1

The intersection between climate adaptation, mitigation, and natural

resources: An empirical analysis of forest management

Yukiko Hashida1

&

David J. Lewis

October 25, 2017

Abstract

This paper develops a new empirical framework to model adaptation to climate change and a carbon price by private forestland owners, with application to the Pacific coast of the United States. The estimated discrete-choice econometric model is used as the empirical basis for a dynamic simulation of the time-path of landscape change under both climate change and carbon price scenarios. We find that along the U.S. Pacific coast, landowners shift out of their current dominant tree species choice of Douglas-fir to species more suitable for the future climate, notably hardwood and ponderosa pine. Results suggest that a carbon price policy would further accelerate such adaptation behavior, where carbon pricing has a larger effect on the adaptation away from Douglas-fir than the effects of climate change. This paper contributes to the literature by developing a framework to econometrically model and simulate extensive margin adaptation in forestry, and by showing the potential for carbon pricing to create other externalities from altering habitat within forests. JEL classification: Q23, Q54, Q57 Keywords: Climate change adaptation, ecosystem services, forestry, landscape simulation, land-use modeling, micro-econometrics

1 Yukiko Hashida is senior author and corresponding author, and is at the Yale University, School of Forestry and Environmental Studies (yukiko.hashida@yale.edu). David Lewis is at the Oregon State University, Department of Applied Economics (lewisda@oregonstate.edu). Funding support from the USDA Forest Service Pacific Northwest Research Station (14-JV-11261955-059) and USDA National Institute for Food and Agriculture is gratefully acknowledged. We are grateful to Darius Adams for his invaluable advice and guidance, and to Andrew Gray, Jeff Kline, David Kling, Christian Langpap, and Brent Sohngen as well as participants at the Oregon Resource and Environmental Economics Workshop, 2016 Association of Environmental and Resource Economists Summer Conference, and seminars at Oregon State University.

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1. Introduction

Recent literature that quantifies the economic damage from climate change has

emphasized the benefits of using empirically-derived human-climate linkages regarding the

effects of climate on the value of agricultural land (Schlenker et al. 2006), labor markets (Graff

Zivin and Neidell 2014), and electricity demand (Auffhammer et al. 2017). Notably absent from

attempts to combine empirically-derived human-climate linkages into damage functions are

estimates of climate’s impact on the market value of forestland and non-market changes in

biodiversity (Carleton and Hsiang 2016). Private forestland value and biodiversity have an

important interactive effect when considering climate impacts. By changing the productive

capacity of land to grow trees, climate change can induce landowner adaptation through

adjustments on the intensive margin (e.g. altering the timing and intensity of harvests) and

through extensive margin changes in tree species planting (Guo and Costello 2013). And since

extensive margin changes in planted tree species are a type of land-use change, climate change

impacts on forest biodiversity operate through landowner adaptation behavior. Habitat loss and

degradation have long been implicated as the primary driver of biodiversity loss (Wilcove et al.

1998), and many forest wildlife species of conservation concern are habitat specialists that are

sensitive to extensive margin tree species changes.2 Further, climate and forests intersect through

the sequestration ability of forests. A carbon price policy aimed at mitigating climate change

creates carbon rents that vary across alternative tree species depending on their sequestration

rates (Ekholm 2016), and so a carbon price can either accelerate or push back on extensive

margin adjustments and corresponding habitat changes which impact biodiversity.

This paper develops a new empirical framework to model adaptation to climate change

and a carbon price by private forestland owners, with application to the Pacific coast of the

United States. We use rich plot-level data from the USDA Forest Service Forest Inventory and

Analysis (FIA) Project to empirically link recent observations of forest management choices with

downscaled climate variables, land quality, tree growth, and stumpage prices. We focus on the

management choices of harvest timing and intensity, and the choice of tree species to replant or

regenerate after harvest. The study area has a substantial portion of its landscape dedicated to

2 For an example from our study region, the U.S. State of Oregon’s Conservation Strategy (Oregon Department of Fish and Wildlife 2016) emphasizes that many wildlife forest habitat specialists (e.g. ringtail, fisher, red tree vole, etc.) require specific forest types like ponderosa pine, oak woodland, and mature coniferous forests.

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commercial forest production, including some of the most productive forests in the world.3 We

estimate a plot-level discrete-choice econometric model of management choices as a function of

timber prices, yields, site productivity, and measures of climate that correspond to the plot. The

discrete-choice econometric framework adopts a nesting structure that accounts for the

simultaneous nature of harvest and replanting choices, as well as climate-influenced natural

disturbances like wildfire. Our key source for identifying climate adaptation in forestry is to

exploit spatial variation in climatic variables and replanting choices across recently harvested

timber plots, controlling for a rich set of fine-scale information on key drivers of rents from

replanting or regenerating specific tree species. By directly modeling forest management

decisions as a function of climate, we estimate how climate influences economic outcomes

through what Hsiang (2016) calls belief effects – effects of climate change that occur because

individual beliefs about climate affect their decisions.

The estimated econometric model is used to develop a set of plot-level management

decision rules that are used in a dynamic simulation of the time-path of landscape change under

both climate change and carbon pricing scenarios. Since forest replanting only occurs upon

harvest, the simulation generates the share of forestland harvested and subsequently replanted in

repeated 10-year intervals as a function of climate and other economic factors. As climate

conditions change, the model reflects changes in climate variables and choice sets of tree species

types that are biophysically suited to each plot under the scenario. To reflect the renewable

characteristics of forest resources, growth in timber volume is accounted for with empirically-

calibrated yield curves. We simulate a carbon price scenario that pays directly for carbon

sequestration on a timber plot using carbon yield curves calibrated to each tree species and site

class, which allows us to analyze carbon rents which differ across planted tree species. The

empirically-driven simulations generate landscape-scale outcomes that represent the fundamental

economic decision rules inherent in private timber management. Wildfire is endogenous in the

simulation. We focus in particular on how the landscape’s composition of tree species will be

affected by both climate change and a carbon pricing policy, as the composition of tree species

affects market timber supply and non-market ecosystem services such as wildlife habitat. Natural

scientists emphasize that a key pathway for climate change to impact wildlife and ecosystem

3 Approximately 30%, 44%, and 45% of non-federal rural lands are forest land in the states of California, Oregon, and Washington, respectively.

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services is through changes in land cover and habitat (Lawler et al. 2014; Settele et al. 2015;

McGuire et al. 2016), and so developing an understanding of forest management decisions under

both climate change and climate policy is essential for better understanding the impacts of

climate change and conservation policy on biodiversity and ecosystem services.

2. Relationship to existing literature

This paper’s primary contribution is to develop an empirically-based framework to

analyze the effects of climate change on adaptation within managed forestry. Our analysis relates

and contributes to at least four broad sets of relevant literature on climate change and land-use

modeling. First, our explicit modeling of how human adaptation to climate change affects

landscape structure is in sharp contrast to the voluminous natural science literature on climate

and natural resources, which largely ignores human management. Understanding the speed of

climate change impacts on a forest landscape requires a representation of four key mechanisms,

including: i) the timing of timber rotation decisions as a function of the current state of the forest

(i.e. age, existing tree species, etc.), ii) the intensity of harvest (i.e. clear-cutting, partial cutting

that leaves some standing trees, etc.), iii) the tree-species with which to replant upon harvest, and

iv) the risk of natural disturbance facing stands of growing trees. Many natural scientists use

empirical approaches to show how different tree types are linked to climate and how these tree

types may respond to changes in climate (Coops and Waring 2011; Hanewinkel et al. 2012;

Iverson and McKenzie 2013; Prasad et al. 2013; Rehfeldt et al. 2014). Importantly, this literature

does not explicitly consider how tree species will move across the landscape, nor does it consider

how human management may facilitate movement. Moving from the current forest landscape to

a new forest landscape in, say, 2100 occurs with gradual dynamic adjustments resulting from the

above four mechanisms of harvest timing, harvest intensity, replanting, and natural disturbance.

Thus, a major gap in the literature on climate change and natural resources is in understanding

the time path of how a landscape can change when it is comprised of many individual

landowners responding to climate change, market conditions and climate policy. Past work in

economics has shown that economic profitability has a strong influence on how managers have

altered tree species in vast swaths of forest in the U.S. southeast (Alig and Butler 2004; Sohngen

and Brown 2006).

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Second, our empirical analysis of forestland owners’ adaptation to climate change

contributes to the forest sector modeling literature (McCarl et al. 2000) and the integrated

assessment model literature that links climate and economic models (Sohngen and Mendelsohn

1998; Hanewinkel et al. 2012; Joyce et al. 2014; Tian et al. 2016). Large-scale integrated

assessment models have greatly advanced our understanding of how climate change – and

carbon pricing – can affect timber prices, forest investments, and the distribution of forests.

However, this literature assumes adaptation behavior in contrast to our approach of empirically

estimating adaptation behavior. In that respect, our analysis shares similarities with the literature

on agriculture and climate change that have empirically studied adaptation implicitly through the

effects of climate change on land prices (Mendelsohn et al. 1994; Schlenker et al. 2006;

Deschênes and Greenstone 2007), and explicitly by econometrically modeling the choice of

crops to plant as a function of climate (Seo and Mendelsohn 2008). No similar econometric

studies of adaptation exist for forestland, though Guo and Costello (2013) and Hannah et al.

(2011) use numerical dynamic programming techniques to examine the value of adaptation and

how climate change can optimally affect forest structure in California. Our approach is inspired

by the theoretical framework advanced by Guo and Costello (2013), and we contribute to this

earlier work by econometrically estimating adaptation behavior with the attendant strength of

basing a land-use model off revealed rather than assumed decisions (Stavins 1999). By using

revealed behavior, we implicitly accommodate landowner unobservables and heterogeneity in

objectives across ownership types.

Third, our integration of an econometric model of forest management with a landscape

simulation model contributes to a similar set of analyses that study changes in broad land uses

(e.g. agriculture to forest; development of forest into urban; etc.) by explicitly modeling land-use

decisions within forestry, rather than treating forest as simply a composite land-use category.

Econometric land-use models integrated with landscape simulations have studied, for example,

broad land use changes in response to carbon payments (Lubowski et al. 2006), how

conservation payments may affect the spatial structure of broad land-use categories (Lewis and

Plantinga 2007), how urban development will respond to changes in local regulatory policies

(Newburn and Berck 2006; Dempsey and Plantinga 2013), and how broad land-use changes can

affect ecosystem service provision (Lawler et al. 2014). Past econometric land-use models have

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largely not incorporated climate change4 and have mostly not analyzed changes within broad

land-use types such as forestry.

