The Time-Varying Effects of Monetary Policy on House Prices in China: An Application of TVP-VAR Model with Stochastic Volatility

The boom of housing market in China in recent years has attracted great concerns from all over the world. How monetary policy affects house prices in China becomes an essential topic. This paper studies the time-varying effects of monetary policy on house prices in China during 2005.7-2017.10, by using a time-varying parameter VAR model. This paper obtains three interesting results. First, there are time-varying features of the responses of house prices to monetary policy shocks half-year and 1-year ahead, no matter through interest rate channel or through credit channel. Second, interest rate channel and credit channel have been enhanced since financial crisis in 2008. Third, the responses of nominal house prices to monetary policy in China are mainly driven by the responses of real house prices, instead of inflation. Finally, this paper gives proper suggestions for each finding respectively to central bank in China.


Introduction
Since the financial crisis in 2008, a great attention has been paid to how monetary policy should properly control house prices.With the turmoil, monetary policy was executed to inject large liquidity into the credit market and real activity market globally.However, the released monetary liquidity in China kept flowing into high-returned markets, especially housing market.The growth rates of house prices and investment both increased rapidly.This circumstance makes most people unable to afford housing.It seems that policymaker tries to control house prices with monetary policy, and as a result, "price puzzle" (Note 1) arose.However, in fact, central bank in China does not target house prices, even when there are the skyrocketing house prices.The lasting slack real activity in China pushes policymaker to conduct a looser monetary policy for a long time; and there is tight credit policy targeting housing market.These two directions of policies were conducted simultaneously, together influencing housing market.
As Min Zhu said, housing market plays an important role in financial stability and real economy.In particular, monetary policy is important to regulate house price bubble coincided with credit boom (Note 2).Generally, in China, real estate developers mainly finance from banks through on-balance sheet; since the continuous rising of house prices, central bank confined banks to make loans to real estate developers, for example, through higher credit costs.However, with adequate liquidity, banks found other ways through off-balance sheet to finance them, such as trust funds or other wealth management products.Consequently, higher interest rate turns out to have limited effects on loans to housing market.One of the reasons is that housing market in China has been developed sharply in recent decades, leading to a far higher return of housing investment than credit cost (Tan and Wang, 2015).Adequate liquidity attracted bankers continuing to lend money to real estate developers.And real estate developers would decide to require loans by comparing their investment return and credit costs, so would households who want to consume or invest housing.Therefore, interest rate and money supply instrumented by the People's Bank of China, PBC hereafter, would influence house prices together.
In particular, since 1996, there were several policies in China to facilitate the reform of interest rate liberalization (Note 3).Also, the development of credit market and the awareness of credit-consumption in China increase the use of housing mortgage, which in turn enhances the financial feature of house and the role of housing market in monetary policy transmission mechanism.Moreover, since the financial crisis, the uncertainty is rising globally, inducing more uncertainties for economic development.These factors would be the reasons to make monetary policy transmission mechanism varying in terms of house prices.Unfortunately, so far this important fact has not been noticed.Therefore, to better integrate with reality, this paper will unfold by a time-varying parameter VAR model to study whether and how the responses of house prices to monetary policy in China would change over time.

Literature Review
This paper analyzes the relationship between monetary policy and house prices in China.Literatures show an unstable relationship between them (Wang and Han, 2009;Lee et al., 2011;Jia et al., 2014;Chen et al., 2016).Especially, the effects of monetary policy on house prices were different by the change of economic environment (Jia et al., 2016;Chen et al., 2016).The most recent development of housing market may cause an uncertainty of house-related transmission mechanism channels (Mishkin, 2007).Consequently, when considering the fact that China has experienced a rapid development of housing market and also a shifting macroeconomic environment from high growth to The New Normal, the effect of monetary policy on house prices faces many changing circumstances, which would make it varying over time.
Intuitively, there are two major channels of transmission mechanism referring to controlling housing market in China: interest rate channel and credit channel.In detail, for interest rate channel, tight money policy lifts real interest rate, causing an increase of capital cost, and, therefore, reducing investment spending and then the aggregate demand and output (Mishkin, 1995).In particular, short-term and long-term interest rate have different effects on house prices; the response of house prices to short-term interest rate is stronger and longer than that to long-term interest rate (Bernanke and Gertler, 1995;Bjornland and Jacobsen, 2010).Also, the type of housing, such as the middle-, luxury-and affordable-segments in housing market, could influence the effects of interest rate (Gupta, Jurgilas and Kabundi, 2010).For credit channel, there are several ways to work out, such as the bank lending channel and the balance-sheet channel (Bernanke and Gertler, 1995).Obviously, the bank-lending channel is applied to the behavior of banks discussed above; similarly, the balance-sheet channel explains the behavior of real estate developers and households mentioned above.Performed as a collateral, house itself plays an essential role in consuming and investing housing, making the effects of monetary policy on house prices more significant (Aoki et al., 2004;Iacoviello, 2005;Calza et al., 2013).Moreover, financial system liberalizations, housing credit system and the development of mortgage market influence the effects of monetary policy on house prices (Goodhart and Hofmann, 2008;Iacoviello and Minetti, 2008;Calza, Monacelli and Stracca, 2013).Surprisingly, by dividing the sample into two sub-periods, Iacoviello and Neri (2010) find that the influence of monetary policy through credit market on house prices was getting stronger in America.Consequently, interest rate channel and credit channel have essential impacts on monetary policy transmission mechanism in terms of housing market.
Nevertheless, there is few to consider the changing effects of monetary policy on house prices; most of them ignore an important fact that this relationship is unstable.To capture the time-varying feature of the responses of house prices to monetary policy, time-varying parameter VAR model would be used.Besides, to avoid the common issue of over-parameterized among most time-varying parameter VARs, this paper will use a time-varying parameter VAR model with stochastic volatility (Nakajima, 2011).It allows the VAR coefficients, a block which relates to the error variances and another relating to error co-variances to evolve by themselves.In a word, this paper tries to explain whether and how the response of house prices to monetary policy changes over time in China.

