Housing Price Dynamics: An ECM Analysis of 35 Cities in Urban China

Abstract

In this study, we examine the dynamics of housing prices across 35 Chinese cities from 2010 to 2024 using an error correction model (ECM). Using two-stage least squares (TSLS), we address endogeneity in housing stock. The results show a stable long-run relation between housing prices, income, user cost, and employment. The findings indicate that user cost exerts a significant negative pressure on housing valuations. While housing stock exhibits a positive, long-run correlation with prices due to rapid urbanization, its expansion effectively dampens price growth in the short term. We also find differences across market segments. The newly built housing market returns to equilibrium in about 33 months, while the second-hand market requires about 60 months. These results underscore the necessity of considering segment-specific adjustment speeds and fundamental drivers when formulating urban housing policies in China.

1. Introduction

After the 1998 housing reform, urban China shifted from state allocation to a market system. The reform triggered a construction boom. Real estate has emerged as a cornerstone of national GDP, yet rapid price escalation raises systemic risk concerns. When housing prices diverge from economic fundamentals, speculation and market instability increase.

Understanding the mechanism of housing price dynamics is crucial for both policymakers and investors. Standard equilibrium models assume immediate market clearing. In practice, housing markets adjust slowly because of supply rigidities and imperfect information. Consequently, market prices frequently deviate from their long-run equilibrium values. In this study, we utilize an error correction model (ECM) approach to analyze how housing prices in urban China respond to changes in fundamentals such as income, user cost, housing stock, and employment. The ECM framework fits urban China well. Restricted land supply, policy interventions, and asymmetric information delay market clearing. As a result, housing prices often deviate from macroeconomic fundamentals for extended periods. Measuring market-specific adjustment speeds is therefore important for policy evaluation. By distinguishing between long-run equilibrium relationships and short-run adjustment dynamics, this paper aims to quantify the speed at which the market returns to its fundamental valuation after a shock.

Stock-flow models are commonly used to analyze housing demand, housing supply, residential construction, and housing price dynamics [1]. Unlike housing markets in developed countries, China’s market is dominated by newly built housing supply, and housing prices strongly influence policy decisions.

This study contributes to the literature on housing market dynamics in several ways. Firstly, it extends the ECM literature on housing prices to the Chinese market, using a recent panel dataset covering 35 major cities from 2010 to 2024, thereby capturing both the period of rapid urban expansion and the post-2021 market correction. Also, the study applies a TSLS-based ECM framework to address potential endogeneity in the housing stock, a topic that has received limited attention in previous studies of China’s housing market. In addition, by estimating separate models for the new-build and second-hand housing markets, the analysis documents substantial heterogeneity in adjustment speeds and market responses that aggregate market models may obscure. Lastly, the robustness analysis based on the Panel ARDL-PMG framework confirms the existence of a stable long-run equilibrium relationship despite mixed integration orders among the variables.

The remainder of this paper is structured as follows. Section 3 introduces the theoretical stock-flow framework; Section 4 describes the variable specifications and data sources; Section 5 presents the empirical results, including unit root tests, cointegration analysis, and the ECM estimations for both newly built and second-hand markets; and finally, Section 6 provides conclusions.

2. Existing Studies

Since the 1960s, dynamic models [2,3] have analyzed housing market stock-flow relations under the assumption of efficient market clearing. However, subsequent empirical studies have suggested that the housing market is often inefficient and adjusts slowly to changes in market conditions [4]. Dipasquale and Wheaton (1994) [5] extended the stock-flow model to account for slow market adjustment. In the improved model, the housing price is represented as a function of the number of households, rent, homeownership, wage, and user cost. TSLS estimates indicate that the US housing market takes several years to reach equilibrium. Similarly, Case and Mayer (1995) [6] developed and tested a simple model of price determination to explore price movements in the Boston metropolitan area. The results show that housing prices depend on location characteristics, employment, accessibility, school quality, and housing supply shocks. A more thorough review can be found in Cho (1996) [7] in the early dynamics literature.

Later studies examined housing market dynamics under the assumption that housing markets adjust gradually rather than immediately. Most studies focus on the US housing market. Capozza et al. (2002) [8] analyzed housing price dynamics using an error correction model. They examined 62 metropolitan areas from 1979 to 1995 and defined housing prices as a function of population, income, construction cost, user cost, and land supply. Their results showed that serial correlation and mean reversion are related to population, income, and construction cost.

Klyuev (2008) [9] examined equilibrium housing prices and short-run price adjustment in four US regions between 1976 and 2002. The results identified the inventory-to-sales ratio as the main driver of short-run price dynamics. Mondragon and Wieland (2022) [10] showed that remote work increased US housing demand during the COVID-19 pandemic. They estimated that remote work explained about half of the increase in house prices during the period. DeFusco et al. (2022) [11] examined how speculative expectations affect house prices and transaction volumes across credit environments. Their study explained the mechanisms behind the rise and collapse of the US housing bubble.