Fourth, our explicit empirical modeling of both harvest and replanting decisions within

forestry expands upon previous studies of the effects of carbon payments on land-use. Previous

studies within forestry focused on the effect of carbon prices on harvest decisions, as carbon

prices alter the trade-offs facing forest owners when they make their harvest decisions (van

Kooten et al. 1995; Guthrie and Kumareswaran 2008; Susaeta et al. 2014; Ekholm 2016; Latta et

al. 2016). In contrast, this study explicitly incorporates carbon prices as a factor that also affects

the replanting choice by differentiating the volume of carbon uptake by each species. Previous

land-use change studies focused on how carbon payments affect the total amount of landscape in

the forest (Lubowski et al. 2006), rather than the tree species composition of the landscape.

3. Econometric Framework

This section extends recent theoretical work on forest management under climate change

(Guo and Costello 2013) by showing how a nested logit discrete choice econometric framework

can be used to estimate the basic relationships between climate and management that are

revealed from observed data on forest landowner decision-making.

3.1 Relevant aspects of the forest management problem for estimation

Private forest landowners periodically harvest their timber at variable rotation lengths

(e.g. 20-60 years). Replanting new trees follows harvest events as required by law in many U.S.

states, which leads to a decision-making structure that simultaneously chooses harvest and

species to replant. We exploit observable spatial variation in both climate and recent forest

management decisions as the basis for our empirical model. Figure 1 illustrates a basic empirical

link between climate on the U.S. west coast and the existing tree species on the landscape. The

data in figure 1 comes from linking observable locations of existing forest plots in the FIA data

to long-run climate averages at that plot. However, because forests are stocks, the existing forest

represents a culmination of a set of adaptations that have been occurring for decades – e.g. a 40-

year-old Douglas-fir stand resulted from a landowner’s replanting choice 40 years ago. In

4 Haim et al. (2011) is an exception.

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contrast, our formal empirical model is not based on the existing forest stock, but rather on

observed management choices during the period 2001 to 2014.

[Figure 1]

A panel approach has been gaining popularity in recent econometric work on climate change

(Schlenker et al. 2006; Deschênes and Greenstone 2007; Burke and Emerick 2016). However,

similar to Albouy et al.’s (2016) analysis of climate and urban quality of life, we adopt a cross-

sectional strategy that is more suitable for our forest management problem. Yearly or daily

changes in weather are unlikely to affect forest landowners’ decisions, which reflect expected

outcomes over many decades. We identify climatic effects on adaptation in forestry by using

spatial variation in climate variables and replanting choices across recently harvested timber

plots, while controlling for a rich set of fine-scale variables reflecting rental values from planting

or regenerating specific tree species (species-specific timber prices, species-specific timber yield

curves, and the plot’s elevation and site class for soils).

3.2 Theoretical foundation for harvest and replanting choice model

Consider a forest landowner that has just chosen a harvest method h and is now choosing

which tree species to replant or regenerate post-harvest. If a landowner chose the clear-cut

harvest method (remove all volume), then their discrete-choice problem is to choose the tree

species 𝑠𝑠𝑗𝑗 to replant. Alternatively, a landowner that recently conducted a partial-cut harvest

(remove a partial share of volume) now owns a stand with potentially mixed ages, described by

the vector a. The partial-cut landowner’s discrete-choice problem is to choose the tree species 𝑠𝑠𝑗𝑗

to leave on the ground as a seed source for new growth. The optimized value of the post-harvest

(ph) land conditional on harvest method (h) is:

𝑉𝑉𝑡𝑡𝑝𝑝ℎ|ℎ(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) = 𝑚𝑚𝑎𝑎𝑚𝑚�

𝑉𝑉𝑡𝑡(𝑠𝑠1,𝑎𝑎, 𝑐𝑐𝑡𝑡)𝑉𝑉𝑡𝑡(𝑠𝑠2,𝑎𝑎, 𝑐𝑐𝑡𝑡)

⋮𝑉𝑉𝑡𝑡(𝑠𝑠𝑆𝑆,𝑎𝑎, 𝑐𝑐𝑡𝑡)

� for ℎ ∈ {𝐶𝐶𝐶𝐶,𝑃𝑃𝐶𝐶} (1)

where S is the discrete number of different tree species that can physically grow on the land, and

𝑉𝑉𝑡𝑡�𝑠𝑠𝑗𝑗, 𝑎𝑎, 𝑐𝑐𝑡𝑡� is the optimized present value of planting (or regenerating) the land with species 𝑠𝑠𝑗𝑗

and which depends on period t climate conditions 𝑐𝑐𝑡𝑡. The vector of climate conditions could

consist of all known and/or expected climate conditions as of period t, including potential future

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changes in climate that the landowner believes will occur. The age vector a consists of all zeros

for bare land that was clear-cut (h=CC), and a potential mix of ages for land that was partial-cut

(h=PC) and still has some standing trees.

Now consider a landowner of a stand with age vector a, whereby the landowner can

choose to clear-cut harvest, partial-cut harvest, or not cut and let their stand continue to grow. If

the landowner harvests their land, they receive a net revenue from current-period harvest equal to

𝑉𝑉𝑡𝑡ℎ(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) = 𝑃𝑃𝑠𝑠𝑣𝑣𝑣𝑣𝑣𝑣ℎ(𝑎𝑎, 𝑠𝑠) − 𝐻𝐻𝐶𝐶ℎ, where 𝑃𝑃𝑠𝑠 is the unit price of tree species 𝑠𝑠, 𝑣𝑣𝑣𝑣𝑣𝑣ℎ represents

timber volume given choice of harvest method h where 𝑣𝑣𝑣𝑣𝑣𝑣𝐶𝐶𝐶𝐶(𝑎𝑎, 𝑠𝑠) > 𝑣𝑣𝑣𝑣𝑣𝑣𝑃𝑃𝐶𝐶(𝑎𝑎, 𝑠𝑠), and the

variable 𝐻𝐻𝐶𝐶ℎ represents harvest costs for harvest method h. The landowner’s forest management

choice problem can be setup as jointly choosing harvest and replanting to maximize their land

value function:

𝑉𝑉𝑡𝑡(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) = 𝑚𝑚𝑎𝑎𝑚𝑚 �𝑉𝑉𝑡𝑡ℎ=𝐶𝐶𝐶𝐶(𝑠𝑠,𝑎𝑎) + 𝜌𝜌𝑉𝑉𝑡𝑡+1

𝑝𝑝ℎ|𝐶𝐶𝐶𝐶(𝑠𝑠, 1, 𝑐𝑐𝑡𝑡+1)𝑉𝑉𝑡𝑡ℎ=𝑃𝑃𝐶𝐶(𝑠𝑠,𝑎𝑎) + 𝜌𝜌𝑉𝑉𝑡𝑡+1

𝑝𝑝ℎ|𝑃𝑃𝐶𝐶(𝑠𝑠,𝑎𝑎′ + 1, 𝑐𝑐𝑡𝑡+1)𝜌𝜌𝑉𝑉𝑡𝑡+1

𝑝𝑝ℎ|𝑁𝑁𝐶𝐶(𝑠𝑠,𝑎𝑎 + 1, 𝑐𝑐𝑡𝑡+1)

� (2)

where 𝜌𝜌 = 1 (1 + 𝛿𝛿)⁄ is a discount factor and 𝛿𝛿 is the discount rate. If the landowner harvests

their land in either a clear-cut (CC) or partial cut (PC), they receive a one-time net revenue from

harvest 𝑉𝑉𝑡𝑡+1ℎ (𝑠𝑠,𝑎𝑎) and their subsequent post-harvest land value is determined by the solution to

equation (1), 𝑉𝑉𝑡𝑡+1𝑝𝑝ℎ|ℎ. The age vector 𝑎𝑎′ represents the period t+1 age vector for the trees that the

landowner left standing in a partial-cut harvest. For the landowner that clear-cuts their land, all

trees are of age 1 in period t+1. If a landowner chooses not to harvest their land, then their post-

harvest value function from choosing “no cut” (NC) is 𝜌𝜌𝑉𝑉𝑡𝑡+1𝑝𝑝ℎ|𝑁𝑁𝐶𝐶(𝑠𝑠,𝑎𝑎 + 1, 𝑐𝑐𝑡𝑡+1), which is affected

by stand and price growth as well as the risk that the stand may be naturally disturbed by

wildfire, insect damage, or diseases. The landowner chooses not to harvest their land when land

value is maximized by leaving the stand to grow an additional period, i.e. 𝑉𝑉𝑡𝑡(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) =

𝜌𝜌𝑉𝑉𝑡𝑡+1𝑝𝑝ℎ|𝑁𝑁𝐶𝐶(𝑠𝑠,𝑎𝑎 + 1, 𝑐𝑐𝑡𝑡+1) = 𝜌𝜌𝑉𝑉𝑡𝑡+1(𝑠𝑠,𝑎𝑎 + 1, 𝑐𝑐𝑡𝑡+1). Equation (2) is similar to Guo and Costello’s

(2013) framework with the exception that we include partial cut harvests as an alternative to

clear-cut harvests. Partial cut harvests comprise about half of all harvest choices in our study

region. The classic Faustmann framework is embedded in equation (2) and would emerge if we

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ignored partial cut harvest and assumed that everyone has static expectations with regards to

future prices, tree growth, and climate.

Now consider the introduction of a carbon price, whereby the landowner is paid for

carbon sequestered and taxed for carbon released, as in van Kooten et al. (1995). If the

landowner harvests their land, they are taxed at harvest by the amount of carbon released, and so

the one-time net revenue from harvest 𝑉𝑉𝑡𝑡ℎ(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) is augmented with a tax of −𝑃𝑃𝐶𝐶(1 −

𝑣𝑣)𝑣𝑣𝑣𝑣𝑣𝑣𝑐𝑐ℎ(𝑎𝑎, 𝑠𝑠), where 𝑃𝑃𝐶𝐶 is the carbon price, 𝑣𝑣 is the faction of harvested timber that continues to

sequester carbon, and 𝑣𝑣𝑣𝑣𝑣𝑣𝑐𝑐ℎ(𝑎𝑎, 𝑠𝑠) is the volume of carbon from harvest method h. The

landowner is also subsidized for the carbon that continues to be sequestered by their land, and so

the post-harvest land value function 𝑉𝑉𝑡𝑡𝑝𝑝ℎ|ℎ now becomes a function of 𝑃𝑃𝐶𝐶, 𝑣𝑣 and 𝑣𝑣𝑣𝑣𝑣𝑣𝑐𝑐ℎ(𝑎𝑎, 𝑠𝑠).

