Exploring the Dynamic Impact between the Industries in China: New Perspective Based on Pattern Causality and Time-Varying Effect

Abstract

Real economy has always been a crucial component of China’s economic development, while fictitious economy has experienced rapid growth in past decades. As a result, the connection between the real and fictitious economy has become increasingly complex. This study utilized a hierarchical framework for classifying real economy and conducted a hidden causality test and EEMD method to explore a causal relationship between markets. Monthly data from July 2001 to September 2022 were analyzed using a TVP-SV-VAR model to investigate dynamic relationships among the manufacturing, construction, real estate, and financial industries as well as the mechanisms between the real and fictitious economies. The study outcomes demonstrated that the financial and real estate industries have only short-term positive effects on the manufacturing and construction industries, and in the later period of sample intervals, both industries had negative effects on the construction industry. The construction industry in the real economy has already shown a trend of moving “from Real to Virtual”, while the core manufacturing industry in the real economy has not yet exhibited this trend. To prevent the spread of this trend in the real economy, it is necessary to guide the fictitious economy to serve the real economy by regulating its development appropriately. This study offers a novel perspective for examining the real economy and the fictitious economy in China.

1. Introduction

1.1. Background

At the beginning of 21st century, China transitioned from being a powerhouse in the agricultural economy to being a powerhouse in the industrial economy as a result of a quick industrialization process following reform and opening-up strategies. China’s gross domestic product (GDP) overtook Japan’s in 2010, making it the second-largest economy in world. In 2020, China became the world’s largest manufacturing country. China’s progress has benefited greatly from real economy, covering manufacturing, services, infrastructure construction, and other fields, providing substantial support for nation’s economic growth. Particularly after the COVID-19 pandemic, the steady operation of the real economy is essential to maintaining the steady growth of national economy and guaranteeing that people can produce goods and live regular lives. Additionally, the fictitious economy serves the real economy and derives its income and objectives from the potential future profits generated by the real economy.

The growth of the real economy has always been a major strategic and policy direction for China’s economic development. China’s real economy has garnered increased attention and investment. The government has implemented regulations to promote and support its development, including tax and fee reductions, lower financing costs, and enhanced intellectual property protection. The implementation of these policies has provided a good environment and conditions for real economy growth. Under highly strategic or policy direction that attaches great importance to the real economy, China has accumulated huge real economic wealth and production supply capacity. Although China has a huge supply of real economy, its quality is not satisfactory, especially in consideration to the economy’s slowing expansion and the epidemic impacts on production and life. Ensuring a stronger and improved real economy, as well as understanding the connection between the real and fictitious economy, are not only issues related to the transformation and upgrading of the real economy but are also crucial aspects of China’s economic structural adjustment. These are immediate core challenges that China’s economy must address. The growth of manufacturing industry deserves attention, as it is the basis of China’s economy and contains the majority of real economy.

Since the 2008 financial crisis, countries around world have chosen to stabilize their financial systems and stimulate economic growth. However, given the ongoing economic downturn, the fictitious economy proportion represented by financial and real estate industries have continued to increase. Looking at housing prices in various countries, their increases have been high, and the finance and real estate industries’ representations of fictitious economy have clearly deviated from the actual economy. China is undoubtedly dealing with a similar circumstance. Since 2012, China’s GDP growth rate has fallen below 8%, and in 2015, it fell below 7%; it was not until 2021 that GDP growth rate returned to 8%. Given the sluggish pace of economic expansion, a large amount funds flowing into fictitious economy sector may lead to a deviation between the fictitious and real economy. From 2008 to the first quarter of 2021, the ratio of added value of China’s real estate industry to GDP climbed from 4.61% to 7.3%. Although under the country’s regulatory policies, this ratio has dropped to 6.5%, which is still high. The proportion of the manufacturing industry to GDP has decreased year by year since 2011 to 26.18% in 2020, although it has rebounded slightly in 2021. However, it is still lower than the proportion during high-speed development period of China’s manufacturing industry. An autoregressive integrated moving average (ARIMA) intervention model was used by Chung et al. [1] to analyze how global financial crisis affected China’s manufacturing sector and their research showed that China’s manufacturing industry was significantly negatively affected by financial crisis for a period of time.

The housing situation influenced by real estate and construction industries has always received extensive attention from all sectors of society. Unlike other commodities, housing is not only related to consumption and living but also has obvious investment attributes. From the perspective of the basic attributes of housing, housing is an important livelihood issue and a primary necessity for people’s survival. The important discourse regarding China’s new era housing system further clarifies the scientific positioning of the residential attribute of “Houses are for living in, not for speculation.” This also has an impact on the development and market positioning of real estate and construction industries. Moreover, under the influence of the epidemic, the residential attributes of housing have once again been emphasized, and this social consensus has clearly had an impact on China’s real estate and construction industries.

The growth of the financial and real estate sectors, as representatives of the fictitious economy, reflects the development of the fictitious economy. The manufacturing and construction industries, as important components of the real economy, also reflect the influence and role of construction industry in real economy. Menkhoff and Tolksdorf [2] analyzed the financial asset ratio in Germany. They believed that research on the finance sector’s fictitious economy should be distinct from research on the real economy. This distinction is warranted as Germany and China share similar national conditions, with a high proportion of manufacturing in their respective economies. However, whether there is a situation in China where the fictitious and the real economy are in opposition, in a manner similar to that in Germany, still requires further research in this study. The empirical part of this study will also focus on the analysis of “from Real to Virtual” in the Chinese economy. Understanding the relationships among the financial, real estate, construction, and manufacturing industries is of great significance for China to formulate strategies, policies, and systems for the healthy interaction of real and fictitious economies. It also helps to further understand the connection with the real and fictitious economies in a market economy. Therefore, studying the interdependence between the real estate and construction industries is crucial for the steady development with real economy and the implementation role of China’s fictitious economy.

