總體經濟影響中國大陸房地產市場之動態研究 - 政大學術集成

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(1)國立政治大學經濟學(系)研究所 博士學位論文. 總體經濟影響中國大陸房地產市場之動態研究 China’s Housing Market Dynamics and Their Reaction to. 治 政 大 Macroeconomic Changes 立. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. 指導教授:林 祖 嘉 博士 研究生:游 士 儀 撰. 中 華 民 國 105 年 6 月.

(2) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v.

(3) 謝辭 經過漫長的 N 年,博士班的生涯總算劃下句點,能夠順利完成學業,有太多人 需要感謝。首先必須感謝我的指導教授林祖嘉老師,帶領我進入中國大陸經 濟的領域,並鼓勵我多參加學術研討會,讓我這幾年來從無到有的積蓄了 許多研究的能量以及論文寫作的能力。對於我的口試委員,陳建良老師、 林柏生老師、謝博明老師以及王信實老師,在論文審定上給予精闢的見解 與啟發,深切表達由衷的謝意。 在這十分煎熬的博士生涯中,我要特別感謝湘菱,總是在我惶恐焦慮的時候想 辦法給予我信心,讓我能在漫長的論文寫作中不至於燃燒殆盡。還要感謝我的 學弟劉世夫,在我最需要協助的時候,毫不吝嗇地將時間撥出來幫我。特別感 謝方中柔老師在投稿上的協助,也感謝莊奕琦老師、李浩仲老師給我研究方向 以及內容提供許多建議,使我獲益良多。還有要感謝這段期間與我互相扶持的 學長姐以及學弟妹,小馬學長、輝培學長、秝宸、學宏以及玫英。. 立. 政 治 大. ‧ 國. 學. ‧. 最後,要謝謝我的父母,謝謝你們在這幾年給我的支持鼓勵,使我的這一段求 學生涯完全無後顧之憂,才得以順利完成學業。僅以本文獻給我的父母以及所. n. al. er. io. sit. y. Nat. 有支持過我的人,感謝你們在我博士班過程中給予我的所有感動與關懷,謝 謝。. Ch. engchi. i n U. v. 游士儀 謹誌於 國立政治大學經濟學系 2016 年.

(4) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v.

(5) ABSTRACT The dynamic nature of real estate market in China has post specific challenges in exploring the relationship between macroeconomic variables and housing cycle as well as the determination of its turning point. There are large number of literature shed light on the relationship between housing price and economic fundamental factors. Most of the existing works however rarely invoked in possible that economy might have different impacts in different phase of housing cycle. Additionally, the structure and dynamics of the China’s housing market are less investigated. The main purpose of this thesis is to study the non-linear relationship between housing. 政 治 大 panel smooth transition model. 立 Our analysis confirms the significance of the nonlinear. price and some basic fundamentals by adopting the Markov switching model and the. ‧ 國. 學. relationship between the housing price and economic fundamental factors in China’s real estate market.. ‧. Key words: Real Estate Market of China, Business Cycle, Markov Switching Model,. y. Nat. n. al. er. io. sit. Panel Smooth Transition Model. Ch. engchi. i n U. v.

(6) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v.

(7) TABLE OF CONTENTS TABLE OF CONTENTS ............................................................................................. I LIST OF TABLES AND FIGURES ........................................................................ III Chapter 1: Introduction .............................................................................................. 1 Chapter 2: Are the responses of real estate activities to macroeconomic changes symmetric in China? ................................................................................. 5 2.1 Introduction ...................................................................................................... 5 2.2 Methodology .................................................................................................... 9 2.3 Data and resources ......................................................................................... 14 2. 4 Empirical Result............................................................................................ 15 2.4.1 Unit root tests ...................................................................................... 15. 立. 政 治 大. ‧ 國. 學. 2.4.2 Model selection and its implications................................................... 18 2.5 Conclusion ..................................................................................................... 25 Chapter 3: A three-state Markov approach to analyze housing prices cycle in. ‧. n. al. er. io. sit. y. Nat. China......................................................................................................... 27 3.1 Introduction .................................................................................................... 27 3.2 Methodology .................................................................................................. 30 3.2.1 Markov-Switching model ................................................................... 30 3.2.2 Markov-Switching model: The shift from two to three regimes ........ 32 3.3 Data and unit root tests .................................................................................. 34 3.3.1 Data description .................................................................................. 34 3.3.2 Unit root tests ...................................................................................... 35 3.4. Estimation Result .......................................................................................... 36 3.4.1 Model selection ................................................................................... 36 3.4.2 Estimates and interpretation ................................................................ 39 3.5 Conclusion ..................................................................................................... 43. Ch. engchi. i n U. v. Chapter 4: Does local governments’ budget drive housing prices up in China? . 45 4.1 Introduction .................................................................................................... 45 4.2 A model of housing activity and local government’s budget deficit .............. 49 4.2.1 Households.......................................................................................... 49 4.2.2 Builders ............................................................................................... 50 4.2.3 Local government ............................................................................... 51 4.2.4 Asymmetric effect and threshold model ............................................. 51 I.

(8) 4.3 Model specification tests and evaluation....................................................... 53 4.3.1 Linearity test: Linear model versus PSTR model ............................... 54 4.3.2 No remaining non-linearity: Logistic or exponential transition function ................................................................................................................ 55 4.3.3 Parameter estimation ........................................................................... 56 4.4 Data description ............................................................................................. 57 4.5 Estimation results .......................................................................................... 59 4.5.1 Linearity tests ...................................................................................... 62 4.5.2 Comparison between linear and nonlinear estimation result .............. 64 4.5.3 Asymmetric effect of land prices on housing prices ........................... 66 4.5.4 Does interest rate matter?.................................................................... 68 4.5.5 China's specific characteristics ........................................................... 71 4.5.5.1 Budget deficit ratio .......................................................................... 71 4.5.5.2 Sex ratio ........................................................................................... 72 4.6 Conclusion remarks ....................................................................................... 72. 立. 政 治 大. ‧ 國. 學. Chapter 5: Conclusion ............................................................................................... 75 Reference ................................................................................................................... 77. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. II. i n U. v.

(9) LIST OF TABLES AND FIGURES Table 2.2. Unit Root tests ......................................................................................... 17. Table 2.1 Table 2.3 Table 2.4 Table 2.5. Summary statistics .................................................................................. 16 The estimation result of Model 1, Model 2, Model 3, and Model 4 ....... 19 The estimation result of Model 5, Model 6, Model 7, and Model 8 ....... 20 Diebold and Mariano test ........................................................................ 21. Table 3.1 Table 3.2 Table 3.3. Summary Statistics .................................................................................. 35 Unit root tests .......................................................................................... 36 Determining the appropriate model using information criteria .............. 37. Table 3.4 Table 3.5. Determining the appropriate model by evaluating forecast accuracy ..... 38 Determining the appropriate model by Diebold and Mariano test .......... 39. Table 3.6. Three regimes fixed transition probability Markov switching model output .................................................................................................. 42. Table 4.1 Table 4.2 Table 4.3 Table 4.4. List of city ............................................................................................... 57 Statistics description ............................................................................... 60 Summary statistics of variables............................................................... 61 Tests of no remaining linearity ................................................................ 63. Table 4.5. No remaining non-linearity ..................................................................... 64. Table 4.6. Linear panel regression and threshold panel regression of national housing price, 2003-2013(all cities of the sample) ............................. 65. Table 4.7. Linear panel regression and threshold panel regression of regional housing price, 2003-2013 ................................................................. 67. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Figure 2.1. Ch. engchi. i n U. v. Time series of real estate climate index, economic climate leading index, and economic climate coincident index ................................. 6 Figure 2.2 Smooth probabilities of regime expansion from Model 1 to Model 4 22 Figure 2.3 Smooth probabilities of regime expansion from Model 5 to Model 8 23 Figure 3.1(a) Two regimes model ............................................................................. 33 Figure 3.1(b) Three regimes model .......................................................................... 33 Figure 3.1 The difference between two and three regimes model ........................ 33 Figure 3.2 Hosing price dynamics and regimes .................................................... 41 Figure 4.1 Average housing price in China and the four regions, 2003-2015. ..... 58 Figure 4.2 Tendency of the coefficients of land price of eastern cities. ............... 69 Figure 4.3. Time series of housing prices, land prices, and coefficients of land price of Shanghai ............................................................................ 70. III.

(10) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. IV. i n U. v.

(11) Chapter 1: Introduction. In recent years, China’s housing market has experienced huge increases in prices and high volatility. In 2009, the rapid credit growth led to incautious loans as well as the increasing house prices. Housing prices in some urban areas are too high to be afforded, and it reveals that the housing bubble is a serious problem. Considering that the stable real estate market plays a significant role in the wider macro-economy, Chinese. 政 治 大 the related policy has been regarded as scarcely effective. 立. government has tried many times to control the real estate market. However, in general,. ‧ 國. 學. Over the past few years, a larger number of theoretical and empirical studies have tried. ‧. to investigate the abnormal increasing price of China’s housing market and the policy effect. Most of the existing works however rarely invoked in possible that economy. y. Nat. io. sit. might have different impacts in different phase of housing cycle. Thus, the main. n. al. er. purpose of this study is to investigate the potential asymmetric impacts from economy. Ch. i n U. to housing markets as well as the real estate cycle in China.. engchi. v. This thesis is constructed as follows: Chapter 2 investigates whether the responses of real estate activities to macroeconomic changes symmetric in China. Chapter 3 emphasizes the importance of stable regime in contrast to contraction and expansion regime in the housing market pricing cycle. Chapter 4 highlights the monopoly power of local government in the land market and further examines its influence on housing prices. Final Chapter is the conclusion of this study.. The study of Chapter 2 is motivated by Seslen (2003), Abelson et al.(2005), and Kim 1.