Thus, since the rate of carbon sequestered in 𝑣𝑣𝑣𝑣𝑣𝑣𝑐𝑐ℎ(𝑎𝑎, 𝑠𝑠) is a function of the planted tree species

s, then a carbon price will change the replanting optimization in equation (1) and incentivize the

landowner to replant the species that sequesters the most carbon. If climate change increases the

volume of tree species 𝑠𝑠𝑖𝑖 at each age a relative to every other species in the landowner’s choice

set, and if carbon sequestered is proportional to the physical quantity of timber, then a fixed

carbon price will reinforce the effects of climate change in terms of raising the land value of

planting 𝑠𝑠𝑖𝑖 relative to the land value of planting the other tree species.5 Therefore, a carbon price

affects an optimizing landowner’s choices associated with harvest timing, harvest method, and

replanting (equation 2).

3.3 Nested logit model of harvest and replanting choice problem.

In order to apply the forest management choices in equation (2) to empirical data, we

require a framework that accounts for the fact that numerous drivers of the value function in

equation (2) are observable to landowners but unobservable to empirical researchers. We

integrate the basic theoretical setup above with a random utility interpretation of a Nested Logit

model, which accounts for both observable and unobservable features of the management

problem in (2) in an estimation structure that explicitly embeds the solution to the discrete-choice

replanting problem in equation (1) into the discrete-choice harvest problem in equation (2). As

shown in Figure 2, we divide the landowner’s forest management choice set into mutually

5 Our assumption is that the land value function for tree species 𝑠𝑠𝑖𝑖 is non-decreasing when the underlying tree growth parameters increase. Ceteris paribus, more tree growth is economically valuable.

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exclusive harvest groups ℎ𝑘𝑘 (𝑘𝑘 = 1, … ,𝐾𝐾), each containing a post-harvest management /

disturbance outcome j (𝑗𝑗 = 1, … . 𝐽𝐽𝑘𝑘). For our application, we have K=3 harvest groups (clear-cut,

partial-cut, no cut). If the landowner clear-cuts their land, then there are 𝐽𝐽𝑘𝑘=6 forest types in

which the land can be replanted. If the landowner partial cuts their land, then there are 𝐽𝐽𝑘𝑘=6

forest types that can be naturally regenerated by choosing which trees are left standing as a seed

source. If the landowner chooses not to cut their trees, then there are 𝐽𝐽𝑘𝑘=2 potential outcomes in

which the stand can be naturally disturbed (e.g. fire, insects) or not.

[Figure 2]

Combining our theoretical framework in section 3.2 with Train’s (2009) decomposition

of a nested logit model into two separate logit models, let landowner n's value function

associated with forest management action j in time t equal:

𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) = 𝑉𝑉𝑛𝑛𝑘𝑘𝑡𝑡ℎ (𝑠𝑠,𝑎𝑎) + 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ(𝑠𝑠,𝑎𝑎, 𝑐𝑐𝑡𝑡) + 𝜀𝜀𝑛𝑛𝑗𝑗𝑡𝑡 (3)

where 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ is unique to post-harvest outcome j, and 𝑉𝑉𝑛𝑛𝑘𝑘𝑡𝑡ℎ is unique to harvest choice k and

common to all post-harvest outcomes in ℎ𝑘𝑘, including k. The term 𝜀𝜀𝑛𝑛𝑗𝑗𝑡𝑡 is observable to the

landowner but not the econometrician, and is assumed to be distributed generalized extreme

value. The primary assumption in section 3.2 is that landowner n chooses management action j in

time t to maximize their land value function 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡, and Train (2009) shows how this type of

discrete-choice maximization problem generates an estimable probability that landowner n

chooses management action j in time t as a product of two logit models, the probability of

harvest action k multiplied by the probability of post-harvest outcome j conditional on choosing

harvest k:

𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛𝑗𝑗𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛𝑘𝑘𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛𝑗𝑗𝑡𝑡|𝑘𝑘 = exp (𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛ℎ +𝜆𝜆𝑛𝑛𝐼𝐼𝑛𝑛𝑛𝑛𝑛𝑛)

∑ exp (𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛ℎ +𝜆𝜆𝑛𝑛𝐼𝐼𝑛𝑛𝑛𝑛𝑛𝑛)𝐾𝐾

𝑛𝑛=1∙

exp (𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛𝑝𝑝ℎ|ℎ/𝜆𝜆𝑛𝑛)

∑ exp (𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛𝑝𝑝ℎ|ℎ/𝜆𝜆𝑛𝑛)𝐽𝐽

𝑛𝑛=1 (4)

The term 𝐼𝐼𝑛𝑛𝑘𝑘𝑡𝑡 = 𝑣𝑣𝑙𝑙 ∑ exp (𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ/𝜆𝜆𝑘𝑘)𝐽𝐽

𝑗𝑗=1 is known as an inclusive value for nest k, and 𝜆𝜆𝑘𝑘 is a

parameter to be estimated. The inclusive value for a nest captures the maximum expected utility

from choosing amongst all alternatives within the nest (Hartman 1988; Train 2009). The

inclusive value 𝐼𝐼𝑛𝑛𝑘𝑘𝑡𝑡 approximates the optimized post-harvest land value associated with picking

the tree species to replant, which is a direct measure of the solution to equation (1). Importantly,

the probability of harvest choice k is a function of the inclusive value and hence, the probability

of harvest is necessarily affected by the drivers of all post-harvest outcomes. Therefore, the

11

nested logit model incorporates a key theoretical point from section 3.2 in that the landowner’s

optimal replanting choice from equation (1) is structurally embedded into the landowner’s

optimal harvesting choice from equation (2).

3.4 Specification of nested logit model of forest management

We have plot-level data for over 6,800 plots on the U.S. west coast with variables

representing forest type, site quality, tree growth, elevation, an indication of recent harvest, and

an indication of recent natural disturbance. We combine the plot-level forest management data

with downscaled climate data and regional stumpage prices that vary across forest types. To

specify the empirical model with observable data, we begin with the lower nest describing the

replanting choice conditional on the landowner having clear-cut or partial-cut their land. In

general, the post-harvest value function 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ depends on a potentially complicated function of

the landowner’s expectations of future prices, tree growth, and climate change, and could include

multiple anticipated switches between planted tree species. Guo and Costello (2013) provide an

example of numerically estimating 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ under the assumption that landowners optimize

management and expect climate change to result from a particular general circulation model, and

by assuming that all landowners know how such climate change will affect growth from

replanting different tree species. However, there is evidence from extension research in the

Pacific Northwest that forest landowners are currently not accounting for future climate change

in their management actions (Grotta et al. 2013). Further, forestland owners and appraisers in our

study region are specifically trained to estimate forestland values using a static expectations

Faustmann formula.6

We specify 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ for replanting (bottom left and center of Fig. 2) as a reduced-form

function of the average per-acre Faustmann value function for planting species sj in region r that

contains plot n, annualized as a rent: 𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡, where the upper bar notation indicates a

regional average. We use regional average Faustmann rents because i) they represent a standard

and widely used method for measuring current annualized forest profitability that can be used

with existing data, and ii) they are easily observable and taught to current landowners as a way to

assess the relative profitability of planting different tree species today. We then use observable 6 For example, Oregon State University Forestry Extension experts teach valuation techniques for small woodland owners using a textbook Faustmann formula.

12

variation in climate within each region (details about regions in the next section) to infer the

relationship between climate and replanting choice, using the revealed behavior of replanting

choice. We do this by including interaction terms between rent and the climate variables in the

replanting equation. We specify the nested logit model for the replanting nest as the following

reduced-form function:

𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ = 𝛽𝛽0𝑗𝑗

𝑝𝑝ℎ + 𝛾𝛾𝑝𝑝ℎ𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡 + 𝛽𝛽1𝑗𝑗𝑝𝑝ℎ𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡 ∙ 𝑐𝑐𝑛𝑛𝑡𝑡 + 𝛽𝛽2𝑗𝑗

𝑝𝑝ℎ𝑟𝑟𝑣𝑣𝑟𝑟𝑣𝑣𝑛𝑛 + 𝛽𝛽3𝑗𝑗𝑝𝑝ℎ𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡 ∙ 𝑐𝑐𝑛𝑛𝑡𝑡+30 (5)

𝑓𝑓𝑣𝑣𝑃𝑃 𝑝𝑝ℎ ∈ {𝑃𝑃𝑟𝑟𝑝𝑝𝑣𝑣𝑎𝑎𝑙𝑙𝑟𝑟|𝑐𝑐𝑣𝑣𝑟𝑟𝑎𝑎𝑃𝑃𝑐𝑐𝑐𝑐𝑟𝑟, 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑙𝑙𝑟𝑟𝑃𝑃𝑎𝑎𝑟𝑟𝑟𝑟|𝑝𝑝𝑎𝑎𝑃𝑃𝑟𝑟𝑝𝑝𝑎𝑎𝑣𝑣 𝑐𝑐𝑐𝑐𝑟𝑟}

where 𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑗𝑗𝑡𝑡 and 𝑐𝑐𝑛𝑛𝑡𝑡 are rent and downscaled long-run climate variables whose interaction

describes observable rent deviations between plot n and the regional average; 𝑟𝑟𝑣𝑣𝑟𝑟𝑣𝑣𝑛𝑛 is the

elevation of plot n, and 𝑐𝑐𝑛𝑛𝑡𝑡+30 is the expected change in temperature based on the forecasted

climate 30 years into the future. Our inclusion of Fautmann rents into the specification of 𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ is

meant to provide a reasonable and observable index for how prices, timber growth, and

approximate expected rotation times influence the post-harvest land value function, recognizing

that landowners have many unobservables (expectations, management skills, etc.) that also affect

the value function and are embedded in the logit unobservable, 𝜀𝜀𝑛𝑛𝑗𝑗𝑡𝑡. Our reduced form approach

in equation (5) provides a test for simple deviations from the static expectations Faustmann

approach by including an interaction between rents and a downscaled climate forecast 30 years

in the future, 𝑐𝑐𝑛𝑛𝑡𝑡+30.

The parameters for the interaction terms in (5) are specific to each replanting choice, thus

revealing the relationship between climate and the value of forestland associated with each

species replanted. Figure 3 graphically illustrates the intuition from this approach. The horizontal

axis represents a climate measure such as temperature. In Figure 3(A), the climate is represented

by a probability distribution, or the likelihood that each temperature occurs. Although plot n and

plot m are located in the same region, they have different climates, where the temperature of plot

m is higher than the temperature of plot n. Figure 3(B) represents the relationship between the

value of forestland and climate. If the landowner of plot n is revealed to choose Douglas-fir for

replanting, while the landowner of plot m is revealed to choose hardwoods, the parameter for the

climate-rent interaction term (𝛽𝛽1𝑗𝑗𝑝𝑝ℎ) would implicitly pick up the effect of climate on the value of

forestland, which is a deviation from the average effect of rent on replanting choice (𝛾𝛾𝑝𝑝ℎ). Thus

if the climate distribution shifts from climate 1 to climate 2 in Figure 3, then our estimated model

13

would predict an increase in probability that landowners will plant hardwoods at the expense of

planting Douglas-fir.

