Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5, 772-811 2025 Publisher: Learning Gate DOI: 10.55214/25768484.v9i5.7006 © 2025 by the authors; licensee Learning Gate © 2025 by the authors; licensee Learning Gate History: Received: 12 February 2025; Revised: 16 April 2025; Accepted: 18 April 2025; Published: 9 May 2025 * Correspondence: alexander.hernandez@lpu.edu.ph Analysis of the mechanism of price and technological progress on economic fluctuations in resource-based areas: The case of Shanxi, China Zihang Zhao1, Alexander A. Hernandez2* 1Claro M. Recto Academy of Advanced Studies, Lyceum of the Philippines University, Manila, Philippines; zihang.zhao@lpunetwork.edu.ph (Z.Z.) 2Information Technology Department, College of Technology, Lyceum of the Philippines University, Manila, Philippines; alexander.hernandez@lpu.edu.ph (A.A.H.) Abstract: This paper draws on the theory of the monetary economic cycle and the theory of the real economic cycle, constructs a theoretical model of economic fluctuations in resource-based regions that takes price levels and technological progress into consideration, analyzes the mechanism of the effect of price levels and technological progress on economic fluctuations in resource-based regions, and derives the key equation of the effect of the two on economic fluctuations. Then, taking Shanxi data as an example, the key equation is verified, and the Shanxi economy is analyzed through two econometric model methods, namely the time series threshold regression model and the Zou test, in two cases of static expectations and rational expectations. The necessity and path of the government's active regulation of economic transformation are proposed. Keywords: Economic fluctuations, Price level, Rational expectations, Static expectations, Technological progress. 1. Introduction After more than 40 years of reform and opening up, China's economy has developed rapidly and has become the world's second largest economy. While the economy is growing, it has also led to a significant increase in demand for resources, which has driven the development of some regions that rely on abundant natural resources. Although these resource-rich regions have achieved rapid economic development by relying on extensive resource exploitation and utilization, they have also formed a resource-dependent economy. During economic prosperity, the prices of resource products are high, and the generous returns and low investment costs attract a large number of production factors to flow into resource-based enterprises, driving the rapid development of resource-based industries and economic prosperity; during economic downturns, in response to supply chain shocks and inflation [1] commodity price fluctuations [2] and falling resource prices [3] resource-based economies have long relied on this development path, resulting in the inability or difficulty of regional industry transformation, thus triggering an economic downturn. At the same time, during the prosperity of resource-based industries, a large amount of capital flowed into resource-based enterprises, making it difficult for other industries to develop, or simply transforming and investing in the development of resource-based industries [4]. This has led to an imbalance in the local industrial structure, difficulty in developing manufacturing, and the inability to produce many non-resource products independently, which need to be imported from outside the province [5]. In addition, the long-term resource- dependent economic development model is unsustainable [6]. The first reason is that these resources are non-renewable and will cause irreversible environmental pollution during the mining process [7]. Second, economies that rely on resources for development for a long time may fall into the "resource curse", which will eventually lead to an imbalance in the industrial structure and stagnation in economic growth [8]. Resource price fluctuations cause price changes in resource-based regions, which in turn 773 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate affect economic fluctuations in resource-based regions [9]. Therefore, resource-based regions need to transform and upgrade, change their original development model, and achieve sustainable economic development [10]. 2. Hypothesis Development The research framework of this paper is as follows： Figure 1. The research sequence diagram of this paper. This paper will adopt the method of quantitative analysis. At the beginning, this paper first introduces the basic concepts and related theories, and then uses the formula provided by the theory to deduce the impact of price changes and technological progress on Shanxi's economic fluctuations. At the same time, it deduces how price changes and technological progress will affect Shanxi's economic fluctuations under static expectations and rational expectations. Next, this paper will use the collected data for empirical analysis. Through the time series threshold regression model and Zou test, we will analyze the impact of price changes and technological progress on the fluctuations of Shanxi's economy in different time periods under static expectations and rational expectations. 3. Materials and Methods 3.1. Data The sample data range used in this article is the data of the whole country and Shanxi Province from 1984 to 2024. The basic data used in the calculations in this article come from the "China Statistical Yearbook" and the "Shanxi Province Statistical Yearbook" respectively. The selected data include: China's nominal GDP value from 1984-2024, Shanxi Province's nominal GDP value from 1984- 2024, and above from 1984-2024 The GDP index with the base period of 1984-2024, the regional GDP index of Shanxi Province with the base period of 1984-2024 and the total employment number of Shanxi 774 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Province from 1984-2024. The growth rate of technological progress in Shanxi Province is calculated based on the nominal GDP value of Shanxi Province from 1984 to 2024 in the above data, the regional GDP index of Shanxi Province from 1984 to 2024 with the previous year as the base period, and the total number of employees in Shanxi Province from 1984 to 2024. income. The price level of China and Shanxi Province is calculated from the nominal GDP value of China and Shanxi Province from 1984 to 2024 and the GDP index of China and Shanxi Province from 1984 to 2024 as the base period. 3.2. Data Gathering and Analysis This paper conducted an empirical study on the impact of price and technological progress on economic fluctuations in Shanxi Province [11]. First, the actual economic situation of economic fluctuations in Shanxi Province, a resource-based region, is described. The HP filter method is used to obtain the required relevant data. On the basis of the theoretical model, time series threshold regression, Chow test and OLS regression methods are further used to analyze the impact of price level changes and technological progress in different stages on economic fluctuations in Shanxi Province from the perspectives of static expectations and rational expectations. 4. Results and Discussion 4.1. Supply Curve 4.1.1. Producer Behavior This section will analyze producer behavior and derive the aggregate supply curve based on the actual economic situation and the idea of Lucas's aggregate supply curve [12]. Assume that the total output level of an enterprise is mainly determined by two parts, namely the level of technological progress and labor. Similarly, let Ai represent the technological progress rate of enterprise i, and L i represent the number of employees in enterprise i, then the producer behavior can be expressed as: 𝑌𝑖 = 𝐴𝑖 ⋅ 𝐿𝑖 In the above formula, the increase in fixed assets per capita and the increase in labor productivity per capita caused by pure technological progress are unified as technological shock A. The producer’s profit is: 𝜋𝑖 = 𝑃𝑖𝑌𝑖 − 𝑤𝑖𝐿𝑖 = 𝑃𝑖𝐴𝑖𝐿𝑖 − 𝑤𝑖𝐿𝑖 Pi represents the price of a product produced by enterprise i, and wi is the wage level of the industry. The formula means: the total output value that an enterprise can obtain is the output it produces multiplied by the product price, minus the cost of paying wages to workers is the enterprise's profit. According to the principle of enterprise pursuit of profit maximization, the conditions for enterprise profit maximization are: 𝜕𝜋𝑖 𝜕𝐿𝑖 = 𝑃𝑖𝐴𝑖 − 𝑤𝑖 = 0 Then we can get: 𝑤𝑖 = 𝑃𝑖𝐴𝑖 When the producer can obtain the maximum profit, the wage paid for each unit of labor is equal to the product A produced by a single labor multiplied by the price of the product. 