Document de travail n° 2011-02

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LLaboratoire d’EEconomie FForestière

Estimating Armington elasticities for sawnwood and application to the French

Forest Sector Model

Alexandre SAUQUET Franck LECOCQ

Philippe DELACOTE Ahmed BARKAOUI

Serge GARCIA

Mars 2011

1

Estimating Armington elasticities for sawnwood and application to the French Forest Sector Model

Alexandre SAUQUET1 Franck LECOCQ3,2

Philippe DELACOTE2,3* Sylvain CAURLA3,2

Ahmed BARKAOUI2,3 Serge GARCIA2,3

Mars 2011

Document de travail du LEF n°2011-02

Abstract

Domestic and foreign forest products consumptions are considered imperfectly substitutable in the French Forest Sector Model (FFSM). This assumption is justified by product heterogeneities that depend on production places, by the consumers habits or by the market structure. It leads us to implement the international trade in the FFSM via the Armington’s theory of the demand for products distinguished by place of production. In this paper we propose a calibration of Armingston’s elasticities of substitution between French and foreign forest products. System-GMM estimators are applied to identify robust parameters using a panel data from France customs service.

Key words : Armington elasticities, International timber trade, Forest Sector Modeling, France.

Résumé Estimation des élasticités d’Armington pour le bois de sciage et application au modèle du secteur

forestier français

Les produits forestiers domestiques et étrangers sont considérés comme des consommations imparfaitement substituables dans le modèle du secteur forestier français (FFSM). Cette hypothèse est justifiée par les hétérogénéités du produit qui dépendent des lieux de production, du fait des habitudes des consommateurs ou de la structure de marché. Cela nous amène à mettre en œuvre le commerce international dans le FFSM via la théorie d’Armington sur la demande de produits distingués par le lieu de production. Dans cet article, nous proposons une calibration des élasticités d’Armington de substitution entre produits forestiers français et étrangers. Des estimateurs GMM de système sont appliqués pour identifier les paramètres robustes en utilisant des données de panel du service des douanes français.

Mots clés : Elasticités d’Armington, commerce international du bois, modélisation du secteur forestier, France.

Classification JEL : C13, C15, Q23, Q28.

1 Centre d’Etudes et de Recherches sur le Développement International (Cerdi), 65 Boulevard François Miterrand, 63 1 2 INRA, UMR 356 Economie Forestière 54000 Nancy, France 3 AgroParisTech, Engref, Laboratoire d’Economie Forestière 54000 Nancy, France

*Corresponding author at : INRA, UMR, 356 Economie Forestière, 54000 Nancy

E- Mail address :pdelacote@nancy-engref.inra.fr

1 Introduction

Most forest sector models (Buongiorno et al., 2003; Kallio et al., 2004) con-

sider that international trade is determined only by transport costs and relative

prices, in line with Samuelson (1952). The implicit assumption behind this ap-

proach is that timber products are perfectly substitutable across countries, and

that international timber markets are perfectly competitive.

Real-world timber trade, however, does not match two key predictions of

Samuelson’s theory. First, timber products are often exchanged in both direc-

tions at the same time. Second, most of the empirical studies of international

timber markets do not find evidence of the law of one price (LOP) predicted by

Samuelson’s theory. For example, Hanninnen (1999) does not find evidence of

the LOP for the imports of soft sawnwood from Finland, Sweden, Canada and

Russia to the United Kingdom. On a broader scale, Toppinen and Kuuluvainen

(2010) find that the LOP rarely holds in European wood markets. However,

Mutanen (2006) finds that the German sawnwood import market, dominated

by Sweden, Finland and Russian, is well integrated.

Alone or in combination, several mechanisms might explain the discrepancy

between Samuelson’s predictions and empirical observations. First, the aggre-

gates for which international trade data is available may not be fully comparable

across countries. For example, sawnwoods differ by species and species baskets

differ by countries1. There may also be hidden transaction costs associated with

imports and exports because of, inter alia, translation requirements, differences

in norms, or differences in consumption habits.2 Finally, consumers might at-

tach (real or perceived) quality differences to foreign goods relative to domestic

1Traditionally, when the LOP does not hold, markets are not considered fully integrated.

However, another explanation is that products are not exactly similar, which leads to imper-

fect substitution between products, and hence to disconnected prices across markets.2Blonigen and Wilson (1999) devote an entire paper to the determinants of Armington’s

elasticities. They investigate the factors influencing elasticities of substitution across several

2

ones and thus have different demands. For example, it is evident that trees

quality and characteristics depend on the climate and soil quality at point of

origin.

To better capture the observed link between domestic and international

prices for wood products, an alternative way of modeling international trade is

to apply Armington’s theory (Armington, 1969). The basic idea is that goods

produced in different countries are imperfect substitutes for one another. This

framework allows for non-rigid links between domestic and international prices,

for simultaneous imports and exports of the same good, and thus allows to relax

the law of one price assumption. In addition, the imperfect substitutability

assumption is compatible with the three possible explanations for domestic and

international price disconnect outlined above.

