Hedonic index

Hedonic index

Hedonic index is any price index, which uses information from hedonic regression.
Hedonic regression describes how product price could be explained by the product'scharacteristics. Hedonic price indexes proved to be very useful when applied for information and communication products (e.g. personal computers) to calculate price indexes, because they can successfully mitigate such problems as new goods and rapid quality change.

Motivation

In the last two decades considerable attention has been drawn to the methods of computing price indexes for Information and Communication Technology (ICT) products: the discussion started in the USA and then has been continued throughout the entire world. Report prepared by Boskin Commission in 1996 raised the problem of biases in the price indexes for ICT products: it showed that traditional matched models indexes can substantially overestimate inflation, because they are not able to measure the peculiarities of ICT industries (i.e. fast rotation of goods, huge quality differences among products on the market, short product life cycle,etc.). The Commission showed that the usage of matched model indexes (traditional price indexes) leads to an overestimation of inflation by 0,6% per year in the US official CPI (CPI-U). Similar result were obtained by Crawford (1998) [Crawford, Allan (1998), ”Measurement biases in the Canadian CPI: An update?”, Bank of Canada Review, Spring, pp. 38-56.] for Canada, Shiratsuka (1999) [Shiratsuka, Shigenori (1999), ”Measurement errors in Japanese Consumer Price Index”, Federal Reserve Bank in Chicago, WP.] for Japan, and Cunningham (1996) [Cunningham, Alastair W.F. (1996), ”Measurement Bias in Price Indexes: An Application to the UKs RPI”, Bank of England, Working Paper, No.47.] for the UK.

Quality adjustments are also important for understanding national accounts deflators (see GDP deflator). In the USA, for example, growth acceleration after 1995 was driven by the increased investment in ICT products that lead both to an increase in capital stock and labor productivity growth (Bosworth and Triplett, 2001). This increases the complexity of international comparisons of deflators. Wyckoff [Wyckoff, Andrew W. (1995), ”The Impact of Computer Prices on International Comparisons of Labour Productivity”, Economics of Innovation and New Technology, 3(3-4), pp. 277-93] and Eurostat [Eurostat Task Force (1999), ”Volume Measures for Computers and Software”, report of the Eurostat Task Force on Volume Measures for Computers and Software, June.] show that there is a huge dispersion in ICT deflators in OECD and European countries, accordingly.

These differences are so huge that it cannot be explained by any means of market conditions, regulation, etc. As both studies suggest, most part of it comes from the differences in quality adjustment procedures across countries and that, in turn, makes international comparison of investment in ICT impossible (as its calculated through deflation). So, it also makes challenging any attempt to estimate the impact of ICT on economy across countries.

Hedonic regression

For example, for a linear econometric model, assume that at each period "t" we have $n\_\{t\}$ goods, which could be described by a vector of "k" characteristics $(z\_\{1it\},...,z\_\{kit\};)^T$. Thus the hedonic (cross-sectional) regression is:

$P\_\{it\}=c\_\{0t\}+sum\_\{j=1\}^\{k\}c\_\{it\}z\_\{jit\}+xi\_\{it\}$,

where $c\_\{it\}$ is a set of coefficients, $xi\_\{it\}$ i.i.e. $N(0,sigma^\{2\})$

Hedonic price index

There are several ways the hedonic price indexes can be constructed. Following Triplett [Jack Triplett, http://www.oecd.org/dataoecd/37/31/33789552.pdf, Handbook on Hedonic Indexes and Quality Adjustments in Price Indexes, OECD] we can distinguish two methods -- direct and indirect. The direct method uses only information obtained from the hedonic regression, while the second method combines information derived from the hedonic regression and matched models (traditional price indexes). In indirect method, data used for estimating hedonic regression and calculating matched models indexes are different.

Time dummy variable method

Direct method could be divided into Time Dummy Variable and Characteristic methods. The Time Dummy Variable is simpler, because it assumes implicit prices (coefficients of the hedonic regression - $c\_\{it\}$) to be constant over adjacent time periods. This assumption generally does not hold [Berndt, Ernst R. and Neal J. Rappaport (2001), ”Price and Quality of Desktop and Mobile Personal Computers: A Quarter-Century Historical Overview”,American Economic Review, 91(2) (May), pp. 268-273.] since implicit prices reflect both demand and supply [Pakes A. (2002), ”A Reconsideration of hedonic price indexes with an application to PC’s”. NBER Working Paper No.8715 (2002), January.] .

Characteristic method

Characteristic method, relaxes this assumption, based on the usage of fitted prices from hedonic regression. This method generally should lead to a more stable estimates, because ordinary least squares (OLS) estimates guarantee that the regression always passes through its mean.

The corresponding characteristic chain hedonic price index looks for period from "0" to "T":

$prod\_\{t=0\}^\{T\}frac\{widehat\{P\}\_\{t+1\}(z^\{\; au\})\}\{widehat\{P\}\_\{t\}(z^\{\; au\})\}$

and

$widehat\{P\}\_\{t+1\}(z^\{\; au\})$ is an estimate of price obtained from hedonic regression at period "t+1" with mean characteristics of period $au:\; z^\{\; au\}$.

The corresponding characteristic base hedonic price index looks for period from "0" to "T":

$HPI(0,T)=frac\{widehat\{P\}\_\{T\}(z^\{\; au\})\}\{widehat\{P\}\_\{0\}(z^\{\; au\})\}$

A specification of $z^\{\; au\}$ - mean characteristics for the certain period, determines the type of index. For example, if we set $z^\{\; au\}$ equal to the mean of the characteristics for the previous period $t:\; z^t$, we would get a Laspeyres-type index. Setting $z^\{\; au\}$ equal to $t+1:\; z^\{t+1\}$ -- Paasche-type index and so on. Fisher-type index is defined as a square root of product of Laspeyres- and Paasche-type indexes. Edgeworth-Marshall - uses arithmetic mean of mean characteristics of two periods "t" and "t+1". Walsh-type index uses geometric average of two periods. And finally, base quality index does not update characteristics (quality) and uses fixed base characteristics - $z^0$.

Hedonic quality indexes

Hedonic quality index is similar to quantity index in traditional index theory -- it measures how the price of obtaining set of characteristics had changed over time. For example, if we are willing to estimate the effect that characteristic growth (or decline) has had on the price of a computer for one period - from "t" to "t+1", then the hedonic quality index would look like:

$frac\{widehat\{P\}\_\{eta\}(z^\{t+1\})\}\{widehat\{P\}\_\{eta\}(z^\{t\})\}$

,where $eta$, as in the case with price indexes, determines the type of the index. So, the chain quality index for the period from "0" to "T" would look like:

$prod\_\{t=0\}^\{T\}frac\{widehat\{P\}\_\{eta\}(z^\{t+1\})\}\{widehat\{P\}\_\{eta\}(z^\{t\})\}$

and base index:

$frac\{widehat\{P\}\_\{eta\}(z^\{T\})\}\{widehat\{P\}\_\{eta\}(z^\{0\})\}$

ee also

* Hedonic Regression
* Price Index
* Consumer price index

References