Production structure and input substitution in Canadian sawmill and wood preservation industry

Transcription

1 Producton structure and nput substtuton n Canadan sawmll and wood preservaton ndustry Rao V. Nagubad and Daowe Zhang 3007 Abstract: We use a translog cost functon to analyze the sawmll and wood-preservaton ndustry n Canada from 1958 to The estmated cost functon s homothetc and Hcks neutral. Allen elastctes of substtuton ndcate that sgnfcant substtuton possbltes exst. Accordng to Morshma elastctes of substtuton, substtuton of by other nputs s easer than the substtuton of other nputs by, and substtuton of other nputs by materals s easer than the substtuton of materals by other nputs. The demand for producton, nonproducton, and electrc power nputs s elastc. In contrast to the prevous fndngs of zero or negatve rate of techncal change, we fnd techncal progress at the rate of 0.57% per annum and a total factor productvty growth rate of 0.54% per annum n the Canadan sawmll and wood preservaton ndustry. Résumé : Nous utlsons une foncton du coût de type translog pour analyser l ndustre du scage et de la préservaton du bos au Canada, de 1958 à La foncton du coût estmée est homothétque et neutre au sens de Hcks. Les élastctés de substtuton d Allen ndquent que de fortes possbltés de substtuton exstent. Selon les élastctés de substtuton de Morshma, la substtuton de la man-d œuvre par d autres facteurs de producton est plus facle que la substtuton des autres ntrants par la man-d œuvre et la substtuton des autres ntrants par les matéraux est plus facle que la substtuton des matéraux par les autres ntrants. La demande pour les ntrants sous forme de man-d œuvre responsable de la producton, de personnel de souten et d énerge électrque est élastque. Contrarement aux conclusons précédentes concernant la mesure d un taux de progrès technque nul ou négatf, nous observons un taux de progrès technque de 0,57 % par année et une productvté globale des facteurs de producton de 0,54 % par année dans l ndustre du scage et de la préservaton du bos au Canada. [Tradut par la Rédacton] Nagubad and Zhang 3014 Introducton The sawmll and wood-preservaton ndustry s an mportant ndustry n Canada, contrbutng 2.06% of the total value of manufacturng shpments n Prevous studes of techncal change n the ndustry n Canada present mxed results. Several studes usng data between 1955 and 1984 (Martnello 1985; Nautyal and Sngh 1985; Sngh and Nautyal 1986) report negatve or no technologcal progress n the Canadan sawmll or softwood lumber ndustry. However, Ghebremchael et al. (1990) estmate 0.4% per year mprovement n total factor productvty (TFP) growth for the lumber ndustry between 1962 and 1985, whereas Bernsten (1994) reports a TFP growth of 3% per year for softwood lumber ndustry between 1963 and The obectve of ths study s to analyze the producton structure and nput substtuton n the Canadan sawmll and wood-preservaton ndustry. We use a translog cost functon approach. The total cost functon s estmated smultaneously wth the cost-share equatons for seven nputs producton (P), nonproducton (N), machnery and equpment captal (Q), plants and structures captal (S), Receved 10 June Accepted 28 June Publshed on the NRC Research Press Web ste at on 20 January R.V. Nagubad and D. Zhang. 1 School of Forestry and Wldlfe Scences, Auburn Unversty, AL 36849, USA. 1 Correspondng author (e-mal: zhangdw@auburn.edu). fuels energy (F), electrc power (R), and materals (M). The output s the sum of all products n the ndustry, ncludng softwood lumber, hardwood lumber, wood chps, woodpreservaton products, wood tes shngles shakes, and other products. In addton to the usual Allen elastctes of substtuton and own and cross prce elastctes of demand, we also compute Morshma elastctes of substtuton between nputs. Ths study dffers from prevous studes n several aspects. Frstly, prevous studes (e.g., Ghebremchael et al. 1990; Abt et al. 1994) cover only lumber and woodchps but not other mportant segments of lumber producton, woodpreservaton products, and shakes and shngles. Snce chemcally treated lumber and wood-preservaton products have become an mportant form of lumber consumed n the outdoor applcatons of home constructon and other uses (Nagubad et al. 2004), we combne the sawmll ndustry and wood-preservaton ndustry n ths study. Secondly, prevous studes use aggregated nputs and do not take nto account the dfference between producton and nonproducton, machnery and equpment (M&E) captal and plants and structures (P&S) captal, and fuels energy and electrc energy. To demonstrate the dfferences between these subdvsons of nputs, we use seven nputs n our analyss. Thrdly, a few studes use value added mnus cost as the cost share of captal n valung captal servces, whch leads to unrealstcally hgh estmates of servce prce of captal as a percentage (n some years as hgh as 151%) of total captal stock. In ths study, we use the Can. J. For. Res. 36: (2006) do: /x06-187

