Forecasting real estate market turning point with leading indicators

Forecasting Real Estate Market Turning Point with Leading Indicators

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A Thesis

Presented to

Faculty of Economics & Business

University of Amsterdam

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In Partial Fulfillment of the Requirements for the Degree

Master of Science

Business Economics:

Real Estate Finance

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by

Yanan He

October, 2014

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Declaration

This thesis is a presentation of my original research work. Wherever contribution of others are involved, every effort is made to indicate this clearly, with due reference to the literature, and acknowledgement of collaborative research and discussion.

The work was done under the guidance dr. Frans Schilder, at Faculty of Economics and Business, University of Amsterdam, the Netherlands.

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Abstract

The forecast of market has never been out of scoop since various models were used to simulate and predict the financial or economic market. Investors who can gain and make use of the market information earlier than average get compensated. Compared to financial market, real estate market shows long-term and distinct cyclic patterns, which investors and policy-makers should be aware of. This paper firstly aims to find out leading indicators that can be used in prediction of Hong Kong real estate market. Then indicators are put into test models to shape the best performing one. Probit models are concerned to be the main forecasting model in this paper. Furthermore, to make the prediction preciser, different indicators are used for ascending and descending market respectively. At last, deep learning neural network (DLNN) method is used as a comparison on accuracy to evaluate the probit models.

With a review of the history of Hong Kong real estate market and lessons from researches on other commercial real estate markets, totally 1 to 24 period-lags of 21 indicators are tested respectively to find out the best performing leading indicators. Indictors perform well by individual are kept to be further added to multivariable models. The result turns out that mortgage loan, car registration, money supply, employment and rent level tend to predict the ascending market best. Credit released, mortgage loan and manufacturing employment tend to manifest the descending market most in advance. The outcome of the prediction is satisfactory with an accuracy rate of more than 80% for predicting either an ascending or a descending trend. And the result is easy to be applied in real estate valuation and investment decision-making. Furthermore, the model is evaluated by comparing result of probit models to other possible models that are considered to be competitive but distinct in method. Hence a DLNN model is deployed to forecast the property price and results are compared to that of probit models briefly.

This paper makes addition to previous research on two ways. Firstly, it adapts probit models to Hong Kong real estate market for the first time. Secondly, it discusses the price prediction in two – ascending and descending- scenarios respectively.

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Contents

1. Introduction ... 5

2. Literature Review ... 7

3. An Overview of Hong Kong Real Estate Market ... 10

4. Methodology ... 14

4.1 Probit Model 4.2 Model Estimation 4.3 Application 4.4 Model Evaluation (DLNN)

5. Data & Variables ... 19

6. Estimated Models ... 23

7. Model Evaluation ... 28

8. Conclusion ... 31

References ... 33

Appendix ... 36

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1. Introduction

Real estate cycles have been a vital concern to property investors and policy makers. As real estate acts as a relative illiquid asset and real estate market is considered to be a less efficient market compared to stock or bonds market, the importance of understanding and forecasting the market cycles cannot be stressed enough. Meanwhile, compared to indirect real estate financial products, the transaction of real property involves huge costs which can even affect the property value directly. Hence the investment decision relies more on specific cases rather than a general criteria for all. We should notice first that the holding period of real property is much longer than other assets. And to appraise the value of a property, we should know or assume an appropriate growth rate of the property value. What’s more, to buy or sell a property, we still need to grasp the right time and opportunity. For these reasons, we can see the importance of noticing the trends of the market and the turning point of the property price changes. Be aware of the turning point is the prerequisite to choose the right growth rate and then to make the correct valuation. For these characteristics of real assets and the valuation method of investment properties, a binary model that can catch the accumulative tendency and can answer the question “whether the market is on the edge of turning” is valuable. In terms of these kinds of questions, ignoring the unpredictable emergency, we should pay attention to the accumulative effects in process that lead to the final outcome. There are quantities of analogous phenomenon in natural world and social science. For example, the breakdown of an ecological environment when the number of a specific species in it reaches a limit threshold. Or the rejection of a loan application by the assessment score based on all previous credit or behavior an applicant have been recorded in the system. For this specific type of question, probit or logit model take their advantages for that they describe the accumulative process and point to a binary outcome just as researchers want. For this reason, probit model comes to the first place when we do model selection to solve the question mentioned above.

Furthermore, there are previous studies on cycle forecast by probit model and the modelling performs well on various asset types in different markets. However, there is no related such simulation on Hong Kong real estate market. And there is no research that measures the probability of ascending and descending separately but simultaneously. This paper first aims to find out indicators that can be used to forecast trend of property price changes, further to predict the trend, in other words, the turning point of property price. To specific, it examines the significance of economic leading indicators that can be used in predicting the trend of price changes in Hong Kong commercial real estate market. Besides, it describes the market improvement from a historical sight in order to give some hints for variable selection at the very beginning. Flowingly, indicators and models for two separate phases -rising and declining- are studied respectively since dynamics for declining real estate markets differ from that of rising ones. Probit models are used in performance simulation and trend forecast. What’s more, deep learning neural network method is used as a comparison on accuracy rate for model evaluation.

Section 2 - literature review introduces previous works related to real estate market simulation and prediction. It includes previous studies on real estate cycles, market simulation and prediction, market dynamics and deep learning neural network. The research on real estate cycles

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started very early as the study on economic cycles began. And the real estate market has tight relations to national or regional economic situation. When it comes to market simulation and prediction, different models have been employed such as error correction model, autoregressive integrated moving average and generalized autoregressive conditional heteroskedastic. There was also papers regarding to property price cycles by approach of probit models. When it comes to market dynamics, there is evidence to demonstrate that the dynamics of a bear real estate market is different from that of a bull market, which could be an important indication to this paper. At last, as a burgeoning method on pattern recognition, deep learning neural network was believed to be an efficient method for economics use.

Section 3 – an overview of Hong Kong real estate market gives an overview of the market from a historic sight. It covers the market improvement from 1972 through 2013, which is also the time period that the data is collected from. An analysis of demand-supply changes with active intervention of the authority is represented in detail. It is worth noting the important roles government plays in the real estate market and the changes of that role from direct intervention to positive non-interventionism and then to selective interventionism. Besides, a short-term cycle of approximate five years and a long-term cycle of around twenty years is noticed in the improvement process. What’s more there is trend that the cycle has become shorter gradually. At last, some advice to policy is given.

Section 4 – methodology illustrates all methodology that appear in the paper. It includes an abstraction of probit model and deep learning neural network. It illustrates the concept of probit model, the application of probit model in this paper and the evaluation method in detail. Probit model is a commonly used model that can conclude binary status ideally. What makes it more attractive in practical use is its ability in explaining the accumulative effects of various factors on final outcome. As the most common “S shape” cumulative distribution function, it describes many phenomenon in natural phenomenon and social science. Compared to deep learning neural network, the estimation methods and especially the applications of probit model can be given concisely in formulas. Furthermore, the concepts of deep learning neural network is introduced by an approach from artificial neural network to the time series application. It is believed to be a competitive method in forecasting the cycle. Hence it is used as an assessment for the performance of probit model in the model evaluation part.

