the price elasticity of demand for wool in the united...

I -

111hK9 IFmi(OO LEnn©i~ @ll[))}EMAW[))

< IF(Q)~ W(Q)(Q)Lto TIN 1flHIIE lUJoI[o

WOOL ECONOMIC RESEARCH REPORT

NUMBER 11OCTOBER 1967

I. --

COMMONWEALTH OF AUSTRALIA

j

The Price Elasticity of

Demand for Wool

in the United Kingdom

An Economic Study of Demandfor a Factor

WOOL ECONOMIC RESEARCH REPORT NUMBER 11

BUREAU OF AGRICULTURAL ECONOMICS, CANBERRA, AUSTRALIA, OCTOBER 1967

REGISTERED AT THE G.P.O. SYDNEY FOR TRANSMISSION THROUGH THB POST AS A BOOK

9516/67

FOREWORD

THE subject of this report is the measurement of the price elasticity of demand forwool in the United Kingdom, one ofAustralia's foremost markets for wool. The estimateobtained gives a measure of how mill consumption of wool in the United Kingdom falls(rises)for every 1 %rise (fall) in worldprices. An informed knowledge ofsuch behaviouris of considerable interest to students of the wool market in so far as it allows a betterunderstanding of the U.K. market and ofsuch problems as the competition between wooland synthetics.

It is also possible to relate such a measure to the elasticities which are relevant tothe investigation of marketing schemes and ofpolicies for increasing Australian woolproduction. It will be recalled that the concept ofa price elasticity ofdemand was givena prominent role by economists in public discussions of a reserve price scheme forAustralian wool held during 1964 and 1965. The range of values of the elasticity usedin the analyses ofthe scheme wasfairly broad, however, because no recent estimate wasavailable.

The study was prepared in the Bureau's Wool Section by Mr M. Emmery under thesupervision of Mr P. Duane. It forms part of the programme of economic researchfinanced by the Wool Research Trust Fund. I wish to acknowledge, on behalf of MrEmmery, the helpful comments and suggestions made in connection with an earlier draftof the report by various other members of the Bureau and by Mr D. Terrell of theAustralian National University.

D. H. McKAY,Director.

Bureau of Agricultural Economics.Canberra. A.C.T.October 1967.

CONTENTSPAGE

Foreword

PART I: INTRODUCTION. 1Definition of Price Elasticity 1The U.K. Market 2Stage of Marketing or Manufacture 3

PART n. AN ECONOMIC MODEL OF FACTORS AFFECTING THEDEMAND FOR WOOL AT THE MILL LEVEL. 4

Theory of Derived Demand 4General Form of an Economic Model . 8The Price Elasticity of Demand for a Factor. 12

PART HI: DERIVATION OF A STATISTICAL MODEL FROM THEECONOMIC MODEL 16

Wool Prices 16The Dependent Variable 17Explanatory Variables 18Period of Study. 23Time Interval of Observation 23Response Period for the Dependent Variable 24Algebraic Form of the Model 25The Statistical Models 25

PART IV: ESTIMATION 30Constant Price Elasticity Models. 30Tests of Two Hypotheses . 33Variable Price Elasticity Models . 39

PART V: DISCUSSION AND APPLICATION OF RESULTS 45Summary of Results . 45Price Elasticity of Demand for Australian Wool 46Other Applications of the Price Elasticity 48

APPENDIXESAppendix A: Tabulation of Basic Statistical Data 50Appendix B: Estimates of all Parameters of Constant Elasticity Employed to Test

Hypotheses No. 1 and No. 2 52Appendix C: Simple Correlations between Variables . 54Appendix D: Propositions Relating to Specification Bias Due to a Proxy Regression

Variable 55Appendix E: Comparison with Horner's Estimates 57

GLOSSARY . 59

GRAPHSGraph I: Derivation of the Demand for Wool 5Graph Il: Fibre Substitution and the Demand for Wool 7Graph Ill: Supply-Demand Relationships for Synthetic Fibres 21Graph IV: United Kingdom Dominion Wool Prices 35Graph V: Price Elasticity of Demand for Wool. 41

Part I

Introduction

THE price elasticity of demand for wool is a measure of the effect of a change inwool prices on the demand for wool. A knowledge of this price/demand relation

ship is of importance to both research workers and policy makers concerned with themarket for wool. Appropriate estimates of the elasticity are essential to the quantitativestudy of such questions as the influence of wool prices on the competition betweenwool and synthetics; the effect of fluctuations in the price of wool on manufacturers'demand; the result of a variation in the exchange rate of an exporting country on therevenue obtained for its wool; or the effect on purchases of wool of attempts to restrictmarket price fluctuations as, for example, under a reserve price scheme.

DEFINITION OF PRICE ELASTICITY

The price elasticity of demand for wool may be defined as the ratio of the percentage change in the quantity of wool demanded to the percentage change in woolprice, when the change in price is 'small' and 'other things' are held constant. Themeasure is independent of the units in which price and quantity are measured.Mathematically, it is expressed either as

dQ P sa P7J = dP . Q or 7J = t:,P • Q

depending on whether a point or arc elasticity is intended.Generally, the possible range of values for 7J will be from 0 to -00. An estimate

of the price elasticity of demand by the D.K. and D.S.A. markets for (world) wool inthe interwar period was given by Homer to range between -0.4 and -0.6. (1)

Owing to a lack of estimates specific to the world market, this latter range has beenwidely adopted to represent the world elasticity in that period also.

Demand for the wool of a single exporting country will be more elastic than thatfor world wool. Speculations about the value of 7J for Australian raw wool in recenttimes have varied. In a RA.E. paper prepared for the Philp Committee, (2) the priceelasticity of demand was taken to range between -0.75 and -2.0. In a later paperprepared for the Wool Marketing Committee of the Australian'Wool Board, theworkings of a reserve price scheme were studied using values of -1.0 and -1.5. (3)

Wider ranges have been used by some other writers.Estimates of the price elasticity are also used to estimate the effect on wool prices

of a change in wool supplies. A more appropriate elasticity in this case, however, isthe price flexibility ratio, which may be defined as the ratio of the percentage changein price to the percentage change in quantity supplied, when the change in quantity

(1) F. B. Homer, 'Elasticity of Demand for the Exports of a Single Country', Review of Economicsand Statistics, Vol. 34, No. 4, November 1952, pp. 326-342.

(2) Bureau of Agricultural Economics, Canberra, 'Estimates of Capital Requirements, RunningCosts and Profits or Losses of a Reserve Price Scheme for Australian Wool' (unpublished), 1961.

(3) E. L. Jenkins, An Assessment of Costs and Capital of a Reserve Price Scheme for AustralianWool. Wool Economic Research Report, No. 7, RA. E., December 1964.

1

2 PRICE ELASTICITY OF DEMAND FOR WOOL IN THE U.K.

is 'small' and 'other things' are held constant. The reciprocal of the price elasticitywill not necessarily be equal to the price flexibility ratio. The things held constant indefining a price elasticity are typically the prices of other commodities; the thingsheld constant in defining a price flexibility ratio are typically the quantities of othercommodities. Under these conditions the reciprocal of one of these elasticities willequal the other only if the cross price elasticities of demand are equal to zero. (4)

Otherwise the reciprocal of the price elasticity will generally underestimate, inabsolute values, the price flexibility ratio.

Price flexibility ratios have a valuable application in assessing the effect of changesin wool production on wool prices and consequently on gross wool receipts.

The price elasticity of demand for wool as defined above is still quite abstract incontent. In order to identify a particular price elasticity, it is necessary to specify(a) the source of demand (e.g. world or U.K. demand for wool), (b) the source ofsupply (e.g. demand for world or Australian wool), and (c) the marketing stage atwhich the elasticity is to be measured (e.g. demand for wool at auction or at the milllevel). These identifying features of the price elasticity to be measured in this reportare discussed below. Other features such as time are dealt with in later sections.

THE U.K. MARKET

There are several reasons underlying the choice of the U.K. market for the study:(i) the data available are reasonably complete and reliable compared with those

of many other countries;(ii) the United Kingdom is a major and consistent buyer of Australian wool;

(iii) there are no arbitrary restrictions on quantities of wool consumed by millsor brought in from overseas;

(iv) although the United Kingdom is one of the world's largest consumers of rawwool in manufactures for both domestic and export markets, its share oftotal world wool consumption is still small enough for one to venture somesimplifying assumptions about the conditions of wool supply to the UnitedKingdom.

In previous writings, and later in the present report, the price elasticity of U.K.demand has been used as an indicator of the world elasticity. The relation betweenthese different elasticities is as follows: the price elasticity of world demand for woolis equal to the weighted average of the corresponding country elasticities, the weightsbeing the quantities of wool used by each country. (5) Therefore, the elasticity ofdemand for wool in the United Kingdom is a good indicator of the world elasticityprovided that the U.K. elasticity is approximately equal to a particular weightedaverage of the elasticities for other countries. One way in which this could arise iswhen all the country elasticities are approximately equal.

It is instructive also to review the relationship between a price elasticity of worlddemand for (all) wool and that for Australian wool. Following Powell, (6) one mayexpress the price elasticity of demand for Australian wool (l'} A) as follows:

(4) See J. P. Houck, 'The Relationship of Direct Price Flexibilities to Direct Price Elasticities',Journal of Farm Economics, Vol. 47, No. 3, August 1965.

(5) H. Wold and L. Jureen, Demand Analysis (New York: John Wiley & Sons Inc., 1953), p, 118.(6) A. Powell, 'Export Receipts and Expansion in the Wool Industry', The Australian Journal

of Agricultural Economics, Vol. 3, No. 2, December 1959, pp. 67,73 and 74.

(1)

INTRODUCTION 3

where

TJ w = the price elasticity of world demand for raw wool;Er = the price elasticity of supply of raw wool from suppliers other than

Australia; and

f = the Australian share of the world market.

In general, the higher the two elasticities TJ wand Er (ignoring sign) and the smallerthe proportion of world wool supplied by Australia, the greater will be the elasticityof demand for Australian wool. The fact that f < I ensures that the demand forAustralian wool is more elastic than that for all wool, given that Er> O. However, ifaccount is taken of transport costs and other trade barriers, the export demand forAustralian wool can be shown to be somewhat less elastic in Australia than is indicatedby (1).(7)

Because of the above relations among elasticities, the results of this study ofdemand by the United Kingdom have a potential application to world market demandfor world wool or for wool from a single exporting country.

STAGE OF MARKETING OR MANUFACTURE

The demand for wool is a derived demand which is transmitted from the finalconsumer through the retailer, wholesaler, garment maker, cloth manufacturer andeventually to the purchaser of raw wool at auction. The price elasticity of demandmay be measured at any of these various manufacturing and marketing stages; theparticular stage considered most appropriate depends on the purpose for which theelasticity is required. For a wool exporting country such as Australia, the priceelasticity of demand for raw wool is of most interest.

The demand for raw wool may be analysed at either of two convenient stagesat purchases at auction or at the level of mill consumption. For this study, mill consumption has been chosen because it is more convenient with respect to the availabilityof data, and because it is more appropriate to the measurement of manufacturers'response to price changes. Wool auction data are expected to include an importantelement of short-term stock changes because of speculative trading. Data on millconsumption, on the other hand, should reflect a longer-run response by manufacturers. It is expected that the use of mill consumption data will lead to an estimteaof a longer-run price elasticity than would a dependent variable defined by auctionpurchases, especially when account is taken (later) of the interval of observation.

(7) See F. B. Homer, op, cit., p. 328 et seq.

Part 11

An Economic Model of Factors Affecting theDemand for Wool at the Mill Level

THEORY OF DERIVED DEMAND

(The demand for raw wool by the wool textile manufacturer is derived from'[rhe

demand for wool products bythe final consumer at the retail level. The relationbetween the demands for a final product and its factors of production is outlined inthe theory of derived demand developed by Marshall. (8)

The demand for such final products as wool textiles may be taken as reflectingdirectly the 'utility' which the consumer attaches to them, while the demand forfactors of production like raw wool must reflect this utility indirectly through thedemand for the final product. The link between final product and factor demands isclosest in the special case where factors must be combined in constant proportion,i.e. where the quantity of each factor used always varies in a constant proportion tothe quantity of the product. The special case of constant proportions is a useful onewith which to demonstrate the construction of a derived demand schedule.

In order to simplify the demonstration, it is assumed that the production of finalwool products for retail sale requires two factors of production in constant proportion-wool and 'other factors'. Graph I (a) shows a set of supply curves for finalwool products and the two prescribed factors of production as well as the demandcurve for wool products. The scales on the quantity and price axes must be such asto reflect the constant factor proportions, thus enabling the final product and factorcurves to be compared in the manner required. For example, if it requires two unitsof wool and six units of 'other factors' to produce one unit of wool products, eachquantity unit on the horizontal axis represents the quantity of two units of wool, orsix units of 'other factors', or one unit of wool products. The price axis will show theprice per two units of wool, the price per six units of 'other factors' and the priceper unit of wool products.

The three supply curves show the minimum prices at which given quantities ofthe final product and the two factors of production will be forthcoming. Given theassumption of constant proportions, the supply curve for wool products (Sy) willnecessarily equal the vertical sum of the supply curves for wool (Sw) and 'other factors'(Srn)'

The demand curve, D y , shows the maximum prices which consumers are willingto pay for given quantities of wool products. The intersection of Sy and D'; gives theequilibrium price and quantity of wool products, and also the equilibrium quantitiesof the two factors of production; prices of the latter are determined simultaneously.

To demonstrate how the demand for a factor is derived, suppose that D; and Srn

(8) Alfred Marshall, Principles of Economics, 9th edition, Book V, Chapt. 6 (London: Macmillanand Co. Limited, 1961).

4

(I

9516/67-2

AN ECONOMIC MODEL OF FACTORS

GRAPH I

DERIVATION OF THE DEMAND FOR WOOL

Prices

oQuantities

Prices

(b)

Srn

au .. n t i t i e s

5


are known as in Graph I (b), and it is desired to complete D w • One may proceed asfollows: the maximum price which purchasers would be willing to pay for a givenquantity of raw wool is equal to the maximum price which consumers would bewilling to pay for the corresponding quantity of wool products, less the minimumprice at which owners of labour, etc., would be willing to supply the correspondingquantity of 'other factors'. Having regard to the definitions of supply and demandcurves given earlier, the preceding sentence provides an operational definition of thederived demand curve for wool. Thus D'; is equal to the demand curve for woolproducts (Dy ) less the supply curve of 'other factors' (Srn)' the difference beingmeasured vertically. For given supply conditions of 'other factors' and demand conditions for wool products, the equilibrium price of wool is given by the intersectionof the supply curve for wool with the derived demand curve for wool.

The demand curve for 'other factors' can be derived in a like manner as thevertical difference between D; and the supply curve of wool (Sw),

In this simplified model of the demand for wool, with its underlying assumptionof constant proportions, it can be shown that all shifts in the demand curve for woolmust arise from shifts in the retail demand curve for wool products and/or shifts inthe supply curve for 'other factors'. With reference to Graph I (b), a shift to the rightin Dy' other things remaining constant, would in turn cause a shift to the right inthe demand curves for both 'factors. Similarly, a shift to the right in the supply curveof 'other factors' would also have the effect of shifting to the right the demand curvefor wool.

For a more realistic study of the demand for wool, it is necessary firstly torecognise the presence of stocks of semi-processed and final wool products in theproduction and distribution pipeline between the demand for wool and consumer

)

demand for wool products. Shifts in the demand curve for wool at the mill level may. arise because of shifts in the demand curves for stocks of semi-processed and final

wool products held by textile manufacturers, garment makers, wholesalers andretailers.

Secondly, it is necessary to relax the assumption of constant proportions. Woolis in competition with substitute fibres, particularly the synthetics, in the productionof wool-type products. The replacement of wool by synthetic fibres has increasedrapidly in many end uses in the past decade. This continued substitution over timeof synthetic fibres for wool cannot be adequately explained by relative fibre prices,for the average ratio of these prices remained fairly stable up to the early 1960s. Thetrend towards synthetics has obviously been favoured by autonomous circumstances

J

consistent with the introduction and exploitation of a new factor. (9) It is most desirabletherefore to specify the supply of competing fibres separately from the supply of

. other factors, in explaining movements in the demand curve for wool.Shifts to the right in the supply curve of fibres competing with wool and the

\

effect on demand for such fibres of a gradual 'acceptance' or recognition of theirqualities have been regarded often as sufficient causes of a decline in wool's share ofthe market for wool-type fibres. The effect of fibre substitution cannot be illustratedwithin the framework of Graph I. However, a simple 'static' illustration of howincreases in the supply of synthetics alone could lead to their substitution for wooland lower wool prices is presented in Graph Il.

(9) A more detailed discussion of the possible factors determining the supply and price of thesynthetic fibres is given in Part Ill, pp. 20-22.

AN ECONOMIC MODEL OF FACTORS

GRAPH II

FIBRE SUBSTITUTION AND THE DEMAND FOR WOOL

Prices

Sw

7

pIW

"---------- --~-----

""

II

____1__ 1.. _I 1 ......I .,t ......I ....

...,. I....... I I

....... I I

.> :I

Ss

SIS

Ow

0 1W

Quantitit's

For the purpose of illustration, the supply of and demand for both wool andsynthetic fibres are shown to be equated initially at equilibrium prices P IV and P,respectively. Some independent circumstance is then presumed to shift SS' the supplycurve for synthetics, to the right and to a new position at S;. Synthetic prices wouldfall from P, to P'. A consequent (first-round) substitution of synthetics for woolwould cause a shift to the left in the demand curve for wool from D w to D~ and alowering of wool prices from P IV to P~. Further rounds of price changes would ensuebefore equilibrium is' regained, but the net effect would be that prices of both fibreswould be lower than they were initially.

It should be noted that the two graphs are presented simply to illustrate thederivation of the demand curve for a factor (Graph I), and the effect of relaxing theassumption of constant proportions (Graph II); they do not reflect the expectedslopes of the demand and supply curves relevant to the U.K. demand for wool.

