1833
A restricted Leontief profit function model of the
Canadian lumber and chip industry: potential
impacts of US countervail and Kyoto ratification
T. Williamson, G. Hauer, and M.K. Luckert
Abstract: Estimation of output supplies and factor demands with a range of functional forms provides a basis for bounding
possible supply responses to exogenous shocks. No prior study, to our knowledge, has used a generalized Leontief functional
form to estimate lumber and chip supply responses in Canada. The own price lumber supply elasticities estimated from the restricted Leontief profit functional form used in this study are lower than those presented in most other studies, while the lumber
supply response with respect to roundwood price change is somewhat higher than some studies. We simulate the impacts of
current US countervail processes on Canadian lumber supply. The simulated responses to duties might be considered to be conservative estimates, while the lumber supply responses to roundwood price increases could be on the high end of expected responses. Estimation of profit and supply functions indicates that rather than being a distinct production decision, chip supply
follows lumber supply. The supply responses of chips and lumber to the various combinations of duty, roundwood price increases, and energy price increases indicate a number of patterns. First, if Kyoto policies increase energy prices (up to 10%),
these changes are not likely to have a large impact on lumber and chip production. Second, British Columbia and Quebec tend
to have lumber and chip supplies that are more sensitive to duties and increased roundwood prices than Ontario. Third, Quebec
is more sensitive to roundwood price increases, while British Columbia is more sensitive to the effects of duties.
Résumé : L’estimation de l’offre d’extrants et de la demande de facteurs avec un ensemble d’équations fonctionnelles fournit
un cadre pour circonscrire les réponses possibles de l’offre face à des chocs exogènes. À notre connaissance, aucune étude
n’a eu recours à une équation fonctionnelle généralisée de Leontief pour estimer les mouvements de l’offre canadienne de
bois d’œuvre et de copeaux. Les élasticités de l’offre de bois d’œuvre par rapport aux prix, estimées à partir d’une équation
de profits de forme fonctionnelle restreinte de Leontief, sont plus basses que celles qui résultent de la plupart des autres études, alors que la réponse de l’offre de bois d’œuvre vis-à-vis de la variation du prix des grumes est un peu plus élevée que
ce qui figure dans ces autres études. Nous simulons également les impacts des droits compensatoires imposés par les autorités américaines sur l’offre de bois d’œuvre canadien. Les réponses aux droits compensatoires générées par la simulation peuvent
être considérées comme des estimations conservatrices, alors que les réponses de l’offre de bois d’œuvre à l’augmentation du
prix des grumes pourraient se situer dans la partie supérieure de la gamme de réponses attendues. L’estimation des fonctions
de profit et d’offre indique que l’offre de copeaux se moule à l’offre de bois d’œuvre plutôt que de relever de décisions distinctes quant à l’orientation de la production. Les réponses de l’offre de copeaux et de bois d’œuvre à différentes combinaisons d’augmentation des droits compensatoires, du prix des grumes et du prix de l’énergie présentent une variété de patron.
Premièrement, si les politiques découlant de l’application du protocole de Kyoto se traduisaient par un accroissement des
prix de l’énergie pouvant aller jusqu’à 10%, il serait peu probable que cela ait un gros impact sur la production de bois
d’œuvre et de copeaux. Deuxièmement, les courbes d’offre de bois d’œuvre et de copeaux de la Colombie-Britannique et du
Québec apparaissent plus sensibles aux variations des droits compensatoires et du prix des grumes que celles de l’Ontario.
Troisièmement, la situation au Québec présente plus de sensibilité à la hausse du prix des grumes, alors que celle qui prévaut
en Colombie-Britannique l’est plus quant aux droits compensatoires.
[Traduit par la Rédaction]
Williamson et al.
1844
Introduction
The Canadian lumber industry is currently facing a number of potentially serious issues. On 2 April 2001 the US
Coalition for Fair Lumber Imports filed countervailing duty
and anti-dumping petitions alleging that Canadian softwood
lumber was subsidized and was being sold to US customers
at below fair market value.2 The US Department of Commerce subsequently determined that Canadian lumber was
subsidized at a rate of 18.7% and a countervailing duty was
brought into effect on 22 May 2002. Also brought into effect
on 22 May was a dumping duty that the US Department of
Received 17 September 2003. Accepted 1 April 2004. Published on the NRC Research Press Web site at http://cjfr.nrc.ca on
15 September 2004.
T. Williamson.1 Canadian Forest Service, Northern Forestry Centre, Edmonton, AB T6H 3S5, Canada.
G. Hauer and M.K. Luckert. University of Alberta, Department of Rural Economy, Edmonton, AB T6G 2H1, Canada.
1
2
Corresponding author ([email protected]).
The information reported here was obtained from the softwood lumber web site maintained by the Department of Foreign Affairs
and International Trade (http://www.dfait-maeci.gc.ca/~eicb/softwood) accessed on 4 November, 2002.
Can. J. For. Res. 34: 1833–1844 (2004)
doi: 10.1139/X04-058
© 2004 NRC Canada
1834
Commerce determined to be 8.43%. The combined duty on
Canadian softwood lumber exported to the US from nonexcluded provinces (British Columbia, Ontario, and Quebec
are among the nonexcluded provinces) is about 27%.
Canada has appealed the US findings to the World Trade
Organization and has exercised its rights for a review of the
findings under the North American Free Trade Agreement.
Canada has also indicated that it is open to a negotiation
process to see if a long-term solution to the ongoing dispute
is possible. Since one of the main concerns of US producers
pertains to noncompetitive pricing for stumpage, it is possible that any negotiated solution to the trade dispute will ultimately involve changes in methods of pricing stumpage and
higher stumpage prices. Higher stumpage prices will in turn
increase roundwood prices faced by lumber producers.
Another possible source of change in the lumber and
chip industry is the ratification of the Kyoto protocol. Canadian commitments under the protocol require Canada to
reduce greenhouse gas emissions to 6% below 1990 levels
by the year 2012. The specific mechanisms and policies
that will be put into place to accomplish these objectives
are under discussion at this point in time. However, increased energy prices are an anticipated result (either because of increases in cost of producing energy products or
because of taxes on the consumption of energy products).
The lumber industry consumes both natural gas and electricity and could therefore be impacted by such changes in
energy prices.
The above situations create a number of possible future
scenarios of simultaneous changes in duties (which affect end
product price realized by producers), changes in roundwood
input prices, and changes in energy prices that could affect
output supply and input demand by the lumber industry. A
number of models have been developed to investigate potential impacts of these types of changes on the Canadian lumber
industry (e.g., Constantino and Haley 1988; Adams and
Haynes 1996; Bernard et al. 1997; Latta and Adams 2000;
Adams 2003). These studies have employed various functional forms including translog and quadratic functional forms
in a profit function systems framework. However, analysis
based on Leontief functional forms has not been undertaken.
Latta and Adams (2000) note “Numerous studies have shown
that findings can vary markedly with alternative forms. Estimates with other forms (e.g., generalized McFadden or generalized Leontief) would be particularly useful for assessing the
finding of elasticity trends in the present study …”.
This study has two objectives. The first is to estimate a
multi-output restricted Leontief profit function (Diewert
1971) and its related output supply and input demand functions for the Canadian lumber industry in British Columbia,
Ontario, and Quebec. The second objective is to use the estimated supply and demand functions to evaluate the potential effects of changes in prices of outputs and inputs on
lumber and chip supply and on demand for roundwood and
labour.
Theoretical considerations
Econometric estimation of output supply and factor demand functions for an industry generally depend on three
