Paper prepared for presentation at the American Agricultural Economics Association Meeting, Denver Colorado, August 1-4, 2004.

Transcription

1 1 Analyss of Producton Structure of the Canadan Pulp and Paper Industry: Paper, # Mchael Habteyonas Unversty of Alberta Department of Rural Economy Edmonton Canada Emal: mzh@ualberta.ca Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Meetng, Denver Colorado, August 1-4, Abstract A translog cost functon wth factor nputs of captal, labor, energy and materals was estmated for the Canadan pulp and paper ndustry over the perod of 1961 to The results show that, the producton technology can not be specfed by a Cobb-Douglas producton functon and t s not Hcks- neutral. It was found out that, the ndustry s characterzed by labor-savng and captal, energy and materals-usng techncal change. The estmated producton functon ndcated the exstence of economes of scale, although the sze of the scale s not as large as those estmated for the European Unon and the Unted States pulp and paper ndustres. Estmates for Allen s elastctes of substtuton show that, all the factor nputs were found to be hghly substtutable among each other. In addton, estmates for prce elastctes were found to be senstve to a change n ther own prce and relatvely speakng, the demand for captal was found to be more responsve to changes n prces of energy and materals and the demand for materals was also found to be senstve to changes n prce of labor and energy.

2 2 I. Introducton Estmaton of producton functons of frms or ndustres s one of the central research topcs n mcroeconomc theory. Economsts estmate producton functon for a varety of reasons. Some estmate t to measure techncal change and effcency. Others estmate producton functons for a specfc polcy analyss and so on. In the process of estmaton, choosng a functonal form s one of the mans tasks that should be handled at the begnnng. Accordng to Grffn et.al (1987), selectng a functonal form s a complcated task for a researcher due to the growng number of avalable functonal forms. The authors dentfed 20 dfferent functonal forms for estmatng a producton functon. Ths paper uses a famly of the translog cost functon usng data from the Canadan pulp and paper ndustry over the perod of 1961 to A lkelhood rato test s also appled to test a Cobb-Douglas specfcaton snce t s a restrcted verson of the translog cost functon. Producton analyss can be carred out usng dentfcaton of a producton functon, a cost functon or a proft functon. By dualty, each approach s n prncple equvalent to others. The above approaches use three dfferent methods to estmate producton functon and measure techncal change. These nclude: ndex numbers, lnear programmng or econometrc approach. Ths study uses the cost functon approach usng econometrc method to estmate a producton functon for the Canadan pulp and paper ndustry. Pulp and paper ndustry s not only Canada s largest manufacturng ndustry but also the naton s leadng manufacturer n terms of producton, employment and net exports. It s also a natonal ndustry n the sense that t s a geographcally dspersed ndustral

3 3 employer. The 162 mlls that comprsed the ndustry n 1994 were located n Quebec (67), Ontaro (34), Brtsh Colomba (28) and Atlantc and Prare Provnces (33) (Halu, 1998). As mentoned above, measurng techncal change s another reason for estmatng producton functons of ndustres. Broadly speakng, techncal change can be defned as the applcaton of new knowledge to the producton processes. Techncally, the rate of techncal change can be measured ether as an ncrease n output obtaned from the same quanttes of nputs, or equvalently, a decrease n nputs needed to produce a gven level of output (Ster and Bengston, 1992). One of the objectves of ths paper s to measure the rate and bas of techncal change for the Canadan pulp and paper Industry. In addton, factor substtuton, scale of economes and own and cross prce elastctes of factor nputs are estmated and dscussed. Ths beng the ntroducton, the rest of the paper s organzed as follows. Secton two revews the lterature on estmaton of producton functon usng a translog cost functon for pulp and paper ndustres across the world. A survey of four papers are presented n ths secton. The models used for estmaton and analyss of the results are outlned n secton three. The parent translog cost functon and the share equatons derved from t are descrbed n ths secton. In addton, formulas for the estmaton of Allen s partal elastcty of substtuton, scale of economes and, prce elastctes of factor nputs are presented. Secton four s devoted to estmaton and analyss of results. At last, conclusons and references are presented n the last sectons and the orgnal data set s attached as an appendx.