(12) and Bhattacharya (2009) which claim that the participants in real estate markets will not respond symmetrically over the real estate cycle. Accordingly, the economy might have asymmetric influence on different phase of real estate cycle. In addition, reviewing the previous studies, we find that though there have been many studies covering various aspects of fluctuations in China’s real estate market, little attention has been made to provide a comprehensive analysis of the real China’s real estate cycle. As a result, the main purpose of Chapter 2 is to apply the Markov switching model to examine China’s real estate cycle, and further to investigate the possible nonlinear relationship between. 政 治 大. macroeconomic variables and real estate market.. 立. The study of Chapter 3 is to apply the two and three-state Markov switching models to. ‧ 國. 學. illustrate China’s residential housing prices growth. Since the standard two-state switching model implies the housing market is either in a contraction (bear) or in an. ‧. expansion (bull).. However, a bull or a bear market occur usually because of the. y. Nat. io. sit. occasionally huge external shocks. Therefore, it is not always appropriate to simply fix the. n. al. er. number of regimes at two. Additionally, the two regimes model ignores the bounce-back. i n U. v. effects during the business cycle. Hence, a switching model that allows three regimes. Ch. engchi. (contraction, expansion, and stable) may be able to capture the dynamics of house prices. In. Chapter 3, we consider a two and three-state Markov switching model, and compare the forecast performance between them.. The most distinctive characteristic of China’s real estate market is the land use rights which have been separated from land ownership since the 1990s. That is to say, the urban land is owned by the state, and the land users can only possess the land use rights. Hence, China’s local government can receive revenue to finance their debt from granting process, and it gives rise to China’s local government deeply relies on land 2.

(13) sales for income, incentivizing the continued sale and development of land. In view of the fact that land market in China is monopolized by the local government, the real estate market has been shaped by the monopoly control over the land supply and the market price is also distorted. As a consequence, the topic of Chapter 4 is to examine if the budget deficit of the local government drives housing prices up in China. Wu et al.. (2015) is the first study which provides a conceptual framework for investing this transmission mechanism, and their empirical results do not support that budget deficit of local government as a driving force of China’s housing prices. In this paper, we use. 政 治 大 Additionally, because the movements of regional housing prices are more correlated 立. a nonlinear smooth threshold model to reexamine the topic proposed by Wu et al. (2015).. with regional economic fluctuations rather than with national ones, therefore, in. ‧ 國. 學. Chapter 4, we not only focus on housing price properties and their determinants at. ‧. national level but also at regional level.. n. er. io. sit. y. Nat. al. Ch. engchi. 3. i n U. v.

(14) 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 4. i n U. v.

(15) Chapter 2: Are the responses of real estate activities to macroeconomic changes symmetric in China?. 2.1 Introduction China’s economy has experienced an astonishing growth during the transition from planned economy to market economy. In the meanwhile, the real estate industry keep. 治 政 大 of the housing price housing prices is over-inflated, and it will bring the possibility 立. fast developing, and the housing prices continue rising. Some studies claim that China’s. bubble. 1 At the same time, the recent slowdown in China’s economic growth has. ‧ 國. 學. caused concern about the crash of the real estate market.. ‧. If we focus on the economic leading index and the real estate climate index, we can. y. Nat. sit. observe the tendency between the economic leading index and the real estate climate. n. al. er. io. index is similar. As well as the tendency between the economic coincident index and. i n U. v. the real estate climate index (shown in Figure 2.1). As a result, in this Chapter, we want. Ch. engchi. to investigate the real estate cycle in China and to ensure the role of economic activities in the real estate cycle.. The research of real estate cycle and its relation to macroeconomics in China started from the 1990s, much later than in other countries. Review the existing studies, the variables used to evaluate the real estate cycle in China can be roughly classified into two groups. One is choosing a single indicator to represent the real estate activities, and then make use of the chosen indictor to analyze the real estate cycle. For example, Liang. 1. See Hu et al. (2006), Sun and Zhang (2008), Ren et al. (2012), and Feng and Wu (2015). 5.

(16) (1996) selects the growth rate of commercial housing sale volume to evaluate the housing market volatility in China. Ho et al. (1996) use various indicators include price of commercial houses, newly built residential buildings in urban areas, floor space of buildings completed, etc., to investigate the relationship between real estate cycle and economic cycle. The other group use various methods to combine multiple indicators into a composite index, and then make use of the composite index to examine the real estate cycle in China (Chou, 2010; Sun and Chang, 2008; Chiou and Wang, 2009).. 108. 政 治 大. 106 104. 立. 102. 108. io. 07. 08. 09. 10. 104. 11. 12. 13. 14. 15. Economic climate Index_Leading Index Real estate climate index. al. n. 106. 06. y. 05. Nat. 04. sit. 92. ‧. 94. er. 96. ‧ 國. 98. 學. 100. 102. Ch. engchi. i n U. v. 100 98 96 94 92 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. Economic Climate Index_Coindident Index Real estate climate index. Note: Data source are CEIC Data's China Economic Database and China National Bureau of Statistics.. Figure 2.1 Time series of real estate climate index, economic climate leading index, and economic climate coincident index. 6.

(17) An overview of the existing literature on China’s real estate cycle, one of the most popular methodology is using Hodrick-Prescott Filter to investigate the real estate cycle in China. HP filter was firstly developed by Hodrick and Prescott who aim to analyze the postwar U.S. business cycles.2 It is a useful econometric toll to detrend data, and then assist the measurement of business cycle. Sun and Chang (2008) create a composite index to represent the real estate activity, and use HP filter to analyze the real estate cycle. They conclude that China has experienced 9 short real estate cycle and 2 long real estate cycle during 1978 to 2008. Similarity, Chiou and Wang (2009) select. 政 治 大 length of real estate cycle in China was 3-5 years. After 1992, the length of real estate 立. 6 indicators into composite index, and use HP filter to identify that before 1992, the. cycle was reduced to 2 years.. ‧ 國. 學. A possible drawbacks of the previous studies may be summarized in the following. ‧. arguments. In the first place, use a single indicator to represent real estate activates is. y. Nat. sit. unreliable, because it is easy to ignore the signals coming from different sectors of the. n. al. er. io. real estate.3 In the second place, though a combination of multiple variables into a. i n U. v. composite index can be better in capturing the information from different sectors, the. Ch. engchi. way of selecting the best index components is very subjective, so is the weight scheme (Marcellino, 2005). In the third place, the HP filter has its limitations, especially when there is a structural break.. 4. The final point is HP filter doesn’t allow us to identify the. 2. See Hodrick and Prescott(1997) for a more detailed discussion of the properties of the Hodrick-Prescott filter 3 See Marcellino (2005) for more detailed information about the shortage of using a single indictor. 4 The HP filter is obtained by minimizing the following objective function: T 1. T. ( y t 1. t. ~ yt ) 2    (( ~ yt 1  ~ yt )  (~ yt  ~ yt 1 )) 2 t 2. where y𝑡 is a given series, ỹ𝑡 is the smooth trend of y𝑡 . Therefore, the term y𝑡 − ỹ𝑡 is the deviation of y𝑡 from the trend, it is then referred to as the business cycle component. λ denotes the smoothing parameter. The choice of λ does not only affect the cycle but also the trend volatility. A possible drawback of HP filter is that when there is s structure change, the HP filter with the fixed smoothing parameter is not reliable. 7.

(18) period of expansion and contraction until the end of business cycle. Accordingly, it is impossible for us to evaluate the macroeconomic shocks on the real estate market under different real estate climate.. Additionally, Chiou and Wang (2009) point out there is more room to improve the studies regarding to China’s real estate cycle since the lack of data information as well as more advanced methodology. In light of this, the main purpose of this Chapter is employing the real estate climate index created by China Economic Monitoring Center as the main variable to represent China’s real estate activities rather than conducting a. 政 治 大. new one. Then we apply Markov switching model developed by Hamilton (1989) to. 立. examine China’s real estate cycle and further ensure the role of macroeconomic factors. ‧. ‧ 國. 學. in the cycle.5. The Markov switching model not only allows us to measure real estate cycle turning. sit. y. Nat. points in China, but also enables us to investigate if the impacts of macroeconomic. n. al. er. io. factors on housing market symmetric in the different phases of real estate cycle. In. i n U. v. particular, the nonlinear relationship between real estate market and macroeconomic. Ch. engchi. factors can be observed in many cases. For example, 1980s Japanese bull market instigated by Japanese yen’s dramatic appreciation against the dollar. Around the same time, the Bank of Japan lowered its interest rate from 5 percent to 2.5 percent by early 1987, and it further pushed up the price of real estate to new high level. At early 1990s, Japan's strong economic growth ended abruptly and entered into its lost decade. Since October 2010, bank of Japan lower its key interest rate to zero in order to boost the economy, however, no recovery is seen in the Japanese real estate market for a long. 5. Hamilton (1989) is the first one who introduce Markov switching approach to evaluate U.S. business cycle. The switching model has then been applying to the modelling of real estate cycle with mixed success. 8.