This study will select models and conduct empirical research based on a hierarchical framework proposed by Huang [3] for classifying real economy. Corresponding to the classification form of the monetary level, Huang believes that the real economy can be divided into three levels. The first level of the real economy (R0) is the manufacturing industry, which is the core part of the real economy and can be considered the narrowest definition. The second level of the real economy (R1) includes R0, agriculture, construction, and other industries, excluding manufacturing, which is the main part. The third level (R2) includes R1, wholesale and retail, transportation and warehousing, postal services, accommodation and catering, and all other service industries, except for finance and real estate, and is the broadest definition of real economy. Figure 1 depicts the model’s organizational structure.

1.2. Hypotheses and Contributions

This study aims to investigate the “from Real to Virtual” phenomenon in the Chinese economy, which refers to the negative impact of the development of the fictitious economy on the real economy. We hypothesize that the “from Real to Virtual” phenomenon may not occur in every sector of the real and fictitious economies. Based on Huang’s [3] classification of the real economy, we selected the manufacturing and construction industries from the real economy, as well as the real estate and financial industries from the fictitious economy, as the subjects of our study. To verify our hypothesis, we employed pattern causality and TVP-SV-VAR methods to study the causal relationships between the manufacturing industry, the construction industry, the real estate industry, and the financial industry, as well as the time-varying impulse response graphs in different dimensions. We expect that this study will provide a deeper understanding of the relationship between the real economy and the fictitious economy. Additionally, we hope that this research will provide empirical evidence for the healthy development of the Chinese real economy.

This study’s main contributions are: (1) when exploring causal relationship between markets, the pattern causality method and the ensemble empirical mode decomposition (EEMD) method are used to construct the decomposed time series. Compared with the traditional Granger causality test, this method is more suitable for complex causality testing among multiple markets. (2) In response to the potential impact of China’s manufacturing, construction, real estate, and finance industries, in this study, the time-varying impulse response is examined using a time-varying parameter stochastic volatility vector autoregressive (TVP-SV-VAR) model. Compared with traditional linear models, nonlinear models provide a more precise analysis of the temporal connection to variables in a more detailed and accurate manner.

2. Literature Review and Interplay among Industries

Since the 2008 financial crisis, scholars, industry professionals, and government agencies, both domestically and internationally, have frequently used the concept of “real economy” to better explain the connection between the fictitious and real economy. According to the Federal Reserve (FED) definition, real economy refers to a part of the economy that excludes real estate and financial markets. In the National Accounts System, the “real economy” includes primary and secondary industries. Cheng [4] believes that the definition of real economy should be based on the perspective of material production. Marx describes the real economy as the process of using monetary capital to hire workers, purchase raw materials, machines, and build factories, and then transform them into products through production. These products become commodities through circulation, and only through exchange can they become money again. This entire process is real economy. Fictitious economy, according to Cheng [5], consists of all the operations of fictional capital, with financial platforms as the main body. Compared to real economy, fictitious economy is another form in economic system. As for the status and link between the real and fictitious in the national economy, Goldsmith [6] first proposed that the financial industry and the real economy can develop in a balanced way, and that the financial industry plays a role in promoting the growth of the real economy. Numerous subsequent studies have provided evidence for this point [7,8]. According to King and Levine [9], the growth of the financial sector may be used to forecast the growth of the real economy. The real economy was essential to growth in the past, while its fictional counterpart performed an auxiliary role. However, as the economy grows, this situation is changing, and the economy must now adjust to the fictional economy’s functioning principles [2].

Numerous academic works have pointed out that the divergence between the real economy and the fictitious economy has become a defining characteristic of the global economic system. Gennaioli and Shleifer [10] argue that the inherent problems within financial institutions have resulted in instability in related manufacturing industries, while Rin and Hellmann [11] suggest that the financial industry’s limited ability to drive manufacturing has hindered its development. Shiller [12] maintains that capital markets are susceptible to irrational behavior, which causes funds to flow rapidly from the real to the fictitious economy, revealing a departure from the “monetary separation” perspective. Chick [13] conducted a segmentation study on the development stages of banks and believed that credit expansion would lead to an increasing divergence between financial industry and real economy. The impact of the fictitious economy on the real economy is beginning to gradually emerge in China. When studying the spillover factors of financial cycles, Liu et al. [14] found that these factors exhibit strong temporal variations. At the same time, industries following financialization are characterized by significant cyclicality and temporal features [14,15,16].

It is evident from the research conducted before 2008 in China that the financial industry [17], as a representative of the fictitious economy, had a profound effect on the real economy, and there was no clear separation between the two. Due to the growth of the real estate sector and the entire country’s economy, the scope of the fictitious economy today is no longer limited to the financial market as it was at that time. Currently, the real estate industry also plays an important role in the fictitious economy. Sun et al. [18] established a competitiveness factor using Porter’s diamond model. After extracting relevant indicators for each category, to examine how each element affected the competitiveness of the real estate market, they employed structural equation modeling. The paper proved that the impact of related industries on the real estate industry is the most significant, followed by demand factors, while the coefficient of productivity factors is very low. However, the real estate market’s fast expansion has limited the actual economy’s room for development, proving its “crowding-out effect” on the real economy. Ren et al. [19] used the assumed extraction method to test the importance of the real estate and construction industries in the Chinese economy. Mishra and Pan [20] analyzed the Chinese real economy and stock market using the IS-LM model with structural break unit root test and ARDL model. When observed through their long-term relationship, the Chinese financial sector has a negative impact on the real sector.

