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Volatility Spillovers in China’s Real Estate Crisis: A Network Approach
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Keywords\textemdash Chinese real estate, connectedness, volatility, spillover, networks, variance decomposition
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In March of 2019, Evergrande\textemdash China's largest real estate developer and one of the largest companies in the world\textemdash was riding high, like much of the Chinese real estate sector. It had just announced that its 2018 core profit rose 93.3 percent compared to the previous year, a “record high" as the company delivered more properties while cutting costs. Some investors were concerned about the company's leverage ratio and other performance indicators, but the outlook was largely positive (jim_china_2019). Fast-forwarding to 29 January 2024, after losing 99% of its share value and struggling to make debt payments, China Evergrande was ordered to wind up by a Hong Kong court\textemdash a far cry from the rosy expectations of just five years earlier (hoskins_evergrande_2021; jim_china_2024).
While Evergrande has been the most prominent Chinese developer to struggle on the global stage, problems in the Chinese real estate market run much deeper: government policies limiting annual debt growth have handicapped the borrowing-dependent industry, creating a massive credit crunch that threatens to expose even the most financially reticent parties. As trouble built and investors realized the extent of their exposure, developers were hit by share selloffs, declines in credit ratings, and fewer willing lenders, further impeding their ability to raise cash. Yet, these massive and decisive share selloffs also offer an opportunity to examine spillover effects in the industry and map the pattern of contagion.
The existing literature on the Chinese real estate crisis focuses on spillover from the real estate sector to the broader economy (hu_risk_2024), the financial sector (huangfu_research_2024; ouyang_interconnected_2023; xu_risk_2021; nong_financial_2024), the industrial/manufacturing sector (xie_characteristics_2025), and the energy market (xie_dynamic_2025). This paper thus fills an important gap in the literature, analyzing spillover patterns among developers themselves across different events/phases of the real estate crisis. Following the work of demirer_estimating_2018 and diebold_network_2014, this paper uses a network approach to measure the daily time-varying connectedness of major real estate companies’ stock return volatilities. Examining how spillover patterns differ by region and state-ownership status, it maps how firms with specific regional focuses are impacted, working to understand where demand for property and real estate firm trustworthiness have deteriorated most\textemdash as well as whether state ownership impacts these perceptions.
In terms of methodology, this paper follows demirer_estimating_2018, first fitting a rolling window vector autoregression (VAR) to stock return volatility data for the Chinese real estate market. After using the elastic net for shrinkage and selection and estimating the VAR with a 100-day rolling window to capture the dynamism of developer relationships, a variance decomposition is then performed to determine how much of a firm's forecast error variance is attributable to shocks from other developers, summing these to obtain the directional Diebold-Yilmaz measures of connectedness. These directional connectedness measures are then plotted as a network to understand how connections between firms evolve across different events.
An event study is performed on four key events that signal different phases of the crisis: the announcement of the “three red lines," the first release of insider news about Evergrande's cash crunch, the initial suspension of share trading by Chinese developer Kaisa, and a key profit warning issued by Country Garden.
Indeed, I ultimately discern how investor sentiment has evolved as the real estate crisis progressed. First illustrating evidence of an external shock to the network with the announcement of the three red lines, connectedness primarily reflects shared exposure to real estate and an experience of a uniform, external shock.
Then, analyzing the network's behavior surrounding the release of news about Evergrande's cash crunch reveals investors' immediate reactions to market exposure: when the news broke, investors' instincts were linked with the regional development pattern of China, as they expected stronger contractions in less developed regions and shifted their investments away. There is also evidence that state-owned firms are seen as slightly more insulated from market shocks than their privately-owned counterparts during this early period.
One year into the crisis, network behavior during the suspension of share trading by Kaisa offers updated insight into investors' beliefs: now, regions that were regarded as relatively stable earlier in the crisis are increasingly at risk as the downturn continues. The network also reflects a change in sentiment surrounding the relative stability of state-owned enterprises, exhibiting a substitution effect towards private developers.
Then, fast-forwarding to nearly two years later, by the time of Country Garden's profit warning in August 2023, the network captures just how much investor sentiment has changed. Unlike in earlier periods, there is much less homogeneity across regions and state-ownership status, likely reflecting how developers have adapted to investing amidst the crisis. Now, when a “shocking" event occurs, the network change is minimal because investors have already priced in their beliefs. Nevertheless, there is evidence of a substitution effect towards state-owned enterprises\textemdash the reverse of that seen under the Kaisa case\textemdash reflecting the market sentiment that state-owned developers are now “safer" bets for investment.
In the process of this analysis, I also develop one of the most comprehensive timelines of the Chinese real estate crisis to date, as well as an R package for graphing networks using Gephi-based layout orientations (manso_gephiforr_2024-1).\footnote{Gephi is a popular network visualization software. The R package (GephiForR) can be found at \href{https://CRAN.R-project.org/package=GephiForR}{https://CRAN.R-project.org/package=GephiForR}.}
This paper first offers a brief primer on the Chinese real estate market, discussing state ownership in China (Section (ref)). Next, after introducing the data (Section (ref)), as well as the methodology and visualization process (Section (ref)), Section (ref) discusses the results. Section (ref) concludes. The comprehensive timeline of the real estate crisis can be found in Appendix (ref).
The Chinese real estate market is unique not only given the depth of State ownership, but also because it is a largely nascent industry that boomed within the past 30 years. Most importantly, though, housing in China is first and foremost a commodity, and the property market is distinctly speculative, with property developers wielding significant market power and housing prices increasing exponentially since 2000 (zhao_playing_2017).
While incredibly complex with many local disparities, the real estate market is the interaction of four groups who collectively influence price movement: local governments, real estate developers, banks, and speculators (liu_urban_2018). First, local governments gain “land revenue" by selling commercial and residential land use rights (wu_evaluating_2016). High land costs are subsequently transferred to high real estate prices, and real estate developers often engage in property hoarding and price discrimination to further increase real estate prices and create artificial scarcity (zhou_real_2021). Local governments then borrow heavily from banks by mortgaging land use rights and using the funds to support infrastructure development, which further drives up its potential for land revenue (liu_formation_2022). Developers also borrow heavily, not only obtaining funds from banks and other financial institutions, but from shadow banks, private financing, and even illegal fundraising channels (liu_formation_2022). Another key source of developer income is presales, wherein buyers pay for properties before their construction has concluded (sometimes even before construction has started), often through mortgages. Lending to all parties involved, banks offer excessive credit support to the real estate industry; this behavior in turn drives prices higher as developers borrow more to build, and buyers borrow more to pay. Indeed, buyers often act as speculators, purchasing property and selling it after prices rise. They too help support a cycle wherein all parties involved have an incentive to increase land value as much as possible, creating an overheating market and a property bubble.