Can. J. For. Res. Vol. 34, 2004
considerations. First, model specification depends on the initial behavioral assumptions of firms in the industry (i.e., cost
minimization, revenue maximization, profit maximization).
Second specification depends on knowledge of the extent to
which an industry is characterized by multi-output technologies.
Third model specification requires determination of which
inputs vary and which inputs are fixed (Coelli et al. 1998;
Chambers 1988).
For the purpose of this analysis, we assume that firms in
the Canadian lumber industry make choices to maximize
profits. This assumption is adopted without explicit evidence
to support it. However, the assumption is consistent with recent studies of the Canadian lumber industry (Constantino
and Haley 1988; Adams and Haynes 1996; Bernard et al.
1997; Latta and Adams 2000).
With respect to output technologies, the Canadian lumber
industry produces both lumber and chips. The fact that the
industry is characterized by a multi-output technology where
tradeoffs can feasibly be made between the amounts of chips
and lumber that firms produce in response to changes in relative prices means that the constraint on the primal profit
maximization problem is a multi-output and multi-input transformation function that represents some unknown (and difficult to measure) production possibility set. Duality theory
provides a link between a firm’s multi-output production
possibility set and the firms profit, output supply, and input
demand functions (Fare and Primont 1995). This linkage
permits direct estimation of profit, output supply, and input
demand functions in industries characterized by multi-output
production technologies such as the Canadian lumber industry. The estimations in other studies in the Canadian forest
sector (e.g., Latta and Adams 2000; Constantino and Haley
1988; Bernard et al. 1997) also rely on similar applications
of duality theory to justify direct estimation of profit and
cost functions.
A final theoretical consideration affecting specification
concerns underlying assumptions regarding the speed of
adjustment of inputs. If all inputs are assumed to be variable, then they adjust instantaneously to price changes. Such
assumptions may be appropriate in the long run; however,
in the short run some inputs (such as capital) only partially
adjust to changes in price. Thus in the short run, firms vary
outputs and variable inputs in response to price changes,
but they are limited in their ability to vary quasi-fixed inputs such as capital stocks (Berndt 1991). Morrison (1988)
notes that estimations based on time series analysis should
not assume full adjustment to long-run equilibrium values of
quasi-fixed inputs such as capital stocks. Berndt (1991)
notes that in cases where some inputs are variable and others
are quasi-fixed, a restricted cost or profit function specification is required. The influence of quasi-fixed inputs on profits and output supply and factor demand is measured in
terms of a stock measure (as opposed to its price). Since the
models estimated in this paper are based on time series data,
a restricted profit function is specified. Profits, output supplies, and factor demands are modeled as functions of output
prices (lumber and chips), prices of variable inputs (roundwood, labour, energy) and capital stock. A time index acts as
a proxy for the state of technical knowledge at time t. The
estimations of Latta and Adams (2000), Constantino and
© 2004 NRC Canada
Williamson et al.
1835
Haley (1988), and Bernard et al. (1997) are based on restricted profit functions and they also include t as a time
trend variable in their specifications.
If the underlying assumptions for the profit maximization problem are satisfied, then the profit function, supply
functions, and factor demand functions possess certain
properties. In some cases these properties can be imposed by
restriction (e.g., symmetry is imposed in this analysis) or
they are automatically satisfied as a result of the particular
specification estimated (e.g., homogeneity properties of the
profit function and the supply and demand functions are
automatically satisfied with the specification used in this
analysis). In other cases, the properties are neither imposed
nor automatic (e.g., curvature properties of the profit function). In these latter cases, the estimation results can be
evaluated to determine if estimated profit functions and
supply and demand functions are well behaved relative to
theoretical expectations.
The indirect restricted profit function is defined as π(p,w,
K,t), where π is short-run profit, p is a vector of output
prices, w is a vector of input prices, K is capital stock, and t
is the state of technical knowledge (Jehle and Reny 1998).
The properties of a well-behaved indirect restricted profit
function are the following: (a) non-negativity; (b) nondecreasing in p; (c) nonincreasing in w; (d) convex and continuous in (p,w) (i.e., the Hessian matrix of second-order
partial derivatives of π(p,w,K,t) with respect to p and w is
positive semi-definite; (e) homogeneous of degree one in
(p,w); and (f) the Hotelling–McFadden lemma is satisfied
(Chambers 1988). This final property provides the basis for
determination of output supply and factor demands from the
profit function:
[1]
∂ π( p, w, K, t)
= Yi*( p, w, K, t) and
∂pi
∂ π( p, w, K, t)
= −X i*( p, w, K, t)
∂w i
where Yi* is the supply function for output i, and X *i is the
demand function for input i.
The required properties of the netput functions are the following: (a) output supply is nondecreasing in own price; (b) factor
demands are nonincreasing in own wage; (c) netputs are homo-
[2]
The economic model and estimation
method
Duality theory provides the basis for direct estimation of
an industry’s profit function and the related supply and factor
demand functions. Flexible functional forms are preferred because they do not impose a priori restrictions on (a) the expansion path (i.e., that allow for nonhomothetic technology),
(b) substitution elasticities, and (c) scale effects. Flexible
functional forms are second-order approximations of some
arbitrary twice-differentiable functional form (Berndt and
Wood 1975).
The flexible functional form selected for this analysis is
the generalized Leontief restricted profit function (Diewert
1971). The Leontief functional form has some limitations.
Although this functional form is flexible, the first-order
terms are linear. This implies underlying technologies with
low elasticities of substitution and relatively inflexible output transformation opportunities (Behrman et al. 1992). If
the true production possibility set characterizing an industry’s multi-output technology contains numerous combinations of inputs and outputs (implying easy substitution
between inputs and easy transformation between outputs),
then a Leontief profit function may underestimate price elasticities and substitution elasticities. As noted by Behrman et
al. (1992) “… we suspect that the GL (generalized Leontief)
variable profit function provides a poor regional approximation if the true technology allows fairly easy input substitution or output transformation”. However, although estimation
errors might occur if a Leontief form is used when the underlying technology is characterized by more flexible technologies, errors introduced by mismatching the translog and
quadratic functional form for profit function estimation from
the true underlying technology can lead to even more severe
errors. For example, Thompson and Langworthy (1989) note
that average deviations from actual price elasticities over a
range of underlying technologies are lower for generalized
Leontief functional forms than for quadratic and translog
specifications.
The fully specified system of equations for the Leontief
profit function model is as follows:
π( p,w,K,t) = (β11 × PL) + [2β12(PL × PC)1/2] + [2β13(PL × WR)1/2] + [2β14(PL × WL)1/2] + [2β15(PL × WE)1/2]
+
+
+
+
+
(β22 × PC) + [2β23(PC × WR)1/2] + [2β24(PC × WL)1/2] + [2β25(PC × WE)1/2] + (β33 × WR)
[2β34(WR × WL)1/2] + [2β35(WR × WE)1/2] + (β44 × WL) + [2β45(WL × WE)1/2] + (β55 × WE)
(α1 × PL × K) + (α2 × PC × K) + (α3 × WR × K) + (α4 × WL × K) + (α5 × WE × K)
(γ1 × PL × K1/2) + (γ2 × PC × K1/2) + (γ3 × WR × K1/2) + (γ4 × WL × K1/2) + (γ5 × WE × K1/2)
(φ1 × PL × T) + (φ 2 × PC × T) + (φ3 × WR × T) + (φ4 × WL × T) + (φ5 × WE × T)
+ (ψ1 × PL × T2) + (ψ2 × PC × T2) + (ψ3 × WR × T2) + (ψ4 × WL × T2) + (ψ5 × WE × T2)
1/ 2
[3]
geneous of degree 0 in (p,w); and (d) cross-price effects are
equivalent (i.e., symmetry) (Chambers 1988).
 PC 
QL = β11 + β12

