This file was created by scanning the printed publication. 

Text errors identified by the software have been corrected; 

however, some errors may remain. 
Authors DARIUS M. ADAMS is a professor at Oregon State University, Department of Forest

Resources, Corvallis, OR 97331-5703; and RICHARD W. HAYNES is a research

forester, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research

Station, Forestry Sciences Laboratory, P.O. Box 3890, Portland, OR 97208-3890.
Errata This errata is to correct error made on page 16, fourth paragraph down.

Paragraph should read as follows:

Stumpage demand and product recovery and conversion—Given the constrained

form of the production functions in equation (11), the derived demand for stumpage is

simply (apply Hotelling's lemma to equation (15), π/ pw),
Abstract Adams, Darius M.; Haynes, Richard W. 1996. The 1993 timber assessment

market model: structure, projections, and policy simulations. Gen. Tech. Rep.

PNW-GTR-368. Portland, OR: U.S. Department of Agriculture, Forest Service,

Pacific Northwest Research Station. 58 p.

The 1993 timber assessment market model (TAMM) is a spatial model of the solidwood and timber inventory elements of the U.S. forest products sector. The TAMM

model provides annual projections of volumes and prices in the solidwood products

and sawtimber stumpage markets and estimates of total timber harvest and inventory

by geographic region for periods of up to 50 years. TAMM and its companion models

that project pulpwood and fuelwood use were developed to support the quinquennial

Resource Planning Act (RPA) timber assessments and assessment updates conducted by the USDA Forest Service. This report summarizes the methods used to

develop the various components of TAMM and the estimates of key behavioral parameters used in the TAMM structure, and also illustrates the use of TAMM with a

base and several scenario projections.

Keywords: Forest sector models, supply, demand, prices, timber supply, RPA.
Contents 1 Introduction

2 Model Components

2 Inventory Linkage

2 Computational Tasks

4 Regions

7 Softwood Solidwood Sector

23 Hardwood Solidwood Sector

29 Fiber Products Sector

29 Timber Inventory Projection

32 Other Model Elements

32 Model Solution

34 Model Behavior in Simulations of a Historical Period

34 Projections, Policy Simulations, and Model Evaluation

42 Base Scenario

48 Increased Public Harvest Scenario

48 Increased Recycling Scenario

51 Increased Public Regulation of Private Practices

53 Canadian Lumber Output Restriction

53 Future Modifications in TAMM Structure and Solution

56 Acknowledgments

56 Literature Cited
Introduction Tne 1993 timber assessment market model (TAMM) is a spatial model of the solidwood and timber inventory elements of the U.S. forest products sector (Adams and

Haynes 1980, Haynes and Adams 1985). The TAMM model provides annual projections of volumes and prices in the solidwood products and sawtimber stumpage markets and estimates of total timber harvest and inventory by geographic region for

periods up to 50 years. Projections of fiber products and fuelwood, which were part

of the earliest TAMM model, are now derived from separate models linked to TAMM

through demands for roundwood and residues.

TAMM and its companion models were developed to support the quinquennial Resource Planning Act (RPA) timber assessments and assessment updates conducted

by the USDA Forest Service.1 Over the past 15 years, TAMM has been used in four

RPA assessments and updates and to provide projections in several special policy

analysis projects conducted by the Forest Service (Haynes 1990, Haynes and Adams

1985, Haynes and others 1994, USDA Forest Service 1982). It also has been used

by various public agencies, private firms, and environmental groups to examine

issues ranging from log export policies to the impacts of carbon sequestration through

tree planting. The acceptance of TAMM as a policy-analysis tool in the United States

has served as a stimulus for similar research and applications in other countries.

The first version of TAMM reported in Adams and Haynes (1980) incorporated the

basic spatial characteristics, two-tiered market structure, and product supply and

stumpage sector representations of the current model but retained many aspects of

the traditional analytical approach to long-term timber market projections used by the

Forest Service. Revisions in subsequent years have updated the product demand,

timber inventory projection, capacity, residue accounting, and hardwood lumber elements. This report documents the structure of TAMM as applied in the 1993 RPA

timber assessment update. The next section, "Model Components," describes the

behavioral relations used for elements of demand and supply, links to other models

such as those for pulpwood and fuelwood, and model solutions, procedures, and

operation of the timber inventory projection module using aggregate timberland

assessment system (ATLAS) (Mills and Kincaid 1992). The third section, "Model

Behavior in Simulations of a Historical Period," illustrates model behavior when used

to simulate historical time periods. The fourth section provides examples of recent

applications of TAMM to examine some key forest policy issues. A final section

addresses changes in the TAMM structure planned for the future.