Prior to 2020, the State's attempts to curb this cycle had been half-hearted: property has been one of the driving forces of China's economy, and to truly curb rising house prices would harm this growth (tan_effect_2022). Further, the onus had traditionally been on local governments to reform their policies and lower land sale prices\textemdash a difficult thing for them to do when 59.8 percent of revenue from property sales goes to the government, and combined revenues from land transfers and special taxes on real estate account for 37.6 percent of local government revenue as of 2020 (zhang_high_2024; ren__2021). When the central government shifted towards persistent tightening with the “three red lines" in 2020, speculators, developers, and banks all thought the government would back down from its measures. Yet, as the real estate crisis began to spiral during 2021, the public did not realize how deep that commitment to tightening\textemdash and its implications\textemdash ran.
When the three red lines policy was imposed, it was done as a pilot program for 12 developers and essentially restricted their ability to borrow capital/grow their debt subject to meeting three limits (“red lines") on the liability-to-asset ratio, the liability-to-equity ratio, and the cash-to-short-term-debt ratio. The maximum allowable annual growth in debt was restricted to 15% if no lines were crossed, dropping by 5% based on the number of lines violated. If a developer failed to meet all three criteria, it could not grow its debt annually at all. Realistically, the structure of the market ensured that almost all developers were violating the first red line on the liability-to-asset ratio, but others like Evergrande were in violation of all three at the time of announcement.
The three red lines pressured firms to internally restructure in order to meet government guidelines, and stress percolated into the market as internal documents\textemdash often describing just how badly firms were violating the red lines\textemdash were leaked to the public. As the situation escalated and the three red lines were expanded to all developers in January 2021, any actions by developers that hinted at financial trouble were met with sharp tumbles in stock price (white_chinese_2021). Developers thus took great pains to project images of financial stability and security, often liquidating assets behind the scenes to make bond payment deadlines. By early 2022, the situation was untenable, with leading firm Evergrande suspending trading of its shares, citing its inability to produce audited results (jim_china_2022; stevenson_china_2022).\footnote{On the Stock Exchange of Hong Kong, listed companies can suspend for up to 18 consecutive months, by which time they must supply results and be relisted or be delisted from the exchange altogether. Suspension is also a type of stop-gap mechanism that prevents the stock from falling in value while giving the company some time to rectify its struggling financial position, such that it can hopefully return to trading in a much stronger position (leung_rare_2024). } Several other struggling firms\textemdash China Aoyuan, Kaisa, Fantasia, Modern Land, and Sunac\textemdash followed almost immediately. Since then, shock after shock has impacted the market\textemdash and trouble continues still to this day. A comprehensive timeline of the events of the real estate crisis, from the three red lines to Evergrande's liquidation in early 2024, is included in the Appendix ((ref)), offering one of the most comprehensive timelines on the topic to date.
Also note that one additional factor further complicates firm behavior in this analysis\textemdash the prevalence of State ownership. Following chow_evergrande_2024, a State-owned enterprise (SOE) is defined here as a company whose largest shareholder is the State. Conversely, privately-owned enterprises (POEs) are understood as companies where the largest shareholder is a private company or individual. In China, these SOEs are legally recognized as corporate entities (rather than government entities) and are managed by State-owned Assets Supervision and Administration Commissions (SASACs). The literature suggests that Chinese SOEs are numerous and powerful enterprises, but less effective and profitable than their POE peers, limited by their ability to engage with and respond to market forces (and therein increase profitability). See, for instance, mei_fortune_2022.\footnote{However, viewing POEs as independent of state influence is essentially a false dichotomy. milhaupt_beyond_2015 argue that in China, virtually all large and successful firms have “close connections to state actors and agencies, access to state largesse, and a role in carrying out the policies of the ruling political party"; in essence, no firm is wholly autonomous (p. 668). Indeed, the POEs who most embrace the State's involvement often become the largest and most successful firms because State support can increase market access and yield business advantage through proximity to state power, among other benefits. Yet, clever real estate firms have also tapped into additional dimensions of State support: the State can provide stability amid high risk-taking and has a deep-seated interest in protecting its own enterprises\textemdash and deep coffers to accompany it. }
In line with diebold_network_2014, I use high-frequency stock market returns and return volatilities to estimate connectedness. This approach is quite intuitive, as those with the most knowledge about the connections under investigation are those financially involved. The data encompass real estate companies domiciled and operating in China from the Shanghai and Shenzhen stock exchanges; data collection and handling procedures are described in Appendices (ref) and (ref). With this raw data, volatility\textemdash the “dispersion from an expected value, price or model" (daly_financial_2008, p. 2379)\textemdash is calculated via the estimator developed by garman_estimation_1980, which applies Brownian motion principles to stocks to estimate daily stock return volatility as a function of the natural logarithms of daily high, low, opening, and closing prices for stock $i$ on day $t$. This specification is used broadly in the literature (as in ji_dynamic_2019, diebold_financial_2015, and longstaff_how_2011) and is “nearly as efficient as realized volatility based on high-frequency [five-minute] intraday sampling" while still being robust under several conditions including microstructure noise (demirer_estimating_2018, alizadeh_range-based_2002).
