A

v

Stumpage Market 

Integration in Western 

National Forests

Jean M. Daniels

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

Research Paper

PNW-RP-586

March 2011

DEPAR TMENT OF AGRICULT URE
Authors

Jean M. Daniels is a research forester, Portland Forestry Sciences Laboratory,

620 SW Main, Suite 400, Portland, OR 97205. 

The Forest Service of the U.S. Department of Agriculture is dedicated to the principle of 

multiple use management of the Nation’s forest resources for sustained yields of wood, 

water, forage, wildlife, and recreation. Through forestry research, cooperation with the 

States and private forest owners, and management of the National Forests and National 

Grasslands, it strives—as directed by Congress—to provide increasingly greater service 

to a growing Nation.

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and 

activities on the basis of race, color, national origin, age, disability, and where applicable, 

sex, marital status, familial status, parental status, religion, sexual orientation, genetic 

information, political beliefs, reprisal, or because all or part of an individual’s income 

is derived from any public assistance program. (Not all prohibited bases apply to all 

programs.) Persons with disabilities who require alternative means for communication of 

program information (Braille, large print, audiotape, etc.) should contact USDA’s TARGET 

Center at (202) 720-2600 (voice and TDD). To file a complaint of discrimination, write 

USDA, Director, Office of Civil Rights, 1400 Independence Avenue, SW, Washington, DC 

20250-9410 or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA is an equal 

opportunity provider and employer.
i

Abstract

Daniels, Jean M. 2011. Stumpage market integration in western national forests. 

Res. Pap. PNW-RP-586. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 27 p. 

This study presents results of statistical tests for stumpage market integration on 62 

national forests in the Western United States. Quarterly stumpage prices from 1984 

to 2007 obtained from cut and sold reports for USDA Forest Service Regions 1, 4, 5, 

and 6 (Northern, Intermountain, Pacific Southwest, and Pacific Northwest, respectively) were analyzed to establish the presence and extent of national forest timber 

markets. Statistical evidence suggests that prices from the Beaverhead-Deerlodge 

and Salmon-Challis Forests and the Kootenai and Idaho Panhandle Forests are 

linked and that only these two sets of forests can be modeled as integrated stumpage markets. Aside from these four forests, there is no evidence that the law of one 

price holds for national forest timber markets in the West.

Keywords: Stumpage prices, national forest timber, timber markets, cointegration, 

stationarity, arbitrage, integration.
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Stumpage Market Integration in Western National Forests

Introduction

This research paper describes preliminary results of time-series analysis of stumpage prices on national forests in the Western United States. This analysis was 

completed as part of an effort to develop a spatially explicit stumpage price model 

for national forest timber in the Northern (Region 1), Intermountain (Region 4), 

Pacific Southwest (Region 5), and Pacific Northwest (Region 6) USDA Forest 

Service administrative regions. The objective of the model is to assist national 

forest planners in estimating the mix of sawtimber and nonsawtimber trees that will 

be sufficient to entice stumpage purchasers to buy sales designed for hazardous fuel 

reduction treatments, ecosystem restoration, and other forest management activities. 

One preliminary consideration for model development is determining whether 

stumpage markets for national forest timber are linked. Linked markets have 

several implications for model development and purchaser behavior. Linkages 

determine whether national forests can be modeled as one effective market or 

several localized markets and the geographic extent of these markets. Market 

linkages also must be addressed when specifying regression equations used to test 

hypotheses pertaining to the model, or else parameter estimates may be biased. 

In addition, links among stumpage markets have implications for how changes in 

harvest flows in one forest can influence prices across several forests and associated private timberlands. Last, market linkages can provide clues about the nature 

of trading behavior among stumpage purchasers. Theoretically, competitive trade 

activity should ensure that prices of timber supplied by different forests tend toward 

uniformity, although short-run deviations may occur. 

Market linkages are identified by examining trends in timber prices among 

forests. In general, markets that appear to be separate can be viewed as one effective market if their prices move together over time. The force that keeps these prices 

moving together is arbitrage, defined as the pursuit of opportunities to profitably 

move commodities across markets until price differences offset transaction costs. 

Arbitrage causes prices in different markets to converge spatially or temporally 

by encouraging people to buy low and sell high. Stumpage purchasers compete by 

using price arbitrage to actively exploit timber price differentials among forests. 

With efficiently linked markets, arbitrage opportunities are eventually exhausted 

and prices differ only by transaction costs. The law of one price (LOP) from international trade theory motivates this argument; it states that in long-run equilibrium, 

efficient arbitrage and trade activity ensure that the prices of homogeneous products 

supplied by different producers in different regions tend toward uniformity (Jung 

and Doroodian 1994). 
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RESEARCH PAPER PNW-RP-586

Market linkages must be identified and accounted for if the stumpage market 

model is to be effective and useful. This preliminary report uses statistical tests to 

determine empirically if national forest stumpage prices are linked and, if so, the 

geographic extent of these linkages. Specifically, prices for 62 national forests in the 

Western United States were examined using correlation matrices, unit root tests for 

stationarity, and cointegration tests for market arbitrage. Tests reported here will be 

applied to enhance the national forest pricing model. Figure 1 shows the study area 

with regional and national forest boundaries delineated. 

Figure 1—National forests of the Intermountain, Northern, Pacific Southwest, and Pacific Northwest Forest Service Regions.
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Stumpage Market Integration in Western National Forests

Background

Many previous studies have examined price trends and integration in forest product 

markets with the methods used here. Cointegration analysis has been used to test 

for market integration, arbitrage, and the law of one price in a variety of forest 

industries. It is well-documented in the forest economics literature. In the United 

States and Canada, cointegration has been used to examine markets for softwood 

lumber (Baek 2006, Jung and Doroodian 1994, Murray and Wear 1998, Nanang 

2000, Shahi et al. 2006, Stevens and Brooks 2003, Uri and Boyd 1990, Yin and 

Xu 2003). Generally, these studies examined the extent of integration in U.S. and 

Canadian regional lumber markets and how trade policies affecting softwood lumber have changed market structure over time. Other North American forest product 

industries have been tested for market integration as well, including pulp and paper 

(Alavalapati et al. 1997, Buongiorno and Uusivuori 1992) and newsprint (Tang and 

Laaksonen-Craig 2007). Cointegration analysis has also been applied extensively to 

study price movements, wood product market integration, price arbitrage, and the 

law of one price in forest industries in Europe. Studies performed in Europe generally investigate whether the easing of trade barriers in European Union member 

countries led to integrated and efficient roundwood markets (Hanninen 1998, 

Hanninen et al. 1997, Riis 1996, Stordal and Nyrud 2003, Thorsen 1998, Thorsen et 

al. 1999, Toppinen and Toivonen 1998, Toivonen et al. 2002). 