[Figure 3]

Average forest rents 𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡 are estimated for each of six forest types, seven site

productivity classes7, and eighteen price regions.8 Using the plot-level FIA data, we empirically

fit a yield curve for each tree species and site productivity classes by yield region9, which are

used to compute the Faustmann optimal rotation lengths required for the calculation of forest

rents 𝑃𝑃𝑟𝑟𝑙𝑙𝑟𝑟������𝑟𝑟(𝑛𝑛)𝑠𝑠𝑛𝑛𝑡𝑡.10 A forest owner can select a tree species to replant from the following six

groups, which represent the predominant species in the study region: (1) Douglas-fir, (2)

Fir/Spruce/Mountain hemlock, (3) Hemlock/Sitka spruce, (4) Ponderosa pine, (5) Other

softwoods11, and (6) Hardwoods12. One of the alternative specific constants is set to zero for

identification.

We account for the risk of natural disturbance (e.g., fire, pests, etc.) in estimation through

the “no-cut” nest (bottom right of Fig. 2), where landowners refrain from cutting their timber in

exchange for letting the trees grow an additional period. By choosing not to cut, the landowner

leaves the stand at risk to the binary outcomes of natural disturbance or no disturbance. The

natural disturbance event is not a deliberate landowner choice as the replanting decision is, but is

rather a random event that is influenced by landowner management and by Mother Nature. Since

resource economic theory suggests that fire risk influences the landowner’s harvest decision

(e.g., Amacher et al. 2005), we jointly estimate drivers of disturbance and harvest decisions by

specifying the nested logit model for the lower “no cut” nest as a reduced form binary model:

𝑉𝑉𝑛𝑛𝑗𝑗𝑡𝑡𝑝𝑝ℎ|ℎ = 𝛽𝛽0𝑗𝑗

𝑝𝑝ℎ + 𝛽𝛽1𝑗𝑗𝑝𝑝ℎ𝑝𝑝𝑃𝑃𝑝𝑝𝑣𝑣𝑛𝑛 + 𝛽𝛽2𝑗𝑗

𝑝𝑝ℎ𝑟𝑟𝑣𝑣𝑟𝑟𝑣𝑣𝑛𝑛 + 𝛽𝛽3𝑗𝑗𝑝𝑝ℎ𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐𝑝𝑝𝑟𝑟𝑠𝑠𝑛𝑛𝑡𝑡 + 𝛽𝛽4𝑗𝑗

𝑝𝑝ℎ𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑡𝑡 + 𝛽𝛽5𝑗𝑗𝑝𝑝ℎ𝑐𝑐𝑛𝑛𝑡𝑡 + 𝛽𝛽6𝑗𝑗

𝑝𝑝ℎ𝑠𝑠𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑛𝑛 (6)

𝑓𝑓𝑣𝑣𝑃𝑃 𝑝𝑝ℎ ∈ {𝑑𝑑𝑝𝑝𝑠𝑠𝑟𝑟𝑐𝑐𝑃𝑃𝑃𝑃𝑎𝑎𝑙𝑙𝑐𝑐𝑟𝑟 𝑟𝑟𝑣𝑣𝑟𝑟𝑙𝑙𝑟𝑟|𝑙𝑙𝑣𝑣 𝑐𝑐𝑐𝑐𝑟𝑟}

7 The site productivity class ranges from 1 to 7, where 1 indicates the most productive plot. This is a classification of forest land in terms of inherent capacity to grow crops of industrial wood expressed in cubic feet/acre/year. 8 There are four sub-regions in Washington, five in Oregon, and nine in California, each corresponding to a price region for which state agencies report regional log-prices. 9 Each of the three states is split into an eastern and western region, which is termed a “yield region”. 10 Appendix A has a detailed explanation of how rents are constructed. 11 Other softwoods include lodgepole pine, redwood, western larch, western juniper, and numerous other pine species including knobcone, bishop, monterey, foxtail, limber, whitebark, and western white. 12 Major species of hardwoods are tanoak (CA and OR), red alder (OR and WA), bigleaf maple (OR and WA), black oak (CA), laurel (CA), canyon live oak (CA), pacific madrone (CA), white oak (OR), and cottonwood (WA).

14

The independent variables that affect the probability of natural disturbance include an ownership

dummy indicating private or state ownership (𝑝𝑝𝑃𝑃𝑝𝑝𝑣𝑣𝑛𝑛), elevation (𝑟𝑟𝑣𝑣𝑟𝑟𝑣𝑣𝑛𝑛), tree species dummy

variables indicating the forest type (𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐𝑝𝑝𝑟𝑟𝑠𝑠𝑛𝑛), the current timber volume (𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑡𝑡), a state dummy

(𝑠𝑠𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑛𝑛), and a vector of climate variables (𝑐𝑐𝑛𝑛𝑡𝑡). Climate variables such as precipitation directly

affect nature’s ability to suppress fires, while other climate variables such as minimum winter

temperatures can affect the susceptibility of certain trees to damage. The parameters for the “no

disturbance” outcome are normalized to zero, and so the lower nest is a binary model where

disturbance is equal to one.

Now consider the upper nest in Fig. 2, whereby the forest landowner makes the harvest

decision by choosing whether to clear-cut, partial-cut, or not cut their stand of trees. We specify

the observable components specific to the net revenue from harvest method h as:

𝑉𝑉𝑛𝑛𝑘𝑘𝑡𝑡ℎ = 𝛼𝛼0𝑘𝑘 + 𝛼𝛼1𝑘𝑘𝑃𝑃𝑛𝑛𝑠𝑠𝑛𝑛𝑡𝑡 ∙ 𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑘𝑘�𝑠𝑠𝑛𝑛�𝑡𝑡ℎ (7)

𝑓𝑓𝑣𝑣𝑃𝑃 ℎ ∈ {𝑐𝑐𝑣𝑣𝑟𝑟𝑎𝑎𝑃𝑃 𝑐𝑐𝑐𝑐𝑟𝑟,𝑝𝑝𝑎𝑎𝑃𝑃𝑟𝑟𝑝𝑝𝑎𝑎𝑣𝑣 𝑐𝑐𝑐𝑐𝑟𝑟}

And we specify the observable components specific to the decision not to cut and let the stand

grow as a function of expected changes in revenue:

𝑉𝑉𝑛𝑛𝑘𝑘𝑡𝑡ℎ = 𝛼𝛼1𝑘𝑘𝑃𝑃𝑛𝑛𝑠𝑠𝑛𝑛𝑡𝑡 ∙ ∆𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑘𝑘(𝑠𝑠𝑛𝑛)𝑡𝑡 (8)

𝑓𝑓𝑣𝑣𝑃𝑃 ℎ ∈ {𝑙𝑙𝑣𝑣 𝑐𝑐𝑐𝑐𝑟𝑟}

In this specification, we use observable time t timber prices for tree species sj from the region

that contains plot n, and multiplied by the observable species sj timber volume for management

choice k as a representation of the one-time revenue that the landowner would receive from

picking harvest choice k. Note that since clear cutting necessarily entails harvesting more volume

than partial cutting13, that the volume variable is indexed by harvest choice k. The post-harvest

value function from not-cutting the land – 𝑉𝑉𝑡𝑡+1𝑝𝑝ℎ|𝑁𝑁𝐶𝐶(𝑠𝑠,𝑎𝑎 + 1, 𝑐𝑐𝑡𝑡+1) in equation (2) – is affected by

the marginal benefit of waiting to cut, which is the change in revenue that could be received by

allowing the stand to grow an additional period. We use radial ten-year increment data on tree

growth for each FIA plot to construct an approximation of plot-specific tree growth – Δ𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑘𝑘(𝑠𝑠𝑛𝑛)𝑡𝑡

13 Partial cut volume is estimated by comparing the measured volumes in 10-year intervals for the re-measured plots that have a record of partial cut treatment in the most recent survey. For the other plots, we assigned the percentage of partial cut portion of total volume according to the available information such as the treatment code that distinguishes “less than 20% removed” or “more than 20% removed”, as well as county average percentage across the re-measured partially-cut plots.

15

– which when multiplied by 𝑃𝑃𝑛𝑛𝑠𝑠𝑛𝑛𝑡𝑡 provides us with a direct measure of the marginal benefit of

waiting to cut.14

Finally, the nested logit structure embeds the inclusive value 𝐼𝐼𝑛𝑛𝑘𝑘𝑡𝑡 of the lower post-

harvest nests into the upper harvest nest of the estimated probabilities in equation (4). For the

two harvest alternatives (clear-cut and partial-cut), 𝐼𝐼𝑛𝑛𝑘𝑘𝑡𝑡 approximates the optimized post-harvest

land value associated with picking the tree species to replant, which is a direct measure of the

solution to equation (1). The inclusive value for the “no cut” nest implicitly accounts for the risk

of disturbance on the harvest decision, although this inclusive value is harder to interpret than in

the clear-cut and partial cut nests since the outcomes from choosing not to cut (natural

disturbance or not) are not a direct choice by the landowner. 15 With the inclusive value from

each nest, climate implicitly affects the harvest decision and so this empirical framework allows

the climate to affect adaptation on the extensive margin (choosing which tree species to plant)

and on the intensive margin (altering the harvest time). The alternative specific constant of “no

cut” is normalized to zero, which allows us to interpret the alternative specific constants on clear-

cut and partial-cut as capturing average harvest costs.

The parameters defining the probabilities of harvest, disturbance, and replanting choices

are simultaneously estimated with maximum likelihood techniques using original Matlab code.

The likelihood function is:

𝐿𝐿𝐿𝐿(𝛼𝛼,𝛽𝛽, 𝛾𝛾, 𝜆𝜆) = ∑ ∑ 𝑦𝑦𝑛𝑛𝑗𝑗 𝑣𝑣𝑙𝑙 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛𝑗𝑗𝑡𝑡𝑗𝑗𝑛𝑛 (9)

where 𝑦𝑦𝑛𝑛𝑗𝑗 equals one if landowner n chooses management j. We index some variables in the

model with time t to represent that different plots are observed at different points in time, and so

different plots have variables measured at different points in time. This is a pooled rather than a

panel data model. Finally, we weight each plot’s likelihood by the expansion factor assigned in

the FIA database, where the expansion factor represents the sampling intensity associated with

the sample plots.

