The Economics of Luckiness the Impact of Number Superstition on Condominium Prices in Singapore Part 1

The Economics of Luckiness: The Impact of Number Superstition on Condominium Prices in Singapore Submitted to the Department of Economics in partial fulfillment of the requirements for the degree Bachelor of Arts with Honors Contents Introduction 1 Theory 4 Data Summary 9 3.1 Description of the Data 9 3.2 Issues Related to Data 11 Empirical Strategy 16 4.1 Characterization of Key Variables 16 4.2 Main Model Specifications 20 4.3 Secondary Model Specifications 24 Results and Analysis 26 5.1 Baseline Regressions: Linear and Quadratic 26 5.2 Fixed Effects Regressions 31 5.3 Price Variation with Income 41 Discussion and Future Research 44 Appendix 46 There was once a country called Singapore Which was scared of the number four Not all condos are created equal! If you think that, you may be killed In the market, ‘cos four makes you poor. - Michael Badain 2 1 Introduction Economists are said to know the price of everything (and accused of knowing the value of nothing.) What, then, is the price of an unusual good like luckiness? * More specifically, what is the additional price that buyers are willing to pay for a lucky unit number in the apartment market? And, second, is luckiness a luxury good—does an increase in income cause an even larger increase in the price of luckiness? This is not a superficial question. Beliefs about lucky or unlucky numbers have considerable impact on behavior; superstitious Chinese families avoid moving into new houses on days of the month with the number 4; Chinese restaurants charge prices like $888.88 on their banquet menus to bring their customers good luck. Markets outside of real estate have long recognized the impact of numerological superstition in Chinese-dominated cities like Singapore and Hong Kong. Auction markets exist, for example, for lucky license plate numbers, which are taken out of general circulation and which sell for hundreds of thousands of dollars—a license plate with the number 8 commanded US$640,000 in Hong Kong in 1992 (Bourassa and Peng, 1999). 1 Parsing what, exactly, “value” means here is important. Because the value of real estate is already notoriously difficult to determine, using the example of cars and license * All prices are in Singapore dollars unless otherwise stated. Exchange rate as of April 22 2008: SGD 1 = USD 0.74004 1 Another example: in February 2008, the United Arab Emirates auctioned off a license plate bearing nothing but the number 1 for US$14 million. Though Arabic culture may consider 1 to be neutral in terms of luckiness, the example still demonstrates that numbers may themselves command substantial prices that seem to have little to do with the productive value they add to the good to which they are attached. 1 plates may be more instructive. The productive or objective value of a car derives from its primary function—getting its owner to his destination quickly, reliably and comfortably. Its lucky license plate, however, could contribute both objectively and subjectively to the overall utility that the owner derives from the car: subjectively because the owner may just value lucky numbers in and of themselves—a direct contribution—objectively because lucky numbers may improve how well the car performs its function by making the owner feel more confident and drive better—an indirect contribution. Often, a decision is considered rational only when it directly produces objective/productive value. As the theory section of this paper discusses, however, rationality is a much more complicated concept. A quick example: the productive value of a license plate number would change if one considers ostentation to be part of a car’s primary function. Little attempt has been made to capture the marginal willingness to pay for lucky numbers. Yet an analysis of luckiness has interesting welfare implications. Suppose that unlucky numbers are discounted—non-superstitious buyers could boost their welfare by focusing their search on unlucky-numbered condominium units. Also, analyzing lucky number premiums over time may unearth some new real estate indicators. Chau, Ma and Ho (2001) claim to find a correlation between housing bubbles peaks and peaks of lucky number premiums in Hong Kong and suggest that the price of lucky numbers could be used to help forecast turning points in the housing market. Unfortunately, as the data section elaborates, the Singapore real estate market suffered a downturn during most of the period of study, making a similar analysis on the Singapore data difficult. Empirical studies on Chinese number superstition’s impact on real estate prices do exist, like Chau et. al., Choy, Mak and Ho (2007) and Bourassa and Peng (1999). However, these studies generally suffer from three limitations. First, they use limited data—Chau et. al. used transaction records from a single estate development in Hong Kong over two separate 2 three-month periods. Second, the models generally leave the analysis at the floor-number level when a unit-level analysis would be more appropriate. Third, though Chau et. al. claimed that luckiness was a luxury good, these studies’ models merely estimated the observed market price of luckiness, which is, by