Although the literature teems with studies examining integration in product 

markets, stumpage market integration studies are more rare. A few studies use 

cointegration to examine the link between stumpage and product markets (Luppold 

and Baumgras 1996, Luppold et al. 1998, Zhou and Buongiorno 2005). The remaining known studies of stumpage prices and market integration focus on the U.S. 

South (Nagubadi et al. 2001, Prestemon 2003, Prestemon and Holmes 2000, Yin 

and Newman 1996). 

Stumpage markets have been modeled, usually for understanding and forecasting national and regional timber supply and demand. Past work assumed price equilibrium across spatial markets. Prestemon (2003) conducted an economic analysis 

for the Environmental Impact Analysis of the Biscuit Fire salvage operation, where 

the Siskiyou-Rogue, Klamath, and Six Rivers National Forests were treated as 

part of an integrated market. Integration was assumed because of proximity of the 

forests. Models such as the Timber Assessment Market Model (TAMM) and the 

Global Trade Model (GTM) also assume that timber markets are fully integrated 

(Binkley and Dykstra 1987). The TAMM model provides annual projections of 

volumes and prices in solid wood product and saw-timber stumpage markets by 

geographic region for up to 50 years (Adams and Haynes 1996). The U.S. West is 
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RESEARCH PAPER PNW-RP-586

assumed to comprise five regional markets but no tests were conducted for market 

integration. The GTM incorporates two U.S. supply regions (East and West) into a 

global market timber model, again without testing for integration. 

I was unable to find any study testing for arbitrage behavior or integration in 

stumpage markets for the Western United States. In addition, no previous study 

has examined the geographic extent of markets for national forest timber or 

employed econometric methods such as unit root testing for price stationarity and 

cointegration analysis for long-run price relationships. Given the vast area of forest 

land in the Western United States and the traditional ties between federal timber 

sales and rural community stability and economic development, this finding was 

surprising. This study is the first known to examine market integration for national 

forest stumpage in the Western United States. Results reported here will be used 

to improve the accuracy of the spatial pricing model for national forest timber by 

incorporating cross-forest price relationships. The next section describes the data 

used for the analysis.

Data 

Data were obtained from Kling (2008), who reported quarterly average sold prices 

for stumpage for the 62 national forests in Regions 1, 4, 5, and 6 between the first 

quarter (Q1) of 1984 and the first quarter of 2007. Sold prices are computed as 

volume weighted averages of high-bid prices for the right to harvest timber at a 

future date. Since 1984, sold prices have been reported as an all-species average of 

high bids, net of purchaser road credits and an allowance for timber stand improvements. Quarterly sold price series typically excluded sales with a total value of less 

than $2,000. Prices less than $1.00/thousand board feet (MBF) were omitted owing 

to the negative values generated from transformation to natural logarithmic form 

required for analysis. Prices were adjusted from nominal published prices to real 

1984 dollars using the Producer Price Index. 

Average sold prices by region over the study period are presented in figure 2. 

This figure illustrates the persistent price differences that have existed between 

regions for decades, although the price spread declined during the mid-1990s. 

Sold prices on all regions rose and then fell over time; prices in 2007 were either 

at or below prices in 1984. The price drop in the Pacific Northwest is especially 

dramatic. Timber prices in all four regions could be reacting to similar external 

drivers, suggesting linkages among the sold prices, which may scale down to 

integration at the forest level. 

Tables 1 through 4 contain descriptive statistics for stumpage prices on each 

national forest by region from Q1 1984 to Q1 2007. At the forest level, median 
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Stumpage Market Integration in Western National Forests

values may provide a more accurate view of prices; averages may be skewed 

for forests with no timber sales for extended periods of time. Each forest has 93 

quarterly price observations, but in many cases the minimum value was $0.00. In 

Region 1, the Clearwater, Idaho Panhandle, and Kootenai Forests had the highest 

median sold timber prices; prices on the Custer National Forest were far below the 

other forests. Prices were lowest for timber in Region 4 forests but were led by sales 

on the Payette. The Shasta-Trinity Forest had the highest sold prices in Region 5 

0

50

100

150

200

250

Average sold price (dollars/thousand board feet)

Northern Region Intermountain Region

Pacific Southwest Region Pacific Northwest Region

Figure 2—Median quarterly sold prices for timber harvests in the Northern, Intermountain, Pacific 

Southwest, and Pacific Northwest Forest Service Regions, 1984–2007.

Table 1—Descriptive statistics of sold prices for Northern Region timber by national forest, Q1 1984 

through Q1 2007

Sample Standard Standard

Forest size Mean error Median deviation Minimum Maximum

- - - - - - - - - - - - - - - Dollars per thousand board feet - - - - - - - - - - - - - - - 

Beaverhead- 

 Deerlodge 93 47.47 5.13 27.24 49.49 4.89 292.09

Bitterroot 93 47.09 3.96 37.19 38.22 1.49 161.82

Clearwater 93 81.72 7.72 63.87 74.42 3.22 325.56

Custer 93 14.76 1.78 8.30 17.13 2.67 97.05

Flathead 93 62.94 5.41 45.79 52.21 0.92 254.99

Gallatin 93 28.12 3.36 16.20 32.39 2.05 175.09

Helena 93 42.67 5.57 19.85 53.76 1.91 276.17

Idaho Panhandle 93 90.53 6.19 81.64 59.66 10.84 347.89

Kootenai 93 105.13 7.56 92.68 72.90 7.41 371.54

Lewis and Clark 93 38.03 4.80 17.34 46.30 3.84 235.68

Lolo 93 65.85 5.96 52.40 57.49 3.45 265.56

Nez Perce 93 47.10 5.56 21.97 53.62 0.96 260.07
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RESEARCH PAPER PNW-RP-586

Table 2—Descriptive statistics of sold prices for Intermountain Region timber by national forest, 