(19) time. The case of Japan reminds us the changes in interest rate have different impacts on real estate prices during the expansionary and recessionary states.. The work of Seslen (2003) and Abelson et al. (2005) provide an explanation on Japan’s case. They claim that households are eager to get into the housing market during the upswing of housing cycle. Oppositely, loss aversion leads the households less likely to trade up during the downswing. Additionally, Kim and Bhattacharya (2009) point out the participants in real estate markets will not respond symmetrically over the real estate cycle. Consequently, the same interest rate policy doesn’t has the same impacts on. 政 治 大. expansionary and recessionary real estate market.. 立. ‧ 國. 學. In addition to the Markov switching model, there are many candidate approaches useful to analyze the asymmetric response of real estate market on macroeconomic changes.6. ‧. In contrast to other nonlinear models, Markov provides us more information about real. sit. y. Nat. estate cycle and its turning point. Accordingly, this paper focus on using Markov. n. al. er. io. switching model to evaluate the real estate cycle in China and further discussing the. i n U. v. empirical results and its implications. The rest of this Chapter is structured as follows.. Ch. engchi. Section 2.2 describes the methodology. Section 2.3 describes the dataset in details. Section 2.4 performs the methodology and presents detailed description of the empirical results. The final section concludes the Chapter.. 2.2 Methodology In the original Markov switching model developed by Hamilton (1989), the change of regime depends only on the history of the process. We therefore present the. 6. e.g., Smooth transition regression model developed by Lüükkonen et al. (1988), threshold regression model proposed by Hansen (1999), and smooth threshold approach proposed by Gonzàlez et al. (2005). 9.

(20) corresponding model as follows:. 𝐻𝑡 =𝛼(𝑠𝑡 ) + ∑𝐾𝑘=1 𝛾𝑘 𝐻𝑡−𝑘 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (1). 𝛼(𝑠𝑡 ) = 𝛼0 (1 − 𝑠t ) + 𝛼1 𝑠𝑡. (2). where 𝐻𝑡 denotes the real estate climate index, 𝑠𝑡 is the unobserved latent variable. 𝑠𝑡 = 1 is interpreted as an expansion while 𝑠𝑡 = 0 is interpreted as an contraction, the corresponding intercepts (or the mean of 𝐻𝑡 ) are 𝛼1 and 𝛼0 , and 𝛼1 >𝛼0 . The parameters of Markov switching model can be estimated through maximum likelihood.. 政 治 大. The log likelihood function of 𝐻𝑡 is:. 立. 𝑙𝑛𝐿 = ∑𝑇𝑡=1 𝑙𝑛[∑1𝑠𝑡 =0 𝑓( 𝐻𝑡 |𝑠𝑡 , 𝐼𝑡−1 ) × 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) ]. (3). ‧ 國. 學. where 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) is prediction probability, and is also interpreted as weighting. ‧. probability. Using the filtered probability 𝑃𝑟(𝑠𝑡 | 𝐼𝑡 ) as the initial value, prediction. er. io. sit. y. Nat. probability 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) can be computed recursively by applying Bayes’ Rule.. Next, the transition probabilities can be described as follows:. n. al. Ch. 00. engchi. i n U. v. 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 0) = 𝑝 , 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 1) = 1 − 𝑝11 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 0) = 1 − 𝑝00 , 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 1) = 𝑝11. (4). where 𝑝00 is the probability that real estate market remains staying in the contraction state, while 𝑝11 is the probability that real estate market remains staying in the expansionary state. Finally, we can adopt the approximation of Kim (1994) to compute the smooth probabilities 𝕡(𝑠𝑡 = 𝑖| 𝐼𝑇 ; 𝛼0 , 𝛼1 , 𝛾0 , … , 𝛾𝑘 , 𝑝00 , 𝑝11 ), for 𝑖 = 0, 1. The smooth probabilities enable us to recognize the periods of recession and expansion.. The original Markov switching model represented by Eq. (1) to Eq. (4) somehow 10.

(21) ignores the fact that some macroeconomic factors could be useful in forecasting the real estate cycles.7 As a result, we next consider the Markov switching model with the explicative variables. The first model is presented as follows:. Model 1:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝛽1 𝐸𝐼𝐿𝐼𝑡−1 + 𝛽2 𝑅𝐼𝑁𝑇𝑡−1 + 𝛽3 𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (5). where 𝐸𝐼𝐿𝐼 is leading economic climate index, and 𝑅𝐼𝑁𝑇 is real interest rate. Model 1 implies the changes in 𝐸𝐼𝐿𝐼𝑡−1 (𝑅𝐼𝑁𝑇𝑡−1 ) has the symmetric effect on 𝐻𝑡 , no matter the real estate market is in an expansion or a contraction. The marginal effect of 𝐸𝐼𝐿𝐼𝑡−1. 政 治 大 nonlinear relationship between 立 real estate market and macroeconomic factors. We then. ( 𝑅𝐼𝑁𝑇𝑡−1 ) on 𝐻𝑡 denoted by 𝛽1 (𝛽2 ). Model 1 is not reliable when there exists. ‧ 國. 學. extend model 1 to model 2.. ‧. Model 2:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝛽1 (𝑠𝑡 )𝐸𝐼𝐿𝐼𝑡−1 + 𝛽2 (𝑠𝑡 )𝑅𝐼𝑁𝑇𝑡−1 + 𝛽3 (𝑠𝑡 )𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). sit. y. Nat. (6). n. al. er. io. In Model2, the marginal effect of 𝐸𝐼𝐿𝐼𝑡−1 on 𝐻𝑡 is 𝛽1 (𝑠𝑡 ), which means the degree. v. of the impacts of 𝐸𝐼𝐿𝐼𝑡−1 on 𝐻𝑡 depends on whether the real estate market is in an. Ch. engchi. expansion (𝑠𝑡 = 1) or in a contraction (𝑠𝑡 = 0).. i n U. It is worth noting that the conduction of climate economic index is through a combination of the single indicator chosen according to its relationship with the economic climate index. If we use the economic index as the main explicative variable, it is easy to ignore the effects of some index components on real estate. In particular, some indicators like M2 or stock turnover value may play a key role in forecasting the 7 Review the previous literature, the main macroeconomic factors that may influence the real estate market are (1) demographic factors (2) interest rate and monetary policy (3) income and investment (3) inflation. See Summers(1981), Kau and Keenan(1981), Brown(1984), Fortura and Kushner(1986), Darrat and Glasock(1993), Glasser and Gyourko(2003), and Neukirchen and Lange(2005) for more discussion. 11.

(22) real estate cycle. Besides, an increase in the economic climate index doesn’t mean all index components are going an upswing, sometimes it is manipulated by the weighting scheme. In the next model, we use the components of leading index as the main explanatory variables rather than using the single composite economic index, described as follows:. Model 3:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝜑1 𝑆𝑇𝑂𝐶𝐾𝑡−1 + 𝜑2 𝑃𝑆𝑅𝑡−1 + 𝜑3 𝐶𝐸𝐼𝑡−1 + 𝜑4 𝑇𝐹𝑇𝑡−1 +𝜑5 𝐹𝐴𝐼𝑁𝑡−1 + 𝜑6 𝑀2𝑌𝑡−1 + 𝜑7 𝑅𝐼𝑁𝑇𝑡−1 + 𝜑8 𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). 治 政 Model 4:𝐻 =𝛼(𝑠 ) + 𝜑 (𝑠 )𝑆𝑇𝑂𝐶𝐾 + 𝜑 (𝑠 )𝑃𝑆𝑅 大+ 𝜑 (𝑠 )𝐶𝐸𝐼 立 𝑡. 𝑡. 1. 𝑡−1. 𝑡. 2. 𝑡. 𝑡−1. 3. 𝑡. (7). 𝑡−1. ‧ 國. 學. +𝜑4 (𝑠𝑡 )𝑇𝐹𝑇𝑡−1 + 𝜑5 (𝑠𝑡 )𝐹𝐴𝐼𝑁𝑡−1 + 𝜑6 (𝑠𝑡 )𝑀2𝑌𝑡−1 +𝜑7 (𝑠𝑡 )𝑅𝐼𝑁𝑇+𝜑8 (𝑠𝑡 )𝐻𝑡−1 + 𝜀𝑡 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (8). ‧. where 𝑆𝑇𝑂𝐶𝐾 is growth rate of Shanghai stock exchange turnover in value (A share),. y. Nat. sit. PSR is product sales rate, 𝐶𝐸𝐼 is consumer expectation index, TFT is growth rate of. n. al. er. io. freight traffic, 𝐹𝐴𝐼𝑁 is growth rate of the number of Fixed asset investment project newly started, and 𝑀2𝑌 is growth rate of M2.8. Ch. engchi. i n U. v. In order to compare the forecast accuracy of economic leading indicator and economic coincident indicator, we then build Model 5, Model 6, Model 7, and Model 8, presented as follows:. Model 5:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝜃1 𝐸𝐼𝐶𝐼𝑡−1 + 𝜃2 𝑅𝐼𝑁𝑇𝑡−1 + 𝜃3 𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (9). 8 The components of economic leading index includes Shanghai stock exchange turnover in value (A share), product sales rate, consumer expectation index, freight traffic, volume of freight handled in major coastal ports, number of fixed asset investment project newly started, contracted value of foreign direct investment, interest-rate spread between domestic interest rate and foreign interest rate, and M2. However, data acquisition has its limitations, and some variables are only available in quarterly frequency. Therefore, we don’t use all components of the leading index in the model. 12.