Section 5 – data & variables deals with data collection, data manipulation and variable selection. All datasets are obtained from Hong Kong Census and Statistic Department or from Datastream. Totally 22 leading indicators are collected and periods span from 1982Q1 to 2014Q2. Not all indicators are available for the whole period. The meanings of each variables is explained in detail in this part. Dickey-Fuller unit-root test is taken for each indicator, it turns out that all series are I(0) or I(1). And to make sure the series is stationary, first difference is take if the series is not I(0).

Section 6 – estimated models is the main part of model generation, which includes univariate probits and multivariate probits. First, each indictor in different lag levels enters the univariate probit model. Criteria are given to select the best performing indicators. Then, indicators in optimal lag levels enter the multivariate probit model. For any model mentioned, two scenarios –

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ascending and descending market- are discussed separately. And for the multivariate probit model, three types of model generated in different methods are given and compared. At last, the optimal forecasting model with selective indictors are given.

Section 7 – model evaluation concerns result evaluation and model evaluation, in which deep learning neural network method is used as a comparison on accuracy rate. In this part, the model is evaluated fist by its accuracy rate on in-sample prediction. Except the prediction of price changes, the more important application is the forecast of turning point. The result and accuracy rate on prediction of turning point is given in appendix. Second, the model is evaluated as a comparison to deep learning neural network models. The result comes out that the probit model performs well in property price prediction. At last conclusions are given.

2. Literature Review

Comprehending the complex and dynamic macroeconomic and microeconomic real estate cycle is believed to be the foundation for understanding property performance in a specific market. Pyhrr et al. (1999) synthesized relevant research on real estate cycles in a microeconomic decision-making context, with special emphasis given to global real estate cycles. In their article, macroeconomic cycle studies are defined as “those whose primary cycle focus on emphasis is at the national, international or regional levels”. In contrast, microeconomic cycle studies are defined as “those whose primary cycle focus or emphasis is at the metropolitan area market, submarket or property location levels”. Much of the early economic cycle research in the U.S. was concerned with growth and contraction in the national economy. Burns (1954) represented that long cycles in residential construction may easily exit in a collectivist economy. Grebler and Burns (1982) analyzed total construction, public construction, private construction and residential property construction and found a cycle of 4.7 years in residential construction and a cycle of 7 years in nonresidential construction. Muller (1995) stratified real estate market cycles into two distinct types: physical cycle that described the demand, supply and occupancy of space and financial cycle that led by the capital flows into the market for both exiting properties and new construction. Mueller (1999) concluded that occupancy levels play the major role in rental growth rates in office and industrial markets throughout the U.S. Pugh and Dehesh (2001) studied the international property cycles since 1980 and viewed property cycles as aggregative phenomenon of precipitating causes, systemic dynamic processes and feedback loops. They demonstrated that property cycles could be broadly separated into endogenous and exogenous types. The endogenous cycles came from mismatch between developing and market demands and the exogenous cycles involved macroeconomic conditions. Nevertheless, they did not conclude the exact factors leading to ascent or descent.

Zhang and Sun (2006) took economic growth, macroeconomic environment and institutional establishment as driving forces for China’s real estate cycle. In specific, they treated urbanization ratio and personal disposable income as indicators of economic growth, and took capital inflow and

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fiscal policy, which was demonstrated mainly by changing in interest rates and mortgage loans, as principle factors indicating macroeconomic environment. Furthermore, they illustrated that investment channels and local government policies played great roles in real estate cycles, contributed by the limited investment ways and self-interests from developing land of local government. According to their empirical research, based on General-to-Specific methodology, real effective exchange rate and exchange rate affected real estate investment amount in a negative way, meanwhile real lending rate and ratio of real estate loans to total loans have significantly positive effects on the real estate investment. However, it is worth noting that the financial system in mainland China is immensely distinct from that of Hong Kong, even though they are blending gradually nowadays. They also mentioned their final model was produced by the General-to-Specific methodology with PcGets software, nevertheless, they did not demonstrate the principles in their paper. It can be figured out from the result that lags of stationary indicators are OLS regressed on real growth rate of real estate investment. A shortcoming of this model rather than time series models is that it does not contain self-variance of interested object. Hence it cannot be used in prediction. Hall et al. (1997) developed error-correction models (ECM) of real house prices in the UK. They took real house prices, real personal disposable income, owner-occupied stock of housing and the mortgage rate of interest from 1996 to 1995 as dataset. The main approach was the Markov-switching regression which characterized parameters of ECM for real house price. They found that home-price booms are actually unstable. Nevertheless, they did not examine the forecasting performance of their model. Malpezzi (1999) employed ECM model modeling US house price changes from 1979 through 1996. They pointed out that the housing price changes were not

random walks and were partly forecastable. Crawford and Michael (2003) compared the

forecasting performances of three types of univariate time series models: Autoregressive Integrated Moving Average (ARIMA), Generalized Autoregressive Conditional Heteroskedastic (GARCH) and regime-switching. They represented that while regime-switching models could perform better in-sample forecasting, ARIMA models generally performed better in out-of-sample forecasting. They also pointed out that the home price growth rate was correlated with the probability of a regime change. If regime-switching models were found to be reliable in providing information in term of turning points of the market, the models could be quite valuable. Krystalogianni et al. (2004) forecasted UK commercial real estate cycle phases by probit approach for the first time. They employed samples from December 1986 to April 2002 to simulate ascents and descents in cycles. Totally 25 leading indicators were deployed, among which M0 money supply, M4 money supply, press recruitment ads, gross trading profits, house building starts, new car registrations, retail sales, industrial production, consumer confidence, 10-year Gilts yields and private to total credit performed well in indicating real estate cycles in industrial, office and retail capital values separately. The results were satisfactory with a correct prediction rate up to 87.9% with 90% threshold probability. While a drawback of their research was the setting of dependent variable. As real estate phase acts as ascent, descent and slight fluctuation, taking ascent and descent only as dependent variable of probit model can lead to data loss, and can bring about the interpretation less accuracy when the prediction is not significant enough. Hendershott et al. (2013) used error correction models to estimate short run rent, vacancy and supply adjustments. The time series analysis was “similar to the three-equation model that EGHS (2008a) and Hendershott et al. (2010)” used. They demonstrated that the short-run rent adjustment is determined by retail sales,

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market supply, natural vacancy rate and the lagged error. Error correction model is considered as an ideal option in simulating real estate price as the assumption is sound that adjustment in price can be explained by current fluctuation of independent terms, ECM from last period and the stochastic term. The model can be used only if the property price cointegrates with time series of input indicators, as the model assumes. However, though it is considered as an ideal solution in short-run forecasting, it is not an optimal solution for market prediction to the aim of this paper. On grounds that this paper aims firstly to figure out leading indicators that can be used and explained in prediction rather than a trend fitting simulation.