 PL 
1/ 2
 WR 
+ β13

 PL 
1/ 2
 WL 
+ β14

 PL 
1/ 2
 WE 
+ β15

 PL 
+ α1K + γ1K1/ 2 + φ1T + ψ1T 2
© 2004 NRC Canada
1836
Can. J. For. Res. Vol. 34, 2004
1/ 2
1/ 2
[4]
 PL 
QC = β22 + β12

 PC 
 WR 
+ β23

 PC 
[5]
 PL 
–QR = β33 + β13

 WR 
[6]
 PL 
–QLAB = β44 + β14

 WL 
[7]
 PL 
–QE = β55 + β15

 WE 
1/ 2
1/ 2
1/ 2
1/ 2
 PC 
+ β24

 WL 
1/ 2
 PC 
+ β25

 WE 
1/ 2
 WE 
+ β25

 PC 
 WE 
+ β35

 WR 
1/ 2
 WR 
+ β34

 WL 
1/ 2
 WR 
+ β35

 WE 
where π (p,w,K,t) is short-run profit; β, α, φ, γ, and ψ are parameters to be estimated; PL is price of lumber; PC is price
of chips; WR is roundwood price; WL is labour price; WE is
energy price; K is capital stock; T is a time index3; QL is
quantity of lumber supplied; QC is chip quantity supplied;
QR is roundwood demanded; QLAB is labour demanded;
and QE is energy demand. The economic model is transformed to a statistical model by adding a disturbance term to
each equation in the equation system. Symmetry is imposed
by restrictions on coefficients across equations (e.g., βij = βji).
Morrison (1988) and Behrman et al. (1992) suggest that
there are numerous ways that the quasi-fixed input(s) (in this
case capital), and time can be incorporated within the equation system. For this analysis, capital is incorporated linearly
and as a square root. Time is incorporated linearly and quadratically for British Columbia and Quebec and linearly and
as a square root for Ontario.
Latta and Adams (2000) and Constantino and Haley (1988)
note the need to account for endogenous right-hand side
variables in profit function estimation of the lumber industry. In particular, output prices and roundwood prices are
jointly determined with output and factor input decisions.
Endogenous right-hand side variables are correlated with the
error term, and therefore the coefficient estimates on variables that include lumber price, chip price, and roundwood
price will be biased. In response to this problem an instrumental variable approach similar to that used by Latta and
Adams (2000) is adopted. The endogenous variables are regressed on exogenous and lagged endogenous variables, and
these regressions are used to generate predicted values for
right-hand side endogenous variables (lumber prices, chip
prices, and roundwood prices). The predicted values then
serve the purpose of instrument variables in the estimation of
eqs. 2–7. Instrument variables in this case are correlated to
the endogenous variable but uncorrelated with the error
terms.
A two-step process was used for estimation using SHAZAM
(V.8.0). In the first step, coefficients were estimated using
the system command. This is a linear estimation method
+ α 2K + γ 2K1/ 2 + φ 2T + ψ 2T 2
1/ 2
 WL 
+ β34

