WEIGHTED COUNTRY PRODUCT DUMMY VARIABLE REGRESSIONS AND INDEX NUMBER FORMULAE

The article considers a very simple type of hedonic regression model where the only characteristic of a commodity is the commodity itself. This regression model is known as the country product dummy method for calculating country price parities in the context of making international comparisons. The paper considers only the two country or two period case and introduces value or quantity weights into the regression. The resulting measures of overall price change between the two countries or time periods are compared to traditional bilateral index number formulae. It is shown how the Geary Khamis, Walsh and Törnqvist price indexes can be obtained as special cases of this framework.     

Multilateral Comparisons of Productivity, Terms-of-Trade and Factor Accumulation

This paper proposes a new approach for multilateral comparisons using index numbers. The new approach combines two recently-proposed innovative techniques to examine differences among economies at various levels. The Minimum Spanning Tree algorithm, based on the idea of minimizing substitution bias of bilateral comparisons, provides a possible ordering for panel data. Making use of the suggested ordering, bilateral Törnqvist price and quantity indexes are calculated and multilateral indexes are obtained by chaining. An index-number based approach is then used to decompose the differences in GDP at the bilateral level. Different sources that contribute to the differences in GDP are considered: productivity differences, terms of trade differences, factor endowments differences and domestic output price differences. The newly formed indexes are base-invariant which provides strong support for using the technique for multilateral comparisons. An illustration of the technique using data from China and four OECD countries is included.     

ON AGGREGATION METHODS FOR INTERNATIONAL COMPARISONS

This paper brings together discussions of Geary–Khamis indexes now available only in scattered sources, and considers their application to a range of uses. The first section traces the development of the method from its initial proposal by Geary in 1953, with the aid of a numerical example illustrating differences among various formulations. The second section considers the least squares properties of Geary-Khamis indexes and some related variants. The final section considers adjustments to the method required for regionalization and spatio-temporal bilateral and multilateral comparisons, as well as to take account of the nature of available data.     

WEIGHTING OF INDEX NUMBERS IN MULTILATERAL INTERNATIONAL COMPARISONS

The article reviews the methods used in practice and/or proposed by various authors for compiling indices in multilateral international comparisons. The various procedures are examined in the light of the following requirements: characteristicity (i.e. the weights should be characteristic to the countries which are compared), unbiasedness, circularity, internal consistency and factor relations.
There is no perfect solution since characteristicity and circularity are always and unbiasedness and internal consistency often in conflict with each other. The indices which are best for bilateral purposes are not transitive and the basic problem of multilateral comparisons is to obtain circularity, without losing too much of the characteristicity of the bilateral comparisons. Different compromises between the two requirements are possible and this is first of all what distinguishes the various methods used in practice.
Two main types of solution are applied in the various international comparisons. The first is based on the inter-spatial Fisher's ideal formula (e.g. the Eltetö–Köves–Szulc method, the van Yzeren method, the "central country" solution); the second type uses some kind of average prices (e.g. the Geary–Khamis method).
In the author's view there is no best method in absolute terms. Every method has some weaknesses and which of these weaknesses is the easiest to accept depends to a large extent on the actual aims of the comparison and on various other circumstances.     

GDP Growth Accounting: A National Income Function Approach

In this paper, we provide a decomposition of GDP growth that is complete and exact for the translog national income function and for the Törnqvist index of real GDP. The contributions of changes in output quantities, factor prices and total factor productivity are identified. Special consideration is given to foreign trade, with imports treated as a negative output. Annual estimates for the United States are reported for the period 1948–98.     

Technological Progress versus Efficiency Gain in Manufacturing Sectors

This study decomposes the nonparametric Malmquist productivity index for 36 Korean manufacturing sectors into two components: technological change and technical efficiency change. The empirical results show that while each sector displays quite different growth patterns, productivity growth is dominated by technological change. Technological change is found to have a negative correlation with efficiency change. Secondary regression performed in this study identifies the relationship between productivity growth measures and several key policy variables, such as effective protection rate, market concentration, and so forth. The productivity estimates are compared with those of the conventional Törnqvist productivity index.     