I follow demirer_estimating_2018's methodology, first basing my variance decomposition on an N-variable vector autoregression, VAR(d)
where $\varepsilon_t \sim {(0,\Sigma)}$. $\ell$ is the lag order of the autoregressive terms, $d$ is the number of lags, $\phi_\ell$ is the $N \times N$ coefficient matrix for lag $\ell$, and $\varepsilon_t$ is the disturbance vector whose covariance matrix is $\Sigma$. Finally, $\sigma^2_t$ and $\sigma^2_{t-\ell}$ are $N \times 1$ vectors of stock return volatilities calculated above, and the logarithm of all volatility terms ($\sigma^2$) is taken to normalize their distribution and remove the skew. This VAR is intentionally nonstructural, as, like diebold_financial_2015, I do not seek to define exactly how connectedness arises.\footnote{Note that I use the VAR with the rolling window specification rather than another version of the VAR from the literature (e.g., the time-varying parameter VAR, TVP-VAR), because it best fits this use case. The leading alternative candidate, TVP-VAR, uses a Kalman filter, and its results are thus sensitive to priors and forgetting factors (antonakakis_refined_2020). In particular, in antonakakis_refined_2020, the TVP-VAR is initialized with the VAR estimate of the first 60 periods, which can bias the results depending on whether this is a calm or turbulent period: a calm pre-period could bias the model to interpret shocks as outliers, while a turbulent pre-period may cause the model to overreact to noise. In addition, hyperparameter selection can also bias the results. In light of these issues, the 100-day rolling window is preferred in this context given the focus is meaningful before and after windows and a model that performs well in the presence of a large number of shocks. }
To estimate the VAR in such high dimensions, I utilize the elastic net, in line with demirer_estimating_2018.\footnote{Note also that while other tools like the adaptive elastic net may be an improvement over the elastic net, they cannot be calculated for the rolling window estimation due to data limitations: the window size of 100 is just enough for the elastic net calculations given the number of developers (97 Chinese firms). Given the number of firms in the sample, there are more regressors than observations when lags are included, and it is thus not possible to use the adaptive elastic net to give dynamic updates without a window of size equal to or greater than $N\times\ell$. This much larger window (in this case, equal to or greater than 291) inherently loses most of the sensitivity that the narrow 100-day one offers, so I utilize the elastic net with 100-day rolling window estimations for the bulk of the analysis. Appendix (ref) offers an example of a network generated under the adaptive elastic net with a larger window size.} Performing simultaneous selection and shrinkage like the lasso, the elastic net includes both ridge and lasso penalties, with a regularization parameter $\lambda$ and an adjustable parameter $\alpha$ that balances the lasso and ridge penalties. Importantly, the elastic net can also select groups of correlated variables since the penalty term is strictly convex for all $\alpha \textit{ }\epsilon \textit{ }(0,1)$ and $\lambda>0$, a particularly valuable feature in this context given that real estate firms' volatilities are often highly correlated (zou_regularization_2005; hastie_statistical_2015). $\alpha$ is regarded as a “higher-level" tuning parameter that is often set on subjective grounds (hastie_statistical_2015). I conduct a sensitivity analysis to investigate how sensitive the results are to different $\alpha$ values in the elastic net estimations. The main specification, whose results are shown in Section (ref), uses $\alpha$ = 0.5, in line with demirer_estimating_2018.\footnote{It is also important to note that while I seek sparsity in the approximating model, I do not necessarily want to impose sparsity in the estimated real estate firm network. In line with demirer_estimating_2018, this shrinkage and selection is thus performed on the approximating VAR rather than the variance decomposition network directly. While performing shrinkage and selection on the VAR, the variance decomposition matrix that is used to calculate connectedness measures is a “nonlinear transformation of the VAR coefficients and is therefore generally not sparse" (Demirer et al. 2018, p. 5). In the Chinese real estate case, the network remains fully connected.}
Following demirer_estimating_2018, I estimate an elastic net-penalized regression with ten-fold cross-validation, extracting the coefficients from the model which minimize the cross-validation error and iterating through the columns to generate the $\phi_\ell$ matrices referenced in ((ref)). The impulse response function is then calculated, iterating through the lag periods and horizon $H$. The impulse response can be viewed as the effect of a hypothetical $N \times 1$ vector of shocks impacting the market at time $t$ compared with a baseline profile at time $t + H$, given the market's history.
Importantly, these impulse responses and variance decompositions allow estimates of connectedness at different time horizons $H$, with shorter time horizons like 1 or 2 days ($H = 1$ and $H=2$, respectively) picking up immediate market reactions while longer horizons like 30 days ($H=30$) reflect more fundamental dependencies or economic relationships. This analysis uses a horizon $H$ value of 10 days to balance longer- and shorter-term volatility comovements; a lag period of 3 is used because the VAR model often selects coefficients for several firms on the third lagged day.\footnote{When a longer lag period (e.g., 5 days) was tested, the model selected very limited numbers of coefficients from the additional days.}
Aggregating this information, the generalized forecast error variance decompositions ($\theta_{ij}(H)$), which provide firm $j$'s contribution to firm $i$'s $H$-step-ahead generalized forecast error variance, can be calculated: the numerator effectively sums up and then squares the shocks from variable $j$ on firm $i$ over all horizons up to $H-1$. This represents the cumulative effects of shocks in variable $j$ on the forecast error variance of variable $i$ up to horizon $H$. The denominator reflects the total forecast error variance, summing the contribution to the forecast error variance from all shocks affecting variable $i$; then, it is normalized by the standard deviation of the disturbance of the $j$-th equation. Subsequently, following demirer_estimating_2018, each $\theta_{ij}$ of the generalized variance decomposition matrix is normalized by the row sum to obtain
This normalization means that $\sum{_{j = 1}^N} d_{ij}^H = 1$ and $\sum{_{i, j = 1}^N} d_{ij}^H = N$, allowing for the resulting $d_{ij}^H$ to be comparable across different time horizons $H$.\footnote{As will be described in Section (ref), these $d_{ij}^H$ values are measures of pairwise directional connectedness.} These $d_{ij}^H$ values form the matrix $D^H$, which is the core of demirer_estimating_2018 and diebold_network_2014's connectedness measures (Section (ref)).
demirer_estimating_2018's connectedness estimation method makes it possible to decompose how much of firm $i$'s future uncertainty at a specified horizon $H$ is due to shocks arising not from entity $i$ itself, but from each other entity $j$ in the sample. As described above, it relies upon $d_{ij}^H$, the fraction of $i$'s $H$-step forecast error variance due to shocks in firm $j$, where $D^H$ = $[d_{ij}^H]$. This full set of variance decompositions is the core of diebold_network_2014's connectedness table, which is in effect an augmented variance decomposition matrix, as shown in Table (ref).
