### Hedonics, Litigation, and Property Value Diminution

By Jack Williamson, PhD, Orell C. Anderson, MAI and Alexander R. Wohl

As the complexity and scale of contaminated property litigation shows no signs of abating, reliance on regression analysis in damage claims has become increasingly common. There are cases where performing a traditional appraisal for each individual property is simply infeasible—for example, when assessing large-scale damage claims or when attempting to establish a class certification. In such cases, regression analysis can be an indispensable tool for litigants. There are hazards, however, when dealing with regression analysis. Like any method, regression can be used and it can be abused. It is important to look under the hood and use common sense when evaluating these types of analyses.

This article will briefly describe the theoretical basis for hedonic regression and will explain its three most frequent uses in contaminated property litigation. The authors hope that this will help readers, whether they are working as defendants or plaintiffs in a contamination case, become more informed consumers and users of hedonic regression analyses.

**The Regression Technique**

Regression analysis is a method used to measure the relationship between two or more variables. The technique was developed in the early 19th century and, in its most basic sense, can be reduced to the familiar problem of drawing a line of best fit through a scatterplot of observed values. Until the late 1950s regression was a tedious exercise, however, and performing a multivariate regression on a large dataset with a paper and pencil is impractical and even impossible given the limited nature of human lifespans. With the leaps in computing during the 20th century, however, regression analysis has become an essential tool in many data-driven disciples and their corresponding industries—from biostatistics and machine learning to marketing research and real property damage economic analysis.

**The Hedonic Model**

Though the regression technique was developed in the 19th century, its widespread application to economics required advances in the economic theory of consumer demand. In the 1960s, economists developed the modern understanding that consumer demand for goods is based not on the goods themselves but on their characteristics. Thus, goods are composites of a set of characteristics, and their prices in a market are set by the demand for those characteristics. In a seminal 1974 paper, the University of Chicago economist Sherwin Rosen combined the statistical techniques of regression and the recent advances in the economic theory of demand into the workable model of hedonic regression analysis.

Much as real property ownership is thought of as a bundle of rights in property law, property traded in a market could be considered a bundle of goods—with prices set by the demand for those goods. In case of a housing market, for example, the hedonic model considers the price for each house to be a function of its characteristics—such as location, neighborhood, lot size, living area, and room count. Lot prices likewise may be determined by view, lot, size and shape, topography, location, utility, and entitlements. The hedonic method allows economists and appraisers to estimate the value of real estate based on a buyer’s willingness to pay for its combined characteristics—even as characteristics change. Though most hedonic models are seen in the context of regression analysis, the real estate appraiser’s sales adjustment grid is a special case of the hedonic model using limited sales data and the appraiser’s experience and judgment.

Since these developments, the most common hedonic regression model, the ordinary least-squares model, has become the workhorse of empirical pricing studies. A quick search through any scholarly database turns up studies measuring anything from ocean views to building age to air quality. The exact design of the models may change, and their datasets may change, but the foundation of the technique in remains the same.

**Contaminated Property Valuation**

As suggested by the breadth of the literature, the shadow prices of property characteristics that can be measured with hedonic regression is not limited to lot size and room count. The advantage of hedonic regression is that it allows economists and appraisers to measure the impact of individual components of features and services on the market value of real property. A hedonic regression may be performed to quantify the value of a certain neighborhood, school district, proximity to a body of water, or view amenity. It can also be applied to air quality or proximity to a Superfund site or recent oil tanker spill.

Contaminated property litigation often follows a familiar timeline. First, there is the accidental release of a chemical contaminant, discovery of past contamination, or publication of new research that suggests that some substance previously though harmless is in fact harmful. Following the announcement, litigants may claim that the events have caused property value diminution (PVD). These claims are often accompanied by demands for compensation. For all parties involved, the key questions are whether PVD has occurred and, if so, by how much. When used properly, hedonic regression analysis may help illuminate these questions.

Three applications of the hedonic regression are commonly seen in contaminated property litigation. The first application is in empirical studies of the existence and magnitude of actual property value losses. The second appears in a related, but distinct method—the application of a damage percentage to point-estimates of unimpaired property values as of the date immediately prior to the incident (the unimpaired condition). The third application is in a regression-based meta-analysis of a collection of studies putatively related to situation at hand.

Though these three approaches are attempting to solve the same basic questions and all three employ a regression analysis, there are important differences in the application of the method that may yield widely divergent damage estimates. These three approaches are examined below.

**1. Empirical PVD Studies**

The first method attempts, through the empirical observation of actual transaction prices, to determine the existence and magnitude of any PVD. Using sales data spanning a sufficient time before and after the event, the appraiser or economist will construct a model to identify any price effects in the treatment neighborhood. Typically, the hedonic regression model will express PVD as a percentage of the property value as if unimpaired.

