# Bank Credit and Housing Prices in China: Evidence from a TVP-VAR Model with Stochastic Volatility

^{*}

## Abstract

**:**

## 1. Introduction

^{2}to 5424 Yuan/m

^{2}. On the other hand, the amount of real medium- and long-term loans in China increased nearly 6.5 times over the same period. Meanwhile, the variation in housing prices and bank credit showed significant consistency. Thus, in order to avoid suffering the same fate as the US, i.e., the collapse of a real estate bubble affecting the whole Chinese economy, the relationship between housing market activity and bank credit is noteworthy.

## 2. Theoretical Analysis of the Interaction Effect between Bank Credit and Housing Prices

## 3. Time-Varying Parameter VAR Model with Stochastic Volatility

## 4. Data and Settings

## 5. Empirical Results

#### 5.1. Bank Credit and Housing Prices

#### 5.2. Housing Loans and Housing Prices

#### 5.3. Real Estate Development Loan and Housing Prices

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | Yuan and Hamori (2014) analyzed the crowding out effect of affordable and unaffordable housing in China. |

2 | In this paper, real estate development loan refers to the loan that bank issues to the borrower to finance construction of real estates and supportive facilities. |

3 | In China, the presale of commercial residential houses allows developers to use the capital that consumers borrow from the bank for construction. |

4 | Hereafter, for simplicity, we use the “TVP-VAR model” to indicate the model with stochastic volatility. |

5 | Here, we use the log-normal SV model, which was originally proposed by Taylor (1986). The simplest model can also be defined: ${y}_{t}=\gamma \mathrm{exp}\left(\frac{{h}_{t}}{2}\right),\text{}{h}_{t+1}=\varphi {h}_{t}+{\eta}_{t}$, ${\eta}_{t}~NID(0,{\sigma}_{\eta}^{2})$, t = 0, …, n − 1, γ > 0. For more details on the statistical aspects of ARCH and stochastic volatility, see Shephard (1996). Yang and Hamori (2018) compared the performances of the GARCH and SV models to analyze international agricultural commodity prices. |

6 | Because of the availability of data, we started the sample period in the second quarter of 2005. |

7 | The CEIC database belongs to CEIC Data Company Ltd., whose headquarters are in Hong Kong. This company compiles and updates economic and financial data series such as banking statistics, construction, and properties for economic research on emerging and developed markets, especially in China. |

**Figure 1.**The Chinese real estate industry contributions to the tertiary industry and GDP in billions of Yuan. Source: China Statistics Bureau.

**Figure 3.**Estimation results of parameters in the TVP-VAR model (bank credit–housing prices). Notes: The figure shows sample auto-correlations (

**top**), sample paths (

**middle**), and posterior densities (

**bottom**). In the top figures, the x-axis is the sample auto-correlation, and the y-axis is the lag; in the middle figures, the x-axis is the sampled value, and the y-axis is the iteration; in the bottom figure, the x-axis is the probability density, and the y-axis is the sampled value. The estimates of ${\Sigma}_{\zeta}$ and ${\Sigma}_{a}$ are multiplied by 100.

**Figure 4.**Impulse response based on the standard TVP model for IR, GDP BC, and HP. Notes: This shows the impulse response based on the standard VAR model for the variable set (IR, GDP, BC, HP); the solid line refers to the posterior mean, and the dotted line refers to 95% credible intervals.

**Figure 5.**Impulse response for three different horizons. Notes: This shows the impulse response of the TVP-VAR model for the variable set of (IR, GDP, BC, HP); HP represents housing prices, BC represents bank credit, and IR represents the interest rate; the solid line refers to the time-varying impulse responses for each quarter; the dashed line refers to half-year responses; and the dotted line refers to yearly responses.

**Figure 6.**Estimation results of parameters in the TVP-VAR model (housing loans–housing prices). Notes: The figure shows sample auto-correlations (

**top**), sample paths (

**middle**), and posterior densities (

**bottom**); in the top figures, the x-axis is the sample auto-correlation, and the y-axis is the lag; in the middle figures, the x-axis is the sampled value, and the y-axis is the iteration; in the bottom figure, the x-axis is the probability density, and the y-axis is the sampled value; the estimates of ${\Sigma}_{\zeta}$ and ${\Sigma}_{a}$ are multiplied by 100.

