Industrial robot employment analysis modeling method based on bidirectional fixed effect model

Abstract

The invention relates to the technical field of employment influence analysis modeling, in particular to an industrial robot employment analysis modeling method based on a bidirectional fixed effect model, which comprises the following steps of: 1, performing non-observation variable significance test, and detecting whether time and regional quality characteristics are significant or not according to F test and R2 test; 2, determining a core variable, selecting industrial robot fixed investment as a core independent variable, and taking the average number of employees in each industry of the manufacturing industry as a core dependent variable; and 3, solving the selected reference industry coefficient by using a bidirectional fixed effect model. And 4, introducing interaction items of other industries (except the reference industry) to research differences among the industries. And 5, checking and summarizing a model calculation result. According to the method, the P values corresponding to the industries are divided and classified into three classes of significant positive correlation, low correlation and significant negative correlation, and the common points of the same class of industries are analyzed from three aspects of production flow, technical requirements and labor force structures, so that guiding significance is generated.

Description

Technical Field

[0001] This invention relates to the field of employment impact analysis and modeling technology, and in particular to a method for employment analysis and modeling of industrial robots based on a two-way fixed effects model. Background Technology

[0002] In the process of accelerating digital and intelligent transformation of global manufacturing, industrial robots, as a key carrier of advanced manufacturing technology, are profoundly reshaping the industrial landscape through their widespread adoption across various industries. With their characteristics such as automatic positioning and control, reprogrammability, and multi-degree-of-freedom operation, industrial robots offer advantages in flexible production processes that are difficult for humans to match, becoming an important means for enterprises to improve production efficiency, enhance product quality stability, and reduce production costs. As the world's largest industrial robot market, China held a 47% market share in 2024, with sales continuing to grow. In the first half of 2024, sales reached 140,000 units, a year-on-year increase of approximately 5%. In core manufacturing sectors such as automobile manufacturing, electronics, metal products, plastics, and chemical products, industrial robots have been deeply integrated into production processes.

[0003] The large-scale introduction of industrial robots has inevitably had a significant impact on the labor market. At the employment structure level, low-skilled jobs with repetitive and predictable patterns are the first to be affected. According to relevant statistics and forecasts, by 2030, hundreds of millions of jobs worldwide will disappear due to robots and AI technologies. In terms of skills demand, the manufacturing industry's skill requirements for labor have undergone a disruptive transformation. Jobs that previously relied on physical labor and simple operational skills are gradually decreasing, replaced by a strong demand for highly skilled personnel with expertise in robot programming, maintenance, and system management. Analyzing the impact of industrial robot introduction on employment across various sectors of the manufacturing industry is challenging due to the significant temporal and regional heterogeneity of these factors, leading to inaccurate analyses. Currently known models have extensively analyzed this issue across major industrial categories, but research in the manufacturing sector lacks data foundations that utilize robot density and penetration. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a modeling method for industrial robot employment analysis based on a two-way fixed effects model. Through innovative modeling, the analysis of the impact of the introduction of industrial robots on employment in various manufacturing industries is made more accurate, and the analysis of the calculation results can provide employment guidance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A modeling method for employment analysis of industrial robots based on a two-way fixed effects model includes the following steps:

[0007] Step 1: Significance test of unobserved variables, based on F-test and R-test. 2 The test examines whether the differences in testing time and regional heterogeneity are significant, and then decides whether it is necessary to control for time fixed effects and regional fixed effects.

[0008] Step 2: Determine the core variables, selecting fixed investment in industrial robots as the core independent variable and the average number of employees in various manufacturing industries as the core dependent variable.

[0009] Step 3: Solve for the selected benchmark industry coefficients using a two-way fixed effects model;

[0010] Step 4: Introduce interaction terms from other industries (excluding the benchmark industry) to study the differences between industries;

[0011] Step 5: Verification and summary of model calculation results. The calculation results are verified using the F-test. Based on the P-values ​​of each industry, they are classified into three categories: significantly positively correlated, weakly correlated, and significantly negatively correlated. The commonalities of the same category of industries are analyzed from three levels: production process, technology demand, and labor structure, thereby generating guidance.

