## 2 Analytical Framework  
The expression \"employment multiplier\" refers to the speed and effect of change in the non-tradable sector brought about by the change in the trade sector. Therefore, it includes both positive and negative aspects. However, most of the multipliers mentioned in the current literature show the positive promotion effect brought about by the growth of the trade or manufacturing sector [23; 28; 32]. [PERSON] argues that the employment multiplier goes beyond a single positive effect to take a more interesting and complex form. This effect is mainly reflected in the process of urban contraction and recession [33]. When jobs in the trade sector are lost, the change rate of total urban employment is different from that of non-tradable sector employment. Economists believe that the rate of change caused by employment increases and decreases in the non-tradable sector is different from that of the trade sector [31]. There are different degrees of effects in creating and reducing trade sector jobs of the same scale within the same city, which means that incorporating all cities into one model would skew the results of the employment multiplier in the presence of shrinking cities. The article combines the multiplier theory with the theory of the urban development stage, and offers the phased view that increases in the trade sector during urban expansion will bring about a significant employment multiplier effect. This is consistent with the results of most studies [20; 21; 27]. When the expansion of a city has gradually slowed to a steady state, the growth rate of the trade sector also slowed. In this state of development, the non-tradable sector will no longer grow in multiplier form, and the two sectors may show a negative relationship in terms of growth rate. When a city enters a recession, the tradable and non-tradable sectors are simultaneously reduced. The decline of the tradable sector then leads to the contraction of the non-tradable sector at a different rate than when cities are expanding. As a result, this study found it necessary to distinguish between expanding and shrinking cities in order to calculate a more precise multiplier effect of employment. [PERSON] proposed a theoretical framework to inform our understanding of the urban employment multiplier effect in China. [PERSON] constructed the formation process and influencing factors of the multiplier from the perspective of economics [34]. She argued that the employment multiplier is affected in two ways. The first is the number of times income passes through different cycles, which is the geometric progression. The second is the degree of residents' consumption, which is reflected by the wage-profit ratio, relief-wage ratio, and savings-profit ratio. [PERSON]'s contribution was to construct a complete dynamic analytical framework of employment multipliers from individuals to cities to countries, rather than simply finding the influencing factors. This is of great help for us to analyze the employment multiplier in China, but [PERSON]'s framework is based on the capitalist market economy, and there are differences in how influencing factors express themselves in Chinese cities. A basic theory of the formation of the multiplier is established based on the theory proposed by [PERSON] [34]. The realization of the employment multiplier effect from the trade sector to the local non-trade sector is based on the consumption demand of the production and life of the practitioners in the tradable sector [11; 15]. Manufacturing sector workers earn wage income, which is used for production and consumption, creating effective demand as a result. New Keynesian economics takes the perspective that in a capitalist market, one part of a household's wages is spent while the rest is saved. The consumption aspect influences the urban labor market in two ways. The first part consists of the demands of the entire trade department for related products and services, including innovation, design, advertisement, and law.