Q1 1984 through Q1 2007

Sample Standard Standard

Forest size Mean error Median deviation Minimum Maximum

- - - - - - - - - - - - - Dollars per thousand board feet - - - - - - - - - - - - -

Ashley 93 29.00 3.43 14.96 33.11 3.66 177.20

Boise 93 68.03 7.57 44.43 73.04 0.00 398.35

Bridger-Teton 93 29.43 3.62 17.29 34.89 0.00 251.10

Caribou-Targhee 92 43.94 4.20 29.38 40.29 0.00 169.50

Dixie 93 32.22 4.31 9.24 41.54 3.97 204.86

Fishlake 93 37.76 3.74 23.53 36.06 5.45 145.57

Humboldt-Toiyabe 93 17.18 1.67 13.60 16.06 5.25 113.62

Manti-La Sal 93 19.72 3.99 8.01 38.43 0.00 301.44

Payette 93 88.56 10.29 62.91 99.22 0.00 509.82

Salmon-Challis 93 45.25 5.47 27.57 52.76 4.21 346.88

Sawtooth 92 18.54 1.97 12.51 18.91 0.00 128.09

Uinta 93 42.46 5.28 16.06 50.91 0.00 210.06

Wasatch-Cache 93 28.50 3.73 13.86 35.97 0.00 180.25

Table 3—Descriptive statistics of sold prices for Pacific Southwest Region timber by national 

forest, Q1 1984 through Q1 2007

Sample Standard Standard

Forest size Mean error Median deviation Minimum Maximum

- - - - - - - - - - - - - - Dollars per thousand board feet - - - - - - - - - - - - -

Angeles 93 36.56 2.36 42.30 22.76 0.00 99.25

Cleveland 93 33.78 7.13 29.77 68.76 0.00 679.87

Eldorado 93 90.87 9.27 78.29 89.44 0.66 607.92

Inyo 93 48.52 6.25 25.72 60.30 0.00 330.57

Klamath 93 66.23 6.49 50.71 62.62 4.38 284.15

LTBMUa 93 23.95 2.47 17.67 23.87 0.00 125.60

Lassen 93 90.97 8.43 64.51 81.31 4.54 366.28

Los Padres 93 14.68 0.99 15.87 9.52 0.00 42.36

Mendocino 93 60.67 7.64 21.81 73.68 0.54 286.23

Modoc 93 94.65 12.74 29.71 122.89 0.62 558.58

Plumas 93 75.24 7.75 46.28 74.71 1.67 386.40

San Bernardino 93 26.43 1.53 28.99 14.80 0.00 72.78

Sequoia 93 55.58 7.92 26.06 76.33 0.00 419.92

Shasta-Trinity 93 112.69 11.10 91.76 107.04 4.11 533.00

Sierra 93 66.42 6.80 47.99 65.60 0.05 341.35

Six Rivers 93 87.10 8.47 60.46 81.72 2.63 335.89

Stanislaus 93 60.75 5.52 44.42 53.22 8.95 296.07

Tahoe 93 76.89 6.63 60.81 63.92 6.42 334.83

a Lake Tahoe Basin Management Unit.
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Stumpage Market Integration in Western National Forests

with the Eldorado Forest a distant second. Region 6 sold prices were the highest 

overall; timber on the Willamette, Umpqua, and Siskiyou Forests commanded the 

highest prices of the 62 study forests. The range of prices both within and between 

regions likely reflects species differences, proximity to manufacturing activity, and, 

in the Pacific Northwest, influence of price premiums in private log export markets 

(Daniels 2005). Unfortunately, the sold price series used in this report represents an 

all-species average and does not allow testing for species differences. The influence 

of manufacturing clusters on prices will be examined in the next stage of spatial 

pricing model development.

Stumpage prices from 2002 to 2007 for all 62 forests were averaged, sorted 

from highest to lowest, and grouped by quartiles. The resulting rankings by price 

are mapped by region in figures 3 through 6 with a color scheme that depicts 

price quartiles from lowest to highest. The same quartile groupings are used for 

all regions. The figures show that Region 4 forests tend to have the lowest timber 

prices and Region 6 prices are highest, especially forests in Oregon.

Table 4—Descriptive statistics of sold prices for Pacific Northwest Region timber by national 

forest, Q1 1984 through Q1 2007

Sample Standard Standard

Forest size Mean error Median deviation Minimum Maximum

- - - - - - - - - - - - Dollars per thousand board feet - - - - - - - - - - - - - -

Colville 93 72.32 4.85 71.23 46.76 6.58 221.37

Deschutes 93 59.53 4.08 54.02 39.32 5.62 172.55

Fremont 93 91.21 8.32 65.35 80.22 0.00 378.97

Gifford Pinchot 93 111.22 10.13 89.54 97.66 3.16 389.43

Malheur 93 97.81 8.81 74.61 84.96 6.38 363.27

Mount Baker-

 Snoqualmie 93 80.87 8.24 53.35 79.47 0.00 362.91

Mount Hood 93 136.37 10.92 107.36 105.30 12.51 445.36

Ochoco 93 105.30 11.36 47.25 109.59 0.00 485.88

Okanogan 93 64.23 6.33 42.20 61.00 2.04 286.94

Olympic 93 80.13 6.54 62.88 63.04 4.89 261.96

Rogue River 93 127.39 12.84 99.64 123.85 6.71 679.62

Siskiyou 92 172.09 17.82 126.52 170.90 5.92 995.59

Siuslaw 93 134.58 9.83 110.41 94.82 12.69 462.75

Umatilla 93 48.74 4.22 38.50 40.73 0.00 220.23

Umpqua 93 150.09 13.95 116.53 134.55 13.57 698.67

Wallowa-Whitman 93 51.16 3.28 48.30 31.63 4.38 131.53

Wenatchee 93 47.05 4.25 35.08 41.01 6.74 285.80

Willamette 93 174.45 10.03 159.60 96.77 14.95 390.22

Winema 93 96.35 8.56 76.50 82.50 3.09 503.56
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RESEARCH PAPER PNW-RP-586

Figure 3—Stumpage price rankings for national forests of the Northern (Region 1) Forest Service Region.
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Stumpage Market Integration in Western National Forests

Figure 4—Stumpage price rankings for national forests of the Intermountain (Region 4) Forest Service Region.
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RESEARCH PAPER PNW-RP-586

Figure 5—Stumpage price rankings for national forests of the Pacific Southwest (Region 5) Forest Service Region.
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Stumpage Market Integration in Western National Forests

Figure 6—Stumpage price rankings for national forests of the Pacific Northwest (Region 6) Forest Service Region.