4 4 II. Lterature Revew A number of studes have been done on estmatng producton functons of pulp and paper ndustres n dfferent parts of the world. A more comprehensve revew of the lterature on ths subject wth a specal emphass on North Amerca s forest sector s gven by Ster and Bengston (1992). These authors have summarzed 24 studes over the perod of 1968 to Bref surveys of four papers for Canada, Untes States and the European Unon whch are more related to pulp and paper ndustry are presented below. Sherf (1983) estmated a long-run translog cost functon for the Canadan pulp and paper mlls usng annual data from 1956 to He specfed captal, labor, energy and wood as nputs of producton n hs analyss. Sherf found out that, nput pars wood-labor and captal-energy are complments, whle the other pars of nputs are substtutes. Further more, hs results show that, techncal change s estmated to be captal and energy usng and labor and wood savng. Smlar to Sherf s work, Martnello(1985) estmated factor substtuton, techncal change and returns to scale of three Canadan forest ndustres. These ndustres nclude: pulp and paper, sawmlls and shngle mlls, and loggng. Martnello employed a translog cost functon to estmate the producton technology usng annual data from 1963 to Each ndustry s output s specfed to be a functon of four varable nputs namely: captal, labor, energy and materals. Marnello (1985) found out that, the technology of the ndustres s non-homothetc and techncal change s nonneutral, captal usng and labor savng for all the ndustres.

5 5 Another related study s the paper by Ster (1985) for the Unted States pulp and paper ndustry. Ster employed a translog cost functon to nvestgate the mplcatons of factor substtuton, returns to scale and based technologcal progress for the aggregate pulp and paper ndustry. Ster used annual US data from 1948 to 1976 and dentfed three factors of producton: captal, labor and wood. Ster s results show that, the US pulp and paper ndustry s characterzed by labor-savng technologcal progress relatve to captal and wood. Ster (1985) reported that, a wood-savng bas suggests that, current projectons of future ncrease n the wood / pulp rato may lead to underestmates of future pulpwood requrements. The average annual rates of the bas were estmated to be 0.011, and for captal, labor and wood respectvely. Recently, Andrade (2000) estmated a producton technology for the pulp and paper ndustry n the European Unon. Andrade used a flexble ndustry cost functon wth three nputs (labor, captal and wood) usng annual panel data over the perod 1970 to Hs results show sgnfcant but small substtutablty between labor and both captal and wood, and complmentarty between captal and wood. Smlar to the above fndngs of the Canadan and US ndustres, Andrade found labor savng and captal usng technologcal change. The estmated average techncal bases are , 0.03 and for labor, captal and wood respectvely. In sum, all the above dscussed papers used an econometrc approach n the estmaton of producton functon and they choose the more flexble translog cost functon. They gve more emphass to the nature and extent of factor relatonshps as measured by the elastctes of factor substtuton, returns to scale and the extent and bas of techncal change. Ths paper wll adopt smlar approach n the analyss.

6 6 III. Models 1 The followng translog cost functon wth the assumpton of homothetc producton structure s used to estmate the Canadan pulp and paper ndustry: ln C( P, Y, T ) o + α y lny + α tt + β ln P β l ln P ln P j + = α δ T ln P (1) Where C s total cost calculated as the sum of quanttes of factor nputs multpled by ther respectve prces. Four nputs are consdered n ths study, namely captal, labor, energy and materals. Y s the aggregate ndustry output, P s a vector of factor prces, the th element of whch s P and T s a tme trend that serves as a proxy for techncal change. Some authors nclude the square of the tme trend and square of logarthm of output as addtonal explanatory varables. However, ths paper opted to deleted them snce they were found to be statstcally nsgnfcant n the prevous studes (Martnello 1985, Andrade 2002). The parameters of the cost functon are assumed to be constants. The followng restrctons must hold for the symmetry of cross partal dervatves and lnear homogenety n factor prces of the cost functon: β = β j j β = 1 β j = j j β = β j j = δ = 0 (2) 1 The models are bascally compled from the works of Ster (1985), Martnello (1985) and Andrade (2000).

