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«Toward More Effective Endangered Species Regulation By Jacob P. Byl Dissertation Submitted to the Faculty of the Graduate School of Vanderbilt ...»

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For landowners in Groups 2 through 4, they also have to decide whether to enter into a safe-harbor agreement or not. If landowners enter into safe-harbor agreements, they limit the amount they can harvest in any period to 5 acres, so there is an added constraint that ℎ ≤ 5. In exchange for limiting their harvests, landowners get assurance from regulators that the landowner will be able to continue harvesting even if woodpeckers do move onto the property, so γ becomes immaterial to them if they intend to stay in the agreement. Landowners in Groups 2 through 4 are offered the opportunity to enter into a € safe-harbor agreement in the first year and have the option of leaving any subsequent year, so each year they decide whether it is more beneficial to be in the agreement or not.

The decision tree including the decisions to enter safe-harbor agreements and whether to harvest are depicted in Figure 1.

To solve this model for the optimal harvest and habitat improvement paths, I use backward induction to solve for the optimal final period behavior, then work forward until all periods have been solved. Optimal harvest and habitat improvement are calculated for landowners who have linear utility functions and place no independent value on conservation, meaning they maximize profit. No discounting is used (෯ = 1), as the time preference for money across the 20 years of the experiment is not likely to matter much in a game that is played in approximately 30 minutes. These optimal behaviors generate predictions for how players in the four groups will play the game.

Group 1 (Strict Regulation): The optimal harvest behavior for landowners in Group 1 who seek to maximize profit is to harvest a large number of trees, 30 acres, in the first year. This lowers the probability that woodpeckers move in to 1%. In each subsequent year, the landowner harvests 5 acres, keeping the probability of woodpeckers close to zero while slowly building money in the account. In the last period, the landowner harvests all 100 acres. The Group 1 landowner does not invest in habitat improvement. The expected profit by following this strategy is $20.44 with an average harvest of 11.0 acres per year and an expected 0.2 woodpeckers on the property at the end of the simulation.

Group 2 (Conservation Agreement): The profit-maximizing strategy for a landowner in Group 2 is to enter into a safe-harbor agreement and harvest zero acres per year for each of the first 19 years. In the 20th year, it is optimal for the landowner to break from the agreement and harvest 100 acres. The Group 2 landowner does not invest in habitat improvement. The expected profit by following this strategy is $25.09 with an average harvest of 5.0 acres per year and an expected 3.0 woodpeckers on the property.

Group 3 (Low Financial Incentives): The profit-maximizing strategy for a landowner in Group 3 is the same as that of a landowner in Group 2 for the first 19 rounds. The Group 3 landowner does not invest in habitat improvement. In the 20th year, the landowner should break out of the agreement and harvest all 100 acres unless there are more than 7 woodpeckers on the property (expected number is 3). Expected profit from following this strategy is $25.12, with an average harvest of 4.9 acres per year and an expected 3.0 woodpeckers.

Group 4 (High Financial Incentives): The optimal strategy for a landowner in Group 4 is to enter a conservation agreement and harvest zero acres per year for the first 19 years. The Group 4 landowner does invest in habitat improvement in each year. In the 20th year, the landowner should stay in the agreement and get paid for woodpecker credits unless there are fewer than 4 woodpeckers on the property (expected number is 5), in which case she should break out of the agreement and harvest all 100 acres. Expected profit from following this strategy is $25.87, with an expected harvest of 2.3 acres per year and an expected 4.5 woodpeckers.

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The optimal harvest paths for landowners in the four groups exhibit properties that can be tested empirically. According to the model, there will be a monotonic decrease in the average harvest as the Group number increases. Group 1 is expected to harvest an average of 11 acres per year, Groups 2 and 3 are expected to harvest 5 acres per year, and Group 4 is expected to harvest an average of 2 acres per year. A second prediction about harvest behavior is that landowners in Group 1 will harvest more acres in the early years of the simulation than landowners in the other groups.

For habitat improvement behavior, the prediction is more stark: the first three groups are not expected to engage in any investment in habitat improvement, while landowners in Group 4 are expected to invest in habitat improvement.

While the above predictions are based on a risk-neutral landowner, the predictions remain similar for risk-averse landowners. For landowners who have a constant relative risk aversion utility function (Mas-Collel et al. 1995), behavior for Groups 1 through 3 remain the same. Landowners in Group 4 switch to a strategy that mimics that of Group 3 landowners when they have a coefficient of relative risk aversion of 1.3 or greater, as those landowners seek the sure profits from timber harvests rather than the uncertain profits from investing in woodpecker habitat.

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more complicated and it is difficult to solve the model for optimal behavior. In general, a taste for conservation is likely to get landowners to harvest fewer acres of trees and invest more in habitat improvement.

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statistics. Since players are randomized into groups, simple averages across groups should be able to tell most of the interesting results. However, regression techniques allow me to control for demographic variables. This can ensure that the experiment’s randomization was successful and allow for additional tests of how demographic variables are correlated with behavior in the game.

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I can also use a double-censored Tobit model for harvest to account for a dependent variable that runs from 0 to 100 and a Probit model for habitat improvement to account for a binary dependent variable. Results are similar with these models, and I report OLS for ease of interpretation of coefficients.

The variables of interest are the dummy variables for groups. The included variables, Groups 2 through 4, can be compared with the omitted category of landowners in Group 1 (Strict Regulation). X is a vector of demographic variables that includes age, sex, race, political party, smoking status, and self-reported risk preferences. Each observation is a participant-year, so each participant has multiple observations.