Finally, the development of the theory has been such that it has not seemed


necessary at any stage to consider the price of wool products as an influence on thedemand for wool. This is interesting because, in most practical applications of a priceelasticity of demand for a factor, it is preferable that the price elasticity be definedwith the price of the product allowed to vary. In this respect, a formal case for theexclusion of the price of the final product from a model of factor demand is givenby Diehl. (10) An interpretation of his explanation may be summarised as follows.

The demand for raw wool can be expressed as:

(2) C = rir., z., Z,)

wherep w = the price of raw wool;Zd = those factors responsible for shifts in the demand for wool products; and

Z, = shifters of the supply of 'other factors'.

The supply of wool products (Sy) is taken as:

(3) s, = g (P w , zs, Py)and the demand for wool products (D y ) as:

(4) n, = h (Py , Zd)

At equilibrium in the product market, S, = Dy , and the solution of (3) and (4)for Py gives -

(5) r, = j (Pw , z., Zs)

Comparing (5) with (2), it is obvious that the price of wool products has alreadybeen excluded from equation (2)-our demand for raw wool-by an implicit assumption of equilibrium in the product market.

GENERAL FORM OF AN ECONOMIC MODEL

The theory of derived demand provides the basis for a generalised economic modelof the demand for raw wool. The formulation of a model specific to the UnitedKingdom, and the statistical model which is derived from it, depend on the natureof the market system of which the U.K. demand for raw wool and the other relationsdiscussed above are a part. The most important other relation in this system is thesupply of wool to the United Kingdom. The economic model chosen for interpreting'the demand for raw wool in the United Kingdom is characterised by the behaviourand interdependence of these four relations:

(i) the supply of raw wool to the United Kingdom;(ii) the U.K. demand for wool products;

(iii) the supply of 'other factors';(iv) the U.K. demand for raw wool.

The shape of the wool supply curve to the United Kingdom and its behaviourover the study period present several of the many problems to be faced in the specification of a statistical model in Part Ill. At issue are the chances of estimating a demand

(IO)W. D. Diehl, Analysis of Derived Demand for Hogs, M.Se. thesis, North Carolina StateCollege, 1962 (unpublished).

relationship from available data and, if the data allow, whether it can be estimatedindependently of the supply relationship. Rather than face such questions just yet, itis proposed instead to anticipate some of the work of Part III and to indicate verybroadly the kind of dependent and explanatory variables which have most relevanceto an understanding of relation (iv), the U.K. demand for wool. The support formost of the variables is derived directly from an earlier consideration of relations (ii)and (iii).

1. The Dependent Variable

The consumption of raw wool by the U.K. wool textile industry is measured atthe carding stage (the first processing stage following the removal of grease andvegetable fault from the wool) and is referred to as the mill consumption of raw wool.

The major stages in the movement of wool from mill consumption to the finalconsumer at home and oversea is illustrated in the diagram on page 10. The box inthe upper half of the diagram lists the main processes which take place in the U.K.wool textile industry. The hosiery and carpet industries are treated as separateentities receiving their raw material from the wool textile industry in the form ofyarn. The final output of the wool textile industry is equal to the sum of all the flowsout of the box in the diagram and is referred to as manufacturers' sales of woolproducts. Foreign trade occurs in the product of each major stage of production. Itis estimated that the total quantity of wool products imported amounts to about 7%and the quantity exported to about 40%of manufacturers' sales of wool products.

The total demand for wool at the mill level is derived from the demand for productsby domestic and foreign consumers. This demand for wool is examined at two levels:

(a) the total demand for raw wool by the U.K. wool textile industryas representedby mill consumption of raw wool; and

(b) the demand for raw wool by the same industry on behalf of the U.K. domesticconsumer, as represented by mill consumption less total net exports of woolproducts and referred to here as wool available for home consumption.

Mill consumption of wool and wool available for home consumption are treated asalternative dependent variables in the analysis; and since the economic factorsaffecting both are of the same nature conceptually, the differences between the twovariables are ignored in the following discussion of the factors which affect thedependent variable.

I

JAN ECONOMIC MODEL OF FACTORS 9

2. Explanatory Variables

The theory of derived demand directs the choice of explanatory variables for theU.K. demand for raw wool to wool prices and those factors responsible for shifts inthe demand for wool products curve and shifts in the supply of 'other factors'curve. (11) Supplies of wool to the United Kingdom come partly from the domesticclip but predominantly from imports purchased on the world market. The price ofraw wool relevant to the U.K. manufacturer is the world price adjusted for freightand insurance costs to the United Kingdom.

Shifts in the demand for wool products may arise from changes in population,disposable incomes, the prices/quantities of competing products, consumer tastes

(11) Henceforth, the words 'curve' and 'schedule' will largely be dropped from such expressions;unless otherwise stated, the words 'demand .. .' and 'supply .. .' will be used to refer to demand andsupply schedules. .


MAJOR STAGES IN THE FLOW OF WOOL FROM MILL CONSUMPTION TO THEFINAL CONSUMER IN THE UNITED KINGDOM

Mill consumption of raw wooland other fibres

Woollensystem

1Production of tops(worsted system)

l~"----H""'~ Foreign trade~Y 1·n tops

Production of yarns

...''''IF

Production ofwoven fabrics

~...

Handknitting yarnfor domestic 1----1-......--------1retail sale .....

Delivery of yarn ..........--+--1...to carpet andhosierymanufacturers

I....~

,,11

Clothing and piecegoods manufacturers

II

JWholesalers

I

I

Retailers

______......Domestic Iconsumer ...----J Foreign I

consume. -----J

AN ECONOMIC MODEL OF FACTORS 11

and fashions. The products and services which compete with wool products can bedivided into three categories:

(i) products which compete with wool in the same end uses, such as those madefrom non-wool fibres, plastics or synthetic foams;

(ii) products or services such as central heating which provide an alternativeform of warmth to wool-type clothing;

(iii) products which compete for the consumer's expenditure in general, particularly other consumer durables.

Products in categories (i) and (ii) are judged worthy of further consideration.However, wool products are thought to account for too small a share of total consumerexpenditure, or of expenditure on consumer durables, to justify the specification ofsuch a broad group of products as category (iii).

Changes in tastes and fashions over time are widely recognised as an importantfactor influencing the demand for wool products. Examples of these changes are thetrends to lighter weight and more casual type clothing, and to clothing which issuitable for machine washing. (12)

Another possible source of variation in the demand for raw wool is the influenceof shifts in the demand for stocks of wool products (i.e. tops, yarns and fabrics) heldby manufacturers. Planned shifts in the demand for these stocks may depend largelyon short-term trade expectations and speculations about future demand for the finalproducts. The specification of an indicator of planned shifts in the demand for stocksof wool products was considered desirable if:

(i) the variation in stocks of wool products appeared to be related to changesin the total demand for wool products; and

(ii) the movements in such stocks were not adequately explained by other variablesaffecting the demand for wool products.

Data are available on stocks of wool tops, but not on stocks of yarns and fabricsheld in the U.K. wool textile industry. This severely limits the coverage of anyexamination of stocks; stocks of tops, however, are sufficiently large and subject toenough fluctuation to warrant consideration on their own. In the proposed studyperiod from 1952 to 1964, stocks of tops at the end of each quarter averaged 54m lbor the equivalent of 2.3 months' consumption of tops (i.e. tops drawn plus exports).The ratio of stocks of tops to consumption fluctuated in the range of 1.4 to 2.9months, and it was clear that these movements were not caused by a seasonal patternof activity. The possibility that shifts in stocks of tops were adequately explained byshifts in consumer demand for wool products was tested using manufacturers' salesof wool products as a proxy for consumer demand. Stocks of tops were found to bearno relationship (r = 0.19 for fifty post-1952 quarterly observations) to this proxyvariable.

It is thought that shifts in the demand for stocks of tops are sufficiently large toexert a significant influence on wool consumption. As these variations in stocks donot appear to be represented by other explanatory variables in the model, it is proposed to include them as an explanatory variable.

Among the 'other factors' of production whose conditions of supply influence thedemand for raw wool, synthetic fibres have already been mentioned as deservingseparate specification because they are close substitutes in production. Two other

(12) B.A.E., Wool Consumption Trends in Western Europe and the United States, Wool EconomicResearch Report, No. 3, January 1961.


factors whose conditions of supply are considered likely to influence the demand forwool are wool textile labour and working capital (credit) for the industry.

If attention is now focused on relation (iv) in the economic model, it is possibleto list the main factors which concern it in principle:

(6) Cm or c, = f(P, N, Y, M, F, T, A, L, K)

where

Cm = mill consumption of raw wool;Ch = raw wool available for home consumption;P = price of raw wool;N = population;Y = disposable incomes;

M = price or quantity of products competing with consumer wool products;F = consumer tastes and fashion;T = an indicator of planned shifts in the demand for stocks of wool tops;A = price or quantity of synthetic fibres competitive with wool in production;L = price or quantity of labour employed in the manufacture of wool products;

and

K = price or quantity of capital (credit) for the wool textile industry.

The variables N, Y, M, F and T are recognised as shift factors in the demand forwool products, and A, Land K as denoting shifts in the supply of 'other factors' ofproduction.

Despite the fact that several of the demand variables have been described in somedetail, it is clear that much remains to be accomplished in the direction of makingequation (6) less abstract. This task is taken up in Part Ill. Before doing this, however,it is convenient to review what can be learned from economic theory about the priceelasticity of demand for a factor of production.

THE PRICE ELASTICITY OF DEMAND FOR A FACTOR

Marshall gives four principles governing the price elasticity of the derived demandfor a factor of production. (13) The demand will be more inelastic:

(i) the more essential the factor concerned is to the production of the finalcommodity;

(ii) the more inelastic the demand for the commodity;(iii) the smaller the share of the final costs of the commodity contributed by the

factor concerned; and(iv) the more inelastic the supply of the other factors of production.

Marshall's second, third and fourth conditions can be illustrated by reference againto Graph I. Remembering that the demand curve for the factor wool, D w ' is derivedfrom the vertical difference between the demand curve of the final product, Dy , andthe supply curve of other factors, Sm, it is clear that D'; will have a steeper slope orwill be otherwise more inelastic:

(13) A. Marshall, op, cit., p, 387 et seq. An excellent account of the application of the theory ofderived demand to statistical estimation is given by W. D. Diehl, op. cit.

(i) the steeper the slope of Dy , i.e. the more inelastic is D y (second condition);

(ii) the smaller the ratio ~;IV, the smaller is wool's contribution to the final costy

of the commodity (third condition); and(iii) the steeper the slope of Srn, i.e. the more inelastic is Srn (fourth condition).Marshall's first condition cannot be demonstrated in Graph I (b) because of the

assumption of constant factor proportions. It is noted that when the assumptionof constant factor proportions is relaxed, the third condition is true only when theelasticity of demand for the final product is greater (in absolute value) than theelasticity of substitution between the factor concerned and other factors.vv Thislatter condition is assumed to hold in the later discussion of Marshall's third conditionin respect of the demand for wool.

It is emphasised that Marshall's four conditions give little indication of thegeneral size of demand elasticities for factors. For example, they offer no supportfor a conclusion that the demand for a factor should be price inelastic (i.e.-1 < TJ < 0) merely because the demand for the corresponding product happensto be inelastic. Rather, the conditions are concerned with tendencies towards a moreor less elastic demand. The following examination of Marshall's conditions in respectof the demand for raw wool leads to two hypotheses about its price elasticity ofdemand, namely:

(i) that it has been growing more elastic over time; and(ii) that it is more elastic in periods of high wool prices.

The kind of factors which are to be held constant in estimating the price elasticityof demand for raw wool in this report are given in equation (6). Note that the priceelasticity so defined allows the price of wool products to vary. Within the frameworkof the partial equilibrium analysis of the report, the price of wool products has beenshown (page 8) to be a function of the price of wool and of those factors responsiblefor shifts in the demand for wool products and for shifts in the supply of 'otherfactors'. Such a relationship followed from an assumption of equilibrium in the woolproduct market. The various shift factors are accounted for in equation (6), but asfar as the price elasticity is concerned, the price of wool products is allowed to varywith the price of raw wool.

Marshall's first condition may be translated into the following terms: the morerestricted the availability of substitute factors is, the more inelastic will be the demandfor a factor. The condition chiefly concerns the degree to which substitute factorscan and will replace a factor as a result of changes in the price of that factor.

Before the advent of the synthetic fibres, there were no close substitutes for woolin the production of wool products. (15) Other fibres such as rayon, cotton and hairhave long been incorporated in wool products but, compared with synthetics, itwould appear that these fibres have been more complementary to wool than substitutesfor it. For some years now, the synthetic fibres have been competing with wool in the

I

I AN ECONOMIC MODEL OF FACTORS 13

(14) For a full discussion of the more rigorous mathematical tests of Marshall's conditions andof the circumstances under which the third condition is true, see M. Bronfenbrenner, 'Notes on theElasticity of Derived Demand', and J. R. Hicks, 'Marshall's Third Rule: A Further Comment', OxfordEconomic Papers, Vol. 13, No. 3, October 1961.

(15) This statement should be qualified perhaps by the recognition that non-virgin wool providesa close substitute for raw wool; however, the role of non-virgin wool as a substitute fibre is rathercircumscribed in the sense that its availability and price are determined predominantly by the consumption and price of raw wool.9516/67-3


latter's traditional end uses, and the rapidity with which their share of the markethas increased has been such that, whatever status wool used to have as an essentialfactor in production, it must surely have been lowered and, ceteris paribus, thedemand for wool made more price elastic.

It has been suggested by Grubel that a raw material undergoing replacement bya substitute becomes more essential to an industry in times of high prices for thefinal product, and therefore, that there is a tendency for the demand for an individualraw material to be more price inelastic when its price is high. The reason advanced isthat firms would be more reluctant to substitute for a factor when the demand forthe final product was high because of the likely technical uncertainties and temporaryreductions in output involved in factor substitution. (16) In the case of wool andsynthetics, however, it is judged that the technical difficulties in fibre substitution,except possibly those associated with the initial introduction of synthetics, are notso large as to influence the time at which fibre proportions are altered or, as the aboveargument would have it, the times at which they are not altered.

Marshall's second condition requires no explanation-the more inelastic thedemand for the commodity is, the more inelastic will be the demand for the factor.Little is known about the value of the elasticity of demand for final wool productsthough several studies of consumer demand for (all) clothing have found it to beprice inelastic. (17) As a broad generalisation, however, there has been a progressiveincrease in the availability of substitutes for final wool products (for example thesubstitution of central heating for heavy wool clothing) and this would tend to makethe demand for wool products, and consequently the demand for wool, more priceelastic.

The contribution of raw wool to the final cost of wool products is estimated to befairly small-about 10-13 %yS) There is evidence from the U.S.A. also that the contribution made by the cost of wool to the retail value of wool products has shownlittle or no trend over the last fifteen years, although it did vary in line with fluctuationsin raw wool prices, ranging from 25%in the boom year of 1951 to 9%in the recessionyear of 1958.(19) According to Marshall's third condition, this relationship betweenwool prices and the contribution of wool to the final cost of wool products indicatesceteris paribus that the demand for wool will be more elastic in periods of high woolprices:

Marshall's fourth condition states that the more inelastic the supply of otherfactors of production is, the more inelastic is the demand for a factor. No estimatesof the elasticity of supply of other factors of production to the wool textile industryare available. One of the major factors concerned is labour and it is not known howprice responsive this factor has become in the United Kingdom or in the textileindustry over the last decade. Nevertheless, it is reasonable to assume that the supplyof so-called 'fixed' factors in the United Kingdom-skilled labour, machinery, factory

(16) H. G. Grubel, 'Foreign Exchange Earnings and Price Stabilization Schemes', The AmericanEconomic Review, Vol. 54, No. 4, June 1964, p. 382.

(17) R. Stone and D. W. Rowe, 'The Market Demand for Durable Goods', Econometrica, Vol. 25,No. 3, July 1957; C. E. V. Leser, 'The Pattern of Australian Demand', Economic Record, Vol. 34,No. 68, August 1958.

(18) M. Fead, 'Cost Components of Manufactured Wool Products', Quarterly Review ofAgriculturalEconomics, Vol. XIV, No. 1, January 1961; and L. D. Howell, The American Textile Industry, U.S.D.A.Agricultural Economic Report, No. 58, 1965, p. 13.

(19) L. D. Howell, op. cit.

space, etc.-should become more inelastic in periods of high U.K. wool consumption,i.e, when the limits of industry capacity are approached and when one might expectwool prices to be higher than usual. As it happens, U.K. mill consumption is nothighly correlated with world consumption or with world prices.(20) Therefore, althoughthere are good reasons for believing that the supply of fixed factors, and consequentlythe demand for wool, should be more inelastic in periods of high U.K. wool consumption, there is not much evidence for presuming that this tendency towards amore inelastic demand will coincide with periods of high prices.

The results of the above examination of Marshall's four conditions, in so far asthey relate to the price elasticity of demand for wool, are summarised in Table No. 1.

I AN ECONOMIC MODEL OF FACTORS 15

TABLE No. 1

EFFECTS OF COMPETITION FROM SUBSTITUTES AND OF PERIODS OF HIGH PRICESON THE PRICE ELASTICITY OF DEMAND FOR WOOL

Direction of Effect of Competition and High Priceson 17] i as Indicated by Marshall's Conditions Hypothesised

Influence Net

1st 2nd 3rd 4thEffect

Condition Condition Condition Condition

Increasing degree of fibre corn-petition increase increase neutral neutral increase

High prices neutral neutral increase possible increasedecrease

Marshall's first and second conditions favour an hypothesis that the demand forwool has been growing more elastic in recent years, particularly since the advent ofsynthetics; the third and fourth conditions appear to be neutral in this regard.

The first and second conditions appear to be neutral to the influence of high woolprices on the price elasticity of demand for wool, while the third condition favours amore elastic demand and the fourth (possibly) a less elastic demand. In arriving atan hypothesis as to the net effect, it was borne in mind that a number of commentators on a reserve price scheme for Australian wool have discussed the possibilityofa more elastic demand at high wool (auction) prices. Consequently, it is hypothesised(for the purpose of later statistical testing) that demand will be more price elastic inperiods of high prices.