1 The Forest and Rangeland Renewable Resources Planning

Act (RPA) of 1974 as amended by the National Forest

Management Act of 1976 directs the Secretary of Agriculture

to prepare a Renewable Resource Assessment. The purpose

of this assessment, in the case of timber, is to analyze the

timber resource situation to provide indications of the future

cost and availability of timber products to meet the Nation's

demand. The analysis also identifies developing resource

situations that may be judged desirable to change and

developing opportunities that may stimulate both private and

public investments.

1
Model Components TAMM IS comprised of two major parts (1) the market model portion that generates

annual production, consumption, and price projections, as well as growing-stock

inventory harvest requests, and (2) an inventory projection module derived from the

ATLAS model that processes the harvest requests and updates inventories at periodic

intervals Flow of control in a TAMM run is shown in figure 1 Boldface names in the

figure are routines or groups of routines that conduct specific computations as will be

described below After reading input and initializing key storage arrays, computations

proceed sequentially through the routines listed in the "annual cycle" loop shown in

figure 1 The annual cycle is repeated until the projection is complete

Inventory Linkage The NEWGRO routine provides the interface between the market module and the

inventory module Computational difficulties arise here because of the annual cycle of

the market module and the periodic cycle (5 or 10 years depending on region) of the

inventory module NEWGRO approximately links the two time scales by means of a

simple annual inventory identity

where

I is growing-stock inventory at the start of year t and t-1,

G is estimated annual growth in year t-1, and

H is harvest in year t-1

Starting with an initial value of inventory (I) from ATLAS, inventory in years between

periodic ATLAS updates is computed by using equation (1) and an estimate of growth

(G) NEWGRO cumulates annual harvests and, when a periodic ATLAS update year

is reached, passes the cumulated cuts to ATLAS ATLAS processes the harvest and

passes an updated inventory back to NEWGRO, which resumes the inventory

approximation process by using equation (1)

The value of Gt-1 used in equation (1) is an estimate because periodic growth in

ATLAS can be determined only when the inventory projection of a period is completed Consequently, the annual inventory projection from equation (1) at the end of

an ATLAS update cycle will differ from the updated inventory returned by ATLAS by

some amount depending on the accuracy of the growth estimate The "optional

growth iteration cycle" shown in figure 1 resolves this problem At the end of a projection, NEWGRO and ATLAS pass periodic harvests and inventories, respectively, to

the routine ATLINK ATLINK recomputes apparent growth for each period in the projection by rearranging equation (1) and feeds these revised growth estimates back to

the input stream as shown in figure 1 The projection is rerun in this iterative fashion

until the growth estimates, or some other convergence measure, differ by less than

some user-specified tolerance between successive iterations The cycle is optional,

because for small changes in projection conditions, activating the cycle may have only

modest impacts on the projection results

Computational Tasks To give a brief overview of the structure of TAMM, this section describes the computations performed in each routine in the annual cycle loop listed in figure 1

2
Figure 1—Flow of control in 1993 TAMM model (boldface names refer to computational routines described

in text)

3
PANEL Establishes consumption, production, and trade of nonstructural panels (hardwood plywood, particleboard, hardboard, and insulating board) These products are

not price-sensitive in TAMM, but their roundwood and residue fiber requirements are

integrated with those from other endogenous products.

HWSOL Initializes and solves the hardwood lumber model

DEMSUB (INITIAL) Initializes the demand module for softwood lumber, softwood plywood, and OSB (oriented strand board). Demand relations are linearized and estimates developed for demand regions.

EXPT Establishes exogenous offshore demand quantities (exports) for softwood

lumber, softwood plywood, and OSB

PCONVT Computes residue generation factors and other conversions essential for

the fiber products-solidwood products interface.

PULP Receives pulpwood requests from the separate pulpwood model and monitors

the production and use of residues.

SCONVT Computes conversion factors for the solidwood sector

STUMP Initializes sawtimber stumpage supply relations for both public and private

ownerships, including delivered wood cost relations for the Canadian softwood

lumber segment

CAPAC. Adjusts production capacity to the start of the current year in the softwood

lumber, softwood plywood, and OSB markets based on the margin between gross

revenue and variable production costs.

SOLVE Initializes the remainder of model equations, including product supply relations, and solves the softwood lumber, softwood plywood, and OSB markets.

DEMSUB (FINAL). Called a second time once the overall market solution is obtained

to compute projections of consumption by end-use category for softwood lumber,

softwood plywood, and OSB using equilibrium prices

Regions For computations involving solidwood product supply and timber harvest, TAMM uses

nine (9) regions in the United States and three (3) in Canada (fig. 2).2 solidwood

demand relations are developed for six (6) regions in the United States for softwood

lumber, softwood plywood, and OSB (fig. 3).3 Canadian demand for these products is

taken as exogenous Only a single national demand relation is developed for hardwood lumber in the United States.

