Unfortunately, there are no reliable data on the number of timber inter- mediaries and on the price elasticity of the timber supply. Still, under the reasonable assumption that N = 3, η =0.2, and using the actual data on the timber market price, the logging cost and the stumpage fee (c≈RUB150 /m3,τ ≈A RUB25 /m3, P≈RUB300 /m3), it follows from (27) that p P/ ≈0.7, i.e., due to the imperfect market structure, the price at which loggers sell their timber to intermediaries could be about 30% lower than the market price. Thus, a substantial share of timber rent is likely to be captured by intermediaries.
7. TAX SHIFTING MODEL
Moreover, it is assumed that within each distance class, the distribution of forest area relative to quality is the same, so that the quality is taken to be constant and equal to the average quality Q. Naturally, from (10), if there are no taxes or stumpage fees, it follows that there is a critical distance d∗, defined by the zero rent condition
( ) ( ) ( ) 0
F k
P ΨQ −P k d∗ −wl d∗ = , (28)
beyond which forests are not logged.
Then the total value of timber rent will be
0
( , ) ( )
d
R=
∫
∗ρ x Q f x dx. (29)Total labor employed in the forestry sector is
0
( , ) ( )
d
LF l x Q f x dx
=
∫
∗ , (30)where l is obtained from (9) under conditions that L=DK and Q=Q,
d, DQ l Ee E
B δ µ
= = . (31)
The output of the forest sector will be as follows:
0
( ) ( )
d F
F Q f x dx
T Ψ ∗
=
∫
. (32)The output in the rest-of-the-economy sector is a function of labor LMand capital KM according to production function
( , )
M M M
F L K , (33)
which is assumed to be linearly homogeneous in its production factors, with capital KM being fixed.
The total regional output is
F F M M
Y =P F +P F . (34)
The government imposes taxes on labor and corporate profits, τL and τK respectively, and collects stumpage fees at the level τA per hectare of timber stand. The government revenues are as follows:
( ) ( )
L M F K M F
G=τ w L +L +τ π + Π + Ω, (35)
where
(1 )
M P FM M KM L wLM
π = −ν − +τ , (36)
0
( ) ( )
d
F ∗πF x f x dx
Π =
∫
, (37)( ) ( ) (1 ) ( ) ( )
F PF Q P k dK Lwl d A d
π = Ψ −ν − +τ −τ , (38)
0
( ) ( )
d
A x f x dx
∗τ
Ω =
∫
, (39)where ν is a tax-deductible capital depreciation rate.
Stumpage fees are set exogenously as a function of distance and are subject to the constraint
( ) ( )
Ad d
τ ≤ ρ . (40)
Employment in the rest-of-the-economy sector is defined by the profit maximization condition, which yields
(1 )
M M L
M
L L w τ P
= +
. (41)
Critical distance d∗ is the solution to the following zero-rent equation:
( ) ( ) (1 ) ( ) 0
1
K K
F L
K
P Q P ντ k d τ wl d
τ ∗ ∗
Ψ − − − + =
− . (42)
Stumpage fees, dependent on distance, should be set at a level that does not exceed the timber rent, taking into account taxes on profit and labor. Let θ be the share of stumpage fees in the after-tax timber rent.
Then,
( ) ( ) ( ) (1 ) ( )
1
K K
A F L
K
d P Q P ντ k d wl d
τ θ τ
τ
−
= Ψ − − − + , 0≤ ≤θ 1. (43)
To estimate the marginal effects of shifting the tax burden from labor to timber rent, under the constraint that total government revenues stay constant, from equations (35)–(39) and (41)–(43), taking into account
M K M F K 0
dG=dK =dτ =dw =dP =dP =dP = , (44) the function dτL(dθ) can be derived. To obtain this function, it is neces- sary, first of all, to define density distribution function ( )f d . Taking into account that the forests are cut within a certain strip along the roads, it can be assumed that ( )f d = =f const. Then, from (30), (37), (39) it fol- lows that
( d* 1)
F Ef
L eδ
= δ − , (45)
(1 ) ( ) 1 ,
(1 ) (1 ) ( 1)
(1 )
F
F K K d
L K
P Q d
f P
w E e
D D
δ θ
ν ντ θ τ θ
δ τ ∗
− Ψ ∗−
Π = − − −− + + − −
(46)
( ) (1 ) ( 1)
(1 )
K K d
F L
K
P E
f P Q d w e
D ντ δ
θ τ
τ δ ∗
∗ −
Ω = Ψ − − + + − . (47)
From (28), (37) we have
( M F) L L ( M F) K( M F) 0
w L +L dτ +τ w dL +dL +τ dπ + Π + Ω =d d . (48) Substituting into (48) the corresponding differentials obtained from (36), (41), (45), (46), (47) and assuming that δd∗ <<1, the following equation can be obtained:
1 (1 )
1
M L F
M K K K L
L M
wL L Efwd d
L
ε τ τ τ τ θ τ
τ ∗
− + − − + − +
+
( ) (1 ) (1 )
(1 )
K K
F L K
K
P Q P w E fd d
D
ντ τ τ θ
τ ∗
−
+ Ψ − − + + − +
( ) (1 ) ( ) 0
F K K
P Q w E fd d
d
τ τ θ ν ∗
+ Ψ + − − + = , (49)
where εM is the wage elasticity of labor demand in the rest-of-the- economy sector.