(20) The coefficient of correlation between U.K. and world wool consumption is +0.33 (forHo: P = 0 versus H; : p ~O, tabulated r for 13 post-1952 annual observations is equal to + 0.53at the 5 %level); while that between U.K. wool consumption and world prices is +0.40 (for Ho:P = 0versus H l : P 7'= 0, tabulated r for 50 post-1952 quarterly observations is equal to +0.27 at the 5 %level). -

Part III

Derivation of a Statistical Model fromThe Economic Model

The development of a statistical model as a basis for estimating the parametersof a demand function depends, in the first instance, on a specification of whichvariables in the economic model are endogenous (i.e. determined within the model)and which are predetermined. Variables exogenous to the particular economic sectorunder consideration and lagged values of endogenous variables can be treated aspredetermined. If either quantity or price is predetermined in a demand function andall other relevant variables are predetermined, the use of a single equation model isjustified. If two or more variables are endogenous, then the statistical model shouldcomprise more than one equation.

A round-up of the variables thought likely to be important in specifying a demandfunction was completed in equation (6). The price of wool is examined first to seeif it can be treated as predetermined.

WOOL PRICES

A sufficient condition for the price of wool to be predetermined with respect tomill consumption in the United Kingdom is for the supply of wool to that countryto be perfectly elastic. Changes in world prices would thus be identified with commensurate shifts in a horizontal wool supply curve and with the tracing out of pointson one or more U.K. demand curves. If true, such a circumstance ensures that theobserved data are amenable to a statistical derivation of a demand curve and, if othercircumstances permit, that a single equation statistical model with quantity as thedependent variable is appropriate.

In fact, the elasticity of supply of wool to the United Kingdom is not known. Thesupply will be perfectly elastic only if the country's demand for wool has no influenceon world prices, or in other words, when either of the dependent variables are minutein relation to world consumption. Over the proposed study period from 1952 to 1964,U.K. mill consumption accounted for 16% of world raw wool consumption, andwool available for home consumption for 9%of world consumption. The U.K. contribution to the world demand for wool is considered to be 'sufficiently small' tojustify the assumption that its supply is perfectly elastic, and consequently that worldwool prices may be treated as a predetermined variable in the model.

A case for treating wool prices to U.K. mills as a predetermined variable can alsobe made from the likelihood that some time lag exists between changes in pricesand the resulting change in mill consumption. A time lag may occur because manufacturers adjust their wool consumption to a change in prices only when they expectthe change to be fairly permanent. When a turning point in prices occurs, manufacturers may wait to see if the new trend in, or level of, prices is likely to continuebefore adjusting their purchases and consumption of wool. In addition, there is a

16

I DERIVATION OF A STATISTICAL MODEL 17

lag of approximately eight weeks between purchases at auction in the main exportingcountries and mill consumption of raw wool in the United Kingdom. The sum ofthese two lags could amount (conceivably) to as much as six months between achange in wool prices and the resulting adjustment to mill consumption. The appropriate price variable, therefore, may indeed be lagged and, as a consequence, predetermined and independent of current wool consumption.

On the above grounds a statistical model will need to contain at least one equationwith U.K. wool consumption as the dependent variable and world wool prices as anindependent variable principally on the assumption of a perfectly elastic supply tothe United Kingdom, and because the price variable might also be lagged.

THE DEPENDENT VARIABLE

In the formation of the economic model, two dependent variables were proposedU.K. mill consumption of raw wool, and wool available for home consumption. Thereason for examining the two dependent variables is to see if there is any apparentdifference between (a) the price elasticity relevant to final domestic demand and (b) theprice elasticity relevant to foreign demand for U.K. products. A true comparison ofcourse is difficult because the problems in formulating the demand equation are somewhat different in the two cases. An observed difference between the estimated priceelasticities corresponding to the two dependent variables may reflect to some extentdifferences in specification and sampling errors. (21)

Data on U.K. mill consumption of raw wool as published by the Wool IndustryBureau of Statistics are considered to be very reliable. Wool available for home consumption, on the other hand, is defined as mill consumption of raw wool minus anestimate of net exports of wool products (i.e. tops, yarns, fabrics and carpets). Somesampling error would occur in the estimate of net exports because of (a) the exclusionof trade in hosiery and (b) the lack of information on the raw wool content of woolproducts traded. However, a demand model with wool available for home consumption as dependent variable appears less open to specification error than onefeaturing total mill consumption because:

(i) it is easier to specify the factors affecting home demand than those affectingthe demand for U.K. exports; in respect of the latter it would be necessaryto specify the populations, incomes, etc., of all the importing countries plusthe supply of all wool products which compete with those from the UnitedKingdom in these markets; and

(ii) the assumption of a perfectly elastic supply of wool to the United Kingdomis more justifiable for the smaller (home) market which takes 9% of worldconsumption than for the larger one which takes 16% as measured by totalU.K. mill consumption.

The empirical counterpart chosen for U.K. wool prices is the weighted averageof the prices of 64's and 56's quality wool (prices of Dominion wools, c.i.f. London),the weights being the total consumption in the study period of merino and crossbredwool respectively by the U.K. wool textile industry.

(21) The unexplained residual or error term in a statistical estimation model may be divided into(a) sampling error which is due to errors in the data used to represent the variables, and (b) specificationerror which is due to the omission of relevant variables or the inaccurate assumption that a variable isindependent, that the model is linear, etc.


EXPLANATORY VARIABLES

The other explanatory variables (besides wool prices) that have been suggestedfor inclusion in the statistical model must be specified in more detail. First, eachvariable is examined to see whether it is predetermined with respect to wool consumption in the United Kingdom and suitable for inclusion in a single equation model,or endogenous and requiring more than one equation. The competing productswhich are responsible for shifts in retail demand for wool products and the forcesresponsible for shifts in the supply of 'other factors' may be represented by theirquantities or prices, depending on the elasticity of their supply to the wool manufacturing industry in the United Kingdom. (22) If the relevant supply curve is completely inelastic, the quantity supplied can be specified as a predetermined variable.On the other hand, if the supply curve is perfectly elastic, price is predetermined andshould represent the variable in the model. If neither quantity nor price is predetermined, the variable may not be suitable for inclusion in a single equation model.Second, a suitable empirical counterpart must be found for the specified form ofeachvariable. Third, anyone of these counterparts might be excluded if its behaviour overthe proposed study period is obviously represented by a counterpart of some othervariable in the model.

1. Factors Shifting the Demand for Wool Products

(a) The growth in population is expected to result in a proportionate rise in thedemand for wool products. It is recognised that changes in the age structure andperhaps also in the geographic location of the population would modify it somewhat,but the proposed twelve-year study period is considered to be too short for significantchanges in the population structure to occur. The influence of population growth ondemand is taken into account by converting all the quantity variables in the modelto a per head basis.

(b) Income is measured as total personal disposable income; it is assumed to beexogenous to the model in view of the small share of national income allocated byconsumers to wool products. One of the difficulties to be faced in interpreting thecontribution of this variable arises from the distinct upward trend in its values overtime. An alternative variable is suggested later in this section.

(c) Movements in the general level of retail prices are accounted for by deflatingthe income and price variables by a retail price index for all items.

(d) The main commodities which compete with wool products in the retail marketare listed on page 11 in order of the degree of directness of their competition. Thefirst category, commodities which compete with those made of wool in the same enduses, is not specified here for two reasons. Firstly, wool products at the retail levelcannot be precisely defined and distinguished from other wool-type goods partlybecause of the extensive blending of fibres in the final products. Secondly, the maincompetitors with wool products are synthetic fibre products and the quantity ofsynthetic fibres is later specified as an explanatory variable. This variable is assumedto represent most of the competition that wool products have encountered fromproducts of other fibres in the retail market.

(22) The slopes of these supply curves will depend partly on the time interval of observation chosen;the hypotheses advanced concerning their slopes take account of the decision (discussed later) to usequarterly data.

DERIVATION OF A STATISTICAL MODEL 19

The second category of competing goods and services was examined more closely.Any increases in the use of central heating, car heaters and electric blankets may beexpected to have depressed the domestic demand for wool products. In particular,indicators of the consumption and price of central heating (23) were examined withthe view to specifying it as an explanatory variable. These indicators show thatconsumption and price both rose steadily over the study period, suggesting that thedemand curve experienced a series of rapid shifts to the right. This positive relationship between the consumption and price of central heating makes it rather difficultto interpret for specification as an explanatory variable. Moreover, the price seriesis adequately represented in the demand equation by disposable incomes with whichit is highly correlated (r = 0.97).

(e) Changes in consumer tastes and preferences are generally not measurable andtherefore cannot be specified directly in a demand model. A popular expedient in thesecircumstances is to include time as an explanatory variable which will pick up anysystematic changes in tastes and, in this way, account for their effects. This courseof action was not taken because of the high correlation already existing betweentime and the income variable.

One possible way of accounting for the influence of tastes and preferences lies inusing a variable which has already been subjected to their influence. Such a variableis manufacturers' sales of wool products; a similar variable has been used in an earlierstudy of the demand for wool, principally as a proxy variable for income. (24)

(f) The reasons for proposing an explanatory variable to represent shifts in thedemand for stocks of tops are given on page 11. The choice of a suitable indicator ofsuch shifts has been limited to those which are consistent with the following twoassumptions, namely:

(i) that manufacturers attempt to maintain a long-run planned level of stocks,and to do this, they adjust wool consumption in period t in order to bridgethe observed discrepancy between the actual and planned levels of stocks int-l; and

(ii) the planned level of stocks is that which maintains a constant ratio of stocksof tops to current consumption.

The variable chosen is the ratio of recorded stocks of tops in t -1 to the quantityof tops drawn and exported in t -1. When stocks at the end of t -1 are high (low)in relation to clearances in t -1, it is hypothesised that wool consumption in t,ceteris paribus, will fall (rise).

Some uncertainty has been acknowledged regarding the best variable to representthe influence of income levels on the demand for wool products and also the bestway of accounting for the influence of tastes, fashions, etc. Instead of trying to resolvethese difficulties on a priori grounds, it is proposed to investigate two alternativestatistical models. In the first model, the income variable is represented by total

(23) The empirical counterpart chosen to represent the consumption of central heating is deliveriesof gas, diesel and fuel oils for central heating in the United Kingdom; it is recognised that this seriesmay tend to exaggerate the increase in central heating over the study period because there has beensome substitution of gas and oils for coal in heating. The price of central heating is represented by aretail price index for fuel and light.

(24) C. E. Ferguson and M. Polasek, 'The Elasticity of Import Demand for Raw Apparel Woolin the United States', Econometrica, Vol. 30, No. 4, October 1962.


disposable income and the influence of tastes, fashions, etc., is ignored; although itis realised that any systematic changes in tastes will be 'picked up' by the incomevariable. In the second model, a measure of manufacturers' sales of wool productsis used as a proxy variable for the joint effect of incomes and consumer tastes. Morespecifically, an estimate of manufacturers' sales of wool products is used in the casewhere mill consumption of raw wool is the dependent variable; and an estimate ofthe availability of wool products for home consumption is used when wool availablefor home consumption is the dependent variable. (25)

The main advantage of the first model lies in the role of disposable income as abasic demand variable which is independent of disturbances in the wool market.The main disadvantage derives from the high correlation of this variable with timeand, consequently, its tendency to represent other unspecified factors changingsystematically over time.

The advantage of the second model is that manufacturers' sales (hereinafter usedto describe loosely both manufacturers' sales of wool products and the availabilityof wool products for home consumption) incorporates the influence on consumerdemand of income and of a number of other unspecified, but probably important,factors such as tastes. Its main disadvantage is that manufacturers' sales may reflect,in addition to shifts in consumer demand for wool products, shifts in the manufacturers' supply curve, in particular those caused by changes in the price of raw wool.To the extent that changes in manufacturers' sales do reflect supply factors, itsinclusion as an explanatory variable may bias the estimators of parameters belongingto the 'true' model. This important problem is examined more closely in Part IV.

2. Factors Shifting the Supply of 'Other Factors'

(a) Synthetic Fibres. These fibres have already been mentioned as deservingseparate specification for being substitutes in production. Ordinarily, the price andnot the quantity of such a variable would be considered of most relevance in a demandmodel, but it appears that the actual quantity supplied has had a greater influenceon the demand for wool during the period of study than has price.

The failure of relative factor prices to explain the rate of substitution of a newfactor for an old one was noted by Griliches in his case-study of hybrid corn inU.S, agriculture, (26) and later by Powell, Polasek and BurIey after they had madean explicit attempt to define the role of relative prices in the substitution of syntheticfibres for wool in the U.S. market. (27) These results have an important bearing onhow the synthetics variable might be featured in the statistical model of demand forwool in the United Kingdom.

In searching for an understanding of the ways in which an innovation likesynthetic fibres is 'generated and propagated', the theories developed by Grilichesare suggestive. He noted that the observed increases in the share of the market gainedby a new factor are not points of 'stable' equilibrium, but points on an adjustment

(25) Referring to the diagram on p, 10, the value of manufacturers' sales of wool products is equalto that of all the flows out of the box in the diagram; the availability of wool products for home consumption is equal to the sum of the two flows of products to the domestic consumer shown in the lefthand side of the chart. The two series of data so derived are given in Appendix A.

(26) Z. Griliches, 'Hybrid Corn: An Exploration in the Economics of Technological Change',Econometrica, Vo!. 25, No. 4, October 1957.

(27) A. Powell, M. Polasek and H. T. BurJey, 'Synthetic Fibres in the Wool Textile Industry: AStudy of the Role of Price in Technological Adjustment', The Australian Journal of AgriculturalEconomics, Vo!. 7, No. 2, December 1963.

path moving more or less consistently towards a new equilibrium position. So pronounced are the adjustment paths that they can be explained, in some cases, almostentirely by trend functions such as the logistic curve. In applying Griliches' theoriesto the case of synthetic fibres, one would argue that particular types of syntheticswould be developed progressively for those end uses in which it was expected thatthey would return the most profit and, concomitantly, that commercial users ofsynthetics would ensure that their fastest rate of adoption would occur in those enduses where the performance of synthetics (in manufacture and especially in consumeruse) relative to the performance of wool was greatest. These theories would lead toan explanation of the order in which various fibre end uses have been entered (andpossibly filled) by synthetic fibres and of the relative rates of adoption in each. (28)

An extension of the above theory to cover the behaviour of synthetic fibre prices,while synthetics still hold a minor share of the market, is illustrated in Graph Ill. Theprice of synthetics at time t is assumed to be determined by a perfectly elastic userdemand and to be equal to the current price of wool times a factor equal to a measureof the superior performance of synthetics in the marginal end use or market at time t.

I DERIVATION OF A STATISTICAL MODEL 21

GRAPH III

SUPPLY-DEMAND RELATIONSHIPS FOR SYNTHETIC FIBRES

oSs

Pri e e of

Synthetic.-'---1---0.

{Qu a n t it y .1 Synthetic.Time

The demand curve for synthetics (D s) is hypothesised to be 'step-like' in slope, witheach step representing the demand in a particular end use; steps which are lower inheight represent demand in end uses in which synthetics' superior performance is less.Movement along D, over time, and hence the rate of displacement of wool (assumingthe wool-type fibre market is restricted to wool and synthetics only), would be determined by shifts to the right in the supply curve of synthetics (Ss), Such shifts arepresumed to result mainly from increased investment in industry capacity. Shifts inD, would occur with changes in the price of wool, consumer preferences, etc., butthese shifts are ignored here. It is noteworthy that this theory requires relative fibre

(28) See, for example, M. Polasek and A. Powell, 'Wool and Synthetics: A Statistical Analysis ofFibre Substitution in the V.S.', The Australian Journal of Agricultural Economics, Vol. 8, No. I, June1964.9516/67-4


prices to be determined, at least in the early stages, by the rate of fibre substitution,or ultimately, by the rate of investment in synthetic plant capacity.

Certain aspects of this theory, in particular its assumption of a perfectly elasticdemand for synthetics in the marginal end use, are simplifications of the real worldsituation. It provides, however, a plausible explanation of the observed downwardstep movements in synthetic prices and of the alleged insensitivity of the marketshares of wool and synthetics to changes in their relative prices in the innovationperiod. At the same time, the theory raises difficulties in later interpretations of the'sources' of the price elasticity of demand for wool. If the price of synthetics is leftout of the demand model, one would tend to argue from the above theory that noneof wool's price elasticity in such a model could be attributed to fibre substitution.It is not intended to make such literal interpretations of later estimates of the priceelasticity. The most important aspect of the theory for this report is not the closenessof the relationship between the prices of wool and synthetics, but the role which isgiven to shifts in synthetic supply.

It is recalled that the real test of how synthetic fibres should be specified in themodel depends on the elasticity of their supply to mill consumers. Having due regardfor the decision taken later to use quarterly observations, it is assumed that the supplyof synthetics to the wool manufacturing industry in time t is perfectly inelastic.Hence, the quantity of synthetics is specified in the model as a predetermined variable.

The specific variable required is the supply of synthetics to those end uses inwhich they compete with wool in the United Kingdom. This end-use information isnot available, and the variable is represented in the statistical model by the availabilityfor home use (production less net exports) of synthetic staple fibres. The case forusing synthetic staple, rather than synthetic staple and filament yarn, to measurethe use of synthetics in wool-type products is given by Polasek and Powell. Theirreasons are, briefly, that it is better to ignore the minor share of synthetic filamentyarn used in wool-type goods than risk distorting the picture by including all filamentyarn, the major share of which does not directly compete with wool. (29) In addition,there are indications that the use of synthetic yarn in wool-type products has showna similar growth pattern to that of synthetic staple; consequently, the latter shouldprovide a suitable counterpart for total synthetics used in wool-type products, eventhough it is not a good measure of the actual quantity of synthetics used in theseproducts.

(b) Labour. The quantity and price oflabour employed in the wool textile industrymay be expected to be influenced by the level of mill consumption. It is assumed,however, that shifts in the supply of labour to the wool textile industry are adequatelyrepresented by the price of labour to the whole textile industry. The wool sector'sshare of total employment in the textile industry (18 %) is taken to be small enoughfor the price of labour to be treated as exogenous to the wool textile industry.

