**5. Empirical Results and Discussion**

### *5.1. The Counter-factual Decomposition of Income Distribution*

From the non-parametric kernel density estimation results of the residents' income distribution (Figure 2, source: [1]), we can see that the income level and the income gap have both changed significantly, and the domestic scholars Sun and Su [31] show that the growth in the income level is dominant. Therefore, if we do not consider the growth in income when discussing the lack of demand, it is bound to exaggerate the negative impact of the income gap and thereby add fuel to the controversy mentioned earlier.

**Figure 2.** Non-parametric Kernel Density Estimation Results of Income Distribution.

Based on the counter-factual decomposition method of Jenkins and Van Kerm [33], the nonparametric kernel density decomposition is estimated for the per capita disposable income of the urban residents in 30 provinces. The results of the decomposition of the income distribution between the other two years are consistent, so we only take the 2005–2006 group in the middle of the study period as an example (Figure 3). The graph is in the form of a probability density curve, which is fitted according to the counter-factual income variables of each province.

**Figure 3.** Decomposition of Income Distribution Changes during 2005–2006.

From the results we can see that the mean change is the dominant effect, the variance change is the second-most dominant effect, and the residual change is the smallest. Furthermore, the mean change is basically always consistent with the total change, whereas the variance and the residual change are opposite to the mean change before income 11910, then consistent with the mean change, and the residual change is slightly ahead of the variance change. It can be speculated that if the shortage of domestic demand is indeed caused by the income factors, focusing only on the income gap may not be comprehensive, because it is not the main feature of the income distribution changes. Therefore, it is necessary to rethink the problem from the whole feature of the change in the income distribution.