7 7 Usng Shepherd s lemma, the cost mnmzng demand functons for the factors of producton, also known as factor share equatons, are obtaned by dfferentatng the translog cost functon wth respect to factor prces as follows: ln C ln P = P X C = S Ths wll gve us: S = β + β ln P + δ T (3) j j j Where S s the share of nput th cost n the total ndustry cost n whch S = 1 for = captal, labor, energy and materals. Ths s commonly called cost exhauston. Returns to scale are usually defned n terms of the relatve ncrease n output resultng from a proportonal ncrease n the quantty of all nputs. From the above specfed translog cost functon, the elastcty of total cost wth respect to output s calculated as: lnc φ = from ths, the returns to scale (SCE) can be derved as lny SCE = 1 φ (4) Ths measure s nterpreted as the postve values of SCE mply economes of scale where as the negatve values mply dseconomes of scale. Let us now turn to the ssue of measurng the degree of substtutablty between any par of factors. One of the most famous ones s the elastcty of substtuton ntroduced by Allen n Formally, the elastcty of substtuton measures the percentage change n factor proportons due to a change n margnal rate of techncal substtuton. Allen s elastctes of substtuton (also known as the partal elastcty of substtuton ) for the translog cost functon can be derved from the parameter estmates and estmated share of nputs as follows:

8 8 σ σ j β j = + 1, SS j β 1 = 1 S S j + 2 j (5) The own and cross prce elastctes of derved demand for factors are usually estmated for purposes of polcy analyss. Estmates of these elastctes, gven constant output and constant prces of all nputs, can be derved drectly from Allen s elastcty of substtuton n the followng manner: η = S σ (6) j j j The technologcal change bas s defned as the nfluence of technologcal progress on factor shares when factor prces and output are held constant. Accordng to Bnswanger(1974), ths bas s measured as: Β S = T * 1 S δ = S (7) where S * denote that relatve factor prces are held constant. If B s postve, technologcal change s sad to be factor -usng, f B s negatve, the process s sad to be factor -savng, and B = 0 mples Hcks neutral techncal change. To gan more effcency, the optmal procedure of the estmaton process s to consder both the parent cost functon gven n equaton (1) and the share equatons derved from t (equaton 3). These equatons are then estmated jontly as a multvarate system ncludng a random dsturbance term n each equaton. The random term s assumed to be a multvarate normally dstrbuted wth zero mean and constant covarance matrx. Accordng to Ster (1985), the random terms n these equatons are assumed to arse from errors n cost mnmzng behavor, and to be contemporaneously correlated. The later

9 9 assumpton s logcal snce overuse of any one nput would lkely mply under-use of one or more other nputs. The four factor share equatons gven n equaton (3) must sum to unty. Hence n performng the estmaton, t s necessary to drop one share equaton n order to avod the problem of a sngular covarance matrx. The share equaton for materals nput s deleted n ths paper and teratve Zellner procedure s performed on the remanng systems of equatons. The Zellner procedure s a computatonally effcent method of obtanng a maxmum lkelhood estmates whch satsfy the restrctons specfed n equaton (2) and t s nvarant to whch share equaton s deleted. Based on the above specfed models, basc data descrptons and the estmated results are dscussed n the next sectons. IV. Data and Descrptve Statstcs Data for the Canadan pulp and paper ndustry are obtaned from Statstcs Canada, Mcro-Economc Analyss Dvson 2. It conssts of annual observatons of pulp and paper gross output, quanttes and prces of factor nputs for the years 1961 to Captal, labor, energy and materals are the four nputs are consdered for analyss. All the data are expressed n Fsher s volume and prce ndces of gross output and nputs takng 1961 as the base perod. The dfferent types of nputs and outputs whch make up a sngle category of nput or output are not assumed to be perfect substtutes. Rather, they are aggregated up accordng to a technology whch s a second-order approxmaton to arbtrary constant returns to scale technology. The data set expressed n Fsher s ndces s attached as appendx 1. 2 I would lke to thank Grant Hauer (PhD),Department of Rural Economy, Unversty of Alberta, for allowng me to use hs data set.