The critical parameter in Armington theory is the so-called Armington elas-

ticity, i.e., the elasticity of substitution between domestic and foreign products.

This parameter captures demand sensitivity to changes in relative prices be-

tween domestic and imported products. As pointed by Balistreri et al. (2003)

and by Welsch (2008), general/partial equilibrium model results are highly sen-

sitive to the values chosen for these elasticities. Thus, they require rigorous

estimation.

Several papers attempt to estimate elasticities of substitution for manufac-

turing industries in the U.S., including wood industries (Shiells et al., 1986;

Shiells and Reinert, 1993; Gallaway et al., 2003). But these studies use esti-

mation methods adapted to time series, thus not taking full advantage of the

time-series and panel structure of their data. And as McDaniel and Balistreri

(2003) suggest, cross-section vs. times-series can lead to large differences in the

estimates of Armington elasticities. On the other hand, there is to our knowl-

edge only one study dedicated to Armington elasticities in the forest sector. Gan

sectors, and find that the presence of foreign-owned affiliates, entry barriers and the presence

of unions have an effect on these variations.

3

(2006) estimates the Armington elasticities for different forest products using

annual series. The range of estimates is rather wide and depends on product

types. Given the limited empirical evidence available, a default value is often

selected, such as in the widely used GTAP (Global Trade Analysis Project)

model, in which the value is set to 2.8 Donnelly et al. (2004).

The present paper aims at estimating Armington’s elasticities for a national-

level forest sector (with view to calibration of the French Forest Sector Model,

the FFSM, Caurla et al. 2009, 2010), using panel data from France and rigorous

methods adapted to a dynamic specification. A detailed econometric analysis

is conducted, based on department-level import/consumption data for France

from 1995 to 2002. GMM estimates of elasticities of substitution between French

and foreign soft sawnwood and hard sawnwood are provided. Three different

GMM estimators are implemented and rigorously tested to account for potential

endogeneity problems.

Even though the numerical application focuses on the French case, we be-

lieve this paper has broader value-added because (i), as noted above, the LOP

assumption does not hold in many contexts besides France, and because (ii), the

method we use to estimate Armington elasticities and the model we calibrate

can be replicated.

Section 2 presents the basic framework of Armington’s theory in the context

of the FFSM. Section 3 presents the calibration of the relevant parameters in the

context of the French forest sector, which are analyzed in section 4. Section 5

presents a short simulation of a price shock to illustrate Armington specification.

Section 6 concludes.

4

2 A Brief Introduction to the FFSM and the

application of Armington theory

The French Forest Sector Model (FFSM, Caurla at al, 2010.) is a dynamic

simulation model of the French forest sector. The model is a combination of a

forest dynamics (FD) module and an economic (E) module. The FD module

simulates the growth of the timber stock. The E module is a partial-equilibrium

model of the French forest sector. It encompasses both raw timber products (fu-

elwood, pulpwood, hardwood and softwood roundwood) and processed timber

products markets (hardwood sawnwood, softwood sawnwood, plywood, pulp,

fuelwood, fiber and particle board). Three groups of agents are thus repre-

sented in the model: forest owners (timber suppliers), the primary-conversion

industry and consumers (demand for primary-processed goods). Inter-regional

trade (the E module distinguishes 22 administrative regions within France)

is modeled assuming perfect competition and full substitutability of products

across regions, a la Samuelson (1952). International trade between France and

the Rest of the World is modeled assuming imperfect substitutability using

Armington’s framework.3

The reader will find in Armington (1969) and Geraci and Prewo (1982) a

detailed description of the Armington framework and of its underlying assump-

tions, which we briefly recall here. A first restriction to the basic Hicksian model

is that consumers preferences for different products of any kind (e.g., French and

German sawnwood) are assumed independent from their purchases of products

of any other kinds (e.g., firewood, boards, etc.). Demands for products of the

same kinds (hereafter composite goods) can thus be determined unambiguously.

Second, each country’s market share (say, each country’s market of the

French sawnwood market) is assumed dependent only on the relative prices

3The E module is calibrated using literature data and specific estimates, as presented in

Caurla et al. (2010).

5

of the same good across countries. Then the price of composite goods (here-

after composite price) depends only on the price of individual products, as the

quantity-weighted average of the prices of individual products.

Third and finally, elasticities of substitution between products competing in

a given market are assumed constant, and equal for each pair. The demand

for any composite good can thus be expressed as a Constant Elasticity of Sub-

stitution (CES) function of the demand for individual products. Demand for

individual products thus depends only on total composite good demand and on

the ratio of product price to composite price—with the corresponding price elas-

ticity (or Armington elasticity) the unique composite good-specific parameter

of the equation.4

The three assumptions above are arguably restrictive. In particular, the

linear relation between individual products demand and composite demand is

an arguable assumption. Nevertheless, the advantage of Armington’s framework

is precisely that it allows to capture weak substitutability between domestic and

foreign products with parsimonious data.