From (42) it follows that ( )
(1 ) (1 )
L
K K
K L
d d w d
P w
D ντ τ
δ τ
τ
∗ = −
− + +
−
. (50)
After substituting (50) into (49), the function dτL(dθ) can be easily ob- tained from the following equation:
1 [ (1 ) ]
1
[ (1 )][ (1 )] (1 )
(1 ) (1 )
M L F
K K K
L M
L K K K L L
K K
K L
a L
L
c d
b w Dw
d cP
ε τ τ τ τ θ
τ
ν τ
τ θ τ θ τ θ τ τ
δ τ ν τ
ν τ
∗
− + − − + − −
+
=
− + + − − − − +
−
− + +
−
1 (1 )
(1 )
K K
L K
K
b cP τ ν τ τ dθ
ν τ
−
= − − − + + − , (51)
where LM
a= E fd∗, PF ( )Q
b Ew
= Ψ , c Dw
= ν .
It is assumed that the economy is on the upward-sloping parts of the Laffer curve for labor tax and stumpage fees, i.e.,
0
L
G τ
∂ >
∂ , G 0
∂ >θ
∂ .
Under these conditions, it can be shown that the terms at dτL and dθ in (51) are positive.
Then, from (51) it follows that under reasonable parameter values in- creasing the share of timber rent appropriated by the state under con- stant total budget revenues leads to decreasing payroll tax, which, in turn, leads to higher employment in the rest-of-the-economy sector. Be- sides, the critical distance of timber hauling increases, which leads to higher employment and, consequently, output in the forest sector. The
higher are the values of PFΨ( ) /Q Aw , εM, θ and the lower the value
M/
L Afd∗, the higher is the positive effect of increasing the share of tim- ber rent appropriated by the state.
To estimate the effect of increasing the share of timber rent collected by the state on the regional economy (Novgorod Oblast), the following pa- rameter values have been used:
300000
LM = , 15000LF = , PF =RUB400 /m3,
3
( ) 200m
Q ha
Ψ = ,
0.22persons
E = ha , 40000 /w =RUB cap yr. , fd∗ =104ha, 0.7 10 5persons
D RUB
= ⋅ − , 1
K 0.32
P = yr,
K 0.3
τ = , 0.4τ =L , 0.5θ = , 1 0.2yr
ν = .
The only parameter in (51) that is not easily observable is the wage elas- ticity of labor demand εM. One of the very few attempts to estimate εM for Russia has been undertaken by Konings and Lehmann (2000). The estimated short-term wage elasticity of labor demand for Chuvashiya (which could be considered as being similar to Novgorod Oblast) is about 0.4–0.5. Taking into account that the above-presented economet- ric estimates of the production function parameters refer to the case when no new roads are being built, it is assumed that ( )d d∗ =0. Under fixed d∗, employment and output in forestry do not change. Then the following dependencies can be obtained:
L 0.05
dτ = − dθ , 0.018
M M
dL d
L = θ,
0.007
M M
dF d
F = θ.
Thus, in the relatively short-term perspective, doubling the share of tim- ber rent appropriated by the state leads to increasing regional emplo-
ment and output in the rest-of-the-economy sector by nearly 1% and 0.35%, respectively. It should be noted that these are relatively short- term effects. In the long term perspective, the effects of tax shifting will be more pronounced since long-term wage elasticity of labor demand is several times higher than the short-term one. Thus, the society as a whole gains from tax shifting. The only party that will lose from increas- ing stumpage fees will be those within the forest sector who appropriate a substantial share of timber rent and, as the actual state of affairs re- veal, do not, as a rule, use these revenues for investment into forestry.
8. POLICY IMPLICATIONS