Supply regions include only the contiguous states. Consumption in Alaska and Hawaii

is included in other demand regions. Inventory projections for Alaska are developed

in other parts of the timber assessment process.

2

 Supply region names and acronyms are Pacific Northwest,

West (PNWW) west side of the Cascade Range, Pacific

Northwest, East (PNWE) east side of the Cascade Range,

Pacific Southwest (PSW), northern Rockies (NR), Southern

Rockies (SR), North-central (NC), Northeast (NE), Southcentral (SC), Southeast (SE), British Columbia coast (CBCC),

Interior Provinces (CINT), and Eastern Provinces (CEST)

3

 Demand region names and acronyms are Pacific

Northwest (PNW), Pacific Southwest (PSW), Rockies (RK),

North-central (NC), Northeast (NE), and South (SO)

4
Figure 2—TAMM supply regions.

5
Figure 3—TAMM demand regions.

6
Softwood Solidwood The softwood solidwood sector includes softwood lumber, softwood plywood, and

Sector OSB. Although OSB uses both softwood and hardwood fiber in its manufacture, it is

grouped with the softwood products because its principal substitute is softwood

plywood.

Product demand—The demand module for softwood products is based on the technology diffusion models developed by Spelter (1984, 1985, 1992).4 In Spelter's approach, the market for a given product (p) is divided into mp end-use categories

(denoted by the subscript i so that i = 1, ... , mp). An end-use category is a specific

industry or group of industries that uses product p as an input; for example, new residential construction. Total U.S. demand for product p (Q) is given by the following

relations (time subscripts are deleted except where essential):

where

where

Qi is the demand for end-use i,

Mi is a measure of output of the ith end-use category (for example, housing starts),

Ui is the consumption of product p per unit of output of end-use category i,

Ui is the maximum use of product p per unit of product i output,

Si is the fraction of the maximum use of product p per unit of output of end-use

category i,

b is a parameter to be estimated,

T is the cumulative price difference, and

Pi,p,t and Pi,s,t are prices (put-in-place) of product p and its substitute (s) in end-use

category i in period t,

4 For an alternative derivation of demand models in "end-use

factor" form based on a more traditional production theoretical

approach, see Adams and others (1992).

7
For "mature" commodities such as lumber and plywood, b < 0, for new commodities

such as OSB, b > 0 The cumulative relative price difference term, T, drives the substitution process As the price difference between the solidwood product and its substitute rises (or persists over time), T grows For lumber or plywood, this would reduce

S and hence the consumption of the solidwood product

The present model includes demand equations for the end-use categories shown in

table 1 Most, but not all, of the relations are of the form shown in equation (2) (see

Spelter 1985 for discussion of other forms used) The equations are too numerous to

include a full tabulation of estimation results In the aggregate, however, softwood

lumber demand is highly inelastic5 with respect to its own price in the short term

(annual elasticities average -0 07 during the 1980s) as is softwood plywood (annual

elasticities average -0 09 during the 1980s with a rising trend after 1982 to -0 1 in

1989) The OSB demand elasticities averaged -0 59 during the 1980s, with a sharply

declining trend (-0 826 in 1980 to -0 361 in 1989)

For lumber and plywood, these annual elasticities are one-quarter to one-fifth the

magnitude of elasticities used in the first application of TAMM in the late 1970s (-0 35

for lumber and -0 3 to -0 4 for plywood, see Adams and Haynes 1980, p 15-18) Demand models in the earliest versions of TAMM included no explicit intertemporal adjustment mechanism and were estimated by assuming constant demand parameters

over a data sample ending in the early 1970s The associated elasticities were

interpreted as long-run or "equilibrium" levels More recently, both Spelter (1985) and

Adams and others (1992), using markedly different methods, have found evidence of

steadily declining short-term (annual) demand elasticities for these products over the

period since 1950 Thus, part of the difference between elasticities in the current and

earlier versions of TAMM may relate to the sample period "averaging" inherent in

earlier constant parameter econometric studies In addition, earlier demand models

were static and the elasticities were treated as the levels obtained after all consumption adjustments had taken place The model of equation (2) includes an explicit

adjustment process yielding, as would be expected, more elastic response for longer

adjustment periods Thus, for the aggregate of all end uses, both lumber and plywood

demand elasticities rise by a factor of 2 to 3 over a 5-year period during a sustained

own price change

The prices employed in Spelter's model represent the costs of the solidwood and substitute products put-in-place