 WR 
 PC 
+ β23

 WR 
1/ 2
1/ 2
1/ 2
 WL 
+ β24

 PC 
+ α 3K + γ 3K1/ 2 + φ 3T + ψ 3T 2
1/ 2
 WE 
+ β45

 WL 
+ α 4K + γ 4K1/ 2 + φ 4T + ψ 4T 2
1/ 2
 WL 
+ β45

 WE 
+ α 5K + γ 5K1/ 2 + φ 5T + ψ 5T 2
based on seemingly unrelated regression. In the second step,
the estimated coefficients from the systems estimation were
used as starting values for estimation of the model using
nonlinear estimation.4
Marshallian price elasticities are derived from the output
supply and factor demand equations. For the generalized
Leontief profit function, the own and cross-price
Marshallian elasticities are derived from the following equations:
4
−1 / 2∑ βij ( p j / pi)1/ 2
[8]
εii =
j =1
j ≠i
,
Qi
i = 1...5
and
[9]
εij =
(1 / 2)βij ( p j / pi)1/ 2
Qi
,
i, j = 1...5 but i ≠ j
Data
The study employs annual data on short-run variable profits, prices, and quantities for outputs and inputs for the period 1963–1999 (37 observations) for the provinces of
British Columbia and Ontario. Significant outliers in the
1999 data for Quebec resulted in rejecting that year from the
sample. The Quebec data covers the period 1963–1998. The
Canadian lumber industry is defined as the sawmill and
planing mill industry.5 The majority of data used was obtained from various Statistics Canada sources including
(a) hard copy sources of Stat Can documents such as “Sawmills and Planing mills” and Wood Industries for early
years, (b) data downloads from CANSIM, and (c) data purchased by special request for recent year principal statistics
and capital stock measures for all years. Some data were
also obtained directly from the B.C. Ministry of Forests and
from the National Forestry Database Program. In some cases
data are unavailable for one or two years in the time series.
3
For the Ontario estimation, T2 is replaced by T1/2 for eqs. 2–7.
Estimation using the nonlinear command in SHAZAM provides greater flexibility relative to addressing issues related to autocorrelation.
Nonlinear estimation with SHAZAM also provides a way of calculating variances and significance levels for elasticities using test commands (which in some cases are functions of multiple coefficients and prices).
5
SIC 2512 under the old classification system and SIC 321111 under the new harmonized North American Industry Classification System.
4
© 2004 NRC Canada
Williamson et al.
When this occurred, values were inserted by linear interpolation between periods or by deriving relationships with other
variables and imputing missing values. Additional information on data sources, data gaps, and methods used to address
gaps in published data are provided in Appendix A.
Short run profits are derived by subtracting expenditures
on all variable inputs from the total value of shipments.
Quantity of roundwood inputs is estimated by applying region and time specific lumber recovery factors to lumber
production data. Quantity of lumber, chips, and labour is obtained directly from published sources. Quantity of energy is
obtained by dividing total energy expenditures by a representative energy price. Labour is defined as total person
hours by wage earning employees. With the exception of
Ontario, lumber and chip prices are obtained by dividing the
value of shipments by quantity of shipments. Chip price data
for Ontario were purchased from Wood Resources International.6 Roundwood price is obtained by dividing value of
shipments in the logging industry by total industrial roundwood produced. Labour price is obtained by dividing total
wage expenditures by person hours. Representative energy
prices are based on cost per kilowatt hour (1kWh = 3.6 MJ)
for purchased electricity in each province in each year. Capital stock is defined as net capital stock. This measure is derived by Statistics Canada for Wood Industries (NAICS
3200) using the perpetual inventory method. Net capital
stock is numerically equivalent to the resale (as opposed to
replacement) value of existing building, machinery, and
equipment. Capital stock for the sawmill and planing mill
industry is obtained by determining the proportion of total
value added in wood industries accounted for by sawmill
and planing mills and then multiplying this ratio by net capital stock in wood industries.
Estimation results
The estimation results, including coefficient estimates and
t ratio values, are provided in Table 1. Autocorrelation (using Durbin Watson tests) was detected in the residuals in
each province in initial estimations. A nonlinear estimation
procedure was used to introduce first-order autocorrelation
into the model and then to estimate the autocorrelation coefficients (ρ) for each province. Autocorrelation coefficient estimates are shown at the end of Table 1. Continuing problems
with the British Columbia residuals were indicated. Subsequently a model with third-order autocorrelation corrections
was estimated for British Columbia. For all provinces, ρ values are below 1 as they should be.
As mentioned, well-behaved and theoretically consistent
profit, supply and factor demand functions should satisfy
certain properties. First, as expected, the estimated profit
function models predict positive profits in 97% of years in
British Columbia, in 100% of years in the sample in Ontario, and in 100% of years in Quebec. Furthermore, the estimated profit functions for the three provinces are nondecreasing
in own price and nonincreasing in factor wages for all observations. The Leontief profit function is homogeneous of
degree 1 by construction. The homogeneity of degree 0 property for output supply and factor demands derived from
6
1837
Leontief profit functions are also automatically satisfied
(i.e., the first derivative of any function that is homogenous
of degree n is homogeneous of degree n – 1). Symmetry is
imposed through restrictions on the coefficients.
An additional property is convexity. Well-behaved profit
functions are convex. Convexity of the profit function occurs
when all own price effects for outputs are positive, own
price effects of inputs are negative, and all inputs are substitutes (i.e., cross-price elasticities are positive) (Lopez 1984;
Morrison 1988). It should be noted that substitutability of input pairs is sufficient for convexity but not necessary. That is
to say, if all inputs are substitutes, and if the own price effects are correct, the profit function is convex. However, it is
also possible for some input pairs to be complements and
that the profit function could still be convex. The own price
effects from this study have the expected signs for all outputs and inputs in all provinces, with the exception of the
own price effect for chips in Ontario. The own price coefficient for Ontario chips is negative but insignificant. In the
British Columbia estimation, roundwood and labour and
roundwood and energy are complements. These findings are
consistent with Constantino and Haley (1988), who found
that sawlogs and labour were complements for British Columbia, and with Latta and Adams (2000), who found that
roundwood and labour were complements in the British Columbia coast and eastern Canada. The same sets of complementary relationships occur in the Ontario and Quebec
estimations. The presence of complementary relationships
for these estimations may be due to the fact that capital is a