[0012] Preferably, step 1 includes the following steps:

[0013] The F-test demonstrates that region has a significant impact on the explanatory variables, thus illustrating the necessity of controlling for region effects. The null hypothesis H0 is established: all region fixed effects are zero, meaning region has no significant impact on the explanatory variables. The blame hypothesis H1 is established: at least one region fixed effect is not zero and has a significant impact on the explanatory variables. The F-statistic is constructed as follows:

[0014]

[0015] Where i is the number of regions, n is the total number of regional observations in the sample, and t is the number of explanatory variables other than regional fixed effects, such as time fixed effects. U It is the sum of squared residuals of the unconstrained model, that is, the sum of squared residuals without including regional fixed effects. It is the residual sum of squares constrained by the model, and the residual sum of squares after adding regional fixed effects.

[0016] R 2 The test combined with the F-test is used to demonstrate that time has a significant effect on the variable, thus illustrating the necessity of controlling for the time effect. The formula for calculating the F-statistic is the same as the one above, R0. 2 The formula for the test is:

[0017]

[0018] Where SSE is the residual sum of squares, SST is the total residual sum of squares, SSR is the regression sum of squares, and the coefficient of determination R is... 2 The value ranges from 0 to 1, R 2 A value close to 1 indicates a higher correlation between variables in the model, suggesting a more significant impact of time on the variables.

[0019] Preferably, step 3 includes the following steps:

[0020] Model setting

[0021] Suppose we have a linear regression model. For n observations, the model can be expressed as:

[0022] y i =β0+β1x i1 +β2x i2 +L+β k x ik +ε i i = 1, 2, ..., n

[0023] Among them, y i The dependent variable, i.e., the explained variable, is the i-th observation; β0, β1, K, β k The unknown parameter that needs to be estimated is β0, where β0 is the intercept term and x is the independent variable. ij coefficient; x i1 ,x i2 ,K,x ik ε is the independent variable, i.e., the explanatory variable, of the i-th observation; i This is the random error term, representing the portion not explained by the model, and is usually assumed to have ε. i The mean is 0, i.e., E(ε) i ) = 0, and have the same variance; the error terms of different observations are independent of each other, i.e., Cov(ε) = 0. i ,ε j If ) = 0, i ≠ j, this model can be represented more concisely in matrix form. Let:

[0024]

[0025] The linear regression model can then be written as: y = Xβ + ∈

[0026] Calculation of the sum of squares of differences

[0027] For the i-th observation, the residual e i Defined as the observed value y i Compared with model predictions The difference between them, i.e. in Based on the parameter estimates of y iThe prediction, the Sum of Squared Residuals (SSR), is the sum of the squares of the residuals of all observations, expressed by the formula:

[0028] Represented as a matrix: SSR=(y-Xβ) T (y-Xβ), where (·) T Represents the transpose of a matrix;

[0029] Sum of squared residuals

[0030] The goal of the least squares method is to find a set of parameter estimates. Minimizing the sum of squared residuals (SSR) is an optimization problem that can be solved by taking the partial derivative of SSR with respect to β and setting the partial derivative to 0.

[0031] Parameter estimates

[0032] If the matrix is ​​X T For X to be invertible, it is usually required that there is no perfect linear correlation between the independent variables, i.e., the full rank condition. Then, multiplying both sides of the normal equation system by (X) on the left is sufficient. T X) -1 The least squares estimate of parameter β is obtained: This is how it was obtained. It is the parameter estimate that minimizes the sum of squared residuals.

[0033] Preferably, in step 4, an industry dummy variable D is introduced. j • ln(y) is used to construct interaction terms to capture the mathematical relationship between fixed investment in industrial robots and the number of employees in different industries;

[0034] The final model is determined as follows:

[0035]

[0036] Among them, industry k in region i and year t is the fixed investment in industrial robots (Robot_invest). itk Average number of employees in the manufacturing industry in region i and year t itk Industry dummy variable D j ·ln(Robot_invest itk ) represents the interaction term, determined by the interaction term coefficient γ. j Capturing the coefficient differences across industries, the intercept term β1 reflects the relationship between the baseline group's industry dependent variable and the core independent variable when the interaction term is included. The variable λ... t To account for the time fixed effect and control for cross-year effects such as time trends and macroeconomic fluctuations, the variable μ is used. i This indicates that regional fixed effects control over unobservable differences in regional characteristics such as policies and resource endowments, εitk This is the random error term.