Furthermore, there is evidence to suggest that dynamics of declining real estate markets differ from that of rising markets. Thus indicators for two phases -ascending and descending- are deserved to be studied respectively. Pritchett (1984) analyzed the impact of real estate cycles on investments and pointed out that demand leaded supply when the construction cycle was ascending to the peak bug lagged supply when cycles were falling to a trough. For an ascending market, Case and Shiller (2003) and Piazzesi et al. (2009) studied the housing boom in U.S. and indicated the importance of momentum in housing market forecast. For a descending market, Hott (2011) researched the circle of bank lending, real estate prices and supply of mortgage, and concluded that market was likely to be influenced by rational expectations as well as irrational expectations. The sharp drop in real estate prices indicated a sudden change in investors’ expectations which can be explained by disaster myopia. Adopting spectrum filtering methodology, Han et al. (2010) researched China market, and has also pointed out that indicators of real estate industry have a more obvious distinction between peak and valley. Among the 13 variables she selected, newly constructed area, constructed area, land acquisition area, development completed area, real estate fund and surplus fund of real estate development turned out to be leading indicators. This paper takes the indicators from previous researches into consideration in data collection.

Artificial Neural Networks (ANNs) are flexible models that do not require a priori knowledge. ANNs are capable of nonlinear-modeling and often robust to noisy data. These properties of ANNs make them a natural solution for time series forecasting. After back propagation algorithm was invented by Rumelhart et al. (1986), Artificial Neural Network (ANN) models, as an artificial intelligence approach, are widely used in many areas such as pattern recognition, prediction, etc. There are many studies on applying ANN to time series forecasting: Cron et al. (2010) studied on feature selection with high-frequency datasets for ESTSP’08 competition and suggested that ANN and other nonlinear algorithms of computational intelligence have preeminent performance in empirical forecasting; Peralta et al. (2008) focused on ANN automatic designed by Genetic Algorithm and indicated that ANN has more difficulty in predicting Dow-Jones time series rather than Temperature and Passengers, on grounds of the greater chaotic component of the former; Ferreira et al. (2008) and Cron (2004) did research by approach of ANN on evolutionary hybrid system and multilayer perceptron respectively. ANN models have also been used in real estate market prediction, for example researches of Worzala et al. (1995), Brooks et al. (2003), Hu and Zhong (2010). Hu and Zhong (2010) studied on prediction of commercial apartment price in Shanghai, China. They applied ANNs on predicting prices of real estate. Beside back propagation algorithm, Elman algorithm was also used. Elman neural network is a special case of Recurrent

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Neural Network (RNN), which is a class of ANN where connections between neurons form a direct cycle. The characteristic of Elman neural network is that the neural network can keep a sort of state, allowing it to perform such tasks as time series prediction which are difficult to be achieved by a standard multilayer perceptron. Through comparison they showed that the Elman neural network can achieve better result in forecasting: the accuracy is higher and the constringency speed is faster. The idea of direct cycle is used in the deep learning neural network, in which the first step is called the auto-encoding.

However, in 1990s ANN were overtaken by some other models like support vector machine (SVM) and boosting due to accuracy and speed matter. Hinton et al. (2006) invented deep learning neural network (DLNN), which demonstrated the ability of neural network and renewed the interest of researchers. There are researches on time series prediction on approach of DLNN, for example Busseti et al. (2012). As far as I know, nevertheless, there is no related research on real estate cycle forecast upon now. The forecasting of turning point is essentially time series analysis combined with signal recognition, both of which can be solved by DLNN. Hence a DLNN model is employed in this paper to forecast the property price and the results are compared to that of probit models.

3. An Overview of Hong Kong Real Estate Market

Hong Kong’s real estate business began in 1841 when U.K. colonized Hong Kong and began to auction the land. Before the WWII, Hong Kong’s real estate market stayed in budding stage. From WWII to 1960, the population increased and the economy took off, during which lack of housing was a severe social issue. In the beginning of 1970, the bloom in stock market gave chance to real estate companies to finance and to develop. From July 1972 to September 1972, the number of IPO for real estate companies was more than 65. The increasing property price and rents from 1968 to 1973 was concomitant with the prosperity of stock market. The bubble burst in March 1973 and Middle East Oil Crisis occurred in 1974, which suppressed the market further. From 1975, the real estate market got warmed by baby boom in 1950s, immigration, economic restructuring and positive prospection by the ending of the Culture Revolution in mainland China. The growth rate for real gross local product was more than 10% during 1975 to 1981. The ascent reached its peak in 1981 on the grounds of speculation, high interest rate and failure of the proposition for an exchange of sovereignty for administration by British government.

Chi-keung (1998) classified the period from 1981 to 1985 to great depression of Hong Kong real estate market. In 1982, the land price decreased averagely from 40% to 60%. The property market greatly declined in 1982 and 1983. As our data begins from 1982, we can see the price dropped by 36% from 1982Q1 to 1983Q4. In 1983, the supply of new private residential property dropped by 6%. People were uncertain about the future because of the conflicts between Britain and China during the negotiations. The market firmed up in certain sectors since the middle of 1984

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and the occupancy rate for residential property declined in this year. After 1984, Hong Kong entered the transition period for handover.

With a positive expectation in politics and economy, real estate market kept escalating for ten years with surges in 1985 to 1989, 1991 to 1994 and 1995 to 1997 respectively, which broke the cyclic pattern of eight years. The 1987 “Joint Declaration of the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the People’s Republic of China on the Question of Hong Kong” protected the corresponding leases and rights of lessees under the law of the Hong Kong Special Administrative Region, which reduced the uncertainty commingled with handover issues.

The surge from 1985 to 1989 was mainly ascribed to The Declaration, declining interest rate, capital inflow and depreciation of HK dollar. From 1986Q3 to 1989 Q2, the property price increased from 8682/m2 _{to 18186/m}2_{, which was 109% growth and rents also climbed by 87%. In 1988, the}

Consumer Index rose by an average of 7.5% and high inflation attracted more investors to real estate market. In the same year, the number of agreements for the sale and purchase of property rose by 68% compared to last year. In 1989 and 1990, political upheaval influenced the consolidation and confidence of market. Just after the June Fourth Event in China, the purchasing price fell 15-20%. Nevertheless, the influence was temporary, leaving several months of fluctuation followed by the nest upsurge.

The second upsurge lasted from 1991 to 1994, during which the economy of Hong Kong kept on flourishing, capital flew in from abroad and mainland China, need for property was driven by both positive expectation and speculation. In 1991, the low mortgage interest rate and high inflation rate stimulated the demand for properties. The Government extended the stamp duty to all residences and reinforced the mortgage requirements, aiming at control the speculation activities. The anti-speculation measures achieved desirable outcomes in 1992. However, the property price did not stop rising. In 1993 the population growth rate was 2%, compared to an average of 1% in previous three years, which drove the property demand. In 1994, Hong Kong government took actions to control and depress the skyscraping housing price under social pressure, during which the market allocation between industry, office and housing was adjusted. The Task Force on Land Supply and Property Prices lunched by the government introduced series of anti-speculation measures to stabilize the property prices. The measures introduced by the government were effective for a short while. From 1990Q4 to 1994Q3, the property price rose by 203% and rents rose by 65%. From 1994Q4 to 1995Q4, the property price dropped by 10% due to the macro-control.