During the rapid growth of the real estate industry, the manufacturing industry has encountered bottlenecks. Han et al. [21] developed a novel hybrid model by integrating the grey incidence clustering model and AP algorithm to analyze panel data from 2014 to 2018. Their paper revealed that the high-quality growth of China’s manufacturing industry is distinguished by notable regional variations, distinct development phases, and diverse limitations. That is, the promotion effect is gradually approaching a “critical value”, and beyond this value, real estate investment’s ability to boost the industrial sector increasingly deteriorates. Andersson et al. [22] used Granger’s causality tests to estimate links among banking types, finance, and economic growth and found that state-owned commercial banks in China even have negative effects on the growth of the manufacturing industry. The construction sector has a large interactive impact on the growth of the real estate industry as a representation of the real estate industry in the real economy. Kaklauskas et al. [23] found that during the COVID-19 pandemic, both the manufacturing and construction industries suffered heavy blows. The impact of the epidemic on the real estate industry was also significant, as it led to a decrease in investment growth by affecting investors’ inclinations. To summarize, existing research has demonstrated the relationship and development between China’s fictitious and real economies, which has strong practical significance. However, there are also some shortcomings. Firstly, scholars both domestically and internationally have extensively studied the financial and real estate markets, but there has been relatively little research on their relationship with industries in real economy. Secondly, there is no consensus on which indicators to use to represent the growth of the fictitious economy and the real economy. Most studies use time series data on the macro level, which may result in limited sample sizes and large research errors. Thirdly, there is room for improvement in model selection. Most literature assumes linear models or models with fixed parameters, which may not reflect real-world situations. A large amount of the theoretical literature and empirical research has demonstrated the strong nonlinear relationship between economic and financial data, which is often manifested as a time-varying relationship. Currently, the real economy in China has been placed in a central position, and the financial and real estate markets are also facing reforms. As the challenge of separating the fictitious economy from the real economy grows, it becomes clear that traditional linear models cannot capture the dynamic relationship and mutual influence between them.

The stability theory and deviation theory, extensively studied in the literature, are widely recognized as approaches to describe the relationship between the fictitious economy and the real economy. According to the stability theory, the growth of the fictitious economy tends to deviate from the equilibrium point but remains relatively stable alongside the real economy within a specific range. On the other hand, the deviation theory suggests that irrational behavior can influence capital markets, and an excessive fictitious economy may “crowd out” the real economy, leading to deviations from its intended development. According to the FED’s definition of the fictitious economy, the financial and real estate industries serve as mature theoretical models to study the relationship between these two markets. These models utilize input–output frameworks and theories of monetary policy transmission. Despite their complex interconnections, both markets have demonstrated significant correlations and closely intertwined cycles. In terms of financial industry, fictitious economy can help raise funds for real economy, lower financing costs, optimize investment structures, etc., by providing financial services and products. Banks, securities, insurance, and other financial institutions, through credit, stocks, bonds, insurance, and other financial products, provide funding and risk management tools for the real economy, providing strong support for its development. In the real estate industry, the fictitious economy is mainly reflected in real estate transaction and financial derivatives markets. Real estate is an important investment asset, and financial derivatives related to real estate transactions highlight the nature of the fictitious economy even more. Fictitious economy growth can provide the real estate industry with more flexible trading methods and new financing channels, thus better meeting the needs of the real economy. Meanwhile, in terms of industries, the manufacturing industry provides material support for the construction industry, while the construction industry provides site support for the manufacturing industry. The financial and real estate sectors’ quick growth may cause the manufacturing sector to become overcrowded. The real estate industry provides a market source for the construction industry, while the construction industry provides fixed asset investment in return. The real estate sector shows a trend towards financialization, and the financial sector provides capital support for the real estate sector. During the Chinese stock market crash, the stock and real estate reacted with similar patterns and large positive or negative responses to shocks [24]. There is an obvious dynamic relationship of mutual influence and mutual restraint among financial industry, real estate industry, construction industry, and manufacturing industry.

The recent related research has shifted its focus from the relationships between industries themselves to the relationships between the products derived from the industry. Chodorow-Reich and Antonio [25] studied the importance of loans in transmitting bank health to the real economy. Peng and Ke [26] utilized various models, including Granger’s causality test and vector autoregression, to study the interaction between financial technology and the real economy. The research found that risk in fintech can have an extreme impact on industry in a short time. Gupta et al. [27] conducted a study on office real estate from the perspective of remote work and found that the impact of the pandemic on lower quality office buildings was greater than that on higher quality office buildings. Samitas et al. [28] investigated the spread of the Subprime Crisis and the European Sovereign Debt Crisis from Eurozone countries to the real economy. The results indicate that spillover effects affected every country and sector without exception. Prah [29] argues that financial development in both developed and developing countries contributes to economic performance. Among these, digital finance, as a product of financial industry’s development, has a positive impact on technological innovation in agricultural enterprises, and it is also influenced by temporal factors [30]. Xie et al. [31] investigated risk spillovers across China’s financial (including stock markets, fund markets, futures markets, and other markets) and shipping markets through dynamic spillover measures based on TVP-VAR and generalized forecast error variance decompositions under COVID-19. Du et al. [32] employed the spatial Markov transition probability matrix to investigate the spatial spillover effect of carbon emission efficiency in China’s construction industry. Zhang [33] focused on the empowerment of corporate green technological innovation via green bonds. Industries that issue green bonds include manufacturing and construction. The theoretical transmission pathway diagram of this study is shown in Figure 2. The main research objects selected in this study are the manufacturing industry, the construction industry, the real estate industry, and the financial industry, for the following reasons. Firstly, as mentioned in the previous section, the manufacturing industry belongs to the 1L of real economy (R0), while the construction industry belongs to the 2L of the real economy (R1). The construction industry represents the real estate industry in entity economy, so the impact of the real estate industry on the 1L of the real economy (R0) and its representation in the entity economy deserves special attention. Secondly, numerous studies have shown that China’s economy may also have a “from Real to Virtual” problem. Therefore, the construction industry, as a representation of real estate in the real economy, and the real estate industry, as a fictitious economy crucial element, have significant practical significance when capturing their time-varying characteristics and their relationship with the entity economy.

