Hedonic regression

In economics, hedonic regression or hedonic demand theory is a revealed preference method of estimating the demand for a good, or equivalently its value to consumers. It breaks down the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic. This requires that the composite good being valued can be reduced to its constituent parts and the market values of those constituent parts. Hedonic models are most commonly estimated using regression analysis, although more generalized models exist, such as sales adjustment grids.
An attribute vector, which may be a dummy or panel variable, is assigned to each characteristic or group of characteristics. Hedonic models can accommodate non-linearity, variable interaction, or other complex valuation situations.
Hedonic models are commonly used in real estate appraisal and real estate economics, as houses have a variety of easily-measured traits (Such as the number of rooms, overall size, or distance from certain amenities) which make them more amenable to hedonic regression models than most other goods. Hedonic regression is also used in consumer price index (CPI) calculations, where it is used to control for the effects of changes in product quality. Price changes that are due to substitution effects are subject to hedonic quality adjustments.
Hedonic pricing method.
Although product characteristics are neither produced nor consumed in isolation, hedonic price models assume that the price of a product reflects embodied characteristics valued by some implicit or shadow prices. In empirical studies, these implicit characteristic prices are coefficients that relate prices and attributes in a regression model. Hedonic price regression models are estimated using secondary data on prices and attributes of different product or service alternatives. In working with longitudinal data, one adds period-specific dummies and uses their regression coefficients to estimate quality-adjusted price indices. In hedonic regression, independent variables typically include performance-related product and service attributes. Such product characteristics represent not only value to the user but also resource cost to the producer. It has been demonstrated however that prices in hedonic regression are not determined completely by technical factors and performance-related characteristics. Brand-name and market-segment effects can explain price distortions and premiums that are charged over and above any allowance made for differences in measurable product performance. 
Certain environmental services often influence the market prices. The Hedonic pricing method is often brought into play in order to assess the economic values of such services.
This method finds its application to reveal the effect of environmental attributes in changes in the local real estate pricing. It is frequently used for estimating costs related to:
It is important to note that the hedonic pricing method is based on the fact that prices of goods in a market are affected by their characteristics. For example, the price of a pair of pants will depend on the comfort, the cloth used, the brand, the fit, etc. So this method helps us estimate the value of a commodity based on people's willingness to pay for the commodity as and when its characteristics change.
A particular example which is used most often is the real estate market, where the value of two different properties which are otherwise comparable will vary depending on the various environmental amenities present in the surrounding areas of these properties.
If there is a measurable price drop of properties located near a dump yard (as compared to other locations), the difference in the prices point towards the external cost of the dump yard. It is the marginal willingness to pay (in higher housing prices) for the given difference in cleanliness and serenity of the locality. Hedonic Regression methods are used to estimate these price differentials.
The Hedonic Pricing Method (HPM) as mentioned earlier is a form of revealed preference method of valuation and it uses surrogate markets to estimate the value of the environmental amenity.
Surrogate market is a concept that one uses when one cannot directly estimate the market prices for certain environmental goods. Therefore, a similar good sold in the market is chosen as a proxy.
For example, if we want to know the value of clean air estimated by an individual, they may reveal their preference in the form of establishing their house in a clean society and paying an extra premium for the same. Thus, with the help of Hedonic Pricing Method, the environmental component of the value and the market price can be separated. In turn, this market price is used as a surrogate for the environmental value.
Hedonic models and real estate valuation.
In real estate economics, hedonic pricing is used to adjust for the problems associated with researching a good that is as heterogeneous as buildings. Because buildings are so different, it is difficult to estimate the demand for buildings generically. Instead, it is assumed that a house can be decomposed into characteristics such as number of bedrooms, size of lot, or distance to the city center. A hedonic regression equation treats these attributes (or bundles of attributes) separately, and estimates prices (in the case of an additive model) or elasticity (in the case of a log model) for each of them. This information can be used to construct a price index that can be used to compare the price of housing in different cities, or to do time series analysis. As with CPI calculations, hedonic pricing can be used to correct for quality changes in constructing a housing price index. It can also be used to assess the value of a property, in the absence of specific market transaction data. It can also be used to analyze the demand for various housing characteristics, and housing demand in general. It has also been used to test assumptions in spatial economics.
The Uniform Standards of Professional Appraisal Practice, or USPAP, provides for mass appraisal standards to govern the use of hedonic regressions and other automated valuation models when used for real estate appraisal. Appraisal methodology treats the hedonic regression as essentially a statistically robust form of the sales comparison approach. Hedonic models are commonly used in tax assessment, litigation, academic studies, and other mass appraisal projects.
Application of the hedonic pricing method.
While studying the application of the Hedonic Pricing Method, the first assumption made is the value of a house is affected by a particular combination of characteristics that it possesses given that properties with better qualities demand higher prices as compared to properties with lower qualities. This is the Hedonic Pricing Function.
The price of a house will thus be affected by the structural characteristics
formula_1 of the house itself, characteristics of the locality/neighbourhood
formula_2, and environmental characteristics
formula_3.
Structural Characteristics could be anything from size of the house, to the number of rooms, type of flooring, etc. Neighbourhood attributes include variables like posh-ness of the locality, quality of roads, etc. And the environmental characteristics are variables such quality of air, proximity to parks, beaches, dumping yards, etc.
The analysis takes place in two stages.
The first stage involves employing regression techniques to estimate the Hedonic Price Function of the property. This function will relate the prices of many properties in the same housing area to the different characteristics.
So the Price Function is of the form
formula_4
This function could be linear or non-linear. The prices may change at an increasing or decreasing rate when the characteristics change.
When you now differentiate the price function with respect to any one of the above characteristics, the implicit price function for that particular characteristic is yielded. It is considered implicit because the price function is indirectly revealed to us by what the people are willing to pay in order to obtain better quality or quantities of the characteristic.
In the second stage, these implicit prices are regressed against the actual quantities/qualities chosen by the people in order to attain the marginal willingness to pay for the amenity. The results of this analysis will indicate the changes in property values for a unit change in each characteristic, given that all the other characteristics are constant. Some variables however may be correlated. This will result in similar changes in their values.
A hedonic price analysis has been applied to smartphones using the least absolute shrinkage and selector operator (LASSO) to identify the functional features that are the best predictors of a smartphone's price. 
Hedonic models have also been used to calculate fair, reasonable, and non-discriminatory (FRAND) royalties for standard-essential patents. 
Criticism.
Many commentators, including but certainly not exclusively Austrian economists, have criticized the US government's use of hedonic regression in computing its CPI, fearing it can be used to mask the true inflation rate and thus lower the interest it must pay on Treasury Inflation-Protected Securities (TIPS) and Social Security cost of living adjustments.
The use of hedonic models to adjust consumer price indexes in other countries has shown that non-hedonic methods produce higher inflation estimates over time because they are not designed to take quality changes into account. But hedonic models have been criticized as underestimating inflation by over estimating the value of quality changes, and by failing to account for aspects of quality deterioration.