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*≈*RUB*150 /*m*^{3},τ ≈_{A} *RUB*25 /*m*^{3}, *P*≈*RUB*300 /*m*^{3}), 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* Ψ*Q* −*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*

*L**F* *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
*L**M*and capital *K*_{M} according to production function

( , )

*M* *M* *M*

*F* *L* *K* , (33)

which is assumed to be linearly homogeneous in its production factors,
with capital *K*_{M} 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, τ_{L} and
τ*K* respectively, and collects stumpage fees at the level τ_{A} 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 F**M M* *K**M* *L* *wL**M*

π = −ν − +τ , (36)

0

( ) ( )

*d*

*F* ^{∗}π*F* *x f x dx*

Π =

### ∫

^{,}

^{(37)}

( ) ( ) (1 ) ( ) ( )

*F* *P**F* *Q* *P k d**K* *L**wl 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

( ) ( )

*A**d* *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* =*d*τ =*dw* =*dP* =*dP* =*dP* = , (44)
the function *d*τ_{L}(*d*θ) 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* *e*^{δ}

= 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 d*τ +τ *w dL* +*dL* +τ *d*π + Π + Ω =*d* *d* . (48)
Substituting into (48) the corresponding differentials obtained from (36),
(41), (45), (46), (47) and assuming that δ*d*_{∗} <<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 ε_{M} 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 *d*τ_{L}(*d*θ) 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 *d*θ

ν τ

−

= − − − + + − , (51)

where
*L**M*

*a*= *E fd*_{∗}, *P*_{F} ( )*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 *d*τ_{L} and *d*θ 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 *P*_{F}Ψ( ) /*Q* *Aw* , ε_{M}, 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

*L**M* = , 15000*L*_{F} = , *P*_{F} =*RUB*400 /*m*^{3},

3

( ) 200*m*

*Q* *ha*

Ψ = ,

0.22*persons*

*E* = *ha* , 40000 /*w* =*RUB* *cap yr*. , *fd*_{∗} =10^{4}*ha*,
0.7 10 5*persons*

*D* *RUB*

= ⋅ − , 1

*K* 0.32

*P* = *yr*,

*K* 0.3

τ = , 0.4τ =_{L} , 0.5θ = , 1
0.2*yr*

ν = .

The only parameter in (51) that is not easily observable is the wage elas-
ticity of labor demand ε_{M}. One of the very few attempts to estimate ε_{M}
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

*d*τ = − *d*θ ,
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**