quasi-fixed input. This may in turn influence substitution relationships between other inputs in the short run.
To further evaluate the curvature property of the estimated
profit functions, the Hessian matrix of second partial derivatives of the profit function was tested at the mean values of
the variables. Convexity requires that this matrix be positive
semi-definite. Convexity is not satisfied for the British Columbia, Ontario, or Quebec estimations. Some possible causes
of failure to satisfy curvature properties include; (a) profit
maximization is an incorrect behavioral assumption, (b) the
technology for the industry is characterized by increasing returns to scale, (c) input markets are not competitive, (d) the
data are wrong, and (or) (e) the model is mis-specified. Failure to satisfy convexity may also be the result of the nature
of the technological relationships between inputs for
short-run restricted profit functions in the lumber industry
(i.e., the fact that some inputs appear to be complements).
Failure to satisfy the convexity property is a common result in profit function studies (Bernard et al. 1997). Diewert
and Wales (1987, p. 43) note “One of the most vexing problems applied economists have encountered in estimating
flexible functional forms in the production or consumer context is that the theoretical curvature conditions (concavity,
convexity, or quasiconvexity) that are implied by economic
theory are frequently not satisfied by the estimated cost,
profit, or indirect utility function”.
For some flexible functional forms, it is possible to impose convexity without losing flexibility or imposing undue
restrictions on the nature of the technological relationships.
The reason for using a different source for chip prices in Ontario is that when the Statistics Canada data were used to estimate chip prices,
the results indicated an own price elasticity of around –0.6. This violates the property of positive own price elasticity for output supply.
© 2004 NRC Canada
1838
Can. J. For. Res. Vol. 34, 2004
Table 1. Coefficient estimates for Leontief profit functions for British Columbia, Ontario, and Quebec.
British Columbia
Parameter
Variable
Eq.
β11
β11
β12
β12
β12
β13
β13
β13
β14
β14
β14
β15
β15
β15
β22
β22
β23
β23
β23
β24
β24
β24
β25
β25
β25
β33
β33
β34
β34
β34
β35
β35
β35
β44
β44
β45
β45
β45
β55
β55
α 16
α 16
α 26
α 26
α 36
α 36
a46
α 46
α 56
α 56
φ17
PL
2
3
2
3
4
2
3
5
2
3
6
2
3
7
2
4
2
4
5
2
4
6
2
4
7
2
5
2
5
6
2
5
7
2
6
2
6
7
2
7
2
3
2
4
2
5
2
6
2
7
2
PL × PC
PC/PL
PL/PC
PL × WR
WR/PL
PL/WR
PL × WL
WL/PL
PL/WL
PL × WE
WE/PL
PL/WE
PC
PC × WR
WR/PC
PC/WR
PC × WL
WL/PC
PC/WL
PC × WE
WE/PC
PC/WE
WR
WR × WL
WL/WR
WR/WL
WR × WE
WE/WR
WR/WE
WL
WL × WE
WE/WL
WL/WE
WE
PL × K
K
PC × K
K
WR × K
K
WL × K
K
WE × K
K
PL × T
Estimated
coefficient
145 210
Ontario
t ratio
92.1*
Estimated
coefficient
14 140
482.44
Quebec
t ratio
2.36*
Estimated
coefficient
5 070
1.12
7 119
7.6*
–2.03*
–10 251
–7.0*
t ratio
2.2*
6 114
8.7*
–43 476
–43.8*
–2 723.2
–22 020
–41.7*
–812.8
–1.55
–17 536
–13.6*
–4 965
–7.8*
–268.97
–0.55
–5 010
–4.7*
43 962
37.4*
–958.71
–0.22
2 431
–16 463
–7.2*
838.4
0.85
–5 066
–3.4*
–12 384
–17.7*
–1 697.6
–1.48
–13 674
–6.9*
–8 191
–9.3*
–399.5
–0.66
–94
–5.3*
–157 100
–89.1*
–5 379.2
27 640
18.2*
317.2
12 860
8.0*
1 955.4
–62 872
–137.4*
1 894.3
1 750
–0.88
36 578
–0.4
1
–2 883
–1.1
0.14
5 935
2.5*
1.76**
2 988
2.0*
–0.07
70 141
38.0*
–10 912
–3.21*
23 047
5.1*
28.7*
41 769
0.98
14 988
2.6*
58 402
43.8*
50 638
2.23*
–2 140
21 718
33.2*
15 797
1.1
–118 550
–38.1*
–58 131
–1.03
–44 311
–16.6*
–74 717
–60.1*
–114 960
–1.34
–64 748
–17.5*
–0.08
–104 170
–1.62
–50 518
–6.6*
–47.8
1 236.8
5.6*
6.03
0.05
–0.5
7 546
1.8**
12.55
0.1
© 2004 NRC Canada
Williamson et al.
1839
Table 1 (concluded).
British Columbia
Parameter
φ17
φ27
φ27
φ37
φ37
φ47
φ47
φ57
φ57
γ1
γ1
γ2
γ2
γ3
γ3
γ4
γ4
γ5
γ5
ψ1
ψ1
ψ2
ψ2
ψ3
ψ3
ψ4
ψ4
ψ5
ψ5
Variable
T
PC × T
T
WR × T
T
WL × T
T
WE × T
T
PL × K
K
PC × K
K
WR × K
K
WL × K
K
WE × K
K
PL × T
T
PC × T
T
WR × T
T
WL × T
T
WE × T
T
Autocorrelation parameters
ρ11
ρ12
ρ13
ρ14
ρ15
ρ16
ρ 21
ρ 22
ρ 23
ρ 24
ρ 25
ρ 26
ρ 31
ρ 32
ρ 33
ρ 34
ρ 35
ρ 36
Eq.
3
2
4
2
5
2
6
2
7
2
3
2
4
2
5
2
6
2
7
2
3
2
4
2
5
2
6
2
7
Estimated
coefficient
Ontario
Quebec
t ratio
Estimated
coefficient
t ratio
Estimated
coefficient
t ratio
1.3
–159.8
–1.62
428.2
3.9*
–2 430.6
–5.6*
254.7
0.7
–1 110.9
–9.3*
964.7
2.4*
820.1
1.35
–3 747
–14.9*
–652.6
–2.5*
1 543.1
1.1
–2 727
–6.7*
7 106
1.2
206.6
–155 430
–292.7*
–54 252
–2.15*
–47 436
–52.8*
–15 303
–0.97
–13 285
314 050
546.4*
58 250
0.92
67 739
129 590
153.2*
109 040
1.18
87 798
–27 405
–28.1*
95 706
1.35
66 590
–1.89**
14.4*
14.0*
5.9*
–22.4
–5.1*
1 225.3
1.2
10.54
–5.4
–1.7**
2 070
2.37*
–0.82
45.5
5.2*
–4 578.3
–1.42
7.56
2.8*
1.4
0.2
–7 809
–1.38
58.79
9.8*
9.93
1.7**
–18 276
–1.22
45.19
5.1*
0.34
0.21
0.21
0.19
0.42
0.59
–0.041
–0.086
–0.325
0.154
–0.191
–0.129
–0.042
–0.997
0.241
0.021
0.094
–0.194
3.0*
1.8**
2.3*
1.8**
4.2*
5.7*
–0.4
–0.8
–3.6*
1.7**
–1.7**
–1.2
–0.4
–1.1
2.5*
0.28
1
–1.98*
0.23
0.55
0.6
0.65
0.64
0.86
1.37
5.14*
4.61*
7.38*
3.42*
27.14*
0.74
0.23
0.23
0.003
0.12
0.63
4.2*
–0.3
6.3*
1.88**
2.2*
0.03
1.2
7.3*
Note: Coefficients are associated with more than one variable and appear in a number of equations. Equation 2 is the profit function, while eqs. 3–7
are equations, respectively, for lumber, chips, roundwood, labour, and energy (see eqs. 2–7 above). t ratios are asymptotic.*, coefficient is significant at
the 5% level; **, coefficient is significant at the 10% level.
© 2004 NRC Canada
1840
Bernard et al. (1997), for example, impose convexity on a
normalized quadratic profit function using a reparameterization
technique developed by Wiley et al. (1973). For Leontief
profit function estimations, however, imposing convexity is
both more complex and more restrictive. Morrison (1988)
and Diewert and Wales (1987) note that convexity can be
imposed by restricting own output price effects to be positive, own input demand price effects to be negative, and the
input pairs to be substitutes (this latter restriction is accomplished by forcing all βij (i ≠ j) to be equal to or greater than
zero). However, this is overly restrictive, because in reality
some input pairs may be complements (Diewert and Wales
1987).
Another complication relative to imposing convexity in a
Leontief profit function model is that the second derivatives
of the profit function are functions of both estimated parameters and variables. Imposing global convexity is difficult in
this circumstance because it would require the convexity
constraint to be satisfied over a range of values for each
variable. In contrast, quadratic profit function second derivatives are functions of the parameters only, and thus convexity can be imposed by applying constraints to functions of
the parameters only (Wiley et al. 1973). Therefore, convexity can be imposed globally in a relatively straightforward
manner.
One option is to isolate possible factors that contribute to
the nonconvexity result. One possible reason is that firms are
not profit maximizers. However, failure to maximize profits
is not the only factor that could result in nonconvexity.
Squires (1987, p. 566) states “A test of convexity cannot be
interpreted as strictly a test of profit maximization because
