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Article Excerpt
The present article proposes a multivariate approach to unsmoothing appraisal-based real estate return indexes to recover the true market volatility information in real estate returns. It scrutinizes the role played by errors in variables, in conjunction with an analysis of other economic activities relevant to real estate returns, to exploit the functional relationship and the mechanism of interactions between real estate returns and these economic activities. Appraisal smoothing can therefore be detected and corrected properly and efficiently, without presuming a weakly efficient real estate market. The approach is then applied to U.K. real estate indexes as empirical examples. The results suggest a reasonable volatility in U.K. real estate investment that is close to reality. It is found that the volatility of the true market return on real estate is 1.5404-1.9282 times that of the return on the appraisal-based indexes, in contrast to figures of 2.4862-5.8720 produced by the fully unsmoothing procedure.
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It is well known that appraisal-based real estate return indexes are smoothed (Firstenberg, Ross and Zisler 1988, Geltner 1989, Giliberto 1988). That is, the variance of real estate returns on such indexes does not accurately measure the underlying volatility in that it is incredibly low, relative to most financial market investments. Therefore, unsmoothing appraisal-based real estate indexes, or recovery of true market volatility in real estate returns, is of prime importance to the evaluation of the true performance of real estate.
Smoothing is neither a univariate process, nor simply an inexplicable human behavioral problem. The economic environment in which the real estate market operates influences real estate performance. Therefore, the degree to which a real estate return index is smoothed can be inferred from a joint examination of the economic forces and the activities that have a causal relationship with real estate performance. More specifically, we should look into the economic forces and activities that interact with the return on real estate to recover the true performance of real estate from the distorted information conveyed by a smoothed index. Demand for, and supply of, real estate are among these forces and activities, as well as returns on indirect real estate investment, for example, stock market returns of REITs. Changes in stock under construction also reflect dynamic and joint adjustments of demand and supply to a changing environment. There exist relationships fundamental to the determination of real estate performance between these activities and real estate returns that can be exploited. Nevertheless, caution must be taken to avoid misinterpretation of links resulting from spurious relationships in data.
The true market return on an investment property is not observed until the property is sold. Instead, what is observed is the return that is not precisely the true market return but contains both the information of the true return and the measurement error. The measurement error, as the difference between the true value and the appraised value, inevitably exists as long as the true value is not observed. Random errors in measurement can only result in an increase in variance, while systematic errors in measurement can lead to an increase as well as a decrease in variance. Because what is encountered in real estate appraisals is smoothing, or reduction in variance, the measurement error in appraisals is systematic rather than random. That is, measurement errors, or errors in variables, are systematically related to the appraisal procedure that has smoothed the real estate return series and reduced their variance. There would be no smoothing in a return index if there were no measurement errors in the index. So, the role played by errors in variables is two-pronged. On the one hand, some estimates are biased due to errors in variables, but the degree of bias is not known. Consequently, the bias cannot be corrected. On the other hand, if the bias is systematically induced, we may be able to correct the bias in the estimates if we are able to look beyond the real estate return index itself. The systematically induced bias in the compilation of real estate return indexes may be inferred by further information embedded in real estate--related activities. Such information can be sensibly utilized and a functional relationship between these variables and real estate returns can be prudently exploited to help explain the bias due to errors in variables. Consequently, the degree of smoothing in the real estate return index can be determined. Nevertheless, exploiting the fundamental and functional relationship between real estate returns and related activities is not a simple task, compared with the existing univariate unsmoothing procedures, which provides an explanation of the lack of such studies in this area. It constitutes a serious challenge in our continuous search for solutions to the smoothing problem in real estate returns. The present article endeavors to make a contribution to this important task.
The rest of the article is organized as follows. The next section reviews the extant smoothing/unsmoothing literature in real estate returns, summarizes and comments on the results of previous studies and discusses the implications for the present research. The third section introduces the errors in variables approach to unsmoothing real estate returns. The approach is a multivariate procedure to recover the true market volatility in real estate returns by scrutinizing a fundamental and functional relationship between real estate returns and the related economic activities. Examples applying the proposed approach are shown in the fourth section. The final section concludes this article.
Review of the Smoothing/Unsmoothing Literature and the Implications
The issues arising from using the appraisal-based real estate return indexes in measuring real estate performance have been widely addressed in recent years, with most attention paid to the second moment estimation. Working (1960) was among the first to call attention to the phenomenon of smoothing. It arises from averaging a time series of thinner intervals to get a new one with wider time span, a process of temporal aggregation. There might be several purposes for averaging; most of them are not the topic of this article. Nonetheless, the desire to get more accurate or reliable data has obviously played an important role. Naively, improvements in data accuracy and reliability could be achieved by gathering as many observations as possible for an estimate in one period. Confidence in the use of an economic time series for research or assessment seems to be proportional to the amount of data, which is similar to the process applying to real estate indexes and valuations. Working's problem mainly involved the prices of agricultural commodities that bear a resemblance to real estate. The multidimensional nature of agricultural commodity prices, for example, heterogeneity in character, distribution of geographical location and nonnegligible costs for the movement of commodities, is distinct from the behavior of financial asset prices.
Working's prominent discovery was the 0.25 rule. It states that averaging a random walk time series will induce serial correlation, and the upper limit of the serial correlation is 0.25. Working's example is clearly a moving average process though he did not refer to this term (the formal econometric estimation procedures for a moving average process had yet to be developed at that time). Since then, many studies have appeared in this area. For example, Tiao (1972) examines the asymptotic behavior of temporal aggregates of time series and provides the extreme values for the first-order autoregression and moving average parameters; Campos, Ericsson and Hendry (1990) investigate the fixed n-period phase-averaging processes and the relationship and structure in the variance and autocorrelation of the original and phase-averaging processes and Abraham (1982) presents useful models for various Auto Regressive Integrated Moving Average processes for aggregated series, provided that the structures of the original ones are known. These studies give us insights to the actual data-generating processes and their properties in many compiled financial and economic data series.
However, as pointed out by Blundell and Ward (1987), smoothing in real estate return indexes, represented by the first-order autoregressive coefficient, is well above 0.25, the extreme value any purely temporal aggregation may cause. The implication is that smoothing in real estate return indexes and temporal aggregation, though similar, are not the same. This has prompted real estate researchers to address the smoothing problem...
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