The price of labour is represented by an index of average weekly earnings in thewhole textile industry. Over the study period, however, the high correlation betweenearnings and disposable incomes (r = 0.97) made it impossible to separate theexpected negative relationship between earnings in the textile industry and woolconsumption from the expected positive relationship between incomes and woolconsumption. Earnings were judged to be the less important of these two factors and

(29) M. Polasek and A. PoweJl, 'Wool versus Synthetics: An International Review of Innovationin the Fibre Market', Australian Economic Papers, Vo!. 3, June-December 1964, pp. 50 and 51.


were excluded from the model; it is noted that this exclusion may tend to bias theestimates of the income coefficient (see Part IV, page 33).

(c) Capital (credit). Changes in the supply of credit or the level of interest ratesto the wool textile industry could restrict purchases of wool and plant activity.However, there are no overt restrictions on credit to the wool textile industry otherthan those which apply to the whole economy, such as the official bank rate. The latterwas regarded as unlikely to influence wool consumption significantly in any waywhich would not be correlated with disposable incomes. For these reasons, a variableto represent shifts in the supply of credit was not included in the model.

PERIOD OF STUDY

The period chosen for the study is mid-1952 to 1964. The analysis is restricted to thepost-war period to capture the expected influence of synthetics on the demand forwool; demand in the period before mid-1952 is considered to have been too stronglyinfluenced by abnormal conditions, in particular the Korean war boom, for inclusionin the study.

TIME INTERVAL OF OBSERVATION

It was decided to test the model with quarterly data. Briefly, it is desirable inparticular to measure the quantity response to wool price changes when the latterare of sufficient magnitude and duration to influence the quantity of wool used bymanufacturers and final consumers. Previous empirical studies indicate that theelasticity of demand for farm products can vary significantly according to the lengthof interval in which observations are recorded for the variables. Several writers havesuggested that as the length of the adjustment period (which in most studies can beapproximated with the time interval of observation) is increased from zero, demandwill tend to become (a) more price inelastic because of a decline in the demand forstocks (stemming from an increasing cost of storage), and (b) more price elasticbecause of greater substitution with other products by both manufacturers andconsumers. (30)

As far as the interval of observation on wool data is concerned, it is surmisedthat the effect of (a) would not be so noticeable for intervals beyond one month,particularly since wool consumption, and not wool purchased by the U.K. industry,has been chosen as the dependent variable. It is reckoned that the use of intervalsof a month or less tends to emphasise the observed short 'saw teeth' like movementsin wool prices to which the quantity response is possibly too speculative in characterfor the purpose of the study.

The effect of (b) is an important one because of the prominence given in the studyto the effect of fibre substitution and also because it raises the length-of-run aspectof the elasticity to be estimated. This aspect is related to the period chosen for thestudy; owing to the relative shortness of the period and the need (statistically) for acertain minimum number of observations, a year would normally be regarded as the

(30) G. S. Shepherd, Agricultural Price Analysis, 5th edition, Iowa State University Press, 1963,pp. 63-66; and E. C. Pasour Jr and R. A. Shrimper, 'The Effect of Length of Run on Measured DemandE1asticities', Journal of Farm Economics, Vo!. 47, No. 3, August 1965.

24 PRICE ELASTICITY OF DEMAND FOR WOOL IN THE D.K.

extreme length of interval which could be contemplated. On reflection, however, itis apparent that too many significant price and quantity fluctuations in the woolmarket are averaged out and lost in annual data.

Having determined the extreme boundaries of the required interval of observationat one month and one year, it was judged that quarterly data would be appropriateto the various requirements of the study.

The choice of quarterly observations necessitated several adjustments to thebasic data. Firstly, the two dependent variables and disposable incomes showed amarked seasonal pattern of fluctuations; these seasonal components were removedfor the statistical analysis. (31) Secondly, annual observations only were available onsynthetic staple fibres for home use. The simplest way of obtaining estimates ofquarterly observations appeared to lie in dividing the annual observations by four.However, the annual data exhibited a strong trend towards increased availabilityover time and it was assumed that a similar trend would describe observations on aquarterly basis. It was decided, therefore, to seek an alternative way of obtainingquarterly figures. An intuitively appealing set of figures was derived from annualdata according to the following combination of moving averages and a system ofweights for each quarter:

A1j = 1/32 (5Aj + 3Aj- 1)A 2i = 1/32 (7Aj + Aj- 1)A 3j = 1/32 (7Aj + Aj+1)

AM = 1/32 (5Aj + 3Aj+1)

whereA,; = the estimate of availability of synthetic staple in the i-th quarter of the

year j; andAj = the known total availability for all four quarters.

Briefly, the above method positions turning points at the middle of each calendaryear and maintains a linear trend in the quarterly estimates over the interveningperiod. By contrast, the rejected method positions turning points at the end ofcalendar years and maintains identical values for quarterly estimates throughout thecalendar year. No optimal properties are claimed for the preferred method, but, ifthe true quarterly data can be described by a trend function and random variable,it is believed that the method is both more efficient and less open to bias in predictingsuch data than is the rejected method, particularly in respect of the first and fourthquarters of each year.

RESPONSE PERIOD FOR THE DEPENDENT VARIABLE

The study aims to measure the total response of mill consumption of wool toquarterly changes in the explanatory variables. This response may occur in the samequarter as the changes in the explanatory variables, some future quarter, or over anumber of such quarters (as in moving average or distributed lag models).

Two possible sources of response lags between changes in the explanatoryvariables and changes in mill consumption are as follows:

(31) The seasonal component in each quarter was estimated as the average (over the study period)of the residual components for the quarter after the trend value (represented by a four-quarter movingaverage) had been removed.


(i) a lag between changes in disposable incomes and their influence on millconsumption may result from a slow reaction by consumers in the adjustment of their expenditure pattern; or there may be a delayed supply responseby manufacturers to a change in consumer demand;

(ii) a lag may occur between changes in wool prices or the prices/quantities of'other factors' and their impact on mill consumption because of the periodrequired to move wool from places of auction to mills in the United Kingdomor owing to a delay in manufacturers' decisions to adjust their wool consumption to changes in the factor market.

Little is known about the length of these response lags, but it is assumed that thelag between a change in anyone of the explanatory variables and the response inthe dependent variable would be either zero, one- or two-quarters (the lag for stocksof tops has been fixed at one-quarter). The length of the lag chosen for each variablewas determined by criteria of best fit and consistency of the regression coefficientsearly in the estimation work and is noted by the subscript to each variable in thestatistical models.

ALGEBRAIC FORM OF THE MODEL

A basic criterion accepted for the choice of the algebraic form is simplicity anda model linear in its parameters was presumed from the beginning. An exponentialform of the model is preferred when the relationship between the variables is believedto be multiplicative; such a form is made linear through a logarithmic transformation.Alternatively, the relationship between the variables may be additive in which casethe form of the model is already linear. Because of the difficulty of recognising thetrue form of the relationship between variables, a limited choice of the above tworelationships was allowed by combining the variables directly in linear form, or bycombining their logarithms in such a form. The actual choice was determined bygoodness-of-fit early in the estimation work.

The goodness-of-fit criterion indicated the existence of a multiplicative relationship between the variables which were subsequently measured only in logarithms andcombined to give a linear form to the statistical model.

THE STATISTICAL MODELS

In the preceding sections, two alternative single equation models, in which woolconsumption is dependent on a number of exogenous variables, have been specified.Their final formulation as statistical models requires the addition to each equationof an unexplained residual or error term (et) and certain assumptions about itsbehaviour.

It is assumed that:(i) the error variable has mean zero and a stable variance a 2

;

(ii) the error variable is serially independent, i.e. et is independent of et-I'... ,et - n ;

(iii) the error variable is independent of each of the explanatory variables.

If the above assumptions about the error term are true, 'best' and unbiasedestimators of the parameters of the single equation model may be obtained by the


method of least squares. The usual tests of significance for the estimates of theseparameters require the additional assumption that the error term be normallydistributed.

The statistical models derived thus far are as follows :(32)

Model S

log CHI}log CM

I

where

CM = mill consumption of raw wool per head (lb);

CH = raw wool available for home consumption per head (lb);

P = weighted prices of raw wool (djlb) deflated by a retail price index for allitems (January 1956 = 100);

Y = personal disposable income per head (£stg) deflated by a retail priceindex for all items (January 1956 = 100);

SM = manufacturers' sales of wool products per head (lb);

SH = availability of wool products for home consumption per head (lb);

T = ratio of stocks of tops to the quantity of tops drawn plus exports;

A = synthetic staple fibre available for home consumption per head (lb);

u, V = error terms;

t = time, in quarters.

The data series for the above variables over the study period, mid-1952 to 1964,and the sources are given in Appendix A. In the equations, each coefficient showsthe proportionate change in the dependent variable which results from a 1%changein the corresponding explanatory variable and is interpreted as a constant elasticity.

In the course of developing an economic model in Part 11, a strong theoreticalargument was presented for expecting the price elasticity of demand for wool toincrease over the study period owing to the rising competition between wool andsynthetic fibres. To the extent that there may have been a measurable increase in theelasticity over the study period, it is obvious that models Y and S do not providefor such measurement. This is a deficiency in their specification. Nevertheless, theywould be adequate if the said hypothesis is false; and even if it is true, they wouldstill constitute a basis from which to estimate an average value of the price elasticity.By dividing the study period up into sub-periods, it is possible to obtain a crude testof the hypothesis through the use of these models.

(32) Strictly speaking, the presentation of different statistical models, such as model Y and model S,requires a change in notation to distinguish the different sets of parameters or statistics appropriate toeach model. To simplify the presentation, however, the same symbols for coefficients of variables aremaintained in the above statistical models and in the further statistical models which are introducedlater on in the report.


The main advantage of models Y and S is their simplicity of form and it is forthis reason that an investigation of their performance is given priority in Part IV.Nevertheless it is clearly desirable to try to specify a variable price elasticity modelwhich will permit improved point estimation as well as a better test of the hypothesisin question. The two models Y and S dealt with so far have featured a variable(A t _ 2) designed to measure the effect of the output of synthetic fibres on the demandfor wool, but it is impossible for that variable to influence directly the price elasticity,the parameter belonging to Pt-2 in the models. It was decided therefore that a moresensitive algebraic form of the model is needed, one which allows the price elasticityto vary as an explicit function of wool's share of the wool-type fibre market. Thelatter variable is preferred to the output of synthetic fibres because it is consideredthat the market share of wool reflects the competitive position of wool and syntheticsmore conveniently and in a way more appropriate to the influence of fibre competition on a price elasticity. The empirical counterpart chosen to represent wool'smarket share is the ratio (R) of mill consumption of raw wool to consumption ofraw wool plus synthetic staple available for home use.

In order that the role of R might be seen more clearly, it is convenient to referback to the basic algebraic form of one of the earlier models, e.g. model Y as itappears in equation (7).

(7)

The parameter bl , previously referred to as the (constant) price elasticity, appearsas the exponent of the price variable. It is well known that exponent terms in suchrelationships may be interpreted as elasticities. With this in mind, it is proposed toreplace bl with a function based on R, i.e. j(R); for example in one of the formsoutlined below, the exponent bIOIR has been used in place of bl • The elasticity nowvaries according to the value of R and so the new model may be termed a variableprice elasticity model. (33) This is shown more clearly in equation (8) which differsfrom (7) mainly in thatj(Rt _

2) has replaced bl •

(8)

(9)

The market share variable is lagged two-quarters to correspond to the lag inwool prices. A logarithmic transformation of (8) leads to:

logCMt}or = log a +!(Rt - 2) log Pt-2 + b210g Yi-t

log CHt + balog Tt - l + b410g At - 2 + log u;The particular functionj(Rt _ 2) , now designated as the price elasticity of demand,

was restricted to one linear in its parameters both for simplicity and the convenience

(33) The variable price elasticity model used in this report is one which seeks to account for aparticular kind of structural change in the demand for wool. The problems of dealing with similarkinds of structural change in supply models are reviewed by Elmer W. Learn and Willard W. Cochranein 'Regression Analysis of Supply Functions Undergoing Structural Change', Agricultural SupplyFunctions: Estimating Techniques and Interpretations, ed. Earl O. Heady et al. (Iowa State CollegePress, Ames, Iowa, 1961); while a particular way of dealing with structural change (in supply), notunlike the solution offered in this report, is given by Earl O. Heady and Yujiro Hayami in 'PoultrySupply Functions (The Relation of Technical Change to Output of Eggs, Broilers and Turkeys)',Research Bulletin 505 (Agricultural and Home Economics Experiment Station, Iowa State University),May 1962, p. 492 et sqq.


of linear models generally. For as long as j(Rt_J is restricted to be linear in itsparameters, the new statistical model is also linear in the parameters. However, leastsquares estimators of the latter must now be regarded (potentially at least) as consistentrather than unbiased, because one of the variables now contains a lagged value ofthe dependent variable. The distinct advantage enjoyed by the estimators of theparameters of j(R t _ 2) , of course, is that they provide an estimate of the priceelasticity of demand for wool which is appropriate to the degree of competitionbetween wool and synthetics as measured by Rt _ 2 and consequently to any point intime during the study period.

Two main forms ofj(Rt_J are used in estimating the parameters of equation (9):'TJt = b10/R t- 2 and 'TJ t = bll + b12R t_ 2; while slight variations of these two formsare also investigated, using either yRt_ 2 or R~_z in place of R t_ 2. Referring nowto the main forms only, these alternative forms give rise to the further statisticalmodels YR I and YR 11:

Model YR I

Model YR II

log CM}log C; = log a + blllog Pt - 2 + b12Rt-210gPt-z +.bzlog Yt- 1

t + b3log Tt _ 1 + b410g A t - 2 + log Ut

The replacement of disposable income with manufacturers' sales leads seriatimto models SR I and SR 11.

lt is of interest to examine the limiting values of the elasticities derived from theabove models when, at one extreme, wool holds 100% of the wool plus syntheticsmarket (i.e. R = 1.0), and at the other extreme, when synthetics hold all the market(i.e. R = 0). In model YR I, for blO < 0, the value of TJ t = b10/R t _ 2 lies between_00 and b10 because 0 ~ R ~ I; and its value decreases monotonically from blO

when R = I to -00 when R = O. In model YR 11, for bll < 0 and b12 ?: 0, thevalue of TJ t = bll + b12Rt _ 2 lies between bll + b12 for R = I and the more elasticfigure of bll for R = O.

Theoretically, a price elasticity of demand of -00 is consistent with wool havinga minute share of the market for wool-type fibres and with synthetics being a perfectsubstitute in the last end use(s) occupied by wool. By contrast, a price elasticity ofsome finite value, b«, requires synthetics to be an imperfect substitute in the lastend use(s) occupied by wool. Though not of much consequence for estimation workin this report, given the limited range of R (0.7 to 1.0) in the United Kingdomduring the study period, the two mathematical forms ofj(Rt_ 2) allow the choice oftwo plausible values of the price elasticity in the extreme event that wool loses marketstosynthetics indefinitely and if this causes the price elasticity to increase. Destinedto be of greater consequence for hypothesis testing, however, is the requirement thatfunctional forms of the elasticity should allow its estimated values to be plausible,especially over the observable range of R, when the hypothesis in question is trueand also when it is false.

I


Some of the statistical properties of the estimators of the 'variable' price elasticitymay be deduced from the properties of the least squares estimators of bl O , bu andb12 • The least squares estimators blO , 1u and bl 2 are biased because their corresponding estimation models contain a lagged value of the dependent variable. If thedisturbance term is distributed normally and independently, however, these estimatorsare approached asymptotically by the maximum likelihood estimators and so theyhave large sample properties of consistency, efficiency and, most importantly, theproperty of invariance under certain transformations. It is with reference to thislast property that one may claim large sample properties of consistency, etc., forthe estimators of the price elasticity of demand in those cases where they are afunction of blO , bu and h12 • For the purposes of comparison with earlier models, itis recalled that when the price elasticity was in fact equal to the wool price parameter bl , the potential small sample properties claimed for its least squares estimatorwere those of unbiasedness and minimum variance, irrespective of the kind ofdistribution of the error term.

In the estimation section, the statistical models are submitted to the followingeconomic and statistical tests:

(i) the algebraic sign of the coefficients is checked with that expected fromeconomic theory;

(ii) the coefficientsare submitted to statistical tests to see if they differ significantlyfrom zero at the 5%level, sign considered;

(iii) the portion of the total variation in the dependent variable accounted for bythe explanatory variables is measured by the coefficient of multiple determination (R2);

(iv) the error term is tested for serial correlation using the Durbin-Watsonstatistic. (34)

(34) For a description of the test and a table of confidence limits, see J. Friedman and R. J. Foote,'Computational Methods for Handling Systems of Simultaneous Equations with Applications toAgriculture', U.S.D.A. Handbook, No. 94, 1955. pp. 77 and 78.

Part IV

Estimation

The statistical models of demand for raw wool in the United Kingdom whichhave been formulated to yield estimates of a constant price elasticity of demand, areapplied first to the selected time series data for the complete study period. Followingthis, two hypotheses concerning the stability of the price elasticity both over timeand at different wool price levels are tested. Finally, the variable price elasticitymodels are investigated.

CONSTANT PRICE ELASTICITY MODELS

Estimates of the parameters of models Y and S for the study period mid-1952 to1964 are presented in Table No. 2. Two equations are given for each model: one

TABLE No. 2

CONSTANT PRICE ELASTICITY OF DEMAND FOR WOOL MODELS: 1952 TO 1964

Model Y

Model S

logC }Mt

logCHt

= log a + b1log Pt - 2 + b2log Yt - 1

+ balog Tt- 1 + b4log At- 2 + log Ut

{

log S }= log a + b1logPt - 2 + b 2 log S;:

+ balog Tt - 1 + b4log A t - 2 + log Vt

I I Estimates

ModelDependent

Parameter Ra d'Variablelog a b l ba ba b.

---

CM b 0.281 -0.231 0.229 -0.101 -0.094 0.41 0.48t s.e, (0.068) (0.427) (0.084) (0.042) (X)

Y ---CH b -0.980 -0.296 0.807 -0.288 -0.149 0.42 1.19

t s.e. (0.092) (0.575) (0.113) (0.056) (X)

CM b 0.097 -0.163 1.094 -0.122 -0.015 0.79 1.20t s.e. (0.041) (0.120) (0.047) (0.012) (X)

SCH b 0.161 -0.261 1.178 -0.226 -0.031 0.63 1.50

t s.e. (0.072) (0.218) (0.085) (0.020) (IC)

s.e. = standard error. (X) indicates the presence of serial correlation. (le) indicatesthat the test for serial correlation was inconclusive. _The error degrees a/freedom number 45 inall equations.