(23) Model 6:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝜃1 (𝑠𝑡 )𝐸𝐼𝐶𝐼𝑡−1 + 𝜃2 (𝑠𝑡 )𝑅𝐼𝑁𝑇𝑡−1 + 𝜃3 (𝑠𝑡 )𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (10). Model 7:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝜂1 𝑉𝐴𝐼𝑡−1 + 𝜂2 𝐹𝐴𝐼𝑡−1 + 𝜂3 𝑅𝑆𝐶𝐺𝑡−1 + 𝜂4 𝐸𝑋𝐼𝑀𝑡−1 +𝜂5 𝑇𝐴𝑋𝑡−1 + 𝜂6 𝐷𝐼𝑡−1 + 𝜂7 𝐼𝑁𝑇𝑡−1 + 𝜂8 𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 )(11). Model 8:𝐻𝑡 =𝛼(𝑠𝑡 ) + 𝜂1 (𝑠𝑡 )𝑉𝐴𝐼𝑡−1 + 𝜂2 (𝑠𝑡 )𝐹𝐴𝐼𝑡−1 + 𝜂3 (𝑠𝑡 )𝑅𝑆𝐶𝐺𝑡−1 + 𝜂4 (𝑠𝑡 )𝐸𝑋𝐼𝑀𝑡−1 + 𝜂5 (𝑠𝑡 )𝑇𝐴𝑋𝑡−1 + 𝜂6 (𝑠𝑡 )𝐷𝐼𝑡−1 +𝜂7 (𝑠𝑡 )𝐼𝑁𝑇𝑡−1 + 𝜂8 (𝑠𝑡 )𝐻𝑡−1 + 𝜀𝑡 , 𝜀𝑡 ~𝑁(0, 𝜎 2 ). (12). 政 治 大 industry, 𝐹𝐴𝐼 is growth rate 立of fixed asset investment, 𝑅𝑆𝐶𝐺 is growth rate of retail. where 𝐸𝐼𝐶𝐼 is economic coincident index, 𝑉𝐴𝐼 is growth rate of value added of. ‧ 國. 學. sales of consumer goods, 𝐸𝑋𝐼𝑀 is growth rate of value of export and import, 𝑇𝐴𝑋 is growth rate of government tax revenue, and 𝐷𝐼 is growth rate of urban disposable. ‧. income per capita.9. sit. y. Nat. io. er. Besides focusing on the implications of estimated coefficients, we also concern on the forecast accuracy among the model. As a result, we then use the Diebold Mariano test. al. n. v i n C hto make pairwiseUforecast accuracy comparisons (hereafter referred to as DM test) engchi. between the models.10. Similarity, due to the limitation of data acquisition, we don’t use all components of the coincident index in the model. 10 Ma and Lin (2009) suggest we can use turning point error, share of correct identification and DM test simultaneously to compare the forecasting performances from different models. The assessment of turning point error and share of correct identification require formal announcements of business cycle turning points. However, there is no China’s formal announcements about the turning points in its real estate cycle. Consequently, we use DM test to select the most appropriate model. The DM statistic is: 9. 𝐷𝑀 𝑠𝑡𝑎𝑡 =. 𝑑̅ √𝑉𝑎𝑟(𝑑) 𝑇. ~N(0,1). Where 𝑑̅ is the sample mean of the loss differential series defined as ∑𝑇𝑡=1[𝑔(𝑒𝑖𝑡 ) − 𝑔(𝑒𝑗𝑡 )] /𝑇. 𝑔(𝑒𝑖𝑡 ) and 𝑔(𝑒𝑗𝑡 ) are loss functions of model i and model j. The significant positive DM stat means the forecast error of model i is statistically larger than the forecast error of model j. 13.

(24) 2.3 Data and resources In this Chapter, we select the monthly real estate climate index conducted by China Economic Monitoring Center as the representative index related to housing activities. According to China Economic Monitoring Center, there are three perspectives paid attention in creating the real estate climate index, includes land acquisition, funds acquisition, and market demand. Thus, eight indicator are selected to conduct the real climate index, they are investment in real estate, the source of funds, revenue from and transfers, floor space of developed land, floor space of newly started project, floor space. 政 治 大. of buildings completed, vacant floor area. The starting point of real estate climate index. 立. is 1999:01. However, in 2004:01, an appropriate adjustment of index creation was. ‧ 國. 學. implemented. Therefore, the sample periods of this study is reduced from 2004:01 to 2015:07.. ‧ sit. y. Nat. Moreover, we select economic climate index and real interest rate as the main. n. al. er. io. macroeconomic variables in this study.11 There are four kinds of economic climate. i n U. v. indexes: leading indicator, coincident indicator, lagging indicator, and the early warning indicator.. Ch. engchi. Since one of the main purpose of this study is to investigate the role of macroeconomic factors in the real estate cycle and the performance of their forecast accuracy in real estate climate. Therefore, we abandon the lagging indicator. Furthermore, according to the statement of China Economic Monitoring Center, the correlation coefficient between coincident indicator and early warning indicator is 0.95, and the lead-lag. 11. GDP could provide a reliable measure of the total economic activities if it were available in monthly frequency from China National Bureau of Statistics. In order to maintain accuracy over large number of samples, we use economic index as an alternative. 14.

(25) relation is zero. Hence, we select coincident indicator rather than early warning indicator.. The data process proceed as follows: (1) firstly, the data are seasonally adjusted by applying X12 methods with Eviews; (2) in order to access the variation associated with cycles, we use HP filter to detrend the data prior to estimation; (3) in order to unified the units among the data, we transfer the Shanghai stock exchange turnover in value, freight traffic, number of Fixed asset investment project, M2, value added of industry, fixed asset investment, value of export and import, government tax revenue, and urban. 政 治 大. disposable income per capita into the form of growth rate.. 立. ‧ 國. 學. The main data sources in this study are CEIC Data’s China Economic Database and National Bureau of Statistics. The summary statistics of all variables are shown in Table. ‧. 2.1.. sit. y. Nat. io. n. al. er. 2. 4 Empirical Result. 2.4.1 Unit root tests. Ch. engchi. i n U. v. Empirical evidence has suggested that various macroeconomic time series are characterized by the presence of a unit root. If we ignore the unit root problem and proceed to estimate a regression with nonstationary variables would occur the spurious regression problem highlighted in Granger and Newbold (1974), and therefore the estimation results may not be reliable. In order to avoid the problem of spurious regression, we have to check whether the variables applied in this Chapter have unit root or not. The unit root approach of ADF (Augmented Dicker-Fuller) and KPSS (Kwiatkowski–Phillips–Schmidt–Shin) are adopted in the Chapter to test the 15.

(26) Table 2.1 Summary statistics Unit 2000 =100 1996 =100 RMB bn % point Ton mn Unit RMB bn 1996 =100 % RMB bn RMB bn RMB bn RMB bn RMB %. Real estate climate index Economic climate Index_Leading Index Shanghai stock exchange turnover in value (A share) Product sales rate Consumer expectation index Freight traffic Number of Fixed asset investment project newly started M2 Economic climate index_Coindident index Value added of industry Fixed asset investment Retail sales of consumer goods Value of export and import Government revenue : Tax Disposable income per capita: Urban Real interest rate. n. er. io. sit. y. ‧. Nat. al. 學. ‧ 國. 立. 政 治 大. Ch. engchi. 16. i n U. v. mean 100.344 99.955 24,533.074 97.92 107.867 2,499.558 81,543.180 33,862.629 101.584 4.321 1,482.506 1,227.762 232.467 586.746 1551.469 1.743. Std. dev. 4.017 2.903 4,336.372 0.67 4.195 880.330 54,052.700 64,410.762 1.917 13.146 2,159.648 615.340 93.361 317.395 583.034 3.562.