The upper left block of Table (ref) is the standard $N \times N$ variance decomposition matrix $D$ composed of the connectedness between each firm $i$ and $j$ for time horizon $H$, with $D^H$ = $[d_{ij}^H]$. This $D^H$ is augmented with a column of row sums in column $N+1$ and a row of column sums in row $N+1$, both for $i \neq j$. The value in cell $[N+1, N+1]$ is the grand average, again for $i \neq j$. The off-diagonal entries of the $N \times N$ variance decomposition matrix reflect the pairwise directional connectedness from firm $j$ to firm $i$. That is,
This means, for example, that $d_{21}^H$ is the pairwise directional connectedness from firm 1 to firm 2 while $d_{12}^H$ is the pairwise directional connectedness from firm 2 to firm 1. These values will not necessarily be equal as firms do not often impact each other symmetrically. For instance, if firm 1 is a massive price maker in the market but firm 2 is a small and relatively isolated firm, shocks to firm 1 may also have significant effects on firm 2, but conversely, shocks to firm 2 will not likely affect the powerful firm 1 in the same way. Thus, generally, $C^H_{i \leftarrow j } \neq C^H_{j \leftarrow i }$. There are consequently $N^2 - N$ separate pairwise directional connectedness measures.\footnote{$N$ is subtracted as we exclude the diagonal elements (which effectively represent self-spillover).} diebold_network_2014 thus defines net pairwise directional connectedness as $C^H_{ij} = C^H_{j \leftarrow i } - C^H_{i \leftarrow j }$, and there are $\frac{N^2 - N}{2}$ net pairwise directional connectedness measures.
When the diagonal entry is excluded ($d_{ij}^H$, where $i = j$), aggregating across each row yields the share of the $H$-step forecast error variance of firm $j$ that comes from shocks arising in all other firms. In line with diebold_network_2014, this total directional connectedness from others to $j$ (“from" connectedness) can be represented mathematically as
The same reasoning is applied to off-diagonal column sums: for each column, excluding $d_{ij}^H$ when $i = j$ and summing the rest of the column yields the share of the $H$-step forecast error variance that firm $j$, when shocked, gives to all other firms. This is referred to as “to" connectedness.
This Diebold-Yilmaz approach to network connectedness is appealing because it bridges the VAR variance-decomposition and the network literature, essentially positing that “a variance decomposition is a network" (diebold_past_2023). The VAR can capture the dynamic interactions among multiple lagged variables without imposing strong a priori restrictions or requiring a structural model. At the same time, it assumes linear relationships among variables, and the subsequent impulse response function and generalized forecast error variance decomposition are sensitive to the shock covariance matrix derived from the VAR, which demirer_estimating_2018 do not choose to regularize.
For the results shown in this paper, network layout is determined by Gephi's ForceAtlas2, created by jacomy_forceatlas2_2014, which calculates the “net forces" acting on each node by summing the node's attraction to and repulsion from each other node it connects to.\footnote{Note that Gephi is a popular software used for visualizing networks.} For clarity, assume that all variables take on new meanings (as defined) unless explicitly specified.
The formulas for each are rooted in eades_heuristic_1984 and his application of physics principles to networks; the attraction formula is an altered version of Hooke's law, which reflects the compression behavior of a spring ($F = -k \times x)$, where $F$ is the spring force, $k$ is the spring constant, and $x$ is the spring compression. In Gephi, the attractive force $F_{a}$ is the product of the edge weight $w(e)^\delta$ between each pair of nodes, multiplied by the geometric distance between them, as shown below:
where $\delta$ is the binary variable “Edge Weight Influence," set to either 0 or 1.
Repulsion is based on Coulomb's law, which calculates forces between electrically charged particles ($F = k\frac{n_1n_2}{d(n_1, n_2)^2}$). Here, $F$ is the resulting force; $n_1$ and $n_2$ are the point charges of particles 1 and 2, respectively; $d(n_1, n_2)$ is the distance between the two particles $n_1$ and $n_2$; and $k$ is the Coulomb's law constant. In Gephi, repulsion $F_r$ is calculated by a slightly modified version of Coulomb's law where node degree takes the place of point charges, the constant becomes scalable rather than fixed, and distance is no longer squared. The key development from previous node repulsion calculations was the addition of “+1" to the degree, as Jacomy et al. wanted to ensure that nodes with degrees of zero still have repulsive force. The formula is thus
This calculation is repeated between every possible node pair in the data. Thus, $d(n_1, n_2)$ is the distance between the two nodes $n_1$ and $n_2$ in the pair, $deg(n_1)$ and $deg(n_2)$ are the degrees of each of the two nodes, and $S$ is a scalable constant that influences the repulsion level in the graph, with higher repulsion making a sparser graph.
This combination of “spring-like" attractive forces and “particle-like" repulsive forces has persisted, with several authors offering slightly modified equations over the past 40 years. In Gephi, the attraction and repulsion forces can be decomposed into vector form and summed to calculate the net forces on each node ($F = F_{r} + F_{a}$); this value is then used to find the resulting displacement. The actual displacement of a node $\Delta(n)$ is then calculated by the formula:
where $s(n)$ is the speed of node $n$. To calculate the speed, Jacomy et al. use two factors\textemdash irregular movement (“swinging") and useful movement (“effective traction"); in effect, they calculate how much the forces on a node compare between two sequential periods and (usually) use lower speeds to update a node's position if there is a large change in forces. Over several iterations calculating each node's displacement and updating its position, networks converge to a stable position. A full explanation of the formulas behind this, as well as a toy example, can be found in Appendix (ref).
All network figures in this paper are created with the GephiForR package (manso_gephiforr_2024-1), which implements the ForceAtlas2 layout algorithm in R and offers several other network visualization tools.
The figures below are color-coded by the region where the developer is primarily focused: pink is the north, light green is the south, teal is the east, bronze is the southwest, light blue is the northwest, and red-orange (of which there is only one node, CN:SOT) is the northeast. As is apparent in Figure (ref), the bulk of the nodes are eastern-focused (teal), with a significant amount focused in the north (pink) and the south (light green). Only four firms have their primary business in the southwest (bronze) and three in the northwest (light blue). These business-centricities reflect the development pattern of China, as coastal regions tended to develop first and became richer (east and south). The north is developing more at present but has the advantage of the Beijing and Tianjin municipalities being within its bounds. The northeast, southwest, and northwest are emerging regions with large areas of sparsely populated land (felice_chinese_2023).
