Academic journal article Economic Inquiry

Hedonic Imputation and the Price Index Problem: An Application to Housing

Academic journal article Economic Inquiry

Hedonic Imputation and the Price Index Problem: An Application to Housing

Article excerpt

I. INTRODUCTION

Price indexes play a significant role in modem economies. The consumer price index (CPI), for example, is used to index various government payments, as a target for monetary policy and as a benchmark in wage negotiations. Our focus in this paper, however, is on price indexes at a more disaggregated level, in markets where it is hard to match products from one period or region to the next. Computers and housing are notable examples of such markets. As well as being important inputs into the CPI, price indexes for such goods are often useful in their own right. Price indexes for computers play a critical role in productivity measurement across market sectors, while house price indexes provide an important indication of the state of an economy.

For the case of computers, the matching problem arises due to technological progress, which leads to the rapid evolution of products in the market, resulting in a short product cycle. For housing, the problem is that every house is different and that they tend to sell relatively infrequently. Hence, there is usually very little overlap in the houses sold from one period to the next and no overlap at all from one region to the next.

The fact that products can often not be matched across periods or regions poses a significant measurement problem in that it is therefore difficult to disentangle price differences from changes in the quality of products. In this paper, we focus primarily on the hedonic regression method for solving this problem. The hedonic method reduces the matching problem to one of comparing products on the basis of their characteristics. The "regression" aspect of hedonic regression refers to how the implicit prices for these characteristics are measured.

In the next section, we explain what is meant by the price index problem. Section III outlines more rigorously the measurement problem created by unmatched products. The hedonic imputation method is introduced in Section IV. Section V shows how the use of the hedonic imputation method complicates the price index problem. In addition to choosing between different formulas such as Fisher and Tornqvist, it is necessary to choose between different varieties of each formula. This is because index compilers have a certain amount of discretion over which prices are imputed. Possible solutions are considered in Section VI. We show that the choice of formula variety can affect the sensitivity of the results to omitted variables bias. The choice of price index formula (as opposed to variety) is also considered in this section. We show that this is intimately connected with the choice of functional form for the hedonic model. Section VII provides an empirical application of the issues raised. The case considered is the construction of house price indexes for three regions in Sydney over a 3-yr period. Section VIII concludes the paper.

II. THE PRICE INDEX PROBLEM

Let [P.sub.js,kt] denote a bilateral price index comparison between region j in time period s and region k in time period t. The price and quantity data of commodity heading n for country k in period t are denoted, respectively, by [p.sup.n.sub.kt] and [q.sup.n.sub.kt]. Six important bilateral formulas are: Paasche, Laspeyres, Fisher, geometric Paasche, geometric Laspeyres, and Tornqvist. These indexes are defined as follows:

(1) Paasche : [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(2) Laspeyres : [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(3) Fisher: [P.sup.F.sub.js,kt] = [square root of ([P.sup.P.sub.js,kt] x [P.sup.L.sub.js,kt])]

(4) Geometric Paasche :

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(5) Geometric Laspeyres :

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(6) Tornqvist : [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Here, [w.sup.n.sub.kt] = [p.sup.n.sub.kt][q. …

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