Forest Management and Landowners’ Discount Rates in the Southern United States

Abstract

In theory, decisions with long-term pay-offs, such as whether to invest in forest management, are influenced by time preferences. However, this relationship is difficult to test empirically and time preferences are often assumed constant across individuals. We examine the relationship between forest management behavior and personal discount rates by modeling forest management choices as a function of individual discount rates elicited through binary choice questions. We focus on “limited resource woodland owners” in the Southern United States, including landowners who are traditionally underserved by public institutions (i.e., minorities and women) and who face financial, social and natural resource constraints that limit their forest management options. We found that the probability of harvesting timber is positively related with personal discount rates, as predicted by theory. However, discount rates are not significantly related to stand improvements or contact with a professional forester, suggesting that lack of investment in forest management is not a result of landowner impatience. Rather, these behaviors are driven by characteristics such as size of property, proximity of residence to woodlands, and tenureship characteristics including whether the woodlands are inherited.

Appendices

Appendix

First Order Conditions

Re-stating the Lagrangean function (from Eq. 5.3)

$$ \begin{aligned} L \,=\, & U_{1} [C_{1} ,N_{1} ;Z] + \lambda_{N1} (N_{1} - N_{1} (K - X_{1} ,E_{1} )) + \lambda_{C1} (C_{1} - P \,\cdot \,H(X_{1} ,E_{1} ) + O_{1} (E_{1} ) + S - M_{1} ) \\ & + \frac{1}{1 + r} \,\cdot \,\left( {U_{2} [C_{2} ,N_{2} ;Z] + \lambda_{N2} (N_{2} - N_{2} (Q_{2} ,E_{2} ))} \right) \\ & + \left( {\frac{1}{1 + r}} \right) \,\cdot\, \lambda_{C2} \left( {C_{2} - P \,\cdot \,H(K - X_{1} - Q_{2} ,E_{2} ) + O_{2} (E_{2} ) - (1 + R)S - M} \right) \\ \end{aligned} $$

(A.1)

Maximize Eq. A.1 with respect to C₁, C₂, N₁, N₂, X₁, E₁, E_2, S, and Q₂

$$ \frac{\partial L}{{\partial C_{1} }} = \frac{{\partial U_{1} }}{{\partial C_{1} }} + \lambda_{C1} = 0 \to \lambda_{C1} = - \frac{{\partial U_{1} }}{{\partial C_{1} }} $$

$$ \frac{\partial L}{{\partial C_{2} }} = \frac{{\partial U_{2} }}{{\partial C_{2} }} + \lambda_{C2} = 0 \to \lambda_{C2} = - \frac{{\partial U_{2} }}{{\partial C_{2} }} $$

$$ \frac{\partial L}{{\partial N_{1} }} = \frac{{\partial U_{1} }}{{\partial N_{1} }} + \lambda_{N1} = 0 \to \lambda_{N1} = - \frac{{\partial U_{1} }}{{\partial N_{1} }} $$

(A.2)

$$ \frac{\partial L}{{\partial N_{2} }} = \frac{{\partial U_{2} }}{{\partial N_{2} }} + \lambda_{N2} = 0 \to \lambda_{N2} = - \frac{{\partial U_{2} }}{{\partial N_{2} }} $$

(A.3)

$$ \frac{\partial L}{\partial S} = \lambda_{C1} - \lambda_{C2} \frac{(1 + R)}{(1 + r)} = 0 \to \lambda_{C2} = \frac{(1 + r)}{(1 + R)} \,\cdot \,\lambda_{C1} $$

(A.4)

$$ \begin{array}{*{20}l} {\frac{{\partial L}}{{\partial X_{1} }} = \lambda _{{N1}} \frac{{\partial N_{1} }}{{\partial X_{1} }} - \lambda _{{C1}} P\frac{{\partial H}}{{\partial X_{1} }} + \lambda _{{C2}} \left( {\frac{1}{{1 + r}}} \right)P\frac{{\partial H}}{{\partial X_{1} }} = 0} \hfill \\ { \to \lambda _{{N1}} \frac{{\partial N_{1} }}{{\partial X_{1} }} + \lambda _{{C2}} \left( {\frac{1}{{1 + r}}} \right)P\frac{{\partial H}}{{\partial X_{1} }} = \lambda _{{C1}} P\frac{{\partial H}}{{\partial X_{1} }}} \hfill \\ \end{array}$$

$$ \frac{\partial L}{{\partial E_{1} }} = \lambda_{C1} \left( {\frac{{\partial O_{1} }}{{\partial E_{1} }} - P \,\cdot\, \frac{\partial H}{{\partial E_{1} }}} \right) - \lambda_{N1} \left( {\frac{{\partial N_{1} }}{{\partial E_{1} }}} \right) = 0 $$

