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Weekly Updates3.3. The Singapore test study
Firstly, the variables used in the model have to be defined. The state space model, is built around two major variables, which are the URA Office Capital Index (UOCV) and the Synthetic Office Land Price Index (LPI), as in,
[Y.sub.t] [equivalent to] URA Office Capital Value Index at time period t
[equivalent to] UOCV, (dependent variable)
and [X.sub.t] [equivalent to] Synthetic Office Land Price Index at time period t
[equivalent to] LPI (independent variable)
Then, the following observation equation and a state equation can be expressed.
Observation equation:
UOC[V.sub.(t)] = [C.sub.1] + [[beta].sub.1] x LP[I.sub.(t)] + [[beta].sub.2] (1)
State equation:
[[beta].sub.1(t)] = [[beta].sub.1(t-1)] + [v.sub.(t)] (2)
[[beta].sub.2(t)] = [C.sub.3] x [[beta].sub.2(t-1)] + {Var = Exp([C.sub.2])} (3)
where: [C.sub.1], [C.sub.2], [C.sub.3] [equivalent to] fixed parameters; [[beta].sub.2] [equivalent to] disturbance term; [v.sub.(t)] [equivalent to] disturbance term at time t.
The slope coefficient follows an unrestricted first-order autoregressive generation process, or a lagging structure of 1 period (1 year).
The Singapore study covers the prime office sector in Singapore's Central Business District (CBD), utilizing the Jones Lang LaSalle Real Estate Intelligence Service-Asia (JLL REIS-Asia) dataset. The dataset comprises the prime office rents and CVs for thirty Grade A buildings in the three main CBD areas--the Raffles Place, Shenton Way and the Marina Centre CBD areas. The dataset period of some thirteen years spans from 1990 to 2002. This paper also utilizes the URA office rental and CV indices, the most widely used indicators of real estate prices in Singapore, and are obtained from the URA Real Estate Information System (REALIS) database.
3.4. Empirical findings of Singapore test study
With the assistance of the EViews software, results obtained from the state space model and Kalman filter for the Singapore study is illustrated in Table 2, and Figure 1 shows the deviation of the de-lagged UOCV from the observed UOCV
[FIGURE 1 OMITTED]
It can be observed that there is a lagging problem of about 1 year for the UOCV in Singapore. The observed UOCV is higher than the de-lagged UOCV most of the time. The opposite happened right around the time when the Asian Financial Crisis took place, and the most recent two years of the studied period. In a sense, the observed (lagged) UOCV tends to overstate the "true" value, except when the economy is going down.
4. THE HONG KONG STUDY
The Hong Kong study focuses on the price discovery of Class A office only. Yearly data from 1990 to 2002 are gathered from the Census & Statistics Department, Rating and Valuation Department (RVD), and HSBC (best lending rate).
The Office Price Index (OPI), conducted by RVD, is primarily transaction-based, buit the information for controlling quality constant is partially valuation-based. Index construction is based of Actual price data (price per saleable floor area) in the Agreement for Sale and Purchase (ASP) of transacted properties in each sub-sector (by property types) (Chau et al., 2005). In short, it is possible for lags to exist in the valuation process of OPI.
However, a trial test on Hong Kong's OPI indicates that LPI is somehow not a significant indicator in explaining price index movements (Table 3). Moreover, it is believed that negative OPI figures could be generated, given the small constant term ([C. sub.1]) and a large negative noise term ([[beta].sub.2]), which renders some very questionable outcomes. Due to the use of yearly data, one may question whether it is the data itself, or the model, that leads to this problem.
As a result, we move to the second stage of the methodology as a multi-variable approach is deployed for the Hong Kong case study, which involves some other market fundamentals as well in capturing Hong Kong's office price adjustments. Under the same background methodology of a State Space Model, the observation equation is as follows:
Observation equation:
OP[I.sub.(t)] = [C.sub.1] + [[beta].sub.1] x [cpicomposite.sub.(t)] + [[beta].sub.2] x [gdpgrowth.sub.(t)] + [[beta].sub.3] x [yieldrate.sub.(t)] + [[beta].sub.4] x [bestlendingrate.sub.(t)] + [[beta].sub.5] x [unemployment.sub.(t)] + [[beta].sub.6] (4)
State equations:
[[beta].sub.1(t)] = [[beta].sub.1(t-1)] + [v.sub.(t)] (5)
[[beta].sub.2(t)] = [[beta].sub.2(t-1)] + [u.sub.(t)] (6)
[[beta].sub.3(t)] = [[beta].sub.3(t-1)] + [s.sub.(t)] (7)
[[beta].sub.4(t)] = [[beta].sub.4(t-1)] + [v.sub.(t)] (8)
[[beta].sub.5(t)] = [[beta].sub.5(t-1)] + [v.sub.(t)] (9)
[[beta].sub.6(t)] = [C.sub.3] x [[beta].sub.6(t-1)] + {Var = Exp([C.sub.2])} (10)
where: [C.sub.1], [C.sub.2] and [C.sub.3] [equivalent to] a fixed parameter/constant term; [m.sub.(t)], [n.sub.(t)], [v.sub.(t)], [u.sub.(t)] and [s.sub.(t)] [equivalent to] disturbance terms at time t.