In the FFSM, only two places of production are considered: France and

Rest of the World. For each processed good p (sawnwood, plywood, pulp,

fuelwood, fiber and particle board and other industrial roundwood), let LDp be

the demand for domestic product and Mp the demand for imports, Pp the price

of locally-produced product p and P ∗

p the price of imports, and let Dp be the

demand for the composite good p and Pp the composite price.

Adopting Armington’s assumptions in the FFSM thus yields the following

demand function for the composite good, where φp is the Armington elasticity

for good p (Time indexes are omitted).

Dp = [(1− bp)LDφp−1

φpp + bpM

φp−1

φpp ]

φp

φp−1 (1)

4The more substitutable local and foreign products are, the larger the corresponding elas-

ticity of substitution is, and the more changes in relative prices impact on trade.

6

Demands for national products and for imports are respectively:

LDp = (1− bp)φpDp(

Pp

Pp

)−φp (2)

Mp = bφp

p Dp(P ∗

p

Pp

)−φp (3)

And the price for the composite good is defined by the budget constraint.

PpDp = LDpPp + MpP∗

p (4)

3 Estimations of Armington elasticities

Elasticities of substitution between French and foreign timber products are

critical to implement Armington theory in the FFSM. Since no estimation of

those elasticities are available in the literature for the French case, we investigate

them empirically.

3.1 Empirical strategy

3.1.1 Data and specification

Within Armington’s framework, for each good, the ratio of demand for im-

ports on demand for domestic products can be expressed as a function of the

price ratio between domestic and imported products, as can be seen by divid-

ing equation 3 by equation 2. Taking the log form and aggregating all constant

values within δ leads to the basic equation for the estimation (with p indexes

omitted).

ln(M

LD) = δ + φ ln(

P

P ∗

) (5)

Six transformed products are present in the FFSM model: soft sawnwood,

hard sawnwood, pulpwood, fiber and particle board and fuelwood. However

7

suitable data is not available to analyze pulpwood, fiber and particle board and

fuelwood markets. Therefore in this paper, we estimate Armington’s elasticities

only for the first two products: soft sawnwood and hard sawnwood.

The dataset used in estimations came from French customs and French in-

dustry ministry statistic services. The latest provides since 1995 prices and

quantities of production and export coming from a yearly survey at the de-

partement level which is a French administrative sublevel unit of the 22 ad-

ministrative regions. Customs statistic service provides prices and quantities

of imports at the same time and spatial disaggregation level. Dataset used in

estimations covers the period 1995-2002.

In order to take into account the long-term movements of our series and to

improve the explanatory power of our regressions by catching inertial effects in

consumption behavior, we adopt a dynamic specification. Thus we estimate the

following equation:

ln(Mit

LDit

) = δ + α ln(Mit−1

LDit−1

) + φ ln(Pit

P ∗

it

) + υi + µt + εit (6)

Mit is the volume of imports by a departement i at year t, LDit is the

consumption volume of domestic goods by departement i at year t. Pit and

P ∗

it are the corresponding prices per unity. υi refers to the individual specific

effects and µt to the time fixed effects. δ, α and φ are the parameters to be

estimated and εit is the remaining error term. α captures the inertia of the

demand patterns (where α is expected to ∈]0, 1[). φ is expected to be positive,

and larger φ describe higher substitutability. The main advantage of using

panel data to estimate elasticities of substitution is that we get the possibility

to introduce individual fixed effects. The individual fixed effects υ allow us

to control for unobserved time invariant departement characteristics such as

distance to border, geographical particularities, urbanization, etc. The time

fixed effects µ captures potential macroeconomic fluctuations.

8

Table 1: Statistics on price and quantity ratios

Variable Mean Std. Dev. Min. value Max. value

hard sawnwood

Pit/P∗

it 0.72023 0.52452 0.06387 5.07088

Mit/LDit 0.19641 0.58804 0.00002 7.04508

soft sawnwood

Pit/P∗

it 0.75778 0.31400 0.08014 3.24615

Mit/LDit 0.70572 1.39892 0.00001 10.55542

One limit of the dataset is that the consumption of local products by de-

partment is not available. We only know the production that departements sell

on the domestic market. Since we only seek to capture an average response to

price variations at the national level, we consider this proxy as satisfactory.5

Descriptive statistics are reported in Table 1. As we can see, the variability

of quantity ratios M/LD is quite important. This underlines the disparities

between French departments and the necessity to introduce fixed effects. It is

also worthwhile to note that the share of imports is larger for softwoods than

for hardwood. Definition and source of the variables are in Appendix A.

3.2 Econometric methodology

3.2.1 Selection of Appropriate Estimator

With the lagged endogenous variable on the right hand side of the equation,

the OLS estimator is no longer consistent. Indeed, by definition the lagged

endogenous variable is correlated with the specific effect. The within estimator

eliminates the individual specific effect, and so is still consistent. However, for

5In order to improve our proxy, we drop out of our sample some departements around

Paris and Lyon cities. These departements do not produce sawnwood. Estimates show that

this adjustment does not affect the estimated values of elasticities

9

short panels like ours (8 periods), there is still a correlation between the error

term and the lagged endogenous variable, which biases the estimator (Araujo

et al. (2004), Harris et al. (2008)). One can show that the Within estimator

underestimates the value of α while the OLS estimator overestimates it. This

ranking is inverted for the other variable coefficients (Harris et al. (2008)).

