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1998 | Buch

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Industrial Price, Quantity, and Productivity Indices

The Micro-Economic Theory and an Application

verfasst von: Bert M. Balk

Verlag: Springer US

Enthalten in: Professional Book Archive

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Industrial Price, Quantity, and Productivity Indices: The Micro-Economic Theory and an Application gives a comprehensive account of the micro-economic foundations of industrial price, quantity, and productivity indices. The various results available from the literature have been brought together into a consistent framework, based upon modern duality theory. This integration also made it possible to generalize several of these results. Thus, this book will be an important resource for theoretically as well as empirically-oriented researchers who seek to analyse economic problems with the help of index numbers.
Although this book's emphasis is on micro-economic theory, it is also intended as a practical guide. A full chapter is therefore devoted to an empirical application. Three different approaches are pursued: a straightforward empirical approach, a non-parametric estimation approach, and a parametric estimation approach. As well as illustrating some of the more important concepts explored in this book, and showing to what extent different computational approaches lead to different outcomes for the same measures, this chapter also makes a powerful case for the use of enterprise micro-data in economic research.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

A single-input/single-output firm

Although we focus in this book on indices for a multi-input/multi-output firm, by way of introduction it is useful to start with looking at a single-input/singleoutput firm. This is of course a highly artificial case, but extremely convenient to illustrate the main concepts. Thus, we consider a single firm through two time periods of equal length: a base period (t = 0) and a comparison period (t = 1). During the base period the firm uses x ⁰ quantity units of input to produce y ⁰ quantity units of output. Let the price (unit value) of the input in the base period be w ⁰ and the price of the output p ⁰. The corresponding data for the comparison period will be denoted by x ^l, y ¹, w ^l, p ^l. All quantities and prices are assumed to be strictly positive. In this case it is quite natural to define the input price index number by

$$ {\omega ^1}/{\omega ^0}. $$

Bert M. Balk

2. Primal Representations of the Technology

Abstract

This chapter reviews and extends some basic materials. Starting with the most general description of a technology, we introduce the input and output distance functions, the technical efficiency measures, the concepts of homotheticity, global constant returns to scale, and Hicks neutrality. Finally, we will discuss measures of local scale elasticity, and provide an interpretation of local constant returns to scale.

Bert M. Balk

3. The Input Side of the Firm: Direct Functions and Indices

Abstract

The central behavioral assumption in this chapter is that the firm minimizes the cost of its input conditional on exogenously determined quantities of output. Consequentially, the first section recalls some basic facts about the cost function. Thereafter three efficiency measures will be discussed. The second section introduces the input price index, discusses its properties, and derives several nonparametric approximations. The third section briefly considers the concept of a marginal input price index. The fourth section is devoted to the input quantity index, which is based on the input distance function. Section 3.5 discusses the relation between the input price index and the input quantity index. In section 3.6 we turn to the input based productivity index numbers. In order to derive nonparametric approximations for these indices it appears necessary to supplement the basic assumption by an assumption concerning profit maximization. In section 3.7 we show why certain assumptions are necessary in order to arrive at empirically computable expressions for the productivity index numbers. We also link these index numbers to measures of total factor productivity change.

Bert M. Balk

4. The Output Side of the Firm: Direct Functions and Indices

Abstract

The basic assumption in this chapter is that the firm maximizes revenue conditional on exogenously determined quantities of inputs. The first section reviews some well-known facts about the revenue function and the output efficiency measures. The second section introduces the output price index, which is based on the revenue function, discusses its properties and develops some nonparametric approximations. In section 4.3 we define the output quantity index, based on the output distance function, and in section 4.4 the relation between the output price and quantity index will be discussed. Then section 4.5 turns to the output based productivity indices. In order to derive nonparametric approximations it appears necessary to add an assumption about profit maximization. Finally, in section 4.6 we show under which condition the input based and the output based productivity indices coincide.