(27) `. Table 2.2 Unit Root tests Real estate climate index Economic climate Index_Leading Index Shanghai stock exchange turnover in value (A share) Product sales rate Consumer expectation index Freight traffic Number of Fixed asset investment project newly started M2 Economic climate index_Coindident index Value added of industry Fixed asset investment Retail sales of consumer goods Value of export and import Government revenue : Tax Disposable income per capita: Urban Real interest rate. 政 治 大. 學. sit. Nat. y. ‧. ‧ 國. 立. ADF -4.367*** -4.452*** -3.595*** -9.901*** -4.56*** -9.201*** -9.480*** -4.480*** -5.099** -4.73*** -10.024*** -5.286*** -3.049* -4.343*** -13.552*** -2.607**. KPSS 0.034+++ 0.036+++ 0.040+++ 0.036+++ 0.049+++ 0.034+++ 0.036+++ 0.041+++ 0.029+++ 0.034+++ 0.042+++ 0.030+++ 0.037+++ 0.026+++ 0.048+++ 0.051+++. n. al. er. io. Notes: 1. ADF stands for the Augmented Dickey-Fuller test with null hypothesis that variable has a unit root. *, **, and *** denotes the rejection of the null hypothesis for 1%, 5%, and 10% criterial levels, respectively. 2. KPSS stands for the Kwiatkowski–Phillips–Schmidt–Shin test with null hypothesis that variable is stationary. +++ denotes the null is not rejected for 1% criterial level. 3. Both ADF test and KPSS test include an intercept, but don’t include a trend.. Ch. engchi. 17. i n U. v.

(28) `. stationarity of the sequences.12 Table 2.2 presents the results of ADF and KPSS unit root tests on all variables we use in this Chapter. We find that the results of ADF test reveal that all of the variables deny the original hypothesis that unit root existed, while the KPSS tests revealed that all of the variables failed to deny the original hypothesis that the series is stationary. Hence, we can implement the Markov switching model to proceed our analysis.. 2.4.2 Model selection and its implications. 政 治 大 investigate the role of macroeconomic factors in the real estate cycle of China. The 立 We build eight models to cope with the different economic implications, and further. ‧ 國. 學. estimation results from Model 1 to Model 8 are illustrated in Table 2.3 and Table 2.4. Besides paying the attentions on the coefficient estimate, we also care about the forecast. ‧. accuracy of the models. Hence, we employ the DM test to select the best model which. sit. y. Nat. has the best forecast performance. The result of DM test is shown in Table 2.5, and the. n. al. er. io. time series of smooth transition probabilities in expansion regime are shown in Figure. i n U. v. 2.2 and Figure 2.3, which are helpful for us to identify the turning points of real estate cycle.. Ch. engchi. Next step, we utilize the DM test to make pairwise forecast accuracy comparisons between the models. The results of DM test are presented in Table 2.5. Table 2.5 shows that the models which use composite index as the key explicative variable (Model 1, Model 2, Model 5, and Model 6) have better forecasting performance than the models which use multiple index components as the explicative variables (Model 3, Model 4,. 12. In the ADF test, the null hypothesis is that there is a unit root. The KPSS test might serve as a complements the ADF tests in which the null hypothesis is there isn’t a unit root. 18.

(29) `. Table 2.3 The estimation result of Model 1, Model 2, Model 3, and Model 4 Model 1 Model 2 Expansion Contraction Expansion Contraction 100.139*** 98.991*** 100.470*** 99.345*** Intercept (0.554) (0.592) (0.683) (0.382) 0.570*** (0.104). Product sales rate. -. M2 (growth rate). Log(𝜎) 𝑝𝑖𝑖 (i= expansion or contraction) Expected duration Log-likelihood. -0.056 (0.537). -. -. 0.920*** (0.037). -0.770***. -. -. -. -. -. y. al. n. AR(1). -. io. Real interest rate. -. -. -. Nat. Fixed asset investment, number of project newly started (growth rate). -. -. -. ‧. Freight traffic (growth rate). -. 政 - 治 大-. 學. Consumer expectation index. 立. 1.185*** (0.209). sit. -. ‧ 國. Shanghai stock exchange turnover in value (growth rate). 0.480*** (0.088). 0.021 (0.803). 0.029. -0.030. (0.056). (0.056). 0.022. 0.009. (0.023). (0.020). 0.005. 0.011. -0.024. (0.007). (0.007). (0.026). 0.002. 0.002. 0.008. (0.002). (0.002). 0.041 (0.047). 0.616*. -0.179** (0.081). (0.76). 0.964 0.872 27.533 7.786 -108.169. 0.963 0.574 26.716 2.356 -105.673. 0.953*** (0.027). -0.603*** (0.064). 0.992 0.872 132.797 7.861 -121.200. Note: Standard errors are reported in parentheses. The stars, *, ** and *** indicate the significance level at 10%, 5% and 1%, respectively.. 19. 0.121* (0.073) 0.511*** (0.190) 0.163*** (0.062). (0.355). (0.105). -. 0.058. (0.068). iv 0.994*** 0.145 n C h (0.039) (0.180) engchi U -0.767***. Model 4 Expansion Contraction 101.541*** 100.985*** (0.743) (0.743). (0.036). -0.098. er. Economic climate leading index. Model 3 Expansion Contraction 99.813*** 97.848*** (1.057) (1.150). (0.007) 0.056 0.163* (0.046) (0.101) -0.149* -0.34* (0.071) (0.183) 1.066 0.731*** (0.023) (0.070) -0.797*** (0.077). 0.923 0.703 13.014 3.372 -110.0511.

(30) `. Table 2.4 The estimation result of Model 5, Model 6, Model 7, and Model 8 Model 5 Model 6. Log(𝜎) 𝑝𝑖𝑖 (i=expansion or contraction) Expected durations Log-likelihood. 0.600***. 0.645***. (0.115). 立. -. -0.203 (0.084). 0.936*** (0.031). -0.691*** (0.072). 0.989 92.747. 0.913 11.442 -110.088. -. -. -. -. -. -. -. -. -. -. al. -. -0.307***. v 0.545***n i C1.066*** h(0.029) i U e n g c(0.078) h -0.916*** (0.065). (2.247). (1.091). (0.096) 治 政 大. -0.154**. 105.539***. (2.245). 97.662***. (0.973). y. -. 106.463***. 99.851***. sit. -. Expansion. (0.189). 0.851***. (0.089). (0.081). 0.875 0.775 8.000 4.446 -103.837. Contraction. -. -. 0.051**. 0.023. 0.101**. (0.026). (0.021). (0.439). 0.001. 0.000. -0032. (0.007). (0.003). (0.021). -0.002. 0.004. -0.022**. (0.005). (0.002). (0.098). 0.002. 0.004. 0.002. (0.010). (0.012). (0.464). 0.001. 0.003. -0.005. (0.002). (0.011). (0.004). 0.003. 0.002. -0.008. (0.010). (0.011). (0.046). -0.174*. -0.052. -0.289**. (0.081). (0.006). (0.120). 0.949***. 1.039***. 0.0889***. (0.028). (0.014). (0.041). -0.605***. -0.930***. (0.065). (0.736). 0.992 0.878 128.47 8.214 -120.755. Note: Standard errors are reported in parentheses. The stars, *, ** and *** indicate the significance level at 10%, 5% and 1%, respectively.. 20. Model 8. Contraction. 99.898***. er. -. -. Expansion. (0.089). n. AR(1). (0.027). io. Real interest rate. 100.3041***. (0.950). Nat. Government tax revenue (growth rate) Urban disposable income per capita (growth rate). 98.416***. (0.719). Model 7. Contraction. ‧. Export and import (growth rate). 100.077***. Expansion. 學. Economic climate coincident index Value added of industry (growth rate) Fixed asset investment (growth rate) Retail sales of consumer goods (growth rate). Contraction. ‧ 國. Intercept. Expansion. 0.932 14.734. 0.804 5.103 -97.014.

(31) `. Table 2.5 Diebold and Mariano test Model 3. Model 4. Model 5. Model 6. Model 7. Model 8. —. Model 2 —. Model 1 Model 2 —. Model 1 Model 2 = —. Model 1 Model 2 Model 5 Model 5 —. Model 1 Model 2 Model 6 Model 6 = —. Model 1 Model 2 Model 7 Model 7 Model 5 Model 6. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6. —. Model 7 —. 立. 政 治 大. 學. Model 7 Model 8. Model 2. ‧ 國. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6. Model 1. ‧. Notes: 1. The significant level is set at 10%, model with better prediction of real estate climate index is recorded in the table. 2. “=” indicates the forecast accuracy is statistically indifferent between two models in forecasting real estate climate index.. n. er. io. sit. y. Nat. al. Ch. engchi. 21. i n U. v.

(32) `. 1.0. 1 . 0. 0.8. 0 . 8. 0.6. 0 . 6. 0.4. 0 . 4. 政 治 大. 0.2. 0 . 2. 0.0 04. 05. 06. 07. 08. 09. 10. 11. 立 14. 0 . 0 15. 04. ‧ 國. 13. 1.0. 06. 1 . 0. 0 . 8. 0.6. 07. 08. 09. 10. 11. 12. 13. 14. 15. 11. 12. 13. 14. 15. (b) Model 2. ‧. 0.8. 05. 學. (a) Model 1. 12. 0 . 6. al. 0 . 2. n. 0.0 04. 05. 06. 07. 08. 09. 10. (a) Model 3. 11. 12. 13. sit. 0 . 4. 14. er. io. 0.2. y. Nat. 0.4. Ch 15. engchi 0 . 0. 04. i n U 05. v. 06. 07. 08. 09. 10. (b) Model 4. Figure 2.2 Smooth probabilities of regime expansion from Model 1 to Model 4.. 22.