Therefore these estimators provide useful benchmarks for the true values of the

coefficients.

The most commonly used approach to get a consistent and unbiased esti-

mator is to apply an instrumental variable method on transformed variables.

If no instrument can be found outside the model, the solution is to use lagged

values of the regressors as instruments. This kind of models can be estimated

by using the GMM estimator.

Arellano and Bond (1991) propose to remove the fixed effect by taking the

first difference of the variable and then use the lagged values of the variables in

level as instruments for the equation in first difference. However, this estimator

often suffers from the problem of weak instruments (i.e., lack of correlation of

the instruments with the regressors). Bond et al. (2001) explain that finding co-

efficients outside of the bounds provided by OLS and Within estimators is often

due to a problem of weak instruments. Therefore we check that our estimators

do not suffer from this bias by checking the robustness of our coefficients and

by comparing our results with the OLS and Within benchmark estimates.

Since the estimations using Arellano-Bond estimator appear to be biased, we

next apply the estimator proposed by Blundell and Bond (1998). They suggest

to solve the problem of weak instruments by estimating a system of equations.

The equation in first difference, instrumented by lagged value of regressors in

level, is estimated simultaneously with the equation in level, symmetrically

instrumented by the regressors in first difference.6

6Note that the equation in level does not include fixed effects. However Roodman (2009b)

underlines that our estimator is still consistent, because the instruments are assumed to

10

In order to check the robustness of our estimates we implement the Arel-

lano and Bover (1995) estimator. This last estimator is less used but do not

have the bias of first difference estimators, i.e., magnifying gaps on unbalanced

panel. Arellano-Bover’s estimator works in the same way as the Blundell-Bond

estimator. This is a system-GMM estimation, but using forward orthogonal

deviation instead of first difference to transform the variables. This means that

it subtracts the mean of all future available observations of a variable instead

of subtracting the past value of a contemporaneous one. Thus it minimizes the

data loss and therefore increases efficiency. It can be showed that the Arellano-

Bover and the Blundell-Bond estimator yield to same values of parameters in

balanced panel Roodman (2009b).

The GMM estimator can be run in two different ways in two steps or in one

step. Two-step estimations are asymptotically more efficient but the reported

standard errors are downward biased in small sample. However Windmeijer

(2005) proposes a finite sample correction for the variance of two-step GMM

estimators, allowing us to report efficient and unbiased estimations. Therefore

only two-step GMM estimations are reported.

3.2.2 Instrumentation

The quality of GMM methods depends on the validity of the instrument

set. A valid instrument should have the first property presented in the pre-

vious section: being correlated with the instrumented variable. Secondly, the

exclusion restriction has to be satisfied as well: the instrument should not be

correlated with the error term (ε). Several assumptions can be made regarding

the exogeneity of regressors (X). We consider that they can take the following

be orthogonal to the fixed effects. Moreover, introducing explicit fixed effect by individual

dummies would lead to a within transformation and therefore caused bias in unbalanced panel

Roodman (2009b).

11

status:

Weakly exogenous

E(Xiτ∆εit) = 0, ∀ t ≥ τ (7)

Contemporaneously endogenous

E(Xiτ∆εit) = 0, ∀ t > τ (8)

where t and τ are time period delimiters and ∆εit the error term take in

first difference.

The lagged endogenous variable is usually considered as weakly exogenous

because of its mechanical correlation with the contemporaneous error term in

level. The other explanatory variables could be considered weakly exogenous

as well. If markets are not perfectly competitive, demand affects prices and

vice versa. In such case, regressing prices on quantities could be subject to an

endogeneity problem. We thus test for these endogeneity issues.

Besides, because of the crucial validity of our instrument set, we implement

several specification tests. First by taking the first difference of our variable,

we should create first-order correlation in the residuals. Therefore the value

of the m1 test should be significantly different from zero.7 However a second-

order correlation among the residuals would reveal a violation of the exclusion

restrictions. Therefore we do not consider as valid the estimations in which

the null hypothesis of the Arellano-Bond’s m2 test is rejected. In addition we

implement the Hansen test of over-identifying restrictions in order to test the

validity of the whole set of instruments. Finally the Hansen-in-difference tests

7Moreover, if there is no first-order correlation among the residuals, the interpretation of

the m2 test does not remain the same. If the errors in level follow a random walk, the OLS

as well as the GMM estimator could be consistent. In that case, the econometrician have to

discriminate between the two estimators, though a Hausman test for example Arellano and

Bond (1991).