convexity can be violated for a number of reasons”. For example, a contributing factor could be a general lack of a
competitive market for roundwood and the accompanying
institutional constraints on roundwood supply. Another possible contributing factor could be distortion caused by frequent disruptions of free trade caused by series of
countervailing duty investigations and rulings that have occurred since the early 1980s. It would be possible to model
these factors as a strategy to develop models that satisfy convexity. However, this is beyond the scope of the present
study.
For the purposes of this study, convexity is not imposed
on the Leontief profit function model. We recognize that the
model fails to satisfy an important property of profit functions and that, as a result of this limitation, the results of this
study should be viewed and interpreted with this in mind.
However, in general the results pertaining to output price
and input demand elasticities are consistent with theory, and
the results showing complementarity between input pairs are
consistent with previous research. Other studies (Squires
1987; Lopez 1984; Constantino and Haley 1988) with similar results regarding nonconvexity have adopted a similar approach.
The final property of well-behaved supply and factor demand functions is that own price effects are positive with respect to outputs and negative with respect to factor demands.
Table 2 provides the estimated own and cross-price
Marshallian elasticities for the three provinces. The own price
elasticities for lumber and chips are positive for each prov-
Can. J. For. Res. Vol. 34, 2004
ince with the exception of the own price elasticity of chips
in Ontario. The cross-price elasticities between outputs are
also positive, suggesting that lumber and chips are complements in production. The Marshallian elasticities provided in
Table 2 show that lumber supply is inelastic with respect to
own price in all regions but relatively more inelastic in Ontario and Quebec compared with British Columbia. This
suggests that output supply responses to US import duties
will be stronger in British Columbia than in eastern Canada.
The elasticity of lumber supply with respect to energy prices
has the expected sign in all three provinces, but the value is
very low. It may also be of interest to understand how
changes in output prices and input wages affect labour markets. The elasticity of labour demand with respect to lumber
price is higher in Quebec than in British Columbia and Ontario. For example, a 10% decrease in lumber price reduces
labour demand by 6.4% in British Columbia and by 13.4%
in Quebec. Alternatively, a 10% increase in roundwood
price decreases labour demand by 4.9% in British Columbia
and by 2.5% in Quebec.
Of the three provinces modeled, Ontario has the weakest
results. For example, the majority of the derived elasticies
shown in Table 2 for Ontario are insignificant. In addition,
the signs on some elasticities are contrary to theory (e.g.,
negative own price elasticity for chips) and the values of the
elasticities for Ontario are, in general, quite low compared
with estimates for British Columbia and Quebec. These results suggest that the Ontario results should be interpreted
with some degree of caution. At the same time, the Ontario
estimations do reveal some limited information that may be
of interest. For example, the own price elasticity for lumber
is statistically significant in the Ontario model. Moreover,
supply response to price changes is relatively more inelastic
in Ontario compared with British Columbia and Quebec. Inelastic lumber supply often occurs when timber supply become inelastic because of increasing scarcity. Another
possible reason for price inelastic lumber supply in Ontario
is a high reliance on public timber and a general insensitivity
in public timber sales to market prices (Catimel et al. 1997).
Another interesting result is that the demand for labour by
the lumber industry is relatively more elastic in Ontario
compared with British Columbia. This may be a reflection
of differences in the roles of labour unions in British Columbia compared with Ontario.
The results in this study can be roughly compared with
the estimation results from other studies. Latta and Adams
(2000) for example estimate output supply and input demands for the British Columbia coast, interior region (British Columbia interior and Alberta), and the eastern region
(rest of Canada) using a normalized restricted quadratic
specification. Constantino and Haley (1988) estimate supply
and input demand functions for the British Columbia coast
using a restricted translog profit function specification. Generally, estimation results are sensitive to functional form selected (Lim and Shumway 1999). This is because even with
flexible functional forms (such as translog, quadratic and
Leontief functional forms) selecting a particular form implies certain characteristics relative to the underlying transformation functions and (or) product transformation sets.
The underlying transformation functions may not, however,
© 2004 NRC Canada
Williamson et al.
1841
Table 2. Estimated Marshallian elasticities for the British Columbia, Ontario, and Quebec
lumber industries.
Ontario
Quebec
Lumber supply
PL
0.586* (0.016)
PC
0.074* (0.008)
WR
–0.507* (0.012)
WL
–0.139* (0.003)
WE
–0.014* (0.002)
British Columbia
0.243* (0.110)
0.058 (0.052)
–0.224* (0.110)
–0.071 (0.046)
–0.006 (0.012)
0.366*
0.331*
–0.351*
–0.293*
–0.052*
Chip supply
PL
PC
WR
WL
WE
0.165
–0.148
0.166
–0.160
–0.023
1.182* (0.156)
0.118 (0.190)
–0.474* (0.138)
–0.624* (0.091)
–0.201* (0.038)
0.625* (0.072)
0.954* (0.097)
–1.03* (0.143)
–0.420* (0.024)
–0.127* (0.014)
Roundwood demand
PL
0.715*
PC
0.172*
WR
–0.703*
WL
–0.151*
WE
–0.032*
(0.016)
(0.024)
(0.011)
(0.008)
(0.004)
(0.147)
(0.178)
(0.196)
(0.108)
(0.035)
(0.081)
(0.044)
(0.050)
(0.022)
(0.011)
0.272* (0.134)
–0.071 (0.084)
–0.159 (0.163)
–0.009 (0.062)
–0.033** (0.019)
0.518*
0.196*
–0.606*
–0.082*
–0.026*
(0.074)
(0.057)
(0.065)
(0.033)
(0.013)
Labour demand
PL
0.640* (0.015)
PC
0.229* (0.013)
WR
–0.492* (0.027)
WL
–0.384* (0.022)
WE
0.008 (0.009)
0.268 (0.173)
0.213 (0.144)
–0.027 (0.194)
–0.727* (0.294)
0.273* (0.085)
1.336*
0.794*
–0.254*
–1.573*
–0.299*
(0.098)
(0.115)
(0.102)
(0.034)
(0.058)
Energy demand
PL
0.549* (0.070)
PC
0.576* (0.062)
WR
–0.872* (0.108)
WL
0.064 (0.073)
WE
–0.318* (0.035)
0.137 (0.249)
0.173 (0.261)
–0.574** (0.325)
1.52* (0.476)
–1.26* (0.314)
1.271* (0.267)
1.375* (0.259)
–0.43* (0.209)
–1.608* (0.312)
–0.611* (0.176)
Note: Elasticities evaluated at mean values of the price variables. The values in the parentheses are
standard errors. The asymptotic normal statistic is equal to the estimate divided by the SE. Values between 1.645 and 1.96 are significant at 10%. Values greater than 1.96 are significant at 5%. *, elasticity
estimate is significant at the 5% level; **, elasticity estimate is significant at the 10% level.
be known. Thus, unless there is a priori knowledge about the
nature of the industries technology in terms of substitution
and (or) complement relationships between inputs and (or)
outputs, there is little basis for preferring one functional
form to another. Therefore, rather than relying on a single
estimate of output supply and input demand functions, it is