The inclusion of the GDP growth rate is quite easy to fathom. The movement of GDP is usually viewed as the general performance of an economy. It is reasonable to say that the higher the GDP growth rate, the better perception of an economy. Hong Kong's becoming of one of the four Little Dragons in Asia was the result of comparatively high GDP growth at the time. Under such circumstances, investors, local or foreign, would be more willing to spend money on a variety of businesses which not only offer lots of job opportunities, but also the demand for office spaces. Then, there would have a positive effect on commercial real estate prices and rents. That would cause a certain degree of impact to the yield rates, thus the appraisal-based price indexes. Moreover, this is the same piece of information that the stock market would digest, only more efficiently and faster. Such discrepancy regarding the handling of the same information is where the controversy concerning appraisal-based index commences.
As far as the CPI growth rate is concerned, one of the basic functions of real estate, as mentioned before, is to be used as a hedge against inflation. This insinuates that a higher inflation rate would likely lead to a higher demand for real estate, either commercial or residential. Also, the effect of inflation may initiatively give us an idea of how well real estate performs, in terms of the yield rate. However, a high yield rate does not necessarily make a real estate investment attractive, as the best lending rate could escalate in inflationary periods, which increases the cost of capital. The less risky savings rate would soar as well, providing a good alternative to real estate investment.
Unemployment situation in a sense gives decision-makers a closer look at the economic situation in a place, aside from GDP movements. An improving GDP may reflect a positive perspective about an economy, but such improvement may not benefit the people at all. Unemployment insinuates the loss of a stable source of income for individuals, which would make them more cautious on the consumption of goods and services. This would impede the economic development in years to come, thus affecting the expected profit level that businesses will obtain. This would influence the demand for office space, thus determining its price movement.
4.1. Empirical Findings of Hong Kong case study
Similar to the trial test under the one-index LPI model, something interesting can be found. The results are shown in Table 4.
According to Fu (2002), if the de-lagged price index is indeed more efficient than the original index, greater volatility in the returns, improved cross-correlation with the returns of other indices, and a smaller serial-correlation in returns should be observed. Therefore, it is impossible to conclude anything before comparing the above two indexes with the more market-efficient indices in the stock market. In this case, we use the Hang Seng Property Index in the same period, to find out the cross-correlation between stock market adjustments and office price adjustments. Actually, financial instruments like Real Estate Investment Trust (REIT) is a closer alternative for real estates traded in the stock market. However, there has been no issuance of REIT in Hong Kong until mid-2003. As a result, it is replaced by the Hang Seng Property Index (HSPI). It is viewed that the HSPI is more updated and more efficient, in terms of handling current market information, than the office price index. Data of the HSPI is collected from the DataStream Database, and yearly averages of the HSPI are calculated for comparison. The results are shown in Table 5.
For some reason, the de-lagged index actually is negatively correlated with the Hang Seng Property Index. Worse, negative predicted values are generated, which is nonsensical as the dependent variable in this model is in the form of an index, which can only be positive. This shows that the de-lagged OPI informs us even less about the market when more market information is put into the model, or we are not able to conclude that there is any lagging problem in Hong Kong's OPI during 1990-2002. However, what is the reason behind such discrepancies from the de-lagged OPI? Does it mean there are really no lagging problems on Hong Kong's OPI, or is it something else that induces this unique outcome?
4.2. Findings on the lagging issues of OPI, using quarterly data
Because of such abnormities, we look for an alternative to find out the possible reason behind such discrepancies. This time, quarterly data is used in order to explore the possible lagging problem in the office price index in Hong Kong in the same period of 19902002. An assumption is needed before further discussions, based on the unique situations involving yearly data, which is that the possible lag term in Hong Kong's OPI is less than a year. There is an advantage of using quarterly data over yearly data, which is the ability to locate a closer estimate of the duration of lagging phenomenon in Hong Kong's office price index. Usually, two options can be found with yearly data, either no lag or a first-order lag (1 year). But by using quarterly data, five options can be looked at, which are no lag, 3-month, 6-month, 9-month, and 12-month lag in the OPI. Table 6 illustrates the results generated by the state space model with Kalman filter, and Figure 2 shows the movement of the predicted OPI throughout the study period.
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