From the end of 1995, the market bounced again and touched the zenith in June 1997. In the stage from 1995 to 1997, oligopoly and trend of global investment shaped and real estate became one of the most important industries in Hong Kong economy. Further inflows of expatriates and Chinese immigrants contributed to a faster growth in the population. The economic growths of first two quarter in 1997 were 5.9% and 6.8% respectively, which led the strong demand for real estate. Optimistic estimate about Hong Kong’s back to China attributed the speculation further. In 1996 and 1997, the property price increased by 63% on the existing high price. In July 1997, with the collapse of Thailand financial market, the Asian Financial Crisis incurred. Hong Kong suffered a lot

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during the Asian Financial Crisis. The real GDP per capita of Hong Kong did not return to its level in 1997 until 2006. As the whole economy was shocked by the financial crisis, the real estate market was impacted heavily. The unemployment rate rose from 2% in 1997 to 6% in 1999. As meanwhile, non-investors stayed out of the transaction because the market kept on descending and was full of uncertainties. Developers and land agents had to lower prices to compete for limited buyers. Many scholars have researched on the real estate bubble emerging in this period. According to Feng (2001), the real estate bubble was mainly attributable to three reasons. First, the supply of land especially land for housing was far less than the need in market. The government was blamed for not taking action in time to relieve the tight supply of land. Second, the imperfection competition by oligopoly led to cartel, price discrimination and following the high property price. Third, the speculation resulted from capital inflow amounted because of the lower interest rate of U.S. and wrong expectation to the handover. All these facts intensified the unbalancing between supply and demand. After 1997 Asian Financial Crisis, the real estate market plunged and did not rebound until 2003.

Both 1998 Policy Address and 2002 “Sun’s 9 Measures” did not stop the property market from declining. In the first half year of 2003, the economy and real estate market was further blown by the outbreak of Severe Acute Respiratory Syndrome (SARS). The average commercial property price was 30702HK$/m2_{, which was close to its value in the beginning of 1992. The property}

market began to recover since the middle of 2003.

In 2004, the overall volume of sales rose by 41%, mainly ascribed to secondary sales with a growth of 66%. The interest rate for time and saving deposits was in historical low point in 2003 and 2004, which conduced to active sales. The bounce of property market was concomitant with the strong economic recovery. The growth rate of GDP was 8.1% in 2004 and 7.3% in 2005, compared to 3.2% in 2003. The unemployment rate continued to drop to 5.3% in 2005. In July 2003, Individual Visit Scheme was launched, which attracted more than two million Chinese visitors to Hong Kong in 2004. It was the first time Hong Kong performed resurgent impetus after the handover. The revived market was attributable to the attractive financial system, open business environment in Hong Kong, also the high GDP growth in mainland China to a great extent. The escalation sustains till the third quarter of 2008, during which the property price escalated from 30702HK$/m2 _{to 83830HK$/m}2 _{with a growth rate of 173%. The global financial crisis gave a}

shock to property market in Hong Kong either, however the influence was transitory, with the price returning to its highest point in 2008 within one year. The next trough came at the fourth quarter of 2011. Though the domestic sector performed remarkably well in 2011, the Hong Kong economy and following the real estate market was plagued by the Eurozone debt crisis. Trading activities were dwindled by 21%, attributed by both the Special Stamp Duty introduced in 2010 and the uncertain outlook about the growth momentum. Since 2010, a series of measures were introduced to stable the property price, such as adding land supply, curbing speculative activities and constraining mortgage lending. The measures had noticeable outcomes as prices and rentals increased at a moderate rate.

The extremely high property price, especially expensive residences for civics, is partially due to the dysfunctional policy during 2002 to 2011. To save the ebb real estate market led by the Asian

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Financial Crisis in 1997, the government stopped the Home Ownership Scheme in 2002, which was the most important social housing plan in Hong Kong, by which 46% families lived in houses supported by the government. From then on, people at all income levels have to compete in the market for any residence. As years passed, lower-income inhabitant along with middle-class cannot afford the apartments, which is a serious social issue. And at the same time, small-scale real estate agents broke up or purchased by conglomerations, the monopoly took shape rapidly. Though the Home Ownership Scheme will be reinstated in December 2014 to some extent, the tight residential situation cannot be reversed in a short period. For the investment properties, it is believed that the government ought to provide and protect a free and efficient market, which in other words the authority should try to not intervene the market. However, the government should never abandon the duty on social housing. Meanwhile, to fulfill the mission on social housing, the government have to take measures to protect the social housing market not being disturbed by speculation. To keep the affordability and availability of social housing, the government should and have to intervene the social part of the market. Except various compensations to social housing, government should also provide some privilege to first-time residence buyers such as a concessional loan interest, by which the authority does not intercede the market directly. However, with higher purchasing power, it may lead to a higher price at last. All in all, the authority should treat social housing seriously and differently with investment properties. Only with more social housing that can tackle the emergent issue of living spaces, the government can get into breaking the monopoly from a relative mitigated way.

Figure 1. Price and Credit to Private Non-financial Sectors(1982Q1 to 2013Q4)

Figure 2. Price and 3-month Treasury Bill Rate (1991Q1 to 2013Q4)

The history of Hong Kong real estate cycles gives us an overview of the whole market. We can see that the government plays a significant role in market control. In reverse, people rely on and have faith in it, which make the implementation more effectively. From a rather long-term

0 1000 2000 3000 4000 5000 6000 0 20000 40000 60000 80000 100000 120000 140000 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 20 12

Credit to Private Non-financial Sectors (Billion $) Price ($/m2) 0 2 4 6 8 10 0 20000 40000 60000 80000 100000 120000 140000 19 82 19 84 19 87 19 90 19 93 19 95 19 98 20 01 20 04 20 06 20 09 20 12

3-month Treasury Bill Rate (%US$) Price ($/m2)

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respective, the period from 1982Q1 to 2013Q4 can be seen as a whole long debt cycle including leveraging, depression and reflation phases. In a short term, it gives us an intuition of an 8-year cycle mainly driven by financial control implemented by the Hong Kong Monetary Authority. Figure 1 and Figure 2 indicate cycles of the property price, credit to private non-financial sectors and 3-month Treasury bill rate. The history sight also notices that the reasons and events leading to descent are highly distinct from that of ascent. This paper focuses on a short term prediction within 5 years. Hence the peak is defined as the quarter before which the property price increased continuously at least two periods and after which the property price decreased continuously at least two periods. The trough is defined exactly in the opposite way. This means a peak only appears in a span longer than one year. Table 1 marks peaks and troughs of real estate market cycles. Details are explained in Section 4 further.

Table 1. Peaks and Throughs in Hong Kong Real Estate Cycles

Peak Trough 1994Q3 1983Q4 2008Q2 1986Q3 2011Q2 2003Q2 2012Q4 2008Q4 2011Q4

4. Methodology

Probit model was introduced by Chester Bliss (1934) on grounds of sigmoid character of the typical dosage-mortality curve and such curves can easily be plotted as straight lines. In terms of model estimation, maximum likelihood estimation method contributed by R. A. Fisher as an appendix to Chester Bliss (1935), Berkson’s minimum chi-square method or Gibbs sampling can be used for parameter estimation in probit model. Maximum-likelihood method is used in this paper.

