Policy Instruments and Incentives for Coordinated Habitat Conservation

Abstract

Nearly half of imperiled species (IS) listed under the US Endangered Species Act have most of their habitat on private land. Management of IS therefore relies on engaging private landowners in conservation to avoid listing and the accompanying land use restrictions. Two types of voluntary policy instruments are used to incentivize conservation on private lands: subsidies and voluntary conservation agreements with assurances (VCAAs), under which landowners implement conservation practices in return for assurance that no land use restrictions will be imposed if the practices are maintained. No prior work compares landowners’ incentives for strategic behavior under these instruments. This is important because habitat quality is influenced by landscape size, connectivity, and composition. The probability that an IS becomes listed—and the economic risks facing landowners—depends endogenously on management decisions by multiple landowners. We use theoretical and experimental approaches to compare conservation effort, spatial allocation of this effort, and cost-effectiveness of species protection under each instrument when species protection requires spatially-contiguous coordination. We find that VCAAs with land use restrictions are no more effective than land use restrictions with or without subsidies in coordinating conservation effort, and they do not result in greater species protection. Land use restrictions—either alone or coupled with subsidies—improve coordination.

Appendix

This “Appendix” contains proofs of Propositions 1–3 and supplementary experimental results.

Proof of Proposition 1

Consider first the payoff-dominant equilibrium of game Γ^LUR. Joint payoffs to both farmers at Nash equilibrium (C, C) and (NC, NC) are $2\left( {\omega - c} \right)$ and $2\left( {\omega - L} \right)$, respectively. The equilibrium (C, C) is payoff-dominant if

$$ 2\left( {\omega - c} \right) - 2\left( {\omega - L} \right) > 0 \Rightarrow L > c, $$

where the final inequality holds by assumption.

Next, consider risk-dominance. By symmetry and homogeneity, the product of the payoff deviations is $\left[ {\omega - c - \left( {\omega - L} \right)} \right]^{2} = \left( {L - c} \right)^{2}$ at the (C, C) equilibrium and $\left[ {\omega - L - \left( {\omega - c - L} \right)} \right]^{2} = c^{2}$ at the (NC, NC) equilibrium. Hence, the equilibrium (NC, NC) is risk-dominant if

$$ c^{2} > \left( {L - c} \right)^{2} \Rightarrow L /c < 2. $$

(4)

Note that L/c > 1 by assumption. However, the relationship in Eq. (4) holds trivially for 0 ≤ L/c ≤ 1 since (NC, NC) would be the payoff-dominant equilibrium in that case; the payoff- and risk-dominant equilibria would coincide and Γ^LUR would no longer be a coordination game.

Proof of Proposition 2

Joint payoffs to both farmers at Nash equilibrium (C, C) and (NC, NC) are $2\left( {\omega - c\sigma \beta } \right)$ and $2\left( {\omega - L} \right)$, respectively. The equilibrium (C, C) is payoff-dominant if

$$ 2\left( {\omega - c\sigma \beta } \right) - 2\left( {\omega - L} \right) > 0 \Rightarrow L > c\sigma \beta . $$

The (NC, NC) equilibrium is risk-dominant if the product of the payoff deviations at (NC, NC) is greater than the product of the payoff deviations at (C, C):

$$ \left[ {\omega - L - \left( {\omega - c\sigma - L} \right)} \right]^{2} > \left[ {\omega - c\sigma \beta - \left( {\omega - L} \right)} \right]^{2} \Rightarrow L /c < \sigma \left( {1 + \beta } \right). $$

Hence, the chance of coordination failure remains under Γ^sub since the payoff- and risk-dominant equilibria may generally differ.

Next, we show that coordination failure is less likely in Γ^sub than in Γ^LUR since p^sub > p^LUR. Formally, p^sub is chosen to make player i indifferent between conserving (s_i = C) and not conserving (s_i = NC) and solves:

$$ \begin{aligned} & p^{\text{sub}} \left( {\omega - c\sigma \beta } \right) + \left( {1 - p^{\text{sub}} } \right)\left( {\omega - c\sigma - L} \right) = p^{\text{sub}} \left( {\omega - L} \right) + \left( {1 - p^{\text{sub}} } \right)\left( {\omega - L} \right) \\ & \quad \quad \quad \quad \quad \Rightarrow p^{\text{sub}} = \frac{c\sigma }{{c\sigma \left( {1 - \beta } \right) + L}}. \\ \end{aligned} $$

Note that β = σ = 1 under land use restrictions alone. Hence, we can write the risk factor in this case as

$$ p^{\text{LUR}} = c /L > p^{\text{sub}} . $$

Proof of Proposition 3

Consider first the payoff-dominant equilibrium of game Γ^V. Joint payoffs to both farmers at Nash equilibria (C, C) and (V, V) are $2\left( {\omega - c} \right)$ and $2\left( {\omega - \hat{c}} \right)$, respectively. The equilibrium (C, C) is payoff-dominant if

$$ 2\left( {\omega - c} \right) - 2\left( {\omega - \hat{c}} \right) > 0 \Rightarrow \hat{c} > c, $$

where the final inequality holds by assumption.

Next, consider risk-dominance. By symmetry and homogeneity, the product of the payoff deviations is $\left[ {\omega - c - \left( {\omega - \hat{c}} \right)} \right]^{2} = \left( {\hat{c} - c} \right)^{2}$ at (C, C) and $\left[ {\omega - \hat{c} - \left( {\omega - c - L} \right)} \right]^{2} = \left[ {L - \left( {\hat{c} - c} \right)} \right]^{2}$ at (V, V). Hence, the (V, V) is risk-dominant if

$$ \left[ {L - \left( {\hat{c} - c} \right)} \right]^{2} > \left( {\hat{c} - c} \right)^{2} \Rightarrow L /\left( {\hat{c} - c} \right) > 2. $$

Next, we show that coordination failure is more likely in Γ^V than in Γ^LUR or Γ^sub. The farmers’ risk factor under VCAAs with land use restrictions, p^V, solves

$$ \begin{aligned} & p^{\text{V}} \left( {\omega - c} \right) + \left( {1 - p^{\text{V}} } \right)\left( {\omega - c - L} \right) = \omega - \hat{c} \\ & \quad \quad \Rightarrow p^{\text{V}} = \frac{{L - \left( {\hat{c} - c} \right)}}{L} > p^{\text{LUR}} = \frac{c}{L} > p^{\text{sub}} \\ \end{aligned} $$

(5)

The first inequality in the second line of (5) follows from the assumption that L − ĉ > 0 (see main text). The second inequality follows from Proposition 2. Note that this result holds for any c < ĉ < L, implying the ordering in (5) will arise for any reasonable model parameterization.

1.1 Supplementary Experimental Results

Table 5 compares the mean experimental outcomes across treatments but restricts the data to the first treatment presented in each session. This comparison controls for possible correlation across groups arising from shuffling group members before each treatment. Table 6 compares the experimental outcomes across treatments but restricts the data to the final round of each treatment. This comparison determines whether differences across treatments are robust to learning by participants.

See Tables 5 and 6.

Table 5 Experimental group-level conservation results for first treatment presented in each session

Table 6 Experimental group-level conservation results using data from the last round of each treatment