14 Appendix C has a detailed description of how tree growth is calculated for each plot. 15 The natural disturbance model estimates the statistical likelihood of getting naturally disturbed, given the physical plot conditions and recent history of disturbance. Therefore, the inclusive values from the disturbance nest may not be justified as the utility gained by optimally choosing the best alternative, nor satisfy the consistency condition for utility maximization (Herriges and Kling 1996). See section 4.2 for robustness checks for specifying the no-cut nest.

16

If a plot is naturally disturbed with wildfire, we use historical spatial-temporal data on

wildlife burn severity to separately estimate a burn severity index as a function of the same

climate and other plot level drivers of natural disturbance from equation (6):

𝑆𝑆𝑉𝑉𝑛𝑛 = 𝐺𝐺(𝑝𝑝𝑃𝑃𝑝𝑝𝑣𝑣𝑛𝑛, 𝑟𝑟𝑣𝑣𝑟𝑟𝑣𝑣𝑛𝑛, 𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐𝑝𝑝𝑟𝑟𝑠𝑠𝑛𝑛𝑡𝑡, 𝑣𝑣𝑣𝑣𝑣𝑣𝑛𝑛𝑡𝑡, 𝑐𝑐𝑛𝑛𝑡𝑡, 𝑠𝑠𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑛𝑛; 𝝑𝝑) (10)

where 𝑆𝑆𝑉𝑉𝑛𝑛 is the most dominant burn severity (1: unburned to low, 2: low, 3: moderate, or 4:

high) that has occurred in the last ten years within a 2km radius around each plot. The vector of

parameters 𝝑𝝑 are estimated as an ordered logit model (see Appendix B) using historical burn

severity data from 2001-2014. Results are intuitive and indicate that less precipitation and more

extreme temperatures significantly increase the probability of severe wildfire.

3.5 Data

The sample used for econometric estimation includes 6,845 privately or state-owned

forest plots that have been sampled in the USDA FIA. The study area of Oregon, Washington,

and California has considerable climate variation and corresponding variation in tree species

types (Figure 4a). Due to a methodological change in data collection, the FIA is only available

since 2001. Therefore, a complete set of panel data does not exist16.

[Figure 4]

The FIA is the main data source for plot attributes and includes data captured by

numerous field crews working under the supervision of the USDA Forest Service17. Plot

locations are slightly “fuzzed” for confidentiality in that each plot’s true location is within at

most 1 mile (1.6 km) of their stated location. Using a national standard for field measurements

for a wide range of site attributes, the FIA presents the most detailed plot-level data available for

our purposes.18 The key dependent variables for econometric analysis include a qualitative

indicator of harvest on an FIA plot (clear-cut, partial-cut, no cut), the forest type replanted upon

harvest19, and the presence of a natural disturbance (e.g., fire, insect damage, etc.). The plot-level

16 FIA surveys a fraction of all plots (10%) every year. Therefore, re-measurements occur every 10 years. For those re-measured, dependent variables reflect data from both measurements over 10 year timeframe. 17 For general background on the FIA data, see http://www.fia.fs.fed.us/. 18 For example, the National Resources Inventory (NRI) lacks most of the site attributes included in the FIA and does not track harvest operations. Remote sensing data neither distinguishes different tree species nor detailed site characteristics. 19 Forest type is based on the live tree stocking of tree species sampled on the plot, and derived using a computer algorithm by the FIA staff. There are 70 forest types defined in the regional FIA database; we grouped them into six major forest groups based on the characteristics with respect to climate.

17

attributes used include forest type, stand volume, incremental volume growth20, owner type,

stand age, and elevation. Each plot is designed to cover 1-acre and is randomly sampled. We

assigned each plot to a specific price region for different forest types, as well as the stand-size

that it produces21. Historical prices are drawn from records available by state-level agencies.22

Since not all forest types can physically grow across the entire region, each plot is assigned a

choice set based on the “plant viability scores” developed by the USDA Forest Service that

reflects the likelihood that the climate at a given location would be suitable for each species in

each plot (Crookston et al. 2010).23

The climate variables observable to the landowners are total precipitation and mean

temperature during the growing season, the maximum temperature in the warmest month

(August), and minimum temperature in the coldest month (December). These variables have

been found by natural scientists to be some of the most influential variables that affect the

growth of trees (Rehfeldt et al. 2014). Plot-level climate data is based on normal monthly data

from the Parameter-elevation Regressions on Independent Slopes Model (PRISM) over a 30-year

period between 1981 and 2010.24 Growing season months are those that have growing degree

days above 10 degrees Celsius (50F), which are determined at a regional level that represents

varying climate zones25. The most significant extreme weather events for forest health are

wildfire, frost, and drought. Frost and drought conditions will be captured by climate variables,

the minimum temperature in the coldest month and total precipitation, respectively. To account

for available climate forecast information, we include an independent variable – expected

temperature increase – which is the difference between the projected temperature according to

the most pessimistic climate projection (RCP 8.5) and the current temperature. The climate 20 The increment growth variables are plot specific and derived from the growth curves that fit a Von Bertalanffy growth equation. Please see Appendix C for more detailed explanation. 21 Stand-size is determined by the predominant diameter class of live trees on the plot, and grouped into three size classes: large, medium, and small diameter classes. The stand-size is matched with the size quality when assigning the timber price. Since the quality/grade of timber is not available in FIA, we assumed that the stand-size is equivalent to the timber grade. 22 California State Board of Equalization, Oregon Department of Forestry, and Washington State Department of Natural Resources. 23 Viability score values near zero indicate a low suitability while those near 1.0 indicate a suitability so high that the species is nearly always present in that climate. Although the score below 0.5 indicates little chance of survival, we use the score of 0.3 as a cut-off point whether the species is included in a choice set, to account for the error disclosed in Crookston et al. (2010). 24 The PRISM data is developed by the PRISM Climate Group, Oregon State University and provided on an 800m grid. 25 Regional climate data is from National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center.

18

projection that we use is of high spatial resolution (1km) and is easily available to the public in

an online26 format that allows the landowner to choose exact coordinates of their forest (Fig.

4.b).

Appendix D presents a full list of data sources and summary statistics of the data, but a

few highlights are covered here. First, 9.3% (9.7%) of forest plots were clear-cut (partial cut)

over the ten-year sample period for each plot. Second, on a per-unit basis, Douglas-fir logs were

the most commercially valuable tree species ($458.50/MBF) and comprise about 55% of total

harvested volume, while Hardwoods are the least valuable ($254.49/MBF). Third, Douglas-fir

and Hemlock/Sitka spruce are more commonly harvested by clear-cut in the wetter region west

of the major mountain ranges, while Ponderosa Pine is more commonly harvested by partial-cut

in the drier region east of the major mountain ranges. Finally, Fir/Spruce forest types are most

commonly found in the mountains at high elevation while hardwoods are most commonly found

in the valleys at a lower elevation.

4. Econometric Estimation Results

4.1 Estimates of parameters and key marginal effects

The full set of nested logit parameter estimates are presented in Appendix E, while

marginal effects for key variables are presented in Table 1. Parameter estimates generally

conform to expectations and yield four general conclusions. First, in the lower replanting nest,

the estimated rent coefficient is positive as expected - landowners are more likely to replant

forest types that are more profitable. Second, the rent-climate interaction parameters are highly

variable in magnitude and statistical significance across replanting choices. Third, the natural

disturbance is more likely on high elevation, large volume, and dry plots that experience cold

winter temperatures and that are hardwood or other softwood forest type. Fourth, in the upper

harvest nest, the estimated coefficients are consistent with standard comparative statics from

harvesting models - a timber harvest is more likely when the marginal costs of waiting to harvest

are high (harvest revenue; inclusive value proxy for optimized bare land value), and less likely

when the marginal benefits of waiting to harvest are high (growth in harvest revenue).

Table 1 presents average marginal effects of a discrete change in a set of the key

independent variables. A $10 increase in annual rent to replanting Douglas-fir increases the

26 https://adaptwest.databasin.org/pages/adaptwest-climatena

19

probability of replanting Douglas-fir by 4%, lowers the probability of replanting other forest

types and increases the probability of clear-cut by 0.6%. The effect of higher Douglas-fir rent on

clear-cut percentage is driven by an increase in the marginal cost of waiting to cut. The

probability of replanting Douglas-fir is significantly lower with a 3 ºC increase in average

temperature, while the probability of replanting Hemlock/Sitka Spruce is significantly affected

by changes in multiple climate variables. Breaking down the effect of temperature on replanting

Douglas-fir by region reveals that the discrete-change effect of a 3 ºC increase in temperature is

much higher in the prime timber growing region of western Oregon and Washington, with an

approximate 30 percentage point fall in the probability of replanting Douglas-fir, which is

statistically significant at the 1% level.

[Table 1]

4.2 Robustness checks of econometric model

We evaluated the robustness of the econometric parameters to seven alternative

specifications. First, we drop state-owned plots (15% of the sample) to see if parameter estimates

are different when estimating privately-owned plots only.27 Second, we use the average

temperature difference between December and August in lieu of minimum and maximum

temperatures as an alternative climate specification. Third, we replace the lower nest for the "no

cut" choice with a reduced form specification of the natural disturbance equation (6) since the

inclusive values from the disturbance nest may not be justified as a maximum utility measure

(Herriges and Kling 1996). Fourth, we examine using the expected temperature increase over the

next 70 years rather than the next 30 years to examine different expectation horizons. Fifth, we

add a variable in the replanting model that measures the distance to the closest mill to check

whether this potentially omitted infrastructure variable affects the climate parameters. Sixth, we

swap climate variables for some plots within each county to examine the importance of the fact

that the FIA data is sometimes randomly swapped within counties to protect the exact location of

plots.28 Seventh, we examine whether a pair of omitted variables proxying for local timber

infrastructure and ownership types might be correlated with climate, and thus, introduce bias into

our estimates. Appendix F presents a comparison of key marginal effects of the base 27 Unlike most federal forestland in the Pacific Northwest, state-owned land is actively managed for timber. 28 Up to 20% of the private plots' coordinates are swapped with another similar private plot within the same county. Swapped plots are chosen to be similar based on attributes such as forest type and stand-size class and may induce some measurement error into the climate variables. We ran 50 different versions of randomly swapping 20% of plots.

20

specification to the alternative specifications. Our overall conclusion is that the model is quite

robust to these alternative specifications, as the marginal effects are very similar across

specifications.

5. Simulation Analysis

5.1 Dynamic landscape simulation of forest management

On their own, the marginal effects from the above section do not give a full picture of the

potential landscape shifts under climate change. Replanting/regeneration does not occur

continuously, but only after infrequent harvest events (~20% probability of a plot being

harvested over 10 years). The impact of climate change is also not identical across plots, as the

marginal effects vary substantially across regions. And since multiple climate variables will shift

in a spatially heterogeneous fashion simultaneously, simulating the combined effects when all

climate variables shift at the same time will render more informative results. A landscape

simulation will need to take these factors into consideration.