4.1.2. Consumer Behavior Assume that the utility function of consumer i is 𝑈 = 𝐶𝑖 − 1 𝛾 ⋅ 𝐿𝑖 𝛾 ，the function γ＞1 Ci is the consumption of consumer i. Li is the labor provided by the consumer. We know that people often consume a package of goods rather than a single product, so the price paid is not the price of a single product pi, but the social average price level P, then the actual consumption expenditure of consumer i is PCi. The consumer's budget constraint is: 𝑃𝐶𝑖 = 𝑤𝑖𝐿𝑖 775 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate The consumer behavior model for maximizing utility is: max：𝐶𝑖 − 1 𝛾 ⋅ 𝐿𝑖 𝛾 ，γ＞1 𝑠. 𝑡. 𝑃𝐶𝑖 = 𝑤𝑖𝐿𝑖 According to the budget constraint: 𝐶𝑖 = 𝑤𝑖 𝑃 𝐿𝑖 From this, we can get the consumer utility as: 𝑈 = 𝑤𝑖 𝑃 𝐿𝑖 − 1 𝛾 𝐿𝑖 𝛾 4.1.3. Balanced Producer behavior analysis shows that:𝑌𝑖 = 𝐴𝑖 ⋅ 𝐿𝑖，𝑤𝑖 = 𝑃𝑖𝐴𝑖 Consumer behavior analysis shows that:𝑈 = 𝑤𝑖 𝑃 𝐿𝑖 − 1 𝛾 𝐿𝑖 𝛾 Substituting the conclusion of the producer's pursuit of profit maximization behavior analysis into the consumer's pursuit of utility maximization behavior equation, we can obtain the common equilibrium condition of producer and consumer behavior [13]: max：𝑈 = 𝑃𝑖 𝑃 𝑌𝑖 − 1 𝛾 ( 𝑌𝑖 𝐴𝑖 ) 𝛾 The optimization condition is that the derivative about Yi is equal to 0, which gives: 𝑃𝑖 𝑃 − 1 𝛾 𝛾 ( 𝑌𝑖 𝐴𝑖 ) 𝛾−1 = 0 It can be deduced that: 𝑌𝑖 𝐴𝑖 = ( 𝑃𝑖 𝑃 ) 1 𝛾−1 𝑌𝑖 = ( 𝑃𝑖 𝑃 ) 1 𝛾−1 ⋅ 𝐴𝑖 At this time, taking the logarithm of both sides of the equation and then taking the derivative at the same time, the growth rate of output can be expressed as: �̇�𝑖 𝑌𝑖 = 1 𝛾 − 1 ( �̇�𝑖 𝑃𝑖 − �̇� 𝑃 ) + �̇�𝑖 𝐴𝑖 Make 𝑦𝑖 = �̇�𝑖 𝑌𝑖 ，𝑔𝑖 = �̇�𝑖 𝐴𝑖 ，𝑝𝑖 = �̇�𝑖 𝑃𝑖 ，𝑝 = �̇� 𝑃 ，The output change rate can be expressed as: 𝑦𝑖 = 1 𝛾 − 1 (𝑝𝑖 − 𝑝) + 𝑔𝑖 When enterprises in this region make production decisions, they need to rely on the information they have, but the information they have is the price of their own products and they cannot know the overall price level. Therefore, they make an expected judgment on the overall price level based on knowing the price of their own products. The formula is: 𝑦𝑖 = 1 𝛾 − 1 [𝑝𝑖 − 𝐸(𝑝|𝑝𝑖)]𝑔𝑖 At this time, the rate of change of output can be determined by the rate of change of the manufacturer's own price, the conditional expectation value of the rate of change of the social price level and the rate of technological progress [14]. 4.2. Theoretical-Based Analysis Assume that there are n companies in a country. 776 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate According to the Wiener theorem: when people want to observe the random variable x but cannot observe it directly, they will use the already observed economic variable a and the relationship between a and x, a=x+z, to further observe x. That is, given the condition of a, find the mathematical expectation of x: 𝐸(𝑥|𝑎) = 𝜎2 𝜎𝑥 2 + 𝜎𝑎 2 𝑎 Assume that:𝑎 = 𝑝𝑖 − 𝐸(𝑝)，𝑥 = 𝑝 − 𝐸(𝑝)，𝑧 = 𝑝𝑖 − 𝑝 According to Wiener's theorem: 𝐸(𝑥|𝑎) = 𝐸[𝑝 − 𝐸(𝑝)]𝑝𝑖 − 𝐸(𝑝) = 𝜎𝑥 2 𝜎𝑥2 + 𝜎𝑧 2 ⋅ [𝑝𝑖 − 𝐸(𝑝)] It can be deduced that:𝐸[𝑝−𝐸(𝑝)|𝑝𝑖] = 𝜎𝑥 2 𝜎𝑥 2+𝜎2 2 [𝑝𝑖 − 𝐸(𝑝)] 𝐸(𝑝|𝑝𝑖) − 𝐸(𝑝) = 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 [𝑝𝑖 − 𝐸(𝑝)] 𝐸(𝑝|𝑝𝑖) = 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 𝑝𝑖 − 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 𝐸(𝑝) + 𝐸(𝑝) = 𝜎𝑥 2 𝜎𝑥 2+𝜎𝑧 2 𝑝𝑖 + 𝜎𝑥 2 𝜎𝑥 2+𝜎𝑧 2 𝐸(𝑝) From this, we can estimate: 𝐸(𝑝|𝑝𝑖) = 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 𝑝𝑖 + 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 𝐸(𝑝) We can finally get: 𝑦𝑖 = 1 𝛾 − 1 [𝑝𝑖 − 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 𝑝𝑖 −（1 − 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 ）𝐸(𝑝)] + 𝑔𝑖 = 1 𝛾 − 1 ⋅ 𝜎𝑥 2 𝜎𝑥 2 + 𝜎𝑧 2 ⋅ [𝑝𝑖 − 𝐸(𝑝)] + 𝑔𝑖 Among them, let b= 1 𝛾−1 ⋅ 𝜎𝑥 2 𝜎𝑥 2+𝜎𝑧 2＞0 , then the key equation of the final output of the regional representative enterprises is: 𝑦𝑖 = 𝑏 ⋅ [𝑝𝑖 − 𝐸(𝑝)] + 𝑔𝑖 We can get the output growth rate formula of all manufacturers in a country as follows: 𝛴𝑦𝑖 = 𝑏 ⋅ [∑𝑝𝑖 − ∑𝐸(𝑝)] + ∑𝑔𝑖，（i=1，2，…，n） Here, let y represent the growth rate of a country's total output, which is the average of the output growth rates of various manufacturers, p represents the average price level of a country, which is the average of the product price growth rates of various manufacturers, and g represent the average technological progress rate of a country. It is the average of the technological progress rates of various manufacturers. Then the output growth rate of all manufacturers in a country is obtained by the formula: 𝑛𝑦 = 𝑏 ⋅ [𝑛𝑝 − 𝑛𝐸(𝑝)] + 𝑛𝑔 𝑦 = 𝑏 ⋅ [𝑝 − 𝐸(𝑝)] + 𝑔 (1) If it is assumed that technological progress is not taken into account, the technological progress rate g=0. The formula can be changed to: 𝑦 = 𝑏 ⋅ [𝑝 − 𝐸(𝑝)] This is equivalent to the Lucas aggregate supply curve formula in the monetary economic cycle model From the results derived from the monetary economic cycle model, we can know that: 777 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate 𝐸(𝑝𝑡) = 𝑚𝑔 + 𝑚𝑡−1 𝑝𝑡 = 𝑚𝑔 + 𝑚𝑡−1 + 𝜀𝑡 − 𝑦 Substituting it into the formula we get: 𝑦𝑡 = 𝜀𝑡 1 + 𝑏 From the formula, we can see that the fluctuation of a country's economy is mainly caused by random monetary shocks, which is completely consistent with the formula of the monetary economic cycle model. If the technological progress rate g=0, then this model degenerates into a monetary economic cycle model. (2) The real business cycle theory holds that monetary factors are exogenously determined by the monetary authorities and have no real impact on economic fluctuations. Therefore, if it is assumed that the money supply can be anticipated by the public, that is, p-E(p)=0 then formula becomes: y=g It can be seen from the formula that economic fluctuations are mainly caused by technological progress. At this time, the formula is equivalent to the formula in the actual economic cycle model, and the model in this paper degenerates into the actual economic cycle model. The above article analyzes the mechanism of price and technological progress on general economic fluctuations, which is similar to the monetary economic cycle model and the actual economic cycle model. Next, we will analyze the mechanism of price and technological progress on economic fluctuations in resource-based regions in detail based on the particularity of resource-based regions [15]. 4.3. Analysis Based on Static Expectations When studying a region or province, the economic situation is very different. Regions or provinces do not have their own independent currencies. The total output of the region is determined by the enterprises in the region based on the price situation to determine whether the market has excess demand for the products they produce, and whether to expand production [16]. Even when the national monetary authorities publicly announce the monetary supply, the national average price level is expected by the public, but if the regional output price level is higher than the national average price level, it also means that there is excess demand for regional output, and regional enterprises will also expand production, causing regional economic fluctuations. Resource-based regions are greatly affected by resource prices, and in many cases, they will deviate from the national average price level to a large extent. Output price fluctuations in resource-based regions often cause economic fluctuations. The specific situation is analyzed as follows. 4.3.1. Output Formula for Resource-Based Regions Assume that there are m enterprises in a resource-based region, m< 𝑇 Among them, 𝑦𝑡 is the dependent variable, 𝑥𝑡 1 and 𝑥𝑡 2 are explanatory variables, t is the set threshold variable, and T is the threshold value. Since the effects of price and technological progress on economic fluctuations studied in this article may vary in direction and magnitude at different times, the threshold variable set in this article is time t. Using this model, the optimal time threshold is identified, and the relationship between variables before and after different times is observed. 4.7.5.2. Chow Test The Chow test is a quantitative method used to measure whether there are structural changes in time series data. It was first proposed by Chinese economist Zou Zhizhuang in 1960. Assuming the existence of a set of time series data {𝑥𝑖}(ⅈ = 1,2, ⋯ , 𝑛), and setting its data model as: 𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝜀 Assuming that the residual 𝜀 follows an independent and identically distributed normal distribution with unknown variance, the basic principle of the model is to divide the data into two stages based on its characteristics and determine whether the coefficients of the model in the two stages are equal. If the 789 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate coefficients are equal, there is no structural change; if they are not equal, there is a structural change between the two. This method can effectively verify whether there are structural changes in time series at different stages, in order to provide more reasonable explanations for different times. The purpose of using the Chow test method in this article is to further verify whether there are structural changes in the relationship between price changes, technological progress, and economic fluctuations at different stages. 