3. Method

3.1. Pattern Causality and EEMD

Due to the existence of complex and highly correlated factors in the real world, the traditional vector autoregression (VAR) models that employ Granger’s causality test cannot capture the true and underlying causal relationships. Granger’s causality test is merely a technique for inferring causal linkages from the observed time series data. Furthermore, the separability assumption, which is a fundamental test assumption, postulates that causes exist independently of their outcomes, and when a causative variable is eliminated from a system or model, no other variables are affected. However, this assumption does not hold in reality, where variables are interdependent and cannot be easily separated. According to Sugihara et al. [34], in deterministic dynamical systems, even in systems with some noise, Takens’ theorem states that if X causes Y, knowledge about X will duplicate itself in Y and cannot be completely eliminated from the system. Additionally, when two variables are simultaneously affected by a common factor, Granger’s causality effect is difficult to demonstrate.

To demonstrate a deeper connection among the four factors, this study will use a method based on cross-convergent mapping (CCM) and pattern causality, as suggested by Stavroglou et al. [35,36]. This technique can identify a variety of causal relationships in several complicated systems. This approach can separate causation into three categories: positive causality, negative causality, and a more complicated form of interaction called “dark causality”, which can be quantified and applied to ecology, neuroscience, and finance.

EEMD is a decomposition method based on empirical mode decomposition (EMD), which can decompose a time series into multiple intrinsic mode functions (IMFs). The underlying principle of the proposed method is as follows.

Step 1. Adding Gaussian white noise to the original signal: The original signal $x(t)$ is combined with multiple realizations of Gaussian white noise, denoted as $h(i,t)$, to create the perturbed signal $y(i,t)$:

$$y(i,t)=x(t)+h(i,t),$$

(1)

From the above formula, $i$ represents the $i-\mathrm{th}$ realization of Gaussian noise and $t$ denotes time.

Step 2. Performing EMD decomposition: The perturbed signal $y(j,t)$ is decomposed using EMD, resulting in intrinsic mode functions (IMFs) for each perturbed signal:

$$y(i,t)={\displaystyle \sum \left[IMF(j,i,t)+R(i,t)\right]},$$

(2)

Here, $j$ represents the $j-\mathrm{th}$ IMF component, and $R(i,t)$ is the residue term.

Step 3. Averaging the IMF components: The IMF components $IMF(j,i,t)$ of the same mode function (IMF) are averaged to obtain the final IMF component $IMF(j,t)$:

$$IMF(j,t)=\frac{{\displaystyle \sum IMF(j,i,t)}}{N},$$

(3)

N represents the number of Gaussian noise realizations.

Step 4. Reconstructing the signal: The reconstructed signal $x(t)$ is obtained by summing all IMF components: $x(t)={\displaystyle \sum IMF(j,t)}$.

By adding multiple realizations of Gaussian white noise to the original signal and performing EMD decomposition, EEMD reduces the impact of noise on the decomposition results by averaging multiple IMF components. This improves the ability to handle nonlinear and non-stationary signals. The reconstructed signal is obtained by summing all IMF components, where each IMF component represents the signal’s characteristics at different time scales. What we need in the study is the IMF components.

3.2. TVP-SV-VAR Modeling

Since the VAR model was proposed by Sims, it has been widely used in various statistical modeling and macroeconomic forecasting. Since the presence of time-varying characteristics in some time series, time-varying elements have been progressively integrated into the VAR model. As research has advanced and deepened, Primiceri [37] was the pioneer in introducing the TVP-SV-VAR, which combines time-varying and SV features, for the analysis of the private sector of U.S. monetary policy and national economy. Empirical research findings demonstrate that this model framework can more fully capture the structural changes in the U.S. economy. Since then, TVP-SV-VAR has been extensively utilized in the field of macroeconomics [38,39,40].

TVP-SV-VAR is obtained by deriving traditional VAR model, and it has the following form:

$$A{y}_t=F_1{y}_{t-1}+F_2{y}_{t-2}+\cdots +F_s{y}_{t-s}+{\mu }_t,t=s+1,s+2,\dots ,n.$$

(4)

From the above formula, $y_t$ is a $k\times 1$ vector of observed variables, $A,F_1,F_2,\dots ,F_s$ are all the $k\times k$ matrices of coefficients, and the disturbing term ${\mu }_t$ is a $k\times 1$ structural shock, ${\mu }_t~N(0,\sum \sum )$. The specific form of $\sum$ is as follows:

$$\sum =\left(\begin{array}{cccc}{\sigma }_1& 0& \cdots & 0\\ 0& \ddots & \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ 0& \cdots & 0& {\sigma }_k\end{array}\right)$$

(5)

Consequently, we suppose that A is a lower triangle matrix. The recursive method can be used to explain the simultaneous relationship of structural shock. The form of A is as follows:

$$A=\left(\begin{array}{cccc}1& 0& \cdots & 0\\ a_{21}& \ddots & \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ a_{k1}& \cdots & a_{k,k-1}& 1\end{array}\right)$$

(6)