In Europe, Wigren and Wilhelmsson (2007) [12] applied a similar error correction model to that of Riddel (2004) [13] to 12 Western European countries between 1976 and 1999. The results showed that housing stock adjusts slowly to demand and supply shocks, while housing prices adjust faster. Wilhelmsson (2008) [14] analyzed housing market dynamics across 281 Swedish municipalities from 1991 to 2005 using an error correction model. The results indicated that adjustment rates are higher in low-density regions and during economic expansions. Tu et al. (2018) [15] identified a long-run equilibrium relation among house prices, household income, mortgage rates, and inflation in the regulated Dutch housing market. They also proposed a cointegration model that improved housing price forecasts. Poghosyan (2020) [16] analyzed 99 lending restrictions introduced in 28 EU countries between 1990 and 2018. The results showed that LTV and DSTI policies affect house prices and credit growth. Ismail and Wilhelmsson (2024) [17] examined how new construction projects affected affordability in Stockholm between 2009 and 2014 using a difference-in-difference approach. Their results suggested positive effects on income and affordability.

In the Asia–Pacific region, Glindro et al. (2008) [18] examined housing price dynamics in nine economies between 1993 and 2006. They applied the two-step framework proposed by Capozza et al. (2002) [8] to analyze housing price determinants. The results suggested that rising housing prices mainly reflected stronger economic fundamentals rather than speculative activity. Kim et al. (2017) [19] showed that household debt is an important long-run determinant of Korean housing prices. They also found that price adjustment slowed after the global financial crisis. Ma et al. (2021) [20] developed a panel error correction model for Australian states and territories. Their results identified a long-run equilibrium relation between housing prices and residential construction costs in several regions, while short-run adjustment patterns differed across markets. The model also produced accurate forecasts for construction prices.

Although many studies examine housing market dynamics, further evidence is needed, especially for urban China [9]. Glaeser et al. (2017) [21] argued that China’s housing boom reflects institutional factors. The fact that high housing prices coexist with high vacancy rates suggests an important role for local government incentives and credit conditions. Wang and Zhang (2014) [22] showed that disposable income remains an important long-run driver of housing prices, while short-run fluctuations are influenced by speculative expectations and policy changes. Zhang et al. (2016) [23] compared housing price dynamics across first-, second-, and third-tier Chinese cities using a VAR model. Their results showed that macroeconomic variables affect city tiers differently. Zhu et al. (2018) [24] found that income and population growth increase housing prices across Chinese cities. They also reported that economic openness and interest rates have different effects across market segments. More recent studies focus on spatial and temporal risks following the housing market correction that began in late 2021. Zhang and Masron (2025) [25] examined 261 Chinese cities and found that a developed financial sector can reduce speculative housing bubbles by providing alternative investment opportunities.

Despite the contributions of these studies, no study has considered the use of an error correction model to address the differences in price movements between newly built and second-hand housing markets. More evidence is needed to examine the post-2021 housing market adjustment in urban China, as the drop in housing prices has continued obviously from 2021, and the market has shifted to be dominated by second-hand housing since then. In addition, this study focuses on the housing market during the Chinese rapid urbanization period, while many existing studies are concerned with the markets in highly urbanized economies. Indeed, this study provides alternative insights into the heterogeneity of housing market dynamics.

3. Theoretical Model

In this study, we examine housing price dynamics using an error-correction approach comprising two models: a long-run equilibrium model and a short-run adjustment model with an error-correction term. Gallin (2006) [26] questioned whether an error-correction relationship exists between housing prices and fundamentals such as income. However, later studies [9,12,14] support the use of the ECM framework.

The general housing price model in equilibrium relates the housing price at time t to the demand for and supply of housing at that time.

$$P_t=f(Q_t^D,Q_t^S)$$

(1)

where Q^D reflects the demand for housing, and Q^S is the supply of housing. Following DisPasquale and Wheaton (1994) [5], Riddel (2004) [13], and Wilhelmsson (2008) [14], the long-run equilibrium stock (Q^S) is defined as a function of price and cost shifting variables (Z_t) such as construction cost, so that

$$Q_t^S={\beta }_0+{\beta }_1{P}_t-{\beta }_2{Z}_t+{\delta }_t$$

(2)

Similarly, the long-run equilibrium demand Q^D is defined as a function of price and a set of demand variables (X_t), which can be written as

$$Q_t^D={\alpha }_0-{\alpha }_1{P}_t+{\alpha }_2{X}_t+{\eta }_t$$

(3)

In equilibrium, the housing demand is by definition equal to the housing supply, so that

$$Q_t^S={\alpha }_0-{\alpha }_1{P}_t+{\alpha }_2{X}_t+{\eta }_t$$

(4)