2 3008 Can. J. For. Res. Vol. 36, 2006 opportunty cost prncple to estmate the servce prces of captal. Fnally, prevous studes have used Allen elastcty of substtuton to explan the substtuton structure n the ndustry. However, accordng to Blackorby and Russell (1989), the Allen measure cannot be nterpreted n the sprt of the margnal rate of substtuton and s not nformatve about the relatve share of nputs and the curvature of the soquant, and the correct measure of the substtutablty s the Morshma elastcty of substtuton (MES). Blackorby and Russell (1989) also state that the MES s a measure of curvature, or ease of substtuton; s a suffcent statstc for assessng, quanttatvely and qualtatvely, the effects of changes n prces or quantty ratos on relatve factor shares; and s a logarthmc dervatve of a quanttatve rato wth respect to a margnal rate of substtuton or a prce rato. Chambers (1988) characterzes the Allen measure as one-factor, oneprce elastcty of substtuton and the Morshma measure as two-factor, one-prce elastcty of substtuton. As such, MES s the correct measure of elastcty of substtuton n the multfactor context. Our results ndcate that sgnfcant substtuton possbltes between maor nputs exst and demand for producton, nonproducton, and electrc power nputs s elastc for the Canadan ndustry. We fnd all nputs are substtutes accordng to the MESs. The next secton dscusses study methods, followed by a bref descrpton of data used n the estmaton. The remanng sectons present the results and conclusons. Methods We use an econometrc approach to study the producton structure and nput substtuton n the ndustry. Unlke the ndex number approach, the econometrc approach (translog functon) enables us to estmate the parameters of nterest, that s, elastctes of factor substtuton, elastctes of factor demand, and economes of scale. The translog functon provdes a second-order approxmaton to an arbtrary twce contnuously dfferentable lnear homogenous functon and s flexble n the sense that t does not mpose any restrctons. The producton functon of the ndustry can be wrtten as [1] Y = f(x, t) where Y s the quantty of output, X s a vector of nputs, and t s tme n years. Under cost-mnmzaton, X s the leastcost combnaton of nputs that can produce output Y. Accordng to dualty theory, there exsts a dual cost functon to the above producton functon: [2] C = f(p, Y, t) where C s total cost, P s vector of factor prces, and Y and t are as prevously defned. In terms of an unrestrcted translog cost functon (Chrstensen et al. 1973), the above functon takes the form: [3] lnc = α + α ln Y α (ln Y) + α t α t 0 Y 2 YY t 2 tt + α Yt lnyt + β lnp + 1 γ lnp lnp 2 + ϕ lnp lny + ψ lnpt Y t where P and P are nput prces (, =P,N,Q,S,F,R,and M); t s tme n years (t = 1,, 46; startng from 1958 = 1); and α, β, γ, φ, and ψ are coeffcents to be estmated. To correspond to a well-behaved producton functon, a cost functon must be homogeneous of degree one n the nput prces and requres the followng condtons to be satsfed: [4] β = 1; γ = 0; γ = γ ; γ = 0; ϕ Y = 0; ψ = 0 t Accordng to Shephard s lemma, the cost mnmzng shares, S, are lnc C P P [5] = = X = S = β lnp P C C + γ lnp + ϕy lny + ψtt + e where e are random errors and the other varables are as defned above. From the above system of equatons, we can derve several measures of nterest. Allen own- and cross- partal elastctes of factor substtuton (σ, and σ ) measure the ease wth whch nputs can be substtuted for one another n the producton of a fxed level of output and are estmated as 2 γ [6] σ + S S = for all, = ; 2 S σ γ = 1 + for,, SS Postve and negatve sgns ndcate that the factors are substtutes and complements, respectvely. Own- and crosspartal elastctes of factor demand (ε and ε ) are estmated as [7] ε = S σ for all, = ; ε = S σ for,, As mentoned prevously, the MES s the correct measure of the ease of substtuton n the multfactor context to assess the effects of changes n prce or quantty ratos on relatve shares of nputs accordng to Blackorby and Russell (1989). The MESs are estmated as [8] σ M = ε ε The rate of techncal change ( T), also known as techncal change parameter, s the negatve of the dervatve of the cost functon wth respect to tme [9] lnc T = = ( α + α t + α lny +ψ ln P ) t t tt Yt t The rate of techncal change not only vares over tme and s nfluenced by output level and factor prces. Factor prces nfluence techncal change through ψ t. The percentage change n the total factor productvty (TFP ) s estmated as (Capalbo 1988, p. 179; Baltag and Grffn 1988) [10] TFP = T + ( 1 ε ) Y CY