The model can be rewritten via transformation into the following simplified VAR model:

$$y_t=B_1{y}_{t-1}+B_2{y}_{t-2}\cdots +B_s{y}_{t-s}+A^{-1}\sum {\epsilon }_t,{\epsilon }_t~N(0,I_K)$$

(7)

where $B_i=A^{-1}{F}_i$ and $i=1,2,\dots ,s$. Superimpose the elements in the row $B_i$ to form $\beta$, and $\beta$ is the vector of $k^{2}s\times 1$, $X_t=I_k\otimes \left(y_{t-1},y_{t-2},{\cdots }_{},y_{t-s}\right)$, where $\otimes$ denotes the Kronecker product and Model (7) can be rewritten as:

$$y_t=X_t\beta +A^{-1}\sum {\epsilon }_t$$

(8)

At this time, all parameters in Model (8) are fixed and do not have time-varying characteristics. Assuming that the model parameters have time-varying characteristics and SV features, introducing time-varying characteristics and SV features can extend traditional VAR to the TVP-SV-VAR model. The extended form is as follows:

$$y_t=X_t{\beta }_t+A_t{}^{-1}{\sum }_t{\epsilon }_t,t=s+1,s+2,\cdots ,n$$

(9)

In this model, both model coefficient ${\beta }_t$, parameter $A_t$ and ${\sum }_t$ have time-varying characteristics. Let $a_t=\left(a_{21},a_{31},a_{32},a_{41},\cdots ,a_{k,k-1}\right)$ be the stacked vector of lower triangular elements in $A_t$, where ${\sigma }_{jt}{}^2=\exp (h_{jt})$, the stochastic volatility matrix $h_t=(h_{1t},h_{2t},\cdots ,h_{kt})$ and $j=1,2,\cdots ,k,t=s+1,s+2,\cdots ,n$. Assume that the parameters in Model (9) obey the random walk process:

$${\beta }_{t+1}={\beta }_t+{\mu }_{\beta t},a_{t+1}=a_t+{\mu }_{at},h_{t+1}=h_t+{\mu }_{ht}$$

(10)

$$\left(\begin{array}{c}{\epsilon }_t\\ {\mu }_{\beta t}\\ {\mu }_{at}\\ {\mu }_{ht}\end{array}\right)~N\left(0,\left(\begin{array}{cccc}I& O& O& O\\ O& {\sum }_{\beta }& O& O\\ O& O& {\sum }_a& O\\ O& O& O& {\sum }_h\end{array}\right)\right)$$

(11)

where $t=s+1,s+2,\cdots ,n,{\beta }_{s+1}~N({\mu }_{\beta 0},{\sum }_{\beta 0}),a_{s+1}~N({\mu }_{a0},{\sum }_{a0})$ and $h_{s+1}~N({\mu }_{h0},{\sum }_{h0})$. The model is based on the following assumptions: the model assumes that all parameters follow a first-order stochastic process with time-varying random shocks that are mutually uncorrelated, and ${\sum }_{\beta }$, ${\sum }_a$, and ${\sum }_h$ are the diagonal matrix to simplify the estimation of the model.

Estimation Method

The incorporation of time-varying parameters into a model via translation is instrumental to enhancing the model’s flexibility. However, the inclusion of non-linear state equations in the model renders the likelihood function considerably more intricate, thereby posing significant challenges to the utilization of maximum likelihood estimation. To address these problems, we employed the Markov chain Monte Carlo (MCMC) method with a Bayesian framework to replace maximum likelihood estimation. This study uses the MCMC algorithm proposed by Nakajima [41] for estimation, which operates based on the Bayesian theory to obtain the joint posterior distribution of the parameters of interest. In this method, the prior probability density is utilized to conduct multiple sampling iterations under the given data. Through the simulation of the Markov chain, the stable distribution was attained after its limit distribution reached the desired posterior distribution. A diverse range of approaches for constructing Markov chains exists, and Gibbs sampling is one of them. In this article, the MCMC algorithm under Gibbs sampling is utilized. The MCMC algorithm utilized in this study is based the blocking sampling strategy of Nakajima [41] and assumes known observed data $y={\left\{y_t\right\}}_{t-1}^n$ and $\omega =({\sum }_{\beta },{\sum }_a,{\sum }_h)$ and an unknown prior density $\pi (\omega )$ for the parameter $\omega$. To obtain the joint posterior distribution $\pi (\omega ,a,h|y)$, samples are drawn from the posterior distribution $\pi (\beta ,a,h,\omega |y)$.

4. Empirical Analysis

4.1. Data

To reflect the dynamic mechanism between fictitious and real economy over a long-term, and explore interlinkages among financial industry, real estate industry, construction industry, and manufacturing industry. Additionally, to avoid the difficulty of research caused by errors between data types and statistical methods, this study selects data of the same type. The sample period is from July 2001 to September 2022, with a total of 255 monthly data points. The descriptive statistical results of the data are shown in

Table 1. Descriptive statistical results.

Variables	Manufacturing Industry	Construction Industry	Real Estate	Financial Industry
Mean	100.8132	2910.157	1324.901	852.9301
Median	101.23	2774.25	1178.676	798.9
Maximum	109.14	8414.358	3285.282	1887.69
Minimum	92.43	571.7488	241.8374	210.18
Std.	3.798669	1584.127	802.6071	387.9543
Skewness	−0.375902	0.498296	0.550211	0.327027
Kurtosis	2.383509	2.974056	2.388729	2.280576
J-B	10.04349	10.55984	16.83618	10.04443
p-value	0.006593	0.005093	0.000221	0.00659

. The sources and descriptions of each indicator are as follows:

Finance index (FI): the financial index used in this study is the one distributed by the Shenzhen Stock Exchange, and its closing price was selected as the financial index in this study. The data source is the Wind database.