Then, the reduced form of the long-run equilibrium price may be represented as

$$P_t={\gamma }_0+{\gamma }_1{X}_t-{\gamma }_2{Q}_t^S+{\epsilon }_t$$

(5)

However, in the short run, the housing market adjusts gradually rather than immediately [5]. This implies that changes in construction cost or interest rate affect housing supply, while changes in income and employment affect housing demand. We therefore test whether housing prices and the explanatory variables share a long-run equilibrium relation. If cointegration exists, observed housing prices may deviate from the long-run equilibrium level by an error term (ε). This deviation reflects short-run disequilibrium in the housing market. Given the cointegrated variables in Equation (5), the short-run adjustment process can be estimated using an error correction model (ECM), defined as follows:

$$\mathrm{\Delta }{P}_t={\sigma }_0+{\sigma }_1\mathrm{\Delta }{X}_t-{\sigma }_2\mathrm{\Delta }{Q}_t^S-\lambda ECT+{\omega }_t$$

(6)

where ECT denotes the error correction term. ECT can be computed by (P_t−1 − P^*_t−1), in which P^*_t−1 is the long equilibrium price at time (t − 1) and is equal to (γ₀ − γ₁X_t−1 + γ₂Q^S_t−1). The coefficient of the ECT, λ, indicates the speed and direction in which housing prices respond to the long-run equilibrium. If the actual price is higher than the long-run equilibrium price at time (t − 1), then λECT will be negative, and the change in housing prices will decrease. Conversely, if the actual price is less than the long-run equilibrium price at time (t − 1), then λECT will be positive, and the change in housing prices will increase.

4. Data and Empirical Model

4.1. Empirical Model and Variable Specification

The empirical error-correction model is estimated in two steps. The first step estimates the long-run equilibrium relationship between housing prices and the explanatory variables using the following model. All variables are expressed in natural logarithms, except for user cost. This transformation improves model fit [13]. Logarithmic variables also approximate growth rates and are more likely to be stationary.

$$\ln Pric{e}_t={\alpha }_0-{\alpha }_{1}User\cos t_t+{\alpha }_2\ln Incom{e}_t+{\alpha }_3\ln Employment-{\alpha }_4\ln Stock+{\mu }_a$$

(7)

where ‘Usercost’ denotes the variable of user cost (1) or user cost (2), α₀ is the fixed regional effect, and α₁, α₂, α₃, and α₄ are parameters to be estimated.

Then, if there exists a long-run relationship of the kind described in Equation (7), the short-run model, or error correction model, could be established as follows.

$$\ln {\displaystyle \frac{Pric{e}_t}{Pric{e}_{t-1}}}={\beta }_0-{\beta }_1\mathrm{\Delta }User\cos t_t+{\beta }_2\ln {\displaystyle \frac{Incom{e}_t}{Incom{e}_{t-1}}}+{\beta }_3\ln {\displaystyle \frac{Employmen{t}_t}{Employmen{t}_{t-1}}}+{\beta }_4\ln {\displaystyle \frac{Stoc{k}_t}{Stoc{k}_{t-1}}}-\lambda \ln {\displaystyle \frac{\mathrm{Pr}ic{e}_{t-1}}{\mathrm{Pr}ic{e}_{t-1}^E}}+{\mu }_b$$

(8)

or

$$\mathrm{\Delta }Pric{e}_t={\beta }_0-{\beta }_1\mathrm{\Delta }User\cos t_t+{\beta }_2\mathrm{\Delta }Incom{e}_t+{\beta }_3\mathrm{\Delta }Employmen{t}_t-{\beta }_4\mathrm{\Delta }Stoc{k}_t-\lambda ECT+{\mu }_b$$

(9)

where β₀ is the fixed regional effect, β₁, β₂, β₃, and β₄ are parameters to be estimated, λ is the speed of adjustment, and PriceE represents the equilibrium price, which comes from the solution to the long-run Equation (7). The variable ln(Price_t−1/PriceE_t−1), i.e., the error correction term (ECT), means how actual prices converge to the long-run equilibrium price. ‘Δ’ means the change in each variable in a natural log form, except for the variable of user cost.

The choice of variables driving housing prices in the empirical model above largely follows DiPasquale and Wheaton (1996) [27], who assume that housing prices are affected by household formation, income, user cost, and housing stock. In this study, the housing price refers to the average nominal selling price, calculated as total sales divided by the total square meters of housing sold. We use employment as a proxy for the number of households, since time-series data for the latter are not available. Correspondingly, the income is defined as the average annual nominal income per worker.

