Measurement "The of Quality Change: Constructing an Hedonic Price Index for Computers Using Multiple Regression Methods". (Berndt Chapter 4)
In this chapter we to apply regression techniques to the construction of hedonic price indexes. The usefulness of the hedonic price index theory will be illustrated with several empirical applications. In particular, we will show how to use hedonic price index techniques to improve the measurement of the CPI (consumer price index).
What is an hedonic price index?.
The answer to this question may be better illustrated with one example. One of the first applications of hedonic price index techniques was in the area of Agricultural Economics. In 1927 Frederick Waugh, an agricultural economist, wrote a paper entitled "Quality Factors Influencing Vegetable Prices.". The goal of this study was, using statistical analysis, "to discover the important quality factors which cause high or low prices." Waugh emphasized the usefulness of his research by stating that: "If it can be demonstrated that there is a premium for certain qualities and types of products, and if that premium is more than large enough to pay the increased cost of growing a superior product, the individual can and will adapt his production and marketing policies to market demand." Waugh inspected 200 individual lots of asparagus in Boston over the time period of May 6 to July 2, 1927. Apparently, a great deal of quality variation existed among lots of asparagus, since even on the single day of July 2, prices per bushel varied from a low of $4.50 to a high of $12.00. To eliminate the effects of seasonal and day-to-day changes in prices, Waugh used as a left-hand or dependent variable in his regression equations the ratio of the actual price recorded for a wholesale market lot transaction of a particular commodity (denoted Pin) to the average market quotation for that commodity that day (Pmi). Call this relative price of the nth lot transaction for the ith commodity pin, and note that it is defined as pin = Pin/Pmi. In order to achieve his goal ("to discover the important quality factors which cause high or low prices."), Waugt regressed pin on the physical characteristics of vegetables that he believed were related to their actual or perceived quality variations. The characteristics selected by Waugh were: The number of inches of green color on the asparagus (GREEN), the number of stalks in the bunches (NOSTALKS) and, in order to capture the effect of uniformity, the variation in size was measured by using the quartile coefficient of dispersion (DISPERSE). This information was used to estimate a regression equation of the form p = $0 + $1GREEN + $2NOSTALKS + $3DISPERSE +ERROR. Waugh reports the following estimates of the previous regression equation parameters: p = $0 + 0.13826*GREEN - 1.53394*NOSTALKS - 0.27553*DISPERSE +ERROR. Waugh reported that green color was by far the most important quality factor influencing asparagus prices in Boston.
This empirical work probably constitutes the first application of hedonic price theory. In general, an hedonic price index represents a equation in which the price of a product is related to its more relevant characteristics. This relation can be estimated empirically using regression techniques. Basically, given a certain generic product (asparagus, computers, cars) it is possible to collect data about the price and specific characteristics of different units of this product in one or several markets, at one point in time or at different points in time. In particular, in the work of Waugh the construction of an hedonic price index had the purpose of studying the characteristics of agricultural products that have the highest impact on the market price of the product. Waugh considered that this information could be very useful for farmers trying to maximize profits. In the next sections We are going to study how hedonic price index theory that can be used to improve the measurement of CPI. This has been the focus of political debate for many years. The last time that this issue was discussed in the political arena was 1996. In the next section we are going to study the economic relevance of the CPI, the methods used to construct this index and the problems associated with this techniques. Finally, we will study how the hedonic price index theory can be used to improve the reliability of this index.
The consumer price index.
The Consumer Price Index (CPI) measures the prices of inputs that consumers buy to produce fundamental services. For example, the CPI measures the price of automobiles, electricity, and hospital days. In order to understand how the CPI is constructed let us think first about how to construct this index in a simple economic framework before thinking about the much more complex problem of defining the CPI in the real economy. Thus, consider a simple "bread and butter" economy. This economy is composed by a single individual that consumes only two types of goods (bread and butter). Assume that the monthly income of this individual is denoted by I. This individual uses a certain percentage wbread of his/her monthly income in the consumption of bread and the remaining percentage wbutter in the consumption of butter wbread + wbutter = 1 Assume that at time t the price of bread is pbread and the price of butter is pbutter. In this framework, the consumption of bread and butter will be as follows: Cbread = wbreadI/pbread Cbutter = wbutterI/pbutter Over time the price of the goods may change. In particular, assume that at time (t+1) the new prices for both goods are p'bread and p'butter. In order to be able to maintain the same level of consumption as in the previous period the amount of disposable income must have changed to, p'breadCbread + p'butterCbutter = I' This expression represents the CPI at time (t+1) in this simple economy. In a more complex economy with many heterogeneous consumers the method used to construct the CPI is to look at what proportion of their income consumers actually spend in each good, which defines a fixed "basket" of goods, and then to figure what it would cost to purchase that basket in latter years.
