Luckiness in Singapore Condo Prices: Number Superstitions (Part 5)

6 Discussion and Future Research This paper’s theory section began with a question on rationality. Is it irrational to pay for one’s superstitious beliefs? Economics is not equipped to make a judgment about the rationality of superstition itself, but it can judge the rationality of a decision to act on that superstition. In Singapore, according to this paper, a person pays an additional $4,156 for a lucky number and discounts unlucky numbers by $14,745. For a person who does believe in lucky numbers, the decision to pay extra for a condominium unit numbered 6 or 8 is rational, as long as this choice maximizes his utility. But what about the person who does not believe in lucky or unlucky numbers, but chooses to act as if he does—to give one example, a nonChinese buyer who chooses to factor in Chinese superstition into his purchasing decisions? At first glance, this might appear irrational. But it might be rational in period 0 for this nonsuperstitious buyer to not take advantage of the unlucky-number discount if he believes that he faces a market of predominantly Chinese buyers who are superstitious in period 1, or if his future buyer will, in turn, act superstitiously because of his beliefs about superstitious buyers in period 2, and so on. This is not a stretch, given that the current market is exhibiting a preference for lucky unit numbers and a marked avoidance of unlucky unit numbers. Thus a seemingly irrational phenomenon could emerge—a market reflecting the superstitious behavior of non-superstitious actors—even if each individual is himself behaving in a rational manner. 44 Survival model analysis might be a way of illuminating the decision making process of market participants. If developers do not take superstition into account during their initial pricing decisions, do lucky-numbered units sell quicker than unlucky-numbered units? And do lucky-numbered units tend to be resold sooner than unlucky-numbered units after the initial sale, indicating that lucky-numbered units are more likely purchased for speculation, while unlucky-numbered units are more likely intended as the buyer’s actual residence? This would accord with the hypothesis that superstitious behavior is driven by beliefs about other peoples’ superstitions—since other people’s perceptions become more important in a speculative purchase—while the more tangible benefits of a unit (like square footage) become more important if one is to live in it. Another area for future research is the income elasticity question. While the results here hint that luckiness is a luxury good whose price increases disproportionately with income, the results could be much more conclusive with better income data. The original justification for more superstitious behavior among lower income populations was education—but education level would vary less among people who can all afford to live in private housing. It would therefore be interesting to include population segments living in government housing for which unit number data is currently unavailable. This examination of number superstition is only part of the broader question of how people respond to the nature of numbers. Other studies have shown how people exhibit preferences for round numbers over other integers and for even numbers over odd numbers. Those considerations are beyond the scope of this paper, but, taken together, studies such as these challenge the current concept of how people make decisions, and the factors that affect utility maximization. 45 7 Appendix I. Background Information: Singapore Real Estate Market Figure I Asian Financial Crisis Condominium Price Index, Base 1Q1996 120 Construction of the first 2 casinos in Singapore announced, sparking off real estate boom 100 80 60 40 1Q96 1Q97 1Q98 1Q99 1Q00 1Q01 1Q02 1Q03 1Q04 1Q05 1Q06 1Q07 Source: Urban Redevelopment Authority of Singapore Glossary Condominium: Condominiums are apartment buildings with access to facilities, which generally include parking lots, swimming pools, tennis courts and children’s playgrounds. They are at least four storeys tall. Condominiums are distinct from apartment buildings, which have no access to facilities. District: Singapore’s district organization (and postal code system) has changed over the years. The district system used in this data set follows the old four-digit postal code system. However, the real estate industry still uses this system to classify buildings; classified ads in the newspaper