Model
This paper refers to Nakajima (2011) for the time-varying parameter VAR model.To introduce TVP-VAR model with stochastic volatility, this paper starts with the basic VAR model defined as where is the × 1vector of observed variables, and , , ⋯ , are × matrices of coefficients.The disturbance is a × 1 structural shock and, it is assumed that ~ (0,∑∑), where . Also, it is specified as the simultaneous relations of the structural shock by recursive identification, and assumes that is lower-triangular, Therefore, model (1) could be rewritten as follows: where = , for = 1, ⋯ , .By stacking the elements in the rows of 's to construct ( × 1 vector), and defining = ⨂( , ⋯ , ), where ⨂ refers to the Kronecker product, the model could be rewritten as follows: Until now, the parameters in model ( 3) are all time-invariant.In this case, it should be extended to the TVP-VAR model by allowing those parameters to be time-variant.Therefore, consider the TVP-VAR model with stochastic volatility defined by where the coefficients , and the parameters and ∑ are all time varying.Specifically, variables are defined to include intercepts as = ⨂(1, , ⋯ , ) , where the intercepts are also time-varying.Following Primiceri ( 2005), let = ( , , ⋯ , , )′ be a stacked vector of the lower-triangular elements in and = ( , ⋯ , )′ with = , for = 1, ⋯ , , = + 1, ⋯ , .And then assume the parameters in model ( 4) to follow a random walk process as follows: , where ~ ( , ∑ ), ~ ( , ∑ ), ~ ( , ∑ ).

Data and Settings
This  ); the number of TVP-VAR lags is two.It is based on the result of BIC for the simple VAR model.And ∑ is assumed to be diagonal matrix and the assumptions of initial values and prior distribution of parameters are following Nakajima's settings (Note 5).This paper also conducts the MCMC algorithm by drawing = 20,000 samples after discarding the initial 1,000 samples in the burn-in period, to obtain posterior draws.Finally, this paper builds impulse response functions to depict how large and how long monetary policy influences house prices, such as the effects of monetary policy at several periods ahead on house prices and at some significant moments when monetary policy in China experienced sharp change, which may induce the enormous shifts of housing market.3 suggest that at the selected time points, monetary policy has different impacts on house prices between 5 months and 24 months, but similar impacts before 3 months.Consequently, the results of impulse responses in figure 2 and figure 3 are consistent: shocks 1-quarter ahead have more characteristics of time-invariant; shocks half-year and 1-year ahead have more feature of time-variant.

Param
Similarly, the responses of CPI to monetary policy, interest rate and money supply, are rather smaller than contemporaneous response of real house prices, no matter in 2008.12,2011.04 or 2014.11.This result is also consistent to that in figure 2.

Conclusions and Suggestions
This paper uses TVP-VAR model with stochastic volatility to study the time-varying effects of monetary policy on house prices in China during 2005.7-2017.10.There are several findings in the paper: First, there are time-varying features for responses of house prices to monetary policy shocks half-year and 1-year ahead, no matter through interest rate channel or through credit channel.Considering some distinct time points, it is obvious to conclude that financial crisis works importantly to the time-varying influences of monetary policy, through interest rate channel and credit channel, on real house prices in China.When central bank in China expects to control house prices, it should take into account the time-variant feature of interest rate channel and credit channel and the timing and magnitude of their impacts.
Second, rate channel and credit channel have been enhanced since financial crisis in 2008.This paper finds that the additive productions of financial crisis in 2008, including the uncertainty of macroeconomic environment and the financialization of housing market and the development of mortgage market in China, are the potential reasons why monetary policy have time-varying effects on house prices, both through interest rate channel and credit channel.This finding confirms the conclusion of (Aoki et al., 2004;Iacoviello, 2005;Iacoviello and Minetti, 2008;Calza, Monacelli and Stracca, 2013).Meanwhile, it could be an alert for central bank in China about the broad influences of uncertainty from macro-economic environment and of the transforming of housing market.
Third, the responses of nominal house prices to monetary policy in China are mainly driven by the responses of real house prices, instead of inflation.Although it is significant that monetary policy plays a great role in the skyrocketing house prices recently, it is crucial to clarify the more responsive one to monetary policy is real house prices, instead of inflation.In this case, when conducting monetary policy to adjust inflation, central bank in China should consider its accompanying results, such as more responsive real house prices.

Future study and limitations
This paper has found the time-varying effects of monetary policy on house prices in China from 2005.7 to 2017.10, by using the TVP-VAR model.Nevertheless, this paper did not offer more evidence or dig more about the reason why the time-varying effects of monetary policy happened during this period.Is it because the economic reform in China changed the macroeconomic environment and then changed the transmission mechanism of monetary policy?Or because the different regimes of business cycle have different transmission mechanism of monetary policy?And this could be the future direction for this paper issue to study.
Figure 1 each row.suggestin indicating Data of industrial production in China are missing for every first two-month in the official website (National Bureau of Statistics of China, hereafter, NBSC), but DataStream offers the complete data series.Therefore, here adopts the Industrial Production data from DataStream.The real loan rate, , offered by the People's Bank of China, is calculated by nominal one-year loan rate minus inflation.Similar treatment is taken to real house prices, .Except for industrial production and interest rate, other data could be found in NBSC.Although the sample duration, from Jul 2005 to Oct 2017, depends on the availability of house price data, it captures the most representative period when housing market in China has experienced sharp development with cyclical and shifting characters.
of monetary policy on house prices in China.Moreover, the results in figure