preferable to understand the possible range of output supply
and input demand responses to price change.
Table 3 shows the Marshallian elasticities derived using a
normalized quadratic specification (Latta and Adams 2000)
and a translog specification (Constantino and Haley 1988).
Direct comparison of the Leontief profit function estimation
results to previous studies is difficult, because the model
specifications and the regions on which the estimations are
based vary. For example, in addition to using a different
functional form and being based on different regional aggregations, the Latta and Adams (2000) study (a) aggregates
forest product outputs into a single category and (b) considers only wood and labour as inputs. Likewise, contrary to
this study, Constantino and Haley (1988) estimate a specification that considers how wood quality affects supply and
demand. Although, direct comparisons between studies may
not be appropriate, a general comparison of the results provides a basis for either confirming the results and findings of
the various studies and (or) identifying where some variation
is indicated. Comparing Table 2 with Table 3 shows that the
results obtained in previous studies are generally consistent
with the results presented in this study. With respect to price
elasticity of lumber supply, Constantino and Haley (1988)
find that lumber supply is slightly price elastic with their
translog specification. However, Latta and Adams (2000)
find that lumber supply is price inelastic in all three of their
studied regions. Moreover, Latta and Adams (2000) find that
lumber supply is relatively more inelastic in eastern compared with western Canada — a result that is consistent with
the current study. As explained by Adams (2003), “…
reestimation (of supply elasticities) over the past decade has
yielded lower and declining values”. The Leontief estimated
© 2004 NRC Canada
1842
Can. J. For. Res. Vol. 34, 2004
Table 3. Marshallian elasticities determined in previous research.
Elasticity type
British Columbia coast
Interior
East
L and A (2000)
(L and A (2000))
(L and A (2000))
C and H (1988)
Lumber or forest product supply
Lumber price
0.84
Chip price
Wood input price
–0.46
Labour price
–0.11
1.11
0.22
–0.93
–0.39
0.38
0.65
–0.13
–0.06
–0.24
–0.09
Roundwood demand
Roundwood
–0.55
–1.43
–0.12
–0.42
Labour demand
Labour price
–0.74
–0.58
–0.05
–0.80
Note: L and A is Latta and Adams (2000), C and H is Constantino and Haley (1988).
Table 4. Summary of supply responses to the six scenarios.
Scenario description
Scenario
Duty (%)
1
2
3
4
5
6
27
27
27
% change from base line
British Columbia
Ontario
Quebec
Roundwood price
increase (%)
Energy price
increase (%)
Lumber
Chips
Lumber
Chips
Lumber
Chips
15
15
15
10
5
0
10
5
0
–10.55
–10.48
–10.42
–6.37
–6.32
–6.26
–12.03
–11.51
–10.95
–14.74
–14.23
–13.67
–3.05
–3.03
–3.01
–2.13
–2.11
–2.08
–1.8
–1.73
–1.64
1.29a
1.37a
1.45a
–4.31
–4.16
–3.99
–6.65
–6.51
–6.36
–11.14
–10.58
–9.93
–10.38
–9.82
–9.17
a
These unexpected responses come from the fact that the price elasticity of chips with respect to roundwood price in Ontario is positive.
This result should be treated with caution, however, since the estimate of the elasticity is not significantly different from zero.
elasticities reported in this study are, however, generally
lower than the Latta and Adams (2000) estimates. These
elasticities, then, probably define a lower bound estimate of
lumber supply responses to changes in price.
Policy simulation results
As mentioned above, current duties on Canadian softwood
lumber bound for the United States are 27%. One possible
scenario is that the duty is eliminated as part of negotiations
that result in increased stumpage prices in Canada. The amount
that roundwood prices might increase cannot be known at
this time. A speculative value of a 15% increase in roundwood prices is used to simulate supply effects in this study.
Estimates of the net impacts of Kyoto on energy prices vary
widely ranging from a plus 4% increase in natural gas prices
and –2% change in electricity rates in Ontario (http://www.
climatechange.gc.ca/english/publications/ecoimpacts/11.html)
to a 60% increase in natural gas prices and a 100% increase
in electricity costs (presumably electricity produced by coal
fired generating stations) (Jaccard 2001). The sawmill industry consumes both natural gas and electricity. For the purposes of simulation, we consider three different energy price
increase possibilities: a 10% increase, a 5% increase, and a
0% increase.
7
Table 4 describes the particular combination of output and
input price changes that characterize each of the six scenarios for which supply responses are simulated. Simulating the
effects of import duties requires some knowledge of the impact on average Canadian supply prices. Since the supply
functions estimated in this study do not differentiate between
domestic supply and export supply, some assumptions need
to be made regarding what the net industry-wide price effect
is of a 27% duty, which is only imposed on that portion of
Canadian lumber production that is exported to the US. The
approach employed is to develop a weighted average price,
where a duty simulating decreased lumber price is applied to
the percent of lumber shipments exported to the US for a
particular province and a normal average price is applied to
the remaining portion of shipments. This assumes that domestic prices and prices of exports to other markets are unaffected by the import duties.7
For the purpose of simulating supply responses to the various scenarios, average prices, wages, production levels, and
input quantities for the last 5 years of the data were used to
provide a base line for prices and quantities. The estimated
output supply equations were then used to predict the
base-line outputs for lumber and chips in each province.
Prices were then adjusted according to the particular scenario. Lumber and chip supply were then reestimated. The
As one reviewer noted this is a somewhat restrictive assumption. In general one would expect that duties will have some effect on domestic
prices.
© 2004 NRC Canada
Williamson et al.
new output levels were compared with base-line outputs,
and the percent change was derived.
The simulation results are provided in Table 4. The complementary relationship between lumber and chip production
is again evident, as their supplies move together in response
to all types of shocks. With respect to the supply effects of a
27% duty, lumber and chip supply falls most in British Columbia, with less change in Ontario and Quebec. Chip production in Quebec falls almost as much as it does in British
Columbia. Roundwood price increases show a somewhat different impact, with both British Columbia and Quebec responding similarly with respect to reduced lumber and chip
supply. As was the case for implementing a duty, increased
roundwood prices have a far smaller impact in Ontario.
Finally, results show that increases in energy prices (up to
15%) would have very little impact on lumber or chip supply, whether duties are in place or roundwood prices increase.
1843
will affect the net impact of exogenous shocks on the economy.
This study has provided some limited insight into the supply responses of the Canadian lumber industry to exogenous