30

ESTIMATION 31

refers to mill consumption of raw wool (CM) and the other to wool available forhome consumption (CH)' The standard errors of the coefficients are shown inparentheses and the coefficient of multiple determination (R2), the Durbin-Watsonstatistic (d ') and the error degrees of freedom are also given. The linear correlationcoefficients (r) between all the variables in models Y and S are given in Appendix C.

The two equations for model Y explain 41% and 42 % respectively of variationsin the demand for wool. The coefficients of all the explanatory variables are of theexpected sign, but those for Yt - 1 in both equations and for Tt - 1 in the equationfor CM t in model Y are not significant at the 5% level.(35) The Durbin-Watsonstatistic indicates the presence of serial correlation in the residuals of both equations,although it is noted that the presence of serial correlation still allows the property ofunbiasedness in the estimators if the disturbance is independent of the explanatoryvariables.

The equations for model S explain 79% and 63 % respectively of the variationin the dependent variables, a marked improvement on the variation explained bymodel Y. The regression coefficients for all the variables except A t _ 2 are significantat the 5 % level. The Durbin-Watson statistic indicates the presence of some serialcorrelation in the equation for CM t and is inconclusive with respect to that for CHt •

The economic interpretation of the regression coefficients is set out below formodel Y with dependent variable CM t :

(i) A 1% rise in wool prices, lagged six months, was associated with a 0.23 %fall in the demand for wool.

(ii) A 1% rise in disposable incomes, lagged three months, was associated witha 0.23 %rise in the demand for wool.

(iii) A 1% rise in the ratio of stocks of tops to their consumption, lagged threemonths, was associated with a O.10%fall in the demand for wool.

(iv) A 1% rise in the availability of synthetic fibres, lagged six months, wasassociated with a 0.09 %fall in the demand for wool.

A general feature of the results is that the estimates of each parameter are consistently smaller in absolute value in the equations having CM t as the dependentvariable compared with the equations for Cn., This implies that the derived demandfor raw wool in the United Kingdom is less responsive, or more inelastic, to changesin wool prices and the other variables under the conditions of a world-wide marketfor wool products than under the conditions of a more limited domestic market.A possible explanation could be that U.K. mills produce a different product mixfor the export market. Or the explanation could lie with a tendency on the part ofmills to work more closely to firm orders on that market. Such a tendency wouldalso provide a possible reason why in model S the manufacturers' sales of woolproducts variable (SMt) explained more of the variation in total mill consumption(CM t) than its counterpart (SHt) explained of the variation in consumption for home

(35) It was anticipated, for example, that the coefficient of P, - 2 would be negative because it washypothesised that the price elasticity of demand would be negative. In devising a test of the latterhypothesis, one proceeds by considering two hypotheses: Ht, that "I is less than zero and Ho, the mostplausible contradiction of such an hypothesis, namely, that "I is zero. The actual estimate of "I is usedin conjunction with a 'I' statistic to find the probability of obtaining a larger value of ij, sign considered,given that Ho is true. It was decided that if such a probability was found to be less than 0.05, Ho wouldbe rejected in favour of Ht. It has become conventional to present the results of testing similarhypotheses about each and every parameter in an econometric model, according to the procedurejust described for 7J. This convention is adopted in respect of the above and all subsequent equations.It is noted, however, that the true error rate for multiple tests of this kind is somewhat larger than thestated error rate, and that the several tests are not necessarily independent.


use (CH); this is reflected in the higher R2 obtained for the CMt version of model S.If mill consumption for export is based largely on firm orders, it is understandablethat consumption for this market would respond more directly to sales of woolproducts and less to wool prices and other factors.

The price elasticity ofdemand for wool is estimated to be either -0.23 or -0.30in model Y and -0.16 or -0.26 in model S. These estimates are considerablylower than the estimates of -0.4 to -0.6 obtained by Homer for the inter-warperiod; the apparent reasons for this difference are discussed in Part V.

It is noticeable that the estimates of the price elasticity from model Y are greaterin absolute value than those from model S; this difference is observed consistentlyin later estimation work using various subsets of the full data.

A possible explanation of the lower estimates of the price elasticity obtainedfrom model S is that part of the total influence of wool prices on the demand forwool may be already reflected in SMt and SHt • Wool prices are expected to influencethe demand for wool mainly through their direct effect on fibre substitution bymanufacturers, but also indirectly through their effect on the price of wool products,and consequently on product substitution by consumers. That is, high wool pricesmay result in shifts to the left in the supply of wool products, and therefore lowersales of wool products (SM and SH)'

The influence of wool prices on S M and S H is likely to be small, as is indicatedby the absence of any direct negative association between them; the simple correlations between Pt-2 and SMt and between Pt-2 and SHt are +0.40 and +0.49respectively. Nevertheless, to the extent that SM and SH do reflect changes in woolprices, this influence of wool prices on the demand for wool may be shared betweenPt- 2 and SM or SH' with a consequent lowering of the coefficient of p t - 2• (36) Inmodel Y, there is no apparent link between wool prices and the other explanatoryvariables. The estimates of the price elasticity of demand for wool in model Y ( -0.23and -0.30) are accepted therefore as more representative of the total effect of woolprices on the demand for wool.

The income elasticity ofdemand for wool is estimated to be 0.23 from the equationfor total mill consumption (CM) and 0.81 from that for U.K. domestic consumption(CH)' Although several earlier studies of the post-war demand for raw wool in theU.S.A. and Western Europe have obtained income elasticities in the range of 0.3to 0.6,(37) the present estimates must be viewed with certain reservations. It hasbeen mentioned that changes in income were highly correlated with time over thestudy period, and consequently, that the income variable may represent systematic

(36) It can be seen that the use of SM and SH pose problems of simultaneous relations. However,in so far as the variable required is one which shifts the demand for wool products only, some supportfor the interpretation in the text is obtained from viewing the problem in part as one of bias owing tomisspecification. For example if it is assumed that the equations in model Y are 'truly' specified, it canbe shown that the substitution of S for Y induces a bias in the estimator of the wool price coefficientequal to PfL, where p is the coefficient of price in an auxiliary regression of income on the other explanatory variables including sales and fL is the income elasticity parameter. Tt can also be shown that thisbias is most likely to be positive and to increase (thus reducing the absolute expected value of the priceelasticity estimator) whenever q, the coefficient of price in an auxiliary regression of manufacturers'sales on the other explanatory variables including income, is negative and decreases. The value of qobtained was -0.065 in the regression of sales of wool products and -0.033 in that of wool productsavailable for home consumption. The author owes this particular interpretation to P. Duane who alsosuggested the related proofs given in Appendix D.

(37) J. Donald, F. Lowenstein and M. Simon, 'The Demand for Textile Fibres in the UnitedStates', U.S.D.A. Technical Bulletin, No. 1301, 1963, p. 81; Bureau of Agricultural Economics, Woolin the EEC, Wool Economic Research Report, No. 6, September 1964, p. 13.

ESTIMATION 33

changes in other factors affecting demand. In particular, the income variable maypartly take on the role of wages as a shifter of the supply of 'other factors'; theeffect on wool consumption in this instance should be opposite to that of incomeas a shifter of retail demand. These apparent limitations in the specification of theincome variable may largely explain why the estimate of the income elasticity is notstatistically significant, and why its contribution to R2 is small.

The elasticity of demand with respect to manufacturers' sales of wool products isestimated to be 1.09, and the elasticity with respect to the availability of wool productsfor home consumption to be 1.18. The size of the coefficients indicates that thedemand for wool tends to rise (fall) rather more than the corresponding rise (fall)in sales of wool products. This suggests that stocks of wool products are increased(decreased) in periods of rising (falling) wool consumption and sales of wool products.

The elasticity ofdemand with respect to the ratio ofstocks of tops to their clearancesis estimated at -0.10 or -0.12 in the equations for CMt> and -0.29 or -0.23in those for Cn, . The large difference between these two pairs of estimates is rathersurprising. It is, however, in accordance with one of the views expressed earlier thatproduction for the export market relies more on firm orders than does that for thedomestic market, with the result that production for domestic orders and hence the(domestic) demand for wool tends to be more responsive to changes in the explanatoryfactors.

Finally, the elasticity of demand with respect to the availability of synthetic staplefor home use is estimated at -0.09 and -0.15 in model Y and -0.02 and -0.03in model S. The higher estimates from model Y are interpreted as a measure of thetotal influence of synthetics on the demand for wool through both fibre substitutionin the factor market and product substitution in the retail market. In model S, onthe other hand, the influence of synthetics through product substitution is expectedto be shared between the synthetics variable and the sales of wool products variables,thus lowering the coefficient of A t _ 2 •

"TESTS OF TWO HYPOTHESES

The following section examines two hypotheses concerning changes in the priceelasticity of demand associated with changes in the degree of fibre competition andin the level of wool prices. These hypotheses were formulated from the earlierexamination of Marshall's four conditions governing the price elasticity of deriveddemand. They are tested by applying the constant elasticity models Y and S toappropriate subsets of the data. The estimated price elasticities pertaining to bothmodels are given; firstly because there may be differences of opinion as to therelative merits of the estimates for each model; and secondly because the resultsfor model S, though not independent of those for model Y, do lend some smallsupport to the conclusions reached in regard to variations in the price elasticity.

Hypothesis No. 1: The D.K. demand for wool is more price elastic in periods(If high wool prices than in periods of low prices.

This hypothesis is tested by the application of models Y and S to periods of 'highprices' and to periods of 'low prices' within the period 1952 to 1964. Periods of highand low prices were chosen by first dividing the total study period into intervalspartitioning the major price fluctuations; four such intervals were recognised and


are identified by A, B, C and D in Graph IV. Within each interval, prices abovethe average price for the interval were defined as high prices and those below theaverage as low prices. The average price for each interval was as follows:

Interval

1st quarter 1952 to 4th quarter 19551st quarter 1956 to 4th quarter 19581st quarter 1959to 3rd quarter 19624th quarter 1962 to 4th quarter 1964

Average Wool Priced (stg)/lb clean

103.695.281.596.2

The method just described for recognising periods of 'high' and 'low' prices isonly one of many plausible methods that could be employed; it was chosen, however,for a special reason. In recent studies of the costs and benefits of a reserve pricescheme for Australian wool, certain assumptions were made about the relative sizeof the price elasticity of demand (for Australian wool at auction) in periods of stockaccumulation compared with those of stock disposal; it was demonstrated thatvariations in these assumptions could have a marked influence on the estimatednet benefits of a scheme. (38) 'For example, it was demonstrated that if the priceelasticity were greater in (high price) periods of stock disposal than in (low price)periods of stock accumulation by a reserve price authority, the net benefits of thescheme would exceed those in the case where the basic price elasticity did not change.In the latter case, the authority's purchase of part of the wool clip would raise (low)prices by, for example, x %; disposal of the same amount of wool would lower (high)prices by the same x %. If the elasticity were greater at the time of disposal, theauthority's trading profits would likewise be greater because sale prices would bedepressed by less than x %.

The preferred definition of periods oflow and high prices between 1952 and 1964is designed to separate the periods when a reserve price authority would be likelyto buy from those when it would be likely to sell wool. Admittedly, the subjectivenature of the judgments made in separating these periods tends to limit the generalityof any test of the hypothesis. At the same time, the method of separation reducesthe risk of confounding the test of Hypothesis No. 1 with the later test of thehypothesis that the price elasticity has increased over time. It is obvious of coursethat Hypothesis No. 1, in so far as it deals with a UiK. demand for wool at themill level, does not provide a critical test of the behaviour of the price elasticity ofworld demand at the auction level which is peculiar to the workings of a reserveprice scheme. Nevertheless, the knowledge gained should narrow the debate on thebehaviour of such an elasticity.

The results of the analysis are shown in Table No. 3 which gives the wool pricecoefficients and differences, their standard deviations, the coefficient of multipledetermination, the Durbin-Watson statistic, and error degrees of freedom for eachequation. (Coefficients of all variables are given in Appendix B). A test of HypothesisNo. 1 is applied to estimates for each of models Y and S and the two alternativedependent variables. Although some interest may be attached to the different values

(38) A. A. Powell and K. O. Campbell, 'Revenue Implications of a Buffer Stock Scheme with anUncertain Demand Schedule', Economic Record, September 1962; and E. L. Jenkins, An Assessmentof Costs and Capital ofa Reserve Price Scheme for Australian Wool, Wool Economic Research Report,No. 7, RA.E., December 1964.

GRAPH IV

UNITED KINGDOM DOMINION WOOL PRICES [d(stg) per lb clean]: CLASSIFIED INTO PERIODS OF HIGH AND LOW PRICES(a):