Methods 

Empirical analysis to determine the extent of national forest timber markets began 

by looking for correlation among stumpage prices (Murray and Wear 1998, Yin 

and Newman 1996). Correlation matrices were developed for forests in each region 

(tables 5 through 8). Values near 1.0 or -1.0 suggest that prices have a strong positive or negative relationship, respectively; values near zero suggest very little or no 

relationship between prices. Values greater than 0.5 are shaded for emphasis.
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RESEARCH PAPER PNW-RP-586 Table 5—Forest Service Northern Region stumpage price correlation matrix Beaverhead Bitter- Clear- Flat- Idaho Lewis and Nez- Forest Deerlodge root water Custer head Gallatin Helena Panhandle Kootenai Clark Lolo Perce Beaverhead- Deerlodge 1.0000 0.3314 0.3413 0.1918 0.1351 0.0905 0.2141 0.5860 0.5527 0.3631 0.5200 0.1314 Bitterroot 1.0000 0.0869 0.0316 0.0173 0.1005 0.0927 0.0983 0.1761 0.1712 0.2311 0.1293 Clearwater 1.0000 0.1292 0.0458 0.1482 0.1463 0.4454 0.3673 0.3640 0.5196 0.2211 Custer 1.0000 0.0326 0.2205 0.1977 0.1958 0.2585 0.1558 -0.0019 -0.0384

Flathead 1.0000 -0.0225 0.2730 0.3590 0.1802 0.4131 0.1529 0.2465Gallatin 1.0000 0.0905 0.2384 0.3400 0.2276 0.0212 0.0309

Helena 1.0000 0.2424 0.2859 0.2574 0.2416 0.3061

Idaho Panhandle 1.0000 0.7060 0.4840 0.5466 0.3004

Kootenai 1.0000 0.3826 0.4787 0.1402Lewis and Clark 1.0000 0.3032 0.3999

Lolo 1.0000 0.2563Nez Perce 1.0000

Correlation values greater than 0.5 are bold for emphasis.Table 6—Forest Service Intermountain Region stumpage price correlation matrix

Bridger- Caribou- Humboldt- Manti- Salmon- WasatchForest Ashley Boise Teton Targhee Dixie Fishlake Toiyabe La Sal Payette Challis Sawtooth Uinta Cache

Ashley 1.0000 0.0718 0.1342 0.3064 0.0095 0.2773 -0.0315 -0.0406 0.1849 0.2953 0.3903 0.2440 0.2760

Boise 1.0000 0.4130 0.2153 0.0486 0.2539 -0.2399 0.2290 0.5386 0.6149 0.2941 0.2353 0.1486

Bridger-Teton 1.0000 0.3234 -0.0369 0.2368 0.0281 0.2154 0.4019 0.3394 0.1792 0.1827 0.1911

Caribou-Targhee 1.0000 0.1363 0.4734 -0.0770 0.2813 0.0746 0.3344 0.2556 0.3398 0.4187

Dixie 1.0000 0.0823 -0.0482 0.1703 0.0740 0.0568 0.3045 0.1836 0.0375

Fishlake 1.0000 0.0521 0.1141 0.0604 0.3700 0.2006 0.4067 0.3559

Humboldt-Toiyabe 1.0000 0.1258 0.0730 -0.1084 0.0006 -0.1053 0.0031

Manti-La Sal 1.0000 0.1705 0.0531 0.1407 0.2693 0.2627

Payette 1.0000 0.4893 0.1944 0.1441 -0.0428

Salmon-Challis 1.0000 0.3325 0.2510 0.2527

Sawtooth 1.0000 0.5371 0.3017

Uinta 1.0000 0.2823

Wasatch-Cache 1.0000

Correlation values greater than 0.5 are bold for emphasis.
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Stumpage Market Integration in Western National Forests

Table 7—Forest Service Pacific Southwest Region stumpage price correlation matrix

Los San Shasta- Six

Forest Angeles Cleveland Eldorado Inyo Klamath LTBMUa Lassen Padres Mendocino Modoc Plumas Bernardino Sequoia Trinity Sierra Rivers Stanislaus Tahoe

Angeles 1.0000 0.0623 -0.1992 -0.1667 -0.1323 0.1367 -0.3430 0.4368 -0.0639 -0.2594 -0.2375 -0.0194 0.0681 -0.0255 -0.1190 -0.3031 0.0110 -0.1906Cleveland 1.0000 -0.0739 -0.2176 -0.3515 -0.1110 -0.3264 -0.1273 -0.4612 -0.1669 -0.2676 -0.2028 -0.4068 -0.2876 -0.2817 -0.1258 -0.2961 -0.2967

Eldorado 1.0000 0.2835 0.1209 0.3382 0.4431 0.0893 0.3741 0.0731 0.2327 0.3130 0.3747 0.1490 0.3049 0.4303 0.3574 0.4862

Inyo 1.0000 0.0504 0.2632 0.3337 -0.0390 0.2322 -0.0091 0.3528 0.1078 0.1426 0.1108 0.2650 0.3072 0.3942 0.2743

Klamath 1.0000 0.0933 0.4175 0.0611 0.1966 0.3648 0.4670 0.2004 0.4716 0.6840 0.4765 0.1434 0.3657 0.4407

LTBMUa 1.0000 0.0506 0.1651 0.1583 -0.0152 0.2944 0.2556 0.2958 0.2410 0.3005 -0.0201 0.3675 0.5978

Lassen 1.0000 -0.2353 0.3566 0.4173 0.6869 0.1846 0.4692 0.4057 0.6857 0.5717 0.3600 0.3684

Los Padres 1.0000 0.0533 -0.1569 -0.0567 0.0997 0.2079 0.0352 -0.0026 -0.1386 0.2005 0.1117

Mendocino 1.0000 0.1158 0.1084 0.4475 0.3101 0.2274 0.3357 0.4809 0.2749 0.2457

Modoc 1.0000 0.3636 0.0383 0.3495 0.3117 0.3143 -0.0045 0.1120 0.2928

Plumas 1.0000 0.2364 0.5168 0.4317 0.5809 0.2527 0.3575 0.6015

San Bernardino 1.0000 0.1639 0.1358 0.1303 0.1452 0.2409 0.4098

Sequoia 1.0000 0.5665 0.6543 0.1306 0.4986 0.5678

Shasta-Trinity 1.0000 0.6265 0.1611 0.4226 0.4349

Sierra 1.0000 0.4743 0.5029 0.5133

Six Rivers 1.0000 0.1407 0.2053

Stanislaus 1.0000 0.4654

Tahoe 1.0000

a LTBMU = Lake Tahoe Basin Management Unit.

