PRODUCTIVITY AND COST COMPETITIVENESS OF CANADIANFOOD AND BEVERAGE MANUFACTURING INDUSTRIESbyDAVID JOHN FEELEYB.Sc.(Agr.), The University of British Columbia, 1986A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDY(Department of Agricultural Economics)We accept this thesis as conforming___to the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober, 1992© David John FeeleyIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of Agricultural EconomicsThe University of British ColumbiaVancouver, CanadaDate October 15, 1992DE-6 (2/88)iiAbstractThis thesis reports an analysis of the competitive positionof the Canadian food and beverage industry with respect to theU.S. industry for the year 1986. The main contribution is inproviding measures of Canada/U.S. variable factor productivityfor 38 food processing and beverage industries. It is animprovement over previous work for two reasons. First, theanalysis is conducted at a more disaggregated level thanprevious studies, that is, below the Canadian SIC level.Secondly, in using 1986 data for analysis it is the most up todate productivity study of the industry available.The study uses the index number approach to productivitymeasurement. For each industry, relative Tornqvist priceindexes for commodity outputs and materials, labour, and energyinputs were constructed. These indexes, along with data forindustry shipments and expenditures on materials, labour, andenergy, were then used to develop input and output relativeTornqvist quantity indexes, and hence, measures of relativephysical productivity. Sources of Canadian data were StatisticsCanada publications containing data for 1986 while data for U.S.industries were obtained from the 1987 Census of Manufacturesand 1986 Annual Survey of Manufactures.The results indicate that in 1986 the Canadian industry wasnot well placed with respect to its U.S. counterpart. Onaverage, relative variable factor productivity for each Canadianindustry was estimated to be 7.6 percent lower. Relativelyiiilower Canadian physical productivity was exacerbated byrelatively higher input prices, so that average output costcompetitiveness was 15.5 percent lower in Canada. Average inputcost competitiveness was found to be 4.8 percent lower inCanada. Correlation analysis found no strong evidence of a linkbetween these two measures of cost competitiveness.ivTable of ContentsAbstract iiTable of Contents ivList of Tables viList of Figures viiAcknowledgements viii1. Introduction a.1.1 Problem Statement 11.2 Outline of the Thesis 21.3 An Introduction to Productivity Measurement 31.4 Methods of Productivity Measurement 72. Literature Review: Canada/U.S. Comparisons . . .. 103. Methodology 183.1. Basic Mathematics of ProductivityMeasurement 183.2 Index Number Theory 213.3 The Empirical Model 324. Database and Variable Construction 394.1 Productivity Measurement for the InternationalCross—Sectional Comparison 394.2 Data Sources 434.3 Variable Construction 444.3.1 Disaggregating Canadian ShipmentsData 454.3.2 Constructing the Canadian MaterialsInput Data forDissagregated Industries 464.3.3 Constructing Relative Output PriceIndexes 504.3.4 Calculation of Relative MaterialsInput Price Indexes 514.3.5 Calculating Relative Input PriceIndexes for Labourand Labour Cost Shares 524.3.6 Calculating the Energy Input Dataand Energy Input Price Index . . 574.4 Database 594.4.1 MTLS Database 594.4.2 OUTPUT Database 624.4.3 INDDTA Database 655. Results . .. 67V6. Discussion of the Results. 757. Conclusions. 82References .. 84Appendix A Canada/U.S. Industry Concordance . . .. 87Appendix B An Example of Disaggregating CanadianMaterials Input Data: Slaughterers andMeat Processors (SIC 1011) 89Appendix C Packaging Cost Calculations 94Appendix D Calculation of a Relative Price Index forEnergy 96Appendix E MTLS Database 98Appendix F OUTPUT Database XAppendix G INDDTA Database Xl-I-1-31-31-3)))P)1)P)))))HbbHHHHHHHHHHftCDCD(D(DCDCDCDCD(D(DC_i)HXj0OOO)MHH‘JftH0OD0CDQ1Q’i0o’01flHQ‘-3,)H.CDrftO(-tp)H.HPHct-tYHP)HH-H-rt-H-ct000CDDJH CDHHF)ftH-ctH-’ci-.)ftCDctCtcc-i-.CDH1Owhere a1,a , and B are parameters.Technological change is reflected by changes in theseparameters. Should only the intercept parameter a1 change,the ratio a1 /a will measure the rate of technical progressbetween periods i and j. In this case there is no inclinationto make one input relatively more productive than another andthe change is “neutral”.Only if both constant returns to scale prevails and asingle input is utilized will productivity growth Z1/ZJgiven by equation (2), be the same as technical progress.Non—constant returns to scale with one input (e.g. a = 0)yieldsaZ1 axf’_______z. -‘ l \P-’, axxli20Productivity growth will equal technical progress only ifinput levels are unchanged between i and j. Under any othercircumstances, productivity growth will be composed of bothscale effects and technical progress.Now consider a commodity produced with more than oneproductive input where we are