[0037] Preferably, in step 5, the result analysis is as follows:

[0038] According to the F-test, when P≤0.15, the probability of the result falling within the numerical range of significant correlation is greater than 85%, indicating a significant correlation between fixed asset investment in industrial robots and the number of employees in the manufacturing industry. When P>0.15, it can be considered that there is no significant correlation.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. This invention uses the fixed investment cost of industrial robots (robot fixed investment) to reflect the introduction of industrial robots, and conducts direct analysis at the capital investment level; it uses the average number of employees in various manufacturing industries to reflect the employment situation.

[0041] 2. This invention utilizes the F-test and R-test. 2 Implementation of the test: The F-test is used to test the significance of regional heterogeneity; the F-test and R... 2 Test combinations are used to achieve significance testing for time-dependent heterogeneity.

[0042] 3. This invention selects a benchmark industry and uses a two-way fixed effects model to calculate the relationship between the introduction of industrial robots and employment in the benchmark industry. Based on the two-way fixed effects model, it optimizes the model by introducing interaction terms and analyzing the relative relationship between other industries and the benchmark industry, thereby further studying the mathematical relationship between the introduction of industrial robots and employment in various industries. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0044] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0045] Example:

[0046] A modeling method for employment analysis of industrial robots based on a two-way fixed effects model includes the following steps:

[0047] Step 1: Significance test of unobserved variables, based on F-test and R-test.2 The test examines whether the differences in testing time and regional heterogeneity are significant, and then decides whether it is necessary to control for time fixed effects and regional fixed effects.

[0048] Step 2: Determine the core variables, selecting fixed investment in industrial robots as the core independent variable and the average number of employees in various manufacturing industries as the core dependent variable.

[0049] Step 3: Solve for the selected benchmark industry coefficients using a two-way fixed effects model;

[0050] Step 4: Introduce interaction terms from other industries (excluding the benchmark industry) to study the differences between industries;

[0051] Step 5: Verification and summary of model calculation results. The calculation results are verified using the F-test. Based on the P-values ​​of each industry, they are classified into three categories: significantly positively correlated, weakly correlated, and significantly negatively correlated. The commonalities of the same category of industries are analyzed from three levels: production process, technology demand, and labor structure, thereby generating guidance.

[0052] Specifically, step 1 includes the following steps:

[0053] The F-test demonstrates that region has a significant impact on the explanatory variables, thus illustrating the necessity of controlling for region effects. The null hypothesis H0 is established: all region fixed effects are zero, meaning region has no significant impact on the explanatory variables. The blame hypothesis H1 is established: at least one region fixed effect is not zero and has a significant impact on the explanatory variables. The F-statistic is constructed as follows:

[0054]

[0055] Where i is the number of regions, n is the total number of regional observations in the sample, and t is the number of explanatory variables other than regional fixed effects, such as time fixed effects. U It is the sum of squared residuals of the unconstrained model, that is, the sum of squared residuals without including regional fixed effects. It is the residual sum of squares constrained by the model, and the residual sum of squares after adding regional fixed effects.

[0056] Generally, the larger the statistic, the more likely it is to reject the null hypothesis. This strongly rejects the null hypothesis H0, which states that the fixed effects for all individuals are zero.

[0057] R 2 The test combined with the F-test is used to demonstrate that time has a significant effect on the variable, thus illustrating the necessity of controlling for the time effect. The formula for calculating the F-statistic is the same as the one above, R0. 2 The formula for the test is:

[0058]

[0059] Where SSE is the residual sum of squares, SST is the total residual sum of squares, SSR is the regression sum of squares, and the coefficient of determination R is... 2 The value ranges from 0 to 1, R 2 A value close to 1 indicates a higher correlation between variables in the model, suggesting a more significant impact of time on the variables.

[0060] Specifically, step 3 includes the following steps:

[0061] Model setting

[0062] Suppose we have a linear regression model. For n observations, the model can be expressed as:

[0063] y i =β0+β1x i1 +β2x i2 +L+β k x ik +ε i i = 1, 2, ..., n

[0064] Among them, y i The dependent variable, i.e., the explained variable, is the i-th observation; β0, β1, K, β k The unknown parameter that needs to be estimated is β0, where β0 is the intercept term and x is the independent variable. ij coefficient; x i1 ,x i2 ,K,x ik ε is the independent variable, i.e., the explanatory variable, of the i-th observation; i This is the random error term, representing the portion not explained by the model, and is usually assumed to have ε. i The mean is 0, i.e., E(ε) i ) = 0, and have the same variance; the error terms of different observations are independent of each other, i.e., Cov(ε) = 0. i ,ε j If ) = 0, i ≠ j, this model can be represented more concisely in matrix form. Let:

