Theory for Real Estate Valuation

Although people often talk as if theory and practice are different things, as in “that is only theoretical,” nothing is more practical than a good theory. Theory helps make sense of complex situations by directing attention to key issues and by guiding methods of analysis. This paper presents an updating of valuation theory and the methodological implications flowing from this theory. The central idea is that instead of teaching based around three approaches to value we should base teaching on concepts of price distributions, pricing models and prediction error analysis. This grounds real estate valuation more firmly in modern economics and finance theory and statistical methods as they have developed in recent academic literature. Outline of the argument In an American Economic Review paper, Peter Kennedy complained that after their first econometrics course students can often use formulas to get answers, but lack understanding needed for practical applications (Kennedy, 1998). Kennedy uses the term “constructivism,” meaning that people construct a version of reality that helps guide their thinking and even perception. The same “facts” can be understood in various ways. He suggests that our constructions of reality act like a “lens” to focus thinking. Most students do not think statistically and never acquire a construction of econometrics that enables them to understand how it works and to interpret the meaning of results. Kennedy suggests sampling distribution as the key construct that can focus thinking correctly. Other key concepts are probability distributions and estimators. He recommends that teachers of econometrics reallocate time to “We need to be able to measure how close the sample mean is likely to be to the population mean. The sampling distribution...plays a key role in statistics, because the measure of proximity it provides is the key to statistical inference.” (p. 289) Keller and Warrack, Statistics 4th Ed. . 2 A probability distribution can be represented by a graph with the value of a variable on the x axis—for example a property price—and a probability density function on the y axis. Area under the curve shows probability of a value between any two prices. 3 Estimators are sample statistics used to estimate values of population parameters such as the mean or standard deviation. Desirable properties of estimators are that they be unbiased and consistent (that is, they approach the population value as sample size increases). teaching students these key ideas. This paper applies Kennedy’s recommendations to property valuation. The profession of real estate valuers arises because each real estate asset is different from all other properties. Real estate assets are heterogeneous, that is, their characteristics vary. Researchers and practitioners have found that hundreds of factors might affect prices in various situations. Moreover, properties trade infrequently, perhaps once every 5-10 years for the average house. The amount of sales evidence varies widely in particular cases, but generally there are few sales of properties similar enough to be considered “comparable” and none of identical properties. So instead of looking up prices in the financial press, as one would do with a share or commodity price, people interested in prices of particular property assets consult valuers who collect and interpret recent sales evidence in order to arrive at a price estimate based on interpretation of differences between properties. The market has the same problem as the valuer—how to discover prices of heterogeneous assets where there are few similar transactions and many property characteristics that influence prices? For any individual property at a particular point in time, different prices are possible due to different circumstances of sale, differing buyer preferences, different buyer information sets or other factors. We may call this variation “random error” because we don’t know its causes. This means that the observed prices used by valuers to infer value of a subject property by sales comparison include random variation. Po, the observed price, is equal to Pμ+ε, the mean of the possible price distribution, plus a random error. We do not know Pμ or ε, we only know Po, the transaction price we observe. Heterogeneity requires valuers to develop models of price differences. Instead of P(t)=P(t-1), where price of the subject property equals recent transaction prices, valuers have to use Psubject(t)=Pcomparable(t-1)+differences. “Differences” means the price implications, positive or negative, of the differences in hedonic characteristics between the properties. This “sales comparison price differences” regression model is mathematically equivalent to the “adjustment grid” used by American valuers (Colwell, Cannaday & Wu, 1983). Modelling price differences due to differing characteristics stems from Kevin Lancaster’s notion that utility and the price people pay for complex commodities like housing or automobiles is a sum of the utility of various characteristics (Lancaster, 1966, Rosen, 1974). Valuer’s tasks therefore include: a) Choosing which sales are best to use to infer price of a particular property. b) Identifying price-affecting characteristics that differ between sales and subject property. c) Estimating the dollar value of these differences for each pair-wise comparison of subject and sale. 4 In a review of a sample of hedonic regression papers, we discovered that literally hundreds of variables have been found to be statistically significant price predictors (Kummerow and Watkins, work in progress). 5 Examples: “Gold is trading at $325 per ounce,” or “BHP shares closed at $9.90.”