Correlation values greater than 0.5 are bold for emphasis.
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RESEARCH PAPER PNW-RP-586

Table 8—Forest Service Pacific Northwest Region stumpage price correlation matrix

Mount

Gifford Baker- Mount Rogue WallowaForest Colville Deschutes Fremont Pinchot Malheur Snoqualmie Hood Ochoco Okanogan Olympic River Siskiyou Siuslaw Umatilla Umpqua Whitman Wenatchee Willamette Winema

Colville 1.0000 0.0717 -0.0115 -0.0266 0.0153 0.1119 0.1592 0.0167 0.2928 0.1030 0.0760 0.2781 -0.0716 0.1706 0.1338 0.1071 0.0698 0.3150 -0.2189

Deschutes 1.0000 0.4230 0.2084 0.3187 0.3673 0.2953 0.3553 0.1009 0.3918 0.0752 0.0995 0.3219 0.1683 0.3319 0.0660 0.2836 0.1724 0.1986

Fremont 1.0000 0.4436 0.6386 0.4918 0.4967 0.4459 0.1162 0.4563 0.2625 0.0486 0.3247 0.2373 0.4374 0.3136 0.2469 0.3606 0.4088

Gifford Pinchot 1.0000 0.4240 0.2404 0.2785 0.3885 0.0338 0.3532 0.4248 0.1137 0.1668 0.1259 0.3387 0.3892 0.1218 0.2492 0.2524

Malheur 1.0000 0.4680 0.5237 0.6031 0.2892 0.4361 0.3716 0.0229 0.1660 0.2795 0.3801 0.2110 0.2425 0.3413 0.5229

Mount Baker- Snoqualmie 1.0000 0.2992 0.4088 0.1170 0.4092 0.3357 0.2160 0.2306 0.1657 0.3495 0.3973 0.2601 0.2518 0.5206

Mount Hood 1.0000 0.4202 0.3186 0.5391 0.3362 0.0839 0.1847 0.2644 0.4743 0.3218 0.1824 0.5350 0.3593

Ochoco 1.0000 0.1817 0.4192 0.1759 0.0745 0.1696 0.4553 0.1366 0.1235 0.2627 0.3037 0.4202

Okanogan 1.0000 0.3152 0.2778 -0.0480 -0.0401 0.2016 0.2879 0.1160 0.0834 0.4109 0.2322

Olympic 1.0000 0.4169 0.1438 0.2265 0.4346 0.3171 0.2058 0.4005 0.4660 0.3554

Rogue River 1.0000 0.2346 0.1917 0.1007 0.4829 0.3514 0.2527 0.4342 0.4341

Siskiyou 1.0000 0.1598 -0.1024 0.2083 0.1415 0.2233 0.2415 -0.0233

Siuslaw 1.0000 -0.0455 0.2336 0.0349 0.0960 0.0399 0.2235

Umatilla 1.0000 0.1057 0.1553 0.2816 0.3648 0.2196

Umpqua 1.0000 0.3047 0.2147 0.4018 0.4028

Wallowa-Whitman 1.0000 -0.0048 0.4188 0.3138

Wenatchee 1.0000 0.3085 0.2441

Willamette 1.0000 0.2936

Winema 1.0000

Correlation values greater than 0.5 are bold for emphasis.
15

Stumpage Market Integration in Western National Forests

In Region 1, prices in the Beaverhead-Deerlodge, Idaho Panhandle, Kootenai, 

Lolo, and Clearwater National Forests show evidence of correlation. Figure 3 shows 

these forests are close to one another. Region 4 contains two groups of correlated 

stumpage prices: (1) the Boise, Payette, Salmon-Challis Forests and (2) the Sawtooth and Uinta Forests. Region 5 forests display another spatial trend; forests near 

the Sierra Mountains are generally correlated, as are forests in northern California. 

In contrast, a strong negative correlation exists between Angeles and Cleveland 

National Forest prices and most other Region 5 forests. Region 6 had few high 

correlation values; stumpage prices on the Malheur National Forest were modestly 

correlated with four other forests: Fremont, Mount Hood, Ochoco, and Winema. 

Correlation matrices provide preliminary evidence of price relationships among 

some western national forests. However, correlation matrices do not provide sufficient statistical evidence of market integration. Tests for market integration are 

equivalent to testing to see if the law of one price holds using the arbitrage price 

condition:

P1

t

 = α + βP2

t

 + εt (1)

where P1

t

 and P2

t

 are prices in markets 1 and 2 and εt is the error term at time t. The 

constant term α represents transportation costs. If the LOP holds, arbitrage opportunities are exhausted and β is not significantly different from 1. Prices differ only 

by transportation costs.

Testing the arbitrage condition has traditionally been an important feature of 

empirical analysis of commodity markets. However, this price regression has some 

statistical problems that may invalidate conclusions based on the estimated parameters. Under the law of one price, prices are jointly determined in linked markets, 

making conventional estimation subject to simultaneity bias. In addition, if the two 

price series are nonstationary, conventional regression procedures fail to provide 

reliable parameter estimates. Thus, all price series must be tested for stationarity 

before undertaking further testing for stumpage market integration.

A price series is stationary when the mean, variance, and covariances of the 

series are constant over time and nonstationary when they are not. In a nonstationary series, observations are generated not only by independent random events, but 

also contain information left over from previous periods. As statistical properties 

are partly a function of time, the error terms are correlated and standard regression 

estimation and inference procedures are invalid. To illustrate, consider this time 

series process:

Pt

 = ρPt-1 + εt (2)

where Pt is the current period price, Pt-1 is the previous period price (the first lag 

of variable P), ρ is a parameter to be estimated, and εt is the residual, assumed to 
16

RESEARCH PAPER PNW-RP-586

be random. If │ρ│≥ 1, the process “explodes” in the sense that P will grow without 

bound as time approaches infinity. If │ρ│< 1, P is a stationary price series; a shock 

to the series would eventually result in a convergence back to a steady state. The 

closer it is to 1, the slower the rate of convergence. Serious problems occur if ρ = 1. 