The percentage change in income required in order to be able to maintain at (t+1) the same level of consumption as at period t is equal to i defined as, i = (I' - I)/I If i >0 we say that the Economy has experienced a period of inflation. If i<0 then we say that the Economy has experienced a period of deflation. In order to construct the CPI the Bureau of Labor Statistics (BLS) collects price quotations for 71,000 goods and services, at about 22,000 retail outlets, either monthly or bimonthly. Additional information is obtained on rent and owners' equivalent rent (that is, how much owners are paying in opportunity cost terms for housing services) from about 35,000 rental units. About once a decade the weights for different commodities are derived from the Consumer Expenditure Index; for the last decade, were weights from the 1982-1984 period. Accurately measuring prices and their rate of change, inflation, is central to almost every economic issue. Some examples include aggregate growth and productivity; industry prices and productivity; government taxes and spending programs that are indexed to inflation; budget deficits and debt; monetary policy; real financial returns; real wages, real median incomes and poverty rates; and the comparative performance of economies. This said, the interpretation of CPI as well as its measurement is an issue of great controversy among economists and lately also among politicians. There are several reasons for this, we will look at the most important two. The controversy surrounding the CPI is to a large extend the result of the way in which this index is used day to day. As I have previously explained, the CPI tracks the cost of purchasing a fixed basket of goods and services. However, In most applications the CPI is used as a cost-of-living index. A cost-ofliving index measures the minimum level of expenditures required to attain a particular level of utility, clearly this value depends on the price of goods. The CPI is in fact a very different from a cost-of-living index. This, creates a great deal of controversy among economists and politicians. Because the major criticisms of the CPI arise from it not being a cost-of-living index it is important to understand the differences. These differences can be better illustrated in the simple bread and butter economy. Consider a certain individual, "Kristen", with an associated utility function of the form u(cbread,cbutter). For the most frequent utility functions, a certain level of utility u can be achieved by different bundles of consumption. This can be represented in a two dimensional graph as bread
butter
In this graph the concave curve, usually called "indiference curve", represents all the possible consumption bundles of bread and butter that provide Kristen with the same level of utility. Consider the price of bread and butter equal to pbread and pbutter respectively and denote the individual's income by I. Then, Kristen has to restrict her level of consumption to the set of affordable bundles of goods. That is, elements of the form (cbread,cbutter) satisfying pbreadcbread + pbuttercbutter <= I. The bundle of goods that maximizes Kristen's utility subject to the previous budget constrains is represented in the next graph, Bread I/pbread (c*bread, c*butter)
(1) (2) I/pbutter butter Any bundle of goods in (1) is preferred to any bundle of goods in (2). However, Kristen can afford a unique bundle of goods in (1), (c*bread, c*butter). This bundle of goods maximizes Kristen's utility from consumption for a given income I, under the current prices (pbread , pbutter). In this simple economy, if the CPI index had to be constructed at this time its value will be CPIt = pbread c*bread + pbutter c*butter. This value is equivalent to the value of a cost of living (CLt) index also constructed at the present time, CPIt = CLt It is interesting to try to understand how a change in prices will affect consumption. Consider then a change of prices of the form pbread = p'bread and pbutter < p'butter. As a result of this change in prices the maximum amount of butter than Kristen can buy has been reduced from I/pbutter to I/p'butter Bread I/pbread (c*bread, c*butter)
(1) I/p'butter
I/pbutter butter
In this new scenario a level of consumption as that given by the bundle of goods (c*bread, c*butter) is unaffordable to Kristen under the current prices. In order to construct the new cost of living index (CLt+1) we need to find the level of income that Kristen needs in order to attain the same level of utility as before. This can be done easily using the previous graph Bread I'/pbread (c'bread, c'butter)
(c*bread, c*butter)
(1)
I'/pbutter
butter
The new level of income necessary to achieve the same level of utility as before is I' and is such that it allows Kristen to consume a bundle of goods (c'bread, c'butter) in the indifference curve (1). In this case, the new cost of living index is, CLt+1 = I'. However, as I will show next this is not equal to CPIt+1. In order to underst...