(33) `. 1.0. 1. 0. 0.8. 0. 8. 0.6. 0. 6. 0.4. 政 治 大 0. 4. 立 06. 07. 08. 09. 10. 11. 12. 1.0. 0. 0. 14. 15. 04. io. 08. 0. 8. 0. 6. al. n. 0.4. 07. 0.2. 0.0. 09. 10. 11. 12. 13. 14. 15. (b) Model 6. er. 0.6. 06. 1. 0. Nat. 0.8. 05. ‧. (a) Model 5. 13. y. 05. sit. 04. 0. 2. 學. 0.0. ‧ 國. 0.2. 0. 4. Ch. engchi. 0. 2. i n U. v. 0. 0. 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. 04. (c) Model 7. 05. 06. 07. 08. 09. 10. 11. 12. (d) Model 8. Figure 2.3 Smooth probabilities of regime expansion from Model 5 to Model 8 23. 13. 14. 15.

(34) `. Model 7, and Model 8). This results stand out the propriety of using the composite economic index to evaluate the real estate cycle. Additionally, Table 2.5 shows the forecast accuracy of the model which use economic leading indicator as the key explicative variable (Model 1 and Model 2) are better than themodel using coincident indicator as the key explicative variable (Model 5 and Model 6). Finally, Table 2.5 gives us an information that the forecast accuracy of Model 2 is better than Model 1. This result amplified the point that the effects of macroeconomic factors on real estate market depend on the climate of real estate market.. 政 治 大 From Table 2.3 and Table 2.4 we can find the estimation results from all models 立 indicate that during the period 2004:01 to 2015:07, the expected duration in the. ‧ 國. 學. expansion regime of real estate market is longer than the expected duration in the. ‧. contraction regime. Secondly, if we focus on the estimation results from the models. sit. y. Nat. which provide more accurate forecasts (Model 1 and Model 2), we can find the expected. io. er. duration in expansion regime in model 1 (27.533 months) is close to the expected duration in expansion regime in model 2 (26.716 months). Moreover, the expected. al. n. v i n duration in contraction in modelC 1 is 7.786 months longer h e n g c h i U than the expected duration in. contraction in model 2 which is 2.356 months. The similar estimation results from Model 1 and Model 2 are also observed in Figure 2.3.. Though the forecast accuracy of the model 1 and model 2 are better than other candidate models. The estimation results presented in Table 2.3 and Table 2.4 illustrate some information worth noting. At first, the estimation results from model 2 show the coefficient of economic leading indicator in the contraction regime (0.480) is significant and larger than the coefficient of economic leading indicator in the contraction regime (1.185), which means the impact of positive economic shock (measured by the 24.

(35) `. economic leading indicator) is larger in contraction regime than in expansion regime. The similar finding can be also observed in the estimation results from Model 5 and Model 6. Secondly, if we compare the estimation results from Model 3 and Model 4, we can find the coefficients of 𝑆𝑇𝑂𝐶𝐾 , 𝑃𝑆𝑅 , 𝐶𝐸𝐼 , 𝑇𝐹𝑇 , 𝐹𝐴𝐼𝑁 , and 𝑀2𝑌 from Model 4 are all insignificant. However, the empirical estimations from Model 4 point out, the coefficients of 𝑆𝑇𝑂𝐶𝐾, 𝑃𝑆𝑅, 𝑇𝐹𝑇, and 𝑀2𝑌 are only insignificant in the expansion regime. The similar result are shown in the estimation results from Model 7 and Model 8.. 政 治 大. To sum up the above-mentioned arguments, firstly, the impacts of macroeconomic. 立. factors on the real estate depend on the housing market in a contraction regime or in an. ‧ 國. 學. expansion regime. Additionally, macroeconomic shocks on real estate market are larger in the contraction regime than in the expansion regime. This results may inflect the. ‧. phenomenon that when the real estate is in the upswing, the market’s participants tend. y. Nat. io. sit. to be optimistic expectation for earning growth, and it gives rise the neglect of the. n. al. er. information from macroeconomic factors. Finally, the upturns are longer than. i n U. v. downturns in China’s real estate market, this result is in line with the findings from. Ch. engchi. Claessens et al. (2011) and Bracke (2011).. 2.5 Conclusion Isabel and Hiebrt (2011) utilize GVAR model (Global Vector Autocorrelation Regression) to prove the existence of spillover of house price shocks within the Eurozone. Taiwan and China are not in a single currency area, however, the cross-strait economic and trade ties continue to deepen. In light of this, it is also important for us to investigate the housing market cycles in China. Compare the forecast accuracy between the models with single composite index 25.

(36) `. (include economic leading index and coincident index) and the models with the multiple index components. We find using the models with the index components are bound to impair predictive accuracy. Besides, the coincident index doesn’t perform well contrast to the leading index. Moreover, our estimation result suggest that the leading indicator has stronger impact on real estate activities when the real estate market is in a downswings. Lastly, during the period from 2004:01 to 2015:07, the average duration of the expansion is 26.7 months, longer than the average duration of the contraction 2.3 months.. 立. 政 治 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 26. i n U. v.

(37) `. Chapter 3: A three-state Markov approach to analyze housing prices cycle in China. 3.1 Introduction In the recent years, China’s housing market has experienced a sharp boom and bust in housing prices, and it also ignites a debate on the relationship between housing price. 治 政 大2013; Hua et al., 2012; Shen reflect economic fundamentals in China (Li and Chand, 立. and the economic fundamentals. For example, many studies claim that hosing price can. and Liu, 2004). Yet an opposing view suggests that housing price appreciation has gone. ‧ 國. 學. beyond changes in fundamentals (Zhou, 2005; Ahuja et al., 2010; Yu, 2010).. ‧. For a long time, analysis of the relationship between fundamental factors and the. y. Nat. sit. housing prices fluctuation in China only focus on the symmetric impacts of changes in. n. al. er. io. macroeconomic variables on housing prices. However, the fundamental factors may. i n U. v. have different impacts on the bull and bear housing market. Kontolemis (1999) and. Ch. engchi. Hamilton (2008) claim that the impacts of some explanatory variables on an economy maybe different between the period of high and low economic growth. The same phenomenon has been observed and investigated in the housing market. Nneji et al. (2013) apply a Markov switching model to investigate the asymmetric impact of the macroeconomic variable on the dynamics of the residential real estate market in the United States. Li (2015) find there exists an asymmetric serial correlation of house prices and income between periods of falling and rising house prices. BahmaniOskooee and Ghodsi (2016) utilize nonlinear ARDL approach to confirm that the change in the fundamentals have asymmetric effects oh house price, no matter the short 27.

(38) `. run or the long run.. Although a large number of studies have been made on the presence of an asymmetric association between housing market and macroeconomic fundamentals. Little attention has been given to investigate the nonlinear characteristic in China’s housing price. Against this backdrop, in this study, China’s housing price cycle will be modelled using a Markov-switching model introduced firstly by Hamilton (1989).. It is worth mentioning that though the standard Markov switching regression allows us. 政 治 大 limitations. For example, the 立standard Markov switching model assume the transition to characterize the housing prices dynamics in different regime. It still maintains some. ‧ 國. 學. probability is fixed. Consequently, the expected durations of expansion and contraction are forcing to be constant over time. However, this setting doesn’t always conform to. ‧. reality. For example, when an economy exists a deep recession, it is less likely to plunge. sit. y. Nat. it back into recession (Filardo and Gordon, 1998). Likewise, when an economy has. n. al. er. io. been experiencing the greatest prosperity and then starts to swing from expansion to. i n U. v. recession, it is not easy for an economy back into an expansion.. Ch. engchi. Additionally, Filardo and Gordon (1998) claim that with fixed transition probabilities, the exogenous shocks or policies are not allowed to change the expected duration. Diebold et al. (1994) argue it is better to explain the variation in economic cycles when transition probabilities are modelled as a functions of economic indicator. Filardo and Gordon (1998) prove that time-varying probabilities for the transition models are better than fixed transition probability model to characterize the economic cycles of the United States. As a result, as an alternative, we also adopt a time-varying transition probabilities Markov switching model proposed by Diebold et al. (1994), Filardo (1994) and later Filardo and Gordon (1998) to analyze the housing dynamics in China. 28.