10 10 Basc descrptve statstcs of the logarthms of prces of nputs, total cost and output, and cost share of each nput s gven n Table 1 below. On average, labor has relatvely hgher value than the others nputs. Energy has the hghest cost share among the other nputs. It s twce as large as captal s cost share. Labor and materals has almost the same cost shares, 24.4 and 26.8 percent respectvely. Table 1 Basc Descrptve Statstcs Varable Mean St. Dev. Mnmum Maxmum LnP K LnP L LnP E LnP M LnC LnY S K S L S E S M Note: LnP refers to logarthms of the prce of nput,, where = captal, labor, energy and materals. LnC and Ln Y refer to logarthms of total cost and output respectvely and S refers to cost share of nputs.

11 11 Average annual rate of change of the quanttes and prces of factor nputs over the study perod are reported n Table 2. Average rates of changes are obtaned by regressng logarthms of the varables on a tme trend. As t s shown n Table 2, a substantal rate of decrease n labor s observed over the study perod. In partcular, labor declned n the 1980s and 1990 s after ncreasng at a rate of 2.54 percent n the 1960 s and 0.51 percent n the 1970 s. 3 Labor and energy costs have ncreased almost three tmes as fast as the cost of captal. The rate of change n the prce of captal has been volatle snce the study perod. A sharp declne n the prce s observed n the early 90s. The declne n captal expendture n 1996 mrrored the rapd prce decrease for pulp and paper products, after the most prosperous year ever on record for pulp prces n 1995 (Statstcs Canada, webste). The cost of materals has shown a 5.6% annual rate of ncrease snce The rates of ncrease n the quanttes of captal, energy and materals are on average between 2.4 and 3.7 percent. Table 2 Average Annual Rate of Change of Factor Quanttes and Prces Rate of change n : Varable Quantty (%) Prce (%) Captal Labor Energy Materals These fgures are calculated from the data set.

12 12 V. Estmaton and Results 4 The estmated coeffcents wth standard errors of the translog cost functon are gven n Table 3 below. The results are based on estmaton of equaton (1) and (3) as a system. All parameters related to materals nput are derved from the restrctons gve n equaton (2). As t s shown n Table 3, all the coeffcents are found to be statstcally sgnfcant. The coeffcents of the logarthm of output (α y ) and factor prces (β ) are all postve, whch shows that, the cost functon s non-decreasng n factor prces and output. Further more, monotoncty of the cost functon s satsfed snce the predcted cost shares are postve at every pont of the data set. Ther average values are gven as 0.16, 0.24, 0.32 and 0.27 for captal, labor, energy and materals respectvely. A lkelhood rato test was employed to test whether the producton technology can be characterzed by a Cobb-Douglas producton functon (β j = 0 or all, j) and to test f the Hcks neutral technologcal change (δ = 0 for all ) would hold. Summary of the tests and the crtcal values from a χ 2 dstrbuton table are gven n Table 4 below. The results show that, nether the Cobb-Douglas specfcaton nor the test for Hcks neutral technology hold. The decson rule s that, the null hypothess of Cobb-Douglas specfcaton or Hcks-neutral techncal change s rejected f the computed value of the log-lkelhood rato s greater than the crtcal value. 4 The Shazam software s used to estmate the translog cost functon and the derved share equaton as a system usng SUR method.

13 13 Table 3 Estmated Coeffcents Parameter Estmate Parameter Estmate (Standard Error) (Standard Error) α o (0.318) α y (0.067) α T (0.002) β k (0.009) β L (0.003) β E (0.009) β M (0.005) δ K (0.000) δ L (0.000) δ E (0.000) Β kk (0.005) β KL (0.002) β KE (.005) β KM (0.003) β LL (0.013) β LE (0.009) β LM (0.016) β EE (0.018) β EM (0.012) β MM (0.024) δ M 0.002