Unless otherwise specified, node size is determined by “to" connectedness, meaning that nodes with higher levels of to connectedness are larger. Node size is set as to connectedness both because to connectedness is more variable than from connectedness (as explored later) and because it offers a helpful way to understand how connectedness evolves over time. Stressed networks are indicated by nodes being drawn more tightly together, a clear core forming, and (sometimes) more regional clustering; the Appendix's Figure (ref) offers a visual comparison between an unstressed and stressed network, for reference. I also clarify how sparse the $\phi_\ell$ matrices from the VAR are in Appendix (ref).
I first focus on the (informal) announcement of the three red lines. While the three red lines were formally announced at a meeting on 20 August 2020, there had been rumors about them in the market starting one week earlier (13 August, after close of business). I compare plots from 13 and 14 August in Figure (ref) below.
This first case provides a litmus test of network sensitivity since the rumor of an imminent policy coincides with a noticeable network contraction as the nodes draw closer together. This is important to see given that this is a rolling window estimation, meaning that the VAR is estimated on 100 days of data. Thus, the network should not (and indeed, does not) oscillate wildly between days due to the carry-over of the previous 99 days in the window, but should simultaneously allow for changes to appear sensitive to the most recent day.
As is apparent in the images above, the network contracts slightly with the first news of the three red lines policy. In particular, most of the nodes are drawn in more toward the core of the network\textemdash a simple visual inspection reveals that the network on 14 August appears smaller in size than that on 13 August. For the most part, nodes are not making radical moves, with many staying near their relative initial positions but pulling in slightly. This behavior suggests that the news of the three red lines indeed impacts the entire market rather than one segment disproportionately, and most nodes (80/97) experienced a decrease in “from" connectedness. The majority of nodes (61/97) also experienced a decrease in “to" connectedness when compared to the previous period (13 August 2020). This relatively uniform behavior likely reflects the impact of the policy change, as the estimate suggests that the majority of firms have a lower level of spillover to and from each other in this period. Simultaneously, the force calculations in ForceAtlas2 register higher attractive forces across the network (meaning some edge weights are stronger), which suggests increased interdependencies between nodes, as is often the case when a market experiences a shock. Both factors are consistent with a shock originating outside of the network, such that the connectedness of most nodes behaves similarly while higher edge weights reflect how ties between firms have strengthened, pulling nodes closer together.\footnote{It may seem counterintuitive for most nodes to experience decreases in “to" and “from" connectedness while the network experiences higher attractive forces. However, both the distribution and magnitude of the edge weights ($d_{ij}$), as well as the normalization, make this result possible, and I explain the phenomenon fully in Appendix (ref). In this case, when examining the edge weights of the network, roughly half of directional node pairs have stronger magnitudes of pairwise directional connectedness on 14 August than on 13 August, and their magnitude and distribution is important as well\textemdash 70% of the node pairs have one or both edges with higher edge weights on 14 August than on 13 August, causing nearly the entire network to draw more tightly together. At the same time, to and from connectedness do not necessarily increase because they depend on the overall distribution of influence patterns in the network: when $d_{ij}$ are summed down a column or row to calculate “to" or “from" connectedness, respectively, the total is lower on average on 14 August than on 13 August. Certainly, this is not the case for every firm, as some experience increases in “to" and/or “from" connectedness, but this asymmetry, coupled with the normalization, helps lead to a decrease in “to" and “from" connectedness on average, as the increase in weights is not proportionate across the network.}
Here, firm interactions by region do not change significantly: no region is suddenly pulled into the core or ejected from it. Rather, as described above, nodes of all colors are pulled towards the center, and the average node's “to" connectedness decreases. Likewise, as I seek to examine the impact of state-ownership on firms, I also generate plots of the network where the nodes are colored based on their state-ownership status. I include these state-ownership plots for this event only in the Appendix (Section (ref)) as they are not particularly insightful: there is no evidence of differing behavior between SOEs and POEs with the announcement of the three red lines.
I next examine the first significant shock to the market from a real estate developer, which occurred when the letter from Evergrande to the Guangdong government circulated on Chinese social media and then in the news. A letter dated 24 August 2020\textemdash just four days after the government's meeting with developers where the three red lines were officially announced\textemdash began to circulate online roughly one month later on 22 September, becoming viral on 24 September. Declaring that Evergrande's capital was significantly reduced and that its cash flow had been disrupted, the letter warned of a possible default (chinaevergrandegroupco_china_2020). Within a few hours of the letter going viral, Evergrande swiftly denounced it, but the damage was done (zhou_-_2020; chinaevergrandegroupco_china_2020). Figure (ref) shows the network at four times: just before the news broke out (21 September 2020), when it had circulated partially (23 September 2020), when it went fully viral (24 September 2020), and approximately two weeks afterward (9 October 2020).
The network in Figure (ref) already shows some clustering, with nodes in the center of the network grouping loosely by region and having relatively high “to" connectedness levels. When the news has been partially circulated (Figure (ref)), nodes closer to the core have an increase in to connectedness, while those at the top and right sides of the network remain pushed out with lower levels of to connectedness. Particularly, teal nodes (eastern-centric firms) in the core tend to shrink slightly while their pink counterparts (north-centric firms) in the core grow, meaning that their to connectedness is increasing. This behavior continues in Figure (ref) as the news goes viral; the to connectedness of several nodes in the core increases significantly as the core nodes pull closer together. At the same time, several nodes at the periphery (particularly on the top and right) remain immune to the attractive forces pulling the other nodes in. Noticeably, to connectedness (and thus node size) increases less on average for firms with a predominantly eastern focus (teal nodes) and southern focus (light green nodes) than those from the other regions. In particular, firms with a northern focus (pink nodes) and southwestern focus (bronze nodes) seem to experience the largest increases in to connectedness, suggesting that market spectators expect some dimension of regional spillover. This higher level of spillover to northern- and southwestern-centered companies thus likely reflects that investors perceive these regions to be less stable and comparatively less insulated from a real estate shock.\footnote{Indeed, the raw stock movements confirm that the increased to connectedness of these firms is not a substitution effect wherein investors view these firms as more stable (which would drive higher prices) but that of a knock-on effect that causes investors to divest from these stocks, which they view as less stable.}
This result is especially interesting because there are no comparative increases in “to" connectedness for southern-focused developers: one would expect that since Evergrande's headquarters and the majority of its properties are there, the developers most exposed to an Evergrande cash crunch would likely be those it interacts with most (i.e., also southern developers). It is then particularly fascinating not to see this effect immediately, as its absence suggests that investors initially anticipate effects at the regional level rather than the developer level. This behavior ties back to entrenched ideas about China's path of development and the property market in China, deriving from housing as a commodity, as discussed in Section (ref). As housing is highly speculative, demand is then linked to speculators' expectations about the broader market\textemdash they expect that demand will dip most in less developed regions like the north, southwest, and northwest, and in turn, their own demand for property in those regions dips, creating a self-fulfilling prophecy.
