W. Erwin Diewert

Flexible Functional Forms and Global Curvature Conditions

Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield satisfactory results. We develop two methods for imposing curvature conditions globally in the context of cost function estimation. The first method adopts Laus technique to a generalization of a functional form first proposed by McFadden. Using this Generalized McFadden functional form, it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally. The second method adopts a technique used by McFadden and Barnett, which is based on the fact that a non-negative sum of concave functions will be concave. Our various suggested techniques are illustrated using the U.S. Manufacturing data utilized by Berndt and Khaled

The decomposition of frontier cost function deviations into measures of technical and allocative efficiency

Abstract This paper presents a method for decomposing the deviations from a full frontier cost function into Farrell (1957) measures of technical and allocative efficiency. The method draws heavily on duality theory and requires no direct knowledge of the primal production frontier specification or its parameters. Thus, the method is applicable to a broad class of cost functions, including flexible functions such as the translog, which do not possess analytically derivable underlying production functions. The method easily generalizes to joint output production technologies where the decomposition of deviations from frontier profit functions would provide measures of technical, allocative, output mix and scale efficiency.

Linear Programming Tests of Regularity Conditions for Production Functions

The main purpose of this paper is to extend the nonparametric tests of regularity conditions on production functions and the related tests for the consistency of a data set with the hypothesis of productive efficiency or with the hypotheses of cost minimizing or profit maximizing behavior suggested by Afriat [1972] and Hanoch/’Rothschild [1972]. The tests suggested by these authors can be regarded as extensions of some tests due to Farrell [1957] and Farrell/Fieldhouse [1962]. Typically these tests involve the solution of a number of linear programming problems where the objective functions and the constraint functions are known functions of the given data; hence the title of the present paper.

Index Number Concepts, Measures and Decompositions of Productivity Growth

This paper explores the definitions and properties of total factor productivity growth (TFPG) indexes, focusing especially on the Paasche, Laspeyres, Fisher, Törnqvist, and implicit Törnqvist ones. These indexes can be evaluated from observable price and quantity data, and certain of these are shown to be measures of TFPG concepts and theoretical indexes that have been proposed in the literature. The mathematical relationships between these and quantity aggregates, financial measures, and price and quantity indexes are explored. Decompositions of the productivity growth indexes are also given. The paper concludes with a brief overview of some limitations on our analysis.

Productivity measurement for a distribution firm

The paper derives a consistent accounting framework for the treatment of inventories when measuring the productivity of a distribution firm. The average purchase price of an inventory item during an accounting period must be distinguished from its average selling price and these two average prices should be distinguished from the corresponding balance sheet prices. The accounting framework is implemented for a distribution firm which sold 76,000 separate items. The firm achieved a 9.6 percent per quarter total factor productivity growth rate over 6 quarters.The paper derives a consistent accounting framework for the treatment of inventories when measuring the productivity of a distribution firm. The average purchase price of an inventory item during an accounting period must be distinguished from its average selling price and these two average prices should be distinguished from the corresponding balance sheet prices. The accounting framework is implemented for a distribution firm which sold 76,000 separate items. The firm achieved a 9.6 percent per quarter total factor productivity growth rate over 6 quarters.

Accounting for Housing in a CPI

Statistical agencies in different nations usually use the rental equivalence approach to the treatment of housing in their CPIs but a few countries use the user cost approach. The paper argues that an opportunity cost approach is the correct theoretical framework for accounting for OOH in a CPI. This approach, first mentioned in a 2006 OECD paper by Diewert, is developed more fully here. We explore the relationship of this new approach to the usual rental equivalency and user cost approaches. The new approach leads to an Owner Occupied Housing Opportunity Cost (OOHOC) index that is a weighted average of the rental and the financial opportunity costs.

The Measurement of Waste within the Production Sector of an Open Economy

A methodology for measuring the loss of output that can be attributed to distortions within the production sector of an open economy is proposed. Examples of distortions are: tariffs on imported intermediate inputs, taxes or subsidies on exports, specific taxes on an output that is used as an input by another industry, (nonneutral) corporate income taxes, interindustry monopolistic markup pricing, and union induced wage differentials. The methodology generalizes the earlier work of Allais and Debreu.

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 six 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; 18 countries across the six 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 Ikle–Dikhanov–Balk multilateral system of index numbers which was used by Africa.

Functional Form Problems in Modeling Insurance and Gambling

Defining the outputs of the property insurance and gambling sectors of an economy has proved to be a difficult problem for national income accountants. It is well known that the traditional expected-utility model is not consistent with economic agents fully insuring their property. Thus the present paper adapts existing non-expected-utility theories to yield useful measures of output for the property insurance and gambling sectors.

INDEX NUMBER APPROACHES TO SEASONAL ADJUSTMENT

A seasonal commodity is one that either (1) is not available during certain seasons or (2) is always available but its prices or quantities fluctuate with the season or time of year. The existence of type-1 seasonal commodities in consumer preference functions means that the usual economic approach to index number theory cannot be applied to construct a short-term month-to-month or quarter-to-quarter consumer price index. We postulate various separability assumptions on intertemporal preferences that can be used to justify various seasonal index number formulas. One of our approaches leads to an index number solution to the problem of seasonal adjustment.