 6 Since different types (grades and species) of lumber

and plywood are used in the various end-uses categories, Spelter incorporated different price measures in some of the end-use demand relations to best represent the

grade of product actually used Softwood lumber is represented by the all softwood

5

 If some economic variable y is determined by some other

variable x as given by the functional relation y = f(x) the

elasticity of y with respect to x is defined as the percentage

of change in y for a 1 percent change in x The relation is

said to be inelastic if the elasticity is less than 1 unit elastic if

just equal to 1 and elastic if greater than 1

6

 Thus for example the price of lumber used in the 'single

family dwelling walls end use would include the cost of

lumber and all other inputs needed to produce one unit of

wall in a single family dwelling This might be viewed as a

composite input to the single family dwelling production

process
Table 1—End-use categories included in TAMM solidwood demand module for softwood lumber, softwood

plywood, and oriented strand board (OSB)

End-use category

Single-family dwellings (total)

Framing

Sheating (total)

Roof

Floor

Wall

Siding

Millwork

Basement

Multifamily dwellings (total)

Mobile homes (total)

Residential repair and alteration

Nonresidential

Building

Farm

Utilities

+Miscellaneous

Shipping

Manufacturing

Pallets

Furniture

Ties

Other

Softwood

lumber

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Softwood

plywood

X

X

X

X

X

X

X

X

X

X

X

X

X

X

OSB

X

X

X

X

X

X

X

X

X

X

X

X

X

End-use output measure

Floor area single starts

Floor area single starts

Floor area single starts

Floor area single starts

Floor area single starts

Floor area single starts

Floor area single starts

Floor area single starts

Floor area multistarts

Floor area mobiles

Real expenditures residential

repair and alteration

Real value of nonresidential construction

For buildings

For farms

For utilities

For all other

Index of manufacturing production

Index of manufacturing production

Softwood pallet production

Index of manufacturing production furniture

Total softwood the production

9
lumber producer price index (in most cases) and the price of ponderosa pine 1- by

12-inch boards (where board grades are important). Plywood is represented by prices

of 1/2-inch CDX southern pine (delivered NE) and 1/2-inch CDX Douglas-fir. Only a

single OSB price is used (7/16-inch delivered NE). Hardwood lumber uses the all

hardwood lumber producer price index. In TAMM, however, all lumber and plywood

species-grade prices in Spelter's original formulation are replaced by functions of their

related producer price index. For example, the 1/2-inch CDX southern pine plywood

price is replaced by a simple linear regression of the southern pine price on the all

softwood plywood producer price index.

Linearization and regionalization—Spelter's model is too complex to incorporate

directly in the TAMM spatial solution process, and it gives only national-level demand

for solidwood products. To simplify the model, a linear approximation is developed in

each year of the simulation at a set of projected product prices. Equations (2, a-e)

can be written in general form as,

where

pp are the national prices of lumber (L), plywood (P), and OSB (O), respectively, and

Z is the set of all exogenous variables in the model.

Estimates of current period equilibrium prices for PL, PP, and Po are obtained by a

simple linear extrapolation of prices in the previous two periods. Setting the exogenous variables to their current period values, equation (2b) is then linearized

by using numerical methods to a form,

Regional demand equations are derived from the linearized national-demand relations in (4). Regional delivered product prices are linked to the national prices, PL,

Pp, and Po by simple linear regressions of the form:

where

p = L, P, O and r = 1, . . . ,nr, and

pp,r is the price of product p in region r, and

nr is the number of U.S. demand regions.

7

 CDX is common grade of exterior plywood with C-grade and

D-grade veneer faces suitable for application in exterior uses.

10
Regional shares of national consumption for product p are derived from exogenous

projections of regional per capita consumption trends and regional population as:

where

sp,r is region r's share of national consumption of product p,

(Q/N)p,r is projected per capita consumption of product p in region r,

Np,r is projected population in region r, and

Qp,r is consumption of product p in region r.

Substituting equations (4)-(6) into (7), regional demand equations can be written as

follows:

The elasticity of regional demand for product p with respect to its own price is,

Replacing the regional price and volume with equations (5) and (7) this is,

where

ep,r is the region r own price demand elasticity for product p, and

ep is the national own price demand elasticity for product p.

Thus the relation of the regional and national elasticities is proportional to the

regional-national price ratio.

Product supply relations and capacity adjustment—In Forest Service timber

assessment projections, trends in the technology of wood products processing and

logging are treated by using specific scenarios or projections of future technical developments. Wood use efficiency in milling is represented by "product recovery factors": product output-log input ratios (for example, board-foot lumber tally output per

cubic-foot log input). To explicitly incorporate these projections in the product supply

11
relations, we assume a constrained form of the production process. Product output is

obtained in fixed proportions to log input (the product recovery factor linkage) but in

variable proportions to all other factors Assuming quasi-fixed capital inputs, the production function for a specific product would appear as,

where

Q is output,

rw is the product recovery factor for logs,

W is log input,

Xi for i = 1, ... , n are nonwood variable inputs, and

K is capital.

