greatly hurts their enthusiasm for consumption. They have to passively save in order to buy a house, so ultimately the mean effect is suppressed, not only in respect of residential consumption but also in respect of other consumption.

Finally, the decline in the mean effect may also be related to the macroeconomic system, such as the price system, industrial policy, financial policy, and other factors ignored by the model. These factors all need to be considered in the next step to expand domestic demand.

The results of this study can also explain the phenomenon of why some individual market demand appears hot in turns. As the mean effect is in a state of inhibition, the potential consumption capacity of the residents has not been fully released, and China's research and development ability for new products is weak, so the consumer structure often reflects "passive" upgrade characteristics when its development has reached a certain level. Once a new product meets the needs of the market, the mean effect and variance effect both will immediately promote the rapid growth of demand and lead to the phenomenon of a local hot market. Furthermore, it is then easier for enterprises to form unified short-term expectations, which will led to investment "wave phenomena" [54] and overcapacity.

#### **6. Conclusions and Policy Implications**

Inadequate domestic demand in recent years has always retarded the sustainable growth of China's economy, but the emergence of a series of local hot markets shows that it is essentially a structural problem, so it is necessary to analyze the problem of insufficient domestic demand from the perspective of the consumption demand structure. The dramatic changes in the income distribution of the residents can be said to be one of the most significant social characteristics in China since the reform, and it is also a very important factor for consumption. Therefore, this study analyzes the problem of insufficient domestic demand in China from the perspective of the effect of the income distribution on the change of the consumption structure. The main contributions of this study are summarized as follows:

First, according to the characteristics of the consumption behavior of the Chinese residents, combined with the process of anti-fact analysis of the income distribution changes, the AIDS model is extended, and the income distribution and consumption structure are placed in a model, which provides a new idea about how to study the transformation of the demand structure. The empirical results of this study are in full compliance with China's economic development practice, by which the reliability of the model is proved.

Second, the results show that the mean effect is the largest effect in all kinds of consumption, by which the size and direction of the total effect is basically determined. The variance effect is much smaller than that of the mean, but it still has some positive effects on the individual markets, such as the promotion of the demand for services, which represents the future trend of the demand structure. The residual effect is the smallest and has a certain individual randomness.

Finally, the discussion is more rational and comprehensive. In contrast to the view that the income gap leads to the insufficient domestic demand, this study argues that the income gap is not the main reason for the lack of domestic demand since 2000, but is likely to be caused by the decline of the mean effect made by the income distribution change on the market demand. There are two reasons for the failure of the mean effect: on the one hand there is the irrationality of the supply side, and on the other hand there are excessive house prices that inhibit the full release of the mean effect, which leaves most of the middle class facing a housing consumption dilemma.

Furthermore, the results of this study can also explain the phenomenon of the local hot market. As the mean effect is in a state of inhibition and China's research ability for new products is weak, the consumer structure reflects "passive" upgrade characteristics, which lead to strong consumer synchronization. Once a new product meets the needs of the market, the mean effect and variance effect will both immediately promote the rapid growth of demand and lead to the phenomenon of a local hot market.

Therefore, in the process of expanding the domestic demand, the following points should be noted. (1) In the early stages of the formation of a new consumption structure, it can be helpful to objectively treat the expansion of the income variance and control and maintain the appropriate income gap so that the positive role played by the variance effect and residual effect of the income distribution change can be fully exploited. (2) Due to the relative hysteresis of the supply structure, taking into account the imperfection of the market, entirely relying on the market mechanism to reduce the supply of surplus products is not realistic. There is still a need for the government to correct and improve the market exit mechanism in the short term in order to avoid unnecessary production [8]. Improving the innovation ability can not only make the economy realize a consumption-driven transformation, thereby fundamentally solving the problem of insufficient domestic demand, but it can also can alleviate the excess capacity caused by the "investment boom." (3) The excessive growth of house prices should be controlled to avoid its weakening impact on the mean effect. This should be accomplished by emphasizing the consumption characteristics of housing, curbing speculative demand, and improving the financial credit system to help the middle class to overcome the current consumption dilemma. (4) Advocating moderate consumption. The results of this study show that the current expansion of income variance has a positive effect on consumption, which is likely to lead to the aggravation of consumption inequality. Therefore, we should guard against irrational overconsumption, which is also not conducive to the sustainability of the economy. Experience shows that Latin American countries caught in the middle-income trap are not under-consuming, but over-consuming. So is it possible for China to have "insufficient overall consumption and excessive consumption of high-income groups" in the future? This maybe a more difficult problem related to the sustainability of economic growth. To solve this problem, we may need not only the guidance of economics, but also other fields, such as psychology, to help forming a reasonable consumption concept in Chinese society.

**Author Contributions:** Conceptualization, P.S.; Data curation, C.Y. and X.F.; Formal analysis, X.J.; Funding acquisition, P.S.; Investigation, X.J. and X.F.; Methodology, P.S. and C.Y.; Project administration, P.S.; Resources, T.W.; Software, T.W.; Writing – review & editing, T.W.

**Funding:** This research was funded by ""Double-First Class" Initiative Key Program of China University of Mining and Technology, grant number 2018WHCC07".

**Acknowledgments:** We thank International Science Editing (http://www.internationalscienceediting.com) for editing this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