A note on decomposing the Malmquist productivity index by means of subvector homotheticity

Summary. This paper introduces a decomposition of the Malmquist productivity index into component indexes. The motivation is to derive an analogue of the decomposition of the T?rnqvist index into productivity and quality change provided by Fixler and Zieschang (1992) to the Malmquist index. Since we employ no second order approximations, this decomposition requires additional structure, namely a generalized version of Shephard's (1970) inverse homotheticity, which we dub subvector homotheticity. We show that subvector homotheticity is necessary and sufficient for our decomposition. Received: July 10, 1998; revised version: August 11, 1999     

CATEGORISATION OF ADDITIVE PURCHASING POWER PARITIES

Additivity is an important property for the aggregation methods used in constructing purchasing power parities. For a practical definition of additivity, this paper categorises all aditive methods. First of all, a generalisation of the Geary-Khamis method of aggregation is defined: this is called the Generalised Geary-Khamis, (GGK), approach. The key result proved is that, within a broad class of possible aggregation methods, the set of additive methods is precisely equivalent to the set of GGK indices. Some implications of this categorisation of additive methods are considered, both in the multilateral and bilateral cases. For example, in the multilateral case, the Iklé index is set in context as another special case of the GGK approach. In the bilateral case, it is shown that there always exists a GGK, (and therefore additive), equivalent to the Fisher Index.     

MULTILATERAL INDICES: CONFLICTING APPROACHES?

This short paper focusses on an apparent conflict between two results from different approaches to the problem of finding multilateral index numbers. The impossibility theorem of Van Veelen (2002 ) is an axiomatic result that rules out the existence of a multilateral index that satisfies four modest requirements. This also implies that no bilateral index can consistently be generalized to a multilateral setting. Adopting a revealed preference approach, Dowrick and Quiggin (1997 ) however construct a multilateral extention of Fisher's ideal index, which preserves a range of desirable properties. This note shows what it is that drives the divergence between those two results. It also gives implications for practical use of results from either approach.     

A restricted‐domain multilateral test approach to the theory of international comparisons*

This article develops a novel multilateral test approach to the problem of international comparisons. Many of the associated tests are justified as “reasonable” using the fact that they are direct analogues to properties of the cost‐of‐living index. Further support is bestowed upon the new approach by showing that it is equivalent to an extended version of Diewert's (1986) multilateral test approach. Finally, a number of alternative multilateral comparison formulas are evaluated and the relative superiority of two of them is established.     

Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition

Caves, Christensen and Diewert proposed a method for estimating a theoretical productivity index for a firm using Törnqvist input and output indexes, augmented by exogenous estimates of local returns to scale. However, in order to implement their method, they assumed that the firm maximized revenue in each period, conditional on the observed input vector in each period, taking output prices as fixed. This assumption is not warranted when there are increasing returns to scale. Thus in the present paper, it is assumed that the firm solves a monopolistic profit maximization problem when there are increasing returns to scale and the results of Caves, Christensen and Diewert are modified in accordance with this assumption.     

Purchasing Power Parities for Industry Comparisons Using Weighted Elteto–Koves–Szulc (EKS) Methods

This study has three main objectives. First, it develops a generalization of the commonly used EKS method to multilateral price comparisons. It is shown that the EKS system can be generalized so that weights can be attached to each of the link comparisons used in the EKS computations. These weights can account for differing levels of reliability of the underlying binary comparisons. Second, various reliability measures and corresponding weighting schemes are presented and their merits discussed. Finally, these new methods are applied to an international data set of manufacturing prices from the ICOP project. Although theoretically superior, it appears that the empirical impact of the weighted EKS method is generally small compared to the unweighted EKS. It is also found that this impact is larger when it is applied at lower levels of aggregation. Finally, the importance of using sector specific PPPs in assessing relative levels of manufacturing productivity is indicated.     

The Relative Price of Services

Prices of GDP relative to the exchange rate increase with income per capita, which is known as the Penn‐effect. This is generally attributed to services being cheaper relative to goods in poorer countries. In this paper we re‐examine the Penn‐effect based on a new set of PPPs for industry output. These are estimated in an augmented Geary–Khamis approach using prices for final goods, exports, and imports. The resulting multilateral PPPs cover 35 industries in 42 countries for the year 2005. We find large variation in relative prices of various services industries. In particular the Penn‐effect appears to be mostly due to the rapidly rising output prices of non‐market services. This seems related mainly to the high labor intensity of that sector.     

A Method of Calculating Regional Consumer Price Differentials with Illustrative Evidence from India

In this paper we propose a method of estimating multilateral regional price index numbers from a given household level data set on item-wise unit values/prices. The method is closely related to the Country-Product Dummy variable model of Summers (1973). This method is likely to be particularly useful in studies of regional comparisons of poverty and inequality, optimal commodity taxes and tax reforms. To illustrate the method, we use it to calculate the regional consumer price index numbers for Eastern, Western and Southern India (taking Northern India as the reference region) separately for three categories of rural and urban households, viz., all households and those below and above the poverty line, using household level unit records of the NSS 50th round (1993–94) Consumer Expenditure Survey.     