(A.5)

$$ \frac{\partial L}{{\partial E_{2} }} = \lambda_{C2} \left( {\frac{{\partial O_{2} }}{{\partial E_{2} }} - P\frac{\partial H}{{\partial E_{2} }}} \right) - \lambda_{N2} \frac{{\partial N_{2} }}{{\partial E_{2} }} = 0 $$

$$ \frac{\partial L}{{\partial Q_{2} }} = - \frac{{\partial N_{2} }}{{\partial Q_{2} }}\lambda_{N2} + P \,\cdot \,\frac{\partial H}{{\partial Q_{2} }} \,\cdot \,\lambda_{C2} = 0 \to \lambda_{C2} = \lambda_{N2} \frac{{{{\partial N_{2} } \mathord{\left/ {\vphantom {{\partial N_{2} } {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}{{{{P \,\cdot \,\partial H} \mathord{\left/ {\vphantom {{P \,\cdot \,\partial H} {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }} \,}} $$

(A.6)

Setting Eq. A.6 equal to Eq. A.4, we get:

$$ \lambda_{N2} \frac{{{{\partial N_{2} } \mathord{\left/ {\vphantom {{\partial N_{2} } {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}{{{{P \,\cdot \,\partial H} \mathord{\left/ {\vphantom {{P \,\cdot\, \partial H} {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}} = \lambda_{C1} \frac{(1 + r)}{\alpha (1 + R)} \to \lambda_{C1} = \lambda_{N2} \frac{(1 + R)}{(1 + r)}\frac{{{{\partial N_{2} } \mathord{\left/ {\vphantom {{\partial N_{2} } {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}{{{{P \,\cdot \,\partial H} \mathord{\left/ {\vphantom {{P \,\cdot\, \partial H} {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}} $$

(A.7)

Substitute Eq. A.7 into Eq. A.5:

$$ \lambda_{N2} \frac{(1 + R)}{(1 + r)}\frac{{{{\partial N_{2} } \mathord{\left/ {\vphantom {{\partial N_{2} } {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}{{{{P \cdot \partial H} \mathord{\left/ {\vphantom {{P \cdot \partial H} {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}\left( {\frac{\partial O}{{\partial E_{1} }} - P \cdot \frac{\partial H}{{\partial E_{1} }}} \right) = \lambda_{N1} \left( {\frac{{\partial N_{1} }}{{\partial E_{1} }}} \right) $$

(A.8)

Substitute Eqs. A.2 and A.3 into Eq. A.8 and rearranging terms:

$$ \frac{{\partial U_{1} }}{{\partial N_{1} }} \cdot \frac{{\partial N_{1} }}{{\partial E_{1} }} = \left( {\frac{\partial O}{{\partial E_{1} }} - P \cdot \frac{\partial H}{{\partial E_{1} }}} \right)\frac{{\left( {\frac{{\partial U_{2} }}{{\partial N_{2} }} \cdot \frac{{\partial N_{2} }}{{\partial Q_{2} }}} \right)}}{{{{P \cdot \partial H} \mathord{\left/ {\vphantom {{P \cdot \partial H} {\partial Q_{2} }}} \right. \kern-0pt} {\partial Q_{2} }}}}\frac{(1 + R)}{(1 + r)} $$

(A.9)

Survey Module for Eliciting Personal Discount Rates

Suppose that you are given 50 acres of woodland about a mile away from your house. This woodland has a mixture of pines and hardwoods and a mixture of different size trees. A forester takes a look at this woodland and gives you two choices: Choice A or Choice B.

(1)	Choice A	Choice B
	You cut and sell all of the trees now and replant with pine seedlings. You earn $(P321) per acre. Every 32 years, you cut and replant all of your trees and earn $(P321) per acre. Your earnings already include all cost	You cut and sell some of the trees now and let them grow back on their own. You earn $(P8 1) per acre. Every 8 years you cut some more trees and earn $(P8 1) per acre. Your earnings already include all costs
	This choice gives you more money each time you sell, but you wait longer between harvests	This choice gives you less money each time you sell, but you don’t wait as long between harvests

Which would you pick?

• □1 Choice A

• □2 Choice B

• □3 Neither

Now suppose that you end up with a different piece of woodland and the forester gives you the following two new choices: Choice A or Choice B.

(2)	Choice A	Choice B
	You cut and sell all of the trees now and replant with pine seedlings. You earn $(P321) per acre. Every 32 years, you cut and replant all of your trees and earn $(P321) per acre. Your earnings already include all costs	You cut and sell some of the trees now and let them grow back on their own. You earn $(P8 1) per acre. Every 8 years you cut some more trees and earn per $(P8 1) acre. Your earnings already include all costs
	This choice gives you more money each time you sell, but you wait longer between harvests	This choice gives you less money each time you sell, but you don’t wait as long between harvests

Which would you pick?

• □1 Choice A

• □2 Choice B

• □3 Neither