1952 TO 1964

Pence Stg per lb

130

120

1'0 11 ~...,.....~

lOO 11 ~.....0

90 11 Z

80

70

'61,60

'63

---- ~~;',tr: I~W' p,; c e s • .---.-. -----.-----.- -.---.----

Average Price In ~Each Interval

~~~~~II I I I I I I I I I I I I I I I I

1952 '53 '51, '55 '56 '57 '58 '59 '60 '61 '62

90

70

80

60

120

Pence Stg per l b

130

110

100

(a) Prices above the average price for the interval are defined as high prices and those below the average as low prices.VJUl

.. I


of the coefficients thus obtained, it has been observed already that not much noticeshould be taken of the correspondence of the actual tests.

The 'goodness of fit' is judged to be satisfactory for all equations. The DurbinWatson statistic indicates no serial correlation in three of the equations, but the testis inconclusive in respect of the other five.

All the wool price coefficients have the correct sign and are significantly differentfrom zero. In both models Y and S, the influence of wool prices on CM and CH isslightly greater at low than at high wool prices. However, the difference between the

TABLE No. 3

PRICE ELASTICITY OF DEMAND FOR WOOL: AT HIGH AND LOW PRICES:1952 TO 1964

Model Y

log C }M Ilog C

HI

= log a + b1log PI-2 + b2log YI - 1

+ balog TI - 1 + b4log A I - 2 + log UI

Estimate R' d'

Periods of: Parameter

CM CH CM CH CM CH

High wool prices (H) b, -0.410 -0.454 0.74 0.71 1.38 1.98standard error (0.109) (0.137) (le) (V)

Low wool prices (L) b, -0.457 -0.601 0.71 0.59 1.65 1.50standard error (0.081) (0.150) ( V) (Ie)

bl(H) - bl(L) 0.047 0.147standard error (0.134) (0.205)

Model S

log C } { log S }IOgC:: = log a + b1 log P I _ 2 + b2 lOgS::

+ balog TI - 1 + b4log A I - 2 + log VI

Estimate R' d'

Periods of: Parameter

CM CH CM CH CM CH---

High wool prices (H) bl -0.268 -0.373 0.88 0.74 1.53 2.16standard error (0.076) (0.136) (le) Cl)

Low wool prices (L) b, -0.286 -0.451 0.77 0.64 1.18 1.18standard error (0.070) (0.136) (Ie) (le)

bl(H) - bl(L) 0.018 0.078standard error (0.104) (0.194)

(V) indicates no serial correlation at the 5 % level of significance. (Ie) indicates that the testfor serial correlation was inconclusive. The error degrees offreedom number 19 in all equationsrelating to periods of high wool prices, and 21 in equations relating to Iow wool price periods.

ESTIMATION 37

elasticity estimates for periods of high and low prices, shown in Table No. 3 asb1(H) - b1(L), is not significant at the 5% level irrespective of which combinationof dependent variable and model is used. (39) The results, therefore, are consistentwith the null hypothesis of a price elasticity which is the same for high and lowprices.

The empirical results suggest that the theory for and against Hypothesis No. Ishould be further examined. In the theoretical section (pp. 12-15), three causes ofchange in the, price elasticity of demand at different price levels were discussed:

(i) demand should be more price elastic during periods of high prices owing tothe greater contribution of wool to the total cost of wool products;

(ii) demand should be more price inelastic during periods of high prices because:(a) wool is then more essential to the industry; and(b) the supply of 'fixed' factors to the industry is more inelastic in periods

of high wool consumption.On a priori grounds, causes (ii) (a) and (ii) (b) did not appear particularly relevant to

the U.K. demand for wool in times of high prices and were dismissed. The empiricalresults, however, suggest one of two possibilities: either cause (i) does not significantlyinfluence the wool price elasticity, or causes (ii) (a) and (ii) (b) have a greaterinfluence on the demand for wool than anticipated and have offset the influence ofcause (i). Alternatively, Marshall's third principle, on which cause (i) is based, maynot be true in this particular case; this would occur if the elasticity of substitutionbetween wool and 'other factors' is numerically greater than the price elasticity ofdemand for wool products (see page 13).

Whatever the explanation of the results may be, it must be concluded that thestudy does not provide any strong theoretical and empirical evidence that the U.K.price elasticity of demand for wool varies significantly between periods of high andlow prices; in particular Hypothesis No. I is rejected.

Hypothesis No. 2: The demand for raw wool in the United Kingdom has becomemore price elastic over the period mid-1952 to 1964.

The hypothesis is first tested by the application of the statistical models Y and Sto the two successive halves of the study period, mid-1952 to 1957 and 1958 to 1964,in order to obtain estimates of the price elasticity in periods corresponding to differentdegrees of competition from synthetics.

The results are shown in Table No. 4, where the regression coefficients for Pi.. 2

are presented along with their differences, standard deviations, the coefficient of(39) The test statistic used is:

where

d = bl(H) - bl(L); and

Sd = the standard error of d.

It is assumed that bl(H) is independent of 6l (L ), so that

Var. [bl(H) - blC£)] = Var. [blCH)] + Var. [blC£)]= a 2 [Cu (H ) + CuCL))

whereCll = the appropriate diagonal element in the familiar C matrix.

The estimator of error variance. &', is obtained from pooling the error sums of squares SS(H) andSSCL) and has ntH) + nCL)-IO degrees offreedom. Since the relevant hypotheses are H l: blCR) < blCL)versus Ho : blCH) = blCL), the value obtained for t is compared with tabulated values of t, signconsidered.

38 PRICE ELASTICITY OF DEMAND FOR WOOL IN THE V.K.

multiple determination, the Durbin-Watson statistic and error degrees of freedomfor each equation. (Coefficients of all variables are given in Appendix B). A test ofHypothesis No. 2 is applied to estimates for each of models Y and S and the twoalternative dependent variables.

The difference between the estimates for the two halves of the study period,shown in Table No. 4 as bl(T+1) - bl(T), is significant at the 5% level irrespectiveof which combination of dependent variable and model is used. There are, however,anomalies in the estimates for the first half of the period (1952 to 1957) in so far as

TABLE No. 4

PRICE ELASTICITY OF DEMAND FOR WOOL: 1952-57 VERSUS 1958-64

Model Y

= log a + b I log P t - 2 + b2log Yt - I

+ ba10g Tt- I + b4log At- 2 + log Ut

Estimate R2 d'

Study Period Parameter

CM CH CM CH CM CH-----

1952-57 (T) bl 0.113 0.300 0.67 0.73 1.67 2.25standard error (0.077) (0.123) (IC) ( v')

1958-64 (T+I) bl -0.302 -0.497 0.66 0.54 0.88 2.26standard error (0.094) (0.130) (X) (t!)

bl(T+I) - bl(T) -0.415 -0.797standard error (0.127) (0.184)

Model S

{IOgSM}

log a + bl log r.: 2 + b2 log SH:

+ ba log Tt- I + b4 log At- 2 + log Vt

Estimate R2 d'

Study Period Parameter

CM CH CM CH CM CH

1952-57 (T) bl 0.077 0.141 0.68 0.73 1.49 1.96standard error (0.074) (0.119) (IC) (t!)

1958-64 (T+I) bl -0.226 -0.373 0.89 0.68 2.34 2.54standard error (0.054) (0.113) (t!) (IC)

bl(T+I) - bl(T) -0.303 -0.514standard error (0.089) (0.165)

(V) indicates no serial correlation at the 5 %level of significance. (X) indicates the presenceof serial correlation. (IC) indicates that the test for serial correlation was inconclusive. Theerror degrees of freedom number 17 in all equations relating to the period 1952 to 1957 and 23 inequations relating to the 1958 to 1964 period.

ESTIMATION 39

all have the 'wrong sign'. Nevertheless, even if all estimates for the early period wereset at zero, the differences between the estimates for the two halves of the studyperiod would still be significant at the 5%level.(40)

The estimates obtained for the second half of the period (1958 to 1964) are-0.30 and -0.50 for model Y and -0.23 and -0.37 for model S. All aresignificantly different from zero at the 5% level. For reasons discussed on pp. 32et seq., the estimates -0.30 and -0.50 are regarded as 'best', but it is of someinterest that all the estimates show a marked increase in elasticity over the corresponding estimates for the study period as a whole. The results in Table No. 4 givestrong support to Hypothesis No. 2 and, on the basis of this first method of testingits validity, Hypothesis No. 2 is provisionally accepted.

VARIABLE PRICE ELASTICITY MODELS

In this section, the variable price elasticity models YR I and YR Il, and SR I andSR Il are applied to data for the study period 1952 to 1964. These statistical modelsare described on pages 26-29. They are designed to allow estimates of the priceelasticity which vary with the ratio of wool to wool plus synthetic staple; the modelsalso allow estimates of constant elasticities of demand with respect to the otherexplanatory variables. The R Il models allow an alternative test of HypothesisNo. 2 which has an advantage over the earlier test using the constant elasticity modelsin that it does not require the time series data to be segmented into two parts inorder to devise a test statistic for the hypothesis. If Hypothesis No. 2 is true, the RIand R Il models both provide estimates of the price elasticity peculiar to given levelsof competition between wool and synthetics as measured by R, and consequentlyto given points in time.

The results obtained from models YR I and YR Il, and SR I and SR Il for eachof the two dependent variables are presented in Tables No. 5, No. 6 and No. 7. InTable No. 5, estimates of the critical parameters, their standard deviations and theprice elasticity of demand are presented together with the coefficient of multipledetermination and the Durbin-Watson statistic for each equation. Estimates of theprice elasticity are given for values of R ranging from 1.0 to 0.7 to correspondapproximately with the observed range of R, i.e. 0.98 in 1952 to 0.80 in 1964. Theprice elasticity estimates from the constant elasticity models Y and S are also givenfor comparison.

A portion of the results is shown in Graph V for the complete range of Randfor comparison with the estimates which result from using VR I _ 2 or R;_2 in placeof R I_ 2 in models R I and R n. Neither of these replacements for R I_ 2 was foundto give a consistent improvement to the performance of the models with the availablerange of data and they were not investigated any further. The extrapolations inGraph V, however, illustrate how important such variations to the form of theelasticities might have been had the models been applied to data for a country suchas the D.S.A. where the comparable value of R in 1965 was 0.33 compared with avalue of 0.90 in 1952.

The estimates of all parameters shown in Table No. 5 are significantly differentfrom zero at the 5% level with one exception-the estimate of b12 in model SR II

(40) The type of test statistic used is given in footnote 39 on page 37.


with dependent variable CH' Comparing the variable elasticity with the constantelasticity models with respect to their overall performance, the statistics R2 and d"indicate an improvement in the specification of models YR I and YR 11 comparedwith model Y, but little change in models SR I and SR 11 compared with model S.This result is interesting in view of the preference that has already been shown forthe estimator of the price elasticity pertaining to model Y.

It is obvious just from scanning the estimates of the price elasticity in TableNo. 5 that the results for models R I and R 11 are consistent with what one mightexpect if Hypothesis No. 2 were true. Nevertheless, model R I does not allow a valid

TABLE No. 5

A COMPARISON OF ESTIMATES OF THE PRICE ELASTICITY OFDEMAND FOR WOOL: 1952 TO 1964

Estimates of Price Elasticity Corre-

Depend- Estima- Wool sponding to Selected Values of Rt- 2ent tion Price Estimates of (b) R2 d'

Model Para- ParametersVariable (a) meters1.0 0.9 0.8 0.7

--- --Y bl -0.231 -0.231 -0.231 -0.231 -0.231 0.41 0.48

(0.068) (X)---

CM YRI blO -0.243 -0.243 -0.270 -0.304 -0.347 0.62 0.69(0.037) (X)

---YRI! bll , bI 2 -0.726 0.622 -0.104 -0.165 -0.228 -0.290 0.71 0.87

(0.087) (0.092) (X)--- ---

Y bl -0.296 -0.296 -0.296 -0.296 -0.296 0.42 1. 19(0.092) (X)

--'CH YRI blO -0.252 -0.252 -0.280 -0.315 -0.360 0.50 1.40

(0.058) (le)---

YRI! bll , bI 2 -0.637 0.429 -0.208 -0.251 -0.294 -0.337 0.50 1.43(0.157) (0.165) (le)

= -- =

S bl -0.163 -0.163 -0.163 -0.163 -0.163 0.79 1.20(0.041) (X)

---CM SR I bl O -0.133 -0.133 -0.148 -0.166 -0.190 0.82 1.13

(0.027) (X)--

SRI! bll , bI 2 -0.333 0.209 -0.124 -0.145 -0.166 -0.187 0.82 1.09(0.077) (0.082) (X)-_.

S bl -0.261 -0.261 -0.261 -0.261 -0.261 0.63 1.50(0.072) (le)

---CH SR I blO -0.170 -0.170 -0.189 -0.213 -0.243 0.63 1.44

(0.048) (le)---

SRI! bll , b12 -0.342 0.106 -0.236 -0.247 -0.257 -0.268 0.64 1.49(0.126) (0.134) (le)

(a) The 'wool price' component in models Y and S is b l log Pt- ; in models YR I and SR Ithe component is (bI O logPt- 2)/Rt-2 and in models YRI! and SR I! it is blllogPt-2+ b12 R t - 2log Pt-2' (b) The price elasticity of demand for wool in models Y and S isgiven by 7[t = b l for all t; in models YR I and SR I the elasticity is given by 7[t = bI O/Rt- 2; and.in models YR I! and SR I! by 7[t = bll + b12Rt- 2 • (X) indicates the presence of serial;correlation. (lC) indicates that the test for serial correlation was inconclusive.

ESTIMATION 41

GRAPH VPRICE ELASTICITY OF DEMAND FOR WOOL (71)

Estimated values of 71 for R = 1.0 for models YR I and YR 11, with dependentvariable CM (a)

1·0

Obs"rvedrangeof R

·4o

_.g

-1,8

--4

-1,7

-1,6

-·3

-1-5

- .,-·2

-H.

IModel1J~ Y R II

dL$~""~}M O d e l»: _,..i Y RI

/~~~-

/-a-r;."".-:;~ ../""

A 1\ 1\ 2 ~/ .... //

''It:bll +bll Rt - 2 --;::"" /'//// /

.)---- " ./ / "" /--- ./" ,,/ ./ "" I

-·5 r-A A /./ /" ./"" / Ii t -bll+\b12R

t - , s-: ",,"" 1/ /-·6 r / I /

,/'1 // I II

" I I-'7 /'1\ I / / I"Ab, / / I''It=~ / I

-·8 \' I I II I I II I I

/ I II I I

-1,0 I I I

I~ I I- 1'" I II I II I I

-1'2 l~t:b,,+bI2~ I, I A I 1\

I" blo 1\ b ,o-1-3 'It: -R- I "1t=~

!J'~! .:I //, I, ', II II I, fI II, I,'-1'9 -----L.- ---'---'-----'------'----'-----'-----'

o ., ·2 ·3 ·4 ·S ·6 ·7 ·8 -s 1·0Ratio (R) of Wool Consumption to Wool

plus Synthetic Staple Consumption

wQI

U

L-

CL

o

"0C",

EQI

Cl

VI",

.....o

L

o.....

oo:s:

(a) The extrapolations over the unobserved range of R are presented to illustrate the behaviour ofthe different functional forms of the elasticity; they should be interpreted accordingly


statistical test of the hypothesis. The complementary null hypothesis requires thatbl O > 0 or, at best, that blO = o. Neither of these forms of the null hypothesis issatisfactory because of prior evidence, both theoretical and empirical, that blO < O.The problem with model R I is that a test of Hypothesis No. 2 amounts to a test ofthe mathematical properties of the expression for the price elasticity. This deficiencyin model R I does not rubbish it as an estimation model if the hypothesis is truealthough, on this point, one can cite other deficiencies. For example its price elasticityis a function of one parameter only and this parameter is expected to fix the valueof the elasticity for a given value of R and also the rate at which the demand forwool grows more elastic with decreasing values of R. (41) It may be argued, therefore,that the parameter blO is required to convey too much information. Having dueregard for these several objections, the estimates of the price elasticity from modelR I are not considered further in this report.

In several important respects, model R 11 is clearly superior to model R I. A testof Hypothesis No. 2 is equivalent to a test of the hypothesis that b12 > 0 against thenull hypothesis that bl 2 = 0, the latter proposition being consistent with bn = bl

and a reversion to model Y (or S) if Hypothesis No. 2 is rejected. Also, given thatHypothesis No. 2 is true, it is of interest that model R 11 requires two parametersinstead of one to describe its price elasticity of demand; one of the parameters (bn)fixes the value of the price elasticity for R = 0, while the other (b12) fixes the rateat which the demand for wool grows more elastic with decreasing values of R.

Against these several merits of model R 11, one must acknowledge the potentialstatistical problem introduced by having two explanatory variables involving log Pt - 2 •

Although a greater range of values for R would have been desirable, none of thecommon symptoms of multicollinearity are apparent in the estimates and the modelis accepted as adequate both for point estimation and for test statistics pertainingto Hypothesis No. 2. Consequently the positive values obtained for the estimates ofbl 2 in model YR 11 are accepted as a verification of the hypothesis.

Now that Hypothesis No. 2 has been verified in two different ways, it is of interestto return to the problem of point estimation and to compare the estimates of bl

obtained from model Y for the two halves of the study period with the estimatesgiven by bn + i.»: 2 for model YR 11. During the first half of the period, theaverage value of R fell from 0.98 in 1952 to 0.94 in 1957; during the second halfit continued to fall, down to 0.80 in 1964. The constant price elasticity (bl ) forthe 1952-57 period was estimated to be positive or, at best, approximately equal tozero. Estimates of the price elasticity obtained for the dependent variable CM inmodel YRII range from -0.12 in 1952 to -0.14 in 1957. The correspondingrange for CH is from -0.22 to -0.23. The results derived from model YR 11clearly provide the more acceptable estimates of the price elasticity for the earlyyears of the study period.

Estimates of bl for the 1958-64 period are rather more elastic than the priceelasticities for model YR 11 at the end of the period, as can be seen from TableNo. 6. The generally superior performance of model YR 11 and its estimatorbn + bI 2R._ 2' especially for the period 1952-57, lend support to the estimates-0.23 and -0.29. On the other hand, the properties of bn + b12R t _ 2 do not

(41 The first derivative of the elasticity with respect to R is -b10/R:- s-

ESTIMATION 43

include unbiasedness for small samples; furthermore, even the large sample properties of consistency, etc., are open to conjecture in the presence of serial correlation,whereas b1 at least remains unbiased under the usual assumptions. As a final compromise, simple averages of the two sets of estimates are presented in the last columnof Table No. 6 and these are presumed, rather arbitrarily, to refer to the year 1964.

The demand models examined are thought to be inadequate for predicting thevalue of the price elasticity beyond the study period. There is a strong case forexpecting a further decline in wool's share of the wool-type fibre market in theUnited Kingdom and this may be expected to lead to further increases in the elasticity.With regard to variable price elasticity models, the observed range of R in the UnitedKingdom is considered to be too small for any conclusions to be drawn about theexpected size of future increases in the elasticity in response to given changes in R.However, the application of similar models to data for a country such as the U.S.A.with a much wider observable range of R appears to be a promising avenue for furtherresearch.

TABLE No. 6A COMPARISON OF ESTIMATES OF THE PRICE ELASTICITY OF

DEMAND: SECOND HALF OF STUDY PERIOD

•Variable' 7JConstant 7J Average

Dependent Estimated by Estimated by (h 1 + s; + C12 R)Variable bll + h1 2 R b1when R = 0.8 2

CM -0.23 -0.30 -0.27CH -0.29 -0.50 -0.40

The coefficients obtained from the variable price elasticity models for the explanatory variables other than wool prices have not been discussed so far. The estimatesof all the parameters in these models, together with their standard errors, are presentedin Table No. 7. It has been noted already that the variable price elasticity modelsshow a marked improvement in performance compared with the constant priceelasticity models for those equations in which income is used to represent shifts inthe final demand for wool products. The coefficients of disposable income in theseequations are consequently of particular interest.