(39) `. Besides the fixed and time-varying Markov switching model, we also consider the circumstance that there may exist more than two regimes in the housing price cycle. A two regimes Markov switching model implies there is only a bull or a bear state. However, a bull or a bear market usually occur due to the occasionally huge external shocks. For example, 1990 United States bear market resulted from the Iraq–Kuwait War. 1980s Japan bull market instigated by Japanese yen’s dramatic appreciation against the dollar. The emergence of the internet boom gave rise to the 1997 Dot-com bubble. 2008 global financial crisis happened because the payment shock initiated by. 政 治 大. the adjustment of Federal funds rate. It simply means, the market is not always in a bull or bear state.. 立. ‧ 國. 學. Actually, a complete business cycle is a repeated three-phase sequence includes expansion, recession, and recovery. Hence, there are many empirical studies focus on. ‧. the investigation of multiple regimes model rather than two regimes. Sichel (1994). y. Nat. io. sit. extend the original work of Hamilton (1989), and find a parsimonious three-regime. n. al. er. model for GNP growth is more robust and plausible. Also, Hamilton (2005) conduct a. i n U. v. 3 regimes switching model to illustrate the dynamic behavior of unemployment. Sims. Ch. engchi. and Zha (2006) conclude the best fit model to analyze primarily capturing changes in conditional volatility is nine regimes model. Medhioub (2015) use a three regime Markov switching model to estimate, date, and forecast the economic activity in Tunisia. Nneji et al. (2013) employ a three-state Markov switching model to examine the relationship between real estate market and key macroeconomic variable in US.. In this study, we conduct four types of Markov switching model: fixed and time-varying transition probability model with two regimes, fixed and time-varying transition probability model with three regimes. And then compare the performance across the 29.

(40) `. models and determine which is the best one for analyzing.. The plan of this Chapter is as follows. Section 3.2 presents the methodology. Section 3.3 describes the data and essential test. Section 3.4 provides estimates and interpretation. Section 3.5 concludes the Chapter.. 3.2 Methodology 3.2.1 Markov-Switching model. 政 治 大. We are interested in examining the housing prices dynamic in China, and their reaction. 立. with exogenous variables, represented as follow:. 學. ‧ 國. to macroeconomics. Hence, we firstly consider a two-state Markov switching model. (1). Nat. sit. y. ‧. 𝛼 + 𝑿′𝒕−𝟏 𝜷𝟏 + 𝜀1𝑡 ; 𝜀1𝑡 ~𝑁(0, 𝜎1𝑡 2 ) 𝑖𝑓 𝑠𝑡 = 1 ∆𝐻𝑃𝑡 = { 1𝑡 𝛼2𝑡 + 𝑿′𝒕−𝟏 𝜷𝟐 + 𝜀2𝑡 ; 𝜀2𝑡 ~𝑁(0, 𝜎2𝑡 2 ) 𝑖𝑓 𝑠𝑡 = 2. io. er. where ∆𝐻𝑃 is annualized housing prices growth rate. 𝑿𝒕−𝟏 = (∆𝐼𝑁𝐶𝑂𝑀𝐸𝑡−1 , ∆𝑆𝑇𝑂𝐶𝐾𝑡−1 , 𝐼𝑁𝑇𝑡−1 , 𝐶𝑃𝐼𝐺𝑡−1 )′ , where ∆INCOME is annualized income growth. al. n. v i n C hindex growth rate,UINT is real interest rate, rate, ∆STOCK is annualized stock engchi. 𝐶𝑃𝐼𝐺. is annualized consumer price index growth rate. Term 𝑠𝑡 is an unobserved latent variable which take on the value 1 or 0.. According to Hamilton (1989), 𝑠𝑡 is governed by a first-order Markov chain with a constant transition probability matrix (P):. 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 0) P= [ 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 0). 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 1) 𝑝00 ] = [ 10 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 1) 𝑝. 𝑝01 ] 𝑝11. (2). where 𝑝𝑖𝑗 is the transition probability from state i to state j. Note that 𝑝01 = 1 − 𝑝00 , 𝑝10 = 1 − 𝑝11 , the transition probability matrix (P) is completely defined by 𝑝00 and 30.

(41) `. 𝑝11 . This version of Markov switching model, where the transition probabilities are time-invariant, named fixed transition probability Markov switching model (hereafter referred to as FTP-MS).. Base on the assumption that error term is normally distributed, the conditional probability density function of ∆𝐻𝑃𝑡 therefore can be computed. Therefore, the parameters of Markov switching model can be estimated via maximum likelihood. The log likelihood function of ∆𝐻𝑃𝑡 can be represented as:. 政 治 大. 𝑙𝑛𝐿 = ∑𝑇𝑡=1 𝑙𝑛[∑1𝑠𝑡 =0 𝑓( ∆𝐻𝑃𝑡 |𝑠𝑡 , 𝐼𝑡−1 ) × 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) ]. 立. (3). where 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) is prediction probability, and is also interpreted as weighting. ‧ 國. 學. probability. Using the filtered probability 𝑃𝑟(𝑠𝑡 | 𝐼𝑡 ) as the initial value, 𝑃𝑟(𝑠𝑡 | 𝐼𝑡−1 ) is computed recursively by applying Bayes’ Rule.. ‧ y. sit. n. al. er. io. formula:. Nat. Base on P, the expected duration spent in each regime is simply computed via following. Ch. 𝑖𝑖. 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑟𝑒𝑔𝑖𝑚𝑒 𝑖 = 1/(1 − 𝑝 ). engchi. i n U. v. (4). Eq. (4) implies that, with fixed-transition probabilities, the expected durations of expansions and contractions are forcing to be constant over time. As we state earlier, this setting is not always conform to reality. The next step, we are going to extend the standard Markov switching model formulated by Eq. (1) and (2) to a time-varying transition probability Markov switching model.. In contrast to the fixed transition probability matrix presented in Eq. (2), the timevariant transition probability matrix is: 31.

(42) `. 𝑷𝒕 = [. 𝑝00 (𝑦𝑡 ) 𝑝01 (𝑦𝑡 ) 𝑝10 (𝑦𝑡 ). 𝑝11 (𝑦𝑡 ). ]. (5). where 𝑦𝑡 is the information variable. The expected duration in regime 𝑖 is therefore altered by the variation of 𝑦𝑡 . Base on the finding of Catte et al. (2004) which note that in all countries, house price turning points tend to lag business cycle peaks and troughs. We attempt to utilize the leading economic index to inform on the future direction of housing prices growth rate. Therefore, 𝑦𝑡 denotes to the leading economic index.. 3.2.2 Markov-Switching model: The shift from two to three regimes. 政 治 大 As stated earlier in this Chapter, 立 the 2 regimes MS model captures the distinct phase of. ‧ 國. 學. recessions and expansion, it does not incorporate other important phrases of the business cycle. As a result, in this section, we construct a Markov switching model with. ‧. the existence of three phases: expansion, stable, and contraction shown as Figure 3.1.. sit. y. Nat. Hence, we assume that China’s housing growth rate is described by the following three. n. al. er. io. state Markov switching model:. Ch. engchi. i n =U1. 𝛼1𝑡 + 𝑿′𝒕−𝟏 𝜷𝟏 + 𝜀1𝑡 ; 𝜀1𝑡 ~𝑁(0, 𝜎1𝑡 2 ) 𝑖𝑓 𝑠𝑡 ∆𝐻𝑃𝑡 = {𝛼2𝑡 + 𝑿′𝒕−𝟏 𝜷𝟐 + 𝜀2𝑡 ; 𝜀2𝑡 ~𝑁(0, 𝜎2𝑡 2 ) 𝑖𝑓 𝑠𝑡 = 2 𝛼2𝑡 + 𝑿′𝒕−𝟏 𝜷𝟑 + 𝜀3𝑡 ; 𝜀3𝑡 ~𝑁(0, 𝜎3𝑡 2 ) 𝑖𝑓 𝑠𝑡 = 3. 32. v. (6).

(43) `. Housing price growth rate. → Expansion regime. → Contraction regime. Time. 政 治 大. Figure 3.1(a) Two regimes model. 立. Housing price growth rate. ‧ 國. 學 → Expansion regime. y. io. → Contraction regime. er. Nat. (Recovery regime). sit. ‧. → Stable regime. n. al. i n C Figure 3.1(b) U h Three e n gregimes c h i model. v. Figure 3.1 The difference between two and three regimes model. A three regimes constant transition probability matrix (P) is then:. 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 0) 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 1) P= [𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 0) 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 1) 𝑃𝑟(𝑠𝑡 = 2|𝑠𝑡−1 = 0) 𝑃𝑟(𝑠𝑡 = 2|𝑠𝑡−1 = 0) 33. 𝑃𝑟(𝑠𝑡 = 0|𝑠𝑡−1 = 2) 𝑃𝑟(𝑠𝑡 = 1|𝑠𝑡−1 = 2)] 𝑃𝑟(𝑠𝑡 = 2|𝑠𝑡−1 = 2). Time.