The function f can be viewed as an aggregator function for the other inputs, and the

two groups of factors, W and (Xi, K), are weakly separable.

If P = [pw.(P1. - Pn)] is the set of prices of wood and other inputs, the cost function for

the production function in equation (11) can be shown to be,

where

Cw is the cost function for the wood input and is,

8

 A production function is a relation describing the conversion

of various inputs into outputs in the production process

Inputs, also called productive factors, in broadest terms may

be classed as labor, raw materials (such as logs), capital

(including physical production facilities and machines as well

as the technique embodied in the process itself), land, and

so on A factor is said to be variable over some time period if

the level or amount of its use in production can be freely

varied A factor is said to be quasi-fixed if its level cannot be

readily varied in the short term Groups of factors are said to

be separable in a production process if the production

process can be thought of as occurring in separate stages

that are then brought together to produce the final product

Changing the levels or mix of inputs in stage 1 would impact

the output of stage 1 and perhaps the output of the overall

production process as well but not the mix or levels of inputs

of stage n This is a strong form of input separability A

weaker form, and one sufficient for the purposes noted in the

text, is that changes in stage 1 might influence the levels of

inputs (and hence output) of stage n but not the relative mix

of inputs

12
and Co is the cost function for all other inputs. Chambers (1988) shows that the profit

function can be written as follows:

where

P is product price,

Q

*

 is optimal output.

Thus the supply function can be found by Hotelling's lemma (see Chambers (1988)

for definition and discussion of the lemma) from,

We normalize the profit and cost functions by the price of one of the inputs (see

discussion below) and assume that Co can be represented by the (normalized,

restricted) quadratic form (see Chambers (1988) for definition and discussion of

functional forms),

Using equations (13) and (17), in equation (16) we obtain, after some simplification,

an expression for the supply function,

In estimation we assume that residues in lumber and plywood production are generated in fixed proportion to output and hence add residue revenues per unit output

to product price in the term in parentheses in equation (19). Nonwood variable factors

are separated into two groups: a first, readily measurable set, comprising direct labor,

13
energy, and certain other materials and services, and a second set of all other variable inputs The first group is treated as a composite input, and its aggregate price is

measured as the average cost of the set of factors per unit output The second group

used as a numeraire is also a composite input Its price is assumed to be measured

by the all commodity producer price index

Capital is the aggregate of all buildings, machinery, and production organization

methods used in the milling process Studies of production typically construct some

real value measure of the stock of structures and machinery to represent capital

input, assuming capital services are proportional to stock In TAMM, capital is

measured by an estimate of output capacity, which might be viewed as the maximum

service level obtainable from the capital stock Capacity data are derived from a

combination of estimates by industry associations and from production, price and,

cost data by using a modified form of the "trends through peaks" method

 9

Estimation results for equations used in the 1993 timber assessment are shown in

table 2, including price and cost elasticities, capacity coefficients, and adjusted coefficients of determination from regressions

 10

 Lumber and plywood equations were

estimated by using two-stage least squares, with the exception of the NC and NE

lumber relations, which were estimated with simple ordinary least squares (OLS)

Given the paucity and poor quality of price and cost data available for these latter

regions, we view these equations as only the roughest of estimates The OSB equations were estimated with three-stage least squares for the United States and Canada

as aggregates Direct estimation of regional OSB supply equations was not attempted

given the limited number of observations Regional equations were derived by scaling

the national relations using proportions of total (U S. or Canadian) capacity at the start