definition, an equilibrium price. They neglected to break out the supply and demand factors that go into determining that equilibrium price—a supply/demand simultaneity problem highlighted in Rosen (1974) and Bartik (1987) and a necessary step to answering a demand-side question like luckiness’ income elasticity. Nor did they consider that luckiness’ income elasticity might itself be income elastic—might change with different income groups in the population. Perhaps luckiness exhibits more luxury characteristics in poorer populations, which tend to be less educated and more superstitious. Alternatively, luckiness may be a luxury good only in higher-income groups because rich people use lucky numbers as a way to consume conspicuously or because only they can afford to take into account such an intangible concept in their purchasing decisions. This paper has the advantage of much more extensive data, capturing all transactions on condominium units that occurred in Singapore over a 12-year period. The models used in previous studies are adapted to give a clearer idea of luckiness’ impact on price, and the analysis is performed separately on different income groups to investigate how luckiness’ income elasticity might change as income changes. 3 2 Theory and Literature Review Is factoring vanity or cultural beliefs into price-making decisions irrational? Much of the current literature implies that it is. In their analysis of the Hong Kong license plate auction market, for example, Woo and Kwok (1993) consider luckiness to have zero “intrinsic” or objective real value; the price that lucky license plates command, they conclude, is determined entirely by arbitrary consumer preferences. Brown, Chua, and Mitchell (2002) found that Hong Kong stock market prices tend to cluster around lucky numbers, especially during culturally significant and auspicious events like Chinese New Year. In their attempt to explain this phenomenon, they posit that the average person is not entirely rational, acting not with exact precision but within “spheres of considerable haziness” (Von Neumann and Morgenstern, 1953). In other words, the average person has “equivalence intervals” (MacCrimmon and Smith, 1986) in their valuation decisions. People choose lucky prices in the stock market (or, in this paper’s case, are willing to pay extra for lucky numbered apartments) because they don’t know exactly how much the good they’re paying for should cost anyway. But it follows from the “sphere of haziness theory” that imprecise decision making would produce random variations; instead, these authors themselves observe a systematic preference for luckiness. People are in fact actively purchasing lucky numbers. Thus it is sophistical to argue that a lucky number has no objective real value. True, luckiness is an intangible concept—and a lucky unit number might be valued in part because people just 4 happen to like them and derive utility from them. But paying for something that yields utility, regardless of what productive or tangible value one might receive, is not an irrational action. Moreover, a buyer may also consider a lucky unit number important because he would feel happier, and thus experience less stress and improved health. In that case, intangible luckiness would be providing a very tangible benefit, and contribute the condominium unit’s objective value by improving its ability to keep its occupants sheltered and happy. Contrary to layman’s intuition, the objectivity/subjectivity of luckiness’ value, and the tangible or intangible benefits it provides, do not necessarily make a decision to pay for it rational or irrational. First, since real estate is often an investment, resale value must be taken into account. A buyer may discount an unlucky-numbered unit because he believes that it would be more difficult to sell at a later date, as Bourassa and Peng (1999) suggest. Or a buyer may be willing to pay extra for a lucky unit because he believes that he can command an even higher price for it in the future. This is not only logical, but smart. Second, opportunity costs must be taken into account. It would be irrational, for example, to spend money on a lucky unit number even if it improved one’s living experience and increased the utility one derived from that new unit if, as a result, one had to forego a vacation to Hawaii that would have yielded even greater utility. But microeconomics tells us that consumers would simply allocate their income so that the marginal utility derived from their consumption would be equal across all goods. It would be interesting to discern the opportunity cost to individual consumers, and the different kinds of benefits luckiness provides, via empirical analysis. First, however, it is necessary to confirm that consumers are indeed paying for lucky numbers and discounting unlucky numbers. Unlike, say, the market for staples, which are all virtually interchangeable, products in a real estate market—apartment and condominium units and houses—are 5 extremely heterogenous. Court (1939) and Griliches (1971) introduced the idea of hedonic price analysis to estimate the value of such heterogeneous goods. As Rosen (1974) explains, hedonic theory conceives of a good as a bundle of utility-bearing attributes. Applying this