The income elasticity of demand for wool is estimated to be 0.76 or 1.30 inmodel YR I and 1.05 or 1.37 in model YR 11. The four estimates are all significantat the 5% level, and are considered to be preferable to the earlier non-significantestimates of the income elasticity obtained from model Y. The preferred estimatesare higher than those obtained from model Y; they are higher also than those obtainedin previous studies of the post-war demand for wool in western countries. Theyindicate generally that a given percentage increase in incomes was associated withan equal, or slightly greater, percentage increase in the demand for raw wool. Theseestimates of the income elasticity, however, should be interpreted with caution in viewof the high correlation between incomes and time over the study period (see p. 32).

The coefficients for the ratio of stocks of tops to their clearances in both theconstant and the variable price elasticity models indicate that demand for stocks oftops has an important influence on the demand for wool. The estimates of this influenceare slightly greater in models YR I and YR 11 than in model Y.

The coefficients for the availability of synthetic staple are both of the expectedsign and statistically significant in model YR I only. The unsatisfactory performance


TABLE No. 7

VARIABLE PRICE ELASTICITY OF DEMAND FOR WOOL MODELS: 1952 TO 1964

Models YR I and SR I Combined

log CM t }

log CHt

{

log Yt - 1 }log Pt _ 2 10 S= log a + blO R + b2 g M t

t-2 log SHt

+ ba log Tt-I + b4 log A t - 2 + log U;

Estimate

Model Dependent ParameterVariablelog a b,• b, b. b.

C b -0.641 -0.243 0.761 -0.168 -0.071

YRIM t standard error (0.037) (0.357) (0.068) (0.031)

C b -1.926 -0.252 1.303 -0.337 -0.112Ht standard error (0.058) (0.560) (0.107) (0.049)

CMb 0.223 -0.133 0.925 -0.123 0.021

t standard error (0.027) (0.122) (0.044) (0.009)

SR ICH

b 0.150 -0.170 1.080 -0.222 0.029t standard error (0.048) (0.221) (0.085) (0.018)

Models YR nand SR fI Combined

{

log Yt- 1 }logS

= log a + bll logPt - 2 + b12 R t - 2 logPt - 2 + b2 M t- 110gSH

t-l

+ ba log Tt - 1 + b4 log At - 2 + log U;

Estimates

ModelDependent ParameterVariable

log a bu b,• b. b. b.

CMb -1.339 -0.726 0.622 1.051 -0.174 0.006

YRII t standard error (0.087) (0.092) (0.324) (0.060) (0.033)

CHb -2.096 -0.637 0.429 1.374 -0.338 -0.080

t standard error (0.157) (0.165) (0.583) (0.108) (0.059)

CMb 0.239 -0.333 0.209 0.894 -0.123 0.033

t standard error (0.077) (0.082) (0.138) (0.045) (0022)

SR IICH

b 0.223 -0.342 0.106 1.130 -0.230 -0.003standard error (0.126) (0.134) (0.227) (0.086) (0.040)t

I

of A t _ 2 in the other models is not unexpected in view of the inclusion of anothermeasure of the degree of competition between wool and synthetic staple (i.e. Rt _ 2)

in the variable price elasticity models. These models were tested without the variableA t _ 2 , and the results indicated that its exclusion does not appreciably alter theestimates of the other parameters, or the coefficient of multiple determination.

Part V

Discussion and Application of Results

SUMMARY OF RESULTS

The major aim of the present study has been to estimate a price elasticity ofdemand for wool which is subject to a general range of applications. This consideration, together with certain limitations imposed by the specification of a suitablestatistical model, led to the particular elasticity being defined as the price elasticityof demand by the United Kingdom for world supplies of raw wool, measured at themill consumption level from quarterly data.

The demand for wool was analysed in Part II of the report in the manner suggestedby Marshall's theory of derived demand. It was argued that the U.K. demand forwool [represented either by total mill consumption per head (CM) , or by woolavailable for home consumption per head (CH) ] depended on (a) the price of wool,(b) shifts in the retail demand for wool products [represented in model Y by incomesper head (Y), or alternatively in model S by manufacturers' sales of wool productsper head (SM' SH) ] , and (c) shifts in the supply of factors other than wool (represented by the supply of synthetic fibres and the supply of labour and capital to thewool processing industry).

An examination in Part III of the behaviour of these causal factors suggestedthat their influence on the demand for wool could be estimated from a single equationmodel with CM and CH as alternative dependent variables, and with wool prices,disposable incomes (or sales of wool products), the available quantity of syntheticstaple, and a measure of the intermediate demand for stocks of wool tops as independent variables. Two forms of the model containing the above variables wereproposed. The first provided for constant demand elasticities, while the second wasdesigned to yield estimates of the price elasticity of demand for wool which arespecific to different degrees of competition between wool and synthetic fibres.

The constant price elasticity model was applied to time series data for the period1952 to 1964 in Part IV. The resulting estimates of the price elasticity were satisfactorywith regard to statistical significance, but in other respects the overall specificationof the demand model was not entirely satisfactory. Although model S explained alarger share of the variation in the dependent variables and appeared to be less subjectto serial correlation than model Y, it seemed likely that the inclusion of SM or SHintroduced a downward bias in the price elasticity estimates. Consequently, somepreference was felt for the elasticity estimates from model Y. The slightly highervalues of the price elasticity which were obtained consistently in those equationswith CH as the dependent variable were not adequately explained, and this differencebetween the results for CM and CH is interpreted in the following discussion asproviding a range of values for the price elasticity. This range of the price elasticityof demand for wool in the period 1952 to 1964 was estimated from model Y to be-0.23 to -0.30.

The application of the same statistical model to periods of high and low woolprices provided no support for the hypothesis that the demand for wool is more

45

46 PRICE ELASTICITY OF DEMAND FOR WOOL IN THE u.x.price elastic in periods of high wool prices. Finally, the hypothesis that the priceelasticity has increased over the study period because of the increased availability ofthe synthetics as substitute fibres was tested by two methods. Firstly, the samestatistical model as used above was applied separately to the first and second halvesof the study period to see if the price elasticity increased; secondly, the alternativestatistical model, which allowed the price elasticity to vary as a function of wool'sshare of the market for wool-type fibres, was applied to data for the whole studyperiod. It was found that both methods of testing the hypothesis supported its contention that the price elasticity had increased over the study period; and after makinga rough compromise between the merits of the two statistical models it was concludedthat the value of the price elasticity at the end of the study period was between -0.27and -0.40. (These results are compared in Appendix E with those obtained byDr Homer in his earlier work.)

PRICE ELASTICITY OF DEMAND FOR AUSTRALIAN WOOL

From the Australian wool industry's point of view the most useful price elasticityof demand is one specific to Australian wool. In the Introduction, it is shown howsuch an elasticity may be derived from a knowledge of:

(i) the price elasticity of world demand for wool ofthe type produced in Australia;(ii) the price elasticity of supply of wool from suppliers other than Australia;

(iii) the Australian share of the world market.

Values of the price elasticity of world demand for Australian wool have beenderived using the estimates of the price elasticity in the United Kingdom to representthe world elasticity. The assumption upon which this use of the U.K. elasticity isfounded is true only if (a) the U.K. elasticity is equal to a weighted average of theelasticities in the other countries of the world, and (b) there is no distinction betweenthe type composition of wool produced in Australia and that consumed in the UnitedKingdom.

The price elasticity of supply of wool in other producing countries is not known.However, several estimates of the supply elasticity for Australian wool have beenmade, and these have been accepted for present purposes as indicative of the supplyelasticity in other producing countries. (42) These estimates indicate that supply isvery price inelastic (E < 0.1) in the short run (adjustment periods of one year), butthat it becomes steadily more elastic as the adjustment period is increased. Powelland Gruen estimate the long-run supply elasticity at 1.2 to 2.2. The appropriatesupply elasticity to apply in deriving an estimate of the elasticity of demand forAustralian wool from an estimate of the U.K. demand elasticity is assumed to bethat with a similar length of run, or adjustment period, to the U.K. elasticity. Thelatter is based on quarterly observations with a lag of two-quarters between pricechanges and the estimated response in demand, thus giving a maximum adjustmentperiod of three-quarters. The corresponding supply elasticity is that based on a minimum adjustment period of one year, and the available estimates of this elasticity for

(42) A. A. Powell and F. H. Gruen, 'A Multi-Sectoral Approach to Agricultural Supply Analysis',paper presented to the annual conference of the Australian Agricultural Economics Society, February1966; and J. M. Malecky, unpublished paper, RA.E., 1965.

DISCUSSION AND APPLICATION OF RESULTS 47

Australian wool suggest a value of about 0.05. This estimate has been taken as theelasticity of supply of wool in producing countries other than Australia.

With the above assumptions, and a knowledge of Australia's share of the worldapparel fibre market, the following estimate of the elasticity of demand for Australianwool (7] A) is obtained from equation (1):

1(1) 7J A = 7(7] w - q + Er

1= - [( -0.27 to -0.40) - 0.05] + 0.05

0.37= -0.82 to -1.17

where7] w' the price elasticity of world demand for raw wool, is represented by the

estimated elasticity of U.K. demand;Er' the price elasticity of supply of raw wool from suppliers other than Australia,

is represented by the estimated short-run elasticity of supply of Australian wool;and

f is Australian wool production as a proportion of world apparel wool production (clean basis), average 1962-63 to 1964-65.The estimation of TJA is based on English price series and so any direct application

of these estimates to the Australian market involves an implicit assumption thattransport costs between Australia and its oversea markets are negligible. By makingan allowance for transport costs, the above estimates of 7] A may be adjusted to giveelasticities in terms of Australian prices; this adjustment gives a range for 7] A of-0.77 to -1.10.(43)

The estimates also involve the assumption that there are no trade barriers onwool's entry into oversea markets; and that Australian wools are substitutable forapparel wools from other producing countries. The first of these assumptions isfulfilled by most markets; e.g. Australian wool has completely free entry into theUnited Kingdom; but where a tariff on raw wool is imposed as in the U.S. market,it tends to have the same effect on the estimate of 7] A as transport costs. Finally,Australian wool is clearly not substitutable with all apparel wools from othercountries, and this will tend to raise the value off, and reduce the estimated (absolute)value of 7]A in equation (1). No attempt has been made to measure this influence on7]A , mainly owing to the lack of data on the quality numbers of world production.The quoted estimates of 7]A , however, should be interpreted as upper limits to theshort-run elasticity in view of this failure to allow for the differences between Australianand other apparel wools.

(43) To allow for transport costs in the estimation of 7]A' we wish to express 7]w (present estimatesof which are assumed to be specific to the U.K. level of prices) and Er (present estimates of which areassumed to be specific to the level of prices in other producing countries) in terms of the level ofAustralian prices. This adjustment is made in equation (1) by multiplying 7] w by PI(P + t), and Er byPI(P + t - t'),where

P = price of wool in Australia,t = transport cost per unit between Australia and the United Kingdom,

t' = transport cost between other producing countries and the United Kingdom.(See F. B. Homer, 'Elasticity of Demand for Exports of a Single Country', Review of Economics andStatistics, Vol. 34, No. 4, November 1952, p. 329.)

For the actual estimation of 7]A' t is taken to be 4d (Aust.) per Ib greasy (from P. H. May, 'Costsof Marketing Australian Greasy Wool', Quarterly Review of Agricultural Economics, Vol. XVIII,No. 3, July 1965, making PI(P + t) equal to 0.938; and it is assumed that transport costs fromAustralia (r) are approximately equal to those from other producing countries (t').


OTHER APPLICATIONS OF THE PRICE ELASTICITY

The main conclusion from the empirical work of this report is that the U.K. and(by assumption) the world demand for wool are price inelastic-a I % rise in woolprices is estimated currently to cause a fall of about 0.27 %to 0.40 %in the quantityof wool demanded. With the growth in competition from synthetic fibres, however,demand has gradually become more price elastic, and there are good reasons toexpect a continuation of this trend. Some of the main implications of the results forthe wool industry are referred to briefly in the following paragraphs.

With regard to the competition between wool and synthetics, the results supportindirectly the hypothesis that this competition to date has been largely determinedby certain technical and promotional advantages of synthetic fibres in a wide rangeof end uses. It is of interest to note in this connection that an increase in the priceelasticity of demand for wool will tend to reduce wool price fluctuations, since agiven change in the quantity supplied will have a smaller effect on price. In the past,price fluctuations have been named by wool manufacturers as a reason for preferringthe more stable-priced synthetics,

The implied world elasticity at the end of the 1952 to 1964 study period is wellbelow the critical value of unity, at which a change in prices would induce a compensating change in demand and leave gross wool receipts unchanged. If the estimatedworld elasticity is interpreted in the form of a price flexibility ratio (see p. 1), itindicates that a 1%increase in world supplies of wool, ceteris paribus, may be expectedto cause at least a 2.5 % to 3.7 % fall in world wool prices, and hence a markeddecline in the gross returns to woolgrowers as a group.

The price elasticity of demand for Australian wool is estimated to be in thevicinity of unity, at which a 1% rise in Australian wool prices (such as could beinduced for instance by a price-fixing authority) would cause a like percentage declinein the demand for Australian wool. A more likely application, of course, concernsthe effect of an autonomous I % increase in Australian supplies of wool. At best,gross returns to the industry would remain unchanged.

In an earlier study Dr Powell has estimated the effect of an expansion in thelong-run output of Australian wool on total wool receipts (with populations, incomes.etc., in wool consuming countries held constant). (44) The effects on receipts of a 10%and 20% expansion in wool production were presented for an Australian elasticitybased on an assumed range of values of the world price elasticity of demand of'-0.3 to -5.0. Estimates from the present study, though admittedly for a shorterrun, suggest elasticities approximating the lower end of the range adopted by Powell,and consequently a less favourable effect of output expansion on Australian woolreceipts than was indicated by the broad range of Powell's results. It is necessary topoint out, of course, that these results deal only partially with the consequences ofthe growth of wool production. A full consideration would require knowledge of theeffects of changes in population and incomes over time as well as more informationon the elasticity of the supply of wool in other countries.

It is worth noting that further increases in the value of the price elasticity willwork to mitigate this effect on gross returns of a given increase in either world orAustralian wool supplies.

(44) A. Powell, 'Export Receipts and Expansion in the Wool Industry', The Australian Journal ofAgricultural Economics, Vol. 3, No. 2, December 1959.

DISCUSSION AND APPLICATION OF RESULTS 49

Among the further applications of the derived price elasticity of demand forAustralian wool featured in the literature, two will be considered very briefly hereto suggest how the results of this report would have affected the conclusions drawnin earlier studies. For example in a study of the effect of a change in the exchangerate on earnings of foreign currency from exports of Australian wool, (45) Homerused his estimates of the price elasticity of demand for Australian wool of -1.59to -2.15; values which are at least twice as high as those obtained in the presentstudy. Had these lower estimates been used, the estimated change in Australia's woolexport receipts in response to devaluation would have been somewhat less favourablethan indicated by Dr Homer.

Several authors have employed an assumed range of values for the price elasticityof demand for Australian wool in studies of the operation of a hypothetical reserveprice scheme for Australian wool. Jenkins (46) assumed the elasticity to be -1.0 or-1.5; and Duloy and Parish (47) adopted twelve values ranging from -0.25 to-3.00. These compare with the estimated value of about -1.0 obtained in thepresent study.

The estimates of price elasticity of demand given in this report are not strictlyappropriate to models of market mechanisms, such as reserve price schemes, whichare concerned with continuous day to day fluctuations in demand at the auctionlevel. They are, however, a useful guide in any examination of the effect of changesin the marketing system, and some aspects of the report are of particular relevance.For instance, a point frequently made in discussions of a reserve price scheme is thatthe net returns from such a scheme would be more favourable if the price elasticitywere higher during periods of high prices, i.e. when stocks accumulated duringperiods of low prices are being sold. The empirical work of this report does not givesupport to the proposition that, in the absence of a reserve price scheme, significantdifferences exist between the elasticities at high and low prices.

(45) F. B. Homer, op. cit.(46) E. L. Jenkins, op. cit.(47) J. H. Duloy and R. M. Parish, 'An Appraisal of a Floor-Price Scheme for Wool', New England

Marketing Studies, No. I, December 1964.

Appendix A

TABULATION OF BASIC STATISTICAL DATA

TABLE A.1

FACTORS USED IN ANALYSIS OF U.K. DEMAND FOR RAW WOOL

1952 to 1964

Raw Wool Availability Ratio 0/ AvailabilityMill Con- Available Real Sales a/Wool Stocks 0/ 0/ SyntheticYear and sumption

/orHome Real Wool Personala/Wool Products for Wool Tops Staple Fibre

Quarter a/Raw Consump- Prices(c) Disposable Products(e) Home Con- to their for HomeWool(a)tion(b) lncomes(d) Per Head sumption(f) Consump- Consump-Per Head Per Head tion(h)Per Head Per Head tion(g)

Per Head

CM CH P Y SM SH T A

1b Ib d(stg) £stg Ib Ib qtr Ibper Ib

1952 I 1.644 0.798 110.88 62.59 2.436 1.732 0.708 0.032511 1.724 1.002 106.68 62.56 2.286 1.637 0.748 0.0328III 1.947 1.057 112.64 63.46 2.682 1.872 0.556 0.0331IV 2.306 1.339 110.73 64.12 2.898 2.027 0.459 0.0334

1953 I 2.440 1.609 123.64 64.52 2.939 2.167 0.521 0.033711 2.501 1.620 131.91 64.70 2.851 2.064 0.602 0.0340III 2.550 1.513 124.10 66.02 2.944 2.090 0.646 0.0347IV 2.381 1.421 119.65 67.33 2.850 2.033 0.659 0.0357

1954 I 2.252 1.365 120.70 67.40 2.872 2.126 0.696 0.036711 2.326 1.449 127.63 67.44 2.856 2.101 0.704 0.0376III 2.371 1.442 117.60 66.91 2.952 2.166 0.714 0.0404IV 2.308 1.411 101.27 68.26 2.963 2.196 0.665 0.0450