4.7.5.3. Empirical Analysis Based on Static Expectations Next, this paper starts from the perspective of static expectations and only considers the impact of price fluctuations in Shanxi Province on economic fluctuations in Shanxi Province. It conducts time series threshold regression analysis on the variables of Shanxi Province GDP fluctuation term𝑦�̃�, Shanxi price level change rate 𝑝𝑠and Shanxi Province technological progress fluctuation term𝑔�̃�. Table 4. Stability test results. Variable Test Statistic Key Value of the Test P Value 1% Level 5% Level 10% Level ADF test 𝒚𝒔 -4.637 -3.662 -2.964 -2.614 0.000 𝒑𝒔 -3.397 -3.662 -2.964 -2.614 0.000 𝒈𝒔 -4.983 -3.662 -2.964 -2.614 0.000 PP test 𝒚𝒔 -4.795 -3.655 -2.961 -2.613 0.000 𝒑𝒔 -4.697 -3.655 -2.961 -2.613 0.000 𝒈𝒔 -5.631 -3.655 -2.961 -2.613 0.000 Source: The data in this table are compiled based on the measurement results. 4.7.5.4. Stationarity Test In empirical regression analysis, if the variables are not stable, it will affect the empirical results. Therefore, this paper uses the ADF test and PP test to test the stability of the required data [25]. As shown in Table 4, the results of the two stationary tests show that all variables are stationary at the 5% significance level, so regression analysis can be performed on the data. 4.7.5.5. Empirical Analysis - Time Series Threshold Regression Time series threshold regression analysis is performed on the variables of Shanxi Province GDP fluctuation term 𝒚�̃�, Shanxi price level change rate 𝒑𝒔 and Shanxi Province technological progress fluctuation term 𝒈�̃�: Model settings: 𝑦𝑡 = { 𝑎1 + 𝛽1𝑝𝑠𝑡 1 + 𝛽2�̃�𝑠𝑡 2 + 𝜀1𝑡, 𝑡 ≤ 𝑇 𝑎2 + 𝜙1𝑝𝑠𝑡 1 + 𝜙2�̃�𝑠𝑡 2 + 𝜀2𝑡,𝑡 > 𝑇 Table 5. Time series threshold regression results. 𝒚𝒔 Regime1 Regime2 Threshold Estimate q<=1993 q>1993 Intercept -0.001 -0.005 𝒑𝒔 0.007 0.143 𝒈𝒔 1.022 0.553 Sum of Squared Errors 0.0004 0.005 R-squared 0.989 0.669 Source: The data in this table are compiled based on the measurement results. As shown in Table 5 above, the best result with 1993 as the threshold is: from 1978 to 1993, the effect of price on economic fluctuations is positive (0.007), and the effect of technological progress on economic fluctuations is positive (1.022); from 1994 to 2024, the effect of price on economic fluctuations is positive (0.143), and the effect of 790 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate technological progress on economic fluctuations is positive (0.553). Comparing the two stages, after 1994, the effect of price shocks has increased, and the effect of technological progress has weakened. Figure 7. Time series threshold regression results. It can be seen from the threshold regression results Figure 7 that there may be more than one threshold value. Therefore, we use the threshold value of 1993 as the stage point and use the staged threshold regression method to conduct further analysis. Stage 1: 1979-1993 The threshold regression results are as follows: 791 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Figure 8. Time series threshold regression results. From Figure 8 above we can see that there may be multiple threshold values in this stage. To further confirm, the threshold value is determined by using staged threshold regression, and the threshold regression results are sorted out to obtain the following table: Table 6. Time series threshold regression results. Threshold Estimate 1979-7983 1984-1987 1988-1993 Intercept -0.003 -0.003 -0.006 𝒑𝒔 0.004 0.210 0.039 𝒈𝒔 0.983 1.006 1.034 Sum of Squared Errors 0.000 0.000 0.000 R-squared 0.992 0.998 0.982 Source: The data in this table are compiled based on the measurement results. Table 6 Results show that there were two threshold values before 1993, which divided the economy into three stages. From 1978 to 1983, the effect of price on economic fluctuations was positive (0.004), and the effect coefficient of technological progress on economic fluctuations was positive (0.983); from 1984 to 1987, the effect of price on economic fluctuations was positive (0.210), and the effect coefficient of technological progress on economic fluctuations was positive (1.006); from 1988 to 1993, the effect of price on economic fluctuations decreased, but was still positive (0.039), and the effect coefficient of technological progress on economic fluctuations was positive (1.034). In short, in the period from 1979 to 1993, the effect of price on economic fluctuations first increased and then decreased, while the effect of technological progress has been increasing. Stage 2: 1994-2024 792 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Figure 9. Time series threshold regression results. From Figure 9 we can see that there is a very obvious threshold value between 1994 and 2024. In 2007, the staged threshold regression results are summarized in the following table: Table 7. Time series threshold regression results. 𝑦𝒔 Regime1 Regime2 Threshold Estimate q<=2007 q>2007 Intercept -0.008 -0.002 𝒑𝒔 0.218 0.033 𝒈𝒔 0.331 1.186 Sum of Squared Errors 0.002 0.001 R-squared 0.729 0.872 Source: The data in this table are compiled based on the measurement results. From the results of different stages, from 1994 to 2007, the effect of price on economic fluctuations was positive (0.218), and the effect coefficient of technological progress on economic fluctuations was positive (0.331). From 2007 to 2024, the effect of price on economic fluctuations was positive (0.033); the effect coefficient of technological progress on economic fluctuations was positive (1.186), which was significantly enhanced. Empirical analysis - Chow test The following further uses the Chow test method to judge structural changes. 793 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 8. Chow test results from 1979 to 2024. Ho: no Structural Change Cut-off point（>=） Chow Test p value 1979 0.23 0.637 1980 0.22 0.803 1981 0.33 0.807 1982 0.64 0.595 1983 0.56 0.647 1984 2.20 0.106 1985 2.10 0.119 1986 2.08 0.121 1987 2.18 0.109 1988 2.36 0.89 1989 3.40 0.029 1990 4.53 0.009 1991 5.70 0.003 1992 5.73 0.003 1993 5.89 0.002 1994 2.72 0.060 1995 2.81 0.054 1996 2.78 0.056 1997 1.14 0.346 1998 1.12 0.356 1999 1.17 0.337 2000 1.36 0.272 2001 1.54 0.222 2002 1.52 0.221 2003 1.08 0.371 2004 0.91 0.445 2005 0.86 0.470 2006 0.37 0.564 2007 0.24 0.665 2008 0.65 0.872 2009 0.17 0.643 2010 0.46 0.549 2011 0.55 0.711 2012 0.02 0.996 2013 0.62 0.608 2014 0.51 0.678 2015 0.46 0.710 2016 0.22 0.883 2017 0.37 0.772 2018 0.22 0.884 2019 0.14 0.937 2020 0.11 0.952 2021 0.22 0.885 2022 0.17 0.843 2023 0.03 0.866 Source: The data in this table are compiled based on the measurement results. According to the Chow test results in Table 8, we can see that the result in 1993 is the best, and the null hypothesis is rejected at the 5% significance level, indicating that there are structural changes in the period around 794 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate 1993. This test result verifies the result of the time series threshold regression. The following uses OLS regression to analyze the effects of these two influencing factors on economic fluctuations in different time periods. Table 9. OLS regression results. 