3 Nagubad and Zhang 3009 Fg. 1. Output revenue shares n the sawmll and wood preservaton ndustry n Canada, where T s the rate of techncal change defned above, Y the rate of change n output, and ε CY the elastcty of cost wth respect to output: ε lnc = = α + α lny + α t + ϕ lnp lny CY Y YY Yt Y The second term, ( 1 ε ) CY Y, n eq. 10 represents the scale effects. 2 When scale effects are present, growth n TFP s not equal to the rate of techncal change. For an ndustry characterzed by constant returns to scale, cost elastcty of output s one and growth n TFP equals the rate of techncal change, T. Data The products ncluded for the ndustry n Canada are lsted as (sawmlls, except shngle and shake mlls), (shngle and shake mlls), and (wood preservaton) after 1997 under the North Amercan Industry Classfcaton System. Pror to 1997, these were lsted as 2512/2513 (sawmll and planng mll products), 2511 (shngle and shake mlls), and 2591 (wood preservaton) under the Standard Industral Classfcaton System. The prmary sources of data are annual census of manufactures and Statstcs Canada publcatons catalogue Nos , , and the Canadan Socoeconomc Informaton Management System (CANSIM-II). Ths study uses the data for the years from 1958 to The quanttes for sx outputs softwood lumber, hardwood lumber, wood chps, wood-preservaton products, wood tes shngles shakes, and other products are mputed from the value of shpments usng the weghted prces constructed from avalable quanttes and values of subcomponents for each output. Snce wood chps are n bone dry tonnes, and wood tes shngles shakes are n squares, they are converted to thousand board feet equvalents usng approxmate converson factors. 3 The unt for producton worker nput s the number of actual hours pad and for nonproducton workers man-years employed. The captal stock nput s n real 2001 Canadan dollars; fuels energy and electrc energy are mputed quanttes n Brtsh thermal unts (Btu) and klowatt-hours (kwh), respectvely; and materal nputs are n thousand board feet (MBF). Materal nputs nclude nonwood materals and contract work. Wherever data are unavalable, sutable nterpolatons and mputatons are made to fll n the gaps. The prces of all nputs, ncludng captal stocks, are converted to the 2001 real Canadan dollars usng the gross domestc product deflator. Ths study uses captal stock data avalable from Statstcs Canada. The servce prce of captal s computed by addng () the bond nterest rate on total captal stock, () deprecaton on M&E based on 12 year lfe (8.33%), and () deprecaton on P&S based on 20 year lfe (5%). For bond nterest rate, we use Scota Captal, Inc., long-term average weghted yeld on bonds for Canada for perod and extendng back to perod usng percent changes n McLeod, Young, Wer s 10 ndustrals bond average yeld rate for Canada. The nomnal value of shpments for the ndustry ncreased dramatcally (nearly 30 tmes) n Canada from CAN$0.53 bllon to CAN$15.79 bllon over the analyss perod. The changng composton of varous products n the ndustry s 2 Accordng to Grlches and Rngstad (1971), dervng economes of scale or scale effects from the aggregated ndustry data (n contrast to frm-level data) has no relevance to the scale ssue (Baardsen 2000). Furthermore, accordng to Damond McFadden s mpossblty theorem, estmaton of economes of scale and techncal change from the aggregates s an mpossble task, because the two concepts are nseparable n the tme-seres settng (Damond et al. 1978). Nevertheless, we provde estmates of scale effects and rates of techncal change to ensure comparablty wth the results of earler studes. 3 The approxmate converson factor for wood chps s one bone-dry ton = 1.15 MBF (1 ton = tonnes) and for wood tes shngles shakes s one square = MBF (Davd Brggs, College of Forest Resources, Unversty of Washngton, Seattle, Wash., personal communcaton, 2004).