12

allows us to test the validity of each instrument’s subset. Both of these tests

accept the exclusion restriction under the null hypothesis.8

Using Monte-carlo simulations, Bowsher (2002) and Roodman (2009a) both

show that the Hansen tests never reject the null hypothesis when the number

of instruments is increasing. They do not give any explicit numerical limit.

However they both consider that keeping the number of instrument under the

cross-section dimension is still too generous. Therefore in order to check the

robustness of our regressions we limit the number of lags used as instruments

to two.

4 Analysis of the estimated elasticities of sub-

stitution

Tables 2 and 3 present the estimations of equation (6), for both sawnwood

types respectively, following the different specifications presented above. We

first display the OLS and Within estimations columns in (1) and (2) respec-

tively. Then Arellano-Bond estimations are presented in columns (3) and (4).

The Blundell-Bond estimations can be found in columns (5) to (8) and the

Arellano-Bover estimations in columns (9) and (10). In columns (7) to (10),

the number of lags used in the instrumentation is limited to two (it is unlimited

otherwise). Finally the price ratio is considered as contemporaneously endoge-

nous in columns (3), (5), (7) and (9) and as weakly exogenous in columns (4),

(6), (8) and (10).

8Hansen instead of Sargan tests are used whereas we apply the Windmeijer correction to

standards errors in every regression. Indeed the Hansen test is a version of the Sargan test

robust to heteroscedasticity.

13

Tab

le2:

Est

imat

ions

ofel

asti

citi

esof

subst

ituti

onbet

wee

nFre

nch

and

fore

ign

har

dsa

wnw

ood

GM

MSyst

em

-GM

M

OLS

Wit

hin

Are

llano-B

ond

Blu

ndell-B

ond

Blu

ndell-B

ond

/In

str.

lim

.A

rellano-B

over

/In

str.

lim

.

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

ln(M

it−

1/L

Dit−

1)

0.8

1(0

.000)

0.2

8(0

.001)

0.2

2(0

.204)

0.2

2(0

.206)

0.4

9(0

.001)

0.4

6(0

.000)

0.4

5(0

.008)

0.3

8(0

.003)

0.5

7(0

.000)

0.4

8(0

.000)

ln(P

it/P∗ it)

0.2

5(0

.028)

0.6

4(0

.004)

1.1

8(0

.000)

1.0

6(0

.000)

0.3

5(0

.190)

0.5

6(0

.038)

0.1

6(0

.605)

0.5

0(0

.044)

0.2

3(0

.360)

0.5

1(0

.034)

Tim

efixed

Effects

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

Num

.ofobs.

382

382

301

301

382

382

382

382

382

382

Num

.ofin

div

.69

69

61

61

69

69

69

69

69

69

Num

.ofin

str.

--

43

49

56

63

36

38

36

38

Test

s

m1

--

-2.2

7(0

.023)

-2.2

0(0

.028)

-2.9

6(0

.003)

-3.0

0(0

.003)

-2.8

0(0

.005)

-2.8

8(0

.004)

-3.1

1(0

.002)

-3.0

8(0

.002)

m2

--

-0.7

0(0

.485)

-0.6

5(0

.517)

-0.2

2(0

.826)

-0.2

7(0

.783)

-0.1

7(0

.867)

-0.2

5(0

.806)

-0.2

0(0

.843)

-0.2

4(0

.812)

Hanse

nte

st-

-39.1

2(0

.290)

46.0

4(0

.272)

50.8

6(0

.324)

56.7

2(0

.374)

32.2

8(0

.222)

29.2

4(0

.453)

30.8

2(0

.279)

32.5

2(0

.297)

Diff

-in-H

anse

nte

sts

:

Lags

ofln

(Mit−

1/L

Dit−

1)

--

30.8

5(0

.085)

32.4

5(0

.053)

35.0

6(0

.137)

35.5

3(0

.126)

19.0

8(0

.324)

20.9

7(0

.228)

20.2

5(0

.262)

19.6

1(0

.294)

Lags

ofln

(Pit/P∗ it)

--

29.9

6(0

.093)

37.1

5(0

.092)

31.6

8(0

.244)

35.7

4(0

.387)

22.6

4(0

.161)

20.0

4(0

.392)

22.6

0(0

.163)

24.1

4(0

.191)

Inst

r.eq.

lev.

--

--

13.8

0(0

.313)

15.5

7(0

.273)

14.5

9(0

.264)

14.7

9(0

.321)

18.2

7(0

.108)

15.3

9(0

.283)

Note

s:Sta

ndard

erro

rs

are

corre

cte

dwith

the

Win

dm

eijer

meth

od.

Tim

efixed

effec

tsare

spec

ified

as

standard

inst

rum

ents

.P-v

alu

es

ass

ocia

ted

with

the

reporte

dco

effi

cie

nts

are

under

bra

ckets

.

”X

”re

fers

toln

(Pit/P∗ it),

”con

t.”

toco

nte

mpora

neo

usly

endogenous

and

”w

ea

k.”

towea

kly

exogenous.