of each period Thus regional and national OSB supply elasticities are identical

9

 In the usual "trends through peaks' method, capacity is

identified as the name implies by simple straight line trends

through peak output levels Our approach uses output prices

and operating margin (gross revenue less variable costs) to

identify key points on the capacity time path For example,

periods when output approaches capacity are identified by

peaks in the basic output series and also by peaks in price

and operating margin Just as critical are the points where

capacity expansion is reinitiated after periods of stability or

decline Here again increases in operating margin, even with

a continued decline in output, help to identify such points

10

 For comparative purposes, the direct price elasticities of

softwood lumber and plywood supply from the 1980 version

of TAMM were as follows

Region

PNWW

PNWE

PSW

Rockies

SC

SE

Canada

Elasticities

Lumber

0 21

60

23

35

79

31

47

Plywood

0 43

98

2 17

97

92

85

14
Table 2—Estimation results for softwood lumber, softwood plywood and OSB

products supply equations: lumber and plywood estimates using 2SLS, OSB

using 3SLS, and elasticities calculated at mean values of estimation sample

Region

PNWW

PNWE

PSW

NR

SR

NCa

NEa

SCb

SEb

BCC^

CINTb

CEST

PNWW

PNWE

PSW

NRd

SC

SE

United States

Canada

Supply elasticities

Product

price

0.335

.586

.794

.866

.395

.848

.188

.937

.963

.935

.447

.492

.748

.444

1.120

.600

.395

.343

.512

.433

Nonwood

cost

Capacity

coefficient

Softwood lumber

-0.204

-.227

-.311

-.456

-1.077

-.265

-.202

-.552

-.456

-.993

-.260

-.405

0.865

.712

1.756

.801

.718

.619

1.446

.665

.610

1.639

.966

.947

Softwood plywoodc

-1.144

-.118

-1.691

-1.000

-.782

-.806

.956

.704

.691

.585

.819

.776

Oriented strand boarde

-.208

-.192

.872

.946

Adjusted

R

2

0.57

.67

.81

.75

.68

.61

.82

.87

.88

.77

.97

.97

.90

.89

.92

.94

.96

.96

.99

.98

a

 NC and NE estimated with OLS, data samples 1951-89 and 1960-89, respectively.

b

 Estimation sample for SC and SE 1951-89, all other regions 1956-89.

c

 Estimation samples: PNWW, PNWE, and PSW 1951-89, NR 1957-89, and South 1968-89.

d

 NR estimates constrained to elasticities shown for both price and nonwood cost coefficients.

e

 Estimation sample 1976-89 for both regions.

15
Capacity is projected by using a two-stage process.

I Initial estimates of capacity change, or net investment in capacity, are derived from

a set of regional adjustment equations. These relations use an accelerator structure in

which change in capacity is a distributed lag in past changes in output

 11

 We experimented with both finite lag structures by using the polynomial distributed lag approach

and with exponential, Koyck-type schemes Forms of the final equations differ across

regions depending on which approach provided the best explanation of historical

behavior

2. Projections from the capacity equations are then adjusted for anticipated operating

margin performance A naive estimate of expected operating margin is developed

from the average margin over the past three years. This is compared to a "target" or

minimum acceptable margin If expected margin is higher than the target, projected

capacity increments are increased or projected decrements are reduced by preset

fractions If the expected margin is below the target, decrements are increased or increments are reduced An upper bound on the absolute level of capacity change also

is imposed Because our basic cost and price data differed from region to region in

the breadth and specificity of costs and products covered and because the quality mix

of products differs across regions, we varied margin targets by region rather than

establish a single national target for a product

This second-stage adjustment was included to mimic the effects of competition,

forcing capacity migration into (or out of) regions that realize high (or deficient)

margins over long periods Ensuring this behavior at the product market level was

particularly critical if we were to obtain reasonable long-term stumpage price

projections at the regional level

Stumpage demand and product recovery and conversion—Given the constrained

form of the production functions in equation (11), the derived demand for stumpage is

simply (apply Hotelhng's lemma to equation (15), / pw),

where

dp is the derived demand for stumpage for product p, and

rw,p is the recovery factor for product p.

11

 An accelerator structure is a model in which capacity

change is driven by levels or changes in past output A

distributed lag relation between a variable y and a "causal"

variable x would have the general form y = aoxt + a1xt 1 +

a2Xt 2 + The variable y is determined by a weighted

summation of various time lags of x (potentially an infinite

number of past values) The coefficients ao, a1, a2, and so on

can be fixed values or functions of other variables The time

patterns of these coefficients (and their methods of

construction or estimation) give rise to their names a

polynomial form (for example, where the a, varies as a

quadratic in the length of the lag) is called a polynomial lag,

one that declines exponentially with the length of lag an

exponential lag structure

16
For OSB, the roundwood-residue and softwood-hardwood mixtures also are prespecified as part of the recovery process. In all cases, stumpage volume is measured

in cubic feet.

Product recovery data are not collected or reported on a systematic basis for any of

the softwood products. Historical estimates used in TAMM are intended to represent

regional average recovery experience and are derived from industry association and

public agency sources, often with extensive adjustments for consistency of units of

volume and types of milling processes. Historical recovery data for softwood lumber

and plywood are shown in figures 4 and 5. Projections of future recoveries, as noted

above, are derived in other portions of the timber-assessment process.

As sawtimber is harvested and processed for lumber and plywood, various residues

are generated in woods and mills. TAMM contains an array of relations to account for

these residues and their use. Estimates of residues generated in milling (see discussion in a later section for estimates of logging residues) are driven by projections of

product recovery, size of logs processed, and the size mix of products produced.