Real estate climate index (RECI): the National Real Estate Development Prosperity Index was employed in this study as the real estate climate index. The data source is the CSMAR database.

Construction index (CI): the construction index used in this study is the one published by the Shenzhen Stock Exchange, and its closing price was used as the construction index in this study. The data source is Wind database.

Manufacturing index (MI): the manufacturing index used in this study is the one distributed by the Shenzhen Stock Exchange, and its closing price was used as manufacturing index in this study. The data source is Yahoo Finance.

4.2. Hidden Interactions

This study uses the algorithm to analyze the connections between the four selected entities. To better demonstrate the connections between the four entities and avoid the interference of the scale of the data, this study standardizes the original data of the four items before analysis. A cumulative adjacency matrix for three distinct spectra (positive, negative, and dark) is shown in Figure 3, the hue corresponds to the cumulative intensity. In order to gain a deeper understanding of their connection, we used the EEMD decomposition method to analyze the original data. Then, the EEMD method was used to separate the four time series into three frequency (long, medium, and short) period time series. The decomposed data are shown in Figure 4. Consequently, a total of 12 time series were analyzed, and the outcomes are illustrated in Figure 5, In the figure, L represents the long period, M represents the medium period and S represents the short period.

Figure 3 shows the cumulative adjacency matrix of positive effects, negative effects, hidden causal effects among the four entities. Darker colors denote stronger links overall. The three cumulative adjacency matrix diagrams illustrate that there are significant relationships between the four markets of manufacturing, construction, finance, and real estate. Figure 3c shows that there is a connection between these four entities, and the dark causality indicates that the relationship between manufacturing and other industries is often more complex and cannot be simply attributed to positive or negative effects. It can be seen from Figure 5 that, after using the data decomposed into three frequencies of long, medium, and short, the positive and negative effects still exist, and some of the impact strengths are higher than before the decomposition. However, after the data are further decomposed via EEMD, all the results of the dark causality are 0. As the decomposition still contains positive and negative effects but not the dark causal effects, it can be understood that the information of the dark causality disappears after the EEMD decomposition.

In Figure 3a and Figure 5a, it can be seen that the main positive impact between construction and real estate industries is reflected in the short-period impact of real estate industry on the construction industry. However, there is no clear positive impact in the opposite direction. The main positive impact between the financial and real estate industries is reflected in the short-to-medium-period impact of the financial industry on the construction industry, and likewise, there is no clear positive impact in the opposite direction. The short-term influence of the real estate sector on the manufacturing sector reflects the major beneficial relationship between the two sectors, while the main positive impact between the financial and manufacturing industries is reflected in the short-to-medium-period impact. Additionally, the short-to-medium-period impact of the manufacturing industry has a positive impact on both the construction and financial industries. Observing Figure 3b and Figure 5b, it can be seen that the negative impact is mainly reflected in the later period of each industry on the previous two periods of each industry, with the construction industry being the most obvious.

In summary, it can be concluded that there are significant relationships among the four selected entities in this study. Furthermore, it was found that the relationships between the manufacturing industry and the other industries are more complex. Additionally, the information of the dark causal effects is lost after the EEMD decomposition.

4.3. Fitted Results of TVP-SV-VAR

To avoid spurious regression problems during model construction, vector autoregressive models require stationary data sequences. Therefore, a stationarity test is performed on the selected data to check whether the data sequence is stationary. Because most financial data series are non-stationary in their original form, it is necessary to preprocess the original data series. In this study, all data were normalized and then subjected to differencing and stationarity tests. Due to the presence of high-order autocorrelation in most time series, the ADF test was utilized. After conducting stationarity tests on the four sets of data generated through differencing, the results showed that the statistical values of indicator data had t-values within the acceptance range at the 1% significance level, indicating that the series were stationary.

After passing the stationary test mentioned above, the optimal lag order for the TVP-SV-VAR was determined to be 1, based on various information criteria. After obtaining the optimal lag order, the parameters of the TVP-SV-VAR were estimated and inferred using the MCMC method. In this study, 20,000 samples were drawn from the dataset, and the first 2000 samples were discarded as the “burn-in period” to obtain stable and effective sample results, as shown in

Table 2. MCMC estimation results of the parameter.

Parameters	Mean	Std.	95% Confidence Interval	Geweke Diagnostic	Inef.
${({\sum }_{\beta })}_1$	0.0023	0.0003	[0.0018, 0.0029]	0.268	12.66
${({\sum }_{\beta })}_2$	0.0023	0.0003	[0.0018, 0.0029]	0.838	17.21
${({\sum }_a)}_1$	0.0202	0.0080	[0.0068, 0.0378]	0.000	132.83
${({\sum }_a)}_2$	0.0051	0.0012	[0.0033, 0.0078]	0.002	47.65
${({\sum }_h)}_1$	0.3528	0.0511	[0.2624, 0.4631]	0.106	25.93
${({\sum }_h)}_2$	0.3185	0.0579	[0.2212, 0.4425]	0.976	48.73

. The parameters in Table 2 represent the first two elements on the main diagonal of the covariance matrix of random walk disturbance term in parameter representation equation. The covariance matrix ${\sum }_{\beta }$, ${\sum }_a$, and ${\sum }_h$ are mentioned in Formula (11). The convergence of the remaining elements was determined by the size of these two parameters. As shown in the table, all convergence diagnostic values are less than the critical value of 1.96 at the 5% level, indicating that the null hypothesis cannot be rejected and the posterior distribution has converged. From the size of non-effective factors in the table, it can be seen that the largest ineffective factor is approximately 132. Therefore, there are about 20,000/132 = 151 independent samples obtained, indicating that the 20,000 samplings provide sufficient and effective samples for our research. In summary, the sampling and estimation of the model are effective, and further analysis can be conducted.