usually note the buildings’ districts. Most people in Singapore have a general idea of which residential districts are more or less desirable relative to the others. Freehold: Residential buildings with freehold ownership rights are owned forever once bought. Leasehold: Residential buildings with leasehold ownership rights have leases that are 99 years long. Developers who wish to build on land designated as leasehold must purchase the lease before they begin building, so buildings’ leases have generally depreciated several years before residents first move into a new building. However, developers have the option of making payments to top up a lease to the full 99 years, which is why leasehold buildings in Singapore generally have at least 80 years remaining on their leases. 46 TOP: Temporary Occupation Permit. Buildings must file a TOP with the Singapore Land Authority before they can be legally occupied, so building ages are generally calculated from the date that a TOP is filed. II. Income Proxy Methods Method Process Advantages Disadvantages Price Cutoffs Method Data divided into four categories by transaction price: low income, lower middle income, upper middle income, high income. Accounts for changes in desirability of buildings and units over time. Not a precise enough measure. May create selection bias and produce biased coefficient estimates. Ranked Districts Method Average transaction price for each district calculated, and districts ranked in order of its average transaction price. Rankings are similar to the generally perceived relative desirability of districts in Singapore. Not a precise enough measure. Static; does not take into account changes over time. Income information Method Calculates average income of district from district-level data from Singapore Population Census 2000, which groups income levels by increments of 1,000 and gives the number of people in each district who fall within each group. Regression is performed with each observation receiving the average income of its district. Uses real income data rather than price as a proxy. District definitions in the census differ from definitions in the real estate data; no average income can be calculated for 8 of the districts (about 10% of observations). III. List of Models Used Model Description 1 Linear regression of price on area, floor, height, (D)top floors, building age, transaction age, (D)freeholdyn, years left in lease, (D)lucky floor, (D)unlucky floor, (D)lucky unit, (D)unlucky unit 2 SEE MODEL 1; with income dummies according to ranked districts method 3 SEE MODEL 1; with income dummies according to price cutoffs method 4 SEE MODEL 1; with income from income information method 47 5 Quadratic regression of price on area, area2 , floor, floor2, height, height2, (D)top floors, building age, building age2,transaction age, transaction age2, (D)freeholdyn, years left in lease, years left in lease2, (D)lucky floor, (D)unlucky floor, (D)lucky unit, (D)unlucky unit 6 SEE MODEL 5; with income dummies according to ranked districts method 7 SEE MODEL 5; with income dummies according to price cutoffs method 8 SEE MODEL 5; with income from income information method 9 Fixed effects regression of price on area, area2 , floor, floor2, height, height2, (D)top floors, building age, building age2,transaction age, transaction age2, (D)freeholdyn, years left in lease, years left in lease2, (D) unit dummy variables 1-8 (9 is base case), (D) floor dummy variables 1-9 (0 is base case) 10 SEE MODEL 9; with income dummies according to ranked districts method 11 SEE MODEL 9; with income dummies according to price cutoffs method 12 SEE MODEL 9; with income from income information method 13 Fixed effects regression of price on area, area2 , floor, floor2, height, height2, (D)top floors, building age, building age2,transaction age, transaction age2, (D)freeholdyn, years left in lease, years left in lease2, (D) unit dummy variables 1-8 (9 is base case), (D) floor dummy variables 1-9 (0 is base case), (D) Special unit combinations 44, 66, 68, 86, 88, 99, 04-04, 06-06, 06-08, 08-06, 08-08, 0909 14 SEE MODEL 13; with income dummies according to ranked districts method 15 SEE MODEL 13; with income dummies according to price cutoffs method 16 SEE MODEL 13; with income from income information method 17A Fixed effects regression of price on area, area2 , floor, floor2, height, height2, (D)top floors, building age, building age2,transaction age, transaction age2, (D)freeholdyn, years left in lease, years left in lease2, (D) lucky