4 3010 Can. J. For. Res. Vol. 36, 2006 Fg. 2. Input cost shares n the sawmll and wood preservaton ndustry n Canada, M&E, machnery and equpment; P&S, plants and structures. total revenue s depcted n Fg. 1. The share of softwood lumber n Canada declned from 76% to 70%; hardwood lumber declned from 6% to 2%; wood chps ncreased from 4% to 12%; wood preservaton products ncreased from 3% to 4%; wood tes shngles shakes products declned; other products, consstng of manly contract work, ncreased margnally. Changes n the cost shares of nputs n the ndustry n Canada are shown n Fg. 2. The share of nput expendture on total declned from 31% to 20%; the cost share of servce prce of both types of captal declned from 5% to 3%; the combned cost share of fuels and electrc energy ncreased from 2% to 4%; and the share of materals cost rose from 62% to 72%. Results and dscusson The total cost functon and cost share equatons are ontly estmated by means of seemngly unrelated regresson equatons usng maxmum lkelhood method whch s equvalent to teratve Zellner effcent estmaton method (Greene 1995, p. 391). Snce cost shares sum to one, one cost share equaton must be omtted. The remanng sx cost share equatons are estmated by normalzng nput prces wth the prce of omtted cost share equaton, whch n ths case s materals prce. The parameter estmates and ther standard errors of omtted equaton are derved usng procedure descrbed n Berndt (1991, p. 473). Snce the maxmum lkelhood estmaton procedure s used, parameter estmates are nvarant to omtted equaton (Greene 1993). Parameter estmates Several specfcatons of the translog cost functon, ncludng unrestrcted, nonhomothetc Hcks-neutral techncal change, homothetc non-neutral techncal change, homothetc Hcks-neutral techncal change, homogeneous (homothetc and no techncal change), and untary elastcty are estmated. However, only homothetc and Hcks-neutral techncal change specfcaton could satsfy the regularty condtons for a well-behaved cost functon and fnal specfcaton ncluded the terms, Y and t. 4 Table 1 presents estmated coeffcents and the assocated p values. Twenty seven of 30 estmated coeffcents are sgnfcant at the 10% level or better. We dscuss the results below n terms of elastctes of substtuton and elastctes of demand. Allen elastctes of substtuton To compare our results wth those n prevous studes, we frst dscuss the Allen measure. Allen own and cross elastctes of substtuton (AES) between nputs and ther approxmate standard errors estmated at mean levels of cost shares are presented n Table 2. Producton has a sgnfcant substtuton relatonshp wth all other nputs n the Allen sense. Nonproducton s a sgnfcant substtute for materals and both types of energy but has a sgnfcant complementary relatonshp wth P&S captal. M&E captal has a substtuton relatonshp wth P&S captal but has a complmentary relatonshp wth both types of energy. Both types of energy have a complementary relatonshp wth P&S captal. Fuels energy and electrc power are substtutes n the Canadan ndustry. These AES also show that nput pars, P&S captal and fuels energy, P&S captal and electrc power, fuels energy and electrc power, and fuels energy and materals are complements n the Allen sense. Only three studes (Martnello 1985; Nautyal and Sngh 1985; Sngh and Nautyal 1986) have provded results on substtuton relatonshps for the Canadan ndustry. The results dffer among the studes and from our results. For example, the substtuton elastcty between producton and materals n our study s 1.16 as compared wth 0.00 found by Martnello (1985) and 0.24 by Sngh and Nautyal 4 The determnants of prncpal mnors of matrx of Allen elastctes of substtuton are, 5.44, , , , , , and 0.00.