Specifically, the user cost of housing has been estimated using two different formulas, one suggested by Riddel (2004) [13] and the other by DiPasquale and Wheaton (1996) [27]. They both define the user cost as a function of interest rates, taxes, and the expected future growth in housing prices. The difference is that DiPasquale and Wheaton use the price changes over the two years before the current year to determine future price appreciation, while Riddel uses those over the current year and the preceding year, represented by “user cost (1)” for the former and “user cost (2)” for the latter. To examine the difference, we calculate the variable using both formulas. Table 1 reports the variables incorporated in the empirical model, which are to be estimated in log form.

Table 1. Specification of variables in the empirical model.

Variables	Definition	Measurement
Price	Average nominal selling price of housing	Yuan (RMB)/square meter
User cost (1)	[(it + tp) (1 − ty) − 1/2(ΔPt−1/Pt−1 + ΔPt−2/Pt−2)]	--
User cost (2)	[(it + tp) (1 − ty) − 1/2(ΔPt/Pt + ΔPt−1/Pt−1)]	--
Income	Annual nominal income per capita	10,000 Yuan (RMB)
Employment	Working people paid by firms, excluding the self-employed	million
Stock	Existing housing privately owned and tradable in the market	100 million square meters

Note: i_t denotes the CPI-adjusted interest rate of mortgage loans over five years (inclusive), P_t means the housing price during different years, t_p represents the marginal tax rates on property, and t_y refers to the marginal tax rate for first-time homebuyers. Here, t_p and t_y are treated as zero (in particular, the t_p in Shanghai and Chongqing has been set at 0.4% because China has officially levied property taxes in these two cities), since property tax has not been imposed in most cities, and there is no tax rate for first-time homebuyers in China.

4.2. Data Sources and Quality

The dataset used in the empirical models is available from the National Bureau of Statistics of China (NBSC) and the People’s Bank of China. Given the potential importance of data quality for the empirical results, it is necessary to expound on data issues such as comparability and reliability, which are of the greatest concern in studies of China’s housing markets.

It was not until 1998 that China reformed its public housing allocation system by issuing an important decision stating that households would have to purchase their own homes. In recent decades, China’s housing stock has continued to grow due to new construction, though the growth rate has begun to slow. Given the long lifespan of buildings, the number of houses demolished accounts for a relatively small proportion. Moreover, such data is difficult to obtain through public channels. Thus, the housing dataset after 2000 appears to be more reliable for econometric analysis. Instead of directly using data from NBSC, in this study, we calculate housing stock by summing newly built housing each year, beginning in 1999.

4.3. Descriptive Statistics

The empirical analysis in this paper is based on a panel dataset with a time series for the period 2010~2024 and a cross-section of 35 cities’ housing markets in urban China. Table 2 presents the descriptive statistics of the dataset. The slight data gaps in income (493) and employment (491) observations arise from sporadic missing records in a few medium-sized Western cities during the early years (2010–2012) of the tracking window. These gaps are treated as missing completely at random. In StataMP 16, the dynamic panel system automatically handles this structure as an unbalanced panel using listwise deletion, thereby maintaining the mathematical consistency of our parameters without introducing selection bias.

Table 2. Descriptive statistics.

Variables	Mean	Std. Dev.	Minimum	Maximum	Observations
Price (Yuan/m2)	12,373	9515	3196	61,601	525
User cost (1)	−5.81	8.79	−37.28	13.59	525
User cost (2)	−4.84	9.22	−37.18	22.75	525
Income (10,000 Yuan)	10.55	0.38	9.55	11.44	493
Stock (100 million m2)	11.38	0.69	9.86	13.44	525
Employment (million)	4.96	0.75	3.02	7.04	491

On average, housing units across these urban centers were sold at 12,373 Yuan (RMB) per square meter over the sample period. The high standard deviation of 9515 Yuan underscores substantial price dispersion and heterogeneity across the selected metropolitan markets. In comparison, the average annual per capita income of urban residents was recorded at 105.5 thousand Yuan, with a standard deviation of 0.69 thousand Yuan, indicating a significant but relatively narrower gap in purchasing power compared to the volatility observed in housing valuations.

Regarding the financial determinants of housing demand, the mean values of user cost, which are calculated under both historical long-run expectations (user cost (1)) and adaptive expectations (user cost (2)), remain consistently negative throughout the period, averaging −5.81% and −4.84%, respectively. These negative figures suggest that, for most of the period between 2010 and 2024, the anticipated rate of housing price appreciation significantly outpaced mortgage interest rates, thereby lowering the real cost of homeownership and incentivizing investment.

In terms of supply and labor market fundamentals, the average housing stock is approximately 1138 million square meters across 35 cities. Concurrently, the mean employment scale is 4.96 million people. Employment, measured by the total number of working individuals in the local labor market, serves as a proxy for the scale of potential demand in the urban housing sector. Both housing stock and employment levels reflect the varying capacities and demographic scales of the core urban markets analyzed in this study.