Bert M. Balk

5. The Input Side of the Firm: Indirect Functions and Indices

Abstract

In this chapter it is assumed that the firm minimizes its input cost subject to the attainment of a target revenue. The input and output prices are considered as given. The theory of the revenue-constrained firm was developed by Färe and Grosskopf (1994). Sidestepping the aggregation issue, Fisher (1995) used the revenue-constrained firm as a model for a small, fully open economy which trades outputs on world markets at fixed prices. The appropriate representations of the technology are now provided by the indirect input distance function and the indirect cost function. Their properties, as well as some efficiency measures, are discussed in the first section. The second section then proceeds to the definition of indirect input price and quantity indices. We discuss their properties and establish some nonparametric approximations. Section 5.3 turns to the indirect input based productivity indices. Using some additional assumptions it appears possible to derive nonparametric approximations to specific index numbers.

Bert M. Balk

6. The Output Side of the Firm: Indirect Functions and Indices

Abstract

In this chapter we assume that the firm maximizes its revenue subject to a constraint on its input cost. The input and output prices are considered as given. The theory of the cost-constrained firm was developed by Färe and Grosskopf (1994). We use the indirect output distance function and the indirect revenue function as representations of the technology. These representations, as well as the efficiency measures based on them, will be discussed in the first section. In section 6.2 the indirect output price index and quantity index are defined. We discuss their properties and derive some nonparametric approximations. In section 6.3 we turn to the indirect output based productivity indices. Using additional assumptions it appears possible to derive nonparametric approximations to specific instances of these indices.

Bert M. Balk

7. Profit Function Based Indices and Indicators

Abstract

The basic assumption in this chapter is the classical one, namely that the firm is a competitive profit maximizer. Accordingly, the appropriate representation of the technology is provided by the profit function. Based on this function we can define a simultaneous input and output price index, and an index of technical change. Section 7.1 then concludes with deriving some nonparametric approximations for these indices. In section 7.2 we relax some of the assumptions made in the previous section. Using the recently developed concept of a directional distance function it appears possible to define primal and dual productivity indicators in difference form. Their nonparametric approximations appear to coincide.

Bert M. Balk

8. An Application

Abstract

This chapter provides an empirical illustration to the theory presented in chapter 3. We will work with a balanced panel of 18 Dutch firms, classified as belonging to the rubber-processing industry, over the period 1978–1992. The basic micro-data come from the yearly production surveys. The firms vary considerably in size, the ratio of the largest to the smallest (measured in terms of the value of output) on average being 70 to 1. Averaged over the whole time period they account for over 80% of the industry’s employment as well as over 80% of its value added. One can, of course, doubt whether all these firms, within every year, indeed have access to the same technology. We will not pursue this, as we are using this dataset for the purpose of illustration only. For the same reason we refrain from questions concerning the accuracy of the data.

Bert M. Balk

9. Some Extensions

Abstract

In this final chapter we will introduce, without pretending to be exhaustive, a number of extensions to the basic theory developed in chapters 3 through 6. The models discussed in these chapters either condition on quantities or on prices. In the first section we will therefore look at models which avoid this dichotomy, and at the same time pave the way towards further generalizations. A strong restriction built into the foregoing theory is that inputs and outputs as such do not change through time. However, in reality we encounter quality change as well as disappearing and newly emerging inputs and outputs. The second section and the third section, respectively, are devoted to theoretical approaches for coping with these problems. All of these sections are by nature only indicative and hopefully helpful for those wishing to do further research.

Bert M. Balk

Backmatter

Titel: Industrial Price, Quantity, and Productivity Indices
verfasst von: Bert M. Balk
Verlag: Springer US
Electronic ISBN: 978-1-4757-5454-4
Print ISBN: 978-1-4419-5054-3
DOI: https://doi.org/10.1007/978-1-4757-5454-4

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Inhaltsverzeichnis

Frontmatter

1. Introduction

2. Primal Representations of the Technology

3. The Input Side of the Firm: Direct Functions and Indices

4. The Output Side of the Firm: Direct Functions and Indices

5. The Input Side of the Firm: Indirect Functions and Indices

6. The Output Side of the Firm: Indirect Functions and Indices

7. Profit Function Based Indices and Indicators

8. An Application

9. Some Extensions

Backmatter