4.1 Probit Model

Assume 𝑈_𝑖1 as the outcome tendency or utility from an occurrence, 𝑈_𝑖0 as the outcome tendency or utility without this occurrence. In linear regression, we treat outcomes as dependent variables determined by multiple regressors, so we have

{𝑈𝑖 1_{= 𝑿} 𝑖 ′_𝜷𝟏_{+ 𝜀} 𝑖 1 𝑈𝑖0= 𝑿𝑖′𝜷𝟎+ 𝜀𝑖0

where 𝑿 is the matrix of observations, 𝜷 is the vector of regression coefficients. Make the difference of equations, we get

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Then we define, when 𝑈𝑖1> 𝑈𝑖0, event 1 occurs, denoted by 𝑌𝑖 = 1. Similarly, we define the event does not occur when 𝑈_𝑖1≤ 𝑈_𝑖0, denoted by 𝑌𝑖 = 0. Thus we get

𝑌𝑖 = 𝑿𝑖′𝜷 + 𝑢𝑖 where 𝜷 = 𝜷𝟏_{− 𝜷}𝟎 _{and 𝑢}

𝑖 = 𝜀𝑖1− 𝜀𝑖0.

Seemingly obvious in proof, the part above shows the logic of binary assumption as an occurrence in real world, where effects accumulate and then individuals alter decision or circumstances change.

When it goes further to probit model, we first set P as the probability of an event happening. Then given observations, we have the probability of event 1 occurred, that is

𝑃(𝑌𝑖 = 1|𝑿) = 𝑃(𝑌𝑖 > 0) = 𝑃(𝑢𝑖 > −𝑿𝑖′𝜷) = 1 − 𝑃(𝑢𝑖 ≤ −𝑿𝑖′𝜷) = 1 − 𝛷(−𝑿𝑖′𝜷) = 𝛷(𝑿𝑖′𝜷) where 𝑢 ~ 𝛷(𝑥) = ∫ 1 √2𝜋𝑒 −𝑧₂2_{𝑑𝑧 = 𝑃(𝑧 ≤ 𝑥)} 𝑥 −∞ .

The use of the standard normal distribution rather than normal distribution causes no loss of generality here.

4.2 Model Estimation

The maximum likelihood estimation for probit model follows the fundamental methods of maximum likelihood estimation. Suppose sampling units {𝑦𝑖, 𝑥𝑖}𝑖=1

𝑛

, their joint log-likelihood function is

𝑙𝑛𝐿(𝛽) = ∑{𝑦𝑖𝑙𝑛𝛷(𝑿𝑖′𝜷) + (1 − 𝑦𝑖)𝑙𝑛[1 − 𝛷(𝑿𝑖′𝜷)]} 𝑛

𝑖=1

.

Under general conditions, estimator 𝜷̂ is consistent, efficient and normally distributed in large samples. The numerical algorithm of 𝜷̂ maximizing likelihood function on the computer is omitted here.

4.3 Application

Before applying probit model to data set, some basic definitions are made. The multivariate probit models in this paper are

𝐸 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑟𝑖𝑠𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for

16

where 𝐹(𝑿′𝜷) is the probit function for ascending scenario. And

𝑃 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑑𝑒𝑐𝑙𝑖𝑛𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for

𝑃𝑟(𝑃 = 1|𝑥) = 𝐺(𝛾0+ 𝛾1𝑥1+ ⋯ + 𝛾𝑘𝑥𝑘)

where 𝐺(𝑿′𝜷) is the probit function for descending scenario.

First, an ascending trend is defined as that the property price keeps increasing in continuous three quarters. Similarly, a descending trend is defined as that the property price keeps decreasing in continuous three quarters. Next, periods left are treated as fluctuation periods. Table 2 shows the criteria defining trends and the representative binomial dependent variable in regression.

Table 2. Definitions to Ascending Trend and Descending Trend

Trend Criteria In Ascending Price Model In Descending Price Model

Ascending 𝑥t > 𝑥t-1 & 𝑥t-1 > 𝑥t-2 E = 1 P = 0

Descending 𝑥t < 𝑥t-1 & 𝑥t-1 < 𝑥t-2 E = 0 P = 1

Fluctuation Periods left E = 0 P = 0

Furthermore, according to the criteria above, a turning point is the transforming from one state to any other state that is different from the original one, which is distinct from the peak and trough points from common sense.

4.4 Model Evaluation (DLNN)

Artificial Neural Networks are a more principled way to add complexity on large datasets. It is a regression model with one input layer, several hidden layers and one output layer (see Fig. 4). Each layer has one or several neurons. Data transferred between layers is linear operation while within layer is non-linear operation (for each neuron). A neuron take input from all the neurons of the previous layer. The neuron calculates a weighted sum of inputs first, then use a transfer function that is specified for the units (often sigmoid function is used) to calculate the output.

ℎ𝑊,𝑏(𝑥) = 𝑓 (∑ 𝑊𝑗𝑥𝑗 𝑁 𝑗=1 ) 𝑓(𝑧) = 𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑧) = 1 1 + 𝑒−𝑧

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So far many kinds of ANNs with different architectures (meaning patterns of connectivity between neurons) are studied, including ones with multiple hidden layers. Here the most common choose, feed forward networks, is implemented to do the forecasting. The connectivity graph of feed forward networks do not have any directed loops or cycles.

Figure 4. Illustration of ANN Structure

Feed forward neural network has an input layer, several hidden layer and an output layer. The process to determine the weights of the connections between layers is called training. Usually ANNs are trained by back propagation algorithms invented by Rumelhart et al. (1986). In our case we would need training examples (𝑋⃗𝑡−1, 𝑋⃗𝑡−2, ⋯ , 𝑋⃗𝑡−𝑘, 𝑋𝑡,1), which will be explain in detail in 4.4.3. 4.4.2 Deep Learning Neural Network (DLNN)

The ANNs which has more than 2 hidden layers are called Deep Learning Neural Networks. The more layer ANN has, the more complexity it can achieve. But as the amount of hidden layer increases, the training algorithm can be not so effective because the sparsity of gradient is increasing and it'll be an easier to fall in local optima. Auto-encoding is a method to help DLNN on training.

When it comes to auto-encoder, one way to better training the multi-layer neural network is to train the first hidden layer of DLNN unsupervisely. Suggested by Hinton and Salakhutdinov (2006), high-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer, following reconstruct high-dimensional input vectors. Back propagation (essentially gradient descent) can be used for fine-tuning the weights in the neuron of ‘‘auto-encoder’’ networks.

Input layer Hidden layers Output layer

Same mapping with different weights Input data

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There are several structures of DLNN and in this paper the simplest one which has two hidden layers are chosen. Using auto-encoder, the DLNN model implemented for forecasting has one input layer, two hidden layers (one initiated by auto-encoder and the other randomly initiated) and one output layer.

4.4.3 Time series and DLNN

To deal with time series problem with DLNN, we considered it as to obtain the relationship between some values of time 𝑡 (here the only value we need is the price) and the values from previous 𝑘 time steps (𝑡 − 1, 𝑡 − 2, ⋯ , 𝑡 − 𝑘).

𝑋𝑡,1 = 𝑓(𝑋⃗𝑡−1, 𝑋⃗𝑡−2, ⋯ , 𝑋⃗𝑡−𝑘)

Here 𝑋⃗𝑡−1 = 〈𝑋𝑡−1,1, 𝑋𝑡−1,2, ⋯ , 𝑋𝑡−1,𝑛〉, where 𝑛 is the dimension of the time series data.