Simultaneously, the continually distanced nodes on the top and right peripheries, apparent in Figures (ref) and (ref), suggests that several nodes remain less connected with the core and are thus continually pushed outwards as they experience high repulsive forces from the other nodes. This implies a degree of segmentation in the market such that investors believe some real estate companies are particularly well insulated from Evergrande and the shock its default would generate, beyond the regional dimension. Investigating the profiles of companies on the periphery that remain pushed out reveals that they are more diversified than the developers in the core. In addition, state ownership also appears to play a role in pushing certain nodes further out than others. In particular, a plot color-coded for state ownership, shown in Figure (ref), illustrates that in the initial shock, non-state-owned companies (pink nodes) on the periphery of the network tend to be pulled in, while their state-owned counterparts (teal nodes) tend to remain pushed out (Figures (ref) and (ref)). Indeed, most of the nodes that remain close to their initial positions farthest out on the periphery are state-owned companies rather than privately held ones; this behavior suggests that investors also hold an underlying belief about state ownership's role in firm stability\textemdash that state-owned firms are more stable than their privately owned counterparts.
Two weeks after the shock, the network has converged toward a new base state: the core of the network has drawn inward, and most of the nodes on the periphery have drawn in as well. Instead, the network seems to have contracted more tightly than it was originally, with several firms (particularly northern ones) having higher levels of to connectedness; indeed, the to connectedness is so high in the core of the network that the nodes are almost overlapping.\footnote{This apparent overlapping is due to high levels of to connectedness; the positions prescribed by ForceAtlas2 have separation between the nodes, and the nodes do not inherently overlap, only doing so here because node size is to connectedness. } The regional dimension still seems to play a role, as the to connectedness has increased for northern-centric firms more on average than any other region. Likewise, firms in the southwest (bronze nodes) end up pulled much closer to the core of the network than they were originally.
Some southern-centric (light green nodes) and eastern-centric (teal nodes) firms have also been pulled towards the center. However, for both these southern- and eastern-centric firms, the magnitude of to connectedness is not as significant as that of the northern firms. This behavior does suggest that investors now have a more nuanced view of what specific firms will be most impacted, but there nevertheless seems to still be a regional slant towards northern firms, the bulk of which still have higher levels of to connectedness than before the news was released.
From the state-ownership perspective (Figure (ref)), the nodes furthest out on the periphery are mostly state-owned companies (teal nodes), and several private companies (pink nodes) have penetrated the core of the network, which was previously composed of mostly state-owned companies. This behavior again reflects how investors view private ownership as less stable in times of high risk, when the market is dominated by state-owned companies. Certainly, though, being state-owned does not make a firm wholly protected from any financial shock: state intervention takes time and is not perfectly efficient, meaning one would not expect all state-owned firms to simultaneously exit the core and have very low levels of “to" connectedness: these firms are still market participants, and their profit will dip in the event of a market contraction, regardless of the contraction's origin8.
While these two events have a relatively clear-cut impact on the network given that it was not in distress before, later events are more complex as the market became constantly stressed. After the previously discussed Evergrande letter, the market spiraled through various cycles and contractions as more developers faced financial trouble\textemdash and it is these events, in which new developers have their first major loss of public confidence, that allow us to understand spillover patterns that emerge when the network is shocked.
I thus analyze the suspension of Kaisa on 5 November 2021, which occurred a day after one of its affiliates missed a payment to onshore investors (galbraith_kaisa_2021). Kaisa became the first Chinese developer to default on its dollar bonds in 2015 but had largely recovered since then; however, combining the bad market with rating downgrades, the developer was under pressure and struggling (jim_exclusive_2021). The shares were suspended pending the release of “inside information" with the resumption of trading ultimately occurring 17 days later (zhu_kaisa_2021). Figure (ref) below illustrates the network around this change, with Figure (ref) depicting the network on 3 November 2021, the day before the missed payment to onshore investors and two days before the suspension. Figure (ref) illustrates the network the day the suspension is announced and begins (5 November 2021).
The core of the network contracts, with several nodes pulling in towards the core while those on the periphery remain on the edge of the network. There are a few interesting observations here: first, unlike previous periods, the companies at the core of the network with the highest levels of connectedness are now eastern-centric companies (teal nodes) rather than northern- or southern-centric ones (pink or light green nodes, respectively). Certainly, there are still pink and light green nodes in the core and many that are drawn in from being more towards the periphery between Figures (ref) and (ref). Yet, the bulk of nodes that experience an increase in to connectedness in Figure (ref) are eastern-centric. Contrarily, the nodes on the periphery, even those that are teal, experience a decrease in to connectedness on average and thus shrink; 20/31 periphery nodes shrink, with 12/17 of teal nodes on the periphery experiencing decreases in to connectedness. “From" connectedness is largely the same across both periods; excluding the seven firms who have larger increases in from connectedness as they are pulled in from the periphery, most firms experience a negligible from connectedness increase of 0.51 between 3 and 5 November.
In earlier periods (such as when Evergrande's letter to the Guangdong government was exposed), eastern-centric companies were largely grouped to one side of the network and comprised most of the periphery. Their new position\textemdash pulled more towards the center of the network and largely surrounded by their southern and northern peers, rather than vice-versa\textemdash suggests investors have an updated belief about regional spillover: the areas that were initially regarded as comparatively more stable are now much more at risk, manifesting in the new node position apparent in Figures (ref) and (ref).
This behavior is interesting given Kaisa has the bulk of its properties in the south, east, and southwest of China: certainly, the southwestern- and southern-centric companies (bronze and light green, respectively) are drawn in slightly, but again, neither comprise the bulk of the core. The shock of the suspension is thus felt through increasing to connectedness mainly in eastern-centric developers as well as increasing pairwise connections between these developers and those around them, as reflected by the contraction of the layout and the increase in attractive force between nearby core nodes.