TAMM's development of factors for estimating residue generation and product conversion is summarized in the following relations:

where

OR is Scribner log scale "overrun" used in converting sawtimber stumpage prices to

a product output basis (product units per board foot, log scale, Scribner rule),

RF is the product recovery factor (product units per cubic foot, log scale),

BFCF is the board-foot per cubic foot scaling conversion for logs (board foot, log

scale, Scribner per cubic foot, log scale),

R% is the residue fraction, the proportion of logs processed that is left as wood

residue of all types (cubic foot, residue per cubic foot, log scale of logs processed),

PVF is the product volume factor, the solid wood volume per unit of product

produced (cubic foot, solid wood per product unit),

RGF is the residue generation factor per unit of product output (bone dry tons or

green tons per product unit), and

RWF is the residue weight factor, the weight in tons of a cubic foot of wood residue

(bone dry or green tons per cubic foot, residue).

17
Figure 4—Softwood lumber recoveries by region 1950-89

Figure 5—Softwood plywood recoveries by region 1950-89

18
The BFCF depends on the average size of logs processed. The PVF differs with the

mix of product sizes and qualities produced (for example, dimensions of lumber, such

as 2 by 4 inches or 2 by 12 inches, and amounts that are produced green and dried

and thickness of plywood sheets) and with standards defining nominal versus actual

product dimensions (for example, a nominal dry 2-by 4-inch board under current

standards is actually 11/2 by 31/2 inches). The RWF differs with the mix of species

processed. In the West, residues are customarily measured on a bone dry ton basis,

whereas in the South, green tons are used. The process described above is intended

to estimate total wood residue production. Additional adjustments of RWF are applied

to estimate portions usable for pulping and reconstituted panels.

Public and private stumpage supply—Total timber harvest in TAMM is divided between sawtimber and nonsawtimber classes based on the product for which the harvested timber is used.12

 Sawtimber includes timber harvested for lumber, plywood,

miscellaneous products and saw-veneer log trade; nonsawtimber includes fiber for

reconstituted panels, pulpwood and fuelwood. TAMM includes models of public and

private sawtimber stumpage supply in the United States and delivered saw-log costs

in Canada. Pulpwood supply equations for the United States and Canada and behavioral relations for fuelwood supply from standing timber are included in the pulpwood

and fuelwood models. These supply relations are linked to the sawtimber relations in

TAMM by means of timber inventories and prices through an iterative solution process

described in a later section. Supplies of timber for reconstituted panels are treated as

a perfectly inelastic portion of the aggregate nonsawtimber supply.

Public supply—In the PNWW, PNWE, PSW, NR, and SR regions, the National Forest component of public timber supply (the volume harvested in the current period) is

treated as price sensitive. Supplies from all other public agencies in the Western

United States, and from all public lands in the Eastern United States, are treated as

fixed (price inelastic). The Western National Forest supply process comprises five elements: volume sold, bid price, harvest price, volume harvested, and the uncut volume

under contract.13 The volume sold is assumed to be equal to the volume offered.

Because our focus here was exclusively on sawtimber, the sold volume is equivalent

to the Forest Service's allowable sale quantity (ASQ). Nonsawtimber volumes (the

difference between total product sale quantity, TPSQ, and ASQ) are treated as price

inelastic.

Bid price is modeled as a simple linear function of lagged softwood lumber price.14

We experimented with various alternative forms to better capture the expectational

structures that must play a key role in the bidding process. None proved as robust to

errors in "input" or provided equivalent historical explanatory power within the TAMM

structure as this simple naive model.

12

 The term sawtimber also is used in Forest Service

inventory statistics to denote trees of certain size and quality

characteristics, but these distinctions are not used in TAMM.

13

 See Adams and Haynes (1989) for a detailed discussion

and model of the National Forest timber supply process in

the Western United States.

14

 This approach follows Cardellichio and others (1988).

19
The volume of timber harvested is determined by a "supply" relation drawn from

Adams and others (1992):

where

CUTt is the harvest volume in period t,

UCVt-1 is the uncut volume under contract at the end of period t-1,

SOLDt is the volume sold during period t,

CPt is the average price of timber harvested (the harvest price) during period t,

LMAX is the age of the oldest sale remaining unharvested in period t (taken as a

constant),

Wi is the (assumed fixed) proportions of the uncut volume under contract remaining

in sales of ages from 0 (just sold) to LMAX years, and

BP is the average bid price for timber sold during period t.