𝒚�̃�, Coef. Std. Err t value p value 1979-1993 Constant term -0.001 0.003 -0.32 0.753 𝒑𝒔 0.007 0.030 0.24 0.814 𝒈�̃� 1.022 0.035 28.98 0.000 1994-2024 Constant term -0.005 0.003 -1.61 0.122 𝒑𝒔 0.143 0.060 2.39 0.026 𝒈�̃� 0.553 0.138 4.02 0.001 Source: The data in this table are compiled based on the measurement results. The overall regression results in Table 9 show that at a significant level of 5%, during the period of 1979-1993, the changes in Shanxi's price level did not have a significant impact on the economic fluctuations in Shanxi, while the role of technological progress was significantly positive. From 1994 to 2024, the role of prices on economic fluctuations increased significantly and was significantly positive. Although the role of technological progress was still significantly positive, its impact coefficient decreased significantly compared with the role in the previous period, which is consistent with the results of threshold regression. Next, the results of staged structural changes are further analyzed using the Chow test. 795 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 10. Chow test results for 1979 to 1993 and 1994 to 2024. Ho: no Structural Change stage Cut-off point Chow Test p value 1979-1993（>=） 1979 1.36 0.268 1980 0.65 0.541 1981 0.51 0.688 1982 0.13 0.943 1983 0.81 0.519 1984 0.25 0.858 1985 0.14 0.936 1986 0.17 0.915 1987 0.33 0.803 1988 0.38 0.768 1989 0.29 0.834 1990 0.70 0.576 1991 1.16 0.352 1992 0.89 0.366 1994-2018（>=） 1994 1.04 1.320 1995 0.60 0.559 1996 0.42 0.740 1997 1.01 0.409 1998 1.06 0.390 1999 0.84 0.487 2000 1.20 0.337 2001 1.46 0.256 2002 1.14 0.357 2003 1.21 0.333 2004 1.24 0.323 2005 1.551 0.244 2006 1.36 0.194 2007 0.95 0.103 2008 1.27 0.95 2009 1.33 0.162 2010 1.23 0.203 2011 1.98 0.102 2012 3.34 0.038 2013 5.55 0.007 2014 1.64 0.213 2015 1.20 0.336 2016 0.94 0.439 2017 1.24 0.324 2018 0.5 0.593 2019 0.30 0.826 2020 0.27 0.848 2021 0.23 0.875 2022 0.29 0.754 2023 0.23 0.634 Source: The data in this table are compiled based on the measurement results. From the results in Table 10, we can see that: between 1979 and 1993, the Chow test results all accepted the null hypothesis, indicating that there was no structural change. However, the Chow test results of the threshold point 2007 between 1994 and 2024 rejected the null hypothesis at a significance level of 5%, which means that there was a significant structural change around 2007, which is consistent with the threshold regression results. We continue to use OLS regression to simply analyze the relationship between the variables in these stages with significant structural changes, also using the OLS regression model. 796 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 11. OLS regression results for 1994 to 2007and 2008 to 2024. Variable Coef. Std. Err t value p value 1994-2007 Constant term -0.008 0.004 -1.89 0.085 𝑝𝑠 0.218 0.067 3.26 0.008 𝑔�̃� 0.331 0.114 2.91 0.014 2008-2024 Constant term 0.002 0.004 0.39 0.705 𝑝𝑠 0.033 0.044 0.73 0.485 𝑔�̃� 1.186 0.162 7.30 0.000 Source: The data in this table are compiled based on the measurement results. From Table 11, we can see that at the 5% significance level, the impact of prices on economic fluctuations was significant before 2007, while technological progress was not significant. After 2007, the role of technological progress began to increase, while the role of prices began to weaken, which is completely consistent with the results of threshold regression. 4.7.6. Empirical Analysis Based on Rational Expectations For enterprises with rational expectations, they often combine various production and price experiences when conducting production analysis and consider changes in the overall market and changes in regional market price levels at the same time. Based on this, this chapter first conducts a time series threshold regression analysis on the variables of Shanxi Province's GDP volatility𝒚�̃�, Shanxi's price level change rate deviation difference pc and Shanxi Province's technological progress volatility gs̃. Considering the price level deviation difference pc between Shanxi and the whole country is exactly the economic behavior of enterprises under rational expectations. 4.7.6.1. Stationarity Test The ADF test and PP test are used to test the stability of the price level change rate deviation pc between Shanxi and the whole country. Table 12. Stationarity test results. variable Test Statistic Key value of the test p value 1% level 5% level 10% level ADF test pc -3.474 -3.662 -2.964 -2.614 0.002 PP test pc -5.836 -3.655 -2.941 -2.613 0.000 Source: The data in this table are compiled based on the measurement results. The results of both stationary tests show that the variables are stationary at the 5% significance level, the regression analysis can be performed on the data. 4.7.6.2. Empirical Analysis - Time Series Threshold Regression Time series threshold regression analysis is performed on the variables of Shanxi Province GDP fluctuation term 𝒚�̃�, Shanxi price level change rate 𝒑𝒔 and Shanxi Province technological progress fluctuation term 𝒈�̃�: Model settings: 𝑦𝑡 = { 𝑎1 + 𝛽1𝑝𝑠𝑡 1 + 𝛽2�̃�𝑠𝑡 2 + 𝜀1𝑡, 𝑡 ≤ 𝑇 𝑎2 + 𝜙1𝑝𝑠𝑡 1 + 𝜙2�̃�𝑠𝑡 2 + 𝜀2𝑡,𝑡 > 𝑇 797 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 13. Time series threshold regression results. 𝒚𝒔 Regime1 Regime2 Threshold Estimate q<=1994 q>1994 Intercept 0.000 -0.001 𝒑𝒔 -0.119 0.123 𝒈�̃� 0.975 0.678 Sum of Squared Errors 0.001 0.006 R-squared 0.965 0.631 Source: The data in this table are compiled based on the measurement results. As shown in the Table 13, the best result with 1994 as the threshold is: from 1978 to 1994, the effect of price on economic fluctuations is negative (-0.119), and the effect of technological progress on economic fluctuations is positive (0.975); from 1994 to 2024, the effect of price on economic fluctuations is positive (0.123), and the effect of technological progress on economic fluctuations is positive (0.678). Before 1994, the effect of price on economic fluctuations was negative, and the effect of technological progress on economic fluctuations was positive; after 1994, both price and technological progress had positive effects. However, the effect of price has increased, and the effect of technological progress has weakened. The threshold regression results are as follows: Figure 10. Time series threshold regression results. The threshold regression results shown in Figure 10 show that there may be threshold values between 1980-1994 and 1994-2010. Therefore, we divide the time series into two stages, 1979-1994 and 798 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate 1995-2024. Then we perform threshold regression on the two stages of 1979-1994 and 1995-2024 respectively: Stage 1: 1979-1994 The threshold regression results are as follows: Figure 11. Time series threshold regression results. The threshold regression results can be summarized into the following table: Table 14. Time series threshold regression results. 𝒚𝒔 Regime1 Regime2 Threshold Estimate q<=1989 q>1989 Intercept 0.0002 -0.009 𝒑𝒔 -0.021 -0.314 𝒈�̃� 1.018 0.778 Sum of Squared Errors 0.000 0.000 R-squared 0.990 0.975 Source: The data in this table are compiled based on the measurement results. According to the results in Figure 11 and Table 14, there was a threshold before 1994, in 1989, the economy was divided into two stages. From 1978 to 1989, the effect of prices on economic fluctuations was negative (-0.021), and the effect coefficient of technological progress on economic fluctuations was positive (1.018); from 1990 to 1994, the effect of prices on economic fluctuations was negative (-0.314), and the effect coefficient of technological progress on economic fluctuations was positive (0.778). After 1989, although the impact of prices on economic changes was negative, the impact of prices on the 799 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate economy became stronger and stronger. The effect of technological progress on the economy was positive throughout the stage, but the effect coefficient was gradually weakening. Stage 2: 1995-2024 Figure 12. Time series threshold regression results. Table 15. Time series threshold regression results. 𝒚𝒔 Regime1 Regime2 Threshold Estimate q<=2006 q>2006 Intercept -0.003 0.000 𝒑𝒔 -0.663 0.046 𝒈�̃� 0.121 0.918 Sum of Squared Errors 0.001 0.002 R-squared 0.694 0.812 Source: The data in this table are compiled based on the measurement results. From a stage-by-stage perspective, from 1995 to 2006, the effect of price on economic fluctuations was positive (0.663), and the effect coefficient of technological progress on economic fluctuations was positive (0.121); from 2007 to 2024, the effect of price on economic fluctuations was still positive (0.046) but significantly reduced, and the effect coefficient of technological progress on economic fluctuations was positive (0.918), which was significantly enhanced. The threshold result diagram in Figure 12 above shows that there may be multiple threshold values after 1994. Therefore, taking 1994 as the boundary, we focus on analyzing the impact of price and technological progress on economic fluctuations at different stages during the period of 1995-2024. 