analysis in the real estate market means that each unique, differentiated apartment unit can be decomposed into much more generic characteristics for comparison. For example, Case and Quigley (1991) and Mok, Chan and Ho (1995), using the hedonic approach, concluded that size, floor level and quality of view increased price, while Robin (1995) found that price also decreased with age. Specifically, a few papers have used hedonic price analysis to estimate the impact of number superstition on prices in predominantly Chinese markets. In this approach, “lucky number” is simply added to the basic hedonic model as another characteristic. Results were mixed, but, in general, they support the hypothesis that number superstition plays a role in real estate pricing. Chau, Ma and Ho (2001) found that floor numbers ending in the number 8 commanded a statistically significant premium of 2.8% in general and higher during housing boom periods; floor numbers ending in the number 4 transacted at discounts, though the result was statistically insignificant. Choy, Mak and Ho (2007) grouped digits into “Lucky” and “Unlucky” dummy variables according to Chinese tradition and found a statistically significant discount associated with unlucky floor numbers but no premium for lucky floor numbers in Hong Kong. Bourassa and Peng (1999) investigated New Zealand neighborhoods with a high concentration of Chinese residents and discovered that lucky numbers had a positive but statistically insignificant effect, while unlucky numbers had little to no negative impact. Auspicious as these findings are, their papers employ models that could use some refinement. For example, classifying 40% of possible observations (3, 6, 8, and 9 out of the digits 0-9) under a single “Lucky” dummy variable as Bourassa and Peng (1999) did 6 produces a variable that is not particularly informative. The positive variation observed with “Lucky” may be due entirely to the number 8, and the effect may be diluted by possible negative effects associated with the other numbers. They also treated subjective observations (such as quality of roof and wall materials as assessed by a valuer) as objective variables and failed to explain how the subjective observations were determined. In a similar vein, Choy, Mak and Ho (2001) included a “MTR” dummy variable that simply noted if the closest Mass Transit Railway stop was less than or more than ten minutes away from a building—a crude measure where a continuous one might be more informative. Further, the papers make only cursory attempts to relax the assumption that utility-bearing attributes have a linear relationship to price. Chau, Ma and Ho (2001) are the most thorough in relaxing the linear assumption, including squared terms to account for changing marginal effects and interaction variables to consider how the effect of luckiness may itself be affected by boom or bust periods in the market. Most importantly, all of the above papers make little attempt to account for Rosen (1974)’s and Bartik (1987)’s critiques of hedonic regressions, such as the problems of simultaneity and endogeneity, which produce biased results. Woo and Kwok (1993) argue that the supply/demand simultaneity problem is mitigated when production costs are negligible (it costs the same to produce a lucky unit number and a normal or unlucky unit number) because there is no supply curve to speak of. However, even without a supply curve from the developer (the “supplier” or manufacturer of lucky numbers,) there still exists a supply of and demand for lucky numbers, and thus the papers manage to deconstruct only the transaction price of the apartment units—that is, the price at supply/demand equilibrium. No conclusions can be drawn about either the price elasticity or income elasticity of demand for luckiness. Further, the models’ simplicity increases the risk of an endogeneity problem. If a lucky number dummy variable, or one of the other listed explanatory variables correlated 7 with a lucky number dummy variable, is also correlated with an omitted factor captured in the error term, results could be biased. Except for Bourassa and Peng (1999), who use house block number data, the papers focus on the implicit price of a lucky floor number and make only minimal effort to control for the other impacts that a unit’s floor may have on its price. Of course, the factors that can be included in the regression are limited by the data at hand, but refining the models they employ, even with just the available data, could make results more robust. One final theoretical issue must be addressed. Ideally, this paper aims to estimate the income elasticity of lucky numbers; that is, how the percentage change in demand for lucky numbers varies with the percentage change in income. With the data available, however, this paper looks at the effect of income variation through the lens of price—how the price of luckiness may change with different income levels. Note, however, that this is a different concept, again, from price elasticity, which refers to the percentage change in the demand for luckiness as price changes. Here, a large difference in price implies that lucky numbers are relatively income elastic; a small difference that lucky numbers are relatively income inelastic. 8