14 14 (0.000) Note: All fgures are approxmated to three decmal places The cost functon s homogenous of degree α y = 0.78 n output. Ths measures the elastcty of total cost wth respect to output. It s nterpreted as an ncrease n total cost by 7.8 percent as a result of a 10 percent ncrease n aggregate output. The correspondng measure of scale economes (SCE) s gven as = Ths suggests the presence of scale economes, though small, n the Canadan pulp and paper ndustry. Ths measure s smaller than the US pulp and paper ndustry (SCE = 0.74) as estmated by Ster (1985) but closer to Sherf s (1983) estmate of the Canadan pulp and paper ndustry (SCE = 0.35) over the perod of 1956 to The presence of scale economes has mportant mplcatons for the structure of the ndustry. If unt cost declnes as output ncreases, large plants and frms may be necessary to capture producton effcences (Ster, 1985). Table 4 Lkelhood Rato Tests Test for: Computed Value* Crtcal Value Decson Cobb-Douglas specfcaton Hcks-neutral techncal change χ 2 10, 0.05 = C-D specf. rejected χ 2 3, 0.05 = 7.82 Hcks neutral rejected * These values are computed as L = -2(L r - L unr ), where L r and L unr are log-lkelhood values for the restrcted and unrestrcted functons respectvely. In addton to the above results, parameters of great nterest from estmaton of the producton functon nclude the nature and extent of factor relatonshps as measured by the elastctes of factor substtuton, return to scale, own and cross prce elastctes of

15 15 factor nputs and the extent and bas of techncal change. These measures and ssues related to them are dscussed n the subsequent paragraphs. Allen s partal elastctes of factor substtuton are reported n Table 5 below. These estmates are obtaned from the expresson n equaton (5) usng the parameter estmates and the predcted average factor shares over the study perod. As t was dscussed brefly on secton 3, Allen s elastcty of substtuton (σ j ) measures the response of the - th nput demand to a change n the j- th nput prce, holdng output Y constant (.e., movng along an so-quant) and other nput prces constant. Normally, Allen s elastcty of substtuton s symmetrc and negatve sem-defnte,.e. σ j = σ j and σ <0. Two nputs and j are sad to be substtutes f σ j > 0 and complements f σ j < 0. The results n Table 5 show that, all nputs were found to be substtutes. In contrast to the prevous studes by Sherf (1983) and Martnello (1985), a hgh degree of substtutablty s observed among the factor nputs. Hgher values of elastctes of substtuton mply that, one factor can easly be substtuted for the other. The elastcty of substtuton can also affect the growth rate of output when factors of producton are ncreasng at dfferent rates so that ther rato s changng. If both factors are ncreasng at the same rate, then the growth rate of output s ndependent of the elastcty of substtuton ( Perera, 2002). It s observed n Table 2 that, energy and materals were ncreasng almost at the same rate, whch mply that the growth rate of pulp and paper s ndependent of the elastcty of substtuton between these nputs, at least for the Canadan case.

16 16 Table 5 Allen s Elastctes of Substtuton ( σ j ) Input Captal Labor Energy Materals Captal Labor Energy Materals Note: All fgures are approxmated to three decmal places Own and cross prce elastctes of demand for the factor nputs are reported n Table 6 below. These estmates are derved from the expresson n equaton (6). The demand for captal and materals are more responsve to prce change followed by the demand for labor and energy. On average, the own prce elastcty of factor nputs suggest that, all the factors for the pulp and paper ndustry are prce senstve. Even though the magntude for the cross prce elastctes are almost the same for all nputs, the demand for captal seems more responsve to changes n prces of energy and materals and the demand for materals s also senstve to changes n prce of labor and energy. The estmated coeffcents of the tme trend n equaton (1) and (3) show that, technologcal change has been based. The measures of techncal change reported n Table 7 below show that, the Canadan pulp and paper ndustry s captal, energy and materals-usng and labor-savng. The fgures are estmated based on the expresson n equaton (7).

17 17 Table 6 Own and Cross Prce Elastctes (η j ) Input P K P L P E P M Captal Labor Energy Materals Total Cost Note: All fgures are approxmated to three decmal places. η j, refers to a percentage change n n put as a result of a percentage change n prce of nput j. Along the dagonal = j. The last row represents the estmated percentage change n total cost from a 1% ncrease n factor prces. It gves the predcted value of factor shares. Table 7 Measures of Techncal Change Captal Labor Energy Materals Consstent wth ths study, prevous studes on techncal change for the pulp and paper ndustres n the Unted States, European Unon and Canada, all show labor-savng and captal-usng techncal change. In contrast to ths study, Martnello (1985) found out that, techncal change s energy and materals-savng for the Canadan pulp and paper ndustry, though smlar to ths study, the fgures are almost close to zero. Sherf s (1983) results show that, techncal change s estmated to be captal and energy-usng and labor and wood savng. Almost smlar results to ths study. In sum, t s worth to note that, snce techncal advances occur n spurts, the use of a smple lnear tme trend to represent