800 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 16. Time series threshold regression results Threshold Estimate 1995-2001 2002-2006 2007-2011 2012-2018 Intercept -0.007 0.010 -0.0004 -0.004 𝒑𝒔 0.806 0.301 0.222 -0.121 𝒈�̃� 0.199 0.043 0.907 1.180 Sum of Squared Errors 0.000 0.000 0.001 0.000 R-squared 0.878 0.654 0.844 0.883 Source: The data in this table are compiled based on the measurement results. The results in Table 16 show that after 1994, there are three thresholds, namely 2001, 2006 and 2011, which divide the economy into four stages. From 1995 to 2001, the effect of price on economic fluctuations is positive (0.806), and the coefficient of technological progress on economic fluctuations is positive (0.199); from 2002 to 2006, the effect of price on economic fluctuations is positive (0.301), and the coefficient of technological progress on economic fluctuations is positive (0.043); from 2007 to 2011, the effect of price on economic fluctuations is positive (0.222), and the coefficient of technological progress on economic fluctuations is positive (0.907); from 2012 to 2024, the effect of price on economic fluctuations turns negative (-0.121), and the coefficient of technological progress on economic fluctuations is positive (1.180). After segmenting the period from 1995 to 2024, it was found that the impact of prices on economic changes was positive from 1995 to 2011, and the impact of prices on the economy weakened after 2012 compared with before 2012. The impact of technological progress on the economy was positive throughout the period from 1995 to 2024, and the impact coefficient gradually became stronger after 2012 compared with before 2012. 4.7.6.3. Empirical Analysis - Chow Test Through threshold regression, we found the best time segmentation point. To further test whether there is a structural change before and after the threshold value in the above time series threshold, we use the Chow test method to conduct an overall analysis. 801 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 17. Chow test results from 1979 to 2024. Ho: no Structural Change Cut-off point（>=） Chow Test p value 1979 0.00 0.986 1980 0.24 0.787 1981 0.16 0.924 1982 0.23 0.876 1983 0.19 0.906 1984 1.16 0.339 1985 1.07 0.376 1986 1.09 0.367 1987 1.15 0.343 1988 1.15 0.343 1989 1.25 0.308 1990 1.45 0.247 1991 1.77 0.171 1992 1.69 0.188 1993 2.05 0.126 1994 2.73 0.059 1995 2.68 0.063 1996 2.72 0.060 1997 1.62 0.203 1998 0.64 0.199 1999 1.74 0.177 2000 1.86 0.156 2001 1.88 0.152 2002 1.93 0.143 2003 0.69 0.565 2004 0.67 0.576 2005 0.70 0.560 2006 0.87 0.601 2007 0.62 0.522 2008 0.34 0.633 2009 0.56 0.624 2010 0.63 0.347 2011 0.49 0.565 2012 0.50 0.683 2013 1.25 0.306 2014 1.32 0.283 2015 0.67 0.577 2016 0.28 0.840 2017 0.23 0.971 2018 0.25 0.861 2019 0.39 0.760 2020 0.15 0.932 2021 0.04 0.991 2022 0..04 0.951 2023 0.09 0.766 Source: The data in this table are compiled based on the measurement results. Comparison in Table 17 shows all the results of the Chow test, it is found that the result with 1994 as the threshold value is closest to the 10% significance level, indicating that there may be structural changes in the previous and next time periods. The results of the Chow test further verify the results of the time series threshold regression. In different time periods, price changes and technological progress have different effects on economic fluctuations. The following uses OLS regression to analyze the effects 802 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate of these two factors on economic fluctuations in different time periods. According to the results of the model formula we set, OLS regression analysis is performed. Table 18. OLS regression results for 1979-1994 and 1995-2024. Variable Coef. Std.Err T Value P Value 1979-1994 Constant term 0.0004 0.002 0.21 0.839 𝑝𝑠 -0.119 0.073 -1.62 0.129 𝑔�̃� 0.975 0.062 15.68 0.000 1995-2024 Constant term -0.001 0.004 -0.17 0.868 𝑝𝑠 0.124 0.096 1.29 0.211 𝑔�̃� 0.678 0.141 4.81 0.000 Source: The data in this table are compiled based on the measurement results. The results in Table 18 show that during the period of 1979-1995, the difference between the price level of Shanxi Province and the national price level had a negative impact on economic fluctuations, and technological progress had a positive impact on economic fluctuations, which is consistent with the results of threshold regression. The regression results also show that before 1994, the effect of price changes on the economy of Shanxi Province was not significant, while compared with prices, the role of technological progress in promoting Shanxi Province was more obvious. After 1994, the impact of prices on the economy turned from negative to positive. Although the role of technological progress was positive, it was lower than before, which was also consistent with the results of threshold regression. The overall Chow test results are consistent with the threshold regression results, and the staged Chow test will be further conducted next. Table 19. Chow test results from 1979 to 1994. Ho: no Structural Change stage Cut-off point Chow Test p value 1979-1994（>=） 1979 0.09 0.775 1980 0.60 0.565 1981 0.88 0.482 1982 0.74 0.553 1983 1.39 0.301 1984 2.77 0.097 1985 3.23 0.069 1986 3.97 0.042 1987 4.34 0.033 1988 5.60 0.016 1989 6.53 0.010 1990 9.99 0.002 1991 10.00 0.002 1992 13.18 0.001 1993 26.58 0.000 Source: The data in this table are compiled based on the measurement results. 803 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 20. Chow test results from 1995 to 2024. Ho: no Structural Change Stage Cut-Off Point Chow Test P Value 1995-2024（>=） 1995 0.10 0.903 1996 0.20 0.897 1997 1.00 0.415 1998 1.08 0.383 1999 1.19 0.341 2000 1.73 0.196 2001 1.73 0.196 2002 1.76 0.190 2003 2.62 0.083 2004 2.55 0.088 2005 2.91 0.063 2006 2.76 0.022 2007 2.25 0.026 2008 1.96 0.136 2009 2.78 0.095 2010 2.04 0.137 2011 3.12 0.121 2012 4.28 0.053 2013 3.97 0.102 2014 2.02 0.147 2015 1.65 0.213 2016 1.46 0.258 2017 1.13 0.364 2018 0.61 0.620 2019 0.31 0.815 2020 0.25 0.863 2021 0.14 0.935 2022 0.17 0.844 2023 0.02 0.884 Source: The data in this table are compiled based on the measurement results. From the Chow test results between 1979 and 1994 in Table 19, we can see that there were obvious structural changes after 1987. The threshold regression results for the period 1979-1994 show that 1989 is the threshold value, and the results in the above table also verify that there were indeed structural changes around 1989, but the most obvious structural change was in 1993. According to the threshold results obtained by threshold regression in Table 20, there is one threshold cutoff point before 1994 and three cutoff points after 1994. From the results in the table above, at the 5% significance level, the Chow test results show that the result at the cutoff point in 2006 is the smallest, which means that there is the most obvious structural change around 2006. 804 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 21. Chow test results from 1995-2006. Ho: no Structural Change stage Cut-off point Chow Test p value 1995-2006（>=） 1995 0.00 0.982 1996 0.20 0.821 1997 0.14 0.930 1998 0.09 0.964 1999 1.11 0.417 2000 3.34 0.097 2001 3.80 0.077 2002 4.62 0.062 2003 5.42 0.038 2004 8.01 0.016 2005 18.30 0.003 Source: The data in this table are compiled based on the measurement results. As can be seen from Table 21, the best structural dividing point between 1995 and 2006 is 2005, which is inconsistent with the result of 2001, the dividing point of the time series threshold regression. Therefore, 2001 is no longer considered as the dividing point in the following stage analysis. Table 22. Chow test results from 2007-2024. Ho: no Structural Change stage Cut-off point Chow Test p value 2007-2024（>=） 2007 5.86 0.042 2008 2.79 0.128 2009 1.68 0.269 2010 0.87 0.505 2011 0.65 0.497 2012 0.32 0.432 2013 0.44 0.312 2014 0.63 0.567 2015 0.51 0.441 2016 0.63 0.423 2017 0.35 0.505 2018 0.28 0.620 2019 0.19 0.788 2020 0.20 0.838 2021 0.25 0.898 2022 0.08 0.891 2023 0.12 0.784 Source: The data in this table are compiled based on the measurement results. The results in Table 22 show that at the 5% significance level, the best structural point is 2007, and the results after 2007 show that there is no structural change, which is inconsistent with the result of the threshold value point in 2011 in the threshold regression results, so the 2011 dividing point is eliminated. In summary, the overall time system is divided by 1989 and 2006 before and after 1994, respectively. Before 1994, it can be divided into two stages: 1979-1989 and 1990-1994. After 1994, it can be divided into two stages: 1995-2006 and 2007-2024. The OLS regression is used to simply analyze the relationship between the variables in these stages, and the OLS regression model is also used. 805 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate Table 23. OLS regression results for different stages. variable Coef. Std.Err t value p value 1979-1989 Constant term 0.000 0.002 0.10 0.925 𝑝𝑠 -0.021 0.037 -0.56 0.594 𝑔�̃� 1.018 0.043 23.73 0.000 1990-0994 