Transcript Folie 1

Introduction
Species conservation in the face of political uncertainty
Martin Drechsler/Frank Wätzold (UFZ)
1. Motivation
2. Literature
3. Basic model structure
4. Model analysis
5. Model results
6. Final remarks
Motivation
Examples point to the risk of a „roll back“ in environmental policy,
meaning there is „political uncertainty “!
Motivation
•
Political uncertainty is particularly problematic when there is the
risk of irreversible damage, like the extinction of an endangered
species
•
What are the options of a present government that has the goal of
long-term protection of species but has to expect that a future
government will give less priority to species conservation?
•
Focus on species that require protection measures and
corresponding financial compensation on a regular basis
Motivation
•
Uncertainty exists over the the availability of a budget in future
periods, such that future budgets may be lower than today with a
certain probability
•
Problems of similar structure arise from economic fluctuations as
well as fluctuating donations to non-commercial conservation
funds like WWF
•
An institutional framework for transferring financial resources
into the future may be an independent foundation that in each
period decides how much money shouod be spent for conservation
in the present period and how much should be saved for future
efforts
Motivation
Aim of the paper
Develop a conceptual model for this dynami optimisation problem to
gain a better understanding of relevant ecological and economic
parameters and their interaction in time.
Literature
Integration of ecological and economic knowledge in models
Ando, A, Camm, J., Polasky, S., Solow, A. (1998) Science
Perrings, C. (2003) Discussion paper
Baumgärtner (2003) Ecosystem Health
Dynamic models for biodiversity conservation
Johst, K., Drechsler, M., Wätzold, F. (2002) Ecological Economics
Costello, C., Polasky, S. (2002) Discussion paper
Micro- and macroeconomic dynamic consumption models
 Leland (1968) Quarterly Journal of Economics
Basic model structure
Ecological benefit function
Starting point:
Maximise the survival probability of a species, T, over T+1 periods
t (Dt )  exp( t Dt )
For period t:
with t the species-specific extinction rate and Dt the length of the
period
The survival probability over T+1 periods, each of length Dt, then
is
T
T
T
t 0
t 0
t 0
T  t   exp( t Dt )  exp(Dt  t )
Basic model structure
According to Lande (1993) and Wissel et al. (1994) the extinction rate in
period t is given by
~
a
t  a
Kt
with
Kt : habitat capacity
ã : species specific parameter
a : positive and inverse proportional to the variance in the
population growth rate
Basic model structure
•
Initial habitat capacity be K(0). If certain measures are carried out in a
given period then the habitat capacity in that period (but no longer)
increases to K(0)+t.
•
Species-friendly land-use measures cause costs (assuming constant
marginal costs, such that t=bct).
•
The conservation objective of the (present) government can be
formulated as the maximisation of the survival probability over T+1
periods:
T  exp(SDt )  max
with
S 
T

t 0
1
K (0)
(
 ct )a
b
Basic model structure
Government
Grant gt
Payment pt
Measures
costing ct und increasing
habitat capacity by kt
Agency
gt  ht  εt
εt   σ ,σ 
Fund Ft
Model analysis
Intertemporal allocation problem under uncertainty.
Solution via stochastic dynamic programming:
Value function J ( pt , t )  max
pt
T
T
 Z j  max  
j t
pt
j t
1
(C  p j ) α
pt: control variable (payment)
Boundary conditions
Ft  Ft 1  gt 1  pt 1
0  pt  pt  Ft  gt
(Equation of motion)
Model analysis
Solution for period T
pT*  FT  gT  pT
Solution for period T-1
pT 1*  min(pˆ T 1 , pT 1 )
ht: deterministic component of the grant
s: stochastic variation (s.d.) of the grant
pT 1  FT 1  gT 1
FT 1  gT 1  hT
σ 2 (α  2) / 6
pˆ T 1 

2
FT 1  gT 1  hT  2
pˆ T 1  pT 1
Interiour solution
pˆ T 1  pT 1
Corner solution
Model analysis
Solution pT-k* depends only on the number of consecutive periods with
interior solution (without a corner solution in between) following the
Present period T-k
In the deterministic case the future and particularly the number of
future consecutive periods with interiour solution is known.
In the stochastic case the probability distribution of the number of
consecutive periods with interiour solution can be approximated.
Model results - Example 1: no stochasticity
Optimal payments (dotted line) when grants (solid line) first
fall, then rise and then fall again. The evolution of the fund is
presented by the dashed line.
12
1
(C  pt ) α
10
Magnitude
8
6
4
2
0
0
2
4
Period
6
8
pt
Model results - Example 2: stochasticity, no trend
Distribution of the number l of consecutive periods with interiour solution: P(l)
Optimal Payment under the assumption of exactly l periods with interiour
solution following: pt(l)
Optimal payment in period t=0:
p0 *  h 
(a  2) s (ln(T )  1)
6 (h  1) 2T (T  1)
2
2
s: uncertainty in the grants
a: ecological parameter
(shape of the benefit function)
h: mean of the grants
Uncertainty reduces the optimal payment („precautionary saving“,
Leland 1968).
The larger a, the more is saved
Model results - Example 3: negative trend plus stochasticity,
3 periods t=0,1,2
For small and for large s (uncertainty in the grants):
σ 2 (α  2) / 12
p0*  h0  δ 
h0  C
Uncertainty reduces the optimal
payment („precautionary saving“)
Für median s :
s: Uncertainty in the grants
a: ecological parameter
h0: grant in periode t=0
d: negative trend in the grants
C: constante
σ 2 (α  2) / 12  3 δ 
p0*  h0 
 δ  
h0  C
 4 2σ 
p0* can increase with s („precautionary spending“)
– effect of s ambiguous!
But latter equation can be approximated by former with error <3%.
Therefore the effect of s is clear with negligible error.
Final remarks
• Even allocation of the payments should be aimed at, as long as the
boundary conditions (non-negativity of the fund) allow for it
• Stochasticity large or small against the trend:
stochasticity reduces the optimal payment, i.e. save more
- the larger a (i.e., in species with weakly fluctuating population
growth), the more should be saved
• Stochasticity of similar magnitude as the trend:
stochasticity may increase optimal payment, but only marginally
• Consideration of interest rates complicated and ambiguous
• Further research: Analysis of the problems of political uncertainty
with respect to a concrete species conservation programme