14

Tab

le3:

Est

imat

ions

ofel

asti

citi

esof

subst

ituti

onbet

wee

nFre

nch

and

fore

ign

soft

saw

nw

ood

GM

MSyst

em

-GM

M

OLS

Wit

hin

Are

llano-B

ond

Blu

ndell-B

ond

Blu

ndell-B

ond

/In

str.

lim

.A

rellano-B

over

/In

str.

lim

.

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(X-c

ont.

)(X

-weak.)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

ln(M

it−

1/L

Dit−

1)

0.9

0(0

.000)

0.3

1(0

.000)

0.3

6(0

.028)

0.3

1(0

.010)

0.8

2(0

.000)

0.8

4(0

.000)

0.7

7(0

.000)

0.8

4(0

.000)

0.7

3(0

.000)

0.8

6(0

.000)

ln(P

it/P∗ it)

0.5

7(0

.001)

0.5

7(0

.080)

0.2

8(0

.546)

0.2

3(0

.489)

0.5

7(0

.105)

0.9

5(0

.029)

0.5

3(0

.169)

1.0

0(0

.011)

0.5

0(0

.184)

0.9

2(0

.010)

Tim

efixed

Effects

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

Num

.ofobs.

446

446

362

362

446

446

446

446

435

446

Num

.ofin

div

.74

74

70

70

74

74

74

74

71

74

Num

.ofin

str.

--

43

49

56

63

36

38

36

38

Test

s

m1

--

-2.3

3(0

.020)

-2.4

9(0

.013)

-2.5

9(0

.010)

-2.4

3(0

.015)

-2.5

8(0

.010)

-2.4

4(0

.015)

-2.5

5(0

.011)

-2.4

9(0

.013)

m2

--

1.1

2(0

.261)

1.1

2(0

.262)

1.2

5(0

.210)

1.1

9(0

.235)

1.2

6(0

.208)

1.2

0(0

.231)

1.4

3(0

.153)

1.1

8(0

.237)

Hanse

nte

st-

-38.7

5(0

.304)

40.8

7(0

.477)

46.5

3(0

.492)

51.7

3(0

.562)

30.9

7(0

.272)

29.0

1(0

.465)

32.9

0(0

.200)

36.8

3(0

.151)

Diff

-in-H

anse

nte

sts

:

Lags

ofln

(Mit−

1/L

Dit−

1)

--

24.3

8(0

.275)

18.3

3(0

.628)

23.4

5(0

.661)

17.3

0(0

.923)

22.9

2(0

.152)

10.9

2(0

.861)

24.4

5(0

.108)

19.5

7(0

.297)

Lags

ofln

(Pit/P∗ it)

--

38.7

5(0

.304)

24.3

8(0

.609)

25.4

7(0

.548)

31.9

0(0

.571)

18.1

2(0

.381)

16.1

8(0

.646)

22.3

4(0

.172)

25.2

2(0

.154)

Inst

r.eq.

lev.

--

--

7.7

5(0

.806)

8.5

0(0

.809)

12.3

5(0

.418)

9.7

6(0

.713)

10.5

2(0

.571)

15.6

3(0

.270)

Note

s:Sta

ndard

erro

rs

are

corre

cte

dwith

the

Win

dm

eijer

meth

od.

Tim

efixed

effec

tsare

spec

ified

as

standard

inst

rum

ents

.P-v

alu

es

ass

ocia

ted

with

the

reporte

dco

effi

cie

nts

are

under

bra

ckets

.

”X

”re

fers

toln

(Pit/P∗ it),

”con

t”

toco

nte

mpora

neo

usly

endogenous

and

”w

ea

k.”

towea

kly

exogenous.

15

First, in the Arellano-Bond’s estimations, the value of the coefficient associ-

ated to the lagged endogenous variable is lower than the Within bound for both

sawnwood types, which suggests a weak instruments problem. Moreover, the

Hansen-in-difference tests reject the null hypothesis of instrument’s exogeneity

at the 10 percent level for the Arellano-Bond estimations of hard sawnwood

Armington’s function. Consequently, the Arellano-Bond estimations, columns

(3) and (4) are invalid and we have to run system-GMM estimations in order

to get unbiased parameters.

Second, the estimations show that the price ratio has to be considered as a

weakly endogenous variable. On the one hand, the additional conditions on the

moments are not rejected by the tests. On the other hand, estimated coefficients

appear to be robust and significantly different from zero, in the line of the OLS

and Within benchmark estimations. Therefore we have to reject the estimations

where the price ratio is considered as contemporaneously endogenous columns

(5), (7) and (9).

Third, considering the problem having too many instruments we have to

be carefull with the results of estimation (6). Therefore reliable values of the

coefficients are given by columns (8) and (10). We consider that the results

given in column (10) are the most accurate, because the Arellano-Bover method

adequately addresses the unbalanced panel data issue.

The coefficient associated to the lagged endogenous variable, here the quan-

tity ratio of the previous year, is 0.48 for hard sawnwood and 0.86 for soft sawn-

wood. The soft sawnwood market seems more stable than the hard sawnwood

one. This may stem from the fact that hard sawnwood markets in France tend

to be smaller, more diversified niche markets with higher aggregate volatility

than soft sawnwood markets.