[0065]

[0066] The linear regression model can then be written as: y = Xβ + ∈

[0067] Calculation of the sum of squares of differences

[0068] For the i-th observation, the residual e i Defined as the observed value y i Compared with the model's predicted value y i The difference between them, i.e. in Based on the parameter estimates of y iThe prediction, the Sum of Squared Residuals (SSR), is the sum of the squares of the residuals of all observations, expressed by the formula:

[0069] Represented as a matrix: SSR=(y-Xβ) T (y-Xβ), where (·) T Represents the transpose of a matrix;

[0070] Sum of squared residuals

[0071] The goal of the least squares method is to find a set of parameter estimates. Minimizing the sum of squared residuals (SSR) is an optimization problem that can be solved by taking the partial derivative of SSR with respect to β and setting the partial derivative to 0.

[0072] Parameter estimates

[0073] If the matrix is ​​X T For X to be invertible, it is usually required that there is no perfect linear correlation between the independent variables, i.e., the full rank condition. Then, multiplying both sides of the normal equation system by (X) on the left is sufficient. T X) -1 The least squares estimate of parameter β is obtained: This is how it was obtained. It is the parameter estimate that minimizes the sum of squared residuals.

[0074] Specifically, in step 4, an industry dummy variable D is introduced. j • ln(y) is used to construct interaction terms to capture the mathematical relationship between fixed investment in industrial robots and the number of employees in different industries;

[0075] The final model is determined as follows:

[0076]

[0077] Among them, industry k in region i and year t is the fixed investment in industrial robots (Robot_invest). itk Average number of employees in the manufacturing industry in region i and year t itk Industry dummy variable D j ·ln(Robot_invest itk ) represents the interaction term, determined by the interaction term coefficient γ. j Capturing the coefficient differences across industries, the intercept term β1 reflects the relationship between the baseline group's industry dependent variable and the core independent variable when the interaction term is included. The variable λ... t To account for the time fixed effect and control for cross-year effects such as time trends and macroeconomic fluctuations, the variable μ is used. i This indicates that regional fixed effects control over unobservable differences in regional characteristics such as policies and resource endowments, εitk This is the random error term.

[0078] Specifically, in step 5, the results are analyzed as follows:

[0079] According to the F-test, when P ≤ 0.15, the probability of the result falling within the significantly correlated range is greater than 85%, indicating a significant correlation between fixed asset investment in industrial robots and manufacturing employment in that industry. Conversely, when P > 0.15, no significant correlation can be considered. Based on the above criteria and combined with… Figure 1 The calculation results are used to classify and categorize various industries, summarizing them from three aspects: production process, technological requirements, and labor structure, providing a basis for employment policies in various sectors of the domestic manufacturing industry.

[0080] After an F-test, the following industries showed P > 0.15, meaning there was insufficient evidence to suggest a significant linear correlation between fixed asset investment in industrial robots and employment. Therefore, it cannot be concluded that changes in industrial robots significantly lead to changes in employment. (See Table 1.)

[0081] Table 1 shows industries with no significant linear correlation.

[0082]

[0083] The practical significance of this study will now be analyzed from three perspectives:

[0084] At the production process level, these industries have been hampered by special factors that limit the scale and speed of robot application in the production process. As a result, the application of robots is unlikely to have a widespread and direct impact on employment, and its impact on the number of employees does not show a significant correlation.

[0085] From a technological perspective, the technological needs are unique, and robotics technology is not the core driving factor. Therefore, the increased investment in robotics does not significantly boost or replace employment.

[0086] At the level of labor force structure, the stability of the labor force structure is protected or limited by industry characteristics.

[0087] The p-values ​​for the remaining industries are all <0.15, according to β0+γ in Table 2. i The value represents the change in the average number of employees in the industry for every 100 million yuan increase in fixed investment in robots; a negative value indicates that the average number of employees in the industry is decreasing as fixed investment in robots increases, indicating a significant substitution effect; a positive value indicates that the average number of employees in the industry is increasing as fixed investment in robots increases, indicating a significant complementary effect.