**Figure 7.**Impulse response based on the standard TVP model for (IR, GDP HL, HP). Notes: This shows the impulse response based on the standard VAR model for the variable set (IR, GDP, BC, HP); the solid line refers to posterior mean, and the dotted line refers to 95% credible intervals.

**Figure 8.**Impulse response for three different horizons. Notes: This shows the impulse response of the TVP-VAR model for the variable set of (IR, GDP, HL, HP); HP represents the housing price, HL represents housing loans, and IR represents the interest rate; the solid line refers to time-varying impulse responses for each quarter; the dashed line refers to half-year responses; and the dotted line refers to yearly responses.

**Figure 9.**Estimation results of parameters in the TVP-VAR model (real estate development loans–housing prices). Notes: The figure shows sample auto-correlations (

**top**), sample paths (

**middle**), and posterior densities (

**bottom**); in the top figures, the x-axis is the sample auto-correlation, and the y-axis is the lag; in the middle figures, the x-axis is the sampled value, and the y-axis is the iteration; in the bottom figures, the x-axis is the probability density, and the y-axis is the sampled value; the estimates of ${\Sigma}_{\varsigma}$ and ${\Sigma}_{a}$ are multiplied by 100.

**Figure 10.**Impulse response based on the standard TVP model for (IR, GDP DL, HP). Notes: This shows the impulse response based on the standard VAR model for the variable set (IR, GDP, DL, HP); the solid line refers to the posterior mean; and the dotted line refers to the 95% credible intervals.

**Figure 11.**Impulse response for three different horizons. Notes: This shows the impulse response of the TVP-VAR model for the variable set of (IR, GDP, DL, HP); HP represents the housing price, DL represents real estate development loans, and IR represents the interest rate; the solid line refers to time-varying impulse responses for each quarter, the dashed line refers to half-year responses, and the dotted line refers to yearly responses.

Variable | Data | Data Source |
---|---|---|

Housing Prices (HP) | The logarithmic growth of real price of housing | CEIC database |

Interest Rate (IR) | The logarithmic growth of the Inter Bank Offered Rate (IBOR) | CEIC database |

GDP | The logarithmic growth of real GDP | CEIC database |

Bank Credit (BC) | The logarithmic growth of real medium- and long-term loan | CEIC database |

Housing Loan (HL) | The logarithmic growth of housing loan | CEIC database |

Real Estate Development Loan (DL) | The logarithmic growth of real estate development loan | CEIC database |

HP | IR | GDP | BC | HL | DL | |
---|---|---|---|---|---|---|

Sample Size | 51 | 51 | 51 | 51 | 51 | 51 |

Mean | 0.5890 | −0.6814 | 1.0724 | 1.5791 | 1.9800 | 1.7245 |

Std. Dev. | 1.2609 | 8.4497 | 0.9204 | 0.9286 | 0.9912 | 1.4552 |

Skewness | −0.3381 | −0.0905 | −0.5015 | 1.6381 | 0.9906 | 2.1208 |

Kurtosis | 4.7143 | 5.0809 | 5.4204 | 6.0717 | 3.7497 | 13.9351 |

Maximum | 3.6529 | 23.7312 | 2.7776 | 4.5034 | 4.8360 | 8.9988 |

Minimum | −3.7025 | −26.2599 | −1.6036 | −0.0115 | 0.3222 | −1.9866 |

Jarque–Bera | 7.2166 | 9.2712 | 14.5874 | 42.8576 | 9.5353 | 292.3303 |

Probability | 0.0271 | 0.0097 | 0.0006 | 0.0000 | 0.0085 | 0.0000 |

Variables | ADF | PP | DF-GLS |
---|---|---|---|

Level | Level | Level | |

HP | −4.3138 *** | −7.3650 *** | −7.3510 *** |

IR | −3.4648 ** | −3.1574 ** | −3.4111 *** |

GDP | −6.5760 *** | −6.5925 *** | −5.0991 *** |

BC | −2.8507 * | −2.9110 * | −2.7068 *** |

HL | −8.7130 *** | −8.5561 *** | −7.2918 *** |

DL | −4.7565 *** | −4.8917 *** | −4.7964 *** |

**Table 4.**Estimation of selected parameters in the time-varying parameter TVP-VAR model (bank credit–housing prices).

Mean | St. Dev | 95%L | 95%U | Geweke | Inef. | |
---|---|---|---|---|---|---|

${\left({\sum}_{\varsigma}\right)}_{1}$ | 0.0227 | 0.0026 | 0.0183 | 0.0286 | 0.2150 | 3.9600 |

