The demand for Q can often be inferred from its role as an attribute of some composite market good.  For example, housing is a composite good, and housing prices or rents (P) can be decomposed via regression analysis to identify implicit prices for the various attributes X and Q (bedrooms, bathrooms, square footage, age of house, etc., as well as local environmental quality attributes). The analyst must choose an appropriate specification (functional form) for the hedonic price model P = f(X,Q) which will yield satisfactory marginal implicit price functions (partial derivatives). A linear hedonic model

                P = B0 + B1X1 + ... + BNXN + BQQ

                P = B0 + B1X1 + ... + BNXN + BQlog(Q)

While the basic theory of hedonic pricing is fairly straightforward, there are several complications that can frustrate empirical applications.  First, X is typically a large vector of house characteristics, and the individual variables may be highly collinear.  For example, the number of bedrooms in a house is likely to be pretty collinear with the number of bathrooms, so these two variables might confound each other in the regression model.  This is generally not a problem as long as we are just including these variables to meet ceteris paribus conditions to estimate effects of Q on housing values across different neighborhoods.  But it is likely to be a problem if any variables in X are highly collinear with Q.

Another problem derives from the basic rule of real estate: housing values are determined by "location, location and location."  Empirical hedonic property models are typically weakened by neighborhood effects, so that a fixer-upper in a tony neighborhood may be worth more than an equivalent house in mint condition in a run-down neighborhood.  So it is important to account for neighborhood characteristics as well as individual housing characteristics.

Another complication of hedonic housing price models is that household incomes and other socioeconomic factors are likely to vary across neighborhoods: for example, higher-income people live in more expensive neighborhoods than poor people, and may have higher demands for Q. In other words, there may actually be several distinct housing markets: e.g., luxury housing, middle-income housing, low-income housing. This means that the marginal implicit price function derived from a hedonic regression on diverse neighborhoods is really the "envelope" of a series of equilibria in distinct housing markets, and the actual demands for Q will be different in each market. We may treat the demand for Q as being shifted by household income or other socioeconomic variables, and we might include a "cross-effect" term (e.g., income I times Q) in the hedonic price model. For example, the estimated hedonic equation

                P = B0 + B1X + + ... + BNXN + BQlog(Q) + BRIQ

                WTP(Q) = BQ/Q + BRI,

Most hedonic housing price studies use market values of properties rather than rental values. The market value P of a house reflects the capitalized stream of expected annual rental values R discounted at rate r over a very long time horizon: P = R/r. If a polluted neighborhood anticipates future improvements in Q, these expectations will be factored into current market values, but not into current rents. In this case a hedonic analysis of market values would probably understate the current costs of the pollution, while a hedonic analysis of current rents would not.
 

Environmental Justice?

This is a good a place as any to discuss the concept of "environmental justice."  It is sometimes claimed that polluters target their pollutants at specific low-income or minority neighborhoods.  These claims are sometimes supported by data confirming that low-income neighborhoods do in fact have lower environmental quality than high-income neighborhoods.  But  mere spatial correlation between neighborhood incomes and pollution does not prove a causal relationship.  A key question is: which came first, the pollution or the poor people?

A number of hedonic property analyses confirm that pollution does in fact degrade residential property values.  More generally, any locally undesirable land use (LULU) is likely to depress neighboring property values.  While it is clear that LULU's are sometimes targeted to low-income communities, it is also clear that low-income households are likely to choose to live in communities with LULU's, or higher pollution levels, precisely because housing is cheaper in those areas.  So what might appear to be an environmental justice issue is just a symptom of a much broader issue of equity in income distributions.
 

Hedonic Wage Models

Another application of hedonics is in labor markets. Assuming that labor is perfectly mobile, and that workers are rational and fully informed about risks of job-related injury or death, we can statistically decompose wages to estimate the wage premiums associated with these risks. Suppose job A involves a 0.0004 risk of death annually, and pays $5,000 per year more than job B, which has no discernible risk of death. Dividing the wage premium by the risk implies a $1,250,000 wage premium for a 100 percent certain "statistical" death.

The topic of placing an economic valuation on human lives is morally distasteful, but most environmental economists argue that any policy decision regarding risks to people implies some valuation, so we should try to base our policies on rational criteria rather than just emotion. We can only value human health and lives under a veil of ignorance, which prevents us from knowing who will suffer the eventual harm our policies tolerate. The fact that we are all potential victims makes us behave responsibly.

Peoples' behaviors imply self-valuations of their lives. Unfortunately, some behaviors (cigarette smoking, failing to wear seat-belts) are clearly irrational, or imply irrationally low self-valuations.