[0088] Industries with a significant positive correlation: The introduction of industrial robots in these industries has a significant complementary effect, meaning that an increase in fixed investment in robots or an increase in the number of robots can significantly lead to an increase in the labor force. As shown in Table 2:

[0089] Table 2 Industries with Significant Positive Correlation

[0090]

[0091] Analyzing its practical significance from three perspectives:

[0092] The production process is relatively continuous and has a certain scale effect. The continuous production process facilitates the efficient operation of robots. When increasing output, more personnel are needed to participate in subsequent links such as production management and maintenance. These industries often have a large number of repetitive and regular production steps. As the fixed investment in robots increases, new robot equipment can be integrated into the existing production system, expand the production scale, and create more new jobs.

[0093] Technological demands create a continuous and relatively clear need for robotics, with a wide range of application scenarios. Enterprises are constantly introducing advanced robotics technologies to improve production efficiency and product quality, which creates demand for skilled personnel in robot operation, programming, and maintenance, thereby increasing employment.

[0094] The labor force structure possesses a degree of flexibility, providing room for employment growth. People with different skill levels can find corresponding positions in the robot application industry chain. It can absorb low-skilled workers who have been trained to perform simple robot-assisted tasks, while also requiring highly skilled technical personnel for the management and optimization of robot systems. This diversified labor demand structure means that as fixed investment in robots increases, the number of people employed at all skill levels can potentially increase.

[0095] Industries with a significant negative correlation include instrumentation and cultural and office machinery manufacturing, and chemical fiber manufacturing. The introduction of industrial robots in these industries has a significant substitution effect; that is, an increase in fixed asset investment in robots or an increase in their number will significantly inhibit labor input. (See Table 3.)

[0096] Table 3. Industries with Significant Negative Correlation

[0097]

[0098] Similarly, we will analyze its practical significance from three perspectives:

[0099] In these industries, production processes may involve many complex, intricate steps that can be highly replaced by robots. With increased investment in robots, their high precision and efficiency can significantly reduce manual labor, leading to a decrease in employment.

[0100] Companies with high technology needs may be in a relatively mature stage of applying robotics technology, and the introduction of robots is primarily aimed at reducing costs and improving quality and stability. At this stage, companies require fewer workers and focus more on the management and maintenance of robots by a small number of highly skilled personnel, resulting in an overall decrease in employment.

[0101] The large proportion of low-skilled jobs in the labor force structure, coupled with the difficulty of job transitions, has led to a decrease in the number of employed workers. Workers who previously relied heavily on low-skilled, repetitive labor are now the first to be replaced by the increased investment in robots. The number of newly added high-skilled jobs is insufficient to compensate for the loss of low-skilled jobs, resulting in a negative correlation between the number of employed workers and the overall workforce.

[0102] In summary, this invention, through innovative modeling, enables a more accurate analysis of the impact of the introduction of industrial robots on employment across various manufacturing sectors.

[0103] The descriptions and practices disclosed in this invention are readily apparent and understandable to those skilled in the art, and various modifications and refinements can be made without departing from the principles of this invention. Therefore, any modifications or improvements made without departing from the spirit of this invention should also be considered within the scope of protection of this invention.

Claims

1. A modeling method for industrial robot employment analysis based on a two-way fixed effects model, characterized in that, Includes the following steps: Step 1: Significance test of unobserved variables, based on F-test and R-test. 2 The test examines whether the differences in testing time and regional heterogeneity are significant, and then decides whether it is necessary to control for time fixed effects and regional fixed effects. Step 2: Determine the core variables, selecting fixed investment in industrial robots as the core independent variable and the average number of employees in various manufacturing industries as the core dependent variable. Step 3: Solve for the selected benchmark industry coefficients using a two-way fixed effects model; Step 4: Introduce interaction terms other than the benchmark industry to study the differences between industries; Step 5: Verification and summary of model calculation results. The calculation results are verified using the F-test. Based on the P-values ​​of each industry, they are classified into three categories: significantly positively correlated, weakly correlated, and significantly negatively correlated. The commonalities of the same category of industries are analyzed from three levels: production process, technology demand, and labor structure, thereby generating guidance.