Therefore, the time series will be transformed into a pattern set depending on the 𝑘 input nodes of a particular DLNN, and each pattern will consist of the following (Fig. 5):

1. 𝑘 input data vectors of dimension 𝑛 correspond to the 𝑡 − 1 to 𝑡 − 𝑘 time steps: 𝑋⃗𝑡−1, 𝑋⃗𝑡−2, ⋯ , 𝑋⃗𝑡−𝑘 .

2. One output data value correspond to the value we care about (the desired target) in the time step 𝑡: 𝑋𝑡,1

Time Series values Total Patterns Set

𝑋⃗1 𝑋⃗1, 𝑋⃗2, ⋯ , 𝑋⃗𝑘 𝑋𝑘+1,1

𝑋⃗2 𝑋⃗2, 𝑋⃗3, ⋯ , 𝑋⃗𝑘+1 𝑋𝑘+2,1

𝑋⃗3 Form the Patterns Set 𝑋⃗4 𝑋⃗5 ⋮ 𝑋⃗6 𝑋⃗7 ⋮ 𝑋⃗𝑚−2 𝑋⃗𝑚−𝑘−1, 𝑋⃗𝑚−𝑘, ⋯ , 𝑋⃗𝑚−2 𝑋𝑚−1,1 𝑋⃗𝑚−1 𝑋⃗𝑚−𝑘, 𝑋⃗𝑚−𝑘+1, ⋯ , 𝑋⃗𝑚−1 𝑋𝑚,1

Figure 5. Process to create patterns set

By the procedure above, we transform a time series problem into a DLNN problem and can use the method to train DLNN to get the expression of 𝑓(𝑋⃗𝑡−1, 𝑋⃗𝑡−2, ⋯ , 𝑋⃗𝑡−𝑘)

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5. Data & Variables

The demand for properties depends on entities that are willing to buy and are capable of buying the property. Fundamental factors measuring number of entities can be population, number of immigrants, employment rate, number of companies, etc. Furthermore, various demographic statistics contribute to the measurement of population change, such as birth rate, aging rate, average lifespan, population base and demographic structure. In the very short run, these factors have subtle effects on property demand. In the long term, most of them are predictable on demographics. Next, when it comes to willingness to buy, investment demand and purchase wants play important roles. In terms of purchase wants, it is impacted by living concept, social culture, housing policies and rent levels. In terms of the investment demand, future price anticipation, rental income, expected rate of return, inflation rate, liquidity and all kinds of investment risk impact the discounted cash flow of the investment, furthermore affect investors’ decision. At last, purchasing power limits the trade volume. Disposable income measures net amount people can spend, and as loans or mortgage are common ways in financing housing, financial policies such as interest rate and assets debt ratio influence the market notably. What’s more, housing policies on social housing, housing allowances, limited purchase etc. also affect the demand side. Chart 1 illustrates commonly used impact factors of demand by aspects.

Entities Willingness to buy Purchasing power

Population Number of immigrants Employment rate Number of companies Demographic statistics Purchase wants: Living concept Social culture Housing policies Rent levels Investment demand: Future price anticipation Rental income

Expected rate of return Inflation rate Liquidity Investment risk Income Savings Financial policies Housing policies

Chart 1. Factors Affecting Property Demand

The property supply relies mainly on market price, expectation on market, construction costs and building regulations. If the supply of building land is less than it would be without constrains then, other things being equal, land prices would be higher and so do the property price. Peng and Wheaton (1993) concluded that restrictions on land sales had caused higher housing prices in Hong Kong. On the other way, any factor increasing the supply of serviced land would also increase supply of housing capital, eventually reduce housing prices. However, Tse (1999) argued that there was no causality between land supply and housing prices in Hong Kong, that was because the land was added to developers’ land bank and thus property was not built and sold within a reasonably short period of time. Same result was found in UK as Grigson (1986) suggested that modifying land supply could not affect housing prices because supply did not adjust significantly and quickly. All in all, the different conclusions are mainly resulted from the extent to which developers’ land banks act as buffers to the added land supply from the government.

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Data are obtained from Hong Kong Census and Statistic Department and Datastream. Totally 22 leading indicators are collected and periods span from 1982Q1 to 2014Q2. Not all indicators are available for the whole period.

The 10-year government bond yields come from “Thomson Reuters Hong Kong Government Benchmark Bid Yield 10 Years (K$)”. The data is available from 1997 on a daily basis. The yields are adjusted to quarterly basis for further use. The 10-year government bond yields describe the regional macroeconomic situation powerfully. The 3-month Treasury bill rate is published by Hong Kong Monetary Authority (HKMA) and is derived from “Hong Kong Exchange Fund Bill Yield -91 DAY (EP)”. HKMA has established a set of official fixings for exchange fund bills and notes. The fixing for each of the benchmark is calculated by taking the arithmetic mean of the middle 8 quotes from the market makers, after excluding the two highest and the two lowest quotes. The 3-month Treasury bill rate can stand for the short-term market changes to some extent and is available from 1991Q3. Hang Seng Share Price Index tracks performance of the listed companies which derive the majority of their sales revenue from the mainland China. It comprises mainly the Hang Sang China Enterprises Index and the Hang Seng China Affiliated Corporation Index. The index is available from the beginning of the research period and the benchmark is the price in July 1964, by which the index equals to 100.

Money supply M0 is the monetary base that is defined as the sum of the currency in circulation (banknotes and coins) and the balance of the banking system held with the central bank (the reserve balance or the clearing balance). The monetary base comprises certificates of indebtedness (for backing the banknotes issued by the note-issuing banks), coin issued, the balance of the clearing accounts of banks kept with the HKMA, and exchange fund bills and notes. The narrow money calculate the money supply in a conservative way. Money supply M3 refers to the sum of M2 plus customers deposits with restricted licensed banks and deposits taking companies plus negotiable certificates of deposits issued by these institutions held outside the banking sector. And money supply M2 refers to the sum of M1 plus customers savings and time deposits with licensed banks, plus negotiable certificates of deposits issued by licensed banks held outside the banking sector. And money supply M1 refers to the sum of legal tender notes and coins held by the public plus customers demand deposits placed with licensed banks.

The personal disposable income is recorded in US dollar and is available from the beginning of the research period. The personal disposable income represents the total value of personal income after taxes and deductions. It describes the purchasing power efficiently. The private car registration comes from “Hong Kong Private Cars New Registrations” published by Census and Statistics Department. As Krystalogianni et al. (2004) suggested that new car registration performed well in forecasting UK property capital value, this paper includes the number of new registration private cars either. Total vehicle licensed and registered figures refer to end of period position whereas new registration figures refer to registration during the period. The data is available from the start of the research period. The consumer confidence is the confidence index based on the consumer surveys. The Centre for Quality of Life at The Chinese University of Hong Kong conducted the survey quarterly. Residents took part in the survey and answered questions about their financial situation, their perception towards the business environment, the economic

21

outlook, as well as their sentiment over consumption. It is an effective indicator that describes individuals’ expectation towards the economic situation.

The changes in inventories is recorded in current prices and in US dollars. It refers to the value of physical change in the inventories of work-in-progress, raw materials and finished goods held by business enterprises, mainly manufacturers and distributors. It describes goods held by firms to meet temporary or unexpected fluctuation in production or sales, and work-in-progress. The index of industrial production measures the changes in local manufacturing output in real term, for example, changes in volume of local production after discounting the effect of price changes. Producer prices are selling prices (net of any discounts or rebates allowed to buyer, plus any surcharges) received by manufacturers. Transportation and other incidental charges are not included.