4.4. Estimation Issues

Panel data are better suited to studying the dynamics of change by combining time-series cross-sectional observations, thus yielding greater variability, lower collinearity, and greater efficiency [28]. However, they pose estimation issues, such as heteroskedasticity across individuals and serial correlation in time-series data [29]. In this paper, we apply the generalized least squares estimation method with fixed province effects to address cross-sectional heteroskedasticity [30].

The endogeneity of housing stock is another econometric issue to be addressed. According to Dispasquale and Wheaton (1994) [5], the housing stock variable depends on other factors, such as new construction, as described in Equation (2). Following DiPasquale and Wheaton (1994) [5], Riddel (2004) [13], Wigren and Wilhelmsson (2007) [12], and Wilhelmsson (2008) [14], we employ two-stage least squares (TSLS) estimation to address potential endogeneity in the housing stock.

4.5. Unit Root Tests and Stationarity

Non-stationary data may lead to spurious regression results. We therefore conduct panel unit root and cointegration tests [31]. The panel unit root test is based on the following AR (1) process:

$$y_{it}={\rho }_i{y}_{i,t-1}+X_{it}{\delta }_i+{\epsilon }_{it}$$

(10)

where i = 1, 2, …, N is the cross-sectional dimension of the data and t = 1, 2, …, T is the time dimension. ρ is an autoregressive coefficient. X_it represents the exogenous variables in the model, including fixed effects and individual trends. ε_it denotes the error term, assumed to be a mutually independent idiosyncratic disturbance. If |ρ| = 1, the dependent variable y contains a unit root and is non-stationary, whereas if |ρ| < 1, the process is stationary.

The Levin, Lin, and Chu (or LLC, 2002) [32] test assumes a common autoregressive coefficient across cross-sections. In contrast, the IPS test (Im et al., 2003) [33], together with the Fisher-ADF and Fisher-PP tests proposed by Maddala and Wu (1999) [34] and Choi (2001) [35], allows the autoregressive coefficient to vary across cross-sections. The LLC assumption may be restrictive because housing markets differ across cities in this study. Breitung (2000) [36] also argued that the IPS test is sensitive to trend specification and loses power when time trends are included. Fisher-ADF and Fisher-PP tests perform better than the IPS test (Maddala and Wu, 1999) [34] and are therefore used in this paper.

Table 3 reports the results of the unit root tests for variables in levels and first differences. All tests are based on the null hypothesis of a unit root. The results indicate that the null hypothesis cannot be rejected for the variables in levels, whereas it is rejected for the first-differenced variables. None of the variables is integrated of an order higher than one.

Table 3. Unit root tests.

Variables	In Levels		First Difference		Conclusion
	Fisher-ADF	Fisher-PP	Fisher-ADF	Fisher-PP
Lnprice	53.45	51.34	100.36 **	217.97 ***	I (1)
User cost (1)	323.92 ***	89.52 *	--	--	I (0)
User cost (2)	222.78 ***	126.84 ***	--	--	I (0)
Lnincome	209.56 ***	724.76 ***	--	--	I (0)
Lnstock	91.06 **	1272.39 ***	--	--	I (0)
Lnemployment	136.04 ***	330.11 ***	--	--	I (0)

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

Table 4 reports the results of the Pedroni (1999, 2004) [37,38] cointegration test. Three specifications are considered to account for individual heterogeneity and time trends: (i) no intercept or trend, (ii) individual-specific intercepts, and (iii) individual-specific intercepts and trends. The results consistently reject the null hypothesis of no cointegration across all specifications, indicating a stable long-run relationship among the variables.

Table 4. Cointegration tests.

Test	Type	Results
Pedroni	No constant demean	Modified Phillips–Perron t	5.3258 ***
		Phillips–Perron t	−3.4998 ***
		Augmented Dickey–Fuller t	−1.5410 **
	Demean	Modified Phillips–Perron t	4.7797 ***
		Phillips–Perron t	−9.2704 ***
		Augmented Dickey–Fuller t	−7.9142 ***
	Trend and demean	Modified Phillips–Perron t	6.1757 ***
		Phillips–Perron t	−13.0640 ***
		Augmented Dickey–Fuller t	−12.1270 ***

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

5. Estimation Results

The empirical analysis examines the relationship between housing prices and housing demand and supply factors. The analysis is divided into three parts. The first part estimates the long-run equilibrium relationship, while the second part examines short-run housing price adjustment. The first two parts use aggregate data from 35 Chinese city markets. The third part examines parameter heterogeneity between the newly built and second-hand housing markets. A fixed effects model is used to estimate Equations (7) and (8). Following Riddel (2004) [13] and Wilhelmsson (2008) [14], we use two-stage least squares (TSLS) with instrumental variables to address endogeneity in housing stock. The instrumental variables are construction cost, income, employment, and user cost.