interested only in theproductivity of input 1. If we define this input as labour,then labour productivity becomesI5 — —a1xfxZ——--——— —a1x1 x21x1iand labour productivity growth is(6) Ziixi1)(aZ y1x1)The proportional rate of change of labour productivitycan be calculated as••(X2(7) Z=a÷(+f3—l)x1+13I‘\x1Equation (7) shows that the proportional rate of changeof labour productivity is the sum of three elements: atechnical progress term, a term corresponding to the influenceof economies of scale, and a term which measures the effect on21labour productivity of altering the quantity of the otherinput at each employee’s disposal.In order to measure the contribution of all inputs, werequire an aggregator to assign a unique value to eachdifferent input bundle. Given perfect competition in inputmarkets and constant returns to scale (a + 13 = 1), theelasticities of output with respect to each input will be thesame as the observed shares of each input in total costs. Forthe two—input Cobb—Douglas case these are the exponents a and13. We can define the aggregator as(8) (&+=i)where a and 13 are their observed cost shares of inputs 1 and2. With perfect competition and constant returns to scale,the change in technical progress a1/a will be the same as thechange in total factor productivity, measured analogously toequation (2) but with and instead of x1 and x.3.2 Index Number TheoryThe index number approach involves collecting detailedaccounts of inputs and outputs, aggregating them into inputand output indexes, and using these indexes to calculate aproductivity index. A troublesome problem encountered by22applied economists in constructing data series is the questionof which functional form of index to use. In this section weconsider this issue and relate certain functional forms forindex numbers to functional forms for the underlyingaggregator function.3 We also introduce the concepts of exactand superlative index numbers and Tornqvist approximations toDivisia indexes. Finally, we introduce a general methodologyfor analysing the sources of intertemporal and interspatialdifferences in outputs and costs. This method is based onapplications of Diewert’s (1976) quadratic lemma, and involvesthe analysis of quadratic approximations to the function whichis generating the data.Define a quantity index between two economic entities sand r(9) Q(psprxsxr)as a function of prices in entities s and r, S > O and r >and the corresponding quantity vectors x5 > and r >where°N is an N—dimensional vector of zeroes4. Now define aprice index between entities s and r3Aggregator function is a neutral term which could denote one of either aproduction function or a cost function.4rhese two economic entities could be either one entity analyzed at twodifferent points in time or two separate entities. That is, the analysispresented here is applicable either intertemporally or interspatiatl.y.H-(fli—30CDP’——CDC)H-(fltDClI-’Cl0C))C)’tftCDciftC))ftXHYCDCDi-lH-CDhCDCDCDciCD0‘<<‘-Q0EnH-CD0HH-H-CDCliH)Cl‘-3CDCDXU)CD(1)Cl)0ftU)CiH-CiJCDEl)tH-CDEl)-CDftftCiU)(nC)0(tCl)HdSC)HctCDgo.Q,op,CDH-(0H-H-(0C/)Cl)—‘Cl:i2H-p.Cl,,H-CDQrtoCl.1‘1HH-CDCD0)0)-)U’(30)0)(3((4U’0)0)0).0(3U’U’(0CC)(00)(30)(3(C)0)(0CC)(3(3CC)(30)0)(0(())(CC0.PPP’toPto0)0)3N)0)(0C))0)(0N)P0)P0)0)U’.0(0C,)N)-0(0N)(C)CON)400C,)(3N)00)U’.0(3-.0)C-3(-0)N)0(N)COO)-‘N).0N)U’C,).0(30(0-3(0U’(0_)N)0-30(0.00)(3(0CC(1H C)HCl)CDoE-,U)HOH—-CC.flCDC’-3-3-3-3-30N)N).0N).0N).0.0N)N)N)N)“N)0)00‘p’p•p--4•ptoto0)PpU’oppopco’.C)0(3(0(3C,)0)0U’(00-0U’.4(3(3U’U’(3)O(3’N)-0-(CC,)0)(3U’C,)0)-000)02t- CD-0)C)H,-Cl)“H.<00(30)0-’(00)_CU’00C,).0-.CN)N)U’(3.0C,)(0.0U’(30)400(3U’(3.0-40)0(000-’o(0H-CDct-CDU)CD(30)0)0)(30)0)(3(0(3(30)U’0)(00)(0(3CC)0)CC)0)(0(0C))(3CC)0)0)(3CC)CC)0)(0(0C)!?iPSPP-’<(0CD.0(3—,(0(0(3(3U’(00CC)N)-3CO0)U’0)_C0)N)C,)U’U’(0(30)0N)CC).00)(30).0N)C,)N)(30)CC03.Cl)H-CDoH-C)ctCCCDLQH-—0H)IHCDII00N)00)(0N)0)N).00)N)N)1N)(0N)0)0)0)N).0(00)N)(3-‘N)C,)(3N)0)0)N)U’(0CD0-C-‘69Table 4 Calculated Canada/U.S. Relative Labour Prices, 1986Relative Labour Price ($Cdfl/$Cdn)1 Beef 0.9722 Pork 0.9723 Pork processing 0.9704 Sausages 0.9705 Inedible tallow 0.9646 PouLtry 0.7757 Canned vegetables 08658 Canned mushrooms 0.8659 Juice 0.86510 Jams & jellies 0.86511 Frozen vegetables 0.76512 Milk 0.91213 Butter 0.86714 Cheese 0.87315 Milk powder 0.84416 Ice cream 084717 Flour 0.68118 Cake mix 0.81519 Breakfast cereals 0.82820 Feed 0.81021 Dog & cat food 0.79922 vegetable oil 1.01123 Biscuits 0.77024 Bread 0.79725 Sugar 0.85526 Chewing gum 0.82227 Confectionery 0.78628 Coffee 0.75429 Pasta 0.93230 Chip & popcorn 0.88 131 Peanut butter 0.85832 Starch 0.86033 Peanuts 0.86234 Shortening & margarine 0.86035 Soft drinks 0.88436 Beer 0.78437 Wine 0.81538 Smoking tobacco 0.968Averaoe 0.864The average values calculated for relative materialsinput and output price indexes are presented in Table 5.These indexes were calculated using equation (64) and equation(63), respectively. 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