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## Über dieses Buch

This research was supported by the World Bank and the Social Sciences and Humanities R~search Council of Canada. Neither institution is responsible for the views expressed in this paper. The author is indebted to V. Corbo, A. Haymer, Y. Kanemoto, K. Lee, K. Mera, Hal Varian and A. Walters for helpful comments and to Elizabeth Lambert, Shehnaz Motani', and Jeanette Leigh Paisley for excellent typing services. I would like to dedicate this book to my wife, Virginia. TABLE OF CONTENTS 1. Introduction . . . •. . ••. . •. ••. •••. . . . •. . . . . •. •. . . •. . . •. •. •. . •. . . •. ••. • 2. A Simple Producer Benefit Measure . . ••. •••. ••••. •••••••••••. ••••••. • 8 3. Willingness to P~v Functions and Marginal Cost Functions ••••••••••• 15 4. Approximate Benefit Measures 30 5. Problems with the Producer Benefit Measure ••••••••••••• ! ••••••••••• 41 5. 1. Static versus Dynamic Benefit Measures ••••••••••••••••••• 41 5. 2. The Problem of Endogenous Prices for Local Goons ••••••••• 48 5. 3. The Neglect of Consumer Benefits' ••••••••••••••••••••••••• 56 6. Alternative Approaches to Benefit Measurement •••••••••••••••••••••• 70 6. 1. The Questionnaire or Sample Survey Approach •••••••••••••• 70 6. 2. Ex Post Accounting Approaches •••••••••••••••••••••••••••• 72 6. 3. Engineering and Mathematical Programming Approaches •••••• 74 6. 4. The Applied General Equilibrium Modelling Approach ~ •••••• 75 6. 5. The Differential Approach •••••••••••••••••••••••••••••••• 77 6. 6. The Econometric Approach . . •••••••••. •. ••••••. •••••••••. •• 79 7.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
A great deal of investment, both in developed and less developed countries, is made by governments and other public agencies in order to provide infrastructure services to consumers and producers in the affected region. The primary purpose of this report is to provide a methodology for evaluating the benefits (particularly to producers) of infrastructure investments.
Walter E. Diewert

### 2. A Simple Producer Benefit Measure

Abstract
Consider a region in which there are a finite number (F say) of profit maximizing firms or enterprises that consume various amounts of government infrastructure services of the types listed in the previous section. We assume that there are three classes of goods in this regional economy.
Walter E. Diewert

### 3. Willingness to Pay Functions and Marginal Cost Functions

Abstract
Recall that the gross measure of benefit change for firm f due to a change in infrastructure services from sf0 to sf1 was defined in the previous section to be the variable profit difference πf (p, sf1, kf) − π (p,sf0, kf). In this section, we explore this measure of firm benefit change in more detail. To save notational clutter, we shall drop the firm superscript f in what follows. Thus ir(p,s,k) refers to the restricted profit function for any one of the firms in our regional economy.
Walter E. Diewert

### 4. Approximate Benefit Measures

Abstract
Recall the net benefits function B defined by (5). The gross benefits of an infrastructure change from s to s for firm f were defined by (2) which we repeat below:
$$G^f \left( {p,s^{f0} ,s^{f1} ,k^f } \right) \equiv \pi ^f \left( {p,s^{f1} ,k^f } \right) - \pi ^f \left( {p,s^{f0} ,k^f } \right),f = 1, \ldots ,F$$
where πf is firm f’s restricted profit function defined by (1).
Walter E. Diewert

### 5. Problems with the Producer Benefit Measure

Abstract
Recall from definition (2) that the gross benefits of a change in infrastructure services for firm f from $$s^{f0} \equiv \left( {s_1^{f0} , \ldots ,s_I^{f0} } \right)$$ to s = $$s^{f1} \equiv \left( {s_1^{f1} , \ldots ,s_I^{f1} } \right)$$ was defined to be πf (p, sf1, kf) − π (p,sf0, kf), where πf is the restricted profit function of firm f defined by (1) above, p ≫ 0N is a reference vector of variable goods prices, and kf is a reference vector of fixed capital stocks that the firm has at its disposal.
Walter E. Diewert

### 6. Alternative Approaches to Benefit Measurement

Abstract
In this section, we list some of the alternative empirical approaches that could be used to measure the benefits of infrastructure investments. We also list some of the difficulties associated with each approach. The reason for putting this section so late in the paper is that before we measure something, we first must have a precise theoretical concept for what we are trying to measure. Thus in this section, we shall draw heavily on the theoretical benefit measures defined in the earlier sections of this paper.
Walter E. Diewert

### 7. The Selection of a Functional Form in the Econometric Approach

Abstract
In this section, we want to find methods for determining the firm technology set Tf or the dual restricted profit function πf (p,sf, kf) = maxx p·x: (x,sf, kf) εTf where x = (x1,.,...,xN) respresents a vector of variable outputs and inputs (if xi < 0, good i is an input), sf ≥ 0I represents a nonnegative vector of infrastructure services utilization by the firm and kf ≥ 0J represents a nonnegative vector of fixed capital stocks. The vector p ≡ (P1...,PN) ≫ 0N is the positive vector of variable goods prices that the firm faces. To simplify the notation, we drop the firm superscript f in what follows.
Walter E. Diewert

### 8. The Selection and Measurement of Variables in the Econometric Approach

Abstract
Our goal is to decompose each set of values for a firm into its price and quantity parts. We assume that our data source is a set of annual (or quarterly) accounting reports for a firm or a set of government census surveys.
Walter E. Diewert

### 9. The Estimation of Restricted Profit Functions in the Time Series Context

Abstract
We turn now to a discussion of certain additional problems that occur if we are attempting to estimate a restricted profit function in the context of time series data.
Walter E. Diewert

### 10. The Estimation of Restricted Profit Functions in the Cross Sectional Context

Abstract
The conceptual and measurement problems involved in empirically implementing our econometric models of producer behavior explained in section 7 above using just cross sectional data are very severe. We shall list some of the more important problems below.
Walter E. Diewert

### 11. Conclusion

Abstract
We have discussed a variety of approaches to measuring the benefits of investments in infrastructure services (or local public goods). Our simplest measure of benefits can be interpreted as the discounted increase in net outputs by producers in the project affected area less the discounted net cost of providing the extra infrastructure services, evaluated at constant (world) reference prices; see sections 2, 3 and 5.1. In section 5.2, we redefined our benefit measure to take into account the possible endogeneity of prices for some goods. In section 5.3, we further redefined our benefit measure to take into account possible benefits to consumers of the infrastructure investment project.
Walter E. Diewert

### Backmatter

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