The resulting model 

Pt = Pt-1 + εt (3)

is a common example of a nonstationary series called a random walk and the model 

is said to have a unit root. In such a model, any shock to the series will have permanent effects and the variance increases with time. This model may be expanded 

by incorporating a constant and/or a deterministic time trend representing a normal 

rate of growth or decline over time. Any shock to the series will still have permanent effects in addition to a traditional drift in one direction. 

Stationarity can often be achieved through differencing operations. A series is 

difference stationary if the first (or higher order) difference of the series is stationary. Using quarterly data, the first difference of P is a series generated by subtracting the previous quarter’s price from each current period price:

Pt – Pt-1 = εt or equivalently ∆Pt = εt . (4)

Sometimes only one differencing operation is necessary to remove correlation 

in the error terms; sometimes additional differencing is necessary. The number of 

differencing operations (or lags) required to make the series stationary is the order 

of integration, denoted as I(d). The original undifferenced series are called the 

levels. Thus, a time series is denoted I(0) when it is already stationary in levels and 

I(d) when it must be differenced d times to achieve stationarity owing to the presence of unit roots in the lags (Greene 2003). For example, the random walk above is 

difference stationary; the first difference of P is stationary, making it an I(1) series. 

There are two important considerations when testing for a unit root. The first 

is whether to include a constant, a constant and a time trend, or neither in the test 

equation. Including irrelevant regressors reduces the power of the test to reject the 

null hypothesis of a unit root. Another critical aspect is the choice of lag length 

to eliminate correlation in the error terms. Unit root tests were conducted using 

the Augmented Dickey-Fuller (ADF) unit root test, which allows for correlation at 

higher order lags (Dickey and Fuller 1979). The ADF test works by adding m lagged 

difference terms of P to the right-hand side of the test regression:

∆Pt = α + βt + δPt-1 + λ1∆Pt-1 + λ2∆Pt-2 + ...+ λm∆Pt-m + εt (5)

where α is a constant, β the coefficient on a time trend, δ = (ρ - 1), and m the number of lags required to remove correlation in the error terms (lag order). The ADF 

test is conducted under the null hypothesis of a unit root H0: ρ = 1 and a one-sided 

alternative H1: ρ < 1. The standard t-distribution of critical values cannot be used 
17

Stumpage Market Integration in Western National Forests

because the test is performed on the residual term. The ADF test statistic is the ratio 

of δ to its standard error. If this ratio is significantly different from zero, the null 

hypothesis is rejected. 

Cointegration theory reconciles findings of nonstationarity with the possibility 

of testing relationships among prices. Cointegration is based on the idea that even 

if prices themselves are nonstationary, a linear combination of them may exist that 

is stationary. The stationary linear combination is represented by a cointegrating 

equation that may be interpreted as a long-run equilibrium relationship between 

prices. There may be co-movement between trending prices such that the prices 

will revert to a common long-run equilibrium relation. The existence of a stabilizing relationship among the series suggests a common fundamental force tying these 

series together. In this study, the hypothesized common force is market integration 

resulting from arbitrage behavior on the part of national forest timber purchasers.

After applying unit root tests, the Johansen maximum likelihood procedure 

was used to test for cointegration among nonstationary series (Johansen 1995). One 

advantage of Johansen’s method is that it accounts for simultaneity when testing 

for relationships among prices. Johansen’s method was applied to determine the 

cointegration rank, r, that defines the number of cointegration vectors among the 

price series. These cointegration vectors define the stationary linear combinations 

that represent long-run relationships among prices.1 EViews software2 (Quantitative 

Micro Software 2008) supports two likelihood ratio tests for cointegration rank, 

trace tests and maximum eigenvalue tests. The trace test statistic with null hypothesis of r cointegrating relations is tested against an alternative of n cointegrating 

relations for r = 0,1,...,n - 1. The maximum eigenvalue test uses the null hypothesis 

of r cointegrating relations against alternative r + 1. The number of cointegrating 

relations r is determined by testing sequentially from r = 0 to r = n - 1 until failure 

to reject. 

For two price series, if the number of cointegrated equations equals zero, r = 0, 

prices are not cointegrated, and ordinary least squares in differences can be used 

in testing. If r = 2, the series are individually stationary or the model is misspecified. If r = 1, the two series are cointegrated and an error-correction model can be 

formulated that incorporates the long-run effects. 

 1 The procedure uses a model that can be reparameterized in error correction form: 

∆Pt = Γ1∆Pt-1 + ,..., + Γk-1∆Pt-k+1 + ∏Pt-k + μ + εt, (6)

where ∆Pt

 is a I(0) vector, μ is a vector of constant terms, εt is a vector of error terms, t is 

time, and k is lag length. ∏ is a matrix of long-run coefficients that can be decomposed into 

a matrix of loadings, α, and a matrix of cointegration vectors, β. The loadings are adjustment coefficients that describe the speed of adjustment toward the long-run equilibrium 

state (Hanninen, 1998).

 2 The use of trade or firm names in this publication is for reader information and does not 

imply endorsement by the U.S. Department of Agriculture for any product or service.
18

RESEARCH PAPER PNW-RP-586

Results

Each of the 62 national forest price series was tested for the presence of a unit root 

in levels using the Augmented Dickey-Fuller test. Three specifications of the ADF 

test equation, including an exogenous constant, constant and trend, and neither, 

were examined for each price series. Lag length in the test regression was selected 

using the Schwarz Information Criterion with a maximum lag length of 14 quarters. 

One specification was selected from the three possibilities based upon the statistical 

significance of the exogenous variables in the test equation. After the initial round 

of ADF tests, prices with a unit root in levels were tested again in first differences. 

Results of unit root tests on the levels and first differences for each forest are 

presented in tables 9 through 12. Lags and exogenous regressors are also provided.