Two indicators to employment are prepared for variable selection. One is the employment of total industry sectors, the other one is employment in manufacturing sector only. Figures on employment engaged include individual proprietors, partners and persons having family ties with any of the proprietors or partners and working in the establishment without regular pay. The employment is the fundamental statistics that describes the number of entities in the market.

The expected volume of real estate output is the expected changes in volume of real estate output. The number comes from business surveys and the surveys gather views on short-term business outlook from the senior of about 400 prominent establishments in the major economic sectors. Views collected are limited only to direction of change, but not magnitude of change. In giving views on a quarter-on-quarter comparison, if the variable in question is subject to seasonal changes, respondents are requested to exclude normal seasonal changes when providing their expectations. Results of this survey are generally presented in the form of net balance, which is the difference between the percentage choosing up over that choosing down. The net balance, with its appropriate sign, may indicate the direction of the business trend. A positive sign may indicate an upward trend, while a negative sign may indicate a downward trend. However, the magnitude of the net balance reflects only the prevalence of relative optimism or pessimism about the near future, but not that the variable would go up/down in magnitude to that extent, as the magnitudes of expected changes are not collected in the survey. The data is available from 2008Q1. The labour cost index used in this paper is the relative unit labour costs published by Oxford Economics. The data is available from 1980Q1 and takes the value in 2008 as the basis. The private property yield is the property market yield. Class C stands for properties with saleable area of 70m2 _{to 99.9 m}2_,

which is the span the average living area of Hong Kong residences drops in.

Retail sales are primarily intended to measure the sale receipts of goods sold by local retail establishments, for gauging the short-term business performance of the local retail sector. It covers consumer spending on goods, but not on services. Moreover, they include spending on goods by visitors in Hong Kong but not by Hong Kong residents outside Hong Kong. Total loans refer to loans that have direct impact on the level of economic activity in Hong Kong. This is usually determined whether the loan is made available or disbursed in Hong Kong, and by the principal business location of the customer. An institution authorized under the Banking Ordinance to carry on the business of taking deposits. Hong Kong maintains a Three-tier Banking System, which comprises

22

banks, restricted license banks and deposit-taking companies. New mortgage loan approved are mortgage loans approved during the surveyed month. Residential mortgage loans are loans (including refinancing loans) to private individuals for the purchase of residential properties, including uncompleted units, but other than those properties under the Home Ownership Scheme, Private Sector Participation Scheme and Tenants Purchase Scheme. Mortgage loans to corporate clients are excluded. The authorized institutions participating in this survey accounted for over 95% of the total residential mortgage lending business. There is a break in data series at December 2000 due to an increase in the number of surveyed institutions. The financial deficit is the Hong Kong government financial deficit from the government balance. Table 3 summarizes fundamental statistics of variables.

Table 3. Summary of Statistics

Variable Obs. Mean Std. Dev. Min Max

Price ($/m2_{) 128 48848 34252 5378 132064}

Rent ($/m2_{) 128 180 69 62 318}

10-year Government Bond Yields (%) 70 4.43 2.28 0.65 10.40

3-month Treasury Bill Rate (%)* _{91 2.84 2.35 -0.08 9.26}

Hang Seng Share Price Index 129 10806 7423 758 27813

Money Supply M0 (Million$) 67 155616 66209 79140 313879

Money Supply M3 (Million$) 67 5190781 2026179 2871178 10100000

Personal Disposable Income (Million$) 130 188630 92353 35040 412303

Private Car Registration 128 6890 2554 1438 12719

Consumer Confidence 56 89 17 50 116

Changes in Inventories (Billion$) 128 2 5 -10 25

Industrial Production – Manufacturing 128 125 28 79 174

Employment - Manufacturing 128 418541 303864 103350 922400

Employment - Exclude Civil Service 128 2289571 191180 1894692 2727884

Expected Volume of Real Estate Output (%) 25 10.92 15.85 -20.00 47.00

Labour Costs Index 130 100 56 0 200

Private Property Yield - Class C (%) 60 3.89 0.89 2.60 5.50

Retail Sales (Million $) 128 48794 26775 12238 129270

Loan - Total (Million $) 128 2506844 1488633 274045 6457345

New Mortgage Loan Approved (Million $) 84 45219 24030 15817 112656

Financial Deficit (Million $) 60 33128 23616 -25953 89673

Credit to Private Non-financial Sectors (Billion $) 127 1913 1295 210 5485 * The 3-month Treasury bill rate is in US dollar.

To make the coefficients more comparable, all variables except those with negative values are transformed by taking logs and hence into quarterly growth at the first step. Then Augmented Dickey-Fuller unit-root test (ADF) with constant and trend term is used in testing series’ stationary. Accordingly, the test model can be written as

23 where 𝑝 = 0, 1, 2, …

To make sure all series are stationary in regression, first difference is taken if the series is not I(0). Furthermore, the results indicate all series are I(0) or I(1). The reason for not using integration test here is that the regression is based on probit model rather than linear regression of time series.

6. Estimated Models

6.1 Univariate Probits

The univariate probit models are

𝐸 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑟𝑖𝑠𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for

𝑃𝑟(𝐸 = 1|𝑥) = 𝐹(𝛽0+ 𝛽1𝑥) where 𝐹(𝒙)is the probit function for ascending scenario. And

𝑃 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑑𝑒𝑐𝑙𝑖𝑛𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for

𝑃𝑟(𝑃 = 1|𝑥) = 𝐺(𝛾0+ 𝛾1𝑥) where 𝐺(𝒙) is the probit function for descending scenario.

I make univariate regressions on the status of property price. To select optimal variables used in multivariate models, different lags, from 1 to 24 periods, of individual indicator are tested first. Whether the indicator enters the multivariate model is determined by the p-value, which should be less than 0.05, and likelihood ratio test statistic, which should be less than 0.05, in the univariate model. The optimal lag of an indicator is determined by maximizing the McFadden pseudo R2 _{in the}

univariate model. With these criteria, 4 and 5 indicators are dropped in model for ascending scenario and descending scenario respectively. Table 4 and Table 5 present indicators reserved and lags used in later regressions.

In the model simulating rising scenario, 10-year government bond yields, industrial production from manufacturing and the difference for yield of class C property generate significantly negative coefficients. A lower yield of 10-year government bond is always concomitant with an added amount of bonds sold from monetary authority to public, which on the other way equals to purchasing currency from the market. Hence this can dwindle investment on property and need for property followed by a drop in property price. The negative coefficient of difference for private

24

property yield is economic meaningful for that a lower yield stands for safer investment and higher growth in cash inflow, resulting in a higher property value. As the most descriptive indicator among individual regressors, the lagged difference for yield of class C property indicates the momentum of property investment to some extent. Nevertheless, the relation between industrial production from manufacturing and property price is not doubtlessly clear. One way to interpret their negative correlation can be that the more industrial production output from manufacturing five years ago, the more available of raw material afterwards and the more supply of new houses at last. This logic can be verified by the positive coefficient of labour cost index to some extent on grounds that higher labour costs can result in higher construction costs and then higher price. Both industrial production and labour costs affect the price from the construction. However the effect of raw materials is interacted with too many other factors, so we cannot conclude this interpretation suits the fact best.