This section uses our econometrically estimated forest management and natural

disturbance probabilities as a set of decision rules to simulate changes in the landscape of forest

types under a changing climate and a carbon price policy. Following the econometric-based

landscape simulation framework developed by Lewis and Plantinga (2007), the estimated

probabilities are used in a Monte Carlo analysis to generate repeated realizations of the time-path

of landscape change. A baseline simulation generates landscape change when rents and climate

are held fixed at current levels. A climate change scenario reflects simultaneous changes in the

climate variables. A carbon price simulation translates a carbon price into a plot-specific rent

which is then added to the timber rent (see below for more details). Natural disturbance

occurrence is endogenous in that it is affected not only by climate directly but also by forest

types chosen by landowners as a result of their adaptation behaviors.

To illustrate how the simulation uses the estimated forest management probabilities to

generate landscape outcomes, consider the estimated probabilities of "clear-cut", "partial cut", or

"no cut" in the harvest nest. We first draw a random vector of estimated parameters for the full

21

model (Krinsky and Robb 1986)29 and then calculate all management and natural disturbance

probabilities. Since the harvest probabilities necessarily sum to one, we next draw a uniform

random number 𝑃𝑃1 between zero and one and compare it to the clear-cut probability. A clear-cut

occurs if 𝑃𝑃1 is less than or equal to the estimated clear-cut probability for that plot; a partial-cut

occurs if 𝑃𝑃1 is above the clear-cut probability but less than or equal to the sum of the clear-cut

and partial-cut probabilities; a no-cut management action occurs otherwise. As in Lewis (2010),

the simulation procedure accounts for the variation in the estimated parameters and random error

terms by using random draws for the estimated parameters and for determining the outcome. We

use all estimated probabilities of management and natural disturbance in a similar fashion.

Figure 5 presents a schematic of the dynamic nature of the simulation. In the first 10-year

time interval we use the estimated probabilities to first determine the harvest outcome for each

plot as described above. Depending on the harvest choice (clear cut, partial cut, no cut), we then

use the appropriate management/disturbance probability to determine the post-harvest outcome

(forest type to replant/regenerate, natural disturbance or not). If the plot is not cut and then

disturbed, we determine the type of disturbance (disease, wildfire, insect) and then determine the

severity level (𝑆𝑆𝑉𝑉) of a wildfire with the wildfire severity model (10), and the damages from

other disturbances (disease; insects) based on average levels of disturbance in the region near the

plot. Once the post-harvest outcomes are determined, we update the forest attributes of forest

type, age, growth, and stand volume using our empirically calibrated timber yield functions. The

process is then repeated for subsequent 10-year intervals until 2100. The above dynamic

simulation is then repeated for 1000 times in a Monte Carlo fashion, generating 1000 realizations

of the time-path of landscape change.

[Figure 5]

5.2 Simulated climate change and carbon price scenarios

Future climate regimes are derived from the IPCC’s Fifth Assessment Report (AR5).

Monthly temperature and precipitation output were based on the results from the U.S. National

Center for Atmospheric Research (NCAR) Community Climate System Model (CCSM) 4.

CCSM4 climate model is ranked as one of the best of 41 Global Climate Models (GCM) as to

the credibility of predicting the future climate according to the models’ abilities to reproduce the 29 A simulated parameter vector is equal to 𝛽𝛽𝑠𝑠 = �̂�𝛽 + 𝐶𝐶′𝑋𝑋𝐾𝐾 , where �̂�𝛽 is the estimated parameter vector, C is the KxK Cholesky decomposition of the estimated variance-covariance matrix, and 𝑋𝑋𝐾𝐾 is a K-dimensional vector of draws from a standard normal distribution.

22

observed metrics (Rupp et al. 2013). The downscaled data at 1km resolution was obtained from

the ClimateWNA model developed by the Center for Forest Conservation Genetics at the

University of British Columbia (Wang et al. 2012). Out of the available scenarios included in the

model, we chose the RCP8.5 scenario, as current CO2 emission rates are closely tracking this

pathway (Sanford et al. 2014; McKenney et al. 2015)30. We also simulated the landscape using

an alternative climate projection of an ensemble of 15 GCMs31 instead of using one GCM, but

the results show little changes from our original results.

Figure 4.b is a descriptive map that highlights an overall projected climate trend of

temperature and precipitation for each FIA plot. The area shown in brown, the majority of

premier private forestland in the west side of the Cascades, is expected to become warmer and

drier. Under the RCP 8.5 scenario, the average temperature is expected to increase by 4.35 ºC by

2100 in the study region.

We consider three scenarios in our simulations. The baseline scenario assumes no climate

change or carbon price and simply extends the observed forest management practices from 2001

to 2014 into the future. In the climate change only scenario, we use the RCP 8.5 climate

projection. In the climate change and carbon price scenario, we use the same RCP 8.5 climate

projection and add a carbon pricing scheme (discussed below). Differences between the climate

change only scenario and the baseline give us the impact of climate change on the resulting

landscape. Differences between climate change/carbon price scenario and the climate change

only scenario give us the impact of carbon pricing alone, while the difference between the

climate change/carbon price scenario and the baseline gives us the combined impact of climate

change and carbon pricing.

We simulate a hypothetical carbon pricing scheme that starts in 2020 and in which

landowners receive fixed payments for the amount of carbon sequestered in their forests.

Consistent with contemporary ideas about an increasing carbon price (Nordhaus 2013), we

assume that a carbon price starts at $15/ton in 2020, rises to $50 in 2050, and again to $80 in

30 While IPCC AR4 used socio-economic scenarios, AR5 uses different approach in which alternative future scenarios depend on so-called Representative Concentration Pathways (RCPs). For example, RCP8.5 represents a pathway with rising radiative forcing leading to 8.5 W/m2 in 2100. RCP6.0 and RCP8.5 correspond to CO2 equivalent concentrations in 2100 of 720-1000 ppm and >1000 ppm, respectively. 31 The ensemble is composed of the following GCMs: ACCESS1-0, CCSM4, CESM1-CAM5, CNRM-CM5, CSIRO-MK3-6-0, CanESM2, GFDL-CM3, GISS-E2R, HadGEM2-ES, INM-CM4, IPSL-CM5A-MR, MIROC5, MPI-ESM-LR, MRI-CGCM3.

23

208032. Given a set carbon price, we calculate the maximum present value of rents from both

timber revenue and carbon payments by solving for the optimal rotation length, assuming that

forest owners will maintain a steady-state level of stand volume. In addition to the tree volume

yield curves that we estimate for calculating the timber rents, we estimate carbon yield curves

from the FIA data expressed as tons of carbon sequestered as a function of age. The carbon price

scheme augments the rents received from forestland – Appendix G has details on calculating the

carbon rent. The landowner then chooses the rotation length that maximizes the sum of timber

and carbon rents. Since carbon sequestration rates vary across tree species and site classes, the

addition of a carbon rent can alter the landowner’s optimal replanting choice. Carbon pricing is

implemented by crediting a forest owner for the carbon sequestered due to forest growth and

taxing for the carbon released at harvest.33 The presence of a carbon price also affects harvest

decisions as we prevent landowners from claiming carbon credits for the trees harvested by

imposing a penalty for the carbon emitted at the time of harvest.34 Similarly, the benefits from

delaying harvest incorporate an incremental revenue gain from the carbon payment in addition to

the increase in timber revenue.

6. Simulation Results

6.1 Landscape changes under baseline, climate change, and carbon pricing scenarios

For each scenario, we calculate the average share of the total non-Federal forestland in

each tree species type and for each time step, averaged over the 1000 Monte Carlo simulated

landscape outcomes. Figure 6 presents our projection of each tree species’ composition in

California, Oregon, and Washington for the baseline, climate change, and climate change &

carbon pricing scenarios. Examining the three scenarios provides three conclusions. First, both

climate change and the carbon price induce a reduction in the share of the non-Federal forests in

the commercially-dominant Douglas-fir in all states. Second, both climate change and the carbon

price induce an increase in the share of the private forest landscape in Ponderosa pine (for

32 As of September 7, 2017, carbon price in California Carbon Allowance Futures is around $13/tonne CO2 equivalent. 33 We followed the approach used in (van Kooten et al. 1995). As the value of carbon to society increases, we find that the optimal lengths of time until trees are harvested increases. Please see Appendix G for more details about how we calculated carbon rents. 34 We assume that 30% of carbon stored in trees is emitted at harvest, based on Smith et al. (2005).

24

California) and hardwoods (all states). Third, the extent of landscape change is fairly subtle even

under the most pessimistic climate change scenario of RCP 8.5 that this analysis is based on.

[Figure 6]

Figure 7 highlights regional differences for the two forest types that experience the

largest changes – Douglas-fir and hardwoods. We compare total landscape change as well as

change on replanted plots only. Compared to the landscape change that includes both replanted

and non-replanted plots, landowners dramatically increase the replanting of hardwood species at

the expense of Douglas-fir in Oregon and Washington in particular – a region that is mostly

predicted to become warmer and drier under the climate scenario we use. Both climate change

and carbon pricing induce the shift from Douglas-fir to hardwoods. The divergence between

changes in the share of the landscape’s tree species and changes in the share of the landscape’s

replanted species is primarily due to the dynamics of forest management – replanting occurs

gradually on a fraction of the landscape during any given ten-year period as the forest is

harvested. For example, clear-cut harvests occur on approximately 10% of the plots over ten

years, while partial-cut harvests occur on another 10% of the plots over ten years, and so

replacement of a landscape’s tree species is gradual. Our simulation results are consistent with

findings from previous natural science literature that predicts Douglas-fir habitat to shift

eastward from the coast to the interior (Weiskittel et al. 2012; Rehfeldt et al. 2014).

[Figure 7]

An important finding is that the carbon price encourages the adaptation behavior of

switching out of Douglas-fir. Although carbon sequestration uptake for Douglas-fir is higher

than hardwoods for old timber stands, the difference for younger stand ages (30-40 years) is

negligible for high site class plots (i.e., the class of 1 and 2) and higher for hardwoods than

Douglas-fir for lower site class plots (i.e., the class of 6 and 7). Since we model private forest

owners who harvest timber well before it reaches old-growth status, owners of hardwood stands

receive higher carbon rents than owners of Douglas-fir stands for a substantial portion of the

medium to low site productivity class plots.35 This differential effect of carbon prices on

Douglas-fir and hardwoods is due to the biophysical growth characteristics of the species and

35 For example, with a $50/ton carbon price, the carbon rent is higher for hardwoods than Douglas-fir for 75% of total plots with medium to low site productivity class of 4, 5, 6, and 7, while only 28% with higher site productivity class (i.e., 1,2, and 3) receive a higher rent from hardwood than Douglas-fir.