2. The industrial robot employment analysis modeling method based on a two-way fixed effects model according to claim 1, characterized in that, Step 1 includes the following steps: The F-test demonstrates that region has a significant impact on the explanatory variables, thus illustrating the necessity of controlling for the region effect. Null hypothesis H0: All regional fixed effects are zero, meaning regions have no significant impact on explanatory variables; Blame hypothesis H1: At least one regional fixed effect is not zero and has a significant impact on explanatory variables; Construct the F-statistic: Where i is the number of regions, n is the total number of region observations in the sample, t is the number of time fixed effect explanatory variables excluding region fixed effects, and SSR U It is the sum of squared residuals of the unconstrained model, that is, the sum of squared residuals without including regional fixed effects. It is the residual sum of squares constrained by the model, and the residual sum of squares after adding regional fixed effects; R 2 The test combined with the F-test is used to demonstrate that time has a significant effect on the variable, thus illustrating the necessity of controlling for the time effect. The formula for calculating the F-statistic is the same as the one above, R0. 2 The formula for the test is: Where SSE is the residual sum of squares, SST is the total residual sum of squares, SSR is the regression sum of squares, and the coefficient of determination R is... 2 The value ranges from 0 to 1, R 2 A value close to 1 indicates a higher correlation between variables in the model, suggesting a more significant impact of time on the variables.

3. The industrial robot employment analysis modeling method based on a two-way fixed effects model according to claim 1, characterized in that, Step 3 includes the following steps: Model setting Suppose we have a linear regression model, for n observations, the model can be expressed as: y i =β0+β1x i1 +β2x i2 +L+β k x ik +e i ,i=1,2,L,n Among them, y i The dependent variable, i.e., the explained variable, is the i-th observation; β0, β1, K, β k The unknown parameter that needs to be estimated is β0, where β0 is the intercept term and x is the independent variable. ij coefficient; x i1 ,x i2 ,K,x ik ε is the independent variable, i.e., the explanatory variable, of the i-th observation; i This is the random error term, representing the portion not explained by the model. Let ε be an example. i The mean is 0, i.e., E(ε) i ) = 0, and have the same variance; the error terms of different observations are independent of each other, i.e., Cov(ε) = 0. i ,ε j Let ) = 0, i ≠ j, and represent this model in matrix form by letting: The linear regression model can then be written as: y = Xβ + ∈ Calculation of the sum of squares of differences For the i-th observation, the residual e i Defined as the observed value y i Compared with model predictions The difference between them, i.e. in Based on the parameter estimates of y i The prediction, the sum of squared residuals (SSR), is the sum of the squares of the residuals of all observations, expressed by the formula: Represented as a matrix: SSR=(y-Xβ) T (y-Xβ), where (·) T Represents the transpose of a matrix; Sum of squared residuals The goal of the least squares method is to find a set of parameter estimates. To minimize the sum of squared residuals (SSR), we can solve this by taking the partial derivative of SSR with respect to β and setting the partial derivative to 0. Parameter estimates If the matrix is ​​X T For X to be invertible, there must be no perfect linear correlation between the independent variables, i.e., a full-rank condition. Therefore, multiplying both sides of the normal equation system by (X) on the left... T X) -1 The least squares estimate of parameter β is obtained: This is how it was obtained. It is the parameter estimate that minimizes the sum of squared residuals.

4. The industrial robot employment analysis modeling method based on a two-way fixed effects model according to claim 1, characterized in that, In step 4, an industry dummy variable D is introduced. j • ln(y) is used to construct interaction terms to capture the mathematical relationship between fixed investment in industrial robots and the number of employees in different industries; The final model is determined as follows: Among them, industry k in region i and year t is the fixed investment in industrial robots (Robot_invest). itk Average number of employees in the manufacturing industry in region i and year t itk Industry dummy variable D j ·ln(Robot_invest itk ) represents the interaction term, determined by the interaction term coefficient γ. j Capturing the coefficient differences across industries, the intercept term β1 reflects the relationship between the baseline group's industry dependent variable and the core independent variable when the interaction term is included. The variable λ... t To control for the time fixed effect and the cross-year impact of time trends and macroeconomic fluctuations, the variable μ is used. i This indicates that regional fixed effects control for unobservable differences in regional characteristics such as policy and resource endowment, ε itk This is the random error term.

5. The industrial robot employment analysis modeling method based on a two-way fixed effects model according to claim 1, characterized in that, In step 5, the results are analyzed: According to the F-test, when P≤0.15, the probability of the result falling within the numerical range of significant correlation is greater than 85%, indicating a significant correlation between fixed asset investment in industrial robots and the number of employees in the manufacturing industry. When P>0.15, it can be considered that there is no significant correlation.

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