4.4. Analysis of Stochastic Volatility

Figure 6 demonstrates stochastic volatility of the four variables mentioned above. Looking at the stochastic volatility of the construction industry, the stochastic volatility of the construction industry index in February 2007 showed an upward trend, reaching its peak in February 2008. After that, the volatility gradually decreased until September 2014 when the stochastic volatility of the construction industry index began to rise again, reaching a new peak in August 2015. Since then, the stochastic volatility has again decreased to a stable level. Because of the financial crisis in 2008, it spread to China’s construction industry. Thereafter, the government implemented a lax fiscal strategy and revitalized the industry to stabilize the fluctuations. The 2015 stock market crisis was the main trigger of the second surge in random volatility, which affected construction industry and led to a rapid increase in random volatility. China regulated and restricted the market to eventually stabilize the stock market.

The manufacturing industry had lower stochastic volatility in February 2008 compared to the construction industry. This may be due to the fact that the 2008 financial crisis initially originated from the real estate industry. Additionally, during that time, the connection between the manufacturing industry and the financial industry was not as strong, making it difficult for fluctuations in the fictitious economy to impact the manufacturing industry within the real economy. However, under the influence of the stock market crash, the manufacturing industry also had a high stochastic volatility during the same period, mainly because the real economy and the fictitious economy were more closely connected between 2008 and 2015, and the impact of the stock market on the real economy was more significant. Since July 2018, the stochastic volatility of the manufacturing index has been on the rise and has not fallen, mainly due to the US raising tariffs on certain raw materials in China as part of the US–China trade war, affecting the production and revenue of the manufacturing industry, leading to an increase in its stochastic volatility. Moreover, the impact of the pandemic on people’s work and life has also affected the production activities of manufacturing industry. From the perspective of real estate stochastic volatility, its index in January 2002 showed an upward trend and reached its peak in the short term. A reason for this was that there were many problems with the domestic real estate industry in early stages and the necessary supervision was not in place. In 2002, China carried out comprehensive rectification of this industry, the scope and strength of which were unprecedented, resulting in real estate industry index having a high stochastic volatility. Similarly, the index also showed an increase in stochastic volatility during the 2008 financial crisis, the 2015 stock market crash, and the 2020 outbreak of COVID-19 pandemic, but their fluctuation duration was relatively short. From major past events, the first two are clearly reflected in the volatility chart of the financial industry. The stochastic volatility of the financial industry index showed an upward trend from 2007 to 2008, and it did not stabilize until September 2010. The stock market crash in 2015 also had a significant effect on the stochastic volatility of the financial industry index. Since the US–China trade war in 2018 had more impact on the real economy, the US–China trade war and the COVID-19 pandemic in 2020 had a relatively small effect on the stochastic volatility of financial industry index.

In summary, except for the manufacturing industry, all other industries experienced significant increases in their stochastic volatility during the 2008 financial crisis. The construction industry’s stochastic volatility showed an upward trend earlier than real estate industry, indicating that construction industry, as a manifestation of the real economy, had already experienced market fluctuations ahead of the crisis in the real estate industry. The stock market crash in 2015 caused the stochastic volatility of these four industries to show an upward trend. From the chart, it can be seen that compared to the other three industries, the real estate industry responds more quickly to fluctuations in timing, with its stochastic volatility rapidly increasing and then returning to a low level. The impacts of the 2018 US–China trade war and the COVID-19 pandemic are also reflected in the stochastic volatility chart, with the impact on the construction and manufacturing industries, which belong to real economy, being more pronounced.

4.5. Impulse Response Analysis

Using the model’s estimated parameters, the estimation of time-varying impulse response functions is conducted. Figure 7 shows the impulse response results under different lag periods, selecting two, four, and six periods to explore the short, medium, and long-term impacts of shocks among variables. Figure 8 shows the impulse response graph with the two lag periods removed. The findings of the impulse response are shown in Figure 9 at various time intervals. Three time intervals, February 2008, August 2015, and February 2020, were selected for analysis, representing the global financial crisis, stock market crash, and the outbreak of the epidemic in China in 2020, respectively. Figure 10 shows the three-dimensional time-varying parameter impulse response graph. The subfigure captions are labeled as the impact of the previous industry on the subsequent industry.

In Figure 7, the lagged impact from the real estate and financial industries on the manufacturing industry has consistently been positive. As time progresses, the impacts increase with different lag periods, and the larger the lag period, the smaller the impact. The lagged impact of manufacturing industry on the real estate and the financial industries is characterized by a diminishing positive effect as the lag period increases. Additionally, there were noticeable fluctuations around 2015. Regarding the lagging impact of the real estate industry on the construction industry, it can be observed that over time, the positive impact gradually decreases to zero and then turn to increasing negative impact. To better examine the effects of financial industry and manufacturing industry on the construction industry, we excluded the data with a lag of two periods, resulting in Figure 8. In Figure 8, it can be seen that the manufacturing industry, real estate industry, and financial industry exhibit the same impact pattern on the construction industry. The impacts gradually decrease over time, reaching approximately zero around 2011 and then shift to a negative impact that gradually intensifies. Additionally, there are minor fluctuations around 2015.