Constant term -0.009 0.006 -1.62 0.246 𝑝𝑠 0.315 0.077 -4.10 0.055 gs̃ 0.778 0.093 8.39 0.014 1995-2006 Constant term -0.003 0.004 -0.62 0.552 𝑝𝑠 0.663 0.113 5.86 0.000 𝑔�̃� 0.119 0.198 0.60 0.563 2007-2025 Constant term -0.0004 0.004 -0.10 0.924 𝑝𝑠 0.046 0.081 0.57 0.582 gs̃ 0.918 0.181 5.06 0.001 Source: The data in this table are compiled based on the measurement results. The results of the phased regression from 1979 to 2024 show that there was no significant correlation between prices and economic fluctuations before 1994, which is the same as the overall regression results. The role of technology also shows that the impact of technology is gradually weakening with the development of the economy, which is basically consistent with the results of the phased threshold regression. During the period 1995-2006, the role of prices was significantly enhanced compared with the previous period, and there was a significant correlation between prices and economic fluctuations, and its effect on the economy was more significant than the effect of technological progress on economic fluctuations. However, after 2007, the role of prices was significantly weakened, while the impact of technological progress on economic fluctuations was significantly enhanced. The phased change results from 1995 to 2024 are completely consistent with the phased change results of the threshold regression. From the overall OLS regression results, the change in the deviation difference between Shanxi Province and China's price level changes does not have a great impact on economic fluctuations, mainly driven by technological progress. The phased results also show that, except for the period of 1995-2006, the impact of technological progress on economic fluctuations is significantly higher than the impact of prices on economic fluctuations. Table 24. Comparison of empirical test results. Stage Static expectations Rational expectations Stage1 1979-1993 Stage2 1994-2024 Stage1 1979-1994 Stage2 1995-2024 The impact of prices on economic fluctuations Positive (0.007) Not significant Positive (0.143) Significant Negative (-0.119) Not significant Positive (0.124) Not significant The impact of technological progress on economic fluctuations Positive (1.022) Significant Positive (0.553) Significant Positive (0.975) Significant Positive (0.678) Significant Source: The data in this table are compiled based on the measurement results. 4.7.7. Analysis of Empirical Results —— Comparison Between Static Expectations and Rational Expectations and Determination of Economic Stages Next, based on the above empirical results, all the conclusions obtained above are sorted out, and the reasons for this phenomenon are further analyzed [26]. Comparing the results of the impact of prices and technological progress on economic fluctuations under static expectations and rational expectations in Table 24, we can see that under static expectations, the impact of prices on economic fluctuations before 1993 was not significant, mainly due to technological progress; after 1993, prices as the main factor had a significant effect on economic 806 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate fluctuations, and the impact coefficient increased significantly. The impact of technological progress on economic fluctuations is still significantly positive, and the impact coefficient has decreased. Under rational expectations, the impact of prices on economic fluctuations in the period around 1994 was not significant, mainly due to technological progress. The comparison results mean that when enterprises conduct decision-making analysis under rational expectations, they can make more rational judgments on prices and will be less affected by price fluctuations, that is, the economic fluctuations in Shanxi Province will not be significantly affected by prices. However, through static expectations, enterprises will be more affected by prices. Combining the empirical results and the economic development of Shanxi Province, we found that the trend of economic fluctuations in Shanxi Province and the trend of price change rate in Shanxi Province have been basically consistent for a long time. When prices rise, the economy is high, and when prices fall, the economy will also fall. From the empirical analysis results table, we can see that in the latter stage of rational expectations, the impact of prices on economic fluctuations is not significant, which is inconsistent with the actual empirical facts in Shanxi Province. However, under the static expectations, the effect of prices on economic fluctuations in Shanxi Province in the latter stage is significant, which is completely consistent with the empirical facts. It can be seen that the forecasts of Shanxi enterprises seem to be more inclined to static expectations rather than rational expectations. In the empirical analysis of static expectations, we used the time series threshold regression and Chow test to determine the stage. Observations found that the threshold regression results were different from the Chow test results. In the threshold regression, there were two thresholds in 1983 and 1987 in the period of 1979-1993, but the Chow test results showed that there was no significant structural change point. Therefore, there was a conflict between the two test results in the period of 1979-1993. However, according to the analysis of the actual economic situation, since China was mainly based on a planned economy before 1993 and the market economy was not yet perfect, the impact of prices on economic fluctuations was relatively small. Therefore, based on the actual situation, we divide this period into one stage. In the empirical results from 1994 to 2024, the analysis results of threshold regression and Chow test are completely consistent, with 2007 as the dividing point, dividing this period into two stages. Thus, through the above analysis, we can divide the overall stage into three stages: 1979-1993, 1994-2007, and 2008-2024. The following is an analysis of the impact of prices and technological progress on economic fluctuations in different stages: Table 25. Empirical test results of static expectations for different stages Stage Static expectations Stage1 1979-1993 Stage2 1994-2007 Stage3 2008-2024 The impact of prices on economic fluctuations Positive (0.007) Not significant Positive (0.218) Significant Positive (0.033) Not significant The impact of technological progress on economic fluctuations Positive (1.022) Significant Positive (0.331) Significant Positive (1.196) Significant Source: The data in this table are compiled based on the measurement results. As can be seen from Table 25, prices and technological progress in different periods have different effects on economic fluctuations in Shanxi Province. In terms of price levels, the biggest special feature of resource-based regions is resource prices. Since the industrial system of a region is composed of different industries in the region, there is a certain correlation between them. Therefore, changes in one industry will affect other industries or all industries in the entire region. As the dominant industry in resource-based regions, resource-based industries can almost affect all enterprises in the entire resource- based region through various transmission mechanisms. Therefore, when resource-based industries change, other industries will change. Resource prices are the main factor affecting resource-based 807 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate enterprises. Once prices change, it will inevitably cause changes in product prices of resource-based industries and then affect changes in product prices of other industries. This means that when the prices of major resources in resource-based regions fluctuate, the price level of the entire resource-based region changes. Figure 13. Coal price change rate and Shanxi price level change rate chart. As can be seen from Figure 13, the change in the price level of Shanxi Province is basically consistent with the change trend of coal prices. When the coal price rises, the price level of Shanxi Province will also rise; conversely, when the price falls, the price level of Shanxi Province will also fall. This shows that the fluctuation of coal prices has a great impact on the fluctuation of the price level of Shanxi Province. Therefore, when we focus on analyzing the impact of prices and technological progress at different stages on economic fluctuations in Shanxi Province under the static expectation, we must analyze the situation of the coal industry. Empirical Results Analysis —— Phased Empirical Results Analysis of the Impact of Prices