events. However, a more thorough assessment of the market
impacts would require incorporating these results into a spatial equilibrium model that considers the supply and demand
interactions between consumers and producers and interactions between sectors.
Acknowledgements
We express our gratitude to Rebbeca Ewing (B.C. Ministry
of Forests), Derek Goudie (Forintek), and a number of west
coast industry mill managers for providing valuable insights
and information that was used in undertaking this study.
References
Summary and conclusions
Estimation of output supplies and factor demands with a
range of functional forms provides a basis for bounding possible supply responses to exogenous shocks. The own lumber price elasticities estimated from the restricted Leontief
profit functional form used in this study are lower than those
presented in most other studies, while the lumber supply response with respect to roundwood price change elasticities
are somewhat higher than some studies. Thus, in terms of
the simulation results presented, the lumber supply response
to duties might be considered to be conservative estimates,
while the lumber supply responses to roundwood price increases could be on the high end of expected responses.
Estimation of profit and supply functions indicates that
chip supplies are sensitive to changes in lumber price and input wages. However, chip supply seems to be complementary
to lumber supply. Rather than being a distinct production decision, chip supply follows lumber supply. An increase in
lumber price has a significant positive effect on chip supply.
Similarly, an increase in chip price has a positive, although
somewhat smaller positive impact on lumber output.
The supply responses of chips and lumber to the various
combinations of duty, roundwood price increases, and energy price increases indicate a number of patterns. First, the
impacts of potentially increased energy prices (up to 10%)
are not likely to have much of an influence on lumber or
chip supply in any province. Thus, if Kyoto policies increase
energy prices, these changes are not likely to have a large
impact on lumber and chip production. Second, British Columbia and Quebec tend to have lumber and chip supplies
that are more sensitive to duties and increased roundwood
prices than Ontario. Third, Quebec is more sensitive to
roundwood price increases, while British Columbia is more
sensitive to the effects of duties.
One limitation of this study is that it concentrates on the
lumber industry only. Larsen (2002) finds that an increased
roundwood price increases the demand for wood chips by
the pulp and paper industry. Thus there are important linkages between the lumber and the pulp and paper sector that
Adams, D.M. 2003. Market and resource impacts of a canadian
lumber tariff. J. For. 101(2): 48–53.
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Appendix A. Data sources
The industry group that this study pertains to is the sawmill and planing mill industry. The North American Industry
Classification Code (NAICS) for this group is 321111 (Sawmills, except shingle and shake mills). Prior to 1997, this industry group was classified under the Standard Industrial
Classification code as 2512 (Sawmill and planing products
industry except shingle and shakes). Some data for this
study, such as capital, are only available at the more aggregated wood industries level.
Principal statistics originate from the annual survey of
manufacturers. Relevant variables include employment,
wage expenditures, cost of fuel and electricity, cost of materials and supplies, value of shipments, and value added.
Principal statistics data for the period 1963–1995 were
obtained from the annual Statistics Canada document Canadian Forestry Statistics Cat. No. 25-202 and from the Canadian Forest Service’s report Selected Forestry Statistics.
Principal statistics data for the period 1996–1999 are obtained by special request from the disclosure and dissemination unit of Statistics Canada.
Lumber production, lumber shipments, and value of shipments data are obtained from Selected Forestry Statistics
(Canadian Forest Service). Lumber price is determined by
dividing the value of shipments by volume of shipments.
Values are converted to dollars per thousand feet board measure ($/M fbm) using a conversion factor of 423.667
fbm/m3. Data for more recent years are obtained from
CANSIM.
Can. J. For. Res. Vol. 34, 2004
Values of chip shipments are obtained from the Statistics
Canada publication Sawmills and Planing Mills (Cat. Nos.
35-204 and 35-003). Chip price is derived by dividing value of
shipments by volume. Data for more recent years (1996–1999)
are obtained by special request from Statistics Canada.
Roundwood price is determined by dividing value of shipments in the logging industry by volume. These data are obtained from the Statistics Canada publication Wood
Industries (Cat. No. 35-250).
Data on capital stock were obtained by special request
from Capital Stock Division of Statistics Canada. Capital
stock data are determined using the perpetual inventory
method. The capital stock in a given year is equal to last
year’s stock plus investment minus depreciation. The information provided by Statistics Canada is only available for
wood industries. The wood industries group includes sawmills and planing mills as well as other types of firms such
as plywood mills, panel board producers, and secondary
manufacturers. A specific capital stock measure for the sawmill and planing mill in each province was estimated by applying a ratio based on percent of wood industry value
added accounted for by the sawmill and planing mill industry. The adjustment ratios change from year to year. For illustration purposes, in 1999 these adjustment ratios were
78% in British Columbia, 35% in Ontario, and 60% in Quebec.
Energy price data were obtained from CANSIM (series
V82928, Electric power selling price index $/kWh). Quantities of energy demanded are estimated by dividing payments for fuel and electricity by price.
Data on the specific amounts of roundwood used by the
sawmill and planing mill industry in particular years are
generally not available. Quantities of roundwood demanded
were estimated by applying time- and region-specific lumber
recovery factors to lumber production. Lumber production
data are available in Selected Forestry Statistics (Canadian
Forest Service). Lumber recovery factors (LRFs) for provinces and for particular time periods were estimated by reviewing a number of Forintek reports investigating lumber
recovery using different types of conversion technologies.
LRF for the British Columbia coast and interior for the period
1988–1999 was estimated by comparing annual data collected by the B.C. Ministry of Forests on lumber production
and roundwood use.
There were some gaps in the observations for particular
years. For example, owing to major changes in the survey of
manufacturers between 1987 and 1988, no data are available
for 1987. Also, for some reason, principal statistics data are
not available for British Columbia in 1997. In cases where
there are missing observations in a particular year, a value is
estimated by interpolating linearly between the previous and
subsequent years.
© 2004 NRC Canada