18 18 the state of technology s a major lmtaton of ths and prevous studes. Ster and Bengston (1992) suggest that, alternatve measures, such as the power ratngs or throughput measures, mght better capture the characterstcs of a technology. VI. Conclusons A famly of the flexble translog cost functon wth captal, labor, energy and materals nputs was used to estmate a producton functon of the Canadan pulp and paper ndustry for the perod 1961 to The results show that, the producton technology can not be descrbed by the smple Cobb-Douglas functonal form and t s not Hcksneutral. Rather, t was found out that, the ndustry s characterzed by labor-savng techncal change and captal, energy and materals-usng technologcal process. These results are almost consstent wth the prevous studes on the Canadan pulp and paper ndustry. Further more, the estmated producton functon ndcated the exstence of economes of scale n the producton process, although the sze of the scale s not as large as those estmated for the European Unon and the Unted States. The elastctes of substtuton, as suggested by Allen were estmated for the study perod. The results show that, all the factor nputs were found to be hghly substtutable among each other. In addton, estmates for own and cross prce elastctes were obtaned by multplyng Allen s partal elastcty of substtuton wth the predcted share of cost for each nputs. All the factor nputs were found to be prce senstve to a change n ther own prce. In addton, relatvely the demand for captal was found to be more responsve to changes n prces of energy and materals and the demand for materals was also found to be senstve to changes n prce of labor and energy.

19 19 Estmatng a producton functon of an ndustry s not as smple task for a varety of reasons. For example, t has been observed that, comparsons among dfferent studes dd not yeld consstent results. One of the reasons could be the use of dfferent functonal forms. However, even studes who used the same functonal forms were observed to come up wth dfferent estmates of coeffcents and measures of techncal change and elastctes. To ncrease the possblty of obtanng meanngful and consstent results, at least from an econometrc approach, followng some strateges mght be useful. For nstance, n measurng techncal change, the state of technology mght not be captured only by a tme trend. Rather, t should ncorporate technologcal varables that accurately reflect both the productve capablty and the rate at whch t changes over tme. The other possble soluton could be ncluson of more relevant factor nputs and more detaled break-down of the nputs. These mght yeld more specfc and consstent results. However, avalablty of data, ncreasng the degrees of freedom once more nputs are consdered and multcollnearty among explanatory varables could also be potentals problems. Accordng to Ster and Bengston (1992), f the goal of the analyss s to forecast factor demand and cost mplcatons of techncal change, smulaton models may offer a more promsng alternatve.

20 20 VII. References Andrade, Isabel C (2000), Producton Technology n Pulp and Paper Industry n the European Unon: Factor Substtuton, Economes of Scale and Technologcal Change Journal of Forest Economcs, 6(1): Bnswanger, H.P (1974), The Measurement of Techncal Change Bases wth Many Factors of Producton. Amercan Economc Journal, 45(4): Grffn R. C, Montgomery J. M, Rster M.E (1987) Selectng Functonal Form n Producton Analyss Western J. of Agrcultural Economcs, 12(2): Halu, Atakelty G. (1998), Envronmentally Senstve Analyss of Economc Performance: Productvty and Effcency n the Canadan Pulp and Paper Industry, 1959 to PhD Thess, Department of Rural Economy Unversty of Alberta, Edmonton, Alberta, Canada. Martnello, Felce (1985), Factor Substtuton, Techncal Change, and Returns to Scale n Canadan Forest Industres Canadan J of Forest Resources, 15: Perera, Claudney M (2002), Varable Elastcty of Substtuton, Techncal Change and Economc Growth Forth-comng, Department of Economcs, North Carolna State Unversty, USA.

21 21 Sherf, F (1983), Derved Demand of Factors of Producton n the Pulp and Paper Industy Forest Products Journal, 33: Statstcs Canada (2003), Webste, Ster J.C and Bengston D.N (1992), Techncal Change n the North Amercan Forestry Sector: A Revew Forest Scence 38(1): Ster, Jeffery C (1985), Implcatons of Factor Substtuton, Economes of Scale, and Technologcal Change for the Cost of Producton n the Unted States Pulp and Paper Industry Forest Scence 31(4):