To compare alternative user cost measures, the model is estimated separately for user cost (1) and user cost (2). The two model specifications reported in Table 5 are therefore estimated.

Table 5. Model types (dependent variable: lnprice).

Variables	TSLS
	Model 1	Model 2
User cost (1)	√
User cost (2)		√
Lnincome	√	√
Lnstock	√	√
Lnemployment	√	√

5.1. Long-Run Price Estimation

As discussed above, the test results indicate that the variables in Equation (7) are integrated of order one, I(1), and cointegrated, since the residuals are stationary, I(0), at the national level. We therefore conclude that a long-run equilibrium relationship exists between housing prices and fundamental variables. The estimation results for Equation (7) at the national level are reported in Table 6.

Table 6. Long-run price equations, 2010–2024 (dependent variable: lnprice).

Variables	TSLS Fixed Effects Model
	Model L1			Model L2
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	1.95 **	2.51	0.012	2.499 ***	3.68	0.000
User cost (1)	−0.080 ***	−13.61	0.000	-	-	-
User cost (2)	-	-	-	−0.009 ***	−28.21	0.000
Lnincome	−0.083	−0.37	0.708	−0.184	−1.00	0.319
Lnstock	0.710 ***	5.21	0.000	0.770 ***	6.84	0.000
Lnemployment	0.056	1.41	0.159	0.029	0.93	0.354
Underidentification test (Kleibergen–Paap rk LM statistic)	12.211 **		0.016	11.642 **		0.020
Weak identification test (Kleibergen–Paap rk Wald F statistic)	30.351			30.203
Adjusted R2	0.976			0.981
Observations	439			439
Instruments: Δconstcost, Δincome, and Δemployment.

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

Equation (7) fits the data well, with an adjusted R² above 0.97. User cost is statistically high in both specifications and has a negative effect on housing prices. The coefficient for user cost (1) is larger than that for user cost (2), suggesting that the expectations based on house price changes over the previous two years have a stronger effect on current house prices.

The long-run coefficients for per capita income (lninc) and employment (lnemp) are statistically insignificant in the baseline TSLS estimates reported in Table 6. This suggests that income growth and employment do not explain long-run housing price movements in our sample of 35 Chinese cities between 2010 and 2024. Their effects are likely captured by housing stock expansion and variation in user cost. During periods of intensive urbanization, housing supply growth and financial conditions appear to dominate demand-side indicators in the long run.

The coefficient for housing stock is positive and significant, contrary to our initial expectation. This result reflects the supply dynamics of urban China during the urbanization period from 2010 to 2024. Local governments allocated more land, and developers concentrated construction activity in rapidly growing metropolitan areas with strong housing demand and rising prices. As a result, housing stock expansion and rising housing prices occurred simultaneously over the long run.

In contrast, the short-run coefficient for Δstock in Table 7 is negative. This result is consistent with the standard economic mechanism in which a short-run increase in housing supply reduces price growth.

Table 7. Short-run price equations, 2010–2024 (dependent variable: Δlnprice).

Variables	TSLS Fixed Effects Model
	Model S1			Model S2
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	0.113 **	2.35	0.019	0.090 *	1.92	0.055
ΔUser cost (1)	−0.003 ***	−5.29	0.000	-	-	-
ΔUser cost (2)	-	-		0.0007	1.18	0.236
Δlncome	0.203 **	2.27	0.024	0.126	1.46	0.144
Δstock	−1.53 × 10−6	−1.03	0.302	−9.07 × 10−7	−0.62	0.533
ΔEmployment	0.042 *	1.87	0.061	0.029	1.33	0.183
ECT	−0.464 ***	−6.96	0.000	−0.499 ***	−6.67	0.000
Underidentification test (Kleibergen–Paap rk LM statistic)	20.322 ***		0.000	20.727 ***		0.000
Weak identification test (Kleibergen–Paap rk Wald F statistic)	22.982			21.954
Adjusted R2	0.174			0.186
Observations	439			439

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

Post-estimation diagnostics support the TSLS specification. The Kleibergen–Paap rank LM statistic rejects the null hypothesis of underidentification at the 5% level, indicating that the instruments are relevant for housing stock. The Kleibergen–Paap rank Wald F-statistic exceeds the Stock–Yogo critical values, suggesting that weak instruments are not a concern. These results support the robustness of the long-run estimates.

5.2. Short-Run Price Adjustment

Based on the long-run estimates, we next examine how housing prices adjust to changes in explanatory variables in Equations (8) and (9). The estimation results are reported in Table 7. Model S2 (‘S’ stands for short-run) provides the best fit, with an adjusted $R^2$ of about 0.18. The short-run housing price dynamics are consistent with economic theory. Changes in income and employment are positively related to housing price growth. When income and employment rise, housing prices increase correspondingly. Higher income and employment increase housing prices, while higher user costs reduce them. Unlike the long-run estimates, the short-run stock coefficient is negative, which is consistent with economic theory.