Market data is the gold standard in this type of hedonic model. If claims are made that an area over a groundwater plume has suffered PVD following a public announcement of contamination—why not attempt to measure the PVD? Why *not* look at prices if they are available? In many jurisdictions, transaction prices are recorded and available from the county assessor-recorder, the state board of equalization, or the local multiple listing service.

Hedonic models can, through careful design, account for a variety of factors that may affect market value. To guard against the possibility that some circumstance other than contamination caused any observed price changes in the treatment neighborhood, a control—plausibly unaffected—neighborhood can be included in the data used to estimate the model. The regression model can also account for macroeconomic influences such as recessions and interest rates. Most importantly, PVD can be estimated depending on the distance from the environmental disamenity or on its intensity.

It is important to note, however, that in this first use of hedonic regression to measure PVD, the regression model is used to estimate the average diminution percentage for the entire treatment neighborhood—not individual property prices. In this respect, it differs markedly from the second approach.

**2. Point-Estimates, Surveys, and Case Studies.**

What if the data do not exist? Perhaps sufficient time has not transpired since the contamination event to build a reliable post-event dataset. Maybe the study area falls in a nondisclosure jurisdiction. Perhaps the contamination zone may occur in a rural area with low density and low property turnover. For a variety of reasons, there may simply not be enough observable transactions. Litigants do not have the luxury of undergraduate econometrics students—they cannot choose their treatment areas based on the availability and cost of data. Treatment areas are chosen for them by circumstance.

What appraisers and litigants frequently do when confronted with a lack of data is turn to contingent valuation survey methods and case studies. Rather than construct a hedonic model with before and after sales, they may rely on surveys and case studies to determine whether diminution has occurred and to estimate its magnitude.

However, simply developing a PVD percentage is not sufficient—prices are needed on which to apply this percentage. What is needed is the value of each property as if unimpaired. Ideally, the entire sample would have sold simultaneously on the day before the event. The authors of this article have yet to see this in thirty years. Lacking simultaneous sales on the date of the incident, the litigants may construct a hedonic regression to estimate the prices of each property on the date of the incident using historical sales data. Now, regression is being used to solve a somewhat difficult problem, namely generating point-estimates of the price of individual properties based on a limited set of publicly available characteristics. (Of course, if sufficient data exist to construct such a model, the question arises as to why a PVD percentage model of the fist type cannot be constructed. But this can happen in certain circumstances.)

The diminution percentage developed from surveys and case studies is then applied to these point-estimates of property values on the day of the event. The PVD percentage applied may be based on each property’s proximity to the contamination source or degree of contamination. Thus, the analyst arrives at an impaired value for each property.

**3. Brief Encounter with the Third Kind: Meta-Analysis**

Though not strictly the hedonic modeling approach described so far, this third application of regression analysis deserves mention because of its appearance in contaminated property litigation. Meta-analysis is another method often resorted to when sales data are lacking. By aggregating several research studies into a single study, meta-analysis yields a higher observation count without the costs associated with a large-scale study. Meta-analysis then uses regression techniques in aggregating and analyzing the results of the separate studies.

Originating in the field of biostatistics as method to reduce the costs of research, meta-analysis as it is sometimes applied to PVD matters is subject to abuse. Such abuse generally falls under the rubric of “garbage in, garbage out”—but it may take other forms. Aggregating poor quality research does not magically transform it to high-grade, insightful work. When confronting or contemplating a meta-analysis, the first considerations should be whether the separate studies are sufficiently alike to be aggregated in a sensible way and whether they are relevant to the situation at hand. The design and execution of the regression itself can be addressed once these issues are settled. Do the studies included concern a similar contamination and similar route of exposure? Are the cases or studies located in the same state? Did the studies or cases take place in the same decade? What is important is not necessarily the subtleties of the regression model itself, but rather the inputs—in this case, the individual studies.

**Regression Doesn’t Have to be Mean**

If the data exist and the goal is to estimate impacts across a treatment neighborhood, statistical methods and regression models are the techniques of choice. However, there are important differences between the first and second applications of hedonic regression analysis discussed here.

The most fundamental difference is that the two methods are based on different theories of how real estate markets process information—or the “efficiency” of real estate markets. Even if market data exists and does not show significant impacts, proponents of the second application may claim that market participants must be poorly informed and, when word gets around about the contamination, there will be a downward market correction to reflect the new information. This line of argument, however, has not been particularly successful in either the judicial and empirical realms. Real estate markets tend to be efficient—so that if price effects are going to appear they will likely appear quickly after the event date, not some indeterminate number of years later. Therefore, the two methods, though they both ultimately aim to measure damages, approach the problem in entirely different ways and often reach correspondingly divergent conclusions.

Ultimately, if the reader is not a professional data analyst and if the stakes are high, expert advice is the order of the day. But, as in life, it is important to become an informed consumer. A basic understanding of hedonic regression can aid both parties in evaluating the evidence presented by their own and their opposing party’s experts. Most importantly, never underestimate common sense.