25

contributes to the acceleration of shifting forest planting away from Douglas-fir toward

hardwood species.

6.2 Probability of changing forest types (extensive margin adaptation)

The above simulation results are averages across 1000 simulated landscape changes. To

exploit further information in the estimated probabilities of forest management, we calculate the

effects of climate change and carbon prices on the probability that landowners change from their

initial forest types to a different forest type by 2100. We interpret this measure as a probability of

adaptation on the extensive margin. For plot n that begins today in forest type 𝑠𝑠𝑖𝑖, the simulations

generate 1,000 realizations of plot n’s forest type by the year 2100. The probability of extensive

margin adaptation for plot n is defined as 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛(𝑎𝑎𝑑𝑑𝑎𝑎𝑝𝑝𝑟𝑟) = [1 − 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛�𝑠𝑠𝑖𝑖,2100 = 𝑠𝑠𝑖𝑖,2010�],

which is calculated as the proportion of the 1000 simulations in which plot n ends the year 2100

in a different forest type than it began in 2010. Subtracting the baseline calculation of

𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛(𝑎𝑎𝑑𝑑𝑎𝑎𝑝𝑝𝑟𝑟) from the climate change calculation of 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛(𝑎𝑎𝑑𝑑𝑎𝑎𝑝𝑝𝑟𝑟) gives the discrete effect

of a 90-year climate path on the probability of adaptation. Similarly, subtracting the climate

change calculation of 𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛(𝑎𝑎𝑑𝑑𝑎𝑎𝑝𝑝𝑟𝑟) from the climate change & carbon price scenario version of

𝑃𝑃𝑃𝑃𝑣𝑣𝑃𝑃𝑛𝑛(𝑎𝑎𝑑𝑑𝑎𝑎𝑝𝑝𝑟𝑟) gives the discrete effect of a 90-year carbon price path on the probability of

adaptation. Table 2 presents results differentiated by initial forest type and region.

[Table 2]

Table 2 shows that the discrete effect of a 90-year path of climate change and carbon

pricing varies across regions and initial forest types. For example, climate change induces a 6.1%

probability that the current owner of a Douglas-fir plot in western Oregon will adapt on the

extensive margin to another forest type by the year 2100, while the current owner of a

hardwoods plot in western Oregon is 12.7% less likely to adapt to another forest type by 2100. A

key result from Table 2 is that both a carbon price and climate change increase the probability

that Douglas-fir owners in all regions adapt to another forest type by the year 2100. Interestingly,

a carbon price increases the probability of adapting away from Douglas-fir by approximately

10% in the commercially important growing regions of western Oregon and Washington. To

examine the forest types that may gain under climate change and carbon pricing, we computed

the discrete effect of a 90-year climate path on the probability of adapting to specific forest types

in Table 3:

26

[Table 3]

Results in Table 3 show that climate change consistently favors adapting to hardwoods,

ponderosa pine, and fir/spruce in all regions and away from Douglas-fir. The 90-year path of a

carbon price has very similar qualitative effects to climate change – especially favoring

hardwoods at the expense of Douglas-fir.

7. Conclusions

The purpose of this paper is to develop a dynamic econometric-based simulation

framework for analyzing changes in the forested landscape due to climate change and to examine

the interaction between climate change, climate mitigation policy and private adaptation

behaviors. We develop a new plot-level discrete-choice econometric model of a forest

landowner’s harvesting and replanting decisions based on revealed management behavior over

the period 2001 to 2014. The econometric nesting structure we develop accounts for the

simultaneous nature of multiple management decisions and distinguishes between replanting and

natural regeneration associated with clear-cut and partial-cut harvest, as well as the effect of

climate change on natural disturbance events. We use the estimated econometric model of forest

management as a set of rules to drive a dynamic landscape simulation that scales up plot-level

management decisions to landscape-scale outcomes in a manner that accounts for the growth of

the natural resource and the key economic incentives driving forest management. A baseline

landscape simulation with no climate change or a carbon price, a simulation with climate change,

and a simulation with both climate change and a carbon price allow us to analyze the spatially

heterogeneous effects of climate change and climate mitigation policy on the potential landscape

outcomes of private adaptation behavior. The results have four primary implications.

First, due to the dynamics of forest management decisions, changes in the share of the

landscape allocated to different tree species occurs gradually, while changes in the share of the

replanted landscape in later periods are large. This finding emerges from simultaneously

modeling forest landowners’ harvest and replanting decisions. A private forested landscape does

not change quickly, but in response to the periodic rotation decisions and subsequent replanting

decisions of landowners as a function of heterogeneous climate, prices, and site characteristics.

Our analysis estimates this relationship by using revealed behavior in the most recent time

period. Estimates of the speed of landscape change under climate change are useful for

27

conservation planning that requires an understanding of the threats of habitat loss such as the

reductions in a currently abundant tree species like Douglas-fir.

Second, there is considerable spatial variation in the direction of extensive margin

adaptations through replanting choices. For example, the commercially-important Douglas-fir

forest type is expected to lose significant shares in the region where it most dominates today –

the temperate, moist coastal region of western Oregon and Washington. Fir, spruce, and

mountain hemlock species shift northward and to higher elevation in our simulations. These

findings are consistent with findings from the natural science literature (Crookston et al. 2010;

Rehfeldt, Jaquish, López-Upton, et al. 2014; Weiskittel et al. 2012), but the dynamic nature of

our empirically-driven simulation allows us to uniquely simulate the magnitude, timing, and

speed of landscape change that are not examined in related literature.

Third, probably the most important land-use change that arises from our simulations is a

clear shift from Douglas-fir to other tree species, particularly hardwoods, under both climate

change and a carbon price scenario. The compositional shift away from Douglas-fir indicates that

we should likely expect future habitat losses for wildlife species that are specialized to Douglas-

fir habitat, and future habitat gains for wildlife species that are specialized to hardwood forests.

West coast state wildlife agencies recognize many wildlife species of conservation concern that

are specialized to both coniferous forests36 and hardwood37 forests, and so our results suggest

that climate change may impart a rich set of tradeoffs in wildlife habitat changes caused by

private landowner adaptation.

Finally, our scenario that simulates the effect of a temporally-increasing carbon price

indicates that a carbon price accelerates the adaptation towards hardwood forests due to increases

in the carbon rents that arise from high sequestration rates at young stand ages. Furthermore, our

results indicate that the effects of carbon pricing on the extensive margin adaptation away from

Douglas-fir actually outweigh the adaptation impact of climate change. This result – possible

because of our joint modeling of climate change and climate change mitigation policy – implies

that a carbon price aimed at internalizing one externality may generate a second externality by

increasing the speed of habitat changes arising from extensive margin adaptations. The social 36 Examples on the west coast are Vaux’s swift, rufous hummingbird, sooty grouse, fisher, white-headed woodpecker, black-headed woodpecker, Sierra Nevada red fox, wolverine, lynx, Yuma myotis, and long-legged myotis. 37 Example hardwoods-only specialists on the west coast are yellow-billed magpie; example hardwoods-ponderosa pine only specialists on the west coast are ringtail, pallid bat, and oak titmouse.

28

optimality of providing a carbon price to landowners is thus questionable, and future research

should examine the possibility of combining a carbon price with further policy incentives aimed

at reducing negative habitat externalities resulting from private adaptation to a carbon price.

There are many areas in which future research could provide improvements to our

modeling framework. First, a useful extension would account for the feedback effect of natural

disturbance on replanting decisions. For example, landowners who have experienced a fire might

be more likely to replant different species that are known to be fire resistant. Second, the

assumption that only unharvested plots are susceptible to natural disturbances can be relaxed38.

Third, it would be useful to include non-forest land uses such as pasture land for the plots that

are unable to grow any tree species in the future (i.e. no choice set is assigned)39. Fourth, the tree

species choice set could be modified so that landowners can choose mixed-species, instead of

single species. Finally, endogenizing timber prices would account for the price effects of the

modeled supply shifts in this paper, though we note that there is a current lack of estimated

demand elasticities across species-specific lumber markets which would be needed to

endogenize timber prices.

38 In the FIA data, disturbance events occurred in 2.5% of the sampled plots that have been clear-cut, while the rate of occurrence is 10% for unharvested plots. When we focus only on the partial-cut plots, however, the occurrence rate is 15%. This is partly because partial-cutting is typically practiced in the eastern portion of the region which is more susceptible to wildfires. 39 There are 138 plots that are not assigned any tree species in their choice sets by 2090. This is based on the plant viability score described in “Data” section, which defines tree species that are likely to survive in predicted climate conditions at each plot.

29

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9. Figures and Tables Figure 1. Relationship between Current Distribution of Tree Species and Climate

Note: Values after each species name represent average temperature and total precipitation over the sampled plots during the growing season in the current climate. Figure 2. Nested Structure of Harvest/Replanting Decisions

Note: Replanting choices 1 through 6 correspond to Douglas-fir, Fir/Spruce/Mountain Hemlock, Hemlock/Sitka Spruce, Ponderosa Pine, Other Softwood, and Hardwood, respectively.

Each forest plot

Clear-cut Partial-cut No-cut

DisturbanceNo

disturbance1 2 3 4 5 6 1 2 3 4 5 6

Harvest Decision

Replanting Decision Disturbance Event

33

Figure 3. Relationship between Climate and Value of Forestland

34

Figure 4. Non-Federal FIA Forest Plots on U.S. West Coast

4.a Current distribution of forest types 4.b Projected climate change

Note: “Much warmer” and “Much drier” indicate 4 degrees Celsius or more increase in temperature and larger than 50 mm precipitation decrease. Source: AdaptWest Project. 2015. Gridded current and projected climate data for North America at 1km resolution, interpolated using the ClimateNA v5.10 software (T. Wang et al., 2015).

Source: FIA

Much drier and much warmerMuch drier and warmerDrier and much warmer

Drier and warmerWetter and warmerWetter and much warmer

Douglas-fir

Fir/Spruce

Hemlock/Sitka Spruce

Ponderosa Pine

Other Softwood

Hardwood

35

Figure 5. Dynamic Landscape Simulation Steps

36

Figure 6. Time Path of Each Species' Total Landscape Share under "Baseline" Scenario with No Climate Change (left), "Climate Change" Scenario (middle), and “Climate Change & Carbon Price” Scenario (right)

Note: DF=Douglas-fir, FIR=Fir/Spruce, HEM=Hemlock/Sitka Spruce, PP=Ponderosa Pine, OS=Other softwood, and HW=hardwood.