The ADF tests on the level price series in Region 1 (table 9) cannot reject the 

null hypothesis of a unit root for the Beaverhead, Idaho Panhandle, and Kootenai 

National Forests. The remaining nine forests in Region 1 had timber prices that 

were stationary over time. Beaverhead-Deerlodge, Idaho Panhandle, and Kootenai 

prices were retested after first differencing and found to be stationary, making 

them I(1) series. Unit root tests on stumpage prices for the 13 forests in Region 4 

(table 10) suggest that only the Salmon-Challis prices were nonstationary in levels; 

these prices were stationary after taking first differences. Table 11 shows that 

Table 9—Northern Region Augmented Dickey-Fuller (ADF) unit root 

test results

Forest Lags c/t ADF test statistic P-value

Levels: 

 Beaverhead-Deerlodge 2 c -2.272542 0.1831a

 Bitterroot 0 c -7.400908 0.0000

 Clearwater 0 c -7.483048 0.0000

 Custer 0 c/t -9.079930 0.0000

 Flathead 0 c -8.310932 0.0000

 Gallatin 0 c/t -7.649239 0.0000

 Helena 0 c -8.800348 0.0000

 Idaho Panhandle 1 c -2.354934 0.1575a

 Kootenai 1 c -2.277512 0.1814a

 Lewis and Clark 0 c -6.330181 0.0000

 Lolo 1 c -3.516631 0.0096

 Nez Perce 0 c -8.453381 0.0000

 

Differenced: 

 Beaverhead-Deerlodge 1 c -11.64789 0.0000

 Idaho Panhandle 1 c -9.802014 0.0000

 Kootenai 0 c -14.43330 0.0000

H0:price series has a unit root. a 5-percent critical values are -3.46 if both constant (c) and trend (t) are significant, -2.89

 if only c or t is significant, and -1.95 if neither is significant.
19

Stumpage Market Integration in Western National Forests

Table 10—Intermountain Region Augmented Dickey-Fuller 

(ADF) unit root test results

Forest Lags c/t ADF test statistic P-value

Levels: 

 Ashley 0 c/t -9.138389 0.0000

 Boise 0 c -4.528322 0.0004

 Bridger-Teton 0 c -7.100780 0.0000

 Caribou-Targhee 0 c/t -5.947208 0.0000

 Dixie 0 c -8.097313 0.0000

 Fishlake 0 c/t -9.032938 0.0000

 Humboldt-Toiyabe 7 c -4.348650 0.0007

 Manti-La Sal 0 c -10.40103 0.0000

 Payette 0 c -4.278887 0.0009

 Salmon-Challis 1 c -2.828698 0.0582a

 Sawtooth 0 c/t -6.616439 0.0000

 Uinta 0 c/t -7.859380 0.0000

 Wasatch-Cache 0 c -7.189601 0.0000

 

Differenced: 

 Salmon-Challis 1 c -10.79841 0.0000

H0:price series has a unit root. a 5-percent critical values are -3.46 if both constant (c) and trend (t) are significant, 

-2.89 if only c or t is significant, and -1.95 if neither is significant.

Table 11—Pacific Southwest Region Augmented DickeyFuller (ADF) unit root test results

Forest Lags c/t ADF test statistic P-value

Levels: 

 Angeles 0 c/t -7.642664 0.0000

 Cleveland 0 c -9.687432 0.0000

 Eldorado 0 c/t -6.524876 0.0000

 Inyo 0 c/t -8.617902 0.0000

 Klamath 2 — -0.677211 0.4210a

 LTBMAb 1 c -4.774505 0.0002

 Lassen 0 c/t -8.322066 0.0000

 Los Padres 0 c -5.577216 0.0000

 Mendocino 0 c/t -7.661781 0.0000

 Modoc 0 c/t -10.19368 0.0000

 Plumas 1 c/t -3.773725 0.0224

 San Bernardino 0 c/t -7.210926 0.0000

 Sequoia 0 c -4.814435 0.0001

 Shasta-Trinity 0 c -6.354482 0.0000

 Sierra 0 c/t -7.320846 0.0000

 Six Rivers 0 c/t -5.845587 0.0000

 Stanislaus 0 c/t -6.929840 0.0000

 Tahoe 0 c/t -4.456949 0.0030

 

Differenced: 

 Klamath 4 c -8.030741 0.0000

H0:price series has a unit root; — = neither c or t were used in the regression equation. a 5-percent critical values are -3.46 if both constant (c) and trend (t) are significant, 

-2.89 if only c or t is significant, and -1.95 if neither is significant.

b LTBMA is the Lake Tahoe Basin Management Area.
20

RESEARCH PAPER PNW-RP-586

the Klamath National Forest in Region 5 has nonstationary stumpage prices that 

became stationary after first differencing. Region 6 also had predominantly stationary stumpage prices; of the 19 national forests in Washington and Oregon, only 

the Mount Hood had nonstationary prices (table 12). The Mount Hood series was 

tested after first differencing and a unit root was rejected. Thus, of 62 forests tested, 

only stumpage prices on the Beaverhead-Deerlodge, Idaho Panhandle, Kootenai, 

Salmon-Challis, Klamath, and Mount Hood were nonstationary I(1) processes. The 

map in figure 7 shows the spatial arrangement of the six forests with nonstationary 

prices.

Cointegration tests to detect market integration were performed on the BeaverheadDeerlodge, Idaho Panhandle, Kootenai, and Salmon-Challis National Forests. The 

Klamath and Mount Hood National Forests were excluded from testing because 

of their isolated locations. The test specification allowed for a linear deterministic 

trend in the data and an intercept in the cointegrating equation. Tests were conducted using from one to four lags; results were the same, so one lag was chosen 

Table 12—Pacific Northwest Region Augmented Dickey-Fuller (ADF) 

unit root test results

Forest Lags c/t ADF test statistic P-value

Levels: 

 Colville 0 c -6.697005 0.0000

 Deschutes 0 c/t -8.182768 0.0000

 Fremont 0 c/t -5.954486 0.0000

 Gifford Pinchot 0 c/t -7.445691 0.0000

 Malheur 0 c/t -7.069117 0.0000

 Mount Baker-Snoqualmie 0 c/t -4.842384 0.0009

 Mount Hood 2 c -1.890142 0.3356a

 Ochoco 0 c/t -8.631505 0.0000

 Okanogan 0 c -6.348353 0.0000

 Olympic 0 c/t -6.370327 0.0000

 Rogue River 3 c/t -3.522482 0.0430

 Siskiyou 0 c -7.167214 0.0000

 Siuslaw 1 c -3.948818 0.0026

 Umatilla 0 c -7.274883 0.0000

 Umpqua 0 c/t -5.020876 0.0004

 Wallowa-Whitman 1 c -3.324856 0.0165

 Wenatchee 0 c -6.510945 0.0000

 Willamette 0 c/t -5.109568 0.0003

 Winema 0 c/t -8.939931 0.0000

 

