# Presentation: 341917

## Market Definition for Hardwood Timber in the Southern Appalachians

- Jeffrey P. Prestemon, John Pye, Karen Lee Abt, Chris LeDoux, and David N. Wear
- Southern Research Station
- USDA-Forest Service
- Research Triangle Park, NC

- SOFEW -- April 18-20 1999 -- Biloxi MS

**Notes:**
Jeffrey P. Prestemon and Karen Lee Abt are Research Foresters, John Pye is Ecologist, and David N. Wear is Project Leader, all in the Forest Service’s Southern Research Station, Forestry Sciences Laboratory, P.O. Box 12254, Research Triangle Park, NC, 27709.  Chris LeDoux is with the Northeastern Research Station, 180 Canfield St., Morgantown, WV, 26505 

## Introduction

- Hardwood timber supply elasticity estimation is tricky
- Understanding supply behavior requires understanding individual decisions
- Decision sets may vary by owner and be modified by the landscape
- We seek to understand how the economic and physical landscape affects supply

**Notes:**
Few analysts have been able to estimate significant and positive elasticities of supply with respect to price for hardwood pulpwood, sawtimber, or logs.

The overarching goal of our research is to estimate a model that permits us to aggregate up from stands to regional supply, allowing stand-level variability in ownership, site characteristics, species make-up, and spatial market factors to influence supply behavior.

Timber inventories and supply decisions are affected by the market, and vice versa.  We seek to understand how the landscape and the market interact to define a forested landscape and, ultimately, the inventory available for harvest.

## This Presentation

- Description of a harvest timing model
- Description of a technique to spatially define the market
- Elaboration of findings consistent with profit-maximizing harvest timing:
- stand ages vary according to factors associated with harvest and transport costs

**Notes:**
We begin our presentation by briefly describing the harvest timing model that serves as the driver of our analysis.  We proceed by outlining a method of defining the spatial distribution of sawmills and pulp mills in the Appalachians of Virginia and North Carolina.

Our results will show that we find significant relationships between stand age and distances to sawmills and pulp mills.  Consistent with theory and expectations, as distances (and therefore costs to transport wood) to mills increase, expected stand age increases.  This finding holds up generally for stands owned by nonindustrial private individuals (NIPFs) and industry-managed stands.  There may also be support for the relationship for government-managed stands as well.

## Harvest Timing Model

- Faustmann-type model:  maximization over time (T) and inputs (L) of SEV (S), given a discount rate (r),volume-variable Prices (P) and volume and distance to market-variable timber harvest costs (C); production costs (wL + k); and site- and time-varying non-timber utility

**Notes:**
If forests are managed at least partly for wood, then there are theoretical bounds on the relationship between stand age and distances to mills, at least under certain conditions. In our most general model, the harvest timing decision is found by maximizing the land value with respect to the harvest age (T) and input quantities (L), given the discount rate and input and output prices.  Inputs are those associated with harvesting, transport, and management.  In this specification the harvest decision is also a stand age-dependent function of non-timber utility derived from the forest

## FOC result

- Optimal harvest age increases with increasing transport cost of material (given fixed $/mile transport cost component)
- Empirical support is obtained if average stand ages (or harvest ages) increase with distance from market (mill)
- Also, distance from market is one gradient that measures the extensive margin--stands far away may never be harvested, or only harvested in rare circumstances

**Notes:**
Based on a Faustmann-type wealth-maximizing harvest timing model, as long as there is a fixed component to transport costs for wood, optimal stand harvest age should increase with distance.  Further, one can imagine a certain distance, delineating the “extensive margin” of profitable timber management, beyond which stands are not harvested.  Under a stochastic version of Faustmann (e.g., Brazee and Mendelsohn 1988*, Haight and Holmes 1991**), this extensive margin could vary with price variability, so that if prices were temporarily highly variable, and prices were abnormally but temporarily high, then some uncut stands very far from mills might be cut.

Hence, after controlling for factors that affect harvest costs, growth rates, and ownership objectives, we might find a positive relationship between stand age with distances to mills.

*Brazee, R., and R. Mendelsohn.  1988.  Timber harvesting with fluctuating prices.  Forest Science 34(2):359-372.
**Haight, R. G., and T. P. Holmes.  1991.  Stochastic price models and optimal tree cutting:  results for loblolly pine.  Natural Resources Modelling 5(4):423-443.

## Identification of Stands, Mills

- FIA Plots in SAA Region of NC and VA
- Mill locations identified using mill address data and Etak, Inc.

