Markku Ollikainen University of Helsinki, Department of Economics and Management

1. Workshop on forest economics, May 30 – June 1, 2012 Laboratory of Forest Economics LEF, Nancy TheUse of Forest Resources and Amenity Benefits Markku Ollikainen University of Helsinki, Department of Economics and Management

2. 1. Motivation Limitations of typical forest models: • Models are often partial, based on an exogenous resource price • They omit the fact that forest capital is transferred from one generation to another • Utility of consumption and amenity benefits are assumed to be additively separable, which omits the weights citizens place on consumption vis-à-vis amenity benefits Overlapping generations model: a macro economic viewpoint • Forest stock is a factor of production, source of amenities and storeof value • General equilibrium analysis: captures the role of fundaments (technology and preferences) in forest utilization • Transfer of forest capital between generations by trade or inheritance

3. 2. Research problem How does the inclusion of amenity benefits impact the steady-state equilibrium and its stability properties in an economy using forest resources? New aspects in focus: • Amenity benefits: separable and nonseparable utility • The role of the weights given to consumption and amenities, respectively • The role of productivity in making consumption goods from wood • Long run analysis: dynamics and stability of steady state equilibria • Joint work: Amacher-Ollikainen-Puhakka: Renewable Resource Use and Nonseparable Amenity Benefits. A manuscript. Renewable Resource Use and Separable Amenity Benefits. A manuscript.

4. 3. A perfect foresight OG modelForest owners - consumers The lifetime utility function of an agent born at the beginning of a period is V = u(ct1)+βu(ct2) - No amenity valuation V = u(ct1)+βu(ct2)+v(xt)+βv(xt+1) - Separable amenity valuation V = u(ct1,xt)+βu(ct2,xt+1) - Nonseparable amenity valuation where ci : periodic consumption of consumer-worker born at time t, xt: level of the forest stock at the end of period β : the consumer’s rate of time preference The periodic budget constraints for the two period lived consumer are ct1 = ptxt+1+ st= wt ct2 = pt+1(xt+1+g(xt+1))+Rt+1st where p: resource price; w: wage rate and R=1+r: interest rate factor

5. 4. A perfect foresight OG model Production Production function: ct =F(Ht,Lt) • H = harvested amount; L=labor • constant returns to scale technology Production per capita:f(ht) • with ht=Ht/Lt • workers supply inelastically one unit of labor • firm harvests Resource stock xt • Current old generation owns the stock and enjoys its growth g(xt) • Stock available for trading: xt + g(xt) Transition equation: xt+1 = xt – ht + g(xt)

6. 5. Steady state equilibrium Harvesting rules No amenity valuation: (1) Rt+1 = (1+g’(xt+1))(pt+1/pt) Separable amenity benefits (2) Rt+1 = (1+g’(xt+1))(pt+1/pt)+ v’(xt+1)/u1(ct2) Nonseparable amenity benefits (3) Rt+1 = (1+g’(xt+1))(pt+1/pt)+ u2(ct2,xt+1)/u1(ct2,xt+1) Interpretation: Forest is harvested in a way that equalizes the market interest rate factor to (1): the rate of growth, adjusted for relative prices (2) & (3):the sum of rate of growth adjusted for relative prices and the marginal rate of substitution between amenities and consumption

7. 6. Steady state equilibriumDefinition of equilibrium Market clearing conditions (1) c1t + c2t-1= f(ht) (2) xt+1 = xt – ht + g(xt) (3) st = 0 (4) f’(ht) = pt and f(ht) - ht f’(ht) = wt Interpretation • Resource constraint; • (2) Transition equation (3) Equilibrium saving (4) Marginal conditions for profit maximization determine the evolution of factor prices, pt and wt We use: Cobb-Douglas production function hα and a logistic growth function g(x)=ax-½bx2.

8. 7. Steady state equilibriumPlanar system Dynamical system of the model: (0) xt+1 = xt – ht + g(xt) and • (1-α)(xt + g(xt)) = α(xt+1-g(xt+1))/β(1+g’(xt+1)) (2) (1-α)(xt + g(xt)) = xt+1+α(xt+1-g(xt+1))/β{1+g’(xt+1)+v’(xt+1)(xt+1+ g(xt+1))} (3) (xt+1 + g(xt+1)) = xt+2+{A}[1/(1-α)γ] where A =

9. 8. Steady state equilibriumProperties Using parametric specification: Cobb-Douglas production and utility functions we demonstrate Nontrivial stationary equilibrium exists and is unique • Holds true for all three specifications of utility function • Parameter restrictions in each case differ • No amenities: (1+a) > (1+α/β)/ (1-α) • Separable: (1+a) > (1+α/β (γ+1))/ (1-α) • Nonseparable:(1+a) > α1-γ(γ/β)[(1+a)/(a- α (1+a))]1- γ Stability & dynamics: • No amenity valuation: stable saddle point equilibrium • Separability: stable saddle point equilibrium • Nonseparability: bifurcation and indeterminacy possible

10. 9. Empirics Finnish forestry in per capital terms Growth function: g(x)=ax-½bx2 = 0.4x - 0.0008*x2 • MSY-point = 500 m3 • MSY growth = 100 m3 • Makes total 25 Mm3 Productivity of technology: Baseline: α = 0. 1 (fulfills restriction in all cases) • Feasible weights in the utility function γ= {0, 0.46} • γ = 0.4434 reflects MSY (nonseparable amenities)

11. 10. Empirics Comparison of the steady states Table 1. Steady-state stocks and harvesting per capita Comments: • We give equal weight to amenity benefits under separable and nonseparable amenity valuation to facilitate some comparison • Amenity valuation leads to higher steady state stock than the case with no valuation • The two amenity cases differ, thanks to the type of utility function • Stocks are higher under nonseparable utility function than separable functions • Impact of α: lower alpha leads to higher stock for all cases

12. 11. Empirics Forest stock and harvesting - nonseparability Comments: • For gamma values higher than 0.4434, equilibrium lies on the LHS of the growth function; for lower values it is on the RHS of the growth function • As gamma decreases (1-gamma increases) the steady-state stock increases and harvest decreases • Resource is productive in consumption, so that the harvest level remains relatively high even for the lowest values of gamma

13. 12. Empirics Stability of the steady-state equilibrium Conditions for saddle point: {D+T+1 > 0 and D-T+1 < 0}; or {D+T+1 < 0 and D-T+1 > 0} Table 2. Trace and determinant and stability of the system as a function of gamma Structural change in the stability properties of the equilibrium: γ ≥ 0.28478 → D+T+1 > 0 and D-T+1 < 0 → saddle γ ε(0.28478, 0.28477) → saddle node bifurcation → indeterminacy γ ≤ 0.28477→D+T+1 > 0 and D-T+1 > 0 → sink

14. 13. EmpiricsGraphical features of stability Figure 3. Illustration stability of the system sink saddle D+T+1>0 D-T+1>0

15. 14. Policy implications 1. The type of utility function matters • Optimal harvest rate and stock differs under the three alternative utility specifications: numerical simulations demonstrate large impacts • Stability properties differ much! 2. Re-examine what is a reliable policy model • Models based on separable preferences do not necessarily guide forest policies well • Need for empirical research: which specification is relevantand what are the relative weights given to consumption and amenities 3. Nonseparability: possibility of indeterminacy provides a new challenge • Indeterminacy undermines the concept of perfect foresight equilibrium. • When an infinite number of equilibria exist, the model cannot be used to make predictions about the future. • Expectations and market psychology may play an increasing role for the use of the resource and provision of amenity benefits.