1955 I 2.381 1.398 107.32 69.02 3.043 2.192 0.680 0.049511 2.404 1.561 104.93 70.07 2.891 2.141 0.789 0.0541III 2.350 1.275 91.52 69.86 3.000 2.070 0.733 0.0601IV 2.393 1.378 83.93 70.05 3.055 2.197 0.688 0.0676

1956 I 2.338 1.333 89.43 70.05 3.005 2.163 0.668 0.075111 2.303 1.236 91.94 69.88 2.912 1.977 0.613 0.0825III 2.376 1.371 96.37 70.92 2.857 2.004 0.623 0.0939IV 2.413 1.395 98.75 72.06 2.930 2.083 0.628 0.1091

1957 I 2.472 1.373 111.49 70.48 3.068 2.176 0.621 0.124411 2.469 1.469 115.55 71.09 2.966 2.109 0.666 0.1396III 2.400 1.399 105.06 71.08 2.884 2.023 0.721 0.1427IV 2.170 1.175 87.65 73.12 2.776 1.920 0.682 0.1336

1958 I 2.166 1.144 81. 81 71.63 2.758 1.908 0.718 0.124411 2.101 1.193 74.77 71.20 2.613 1.821 0.762 0.1153III 2.149 1.198 70.20 71.58 2.712 1.896 0.736 0.1151IV 2.330 1.416 62.50 73·.27 2.820 2.019 0.720 0.1239

1959 I 2.423 1.499 64.44 71.99 2.689 1.879 0.893 0.132611 2.471 1.427 75.12 75.28 2.929 2.049 0.900 0.1414III 2.548 1.475 78.37 74.49 2.959 2.025 0.880 0.1650IV 2.531 1.430 77 .19 76.57 2.948 2.000 0.920 0.2035

1960 I 2.441 1.297 79.01 76.94 2.975 2.004 0.915 0.242011 2.344 1.319 79.00 79.36 2.906 2.011 0.912 0.2805III 2.282 1.328 68.67 79.44 2.821 1.999 0.929 0.2979IV 2.277 1.314 66.00 78.58 2.800 1.984 0.883 0.2943

(Continued on next page)

APPENDIX A: TABULATION OF BASIC STATISTICAL DATA 51

TABLE A.I-continued

FACTORS USED IN ANALYSIS OF U.K. DEMAND FOR RAW WOOL

Raw Wool Availability Ratio of AvailabilityMill Con- Available Real Sales of Wool Stocks of of Synthetic

Year and sumption for Home Real Wool Personal of Wool Products for Wool Tops Staple FibreQuarter of Raw Consump- PricesCc) Disposable Productsiey Home Can- to their for Home

WoolCa) tionCb) Incomesid) Per Head sumptiont fv Consump- Consump-Per Head Per Head Per Head Per Head tionCg) lionCh)

Per Head

CM CH P y SM SH T A

Ib Ib d(stg) £stg Ib Ib qtr lbper Ib

1961 I 2.252 1.245 70.49 80.24 2.824 1.984 0.833 0.2906Il 2.363 1.396 75.78 81.67 2.845 2.101 0.855 0.28701II 2.299 1.357 70.62 80.24 2.807 2.057 0.776 0.2890IV 2.208 1.287 66.29 78.78 2.650 1.931 0.761 0.2968

1962 I 2.162 1.363 70.40 80.13 2.566 1.894 0.879 0.3046Il 2.128 1.253 71.93 78.90 2.633 1.921 0.870 0.31241II 2.100 1.334 68.15 80.19 2.567 1.937 0.900 0.3249IV 2.164 1.299 70.66 79.65 2.638 1.887 0.855 0.3421

1963 I 2.178 1.205 76.76 80.77 2.674 1.855 0.769 0.3593Il 2.211 1.177 78.43 80.50 2.779 1.900 0.732 0.37651II 2.164 1.289 78.53 84.48 2.731 1.999 0.767 0.3965IV 2.122 1.227 85.36 82.21 2.666 1.929 0.808 0.4193

1964 I 2.133 1.301 88.93 86.58 2.626 1.912 0.868 0.4421Il 1.979 1.052 79.16 83.54 2.724 1.920 0.803 0.46491II 1.928 1.233 75.16 84.31 2.450 1.870 0.958 0.4903IV 1.806 1.004 69.80 83.17 2.416 1.743 0.893 0.5185

Footnotes (the numbers after each item refer to the sources of data):(a) Mill consumption of raw wool by the U.K. wool textile industry is measured at the carding

stage (I). (b) Estimated as mill consumption of raw wool (I), plus imports less exports of tops, noilsand waste, yams, woven fabrics and carpets (3). (c) Obtained from the U.K. Monthly Prices ofRepresentative Types of Dominion Wool prepared by the New Zealand Wool Commission, London (4).The series used is the weighted average of the prices of 64's and 56's quality wool, the weights beingthe total consumption in the study period of merino and crossbred wool respectively by the U.K. wooltextile industry (3). The series is deflated by a retail price index for all items (5). (d) Personaldisposable incomes in the United Kingdom (5) are deflated by a retail price index for all items (5).(e) Estimated from statistics of selected items, and thus may not cover all the output of the industry.They represent the sum (in terms of weight) of:

-deliveries of woven wool fabrics, worsted and wool1en (1), converted from square measure topoundage at a constant rate of O. 65 lb per square yard, see (2), 1963-64, p. 21;

-deliveries of blankets (I), converted from square measure to poundage at the variable rate shownin (2), various issues;

-deliveries of worsted yarn to hosiery mills and to retailers as hand-knitting and other yarn (I);-manufacturers' sales of woven carpets that are predominantly of wool (3), converted from square

measure to poundage at an estimated constant rate of 1.85 lb per square yard;-net exports of wool tops and yarns (3); the delivery of finished fabric for export is included in the

above categories;~stimatesof the sales of felt, mechanical cloth and wool1en hosiery yarn. (Because of the lack of a

complete statistical series for the last group, it was assumed that it had a constant share of sales overthe period.)

(f) Estimated as sales of wool products less net exports of tops, yarns, woven fabrics (includingblankets), and carpets (3). (g) Ratio of stocks of wool tops (I) to their consumption [Le. wool topsdrawn plus tops exported (3)]. (h) Quarterly data are derived (as shown on p. 24) from annualdata on the production, plus imports, less exports of synthetic staple fibres (6).

Sources: (I) U.K. Wool Industry Bureau of Statistics, Monthly Bulletin of Statistics (various issues).(2) Commonwealth Economic Committee, International Wool Textile Organisation and InternationalWool Study Group, Wool Statistics (various issues). (3) Commonwealth Economic Committee,Wool Intelligence (various issues). (4) RA.E., Statistical Handbook of the Sheep and Wool Industry,3rd edition, 1961, p. 83, and Supplement, 1964, p. 75. (5) Great Britain: Central Statistical Office,Monthly Digest of Statistics (various issues). (6) Textile Economics Bureau, Inc., Textile Organon(various issues).

Appendix B

ESTIMATES OF ALL PARAMETERS OF CONSTANTELASTICITY EMPLOYED TO TEST HYPOTHESES

No. 1 AND No. 2

TABLE B.I

PRICE ELASTICITY OF DEMAND FOR WOOL AT HIGH OR LOW PRICES: 1952 TO 1964

(Summarised in text as Table No. 3, p, 36)

Model Y

log CM t }log C = log a + bIlog Pt- 2 + b2log Yr-I + balog Tt-I + b4log At- 2 + log Ut

Ht

EstimatesDependent Periods of: ParameterVariable

log a b, b. b. b(

High wool b 3.707 -0.410 -1.369 -0.093 -0.009

CMprices standard error (0.109) (0.506) (0.135) (0.046)

t Low wool b -2.567 -0.457 1.892 -0.246 -0.261prices standard error (0.081) (0.406) (0.071) (0.044)

High wool b 2.902 -0.454 -1.045 -0.136 -0.059

Cprices standard error (0.137) (0.640) (0.171) (0.058)

u,Low wool b -3.805 -0.601 2.530 -0.537 -0.319

prices standard error (0.150) (0.751) (0.132) (0.081)

Model S

{

lOg S }= log a + bI log r.: 2 + s, log S::

+ ba log Tt"-I + b4 log At _ 2 + log VI

EstimatesDependent Periods of: ParameterVariable

log a bI b. b. b(

High wool b 0.378 -0.268 1.000 -0.170 -0.044

CMprices standard error (0.076) (0.155) (0.081) (0.018)

t Low wool b 0.415 -0.286 0.995 -0.198 -0.022prices standard error (0.070) (0.173) (0.061) (0.016)

High wool b 0.494 -0.373 0.885 -0.185 -0.083

CHprices standard error (0.136) (0.372) (0.147) (0.036)

t Low wool b 0.560 -0.451 1.137 -0.403 -0.036prices standard error (0.136) (0.287) (0.119) (0.028)

52

APPENDIX B: ESTIMATES OF ALL PARAMETERS

TABLE B.2

PRICE ELASTICITY OF DEMAND FOR WOOL: 1952-57 VERSUS 1958-64

(Summarised in text as Table No. 4, p. 38)

Model Y

logC }Mtlog C = log a + b1 log Pt - 2 + b2log Yt - 1 + balog Tt - 1 + b4log A t - 2 + log UI

HI

53

EstimatesDependent Study ParamelerVariable Period

Ilog a b I b. bs b.

1952-57 b -3.292 0.113 1.777 -0.403 -0.080

CMstandard error (0.077) (0.396) (0.075) (0.030)

I 1958-64 h -0.865 -0.302 0.874 0.088 -0.211standard error (0.094) (0.639) (0.117) (0.074)

1952-57 b -5.953 0.300 2.800 -0.748 -0.168

CHstandard error (0.123) (0.632) (0.119) (0.048)

I

I

I1958-64 b -0.081 -0.497 0.539 -0.106 -0.149

standard error (0.130) (0.882) (0.161) I (0.102)I

Model S

!ogC }M t

log CH, {

log S }= log a + bI log r.: 2 + b2 log S::

+ balog Tt - I + b410g A t - 2 + log VI

I

EstimatesDependent Study ParameterVariable Period

log a bI b. bs b.

1952-57 b -0.331 0.077 1.142 -0.235 0.022

CMstandard error (0.074) (0.244) (0.064) (0.018)

t 1958-64 b 0.306 -0.226 0.989 -0.079 -0.044standard error (0.054) (0.133) (0.070) (0.015)

1952-57 b -0.618 0.141 1.277 -0.445 0.014

C standard error (0.119) (0.286) (0.104) (0.030)

Ht1958-64 b 0.469 -0.373 1.000 -0.163 -0.063

standard error (0.113) (0.305) (0.134) (0.026)

Appendix C

SIMPLE CORRELATIONS BETWEEN VARIABLES

TABLE C.1

LINEAR CORRELATION COEFFICIENTS (r) BETWEEN ALL VARIABLES INMODELS Y AND S: 1952 TO 1964

(All variables measured in logs)

Mill Raw Wool Real Availability Ratio of Availabilityconsu:;jPtion Available Personal Sales of of Wool Stocks of of Synthetic

for Home Real Wool Disposable Wool Products Wool Tops Staple FibreRaw Wool Consumption Prices Incomes Products for Home to their for HomePer Head Per Head Per Head Per Head Consumption Consumption Consumption

Per Head Per Head

C C Pt-2 Yt - 1 S SH Tt - 1 At - 2M t Ht M t t

CM 1.0000 0.8400 0.1821 -0.4997 0.8403 0.7346 -0.3842 -0.5141t

CH 1.0000 0.2165 -0.4706 0.5594 0.7059 -0.4725 -0.4989t

P t- 2 1.0000 -0.7539 0.4025 0.4880 -0.6860 -0.7884

Yt - 1 1.0000 -0.5836 -0.5489 0.7467 0.9692

S 1.0000 0.8636 -0.3840 -0.6310M t

S 1.0000 -0.4681 -0.6381Ht

Tt - 1 1.0000 0.7205,

A t - 2 1.0000

54

Appendix D

PROPOSITIONS RELATING TO SPECIFICATION BIASDUE TO A PROXY REGRESSION VARIABLE

(i) Specification Bias Due to a Proxy Variable

Suppose the true model is:

z = Xf3 + u

where

X = an n x k matrix of non-stochastic variables;

f3 = a k x 1 vector of parameters; and

u = an n x 1 vector of random variables with an expected value of zero

Instead, we estimate:

z = wp + v

where W is an n x k matrix similar to X but having a proxy variable s in place ofthe true variable y. The ordering of these latter two variables relative to the otherexplanatory variables in X and W is not important, but let us suppose that X and Wcan be partitioned into (X i y) and eX is) respectively, where y and s are n x 1, ,

vectors. The least squares estimator Pis given by:

P= (W'W)-IW'z

= (W'W)-IW'Xf3 + (W'W)-IW'U

Therefore:

E[Pl = (W'W, -IW'Xf3

= (W W)-I(W'X ! W'y)f3

[

I Ck - l ) i ]= ~------------l (W'W)-IW'y f3

= [~~~-~!_----! PJf3where p is a k x 1 vector of coefficients from a regression of y on W. Hence

for i =1= kfor i = k

bias L8;] = {Pi ~k _ RPk fJk r,

55

Consequently, the bias of the estimator is given by

for i=l= kfor i = k


(ii) The Relation Between the Coefficients of Price from Auxiliary Regressions ofDisposable Income and Sales of Wool Products Respectively on All OtherExplanatory Variables

Let us consider the following explanatory variables used in the model of demandfor wool in the United Kingdom. (The notation has been changed slightly.)

Price of wool (XJ

Disposable income (X2)

Sales of wool products (X3)

Stocks of tops . (XJAvailability of synthetic fibres (X5)

It is well known that least squares estimators of the multiple regression parameters relevant to footnote 36 can be broken down as follows:

(01)

(D2)

b - b21 ' 45 - b23' 45 b31' 4521'345 - 1 - b

13'45

b31

'45

b - b31' 45 - b32' 45 b21' 4531'245 - 1 - b

12'45

b21

'45

b21' 45 - b23' 45 b31' 45

1 - r213'45

b31' 45 - b3 2' 45 b21' 45

1 - r212'45

From equation D2 is obtained

b31' 45 = b31 ' 245 (1 - ,212'45) + b32' 45 b21' 45

which may be substituted in equation Dl to give

(D3)

Since (1 - ,21 3 ' 4 5) > 0, it is clear that the sign of b21'345 depends on the sign ofthe numerator in equation D3. In addition to the positive quantities (1 - r 2

1204 5)

"and (1 - r223'45) which occur in the numerator, it is known that the quantities.b 21' 4 5 and b 23' 4 5 are also positive because r 21' 4 5 and r 23' 4 5 have values of 0.16 and0.14 respectively. Hence, the numerator is positive if

b b21' 45 (l - r2

23'45)

31'245 < b23' 45 (l - r\2'45)

in which case a negative value for b31'245 (i.e. the hypothesised effect of wool priceson sales of wool products) is a sufficient condition for a positive value of b21• 345 •

The value of b3102 45 (q in footnote 36) was found to be -0.065 in the regressionof sales of wool products and -0.033 in that of wool products available for homeconsumption. Although these results support the interpretation offered in footnote 36.it is noted that the maximum value of b31'245 consistent with the necessary condition(for a positive value of b 21• 345) is actually positive, the maximum value being 0.469in the case of sales of wool products and O.136 in the case of wool products availablefor home consumption. Finally, it is clear from an examination of equation D3 thatdecreasing values of b31'245 give rise to increasing values of b21'345 •

Appendix E

COMPARISON WITH HORNER'S ESTIMATES

The best known estimates of the price elasticity for the U.K. and the U.S.markets have been those made by Homer in his pioneering work in this field basedon pre-war data. (48) In view of the fact that Horner's estimates of -0.4 to -0.6are higher than those obtained in the present study, some explanation of the differencesbetween the two sets of estimates is warranted. The price elasticity of demand forwool on which he based his estimates was defined by Homer (page 27) as:

TJ = cu + rwhere

c = price elasticity of consumers' demand for wool clothing;u = price of wool -i- (price of wool + the cost of transformation);r = price elasticity of manufacturers' demand for wool.

However, on page 25 of his article, Homer presents two equations of manufacturers' demand for wool:

'Quantity variation only:Log (quantity of wool consumedper unit of output)

= m + n log (price of wool) . . . (3a)

'Quantity and quality variation:Log (value of wool consumed --:- standard-qualityprice of wool, per unit of output)

= q + r log (price of wool) . . . (3b)'

For the United Kingdom (1924--38), Homer estimates n (which he describesas the elasticity due to quantity variation only) to be -0.09, and r (the elasticitydue to quantity and quality variation) to be -0.37. Judging r to be the appropriatecomponent to use for his estimate of the total elasticity, Homer calculates7J = cu + r = -0.43 to -0.55.

The estimated elasticity in the present study relates to the total quantity of woolconsumed in terms of weight and irrespective of any changes in the quality of woolconsumed, A comparable elasticity estimate can be derived from Horner's data bymeans of the formula TJ' = cu + n. If the total elasticity is interpreted in this way,his estimates would be -0.15 to -0.27 for the period 1924 to 1938. These wouldcorrespond approximately to the estimates of -0. 12 to -0.22 obtained with modelYR 11 in the present study for the year 1952, i.e. before the major impact ofsynthetics,

The difference between the two sets of elasticity estimates can therefore beexplained partly in terms of differences of concept. Horner's estimates are based onthe use of a dependent variable which caters for variation in both the quantity and

(48) F. B. Homer, 'The Pre-war Demand for Wool', Economic Record, Vol. 28, No. 54, May 1952.In a subsequent article by Philpott, a price elasticity of world demand of -0.55 was obtained withdata for the period 1921-56, but preference was given to a value of -0.4 secured by different methods:B. P. Philpott, 'Wool in the New Zealand Economy', The Economic Record, Vol. XXXIII, No. 65,August 1957.

57


quality of wool consumed. In the present study, on the other hand, it has beenassumed that manufacturers as a group do not substitute appreciable quantities ofone grade of wool for another in response to changes in the level of wool prices andthe estimated elasticity relates to the total quantity of wool consumed in terms ofweight and irrespective of any changes in the quality of wool consumed.

While this question has not been tested empirically in this study, there wouldseem to be good a priori reasons for preferring an elasticity such as that used inthe present study; i.e. one which, at the aggregative level, ignores the possibility ofsubstitution of types in response to price changes.

On the world level, the type composition of the world wool supply is in generalpredetermined by the production process. Substitution, on the demand side, couldonly occur in the very long run when a change in relative prices induced a changein the type composition of world supplies. In the short run, the availability of stockspermits some degree of substitution by manufacturers from type to type as priceschange. Substitution between types, however, must eventually be corrected by anadjustment in relative prices and there would seem to be good reason to expect thisadjustment to be a fairly rapid one.

It is not clear whether a similar situation to that described for world demandprevails in the case of demand for wool by the U'K, wool textile industry. A substantial part of the U.K. top production still appears to be sold forward, though it isprobably considerably less than in the pre-war period to which Horner's estimatesrelate. With unchanged selling prices for tops, topmakers either accept lower profitmargins or, as Homer suggests, move to cheaper wool types. The acceptance oflower profit margins is unlikely to be other than a relatively short term phenomenonand can be expected to be adjusted in new contracts for forward sales. The skillsavailable in the topmaking sector of the industry are such as to make it conceivablethat they can produce a satisfactory end product with wools which may be less thanideal for the purpose. However, this explanation does raise two questions. The firstis whether and to what extent the consumer can judge between different qualitywools in the end products. The second concerns the reasons why the topmaker doesnot use the cheaper wools all the time.

It must be acknowledged that Horner's empirical results for the pre-war periodare not inconsistent with the argument that the consumption of lower quality woolincreases when prices rise. But the same results could also have been brought aboutby independent supply changes: for example, they could have been caused by changesin the relative prices of types consumed on the U.K. market owing to long termtrends or even short term fluctuations in the type composition and total volume ofworld supplies.

As a matter of judgment, a price elasticity of demand which relates solely toquantity variation has been preferred in this report to one which allows for variationsin both the quantity and the quality of wool consumed.

Of course, to the extent that there is an attempt to substitute lower quality wooltypes for more expensive types in the U.K. industry as a whole as wool prices rise,there must exist a corresponding substitution among wool types in the oppositedirection elsewhere. Nevertheless, there has been a tendency for Horner's higherelasticity estimates to be used as indicators of the world elasticity. Since, irrespectiveof what may be possible in the case of a single country, net substitution of wool typesby manufacturers is unlikely on a world scale, given the relative levels of stocks

APPENDIX E: COMPARISON WITH HORNER'S ESTIMATES 59

compared with world production, an elasticity which takes account of quality changesis clearly not appropriate. While not themselves free from other objections, clearlymore appropriate for purposes of this kind are estimates based on quantity variationsalone such as the lower estimates derived from Homer's study or those presented inthis study.

Glossary

The following Greek letters and mathematical signs are used in this report:

f3 Beta > Greater than

LI Delta < Less than

c; Epsilon· :::;; Less than or equal to

'TJ Eta ~ Greater than or equal to

fL Mu 00 Infinity

p Rho =1= Not equal to

Cl Sigma Estimate of

WOOL ECONOMIC RESEARCH REPORTS

Wool Economic Research reports currently available:Number 6: Wool in the EEC (1964)Number 9: Wool in Italy (1966)Number 10: Wool in India (1967)Number 11: The Price Elasticity of Demand for Wool in the U.K. (1967)

Copies of any of these reports may be obtained on application to the Director, Bureauof Agricultural Economics, Canberra, A.C.T. (2600).

By Authority: A. J. ARTHUR, Commonwealth Government Printer, Canberra

~.

Date post:	19-Aug-2018
Category:	Documents
Upload:	trinhbao
View:	212 times
Download:	0 times

the price elasticity of demand for wool in the united...

Documents