**Notes:**
The study area for this analysis was the Appalachians of North Carolina and Virginia, a sub-part of a region originally delineated by the Forest Service as part of the Southern Appalachian Assessment.  Data on stands were obtained from the Forest Service’s Forest Inventory and Analysis (FIA) unit.  FIA makes periodic stand measurements at fixed inventory plots that are distributed in a regular pattern throughout the United States, including North Carolina and Virginia.  The FIA plots that we used in our analysis were plots that were measured in both the FIA’s Fifth and Sixth inventory cycles (early and late 1980s) and that were classified as timberland (producing at least 20 cubic feet of wood per acre per year).  They numbered 2,480.  Of these, 1,536 were NIPF-owned and NIPF-managed, 338 were industry-owned or industry-managed but NIPF-owned, and 606 were government-owned (mostly National Forest lands).

Sawmill and pulp mill addresses were used to pinpoint the locations of the mill of each type closest to each FIA plot. Mill mailing addresses were provided by FIA units based in Asheville, NC and Radnor, PA plus the Texas Forest Service. These were converted to latitude and longitude coordinates using a geocoding service provided by Etak, Incorporated.

## Mill Locations

**Notes:**
This map shows all reported wood-consuming mills (besides sawmills) found in the eastern and southern U.S. 

## Sawmill Locations

**Notes:**
Here are sawmills (hardwood and softwood-processing) of the eastern and southern U.S.  Note the variation in spatial density of sawmills. Mill location data for each state ultimately come from state reporting agencies.  These agencies sometimes have differing size thresholds.  Hence, part of the observed variation in mill spatial densities across states is related to these varying thresholds.  
Additional spatial variation is caused by the amount of available forest inventory, the landscape, and species.  With respect to the latter, it might be that hardwood sawmills are smaller, on average, than sawmills that consume southern pine, so that a hardwood forested landscape supports more mills than a landscape of dominated by southern pine species.  If this is true, then it could explain the high spatial density of sawmills in hardwood-rich Kentucky and Tennessee, relative to the sawmill spatial densities found in states along the Gulf of Mexico.

## FIA Plot Locations

**Notes:**
This map shows the outline of the Southern Appalachian Assessment region, stretching from northeast Alabama to northeast West Virginia and northern Virginia.  The study area for this report is based on FIA plots in the yellow-colored region.  The green points are FIA plots.

## Calculation of Distances to Mills 

- ArcView used to identify closest mills by type (straight-line)
- Road distances estimated using a circuity factor
- Road distances for a subset of pairs calculated using Expedia Streets and Trips 2000
- Circuity factor applied to all straight-line distances

**Notes:**
ArcView, a geographical information system by ESRI, Inc., was used to identify the mill of each type closest to each FIA plot using straight line distance.
We recognized that the road distance between two points is the relevant measure for explaining stand age.  And we also believed that the relationship between straight line distance and road distance might not be linear.  
We therefore estimated a circuity relationship between road distance and straight line distance using a sample of 25 pairs of points in the study area. Road distances were computed by Microsoft’s Expedia Streets and Trips 2000, a road mapping software package.

## Road Distance Estimation

- source: MS Expedia Streets & Trips 2000

**Notes:**
This map shows an example road distance estimate using Expedia Streets and Trips 2000.  The green line traces the road distance between the FIA plot (the green square in the upper left of the map) and the mill (the red square in the center-right of the map).  The distance used in our representation of “road distance” does not include the distance from the FIA plot center to the nearest road.  That variable, called “distance to nearest road” by FIA, is a separate variable in our analysis.

## Circuity Factor (C) Equation Estimate

- where R= road distance, L = straight line distance
- Estimate:  R = 1.60 + 1.39L
- Forced intercept to zero:  R = 1.45L

**Notes:**
Somewhat surprisingly, although the original model specified that the road distance would be a nonlinear function of the straight line distance, only the coefficient on the linear distance term was statistically significantly different from zero.  The intercept was weakly significant (i.e., at 10%).  A reestimation of the model, forcing a zero intercept, revealed a linear circuity factor of 1.45, applicable to the entire study area and any straight line distance.

## Circuity Factor Estimate

**Notes:**
This plot shows the estimated equation that included an intercept.  The relationship produced an R-squared of 0.98.  Dropping the intercept did not change the R-squared much.