floor, (D) unlucky floor, (D) lucky unit, (D) unlucky unit, with income dummies according to ranked districts method 17B SEE MODEL 17A; with log price as the dependent variable 17C SEE MODEL 17A; on a subset of the data with only condominium buildings that had more than five units per floor 17D SEE MODEL 17D; with log price as the dependent variable 18 SEE MODEL 17A; without income controls 19 SEE MODEL 17A; with income dummies according to price cutoffs method 20 SEE MODEL 17A; with income from income information method IV. Results Table for Income Elasticity Results PRICE 1 3 LOGPRICE luckyunitdum unluckyunitdum -32619.14 -133223.4 0.163 0 -1786.811 -18867.37 ** ** 48 luckyunitdum unluckyunitdum -0.0172041 -0.0734812 0.0140501 0.0179972 -0.0023591 -0.0358353 *** *** 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 26 27 28 0.757 0.011 17361.1 -45972.72 0.338 0.033 0.0077995 0.0092826 -2099.233 0.0074067 -0.0018098 7932.519 * 0.092 0.721 -11588.21 33021.2 0.042 0 43841.09 *** 0 12912.96 ** -22319.22 * -52322.4 0.005956 0.0089488 -0.001036 0.0044603 *** 0.0146394 0.0055774 ** 0.0058605 *** 0.002 0.185 15441.3 -33774.65 ** 0.0046468 0.0351174 0.0293759 *** -0.0039504 0.005039 0.0057817 ** -0.0048721 -0.002723 0.004955 0.0049366 *** 0.0068165 -0.0263061 0.0056411 0.0063351 0.022 0.068 0 -8410.953 -35434.03 0.0157864 -0.0433357 0.377 0.007 0.0110519 0.0152018 -29339.48 -41600.25 -0.017993 -0.0507904 0.158 0.111 0.0145406 0.0182558 9363.139 57.40445 0.0129336 0.033 0.992 0.0055247 0.0068419 -2988.565 -15157.7 0.0019831 -0.0201494 0.59 0.014 0.0038513 0.004287 4680.968 5863.43 0.0142032 0.226 0.174 0.0035267 11994.25 ** *** ** -8649.231 ** *** 0.0113954 ** *** 0.0112237 * -0.0206609 0.0058948 0.0066604 150.6657 -16555.7 0.0016076 -0.0200075 0.963 0 0.0039662 0.0044259 214.6339 -6202.867 0.003084 -0.0093826 0.956 0.185 0.0039081 0.0047307 20245.57 * 0.0114615 ** -0.0241612 0.022 0.065 0.0049221 0.0061255 -5702.338 -9510.899 -0.0040755 -0.0078367 0.353 0.169 0.0048155 0.0054168 381.567 -6787.195 -0.0042964 -0.0088409 0.95 0.346 0.0064437 0.0076845 -224.3542 -11320.81 0.0030057 -0.0190117 0.922 0 0.0026201 0.0032493 -5488.948 4174.426 -0.0058282 0.0036372 0.143 0.401 0.005445 0.0072253 -10222.53 16767.18 0.001442 0.0273422 0.339 0.114 0.0139312 0.0138298 475.3766 9609.116 -0.0003137 0.0136263 0.901 0.05 0.0050979 0.006569 2268.202 -2255.702 0.0000827 -0.0144799 0.749 0.781 0.0090276 0.0103433 *** ** 49 *** *** *** *** 0.0039344 0.121 ** *** 0.0015245 0.015 -20300.78 *** 0.0072759 *** *** ** *** *** ** ** 8 Works Consulted Bartik, T. 1987. “The Estimation of Demand Parameters in Hedonic Price Models.” The Journal of Political Economy, 95(1), pp. 81-88. Bourassa, S. and Peng, V. 1999. “Hedonic Prices and House Numbers: The Influence of Feng Shui.” International Real Estate Review, 2(1), pp. 79-93. Brown, P., Chua, A. and Mitchell, J. 2002. “The Influence of Cultural Factors on Price Clustering: Evidence from Asia-Pacific Stock Markets.” Pacific-Basin Finance Journal, 10(3), pp. 307-32 Chau, K.; Ma, V.; Ho and Daniel C. 2001. “The Pricing of 'Luckiness' in the Apartment Market.” Journal of Real Estate Literature, 9(1), pp. 31-40 Choy, L., Mak, S., and Ho, W. 2007. “Modeling Hong Kong Real Estate Prices.” Journal of Housing and the Built Environment, 22, pp. 359-368. Epple, D. 1987. “Hedonic Prices and Implicit Markets: Estimating Demand and Supply Functions for Differentiated Products.” The Journal of Political Economy, 95(1), pp. 59-80. Fan, G., Ong, S. and Koh, H. 2006. “Determinants of House Price: A Decision Tree Approach.” Urban Studies, 43(12), pp. 2301-15 Haurin, Donald R. 1988. “The Duration of Marketing Time of Residential Housing.” American Real Estate and Urban Economics Association Journal, 16(4), pp. 396-410 Hwang, M. and Quigley, J. 2002. “Price Discovery in Time and Space: The Course of Condominium Prices in Singapore.” Working Paper. Version March 22, 2002. Institute of Business and Economic Research, Department of Economics; UCB. Kendall, M. and Smith, B. 1939. “Randomness and Random Sampling Numbers.” Journal of the Royal Statistical Society, 6(51), pp. 51. Rosen, S. 1974. “Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition.” The Journal of Political Economy, 82(1), pp. 34-55. Wolverton, M. 1997. “Empirical Study of the Relationship between Residential Lot Price, Size and View.” Journal of Property Valuation and Investment, 15(1), pp. 48-57. Woo, C. and Kwok, R. 1994. “Vanity, Superstition and Auction Price.” Economics Letters, 44(4), pp. 389-95 50