Table 4. Result of Univariate Probit Model for Ascending Price Model

No. Indicator Lag number Coefficient P-value Pseudo R2

1 ∆Private Property Yield - Class C 1 -21.47 0 0.2476

2 ∆New Mortgage Loan Approved 1 2.14 0 0.1314

3 Industrial Production - Manufacturing 21 -2.10 0.001 0.0789

4 ∆Loan -Total 1 9.66 0.001 0.0742

5 ∆Credit to Private Non-financial Sectors 1 11.62 0.002 0.0574

6 ∆Labour Costs Index 13 2.63 0.003 0.0667

7 ∆Rent 11 8.09 0.003 0.0641

8 Changes in Inventories 5 0.07 0.004 0.055

9 ∆Hang Seng Share Price Index 2 2.31 0.004 0.0496

10 ∆Private Car Registration 1 1.86 0.005 0.0495

11 ∆Retail Sales 2 6.36 0.005 0.0469

12 ∆Money Supply M3 2 22.75 0.006 0.0969

13 ∆Consumer Confidence 2 4.43 0.011 0.1051

14 ∆Employment - Manufacturing 17 11.60 0.013 0.0422

15 10-year Government Bond Yields 7 -0.87 0.018 0.0714

16 ∆Personal Disposable Income 3 22.75 0.028 0.0283

17 ∆Employment –Exclude Civil Service 20 20.29 0.045 0.0284

When it comes to subdued market, number of private new car registration, personal disposable income and total employment excluding civil service do not have significant effects on price trend anymore. This result implies that the demand for property has fewer effects on property price during the bear market than in a bull market and this phenomenon can be explained by excessive demand in most cases. And real estate, especially real estate in a developing economy does belong to goods for which the demand surpasses the supply in most circumstances. In Hong Kong, the housing space per capita is only 15 square meter in 2013, which is lower than in most Asian cities. What’s more, factors related to macroeconomic policy including total loan amount, 10-year government bond yields and credit to non-financial sectors tend to affect the downward trend more

25

significantly compared to the upward model. The asymmetry between models can be ascribed to that real estate price is sensitive to financial contraction induced by government policy. Indicators that generate significantly positive coefficient in the model simulating rising trend are 10-year government bond yields, industrial production from manufacturing and difference for yield of class C property, which are exactly the opposite to the outcomes from the rising model. It is also worth pointing out that the stock market does not dent the real estate market as much as expectation when it comes close to a turning point or is in a subdued trend.

Table 5. Result of Univariate Probit Model for Descending Price Model

No. Indicator Lag number Coefficient P-value Pseudo R2

1 ∆Loan - Total 8 -16.34 0 0.1892

2 Industrial Production - Manufacturing 22 3.08 0 0.1506

3 10-year Government Bond Yields 9 1.84 0.001 0.219

4 ∆Credit to Private Non-financial Sectors 2 -15.42 0.002 0.0957

5 Changes in Inventories 5 -0.10 0.003 0.0905

6 ∆Employment - Manufacturing 20 -16.64 0.005 0.0857

7 ∆Rent 2 -7.74 0.005 0.069

8 ∆Labour Cost Index 18 -3.38 0.011 0.0821

9 Financial Deficit 6 -0.00 0.012 0.1590

10 ∆Money Supply M0 10 -18.78 0.013 0.1112

11 ∆Money Supply M3 3 -21.74 0.013 0.0922

12 ∆New Mortgage Loan Approved 1 -1.47 0.017 0.0699

13 ∆Retail Sales 1 -6.27 0.018 0.048

14 ∆Consumer Confidence 7 -4.74 0.027 0.1553

15 ∆Private Property Yield - Class C 12 18.67 0.028 0.1912

16 ∆Hang Seng Share Price Index 1 -1.76 0.041 0.0341

6.2 Multivariate Probits

In this part the paper comes to how combination of leading indicators explains the price trend. There are three criteria in the procedure of variable selection for the multivariate model: (1) all coefficients participating in the model are statistically significant at 10% significance level; (2) minimizing the value of AIC (Akaike Information Criterion) and BIC (Bayesian Information

Criterion); (3) maximizing the value of McFadden pseudo R2_{. Again multivariate probit models are}

formed as

𝐸 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑟𝑖𝑠𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for

𝑃𝑟(𝐸 = 1|𝑥) = 𝐹(𝛽0+ 𝛽1𝑥1+ ⋯ + 𝛽𝑘𝑥𝑘)

26 And 𝑃 = {1, 𝑖𝑓 𝑥 𝑖𝑠 𝑖𝑛 𝑎 𝑑𝑒𝑐𝑙𝑖𝑛𝑖𝑛𝑔 𝑡𝑟𝑒𝑛𝑑 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 for 𝑃𝑟(𝑃 = 1|𝑥) = 𝐺(𝛾0+ 𝛾1𝑥1+ ⋯ + 𝛾𝑘𝑥𝑘)

where 𝐺(𝑿′𝜷) is the probit function for declining scenario. 6.2.1 Ascending Price Model (APM)

There are different ways in selecting well performed indicators to form the best performed multivariate probit model. Three different but similar methods, namely model I to III, are on trial to help figure out the best performed model under the three criteria mentioned above. Model I is generated by straightly forward selection method, by which the most significant indicator enters the model first and then less significant ones are added and kept or dropped while stipulating all indicators entered are significant at 10% significant level. Model II is generated by stepwise forward selection in STATA, by which a model of the dependent variable on nothing is fitted first; then independent variable is considered to be added one by one; at last the most significant term is found out and is added if its significance level is less than 10%. The process would continue until no consistent term exits. Model III is generated by stepwise backward selection in STATA, by which a model of the dependent variable on all indicators is fitted first; then independent variable is considered to be dropped one after one; at last the least significant term is found and is removed if its significance level is greater than or equal to 10%. Similarly, the process would continue until no consistent term exits. Besides, likelihood-ratio test instead of Wald test is performed for models applying stepwise selection method.

Table 6 shows the result from three models. Model II is considered performing best with the

highest pseudo R2 _{of 0.5317 and reasonable AIC value as well as BIC value. As we can see only 5}

indicators enter the final model among 17 indicators from univariate probit models. As has been expected, the difference for new mortgage loan approved is significantly positive in all three models, which demonstrates evident effects of mortgage from the demand side. Armed with coefficients for M3 money supply and lagged value of overall employment, the model embodies macroeconomic condition well both in short and long run. Number of private car registration deserves the nomination for price prediction amid all indicators in terms of its optimal time lag. Furthermore, rent tends to influence the property price in the long-term with its lag of almost three years. Notwithstanding, the long-term indicators are equally important for that economic cycle is composed by long-term cycles and short-term cycles, none of which can be neglected though the investment scope is always limited to a short period. It is worth pointing out Model II is considered as the final model even though Model III performs better in prediction with a correctly predicted fraction of 89%. That is because the samples which can be used to test accuracy are relatively limited, which have 64 time periods for Model II and III. Thus a fault in prediction matters a lot to