In Figure 9, it can be observed that the impact of the real estate industry on the construction industry varies at different time points. During the 2008 financial crisis, the real estate industry exhibited a short-term positive impact on the construction industry, reaching its peak after a lag of two periods and dissipating after a lag of six periods. However, during the stock market crash in 2015 and the COVID-19 period, it exhibited a negative impact, reaching its peak after a lag of one period and dissipating after a lag of six periods. From the real estate industry to the manufacturing industry, it can be observed that the impacts are mostly positive, with peaks occurring at a lag of two periods and dissipating after a lag of eight periods. Over time, the positive impacts gradually decrease. In terms of the impact of manufacturing industry on the real estate and financial industries at different time points, the impact reaches its peak quickly after a lag of one period and rapidly declines to zero. Compared to the impact of the real estate and the financial industries on the manufacturing industry, the impact received by the manufacturing industry is slightly stronger than its impact on the real estate and financial industries. On the other hand, the impact of the real estate and financial industries on each other at different time points remains highly similar, characterized by rapid positive shocks reaching their peak at a lag of one period and dissipating after a lag of six periods.

From Figure 10, the specific form of the shocks can be observed in terms of lag and time dimensions. It was found that most of the shocks were concentrated in the short term, indicating that these industries have strong capacities to absorb shocks. The figure also reveals the transformation of the real estate industry’s impact on the construction industry from positive in the early time period to negative. Regarding the impact of these four industries on themselves, they are characterized by short-term positive effects and no negative effects, reflecting the healthy development of each industry itself.

5. Conclusions and Discussion

Based on the empirical results of Section 4.2, a “dark causality” relationship exists between manufacturing industry and construction industry, real estate industry, and financial industry. This implies the presence of more complex relationships. By applying the EEMD method to decompose the time series into three different periods, we further investigated the “dark causality” phenomenon. Interestingly, after decomposing the time series, the “dark causality” disappeared, while positive causality and negative causality showed significant differences across the three periods. This suggests that using the pattern causality method as an alternative to Granger’s causality test not only allows us to explore the existence of connections between industries but also provides a more comprehensive understanding of the selected relationships from a more complex perspective.

The impulse response results of the TVP-SV-VAR model show that the impact of China’s real estate market on the construction industry exhibits obvious time-varying characteristics, yielding different outcomes at different time points. During the 2008 financial crisis, the real estate industry had a significant positive short-term impact on the construction industry. However, during the 2015 stock market crash and the 2020 epidemic outbreak, the real estate industry had a notable negative short-term impact on the construction industry. The influence of the financial and real estate industries on the manufacturing demonstrated a positive effect, which gradually strengthens over time but is confined to the short term. Conversely, the impact of the financial and real estate industries on the construction industry displayed a positive effect in the early stage but transitioned to a negative effect in the later stage. This indicates that the financial and real estate industries exert a significant “crowding-out effect” on the construction industry. Combining the results of pattern causality and impulse response, it can be observed that the manufacturing industry, as a part of real economy at the R0 level, exhibits greater complexity compared to construction industry, which is part of the real economy at the R1 level. Furthermore, it is found that the real estate and financial industries, as components of the fictitious economy, have a consistent impact on the construction industry, and their impact on the manufacturing industry is similar. For the construction industry, in particular, there exists the phenomenon of “from Real to Virtual”, whereby the financial and real estate industries, as components of the fictitious economy, have a restraining effect on the development of the construction industry rather than promoting its growth. In contrast, the manufacturing industry does not exhibit this phenomenon. This is consistent with the hypotheses stated in our previous paper, confirming the existence of industries that undergo a “from Real to Virtual” phenomenon, while others do not.

Previous studies have reached the following conclusions. Shiller [12] observes the phenomenon of “from Real to Virtual” from the perspective of “monetary separation”. The capital market is easily influenced by irrational behavior, causing funds to flow rapidly from the real economy to the fictitious economy. The research of Andersson et al. [22] indicates that state-owned commercial banks in China have a restraining effect on the manufacturing industry. The research of Pan and Mishra [20] shows that in the long-term relationship, the Chinese stock market has a negative impact on the real sector, indicating the irrational prosperity of the stock market. Lv et al. [42] use the pattern causality method in their study and found that there was a predominance of “dark causality” relationships between China’s urban development and economic growth. Compared to previous studies, our study, while reaching the same conclusions, also explores the specific timing of the “from Real to Virtual” through the time-varying nature of the model. Additionally, the phenomenon of “from Real to Virtual” in the real economy can be explored from a more complex perspective. Furthermore, we utilize a more complex and applicable pattern causality approach instead of Granger’s causality test.

This study still has the following limitations. Firstly, further research and evidence are needed to investigate and demonstrate whether the absence of the “from Real to Virtual” phenomenon in the manufacturing industry is related to its dark causality. Secondly, this article did not utilize multiple variables to describe the four industries. Perhaps using multiple variables would provide a more comprehensive and nuanced perspective to reflect the real situation from different angles and complexities.

Based on the empirical results, this study provides the following policy recommendations that contribute to economic growth and coordinated development. Firstly, the status of fictitious in the national economy should be clarified, and the signs of “from Real to Virtual” should be included in the important indicators of national supervision of real economy development to ensure the healthy development of fictitious and real economies. Secondly, strong support should be given to the development of the real economy to achieve high-quality growth and to keep up with the pace of the fictitious economy. Thirdly, the flexible use of regulatory technology, big data technology, and risk prediction and warning means should be used to promote the healthy growth of a country’s economy. From the study of the four industries in this study, effective supervision and control should be carried out on the construction industry to eliminate the “from Real to Virtual” situation. Although the manufacturing industry has not yet exhibited the “from Real to Virtual” situation, the positive effects of the fictitious economy on it are gradually decreasing, so more support should be given to the manufacturing industry to allow it to keep up with the growth of fictitious economy. At the same time, more supervision should be carried out on the two sectors of the fictitious economy to prevent the uncontrolled growth and imbalance in economic development.