Accordingly, standard errors are clustered at the participant level to allow for arbitrary correlation among the responses of each participant. Observations include only active participants, meaning that landowners who have been sent to the end of the game because they have woodpeckers on their property that is not currently in a conservation agreement are not included for those years as they had no choices in those years.

Regressions of habitat improvement use a similar model except with a binary dependent variable. Variables of interest and explanatory variables are similar and standard errors are again clustered at the participant level.

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As seen in Chart 1, landowners in all four of the groups tended to harvest a large number of acres in the final rounds, which fits with predictions for rational profitmaximizing behavior. There were also differences across the four groups in both harvest and habitat improvement activity, some of which are harder to explain with a simple profit-maximization model.

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which is significantly more than any other group.7 This behavior fits with the profitmaximizing strategy of harvesting enough in the first few years to get the average age of trees low enough so the probability of woodpeckers moving in was close to zero.

Landowners in the other three groups did not display this behavior of early habitat destruction, probably because most of the landowners in Groups 2-4 (91%) started in conservation agreements that mitigated the consequences if woodpeckers did move in.

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Group 1 facing strict regulation was 8.8 acres. 8 Those in Group 2 harvested an average of

7.8 acres while those in Group 3 harvested 13.0 acres. Since landowners in Group 3 had a financial reason to favor woodpeckers relatively more than landowners in Group 2, it is difficult to explain substantially more harvest activity, which harms woodpeckers, in Group 3. The above profit-maximization model would predict that those offered cash for woodpeckers would harvest fewer trees. The average harvest for Group 4 was 5.8 acres, so higher financial incentives did seem to move landowners toward more habitat conservation.

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model, as reported in Table 4. Groups 2 and 4 have statistically significant coefficients that indicate landowners in these groups harvest an average of 2.4 to 2.9 fewer acres per Statistically significant at 1% level compared with Groups 2 and 4 and at 5% level compared with Group 3 in an ordinary least squares (OLS) model of harvest controlling for age, sex, race, political party, environmentalist, and self-reported risk aversion.

These averages include all landowners who are still active, excluding those who have been sent to the end of the game because they were not in agreements and had woodpeckers on the property.

year, which is a 44% to 53% decrease from the sample-wide average harvest level of 5.5 acres per year. Controlling for demographic and risk-tolerance variables did not meaningfully change the size or significance of coefficients on the variables for the randomly assigned groups.

As seen in the large spikes in the last periods in Chart 1, the average landowner harvests the majority of their trees in the final period. Many landowners (39%) in Groups 2-4 break out of conservation agreements to make these large harvests, with an average 91-acre harvest for this subsample. Table 5 reports regression results predicting which landowners break out of their conservation agreements in the final periods. The only meaningful significant result is that landowners in Group 4 are less likely to break out of their agreements than landowners in Groups 2 and 3.

B. Habitat Improvement Behavior As shown in Table 6, landowners in Groups 1 and 2 did not engage in a substantial amount of habitat improvement, as expected because landowners tend to have no incentives (Group 2) or negative incentives (Group 1) to do so. With relatively weak financial incentives in Group 3, landowners start to invest more in habitat improvement with an average of 19% of landowners improving habitat each year. With stronger financial incentives in Group 4, 30% of landowners improve habitat each year.

Many landowners pair habitat improvement with a large harvest of trees. Of those who improve habitat, 7% of them have recently harvested 20 acres or more of trees. This percentage is even larger for those in groups 1 and 2, with 32% of the habitat improvement behavior coming immediately after a tree harvest over 20 acres. This goes against predictions of profit maximizing behavior, as it is not rational to invest in habitat improvement, which increases the probability of woodpeckers in a multiplicative fashion, directly after a large harvest because the probability of woodpeckers moving in is then zero.

The general result that Group 3 and, especially, Group 4 invest in habitat improvement is confirmed with regression analysis, as reported in Table 7. Those in Group 3 have an 11 percentage point increase in the probability of improving habitat, which is an 80% increase over the sample mean. Those in Group 4 are 20 percentage points more likely to improve habitat, which is a 154% increase over the mean.

C. Landowner Profits The final profits of players in the different groups can tell us something about how well landowners will tend to fare financially in the alternative regulatory regimes.

As seen in Chart 2, average profits increase as landowners make their way to later years in the simulation, with a spike in the final years as many landowners make large tree harvests or redeem credits for woodpeckers on their properties. As shown in Table 8, the average final payout is $16.22 for landowners in Group 1, $20.03 for those in Group 2, $20.33 for those in Group 3, and $22.00 for those in Group 4. All of these amounts are lower than the average payoffs for landowners who follow the optimal profit-maximizing strategy, with average profits about $4 to $5 lower than the predicted payoffs.

D. Woodpecker Populations Although the simulation’s simple model of woodpecker behavior only accounts for the average age of trees on sites, it can still be informative as a proxy for how much potential habitat there is for woodpeckers under the alternative regimes. Chart 3 shows the number of woodpeckers across the 20 years of the simulation for the four groups. In all of the groups, the average number of woodpeckers increases as the simulation progresses and more woodpeckers move onto properties. As shown in Table 9, the average number of woodpeckers in the final year is 1.3 for Group 1, 1.5 for Group 2, 1.8 for Group 3, and 2.1 for Group 4. As predicted in the model, woodpeckers fare better when landowners are offered safe-harbor agreements, and even better when financial incentives are offered.

VII. Discussion of Results and Deviations from Profit-Maximization The results of the experiment suggest that there are regulatory tools that have promise at improving the current adversarial status quo under the ESA. Tools like safeharbor agreements can decrease the amount of habitat destruction, which improves profits for landowners while providing benefits to endangered species. Financial incentives can further encourage landowners to actively invest in habitat improvement, especially when payoffs are high.

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