(44) `. 𝑝00 = [𝑝10 𝑝20. 𝑝01 𝑝11 𝑝21. 𝑝02 𝑝12 ] 𝑝22. (7). Similarity, we also consider a TVTP-MS model with 3 regimes. In contrast to the fixed transition probability matrix in Eq. (7), the time-variant transition probability matrix 𝑷𝒕 is: 𝑝00 (𝑦𝑡 ). 𝑝01 (𝑦𝑡 ) 𝑝02 (𝑦𝑡 ). 𝑷𝒕 = [ 𝑝10 (y𝑡 ) 𝑝11 (𝑦𝑡 ) 𝑝12 (𝑦𝑡 )] 𝑝20 (𝑦𝑡 ) 𝑝20 (𝑦𝑡 ) 𝑝22 (𝑦𝑡 ). 3.3 Data and unit root tests 3.3.1 Data description. 立. (8). 政 治 大. ‧ 國. 學. The data sample covers the monthly residential housing prices for the period of 2002:01. ‧. until 2015:12. Our conditioning variable using in the TVTP-MS model 𝑦𝑡 is leading. sit. y. Nat. economic index, and the other key variables for the analysis of house price cycles are. n. al. er. io. income (INCOME), stock index (STOCK), interest rate (INT), and growth rate of. i n U. v. consumer prices (CPIG). Stock index (STOCK) is referred to Shanghai Composite. Ch. engchi. stock exchange index. The variables we use in this Chapter have been mainly drawn from CEIC database. Note that consumer price indices are used to deflate residential housing prices, income, and nominal interest rate to obtain their respective real values. In order to deal with the unit root problem, we transform the real residential housing prices, real income, and stock index into annual percentage rate of change form (represented as ∆HP, ∆INCOME, ∆STOCK, respectively) for the empirical analysis. The corresponding descriptive statistics values are presented in Table 3.1.. 34.

(45) `. Table 3.1 Summary Statistics HP STOCK Unit. RMB /sq. m.. Dec 1990. Mean Median Maximum Minimum Std. Dev Skewness Kurtosis. 2468.855 2305.210 6251.530 1113.290 1021.720 1.169 4.452. 4132.666 3752.872 6510.990 2119.744 1435.026 0.138 1.615. =100. INCOME. INT. CPIG. LEAD. RMB. %. %. 1996=100. 1434.398 1361.086 2834.606 578.175 632.181 0.407 1.964. 2.507 2.100 8.700 -1.800 2.232 0.461 3.037. 3.323 3.500 7.110 -1.230 1.829 -0.209 2.686. 101.613 101.911 106.130 97.641 1.889 0.010 2.537. Notes: 1. HP represents housing prices, STOCK represents stock index, INCOME represents disposable income, INT represents real interest rate, CPIG represents growth rate of Consumer price index, and LEAD means leading economic index. 2. The data series for housing prices and disposable income are deflated to currency by CPI.. 立. 政 治 大. ‧ 國. 學. 3.3.2 Unit root tests. ‧. Empirical evidence has suggested that various macroeconomic time series are. y. Nat. sit. characterized by the presence of a unit root. If we ignore the unit root problem and. n. al. er. io. proceed to estimate a regression with nonstationary variables would occur the spurious. i n U. v. regression problem highlighted in Granger and Newbold (1974), and therefore the. Ch. engchi. estimation results may not be reliable. In order to avoid the problem of spurious regression, we have to check whether the variables applied in this Chapter have unit root or not. The unit root approach of ADF (Augmented Dicker-Fuller) and KPSS (Kwiatkowski–Phillips–Schmidt–Shin) are adopted in the Chapter to test the stationarity of the sequences. Table 3.2 presents the results of ADF and KPSS unit root tests on ∆HP, ∆INCOME, ∆STOCK, INT, and CPIG. We find that ADF test results reveal that all of the variables deny the original hypothesis that unit root existed, while the KPSS tests revealed that all of the variables failed to deny the original hypothesis that the series is stationary. The absence of unit root implies that all shocks have no 35.

(46) `. persistent impacts, and current shocks will disappear in the future. Hence, we can implement the Markov switching model to process our analysis in the following section. Table 3.2 Unit root tests ADF test -2.781* -3.168** -2.746* -3.689*** -2.960***. ∆HP ∆INCOME ∆STOCK INT CPIG. KPSS test 0.244+++ 0.161+++ 0.096+++ 0.128+++ 0.158+++. Notes: 2. ADF stands for the Augmented Dickey-Fuller test with null hypothesis that variable has a unit root. *, **, and *** denotes the rejection of the null hypothesis for 1%, 5%, and 10% criterial levels, respectively. 3. KPSS stands for the Kwiatkowski–Phillips–Schmidt–Shin test with null hypothesis that variable is stationary. +++ denotes the null is not rejected for 1% criterial level. 3. Both ADF test and KPSS test include a constant only.. 政 治 大. 立. ‧ 國. 學. 3.4. Estimation Result. ‧. In this Chapter, we consider the following models: FTP-MS with 2 regimes, FTP-MS. Nat. sit. y. with 3 regimes, TVTP-MS with 2 regimes, and TVTP-MS with 3 regimes. In this. n. al. er. io. section, we firstly compare the fitness and forecast accuracy among the aforestated. i n U. v. models. And then we choose the most appropriate model for analyzing.. Ch. 3.4.1 Model selection. engchi. In order to compare the fitness among the models. We utilize Akaike information criterion (AIC), Hannan–Quinn information criterion (HQIC), and Schwarz information criteria (SIC) to compare different models, and then extract the best fitting model. The model with the smaller AIC, HQIC, and SIC fits data better. The results are shown in Table 3.3. Table 3.3 reveals that AIC, HQIC, and SIC filter FTP-MS with 3 regimes as the best fitting model.. 36.

(47) `. Table 3.3 Determining the appropriate model using information criteria Information FTP-MS TVTP-MS Criterion 2 regimes 3 regimes 2 regimes 3regimes AIC 5.834 5.618 5.896 6.021 HQIC 5.939 5.799 6.018 6.247 SIC 6.094 6.064 6.194 6.578 Secondly, we use four indicator related to forecast accuracy to measure the forecast performances of the models. The four measures of predictive accuracy are mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), and Theil's U coefficient (Theil's U). The equations for these associated. 政 治 大. statistics are:. 立. ̂𝑡 )/∆𝐻𝑃𝑡 |/𝑇 × 100 1. MAPE(%)= ∑𝑇𝑡=1|(∆𝐻𝑃𝑡 − ∆𝐻𝑃. ‧ 國. 學. ̂𝑡 )2 /𝑇 2. RMSE=√∑𝑇𝑡=1(∆𝐻𝑃𝑡 − ∆𝐻𝑃. ‧. 2 ̂ (∆𝐻𝑃𝑡+1 −∆𝐻𝑃 𝑡+1 ). (∆𝐻𝑃𝑡+1 −∆𝐻𝑃𝑡 )2. n. al. )/(√∑𝑇−1 𝑡=1. ∆𝐻𝑃𝑡. ). er. io. ∆𝐻𝑃𝑡. sit. Nat. 4. Theil's U=(√∑𝑇−1 𝑡=1. y. ̂𝑡 )|/𝑇 3. MAE=∑𝑇𝑡|(∆𝐻𝑃𝑡 − ∆𝐻𝑃. Ch. i n U. v. ̂𝑡 is forecasting value, Note that ∆𝐻𝑃𝑡 is annualized housing price growth rate, ∆𝐻𝑃. engchi. T is number of periods used in calculation. MAPE measures the forecast error in terms of percentage, both RMSE and MAE measure the distance of the forecast error, and Theil's U measures the ratio of proportional forecast error to the native forecast. As a result, the lower value of MAPE, RMSE, MAE, and Theil’s U, the better forecast performance. This result is shown in Table 3.4. Both MAPE and MAE choose FTP-MS with 3 regime, while both RMSE and Theil’s U select TVTP-MS with 2 regimes.. 37.

(48) `. Table 3.4 Determining the appropriate model by evaluating forecast accuracy Information FTP-MS TVTP-MS Criterion 2 regimes 3 regimes 2 regimes 3regimes MAPE 710.120 639.177 765.867 662.607 RMSE 8.143 8.028 7.942 8.232 MAE 6.811 6.747 6.879 6.895 Theil’s U 0.391 0.387 0.357 0.390 The four indicators provide different measures to evaluate the difference of forecasting performance among the models. However, they don’t indicate the models are significantly better than another. Therefore, in order to further examine the relative performance between the models, the Diebold-Mariano (DM) test, which allows to test. 政 治 大. the differences of statistical significant forecast errors between two models, is proposed. 立. 𝑉𝑎𝑟(𝑑) DM stat = 𝑑̅/√ ~𝑁(0,1). 學. ‧ 國. in this Chapter.13 The equations for DM statistic is:. 𝑇. ‧. sit. y. Nat. Where 𝑑̅ is the sample mean of the loss differential series defined as ∑𝑇𝑡=1[𝑔(𝑒𝑖𝑡 ) −. io. er. 𝑔(𝑒𝑗𝑡 )] /𝑇. 𝑔(𝑒𝑖𝑡 ) and 𝑔(𝑒𝑗𝑡 ) are loss functions of model i and model j. Hence, the null hypothesis is two forecasts have equal accuracy if the loss differential has zero. al. n. v i n C h positive DMUstat means the forecast error of expectation for all time. The significant engchi. model i is statistically larger than the forecast error of model j. The result of DM test is shown in Table 3.5. Table 3.5 highlights the inadequacy of the TVTP-MS model with 3 regimes, and fails to show a statistically significant difference between FTP-MS with 2 regimes vs. FTP-MS with 3 regimes, FTP-MS with 2 regimes vs. TVTP-MS with 2 regimes, and FTP-MS 3 regimes vs. TVTP-MS with 2 regimes.. 13. The Diebold-Mariano (DM) test was introduced by Diebold and Mariano (1995). 38.

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