5 Nagubad and Zhang 3011 Table 1. Estmated coeffcents of translog cost functon for sawmll and wood preservaton ndustry n Canada, Coeffcent a Estmate P α ** < α Y ** < α t ** β P ** < β N ** β Q * β S ** < β F ** < β R ** γ PP ** < γ PN ** γ PQ ** < γ PS * γ PF ** < γ PR ** < γ NN ** γ NQ * γ NS ** γ NF ** < γ NR ** < γ QQ γ QS γ QF ** < γ QR γ SS ** γ SF γ SR ** < γ FF ** < γ FR ** < γ RR ** Note: **, *, and ndcate sgnfcance at 1%, 5%, and 10% levels, respectvely. a The subscrpts are as follows: P, producton ; N, nonproducton ; Q, machnery and equpment captal; S, plants and structures captal; F, fuels; R, electrc power; Y, output quantty; t, tme trend. Indrectly estmated coeffcents related to prce of materals (and ts nteracton terms wth other nput prces) are not presented here. (1986) for Canada. Interestngly, ths s smlar to the substtuton elastcty of 1.15 between producton and wood for the Unted States found by Abt and Ahn (2003). In the case of captal and, we estmate a substtuton elastcty of 4.11 between producton and M&E captal, and 2.21 between producton and P&S captal, dfferng from 0.23 by Martnello (1985) and 2.58 by Sngh and Nautyal (1986) between all and all captal. These estmates are consderably larger than the correspondng estmates of 0.10 and 0.19 between and captal for the US ndustry estmated by Ster (1980a, 1980b). For other countres, Baardsen (2000) estmates a substtuton elastcty of 0.73 between and captal n Norwegan sawmllng ndustry, and Campbell and Jennngs (1990) estmated a value of 0.33 for Tasmanan sawmllng ndustry. Morshma elastctes of substtuton The results of MES reported n Table 3 show that, n the Canadan ndustry, 32 of 36 nput pars are sgnfcant substtutes, whereas there s no evdence of any complementary relatonshp among nput pars n the Morshma sense. The MES, for example, σ M NP, s nterpreted as the percent change n the nonproducton to producton quantty rato when the relatve prce rato P P /P N s changed by changng P P and holdng P N constant. The most strkng feature s that, unlke the AES, the MES are not symmetrc, that M M s, σ σ. For example, a 1% rse n the wages of producton causes 1.815% ncrease n the rato of nonproducton to producton nputs, whle a 1% rse n the wages of nonproducton causes 1.382% ncrease n the rato of producton to nonproducton nputs. Ths mples that the substtuton of nonproducton for producton s easer than the substtuton of producton for nonproducton. Snce the MES are not symmetrc, there s a dfference between the substtuton of frst nput by second nput and the substtuton of the second nput by the frst nput. Lookng at the numbers n the frst row and frst column n Table 3, we note that σ M NP (1.815) > σ M PN (1.382), σ M M QP (2.092) > σ PQ (1.008), σ M SP (1.677) > σ M PS (0.721), and so on. These relatonshps mply that the substtuton of producton by other nputs s easer than the substtuton of other nputs by producton n the Morshma sense. Also from the relatonshps between MES n second row and MES n second column from the blank cell, t s evdent that the substtuton of nonproducton by other nputs s easer than the substtuton of all other nputs by nonproducton. Smlarly, for a 1% ncrease n the prce of P&S captal, the rato of M&E captal to P&S captal ncreases by 0.951%, whereas a 1% ncrease n the prce of M&E captal causes an ncrease of 1.479% n the P&S captal to M&E captal nput rato, mplyng easer substtuton of M&E captal by P&S captal than the substtuton of P&S captal by M&E captal. Among the two energy nputs, substtuton of fuels by electrc power s easer than the substtuton of electrc power by fuels energy. Judgng from the numbers n the last row and last column n Table 3, t s evdent that the substtuton of all other nputs by materals s easer than the substtuton of materals by all other nputs. Demand elastctes Own-prce elastctes of demand for producton, nonproducton, and electrc power exceed one ndcatng elastc demand for these nputs (Table 4). Own-prce elastctes of producton ( 1.19) and nonproducton ( 1.25) are hgher than prevous estmates of 0.24 (Martnello 1985), and 0.86 (Sngh and Nautyal 1986) for all. These own prce elastctes for both types of for Canadan ndustry are also hgher than Ster s (1980b) estmate of 0.35 for the Unted States, and Abt s (1987) average estmate of 0.32 for western, southern, and Appalachan regons of the Unted States. These estmates