Trading gains: terms-of-trade and real-exchange-rate effects

This paper considers alternative measures of a country's trading gains, i.e., the extra income that it earns (or loses) as the result of changes in the relative prices relevant for international trade, and which makes up the difference between real gross domestic product (GDP) and real gross domestic income (GDI). Looking at both the Laspeyres and the Törnqvist aggregation, we show that the trading gains really consist of two components, a terms-of-trade effect and a real-exchange-rate effect. Nearly all national statistical agencies, receiving no firm guidance from international organizations in this matter, merely consider the first effect, which suggests that the so-called trading-gain estimates they publish are incomplete and misnamed. Even more seriously, it implies that the corresponding measures of real GDI they derive are conceptually flawed. A straightforward way to circumvent these difficulties is to use the gross domestic final expenditure price index as deflator when computing real GDI and the trading gains. Some numerical estimates for Australia are provided as an illustration. The paper also identifies the underlying linear and Translog real GDI functions for which the Laspeyres and Törnqvist terms-of-trade and real-exchange-rate effects are exact.     

Decomposing growth in revenues and costs into price,quantity and total factor productivity contributions

This article employs the superlative Fisher and Törnqvist indexes for exact decomposition of growth in nominal revenues and costs. The findings confirm the well-known result that these indexes very closely approximate each other, implying that the mathematically simpler and computationally easier Törnqvist is the more practicable index. Moreover, this article's nominal growth decomposition yields all the results from the more common real growth decomposition and is also more informative for policy purposes. Application to the US agricultural sector during 1948–2001 shows that of the 3.31% average annual growth in revenues, TFP growth contributed 1.90 percentage points (pct. pts.); growth in output prices added 1.43 pct. pts.; while growth in input quantities contributed?–?0.02 pct. pts. (i.e. fewer inputs). Therefore, real output growth (or revenue growth less output price growth) was 1.88 pct. pts., revealing that TFP's 1.90 pct. pts. growth contribution was fully responsible for real output growth with fewer inputs. Since revenues measure incomes, these results suggest that policy should focus more on measures to foster TFP growth than on specific price or quantity instruments to enhance income growth.     

A general class of additively decomposable inequality measures

Summary. This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a generalized mean in place of the arithmetic mean. Our characterization result is proved without invoking any regularity assumption (such as continuity) on the functional form of the inequality measure; instead, it relies on a minimal form of the transfer principle – or consistency with the Lorenz criterion – over two-person distributions. Received: October 27, 1997; revised: March 25, 1998     

Using Scanner Data to Estimate Country Price Parities: A Hedonic Regression Approach

This paper uses scanner data from the bar-code readers of retailers to provide estimates of inter-country price parities at the level of the basic heading. The use of such data is appealing given its extensive coverage of transactions, information on weights, prices and characteristics of items at a highly detailed level. The study uses dummy variable hedonic and exact/superlative hedonic index number formulations applied to an inter-country context for both bilateral and multilateral comparisons. Unlike conventional methods, such methods are not confined to matched samples comparisons and thus make use of the entire sample. Their application extends to price survey data using checklists on characteristics. The application is to scanner data on about 1 million transactions for television sets over two months in three countries. It is, to the authors' knowledge, the first such use of scanner data and application of the above hedonic frameworks in this context.     

Rationality, path independence, and the power structure

The justification of the requirement of consistency in aggregating individual preferences is to make the choice rational and path independent. This paper shows that a Paretian social choice mechanism that satisfies even the weakest rationality requirement which is related to the principle of some sort of maximization or path independence alone generates an extremely asymmetric power structure, e.g., almost dictatorship. Consequently, some well-known and interesting impossibility results are generalized.     

Environmental Policies, Comparative Advantage and the Gains/Losses from International Trade

A multihousehold economy with multilateral nondepletable externalities, environmental (output) taxation and governmental production of pure, nonexclusive and nonrivalrous public goods is assumed. Modelling many different households the "almost perfect" isomorphism between the normative analysis of public goods and environmental policies is highlighted. Globally valid necessary and sufficient conditions for gains from international trade are derived and interpreted. A simple yet general environmental policy rule ensuring trade gains is put forward. The law of comparative advantage is generalized to economies with multilateral nondepletable externalities and over or underproduced pure public goods.