The estimated error correction term (ECT) has the expected negative sign. The estimated coefficients imply that housing prices require approximately 26 months to return to equilibrium in Model S1 and 24 months in Model S2. After accounting for endogeneity, these adjustment speeds appear reasonable. Wilhelmsson (2008) [14] found that housing market adjustment proceeds more rapidly during economic expansions than during downturns. Given China’s rapid economic growth during the sample period, a relatively fast housing price adjustment is therefore plausible. Riddel (2004) [13] estimated an adjustment period of 1.58 years for the US housing market, while Wigren and Wilhelmsson (2007) [12] reported an adjustment period of less than one year for 12 Western European countries.

Similarly to the long-run specification, the short-run equation with user cost (1) provides a better fit than the specification with user cost (2). This suggests that housing price changes during the previous two years exert a stronger influence on current housing prices. Hence, user cost (1) appears to be the more suitable specification.

The relatively low adjusted $R^2$ (approximately 0.18) in the short-run differenced models is common in error correction analysis. Differencing removes long-run growth trends and isolates short-run variation and residual volatility. The limited explanatory power also suggests that short-run housing price movements in China are influenced by institutional frictions, local policy interventions, and changing market sentiment that are not fully captured by standard macroeconomic variables.

Post-estimation diagnostics support the validity of the TSLS specification. The Kleibergen–Paap rank LM statistic rejects the null hypothesis of underidentification at the 5% level, indicating that the instruments are relevant for the endogenous housing stock variable. In addition, the Kleibergen–Paap rk Wald F-statistic exceeds the Stock–Yogo critical values, suggesting that weak instrument bias is unlikely to affect the estimates.

5.3. Newly Built and Second-Hand Housing Market Heterogeneity

The previous analysis assumes homogeneous effects across local markets, implying that the aggregate estimates provide a representative description of the market. However, the estimates for newly built and second-hand housing markets may differ because of differences in market structure and adjustment processes. This comparison helps identify differences across housing market segments. To examine parameter heterogeneity between newly built and second-hand markets, we estimate the models separately for both market segments and compare the results.

5.3.1. Long-Run Equation

Both user cost (1) and user cost (2) have a significant negative impact on the house price index at the 1% level (Table 8). A comparison of the new and second-hand housing markets shows no significant difference in the effect of user cost. The adjusted $R^2$ values indicate that Models L1 and L2 fit the newly built housing market better than the second-hand market.

Table 8. TSLS long-run price equations, 2010–2024 (dependent variable: lnprice_index).

Variables	New			Second-Hand
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	1.210 *	1.78	0.074	2.979 ***	2.70	0.007
User cost (1)	−0.004 ***	−12.34	0.000	−0.004 ***	−10.01	0.000
Lnincome	−0.442 **	−2.44	0.015	−0.608 **	−2.16	0.031
Lnstock	0.697 ***	6.37	0.000	0.686 ***	4.08	0.000
Lnemployment	0.007	0.21	0.836	0.032	0.75	0.451
Adjusted R2	0.924			0.840
Observations	439			439
Variables	New			Second-Hand
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	1.548 **	2.17	0.030	3.353 ***	2.98	0.003
User cost (2)	−0.003 ***	−5.97	0.000	−0.004 ***	−5.83	0.000
Lnincome	−0.470 **	−2.43	0.015	−0.657 **	−2.28	0.022
Lnstock	0.707 ***	6.00	0.000	0.710 ***	4.09	0.000
Lnemployment	−0.012	−0.42	0.674	0.014	0.38	0.708
Adjusted R2	0.910			0.826
Observations	439			439
Instrumental variables: Δconstructioncost, Δincome, and Δemployment.

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

5.3.2. Short-Run Equation

The short-run results in Table 9 show that employment growth is positively related to changes in newly built housing prices. This suggests that employment growth increases prices in the newly built housing market. In contrast, employment does not have a significant effect on prices in the second-hand housing market. Higher user costs are associated with lower housing prices in both the newly built and second-hand housing markets.

Table 9. TSLS short-run price equations, 2010–2024 (dependent variable: Δlnprice_index).