37

Figure 7. Regional Effects of Climate Change and Carbon Pricing on Douglas-fir and Hardwoods by 2100

7.a Effects of climate change by 2100: Difference in Douglas-fir's total shares (left) and shares replanted (right) with and without climate change

7.b Effects of climate change by 2100: Difference in Hardwood’s total shares (left) and shares replanted (right) with and without climate change

7.c Impact on Douglas-fir of carbon price (left) and combined impact of climate change and carbon price (right)

7.d Impact on hardwoods of carbon price (left) and combined impact of climate change and carbon price (right)

-13% - -10%

-9% - 0%

1% - 9%

No change/Too few plots

g g

-64% - -40%-39% - -20%-19% - 0%1% - 33%No change/Too few plo

-20% - 0%

1% - 15%

16% - 30%

31% - 69%

No change/Too few plo

-3% - 0%

1% - 5%

6% - 16%

No change/Too few plots

-13% - -5%

-4% - 0%

1%

No change/Too few plots

g p

-25% - -15%

-14% - -5%

-4% - 0%

1% - 10%

No change/Too few plo

-5% - 0%

1% - 5%

6% - 10%

11% - 19%

No change/Too few plot

-5% - 0%

1% - 5%

6% - 11%

No change/Too few plots

38

Table 1. Key Estimated Average Marginal Effects

Replanting Douglas-fir

Replanting Fir/Spruce

Replanting Hemlock/Sitka

Spruce

Replanting Ponderosa

Replanting Other Softwoods

Replanting Hardwood Natural Disturbance Clear-cut

Change in variable Avg. ME Avg. t

value Avg. ME Avg. t value Avg. ME Avg. t

value Avg. ME Avg. t value

Avg. ME

Avg. t value Avg. ME Avg. t

value Avg. ME Avg. t value Avg. ME Avg. t

value

Doug-fir rent up by $10 CA 2.9%*** 3.02 -0.2%* -1.66 0.0% -0.86 -1.4%** -2.45 -0.5%* -1.76 -0.8%* -1.93 - - 0.2%* 1.92 E OR 5.0%*** 4.00 -1.4%*** -2.94 -0.1%* -1.84 -2.2%*** -3.00 -1.0%** -2.29 -0.4%** -2.41 - - 0.2%** 2.29 E WA 7.1%*** 3.89 -1.4%** -2.38 -0.4%** -2.30 -2.4%*** -2.93 -1.0%** -2.32 -2.0%*** -2.72 - - 0.3%** 2.50 W OR 3.6%*** 4.21 -0.4% -1.22 -0.9%*** -2.61 -0.4%* -1.70 -0.2% -1.57 -1.7%*** -3.18 - - 1.3%*** 3.26 W WA 3.5%*** 3.74 -0.1% -1.15 -1.4%*** -2.82 0.0% -1.51 -0.1% -1.61 -1.9%*** -3.04 - - 0.6%*** 2.67 Average 4.0%*** 3.75 -0.5%* -1.69 -0.6%*** -2.59 -1.1%** -2.51 -0.5%* -1.94 -1.4%*** -2.74 - - 0.01*** 2.60

Hardwood rent up by $10 CA -1.6% -1.20 -0.1% -1.01 0.0% -0.76 -1.6% -1.26 -0.4% -1.11 3.7% 1.33 - - 0.2% 1.11 E OR -0.5%* -1.68 -0.3%* -1.67 0.0% -1.39 -0.9%* -1.69 -0.3% -1.52 2.1%* 1.89 - - 0.1% 1.56 E WA -2.8% -1.61 -0.8% -1.38 -0.3% -1.32 -1.7% -1.56 -0.7% -1.42 6.3%* 1.73 - - 0.3% 1.23 W OR -3.8% -1.64 -0.2% -0.88 -0.5% -1.41 -0.2% -1.12 -0.1% -1.05 4.7%* 1.68 - - 0.4% 1.37 W WA -4.0%* -1.85 -0.1% -0.90 -1.2%* -1.69 0.0% -1.13 -0.1% -1.18 5.3%* 1.89 - - 0.5% 1.35 Average -2.7% -1.59 -0.2% -1.05 -0.4% -1.50 -0.8% -1.34 -0.3% -1.22 4.5%* 1.66 - - 0.00 1.28

Avg. temp up by 3 C CA -4.2% -1.35 -1.5% -0.89 0.6%* 1.79 1.8% 0.25 2.2% 0.76 1.1% 0.70 1.1% 1.26 -0.7% -1.21 E OR -1.3% -0.58 -3.8% -1.20 0.2% 1.29 1.3% 0.21 3.3% 0.82 0.2% 0.42 1.4% 1.26 -0.7% -1.15 E WA -2.8% -1.26 -2.8% -1.00 1.1% 1.72 2.5% 0.70 2.1% 1.06 -0.2% 0.01 1.2% 1.26 -0.7%* -1.65 W OR -29.8%*** -3.79 -0.9% -0.30 22.5%*** 3.34 2.2% 0.51 1.2% 0.78 4.9% 0.72 0.4% 1.23 -4.9% -1.54 W WA -29.9%*** -4.35 -0.2% -0.23 31.8%*** 3.21 0.0% 0.53 0.6% 0.49 -2.3% -0.37 0.6% 1.24 -4.4% -1.02

Average -15.7%*** -2.74 -1.5% -0.61 13.0%*** 3.04 1.5% 0.40 1.7% 0.82 0.9% 0.32 0.9% 1.25 -2.6% -1.30

Precip. down by 20% CA 0.1% 0.53 0.1% 0.46 -0.1%** -2.48 -0.2% -0.16 0.1% 0.16 -0.1% -0.72 0.9%*** 5.56 -0.5%*** -3.43 E OR 0.0% -0.08 0.1% 0.59 0.0% -1.60 -0.1% -0.44 0.1% 0.37 0.0% -0.70 0.3%*** 5.64 -0.1%*** -4.17 E WA 0.0% 0.42 0.1% 0.68 -0.1%** -2.18 -0.1% -0.46 0.0% 0.37 0.0% -0.23 0.5%*** 5.42 -0.2%*** -4.61 W OR 3.7%* 1.95 0.3% 0.46 -3.2%*** -3.43 -0.1% -0.21 0.0% 0.00 -0.7% -1.01 0.6%*** 6.29 -0.1% -0.90 W WA 3.0%** 2.30 0.0% 0.40 -3.1%*** -3.50 0.0% -0.40 0.0% 0.46 0.0% -0.04 0.6%*** 5.37 -0.7%** -2.20

Average 1.6% 1.32 0.1% 0.51 -1.5%*** -3.29 -0.1% -0.29 0.1% 0.26 -0.2% -0.55 0.6%*** 5.68 -0.4%*** -2.80 Note: * p<0.1; ** p<0.05; *** p<0.01

39

Table 2. Discrete Effect of a 90-year Climate and Carbon Price Path on the Probability of Extensive Margin Adaption by Switching from Forest Type

Region Initial forest type Number of Plots

Average discrete effect of climate change (RCP 8.5)

Average discrete effect of carbon price

West California Douglas-fir 189 5.0% 7.1% Fir/Spruce 97 2.1% 4.4% Hemlock/Sitka 9 -1.3% 0.7% Ponderosa Pine 255 -1.0% 2.8% Other softwood 274 -1.3% 4.6% Hardwood 660 -0.9% 1.9% East California Douglas-fir 42 7.3% 7.7% Fir/Spruce 55 4.9% 7.6% Hemlock/Sitka 1 7.6% 21.0% Ponderosa Pine 120 -4.3% 0.6% Other softwood 17 5.3% 11.2% Hardwood 158 -1.9% 3.3% West Oregon Douglas-fir 1012 6.1% 9.9% Fir/Spruce 35 -7.6% 5.0% Hemlock/Sitka 115 -3.6% 2.7% Ponderosa Pine 36 -7.1% 4.0% Other softwood 9 -6.9% 1.5% Hardwood 409 -12.7% -2.8% East Oregon Douglas-fir 92 6.5% 3.8% Fir/Spruce 84 3.2% 3.5% Hemlock/Sitka 1 1.2% 2.3% Ponderosa Pine 289 1.6% 2.9% Other softwood 263 3.5% 2.7% Hardwood 40 4.9% 2.1% West Washington Douglas-fir 791 0.8% 10.5% Fir/Spruce 51 -6.3% 9.5% Hemlock/Sitka 342 -3.1% 5.1% Ponderosa Pine 0 NA NA Other softwood 11 -9.6% -1.5% Hardwood 394 -13.3% -3.9% East Washington Douglas-fir 382 5.1% 3.0% Fir/Spruce 96 2.5% 3.5% Hemlock/Sitka 29 3.6% 2.5% Ponderosa Pine 339 6.8% 3.7% Other softwood 62 3.5% 1.3% Hardwood 86 4.5% 1.0%

40

Table 3. Discrete Effect of a 90-year Climate and Carbon Price Path on the Probability of Extensive Margin Adaption by Switching to Forest Type

Discrete effect of a 90-year path of climate change (RCP 8.5)

Switch to Douglas-fir

Switch to Fir/Spruce

Switch to Hemlock/Sitk

a Sprue

Switch to Ponderosa

Pine

Switch to Other

Softwood

Switch to Hardwoods

West California -1.8% 1.0% -0.3% 1.4% -0.8% 0.5%

East California -2.6% 0.7% 0.0% 2.3% -0.9% 0.0%

West Oregon -4.5% 1.5% -3.7% 1.9% 0.7% 3.9%

East Oregon -0.6% 2.9% 0.3% 0.6% -1.3% 1.2%

West Washington -4.9% 0.2% -3.1% 0.0% 0.8% 3.1%

East Washington 0.5% 1.7% 0.5% 0.7% 0.2% 1.5%

Discrete effect of a 90-year path of increasing carbon price

Switch to Douglas-fir

Switch to Fir/Spruce

Switch to Hemlock/Sitk

a Spruce

Switch to Ponderosa

Pine

Switch to Other

Softwood

Switch to Hardwoods

West California -0.3% 0.5% 0.0% 1.8% 0.1% 1.3%

East California -0.2% 0.1% 0.0% 3.3% 0.4% 0.4%

West Oregon -1.7% 0.6% -0.3% 1.2% -0.1% 6.2%

East Oregon -0.1% 0.1% -0.1% 0.6% 1.3% 1.2%

West Washington -2.4% -0.1% -1.0% 0.0% 2.3% 6.7%

East Washington 0.1% -0.5% -0.2% -0.2% 2.1% 1.6%