## Estimated Age Relationships

- Estimated Stand Age = f(RL,RP,S,D,Q)
- where RL is road distance to sawmill, RP is road distance to pulpmill, S=percent slope, D=distance to road, and Q is site quality
- Quadratic estimated by ownership (NIPF, Industry, Government)
- Box-Cox method, assuming heteroscedastic covariance matrix

**Notes:**
We applied the 1.45 circuity factor to all of the observations in our study. We then estimated using generalized least squares (i.e., allowing a heteroscedastic covariance matrix) a quadratic model that related stand age as measured in FIA's sixth inventory (1990 in North Carolina, 1992 in Virginia) to distances to nearest mill (miles), distance to nearest road (miles) as recorded by FIA, site slope (percent), and site quality as recorded by FIA (varying in our sample from 1 to 5, where 1 is the highest productivity, 5 is lowest). 
In a Box-Cox approach, where parsimony is perceived as an important model selection criterion, variables that had t-values less than unity in absolute value in a first round of estimates were dropped for a second round.  The second round produced a parsimonious estimate.  We report in the following slides  relationships between stand age and these variables corresponding to the final, parsimonious models.

## Stand Age vs. Sawmill Distance

**Notes:**
The above graph plotted expected stand age against road distance to the nearest sawmill, holding other variables constant at sample means or modes.  We see a generally positive relationship between stand age and distance to the nearest sawmill.  The government relationship is increasing for all relevant observations, while industry-managed and NIPF-managed stands show a curvilinear relationship.  Note that the number of FIA plots that are more than 20 miles from their nearest sawmill are very few (64 out of 1,536, or 4.1% of NIPF plots, and 18 out 338, or 5.3% of industry plots), so less confidence should be attached to the downward-sloping portion of the distance curves. 

For both NIPF and industry, at sample average and modal values for other variables in each ownership, through the first 15 road miles, each road mile of distance adds about 0.8 years to the expected age of the stand. For government-owned stands, each road mile adds 0.36 years. 

## Stand Age vs. Pulp Mill Distance

**Notes:**
At least for NIPF-managed and industry-managed stands, the relationship between stand age and pulp mill distance, other things held constant, is positive throughout the observed range of the data.  For NIPF-managed stands, each mile of road distance to the nearest pulp mill adds about one-sixth of one year.  For industry, each mile adds one-third of one year.  

By way of illustration, this means, ceteris paribus, at mean values of other variables, an NIPF stand is expected to be seven years older eighty road miles from its nearest pulp mill than a comparable one growing next to the pulp mill. An industry-managed stand located eighty road miles from its nearest pulp mill is expected to be 13.5 years older than a comparable stand located next to the pulp mill. 

## Stand Age vs. Slope of Site

**Notes:**
Slope is generally positively related to stand age.  NIPF and government-owned stands’ ages increase with slope across all ranges of the data. A level NIPF-managed stand is expected to be 5 years younger than one growing on a 50% slope, ceteris paribus.  For government, a level stand would be 8.5 years younger than a stand on a 50% slope.

Industry appears to have a curvilinear relationship with slope.  Again, as for mill distances, few stands are found in the extremes of the data, so less confidence should be placed on expected ages of stands growing on the steepest slopes.  An industry-managed stand growing on flat land is expected to be eleven years younger than one growing on a 50% slope.  

## Stand Age by Site Class

**Site Class**

- 0

- 20

- 40

- 60

- 80

**1**

**2**

**3**

**4**

**5**

- Stand Age (Years)

**Notes:**
As consistent with theory on optimal harvest age, stands that grow slower should be older, on average.  We find that this is true for all ownership categories examined.  Going from a fast-growing site class 2 to a slow-growing site class 5 and holding other variables held constant, stands are expected to be 11, 10, and 17 years on NIPF, industry, and government stands, respectively.

## Summary and Conclusions

- We expected to find relationships between stand age and cost factors, and we found them
- Proximity to markets is correlated with stand age
- New mills should bring down harvest ages; stands closer to mills may well produce more pulpwood and less sawtimber; and other stand age-dependent values obtained from forests should be similarly affected by mills

**Notes:**
As we expected, our analysis found statistically significant relationships between stand ages and variables associated with harvest and transport costs.  Most significantly, distance to mill does affect the age distribution of stands, and this finding has implications for economic and ecological research.  

One implication of the research is that an area with a new mill should experience general reductions in stand ages in the vicinity of the mill, and the reductions should correspond with the distance to that new mill.  While we did not test this question directly, there are sound theoretical reasons why the relationship should be causal.  

Our research showed that, at least within fifteen road miles of a sawmill, stand ages increase by 0.8 years per road mile for NIPF and industry-managed stands. For government-owned stands, stand age increases by 0.36 years per road mile. Pulp mills also apparently affect stand ages in the southern Appalachians of Virginia and North Carolina: within 80 road miles of the mill, each road mile of distance adds 0.17 years for NIPF-managed stands and 0.33 years for industry-managed stands.