${\left({\sum}_{\varsigma}\right)}_{2}$ | 0.0230 | 0.0027 | 0.0185 | 0.0290 | 0.3410 | 2.8200 |

${\left({\sum}_{a}\right)}_{1}$ | 0.0453 | 0.0092 | 0.0310 | 0.0667 | 0.0230 | 8.3900 |

${\left({\sum}_{a}\right)}_{2}$ | 0.0444 | 0.0086 | 0.0309 | 0.0641 | 0.0930 | 11.4500 |

${\left({\sum}_{h}\right)}_{1}$ | 0.5335 | 0.3378 | 0.0752 | 1.2870 | 0.1080 | 125.3200 |

${\left({\sum}_{h}\right)}_{2}$ | 0.3431 | 0.1722 | 0.1036 | 0.7669 | 0.6420 | 63.5400 |

Mean | St. Dev | 95%L | 95%U | Geweke | Inef. | |
---|---|---|---|---|---|---|

${\left({\sum}_{\varsigma}\right)}_{1}$ | 0.0228 | 0.0027 | 0.0184 | 0.0287 | 0.3550 | 4.5000 |

${\left({\sum}_{\varsigma}\right)}_{2}$ | 0.0230 | 0.0027 | 0.0185 | 0.0289 | 0.5260 | 3.2000 |

${\left({\sum}_{a}\right)}_{1}$ | 0.0445 | 0.0088 | 0.0308 | 0.0650 | 0.5580 | 10.3100 |

${\left({\sum}_{a}\right)}_{2}$ | 0.0505 | 0.0108 | 0.0336 | 0.0754 | 0.4100 | 12.0700 |

${\left({\sum}_{h}\right)}_{1}$ | 0.4923 | 0.3177 | 0.0858 | 1.1984 | 0.2590 | 103.9000 |

${\left({\sum}_{h}\right)}_{2}$ | 0.4434 | 0.2130 | 0.1547 | 0.9810 | 0.2930 | 78.8900 |

**Table 6.**Estimation of selected parameters in the TVP-VAR model (real estate development loans–housing prices).

Mean | St. Dev | 95%L | 95%U | Geweke | Inef. | |
---|---|---|---|---|---|---|

${\left({\sum}_{\varsigma}\right)}_{1}$ | 0.0228 | 0.0026 | 0.0183 | 0.0284 | 0.4130 | 2.9400 |

${\left({\sum}_{\varsigma}\right)}_{2}$ | 0.0230 | 0.0027 | 0.0184 | 0.0291 | 0.3460 | 4.6700 |

${\left({\sum}_{a}\right)}_{1}$ | 0.0462 | 0.0096 | 0.0316 | 0.0686 | 0.1720 | 19.6300 |

${\left({\sum}_{a}\right)}_{2}$ | 0.0599 | 0.0157 | 0.0373 | 0.0971 | 0.2420 | 14.9100 |

${\left({\sum}_{h}\right)}_{1}$ | 0.4279 | 0.2924 | 0.0743 | 1.1305 | 0.5250 | 138.0900 |

${\left({\sum}_{h}\right)}_{2}$ | 0.4495 | 0.2496 | 0.1159 | 1.1173 | 0.9050 | 107.8300 |

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## Share and Cite

**MDPI and ACS Style**

He, X.; Cai, X.-J.; Hamori, S.
Bank Credit and Housing Prices in China: Evidence from a TVP-VAR Model with Stochastic Volatility. *J. Risk Financial Manag.* **2018**, *11*, 90.
https://doi.org/10.3390/jrfm11040090

**AMA Style**

He X, Cai X-J, Hamori S.
Bank Credit and Housing Prices in China: Evidence from a TVP-VAR Model with Stochastic Volatility. *Journal of Risk and Financial Management*. 2018; 11(4):90.
https://doi.org/10.3390/jrfm11040090

**Chicago/Turabian Style**

He, Xie, Xiao-Jing Cai, and Shigeyuki Hamori.
2018. "Bank Credit and Housing Prices in China: Evidence from a TVP-VAR Model with Stochastic Volatility" *Journal of Risk and Financial Management* 11, no. 4: 90.
https://doi.org/10.3390/jrfm11040090