# Estimates and interpretation

## Chapter 3: A three-state Markov approach to analyze housing prices cycle in

### Table 3.5 Determining the appropriate model by Diebold and Mariano test

FTP-MS

1. The significant level is set at 10%, model with better prediction of housing growth rate (∆HP) is recorded in the table.

2. “=” indicates the forecast accuracy is statistically indifferent between two models in forecasting housing growth rate (∆HP).

To sum up the above-mentioned arguments, we choose TFP-MS with 3 regimes as the most appropriate model for analyzing the housing prices dynamics in China.

### 3.4.2 Estimates and interpretation

In this section, we present the estimation result of TFP-MS with 3 regimes model, and its implications. Firstly, we show the estimation result of transition probability matrix by the following equation:

### P= [

where 0=stable state, 1=contraction state, 2=expansion state.

Substitute Eq. (9) into Eq. (4), we can get the expected durations of being in each of the regimes are:

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𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑠𝑡𝑎𝑏𝑙𝑒 𝑟𝑒𝑔𝑖𝑚𝑒 = 6.629 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 𝑟𝑒𝑔𝑖𝑚𝑒 = 7.885 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑟𝑒𝑔𝑖𝑚𝑒 = 13.516

Eq. (9) shows the probability that housing market remains in the expansion period (𝑝22) is 0.926 higher than 𝑝00= 0.849 and 𝑝11 = 0.873. As a result, the expected duration in expansion regime is relative longer than the expected duration in stable and recession regime. In other words, the expansion state is the most persistent regime in China’s housing market. Furthermore, the probability that contraction state switches to the extension state (0.004) and the probability that extension state switches to the contraction state (0.009) are both lower than the probability that contraction (extension) state switches to the stable state (0.117 and 0.069, respectively). This result is quite reasonable, since the end of the bull market is not always followed by an immediate bear market, and vice versa. The normal situation is the market smoothly turns to the stable state from a deep recession or a prosperity.

Figure 3.2 depicts real housing growth rate, the blank areas represent expansion periods, grey areas indicate expansion periods of China’s housing market, and dotted lines denote the recession period. Figure 3.2 illustrates that during the 2009, the historically highest housing prices growth rate are followed by a sharp drop in housing prices growth rate. Nonetheless, the market switches from expansion state to stable state rather than dramatically switches to contraction state.

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-10 0 10 20 30 40

02 03 04 05 06 07 08 09 10 11 12 13 14 15

Note: Grey areas indicate expansion periods of housing market in China. Dotted lines denote the recession period, and the stable periods are represented in blank areas.

### Figure 3.2 Hosing price dynamics and regimes

Table 3.6 provides the estimated parameter of the TFP-MS with 3 regimes model which aim to investigate the nonlinear relationship between fundamental factors and the housing prices. Firstly, our empirical results show that there is no significant relationship existing between the housing market and income in any regime. The second conclusion to be drawn is that the stock index growth rate (∆STOCK) have positive and significant effects on housing price growth rate for all regimes, moreover, the absolute value of the coefficient are found to be quiet symmetric in each regime. (0.042, 0.050, and 0.044 in stable, expansion, and contraction regime, rexpectively). Our result is corresponding to Chan and Chang (2014) which argue that there exists significant price transmission effects from the stock market to the real estate market in China.

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### Table 3.6 Three regimes fixed transition probability Markov switching model output

Dependent variable: Housing growth rate (∆HP)

Regime Constant ∆INCOME ∆STOCK INT CPIG

1. Standard errors are reported in parentheses. The stars, *, ** and *** indicate the significance level at 10%, 5% and 1%, respectively.

Focusing on the coefficients of interest rate, the result for three regimes FTP-MS model indicates there is a significant and negative relationship between housing price growth rate and interest rate in the stable regime and contraction regime, although the effects in both regimes are different. Additionally, there is no significant relationship existing between interest rate and housing dynamics in the expansion regime. This empirical finding is similar to the previous studies which claim that the finance constraint is more likely binding during recessionary period, therefore the effects of a monetary shock is larger during the recession than in expansion. (Bernanke and Gertler, 1989; Garcia and Schaller, 2007; Zakir and Malik, 2013). However, our empirical result illustrates that the effect of negative interest rate shock is larger in stable regime (-3.350) than in contraction regime (-1.635).

Finally, from Table 3.6, there is a negative and significant effect of the CPI growth rate on housing growth rate in every regime. For a long time, investment in real estate regards as a hedge against inflation. Hence, a higher inflation results in an increasing demand for the housing assets. However, CPI is closely related to a cost-of-living index.

Our empirical result suggests the negative effect of CPI on housing dynamics is larger than the positive effect in the long run.

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### 3.5 Conclusion

In this study, we investigate the fluctuations in housing prices in China for the period of 2002:01 until 2015:12, by introducing the Markov switching model with explanatory variables. Our empirical result suggest that the FTP-MS model with 3 regimes is preferable to FTP-MS model with 2 regime, TVTP-MS model with 3 regime, and TVTP-MS model with 3 regime. We also examine the reaction of housing price to macroeconomic changes in the state of stable, recession, and expansion.

Our empirical result suggests that the bull (bear) housing market does not always followed by an immediate bear (bull) housing market. It is likely for the housing market smoothly turns to the stable state during a deep recession or a prosperity. Additionally, the expansion state is the most persistent regime in China’s housing market. The second finding in this Chapter is in accordance with the previous work which claim the effects of an interest rate shock is larger in recession regime than in expansion regime.

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