6 3012 Can. J. For. Res. Vol. 36, 2006 Table 2. Allen own and cross partal elastctes of substtuton for sawmll and wood preservaton ndustry n Canada, Producton Nonproducton Machnery and equpment Plants and structures Fuels Electrc power Materals Producton 5.438** (0.24) Nonproducton 2.846** ** (0.63) (2.19) Machnery and equpment 4.110** ** (0.51) (1.30) (4.23) Plants and structures 2.215** 4.172** * (0.51) (1.40) (8.25) (17.17) Fuels 3.608** 8.658** 7.721** 4.348* ** (0.42) (1.44) (1.45) (1.74) (1.96) Electrc power 3.684** ** 6.265** ** ** (0.60) (2.06) (2.19) (3.73) (2.34) (4.84) Materals 1.162** 0.802** ** (0.10) (0.28) (0.40) (0.73) (0.21) (0.32) (0.05) Note: Elastctes were evaluated at the means of estmated cost shares. **, *, and ndcate sgnfcance at 1%, 5%, and 10% levels, respectvely. Values n parentheses are approxmate standard errors (Bnswanger 1974): SE (σ )=SE(γ )/S S. Table 3. Morshma elastctes of substtuton for sawmll and wood preservaton ndustry n Canada, Producton Nonproducton Machnery and equpment Plants and structures Fuels Electrc power Materals Producton 1.382** 1.008** 0.721* 0.715** 1.213** 1.031** (0.10) (0.17) (0.29) (0.03) (0.06) (0.07) Nonproducton 1.815** 0.890** 0.611* 0.792** 1.299** 0.797** (0.14) (0.18) (0.29) (0.04) (0.06) (0.18) Machnery and equpment 2.092** 1.163** 0.951** 0.542** 1.097** (0.12) (0.11) (0.33) (0.04) (0.06) (0.26) Plants and structures 1.677** 1.062** 1.479** 0.594** 1.163** (0.12) (0.12) (0.38) (0.04) (0.07) (0.47) Fuels 1.982** 1.646** 0.518** 0.608* 1.316** (0.10) (0.12) (0.18) (0.29) (0.06) (0.14) Electrc power 1.999** 1.754** 0.578** 0.672* 0.851** (0.14) (0.14) (0.20) (0.30) (0.05) (0.21) Materals 1.446** 1.289** 0.834** 0.678* 0.653** 1.169** (0.06) (0.10) (0.17) (0.29) (0.03) (0.06) Note: Elastctes were evaluated at the means of estmated cost shares. ** and * ndcate sgnfcance at 1%, and 5% levels, respectvely. Values n parentheses are approxmate standard errors (Frondel 1999): SE( σ ) = +. Var( γ Var 2Cov M ) ( γ ) ( γγ ) 2 2 S S S S are also hgher than 0.57 for Norwegan sawmllng ndustry found by Baardsen (2000) and 0.58 for Australan sawmllng ndustry (Bgsby 1994). The demand elastcty for M&E captal for Canada s 0.84, hgher than prevous estmates of 0.30 (Martnello 1985) and 0.24 (Sngh and Nautyal 1986) for the Canadan ndustry for all captal. The demand elastcty for M&E captal s hgher than the estmate of 0.66 for Norwegan sawmllng (Baardsen 2000) and 0.69 for Australan sawmllng (Bgsby 1994) for all captal. The demand elastcty for materals s 0.28 for the Canadan ndustry, whch s lower than Martnello s (1985) estmate of 0.37 and Sngh and Nautyal s (1986) estmate of 0.69 for materals n Canadan ndustry. The correspondng estmates reported for materals for Norway and Australa are 0.70 and 0.30, respectvely. The prce elastcty of demand for fuels n the Canadan ndustry s 0.66, whch s lower than the Norwegan ndustry estmate of 1.92 and hgher than Australan ndustry estmate of The prce elastcty of demand for electrc power for the Canadan ndustry s 1.17, whch s hgher than the correspondng estmates for Norwegan ( 0.70) and Australan ( 0.47) ndustres. Rate of techncal change and total factor productvty change Canada experenced a mean percent techncal change of 0.57%/year n the ndustry durng the perod of analyss.