and Technological Progress on Economic Fluctuations (1) Phase 1, 1979-1993: The impact of price on economic fluctuations was relatively weak, and technological progress played a major role. In 1978, the Third Plenary Session of the 11th Central Committee was held, proposing to shift the focus of work to economic construction. In order to alleviate the shortage of coal supply during the rapid development of the national economy, the Party Group of the Ministry of Coal Industry held an enlarged meeting in 1979 and proposed to make the rapid expansion of coal production and meeting the needs of economic development the primary goal of coal industry development. In 1979, the Shanxi Provincial Party Committee and the Provincial Revolutionary Committee formally submitted a report entitled "Report on Building Shanxi into a National Coal Energy Base" to the Party Central Committee and the State Council. In 1980, the state responded by supporting Shanxi to strengthen its energy base and support the development of the coal industry, and the Shanxi coal industry began to develop rapidly. In 1982, the government issued the "Interim Price Management Regulations", which stipulated that "state pricing is the main situation" and coal prices are basically controlled by the state. In 1983, the state required that management policies be relaxed on the premise of ensuring safe production and 808 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate encouraging the masses to raise funds to run mines. Before 1984, my country's coal price level has always maintained the government's minimum pricing, and coal is regarded as a means of production rather than a commodity. The role of the market is completely ignored, and the government mainly regulates it. After 1984, in order to improve the large-scale losses in the coal industry, the regulation began to loosen, and a combination of regulation and release was implemented, and price fluctuations were not very obvious. The "Price Management Regulations" of 1987 stipulates that "the state adopts the principle of combining direct management and indirect control for price management", and coal prices are still state-set. During the period from 1979 to 1993, prices were mainly regulated by the state, so they would not change much, and the impact on the economy was relatively small. Therefore, there is no significant correlation between price fluctuations and economic fluctuations. From 1979 to 1993, the country was in the stage of economic takeoff due to reform and opening up. In order to promote the development of the coal industry, the Ministry of Coal Industry successively formulated a series of policies to promote technological progress in the coal industry, such as "Quality Standards for Coal Mining Faces" and "Technical Policies for the Coal Industry". Shanxi Province also responded to the call of the reform policy and actively introduced foreign-funded enterprises to focus on the development of the coal industry. The "Interim Regulations of the Shanxi Provincial People's Government on Further Accelerating the Development of Local Coal in Our Province" issued in 1984 proposed "whoever invests, whoever benefits", encouraging investment and introducing capital and technology. In 1998, Shanxi Province began to implement resource integration, actively adjusted the industrial structure, changed the development ideas of the coal industry, and improved the technical level of the coal industry. It formulated the policy of "mining to support the mine, phased transformation, from small to large, and gradually improving", which promoted the improvement of the production technology level of state-owned coal mines and played a positive role in promoting economic development. Before 1993, the price level was basically controlled by the state, and the overall price level did not fluctuate greatly. As the national coal supply base, Shanxi Province has not experienced major fluctuations due to the long-term state control of coal prices. Since the development of the coal industry requires the establishment of factories and the introduction of technical talents and advanced equipment, it has greatly promoted the development of Shanxi Province's technical level. Therefore, this stage shows that the role of technological progress is significant, while the role of price is very small. 4.8. Implications Based on the theory of monetary economic cycle and the theory of real economic cycle, this paper mainly analyzes the economic fluctuations in Shanxi Province and studies the mechanism of price and technological progress on economic fluctuations in resource-based regions. It is found that in theory, the impact of technological progress on economic fluctuations in resource-based regions is greater than that of price. However, due to the high degree of dependence on resources in resource-based regions, they pay more attention to the changes in price factors and ignore the role of technological progress. As a result, resource-based regions pay too much attention to price factors in the process of economic development, while the level of technological progress gradually declines, which eventually leads to the solidification of production models and backward production methods, and the transformation and upgrading are stuck in a quagmire and difficult to extricate themselves. 5. Conclusion Based on existing theories, this paper conducts an in-depth study and analysis on the impact of prices and technological progress on economic fluctuations in resource-based regions. Combining the monetary economic cycle theory and the real economic cycle theory, this paper analyzes the impact of prices and technological progress on economic fluctuations through theoretical derivation, time series threshold regression and Chou test. The main conclusions are as follows: 809 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate (1) Theoretical model analysis finds that price shocks and technological progress are important factors leading to economic fluctuations in resource-based regions. Since resource-based regions have long relied on an industrial system dominated by resource-based industries, the overall price level of the region is greatly affected by the special factor of resource prices. When resource prices fluctuate, the overall price level of resource-based regions will also fluctuate significantly, resulting in a deviation between the price level of resource-based regions and the overall price level of the country. When this price level deviation is positive, it represents an excess demand for products in resource-based regions, which will lead to enterprises in the region expanding production; conversely, when the price deviation is negative, it will lead to enterprises in resource-based regions reducing production, which will then cause shocks and lead to regional economic fluctuations. This conclusion is contrary to the monetary economic cycle. The effect of price deviation on the economy is affected by the expectation tendency of enterprises. When enterprise expectations are more inclined to static expectations, economic fluctuations are completely affected by fluctuations in regional price levels. When enterprise decisions are more inclined to rational expectations, economic fluctuations are affected by changes in the difference between the price level in resource-based regions and the overall price level in the country. Technological progress will have a direct impact on economic fluctuations in resource-based regions, which is consistent with the actual economic cycle theory. (2) The final results of the empirical analysis of Shanxi's economy show that the fluctuations in Shanxi's economy are more in line with the assumption of static expectations. The empirical results show that: from 1978 to 1993, due to the dominant economic policy of planned economy, the role of price was significantly weaker, while the role of technological progress was more obvious. From 1994 to 2007, with the establishment of the market economy system, the price factor continued to strengthen and became the dominant factor, while the impact of technological progress on economic fluctuations was weaker. At this time, Shanxi's economic growth was more dependent on the rise in resource prices. After the 2008 financial crisis, coal prices fell and resource-based economic advantages weakened. In order to seek new economic growth points, Shanxi's economy began to transform. With the elimination of overcapacity and supply-side reform, the impact of prices on Shanxi's economic fluctuations has been greatly reduced. The government and enterprises attach importance to