Measurement of diverse, irreversible capital

• Published date: 01 December 2023
• Author: Robert D. Cairns
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/roiw.12614

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Review of Income and Wealth

Series 69, Number 4, December 2023

DOI: 10.1111/roiw.12614

MEASUREMENT OF DIVERSE, IRREVERSIBLE CAPITAL

BY ROBERT D. CAIRNS*

Department of Economics and Cireq, McGill University

CESifo

This paper revisitscapital measurement through a microeconomic analysis of a simple project consisting

of diverse types of irreversibly invested capital. Capital is aggregated using the numeraire. Thus, the

proposed method of measurement is a formof accounting. It associates all types of capital in a common

framework. Under certainty,user cost and depreciation take internal accounting values that obey three

axioms that comprise ve conditions. The accounting values proliferate, but they have only a limited

relation to market prices or shadow prices. Each type of capital earns the market rate of interest. In

practice,under uncertainty, calculation of the accounting values would require projectionsof basic data,

and would be hard to comprehend, especially for outsiders, and would leave room for moral hazard.

Because of these obstacles, accounting practice departs from the ideal based on cash owsand strictly

limits choice by using prescribed schedules of depreciation. These schedules are interpreted from an

economic perspective.

JEL Codes: D24, D92, M4

Keywords: accounting values, capital measurement, intangible capital, irreversible investment,

sunk capital

1. INTRODUCTION

The measurement of capital has long been subtle in economics (see Hicks,1974;

Usher, 1980). Traditionally, it has been predominantly a macro question. However,

decisions about investment and the use of capital are made by microentities, rms.

Partial irreversibility is a dening property of capital.It has a strong similarity

to full irreversibility but none to full reversibility (Davis and Cairns, 2017). Mea-

surement requires a periodic schedule of payments to capital (Baumol et al.,1982)

by which a rm can recover many forms of partially irreversible, or sunk, assets

over their useful lives. Explicit study of the problem is uncommon in capital theory,

which routinely assumes full reversibility and a single capital aggregate.1Diversity

Note: This work was supported by FRQSC. Thanks to two referees for their insightful and chal-

lenging comments. Thanks to LeonardCheung, James Cone, Graham Davis,Erwin Diewert, Rolf Färe,

KevinFox, Chris Green, JohnHartwick, Daniel Leonard, Alice Nakamura, KwangNg, Aude Pommeret,

Karen Pittel, Rick van der Ploeg, Michel Poitevin,Panu Poutvaara, Maxim Sinitsyn, Yi˘

git Sa˘

glam, Bill

Schworm, Dan Usher,Jo Voola, and Jun Zhou for their comments.Thanks to FRQSC for its nancial

support.

*Correspondence to: Robert D. Cairns, Department of Economics, McGill University, Montreal,

QC, Canada (robert.cairns@mcgill.ca).

1There are exceptions.Dixit and Pindyck (1994) and many others study real options for irreversible

capital. Stressis onoptimal investmentrather than the measurement on which it depends. Mitra and Ray

© 2022 International Association forResearch in Income and Wealth.

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Review of Income and Wealth, Series 69, Number 4, December 2023

and irreversibility compound the difculties foundby earlier economists in measur-

ing and aggregating capital (see Usher, 1980; Berndt, 1991; Hulten, 1991).

Incorporating the features of a rm’s capital stock requires methodological

revisions akin to those made for a multiproduct rm (Baumol et al.,1982). The

present study proposes to measure diverse types of capital under minimal assump-

tions by dening schedules of user costs to recover capital (Jorgenson, 1963). The

prototype for the analysis is an investment project that consists of a point input

of several forms of capital and ows of inputs and outputs of goods and services.

A project operates within an economic context that includes a technology and a

market structure.

Because nonoptimal programs arise in reality, the method must apply to them.

The manager makes decisions according to a criterion called a resource-allocation

mechanism (RAM). In introducingthis concept, Dasgupta and Mäler (2000)makea

major contribution by acknowledging thata RAM need notbe optimal. Therefore,

the role of marginal conditions must be claried.

For any economic context or RAM, the outcome of a project is a series of

observed cash ows. A crucial question is the measurement of the many types of

sunk assets using the observed ows. The rst part of the paper is a study under

certainty. Using net cash ows as the basis of accounting, it reveals the fundamen-

tal problem of accounting (Diewert, 2005a), that accounting schedules of user cost,

depreciation, and income are not unique.Under uncertainty, the problem is deeper

because most of the data used to derive schedules under certainty are unknown.

Furthermore, the nonuniqueness of legitimate accounting schedules for sunk capi-

tal leaves room for the misrepresentation of results.

In practice, accountancy confronts these problems by limiting choice through

adopting predetermined, algebraic schedules of depreciation. They do not obey

theoretic properties but provide well-understood indications, if not indicators, of

short-term performance.

2. MEASUREMENT OF SUNK ASSETS

As the papers edited by Usher (1980) illustrate,it is not feasible to dene a phys-

ical capital aggregate. Hicks (1974) asserts, “We cannot aggregate [capital] except

by adding money values.” Pecuniary aggregation over assets and time is a form

of accounting. Dasgupta and Mäler (2000) aggregate changes in multiple capital

stocks through time using “accounting prices.” Laffont and Tirole (1993,6;36,

Assumption 2) begin by noting that a regulator’s observations of cost are conned

to accounting measures.

The celebrated accounting scholar Demski (2008) considers ambiguity to be

omnipresent in capital accounting. Herein, ambiguity is argued to be fundamental

to production and allocation and therefore to economic measurement. The features

of capital addressed are that

(1983) consider the implications of irreversibility forpricing in competitive equilibrium. Most analysts,

including these, postulate a single type of capitalor else attempt to construct a scalar, physical measure

of capital if multiple types are considered. Competition and constant returns arefrequent assumptions.

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