7 Nagubad and Zhang 3013 Table 4. Own- and cross-prce elastctes of demand for sawmll and wood preservaton ndustry n Canada, % change n the quantty demanded of For a 1% change n the prce of Producton Nonproducton Machnery and equpment Plants and structures Fuels Electrc power Materals Producton 1.191** 0.130** 0.170** 0.038** 0.055** 0.043** 0.755** (0.05) (0.03) (0.02) (0.01) (0.01) (0.01) (0.06) Nonproducton 0.624** 1.252** ** 0.132** 0.128** 0.521** (0.14) (0.10) (0.05) (0.02) (0.02) (0.02) (0.18) Machnery and equpment 0.900** ** ** 0.073** (0.11) (0.17) (0.17) (0.14) (0.02) (0.03) (0.26) Plants and structures 0.485** 0.190** * 0.066* (0.11) (0.06) (0.34) (0.30) (0.03) (0.04) (0.47) Fuels 0.790** 0.394** 0.320** 0.075* 0.660** 0.146** (0.09) (0.07) (0.06) (0.03) (0.03) (0.03) (0.14) Electrc power 0.807** 0.502** 0.259** ** 1.170** (0.13) (0.09) (0.09) (0.06) (0.04) (0.06) (0.21) Materals 0.255** 0.037** * ** (0.02) (0.01) (0.02) (0.01) (0.003) (0.004) (0.03) Note: Elastctes were evaluated at the means of estmated cost shares. **, *, and ndcate sgnfcance at 1%, 5%, and 10% levels, respectvely. Values n parentheses are approxmate standard errors (Bnswanger 1974): SE(ε )=SE(γ ) / S. Ths s n contrast to prevous fndngs of negatve or zero rate of techncal change (Martnello 1985; Sngh and Nautyal 1986), but less than 2.35% estmated for softwood lumber ndustry by Bernsten (1994). From the results of the translog cost functon, usng the values from eq. 10, we estmate the total factor productvty growth of 0.54%/year for Canada. 5 Ths estmate s closer to the estmate of growth rate of 0.61%/year for Canada usng Törnqvst Thel ndex under growth accountng procedure (Zhang and Nagubad 2006). Our results dffer from 0.4%/year growth for the lumber ndustry for perod (Ghebremchael et al. 1990) and from 3.24%/year TFP growth estmated for Canadan softwood lumber ndustry (Bernsten 1994). Summary and conclusons In ths paper, we examne varous aspects of producton n the sawmll and wood-preservaton ndustry n Canada over the perod We use the translog cost functon approach wth seven nputs and output quantty as a sum of sx products. The cost functon for Canadan ndustry was homothetc, Hcks-neutral, and satsfed all condtons of an deal cost functon. Accordng to the estmated Allen elastctes of substtuton, sgnfcant substtuton possbltes exst between producton and M&E captal, producton, and materals n the Canadan ndustry. Sgnfcant substtuton possbltes also exst between both types of captal, between both types of energy, and between nonproducton and both types of energy n the Allen sense. Complementary relatonshps exst between captal and energy, between nonproducton and P&S captal, and between materals and fuels energy n the Allen sense. Thus, the Canadan ndustry s n a better poston n controllng producton costs n case of an nput prce hke by substtutng low cost nputs to hgh cost nputs. Morshma elastctes of substtuton ndcate that the substtuton of producton by other nputs s easer than the substtuton of other nputs by producton. Ths may ndcate rgdtes related to producton compared wth other nputs n the Canadan ndustry. Smlarly, substtuton of all other nputs by materals s easer than the substtuton of materals by all other nputs. Ths may suggest that effcency related to materals s a not a prorty compared wth effcency related to other nputs as Canada has relatvely abundant forest resources. Demand for all nputs except fuels energy and materals s elastc n the Canadan ndustry. Among the cross-prce elastctes of nputs n the Canadan ndustry, only prce of M&E captal nput has a postve elastc response on quantty demanded of P&S captal nput. The Canadan ndustry experenced a compound growth rate of 0.57%/year n techncal change and 0.54%/year n total factor productvty durng the study perod. Further studes are warranted for the sawmll and wood-preservaton ndustry n the Unted States and other maor wood products producng countres. Acknowledgements The authors gratefully acknowledge helpful comments from Henry Knnucan, Henry Thompson, Shash Kant, and two revewers and an assocate edtor of ths ournal on an earler draft. However, the authors are solely responsble for any remanng errors. 5 Rate of techncal change, cost elastcty of output, and rate of change n output for Canada are 0.57, 1.009, and 3.567, respectvely. The frst two statstcs are estmated from translog cost functon at mean levels of varables, and the last statstc s derved from sem-log equaton, ln Y = a + bt, where ln Y s natural logarthm of quantty of output, t s tme n years (1958 = 1), a, and b are parameters, and the rate of change n output s estmated as (e b 1)100.

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