technological innovation, making technological progress the main factor causing economic fluctuations and promoting economic growth. (3) Based on theoretical and empirical analysis, under the market economy, resource-based regions have long relied on rising resource prices for economic development, and the industrial structure tends to be solidified, resulting in market failure. When resource prices are high, enterprises enter resource- based industries for profit, invest in extensive expansion, ignore technological progress and are unwilling to transform. When the economy falls into depression, resource prices fall, demand decreases, and corporate profits fall into difficulties, but they are difficult to transform due to lack of funds and backward technology. It shows that corporate development is more dependent on price changes rather than technological progress, which leads to the solidification of industrial structure and backward technological progress in resource-based regions. Market failure occurs, and the government needs to take the initiative to adjust. In a market economy, changes in resource prices will make it easier for enterprises to focus their forecasts on changes in resource prices, which will make enterprises in resource-based regions more inclined to static expectations when making expected decisions, making the impact of prices in resource-based regions on economic fluctuations stronger. (4) Based on the conclusions of previous literature research, this paper draws on traditional economic theory to build a model that combines price levels with technological progress for analysis, and verifies it with empirical evidence, and finally draws corresponding conclusions. Combined with the actual experience of Shanxi, this paper puts forward several policy suggestions for the economic transformation and development of resource-based regions, especially Shanxi. However, since the empirical information and data obtained in the research process are mostly collected from existing literature and existing data, and the practical investigation of Shanxi's economy is still insufficient, the 810 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate policy suggestions in this paper may be insufficient in operability or feasibility. In addition, for the impact of economic fluctuations in Shanxi Province, it is also possible to study the "institutional dividend" and "institutional defects" from the perspective of reflecting the process of the impact of institutional changes on productivity. In future research, we will further deepen practice and combine more actual situations for more in-depth analysis and research. In addition, resource-based regions may prosper because of their resources or be trapped by them. Although this article demonstrates the impact of price and technological progress on resource-based regions, there is still a long way to go for resource-based regions to achieve transformation and development. Further exploring the impact relationship between resource price fluctuations and technological fluctuations is also an important direction for future research. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. This study followed all ethical practices during writing. Copyright: © 2025 by the authors. This open-access article is distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). References [1] A. Cavallo and O. Kryvtsov, "What can stockouts tell us about inflation? Evidence from online micro data," Journal of International Economics, vol. 146, p. 103769, 2023. https://doi.org/10.3386/w29209 [2] C. Baumeister and J. D. Hamilton, "Sign restrictions, structural vector autoregressions, and useful prior information," Econometrica, vol. 83, no. 5, pp. 1963-1999, 2015. [3] C. J. S. Baumeister and J. D. Hamilton, "Structural interpretation of vector autoregressions with incomplete identification: Revisiting the role of oil supply and demand shocks," American Economic Review, vol. 109, no. 5, pp. 1873–1910, 2019. https://doi.org/10.1257/aer.20170691 [4] D. Acemoglu, U. Akcigit, D. Hanley, and W. Kerr, "Transition to clean technology," Journal of Political Economy, vol. 131, no. 3, pp. 1–45, 2023. https://doi.org/10.1086/684511 [5] R. Reis, "The inflation bias after COVID-19," Brookings Papers on Economic Activity, vol. 2022, no. Fall pp. 1–80, 2022. [6] E. Brynjolfsson, D. Rock, and C. Syverson, "The productivity J-curve: How intangibles complement general purpose technologies," American Economic Journal: Macroeconomics, vol. 13, no. 1, pp. 333-372, 2021. https://doi.org/10.1257/mac.20180386 [7] N. Bloom, S. J. Davis, and Y. Zhestkova, "How working from home works out," Quarterly Journal of Economics, vol. 137, no. 4, pp. 165–218, 2022. https://doi.org/10.1093/qje/qjac010 [8] P. Aghion, A. Dechezleprêtre, D. Hemous, R. Martin, and J. Van Reenen, "Carbon taxes, path dependency, and directed technical change," American Economic Review, vol. 113, no. 2, pp. 1–51, 2023. https://doi.org/10.1257/aer.20211560 [9] D. Autor and A. Salomons, "New frontiers: The origins and content of new work, 1940–2018," Review of Economics and Statistics, vol. 104, no. 5, pp. 1–45, 2022. https://doi.org/10.1162/rest_a_01059 [10] A. Goldfarb and C. Tucker, "Digital economics," Journal of Economic Literature, vol. 57, no. 1, pp. 3–43, 2019. https://doi.org/10.1257/jel.20171452 [11] D. Simchi-Levi, "From predictive to prescriptive analytics," Management Science, vol. 69, no. 2, pp. 885–903, 2023. https://doi.org/10.1287/mnsc.2022.4458 [12] Z. Li and Y. Wang, Research on the transformation path of Shanxi's resource-based economy under the 'Dual Carbon' Goal. China: Shanxi University, 2022. [13] F. Zhang and P. Jing, Mechanisms and paths of digital economy empowering Shanxi's resource-based economy transformation. China: Shanxi University Press, 2021. [14] J. Wang and Z. Liu, Evaluation and enhancement strategies of ecological resilience of resource-based cities in Shanxi. China: Shanxi University Press, 2020. [15] X. Zhang, L. Liu, and L. Li, "Financialization of international commodity markets and China's macroeconomic fluctuations," Financial Research, vol. 2017, no. 1, pp. 39-55, 2017. https://doi.org/10.12094/1002-7246(2017)01- 0035-17 [16] W. Wei, Z. Gao, and X. Peng, "Energy shocks and China's economic fluctuations: An analysis based on a dynamic stochastic general equilibrium model," Financial Research, vol. 2012, no. 1, pp. 51-64, 2012. https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.3386/w29209 https://doi.org/10.1257/aer.20170691 https://doi.org/10.1086/684511 https://doi.org/10.1257/mac.20180386 https://doi.org/10.1093/qje/qjac010 https://doi.org/10.1257/aer.20211560 https://doi.org/10.1162/rest_a_01059 https://doi.org/10.1257/jel.20171452 https://doi.org/10.1287/mnsc.2022.4458 https://doi.org/10.12094/1002-7246(2017)01-0035-17 https://doi.org/10.12094/1002-7246(2017)01-0035-17 811 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 772-811, 2025 DOI: 10.55214/25768484.v9i5.7006 © 2025 by the author; licensee Learning Gate [17] Y. Xu, "Risk transmission of international commodity price fluctuations to my country's price level," Times Finance, vol. 2018, no. 8, p. 32, 2018. [18] Q. Wang, J. Li, and X. Sheng, "Research on the mechanism of the impact of international commodity price fluctuations on my country's macroeconomics - a two-country DSGE model based on an open economy," China Soft Science, vol. 2019, no. 6, pp. 35-49, 2019. [19] X. Zhao, "Sticky prices, welfare losses and China's economic fluctuations," Shanghai Economic Research, vol. 2019, no. 8, pp. 64-77+97, 2019. [20] M. Tussupbayeva, Research on the impact of international oil price fluctuations on Kazakhstan's economy. China: Shanghai International Studies University, 2018. [21] X. Chen, Impact of mineral resource price fluctuations on Mongolia's economy. China: Jilin University, 2019. [22] M. Zhang and X. Ren, "Research on the interaction between economic fluctuations and industrial structure rationalization," Economic Issues, vol. 478, no. 6, pp. 61-70, 2019. [23] H. Tong, Threshold models in time series analysis. Berlin: Springer-Verlag, 1978. [24] B. E. Hansen, "Sample splitting and threshold estimation," Econometrica, vol. 68, no. 3, pp. 575-603, 2000. https://doi.org/10.1111/1468-0262.00169 [25] X. Sun and H. Zheng, "Economic transformation model of resource-based regions: International comparison and reference," Economist, vol. 2019 no. 11, pp. 104-112, 2019 [26] D. Shan, "Construction of evaluation index system for innovation capability of resource-based regions," Statistics and Decision, vol. 36, no. 2, pp. 38-42, 2020. https://doi.org/10.1111/1468-0262.00169