Species conservation in the face of political uncertainty

Martin Drechsler/Frank Wätzold (UFZ)

1. Motivation2. Literature3. Basic model structure4. Model analysis5. Model results6. Final remarks

Introduction

Examples point to the risk of a „roll back“ in environmental policy, meaning there is „political uncertainty “!

Motivation

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.

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

Literature

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

Ecological benefit function

Basic model structure

Starting point:Maximise the survival probability of a species, T, over T+1 periods

The survival probability over T+1 periods, each of length t, then is

T

t

T

ttt

T

ttT tt

0 00

)exp()exp(

with t the species-specific extinction rate and t the length of the period

For period t: )exp()( tt tt

According to Lande (1993) and Wissel et al. (1994) the extinction rate in period t is given by

with

Kt : habitat capacity

ã : species specific parameter

: positive and inverse proportional to the variance in the population growth rate

t

tK

a~

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).

T

ttc

bK

S0

)0(

)(

1

max)exp( tST with

• The conservation objective of the (present) government can be formulated as the maximisation of the survival probability over T+1 periods:

Basic model structure

Government

Agency

Fund Ft

Measurescosting ct und increasing

habitat capacity by kt

Grant gt

Payment pt

ttt εhg

σσεt ,

Basic model structure

T

tjα

jp

T

tjj

pt pC

ZtpJtt )(

1maxmax),(Value function

pt: control variable (payment)

Model analysis

tttt gFpp 0

111 tttt pgFF (Equation of motion)Boundary conditions

Intertemporal allocation problem under uncertainty.

Solution via stochastic dynamic programming:

2

6)2(

2ˆ

11

211

1

TTT

TTTT hgF

/ασhgFp

111 TTT gFp

),ˆmin(* 111 TTT ppp

Solution for period T-1

11ˆ TT pp

11ˆ TT pp

Interiour solution

Corner solution

Model analysis

TTTT pgF*p

Solution for period T

ht: deterministic component of the grant: stochastic variation (s.d.) of the grant

Model analysis

Solution pT-k* depends only on the number of consecutive periods withinterior solution (without a corner solution in between) following thePresent 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.

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.

Model results - Example 1: no stochasticity

Period

0 2 4 6 8

Mag

nitu

de

0

2

4

6

8

10

12

αtpC )(

1

tp

Distribution of the number l of consecutive periods with interiour solution: P(l)

Optimal Payment under the assumption of exactly l periods with interioursolution following: pt(l)

Uncertainty reduces the optimal payment („precautionary saving“,Leland 1968).The larger , the more is saved

Model results - Example 2: stochasticity, no trend

)1(2

)1)(ln(

)1(6

)2(*

22

0

TT

T

hhp

Optimal payment in period t=0:

: uncertainty in the grants: ecological parameter(shape of the benefit function)h: mean of the grants

Model results - Example 3: negative trend plus stochasticity, 3 periods t=0,1,2

: Uncertainty in the grants: ecological parameterh0: grant in periode t=0: negative trend in the grantsC: constante

For small and for large (uncertainty in the grants):

Ch

/ασδh*p

0

2

00

12)2(

But latter equation can be approximated by former with error <3%. Therefore the effect of is clear with negligible error.

Uncertainty reduces the optimal payment („precautionary saving“)

Für median :

σ

δδ

Ch

/ασh*p

24

312)2(

0

2

00

p0* can increase with („precautionary spending“)– effect of ambiguous!

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

• Consideration of interest rates complicated and ambiguous

• Stochasticity large or small against the trend: stochasticity reduces the optimal payment, i.e. save more - the larger (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

• Further research: Analysis of the problems of political uncertainty with respect to a concrete species conservation programme