Index Numbers

Index numbers are used to aggregate detailed information on prices and quantities into scalar measures of price and quantity levels or their growth. The paper reviews four main approaches to bilateral index number theory where two price and quantity vectors are to be aggregated: fixed basket and average of fixed baskets, stochastic, test or axiomatic and economic approaches. The paper also considers multilateral index number theory where it is necessary to construct price and quantity aggregates for more than two value aggregates. A final section notes some of the recent literature on related aspects of index number theory the construction of indexes when there is seasonality in the underlying data, sources of bias in consumer price indexes, the use of index numbers in measuring productivity, the problem of quality change and index number theory that is based on taking differences rather than ratios.Index numbers, stochastic, test and economic approaches to index number theory, hedonic regressions, bilateral index number theory, multilateral index

Afriat's Theorem and Some Extensions to Choice under Uncertainty

The first part of the paper reviews the methodology developed by Sydney Afriat for determining whether a finite set of price and quantity data are consistent with utility maximizing behavior by a consumer. Some extensions of his basic model to models of consumer behavior where the structure of preferences is restricted in some way are also explained. Examples of special structures are homotheticity, separability and quasilinearity of the utility function. The second half of the paper is devoted to developing Afriat type consistency tests for expected and nonexpected utility maximizing behavior.Revealed preference theory, Afriat inequalities, nonparametric approach to demand theory, homotheticity, separability, quasilinearity, testing for max

The Measurement of Nonmarket Sector Outputs and Inputs Using Cost Weights

In many sectors of the economy, governments either provide various services at no cost or at highly subsidized prices. Examples are the health, education and general government sectors. The System of National Accounts 1993 recommends valuing these nonmarket outputs at their costs of production but it does not give much guidance on exactly how to do this. In this paper, an explicit methodology is developed that enables one to construct these marginal cost prices. However, in the main text, an activity analysis approach is taken in order to simplify the analysis, so in particular, constant returns to scale, no substitution production functions for the specific activities in the nonmarket sector are assumed. It is shown that it is possible to obtain meaningful measures of Total Factor Productivity growth in this framework. An Appendix relaxes some of the restrictive assumptions that are used in the main text.Measurement of output, input and productivity, nonmarket sector, health, education, general government, cost functions, duality theory, marginal cost

User Costs versus Waiting Services and Depreciation in a Model of Production

The paper develops an extension of a one period model of production involving beginning and end of the period capital stocks along with output and input flows that is due to Hicks and Edwards and Bell. This generalized Austrian model of production takes into account that end of the period capital stocks result from: (i) purchases of new investment goods; (ii) internal construction of firm capital stock components and (iii) holdings of (depreciated) capital goods that were held by the firm at the beginning of the period. These different methods of creating end of period holdings of capital stocks generally have different resource requirements and hence the one period production possibilities set is more complex than the usual one. This general model of production is used to justify the decomposition of the Jorgensonian user cost of capital into separate waiting services and depreciation components.Production theory, user cost of capital, waiting services, depreciation, Austrian models of production, net versus gross investment

The Paris OECD-IMF Workshop on Real Estate Price Indexes: Conclusions and Future Directions

The paper summarizes the main ideas suggested in OECD-IMF Workshop on Real Estate Price Indexes which was held in Paris, November 6-7, 2006. The paper discusses possible uses and target indexes for real estate price indexes and notes that a major problem is that it is not possible to exactly match the quality of dwelling units over time due to the fact that the housing stock changes in quality due to renovations and depreciation. Four alternative methods for constructing real estate price indexes are discussed: the repeat sales model; the use of assessment information along with property sale information; stratification methods and hedonic methods. The paper notes that the typical hedonic regression method may suffer from specification bias and suggests a way forward. Problems with the user cost method for pricing the services of owner occupied housing are also discussed.Real estate price indexes; housing, index number theory; hedonic regression techniques; repeat sales method; system of national accounts; user costs;

On the Tang and Wang Decomposition of Labour Productivity Growth into Sectoral Effects

Tang and Wang provided a decomposition of economy wide labour productivity into sectoral contribution effects. The present note reworks their methodology to provide a more transparent and simple decomposition. This new decomposition is then related to another decomposition due to Gini and analyzed by Balk. Overall growth in labour productivity is due to three factors: (i) growth in the labour productivity of individual sectors; (ii) changes in real output prices of the sectors and (iii) changes in the allocation of labour across sectors.Index numbers, labour productivity, decompositions of aggregate labour productivity into sectoral effects.

New Methodological Developments for the International Comparison Program

The paper explains new methodology that was used in the 2005 International Comparison Program (ICP) that compared the relative price levels and GDP levels across 146 countries. In this round of the ICP, the world was divided into 6 regions: OECD, CIS, Africa, South America, Asia Pacific and West Asia. What is new in this round compared to previous rounds of the ICP is that each region was allowed to develop its own product list and collect prices on this list for countries in the region. The regions were then linked using another separate product list and 18 countries across the 6 regions collected prices for products on this list and this information was used to link prices and quantities across the regions. An additional complication was that the final linking of prices and volumes across regions had to respect the regional price and volume measures that were (separately) constructed by the regions. The paper also studies the properties of the Iklé Dikhanov Balk multilateral system of index numbers which was used by Africa.Index numbers, multilateral comparison methods, GEKS, EKS, Geary-Khamis, Balk, Dikhanov, Iklé, Country Product Dummy (CPD) method, basic headings, St

Alternative Approaches to Measuring House Price Inflation

The paper uses data on sales of detached houses in a small Dutch town over 14 quarters starting at the first quarter of 2005 in order to compare various methods for constructing a house price index over this period. Four classes of methods are considered: (i) stratification techniques plus normal index number theory; (ii) time dummy hedonic regression models; (iii) hedonic imputation techniques and (iv) additive in land and structures hedonic regression models. The last approach is used in order to decompose the price of a house into land and structure components and it relies on the imposition of some monotonicity constraints or exogenous information on price movements for structures. The problems associated with constructing an index for the stock of houses using information on the sales of houses are also considered.Property price indexes, hedonic regressions, stratification techniques, rolling year indexes, Fisher ideal indexes

Irving Fisher and Index Number Theory

There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test and economic approaches. The paper reviews the contributions of Irving Fisher to these approaches to index number theory which are still in use today. The paper also reviews Fisher’s contributions to multilateral index number theory. The main themes of the paper are developed in the context of a review of the early history of index number theory: a history that conveys a wealth of information and insight into the making and use of index numbers today.Price indexes, quantity indexes, bilateral price indexes, multilateral price indexes, the Fisher ideal index, the test approach to index number theory