In terms of state ownership (Figure (ref)), several private firms remain pulled into the core, as in Figure (ref). While most of the periphery is composed of private firms in Figure (ref), these firms are largely pulled towards the core in (ref), such that even though they mostly remain on the periphery after the suspension, their pairwise connectivity with the core nodes increases, resulting in closer positions. Noticeably, most of the private firms that are pulled towards the core (such as CN:HHA, CN:SWX, CN:HBR, and CN:COD) experience very small or no increases in to connectedness; comparatively, those that are state-owned in the core, like CN:JIA, CN:SJI, and CN:TCC, and even state-owned firms on the edges of the core, like CN:PRP, CN:DON, and CN:BJG, experience increasing to connectedness, as reflected by a larger node size.\footnote{The full company names of the nodes mentioned are as follows: the private firms pulled towards the core are CN:HHA (Hubei Fuxing Science and Technology Co.), CN:SWX (Shanghai Shimao `A'), CN:HBR (Hangzhou Binjiang Real Estate Group Co.), and CN:COD (Dima Holdings `A'). The state-owned firms in the core are CN:JIA (Greenland Holdings `A'), CN:SJI (Everbright Jiabao `A'), and CN:TCC (Tianjin Tianbao Infrastructure `A'). The state-owned firms on the edges of the core are CN:PRP (Shenzhen Properties & Resources Development Group Ltd.), CN:DON (Bright Real Estate), and CN:BJG (Beijing North Star `A').} Underpinning this behavior is an interesting substitution effect towards private firms: returning to the raw stock return data reveals that the majority of privately owned firms on the periphery (10/17) experience increases in closing price for their stocks on 5 November, compared to 3 November. Meanwhile, most state-owned companies on the periphery (11/16) experience price decreases, like the nodes in the core; only a select few state-owned companies, mostly on the right edge of the periphery, experience price increases. Appendix (ref) contains plots showing periphery nodes with this color coding.
This behavior suggests investors implicitly consider state ownership in their risk calculations: unlike in earlier periods, state-owned firms appear riskier than their private counterparts, and with the shock to Kaisa, investors seem to divert funds away from state-owned firms and towards privately held ones. This is a fascinating effect that runs counter to standard expectations; it is likely because at this point, state-backed developers were asked to purchase or take on some projects of struggling private developers, whether through buying the property outright or increasing their stake to be the majority shareholder in a development (chow_evergrande_2024). These deals often were designed to give the struggling private developer a substantial cash injection and/or a share of the future revenue of the property, meaning the deal was often not profitable for the SOE buyer (jim_china_2021).
Thus, these plots seem to reflect investor sentiment that with policy changes in 2021, state-owned firms are no longer the safest bet\textemdash and may even be riskier because of the suboptimal bailout investments they are made to take on. The private firms on the periphery are mostly those with diversified investments and operating sectors, factors which likely catalyze the substitution effect apparent above.
As the crisis dragged on, a new phase emerged in mid-2023: developers who had previously avoided financial trouble were now getting dragged into the fray, chief among them Country Garden. In early August, Country Garden\textemdash at this point the largest private property developer in China, with four times as many pending developments as Evergrande\textemdash began to exhibit signs of financial trouble (liu_how_2023; choi_country_2023; jim_country_2023). I analyze two parts of this event: the scrapping of a share sale (1 August 2023) and the issuing of a profit warning (10 August 2023).
The aborted US\$300 million share sale happened at the last minute on 1 August 2023 as Country Garden shared that it had not reached a “`final agreement' for the deal to go ahead" (jim_country_2023-1). Then, after a relatively calm couple of days, rumors began to quietly circulate again: Country Garden had apparently missed a payment that was due on 8 August, and then, after close of business on 10 August, it issued a profit warning.\footnote{I do not include the networks before and after the 8 August news in the body of the text, largely because, as with the case of the profit warning on 10 August, there is little change in the network. They are included in the Appendix, Section (ref), for reference.} The company revealed that it expected to record a net loss between US\$6.24-7.63 billion for the first 6 months of 2023 (unlike its net profit of US\$265 million for the first 6 months of 2022) (countrygardenholdingscompanyltd_profit_2023).
In Figure (ref), I thus include 4 dates: the business day before any Country Garden-related news circulates (31 July 2023), the day the news of the aborted share sale breaks (1 August 2023), the business day before the profit warning was issued (10 August 2023), and the day after the profit warning was released (11 August 2023).\footnote{Note that 10 August is the “before" period for the profit warning because Country Garden only issued it after close of business; the aborted share sale news broke early in the morning, so 1 August 2023 is the appropriate “after" period for the share sale news.}
As is apparent in Figure (ref), the network has a larger reaction to the news of the aborted share sale than to the profit warning\textemdash an interesting result given that aborting the share sale does not in itself imply financial struggle. Indeed, Country Garden's rhetoric around the canceled share sale took great pains to emphasize that it was not the buyers who backed out, but Country Garden itself who prevented the deal (jim_country_2023-1). The above plots indicate that market participants were not entirely convinced that the firm was free from trouble as it claimed.
The effect on the network comparing Figure (ref) and (ref), then, is more obvious than that between (ref) and (ref) but, at the same time, is nowhere near the larger-scale changes seen in earlier plots like Figure (ref). Indeed, with the news breaking out on 1 August, only 56/97 firms experience increases in to connectedness, and for all but two firms, this increase is very minor. Compared to other events such as Evergrande's letter to the Guangdong government and Kaisa's suspension, this is the first time that a southwestern-centric firm (bronze node) has been in the very core of the network. Indeed, two of these nodes are in the core in Figure (ref) and get pushed out slightly between 31 July and 11 August. The core is thus extremely diverse; southern-focused, northern-focused, eastern-focused, and now southwestern-focused companies all occupy key positions in the core. While southern companies (light green nodes) seem to get pushed slightly away from the network's core with the news of the aborted share sale, nodes at the center are drawn closer as the core tightens, and some of the periphery nodes become drawn in as well, particularly on the bottom and the left of Figure (ref). Overall, though, the network is remarkably stable.
Now looking at the announcement of the profit warning, the stability of the network between periods is even more apparent between Figures (ref) and (ref); apart from some slight movement around the core, most nodes remain relatively close to their initial positions\textemdash even the periphery has minimal movement. In terms of to connectedness, only 44 firms experience an increase in to connectedness between 10 and 11 August, and the magnitudes of increase are relatively small across the board.