Variables	New			Second-Hand
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	0.056 ***	2.92	0.004	0.043 *	1.66	0.098
ΔUser cost (1)	−0.002 ***	−9.96	0.000	−0.002 ***	−8.81	0.000
ΔIncome	−0.061	−1.19	0.232	−0.011	−0.25	0.806
ΔStock	1.75 × 10−7	0.31	0.760	4.97 × 10−7	0.67	0.503
ΔEmployment	0.038 **	2.33	0.020	0.013	1.06	0.288
ECT	−0.371 ***	−10.59	0.000	−0.202 ***	−5.66	0.000
Adjusted R2	0.296			0.241
Observations	439			439
Variables	New			Second-Hand
	Coefficient	t-Value	Prob.	Coefficient	t-Value	Prob.
C	0.043 **	2.26	0.024	0.036	1.40	0.160
ΔUser cost (2)	−0.001 ***	−3.79	0.000	−0.001 ***	−4.83	0.000
Δincome	−0.067	−1.34	0.182	−0.019	−0.44	0.661
Δstock	5.50 × 10−7	0.99	0.322	4.73 × 10−7	0.90	0.367
ΔEmployment	0.036 **	2.23	0.026	0.011	0.92	0.356
ECT	−0.355 ***	−10.29	0.000	−0.196 ***	−5.44	0.000
Adjusted R2	0.283			0.237
Observations	439			439
Instrumental variables: user cost (1)/user cost (2), lnconstructioncost, lnincome, and lnemployment.

Note: * significant at 10%, ** significant at 5%, *** significant at 1%.

The estimated error correction term (ECT) differs between the newly built and second-hand housing markets. The adjustment period is about 33 months in the newly built housing market and 60 months in the second-hand market. This indicates that housing prices return to equilibrium faster in the newly built housing market.

5.4. Robustness Check: Alternative Panel ARDL Estimation

To test the robustness of the ECM results, we also estimate a Panel Autoregressive Distributed Lag (Panel ARDL) model using the Pooled Mean Group (PMG) estimator. The results are reported in Table 10 and support the existence of a stable error correction mechanism.

Table 10. Estimation results of the Panel ARDL (PMG) model (dependent variable: ΔLnprice).

Module and Variable	Coefficient	z-Statistic	Prob.
Long-run Equilibrium
User cost (1)	−0.0171 ***	−7.22	0.000
Lnincome	−1.3196 ***	−4.96	0.000
Lnstock	1.3028 ***	12.32	0.000
Lnemployment	0.0799 ***	3.07	0.002
Short-run Dynamics
ECT_ardl	−0.5771 ***	18.69	0.000
ΔUser cost (1)	−0.0034 ***	−5.27	0.000
ΔIncome	−0.4176 **	−2.46	0.014
ΔStock	3.0391 ***	9	0.000
ΔEmployment	−0.0632	−0.9	0.366
C	−4.8202 ***	−21.09	0.000
Observations	439

Note: * significant at 10%; ** significant at 5%; *** significant at 1%.

The error correction coefficient ($EC{T}_{ardl}$) in the short-run specification is statistically significant ($\beta =-0.577$; $z=-18.69$; $p<0.01$). This result supports the existence of a long-run equilibrium relationship and confirms that short-run deviations gradually return to equilibrium. The estimates suggest that about 57.7% of market deviations are corrected each year, implying an adjustment period of about 21 months. This adjustment speed is consistent with the baseline ECM estimates.

The long-run estimates also show that user cost has a significant negative effect on housing prices ($\beta =-0.017$; $p<0.01$). In contrast, housing stock is positively related to long-run housing prices during China’s rapid urbanization period ($\beta =1.303$; $p<0.01$). These results support the robustness of the baseline findings.

6. Conclusions

6.1. Summary of Empirical Findings

This study examines housing price dynamics across 35 Chinese cities between 2010 and 2024 using an error correction framework. The results provide several conclusions.

Long-run equilibrium: The analysis identifies a stable cointegration relationship between housing prices and the main economic fundamentals, including income, user cost, housing stock, and employment.

Determinants of housing prices: User cost has a significant negative effect on housing prices in both the long run and the short run. User cost based on two-year price expectations has a stronger effect on housing prices than user cost based on short-run expectations.

Housing stock dynamics: In the long run, housing stock is positively related to housing prices, reflecting simultaneous urban expansion and price growth during rapid urbanization in China. However, in the short run, increases in housing stock reduce housing price growth.

Market adjustment: The error correction term (ECT) is negative and significant, indicating that housing prices gradually return to equilibrium after short-run shocks. The estimated adjustment period ranges from 24 to 26 months.

Market heterogeneity: The results show differences between the newly built and second-hand housing markets. The newly built housing market returns to equilibrium faster, with an adjustment period of about 33 months, compared with about 60 months for the second-hand market. Employment growth also has a significant effect on newly built housing prices, but not on prices in the second-hand market.

6.2. Limitations and Future Research

This study has several limitations that may guide further research. The housing stock variable is constructed from cumulative new construction since 1999 and does not fully account for the depreciation or demolition of older housing units. This may create a persistent upward trend and inflate the long-run adjusted $R^2$. More accurate estimates of housing stock would improve the precision of the long-run supply-side coefficients. Although economic fundamentals are important, administrative interventions also shape the Chinese housing market, including purchase restrictions and lending caps. Future studies could include policy dummy variables to measure how regulatory changes affect housing price adjustment.