According to our estimates, when the domestic to import price ratio of hard

sawnwood in France decreases by 1 percent, the demand of domestic hard sawn-

wood relative to import increases by 0.51 percent. Symmetrically, for the soft

16

sawnwood, when the price ratio decreases by 1 percent, the corresponding quan-

tity ratio increases by 0.92 percent. These values indicates that hard sawnwood

and soft sawnwood are normal goods and that consumers report their consump-

tion on the cheapest product. Moreover the largest elasticity for soft sawnwood

indicates a higher substitutability between domestic and foreign goods than for

the hardwood case. This may be explained by the fact that softwood may be

considered as more common and less specific timber species than hardwood.

This leads to the fact that soft sawnwood is quite an homogenous good, while

hard sawnwood is more heterogenous.

Finally, long-run elasticity estimates can be computed as φ/(1 − α) from

Equation (6).9 Even if the FFSM needs to use the short-run elasticities, long-

run estimates are often more relevant to applied policy in applied and general

equilibrium modeling. From the estimates reported in column (10) in Tables

2 and 3, the long-run Armington elasticities are found to be equal to 0.98 and

6.57, respectively for hard and soft sawnwoods. These values are consistent with

the differences between short and long-run elasticities found by Gan (2006) for

the US case.

5 Conclusion

The fact that the LOP is frequently not met is crucial when considering

international trade. A way to deal with this price heterogeneity is to introduce

Armington theory in products demand function. In this context, estimating

the elasticities of substitution between local and foreign products is essential.

As underlined by Balistreri et al. (2003) and Welsch (2008) model’s results are

highly sensitive to elasticity values. This paper introduces a comprehensive

9In the long run, equilibrium is assumed such that ln( Mit

LDit

) = ln( Mit−1

LDit−1

). The long-run

elasticities are then obtained by dividing each of the estimated coefficients (interpreted as

short-run elasticities) by (1− α).

17

method to estimate those elasticities in the context of forest sector models

with an application to the French case. Using a dynamic representation of

Armington formulation and a panel dataset from French customs and industry

statistic services we propose, in an econometric framework, accurate estimates of

the Armington elasticity of substitution for soft sawnwood and hard sawnwood

products.

Estimation results show an elasticity of substitution around 0.51 for hard

sawnwood and 0.92 for soft sawnwood. This is consistent with the fact that soft-

wood is more homogeneous in its production and using than hardwood. Also,

a significant and small value estimation of the elasticity parameters prove and

justify the interest of using Armington’s approach in national models such as

FFSM. A spatial equilibrium based only on Samuelson theory without imper-

fect substitution between domestic and foreign products will be driven more by

international prices and less by consumption and production behaviors.

To illustrate the implication of our results for the FFSM, we simulate a 30 %

price increase in international sawnwood prices in 2013. The 2013 price increase

leads to a 13 % decrease in hard sawnwood import and a 15 % decrease in soft

sawnwood import. The result is more complex for local demand. Indeed, an

increase in international prices has two effects on local demand (Hicks (1956)).

First, the income effect (real income decreases because of the price increase)

tends to reduce local demand. Second, the substitution effect (consumer switch

a part of their consumption from foreign wood to local wood) tends to increase

local demand. The net effect depends on the elasticities of substitution. Since

soft sawnwood is more substitutable than hard sawnwood, the income effect

dominates for hard sawnwood (local demand slightly decreases by 0.1 %), while

the substitution effect dominates for soft sawnwood (local demand increases by

0.3 %). The negative impact on import is larger than the potential positive

impact on local demand, which results in a decrease in total demand (- 3.3 %

for hard sawnwood and - 3.8 % for soft sawnwood).

18

Further work requires to gather reliable data on the other timber product

markets to extend this analysis beyond sawnwood. This data collection effort

is crucial, since the knowledge of Armington’s elasticities is very useful to accu-

rately simulate the impact of political measures affecting prices on the French

forest sector (Caurla et al., 2009, 2010).

19

Appendix A: Source and definition of the vari-

ables.

Variable Acronym Definition Source

Imports volume M volume of imports in cube

meters, by departments

French Custom Office

Import price P* price of imports in con-

stant euros 2001, by de-

partments

French Custom Office

Local consumption LD volume of sawnwood pro-

duced by department and

consumed in France in

cube meters

SESSI

Local price P price sawnwood produced

by departments and con-

sumed in France in con-

stant euros 2001

SESSI

20

References

Araujo, C., Brun, J.-F., and Combes, J.-L. (2004). Econometrie : Licence-

Master. Breal.

Arellano, M. and Bond, S. R. (1991). Some tests of specification for panel data:

Monte carlo evidence and an application to employment equations. Review

of Economic Studies, 58(2):277–97.

Arellano, M. and Bover, O. (1995). Another look at the instrumental variable

estimation of error-components models. Journal of Econometrics, 68(1):29–

51.