Both of these events were accompanied by sharp drops in Country Garden's share price, per the raw stock data, with the stock dropping to a “record low" after the 10 August profit warning\textemdash making the network's stability that much more interesting (lim_country_2023). Indeed, analyzing these two closely related events in tandem reveals an interesting picture: more so than in other periods, there is less concern about regional spillover and more emphasis on specific firm attributes. The firms who do experience increases in to connectedness and maintain positions in the network's core are a specific subset with no central geographic focus or SOE vs. POE status: they instead seem to be those with the most perceived exposure to Country Garden, like China Vanke (CN:VAN) and Dima Holdings (CN:COD).
Indeed, one of the most critical things to observe here is that node movement and to connectedness changes are much more limited than in the previous events. This is likely because investors have been forced to become more reticent about their investments as the real estate crisis has dragged on: gone are the immediate, region-based, knee-jerk reactions to the three red lines (2020) or the emergency shock suspensions of developers like Kaisa (2021). Now, a full two years later, investors have examined company financials, performed their due diligence, and mapped expected exposure patterns. The result is that there is less sensitivity to “shocking" news because the majority of market participants have already “priced in" the information: at the first hint of concern, price-makers quickly divest from exposed developers, such that when major events occur\textemdash like the aborted share sale or the profit warning announcing an expected loss of over US\$6 billion\textemdash the network does not experience a quick and drastic change like before. This is even the case for major, market-making events such as the liquidation of Evergrande in January 2024 and the suspension of Country Garden in March 2024; I include plots of these in the Appendix (Section (ref)).
Examining state ownership status also provides insight into a fascinating dynamic occurring in Figures (ref) and (ref). On the surface, nearly all of the state-owned enterprises have initial positions more towards the core than the periphery. Indeed, in Figure (ref), there are few SOEs at the outskirts of the network compared to POEs. As time passes, several POEs tend to be pulled more towards the core of the network\textemdash particularly those on the bottom of the network, as is most apparent in Figure (ref).
On the surface, this behavior suggests that private firms are seen as more exposed than state-owned ones, but the effect is not uniform. Instead, returning to the raw price data offers further insight. In fact, the substitution effect of the Kaisa suspension has reversed: in that case, the to connectedness measures and network layout suggested that private firms were seen as more stable than their state-owned counterparts, likely due to investor expectations about state-owned firms being compelled to enter into disadvantageous agreements with failing private developers. Now, there is prominent evidence of the opposite happening: when the first signs of trouble are apparent at Country Garden, there is a shift to state-owned developers. Of the companies on the periphery\textemdash whose position further away from the core suggests that they are more insulated from real estate shocks\textemdash the bulk of those who experience a price increase (7/10) are state-owned.
In fact, this seems to be the prevailing sentiment among market participants, as 2023 land market data suggest a prominent shift toward state-owned developers: the top six Chinese developers of 2023 in terms of home sales all had state-backing, and many of the most prominent private developers slid down the rankings (jim_chinas_2024). Some predictions even expect real estate troubles will last for the next ten years, positing that private developers will continually struggle to make debt payments as sales remain sluggish (ao_chinas_2024). In the face of these recently emerging expectations, this substitution towards state-owned developers is largely expected.
Certainly, many more developers experience decreases in share value than increases between 31 July and 1 August, but the pattern is prominent among those who do experience increases in share value. The behavior again reflects how firms of a certain regional focus or state-ownership status are not homogeneous in the eyes of investors: the balance sheet trumps all, and discerning investors will work to uncover where exposure lies.
Offering evidence of an external shock to the network with the announcement of the three red lines, the 100-day rolling window estimation allows insight into the more nuanced behavior of speculators and investors as the real estate crisis progressed. Further, it confirms there is a basic level of connectedness that comes from being listed on a Chinese exchange and having real estate exposure.
In one of the first major events of the real estate crisis\textemdash the release of Evergrande's letter to the Guangdong government\textemdash investors immediately expected stronger contractions in less developed regions. There is also evidence that state-owned firms are seen as slightly more insulated from shocks than their privately owned counterparts. As usual, the most diversified companies took up positions on the periphery, while those most exposed to real estate tended to be drawn towards the core.
One year into the crisis, network behavior during the suspension of share trading for Kaisa offers updated insight into investors' beliefs: unlike before, eastern-centric firms are drawn most heavily into the core of the network, capturing how areas that were regarded as relatively stable earlier in the crisis are now increasingly at risk\textemdash it is not just the less developed regions of China feeling pressure on real estate, but the richest and most developed as well. The network also reflects a change in sentiment surrounding the relative stability of state-owned enterprises, exhibiting a fascinating substitution effect towards private developers. This behavior is likely reflective of the recent failure of prominent SOEs, as well as knowledge about how SOEs were forced to bail out private developers in disadvantageous deals.
Then, fast-forwarding to nearly two years later, by the time of Country Garden's profit warning in August 2023, the network captures just how much investor sentiment has changed. Unlike in earlier periods, there is much less homogeneity across regions and state-ownership status, likely reflecting how developers have adapted to investing amidst the crisis. At this point, likely because they have delved into the financial statements of companies, conducted their due diligence, and mapped exposure patterns, companies behave in more nuanced ways: this means that when a “shocking" event occurs, the network change is minimal because investors have already priced in their beliefs. Nevertheless, there is evidence of a substitution effect towards state-owned enterprises\textemdash the reverse of that seen under the Kaisa case\textemdash and this seems to reflect the market sentiment that state-owned developers are now “safer" bets for investment.
Taken together, these cases offer insight into how investor behavior and spillover patterns have changed as the real estate crisis evolved. No longer expecting spillover by region or state-owned status, investors actively conduct dynamic, nuanced market research. Moreover, with the VAR estimation appearing to be relatively consistent and robust across sequential rolling window specifications, the most significant implication of these findings and methodology is the insight they can offer active market participants\textemdash those investors themselves who have become reticent. If the relevant data could be pulled daily and the estimation recalculated for each real-time window, investors could have an up-to-date picture of firm connectedness and general market sentiment; it is certainly possible to determine firms “less exposed" to the real estate crisis based on the network results and connectedness measures, as well as those most at risk of being net receivers of spillover.
Future extensions of this paper will delve into more complex modifications to increase the robustness of estimation and circumvent network size limitations, but this specification applying demirer_estimating_2018 in a new context still highlights the potential gains from analyzing connectedness\textemdash and just how much it can capture market sentiment.