Differenced: 

 Mount Hood 1 — -12.37289 0.0000

H0:price series has a unit root; — = neither c or t were used in the regression equation. a 5-percent critical values are -3.46 if both constant (c) and trend (t) are significant, -2.89 if only c 

or t is significant, and -1.95 if neither is significant.
21

Stumpage Market Integration in Western National Forests

for model parsimony. Both the trace and the maximal eigenvalue tests rejected the 

hypothesis of no cointegration (r = 0). The trace (table 13) and maximal eigenvalue 

(table 14) tests agreed that there was evidence of two cointegrating equations at 

the 0.05 level. Pairwise tests were then used to identify which forests were fully 

integrated. Test results indicated that the four forests can be grouped into two sets 

of integrated markets. The Beaverhead-Deerlodge and Salmon-Challis compose one 

market while the Idaho Panhandle and the Kootenai make up the other (fig. 8). 

Figure 7—National forests with nonstationary stumpage prices.
22

RESEARCH PAPER PNW-RP-586

Figure 8—National forests with cointegrated stumpage markets.

Table 13—Results of trace tests for the number of cointegration 

vectors (r) for stumpage prices on the Beaverhead-Deerlodge, 

Idaho Panhandle, Kootenai, and Salmon-Challis National Forests

Null Trace Critical

hypothesis Lags Eigenvalue statistic value P-value

r = 0 1 0.4470 112.5023 63.8761 0.0000

r ≤ 1 0.3347 58.5926 42.9152 0.0007

r ≤ 2 0.1760 21.5038 25.8721 0.1590

r ≤ 3 0.0418 3.8875 12.5180 0.7583
23

Stumpage Market Integration in Western National Forests

Conclusion and Direction of Future Research

This analysis suggests that 4 of the 62 national forests in the Western United States 

belong to two fully integrated stumpage markets. There is no evidence to support 

aggregation beyond these two markets. The majority of stumpage prices were stationary; market integration and the law of one price were rejected in 58 cases. Other 

than the two markets comprising the Beaverhead-Deerlodge and Salmon-Challis 

Forests and the Idaho Panhandle and Kootenai Forests, the LOP was rejected in 

every case, suggesting that arbitrage opportunities exist for national forest timber 

purchasers. There is no single regional market but instead a collection of independent localized markets reflecting greater differentiation than expected or modeled in 

the past. 

Although Yin and Newman (1996) found stationarity in the 14 stumpage 

markets they examined in the U.S. South, price time series are rarely stationary 

(Stevens and Brooks 2003). Stationarity implies mean reversion; the influence 

of changes dissipates with time and prices converge back to a steady state. One 

possible explanation for stationary stumpage prices across the West is informational 

inefficiency of stumpage markets (Yin and Newman 1996). Errors and inefficiencies in stumpage pricing do not persist in price patterns, so potential purchasers do 

not receive the market signals necessary to capture potential gains. Even great price 

run-ups experienced in the early 1990s (Sohngen and Haynes 1994) do not persist; 

prices slowly decay back to their original level and purchasers cannot be confident 

that one windfall period will persist or be followed by another. Another possibility 

is that prices are determined by a bid process. Each timber sale and the timber price 

associated with the winning bid could be considered an independent event that is 

uncorrelated with time and previous sales.

Table 14—Results of maximal eigenvalue tests for the number of 

cointegration vectors (r) for stumpage prices on the BeaverheadDeerlodge, Idaho Panhandle, Kootenai, and Salmon-Challis 

National Forests

Null Max-eigen Critical

hypothesis Lags Eigenvalue statistic value P-value

r = 0 1 0.4470 53.9098 32.1183 0.0000

r ≤ 1 0.3347 37.0888 25.8232 0.0011

r ≤ 2 0.1760 17.6162 19.3870 0.0887

r ≤ 3 0.0418 3.8875 12.5179 0.7583
24

RESEARCH PAPER PNW-RP-586

Managers on the Beaverhead-Deerlodge, Salmon-Challis, Idaho Panhandle, 

and Kootenai National Forests should be aware that one implication of integrated 

stumpage markets is that policies that change prices of stumpage in one forest may 

lead to changes in others. These unintended consequences may arise because the 

markets are not independent (Nanang 2000). This could be especially problematic 

for the Beaverhead-Deerlodge and Salmon-Challis Forests, as they are administered 

by different Forest Service regions.

And last, anyone conducting statistical tests using national forest stumpage 

prices is cautioned to conduct analyses only after first differencing prices. Time 

series processes with a unit root are prone to appear to trend over time, but this 

trend is entirely spurious. One way to prevent this problem is to take first differences before estimating regression models. This removes correlation among error 

terms over time, resulting in unbiased parameter estimates. This again is why it is 

so important to account for price stationarity as a precautionary measure to avoid 

erroneous results. 

Future efforts will incorporate the surprising results reported here into the spatial pricing model. Since most of the prices were stationary, vector error-correction 

(VEC) models that account for cross-forest interactions only need to be included 

in two cases. Developing these VEC models is the next step in model formation. 

Then, the relationship between distance to wood product manufacturing clusters 

and stumpage prices will be examined for each forest. Afterwards, the relationship 

between sawtimber and nonsawtimber prices will be estimated for each forest, 

using export chip prices as a proxy for nonsawtimber (Busby 2006). Finally, a 

forest-level spreadsheet tool will be developed that asks for input on the percentage 

of sawtimber, nonsawtimber, and firewood to be harvested from a timber sale and 

allow the user to vary these percentages until the total value is expected to be great 

enough to entice purchasers. The hope is that the tool will assist forest managers by 

increasing the likelihood that advertised sales will contain the right combination of 

timber sizes to be profitable for potential purchasers while accomplishing management objectives. 

Acknowledgments

Many thanks to reviewers Dennis Dykstra, Richard Haynes, John Perez-Garcia, 

and Stanislav Petrasek for their comments and input, Judy Mikowski and Lynn 

Sullivan for assistance in manuscript preparation, and John Chase for assistance 

with the maps. Funded through National Fire Plan Portfolio E. Any errors are solely 

my responsibility.
25

Stumpage Market Integration in Western National Forests

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