Armington, P. S. (1969). A theory of demand for products distinguished by

place of production. IMF Staff papers, 16(1):159–176.

Balistreri, E. J., McDaniel, C. A., and Wong, E. V. (2003). An estimation

of US industry-level capital-labor substitution elasticities: support for Cobb-

Douglas. The North American Journal of Economics and Finance, 14(3):343–

356.

Blonigen, B. A. and Wilson, W. W. (1999). Explaining Armington: What

determines substitutability between home and foreign goods? Canadian

Journal of Economics, 32(1):1–21.

Blundell, R. and Bond, S. (1998). Initial conditions and moment restrictions in

dynamic panel data models. Journal of Econometrics, 87(1):115–143.

Bond, S. R., Hoeffler, A., and Temple, J. (2001). GMM estimation of empirical

growth models. CEPR Discussion Papers 3048, C.E.P.R. Discussion Papers.

Bowsher, C. (2002). On testing overidentifying restrictions in dynamic panel

data models. Economics Letters, 77(2):211–220.

21

Buongiorno, J., Zhu, S., Zhang, D., Turner, J., and Tomberlin, D. (2003). The

Global Forest Products Model. Academic Press.

Caurla, S., Delacote, P., Lecocq, F., and Barkaoui, A. (2009). Fuelwood con-

sumption, restrictions about resource availability and public policies: impacts

on the French forest sector. Cahier du LEF, (2009-03).

Caurla, S., Lecocq, F., Delacote, P., and Barkaoui, A. (2010). The french forest

sector model: version 1.0. presentation and theorical foundations. Work-

ing Papers - Cahiers du LEF 2010-04, Laboratoire d’Economie Forestiere,

AgroParisTech-INRA.

Donnelly, W. A., Johnson, K., Tsigas, M., and Ingersoll, D. (2004). Revised

Armington elasticities of substitution for the USITC model and the concor-

dance for constructing a consistent set for the GTAP model. Working Papers

15861, United States International Trade Commission, Office of Economics.

Gallaway, M. P., McDaniel, C. A., and Rivera, S. A. (2003). Short-run and

long-run industry-level estimates of U.S. Armington elasticities. The North

American Journal of Economics and Finance, 14(1):49–68.

Gan, J. (2006). Substituability between us domestic and imported forest prod-

ucts: The armington approach. Forest Science, 52(1):1–9.

Geraci, V. J. and Prewo, W. (1982). An empirical demand and supply model of

multi-lateral trade. The Review of Economics and Statistics, 64(03):432–441.

Hanninnen, R. (1999). Modern Time series Analysis in forest products markets,

chapter The law of one price in United Kingdom soft sawnwood imports - A

cointegration appoach, pages 55–68. Kluwer Academic Publishers.

Harris, M. N., Matyas, L., and Sevestre, P. (2008). Dynamic models for short

panels. In Matyas, L. and Sevestre, P., editors, The Econometrics of Panel

22

Data, volume 46 of Advanced Studies in Theoretical and Applied Economet-

rics, pages 249–278. Springer Berlin Heidelberg.

Hicks, J. (1956). A revision of Demand Theory. Oxford University Press.

IFN (2008). La foret francaise en 2005, 2006 et 2007. Inentaire Forestier

National.

Kallio, A. M. I., Moisyev, A., and Solberg, B. (2004). The Global Forest Sector

Model EFI-GTM – the model structure. Internal Report 15, European Forest

Institute.

McDaniel, C. A. and Balistreri, E. J. (2003). A review of armington trade

substitution elasticities. Economie Internationale, 94-95:301–314.

Mutanen, A. (2006). Estimating substitution in coniferous sawnwood imports

into Germany. Journal of Forest Economics, 12(1):31 – 50.

Roodman, D. M. (2009a). How to do xtabond2: An introduction to difference

and system GMM in Stata. Stata Journal, 9(1):86–136.

Roodman, D. M. (2009b). A Note on the Theme of Too Many Instruments.

Oxford Bulletin of Economics and Statistics, 71(1):135–158.

Samuelson, P. A. (1952). Spatial price equilibrium and linear programming.

American Economic Review, 42(3):283–303.

Shiells, C., Stern, R., and Deardorff, A. V. (1986). Estimates of the elasticities of

substitution between imports and home goods for the United States. Review

of World Economics (Weltwirtschaftliches Archiv), 122(3):497–519.

Shiells, C. R. and Reinert, K. (1993). Armington models and terms-of-trade

effects: Some econometric evidence for north america. Canadian Journal of

Economics, 26(2):299–316.

23

Toppinen, A. and Kuuluvainen, J. (2010). Forest sector modelling in europe –

the state of the art and future research directions. Forest Policy and Eco-

nomics, 12(1):2–8.

Welsch, H. (2008). Armington elasticities for energy policy modeling: Evidence

from four European countries. Energy Economics, 30(5):2252–2264.

Windmeijer, F. (2005). A finite sample correction for the variance of linear

efficient two-step GMM estimators. Journal of Econometrics, 126(1):25–51.

24