We assumed a competitive regional market in timber for immediate harvest. Thus

CPt is also the average regional price for timber for immediate harvest across all

ownerships. As CPt rises relative to the average cost of timber in the uncut backlog,

the fraction of the adjusted uncut volume that is harvested also rises.15

Finally, the uncut volume under contract is updated by a modified inventory relation:

where the β's differ from 1 in several regions owing to errors and adjustments in the

timber sale and execution process.

Private supply— Private timberland owners are divided into forest industry and nonindustrial groups based on integration of the owner with wood or fiber products processing facilities. When TAMM was first developed in the late 1970s, this split was

thought to provide a rough distinction between the broad objectives for holding timberland as well: industry owners being primarily concerned with present value maximization, whereas the objectives of nonindustrial owners might include various nontimber

or amenity concerns in addition to wealth maximization. Developments over the past

15 years suggest that a further division within the nonindustrial group would now be

appropriate, with an "industrylike" group to represent the growing number of nonintegrated owners that hold timberland purely as an investment, and a "miscellaneous"

group to represent the traditional farm and diverse other private owners with a more

heterogeneous set of ownership objectives. Unfortunately, sufficient data on timber

harvest and timber inventory using this more detailed categorization are not available.

Including the 1980s in the estimation sample with the old owner classification scheme,

15

 Adams and Haynes (1989) and Adams and others (1991)

present two complementary rationales for this behavior.

20
however, leads to several problems. For example, in some regions there seems to be

a shift in behavior of the nonindustrial group after 1980, with a marked increase in

price responsiveness. Although we believe that changing ownership composition was

the cause of this shift, we have few ways to test this supposition.

As noted above, we assumed that forest industry owners act as present value maximizers. Following Ovaskainen (1992), a simple two-period representation of the

industrial owner's intertemporal harvest optimization problem would be,

subject to

where

Ct is harvest in period t,

Pt is stumpage price in period t,

r is the discount rate,

l

0

 is initial inventory, and

g is the growth function of residual inventory, g' > 0, g" < 0.

Assuming constant future price expectations (P2 = P1), the formulation in equation

(24) yields a current (first) period timber harvest function that depends on price,

inventory, and the discount rate:

Assuming all else constant Hp > 0, Hi > 0, and Hr > 0.

Nonindustrial owners were assumed to be intertemporal utility maximizers who derive

benefits from (1) the consumption of goods purchased with income earned either

selling timber or from other "nonforest" sources, and (2) the standing stock of timber

itself. Again, following Ovaskainen (1992), a simple, two-period version of the typical

owner's intertemporal maximization problem can be written as,

subject to:

where

δ is the owner's rate of time preference,

l

0

, l1, and I2 are inventories at times 0 (given), 1, and 2,

21
C1

 and C2 are harvests in periods 1 and 2,

M is exogenous nonforest income,

P1 and P2 are exogenous prices of stumpage in periods 1 and 2,

S is period 1 savings, and

r is the exogenous earnings rate on savings.

We assumed an additively separable utility function both over time and between commodities and noncommodities.16

 The utility functions for commodities, U, and noncommodities, V, are assumed to display positive but diminishing marginal utilities so

that V and U' > 0, and V" and U" < 0. Noncommodity benefits are assumed to derive

from the stock of timber, l1 and I2, in each period after harvest. Only G1, C1, and C2

need be considered in the optimization, because S can be replaced by a function of

C1 and G1, G2 is then a function of G1, C1, and C2 and the inventory terms depend

only on the C1 and C2. Finally, the growth function, g, has the same properties as

assumed in the industrial case.

Solution of the problem in equations (26) yields a first period harvest function dependent on the Pi

, r, M, initial inventory (I), and the unobservable δ. Dropping the

latter and assuming constant future price expectations (P2 = P1), we have,17

We implemented these theoretical developments by using a partial adjustment form

of the supply relation in which the elasticity of harvest with respect to inventory is

constrained to unity for both owners:

and the functions H are linear in arguments. The inventory elasticity restriction limited

the generality of our results but resolved significant collinearity problems between the

inventory, price, interest rate, and income terms. The forms in (28) also have proven

to be quite powerful in explaining historical harvest behavior across all regions.

Stumpage price elasticity results are shown in table 3.

16

 See our previous definition of separability in the case of

the production function. In this case the function is strongly

separable in consumption and investments in the two time

periods. Aggregate utility over the full two-period time horizon

is obtained by summing contributions from the two periods.

17

 Comparative statistics using the first order conditions from

optimization of (26) reveal that HM < 0 and Hr 0, but the

expected signs of Hp and Hi cannot be unambiguously

determined.

22
Table 3—Stumpage price elasticities of private timber

supply by U.S. region computed at sample period

averages

Region

PNWW

PNWE

PSW

NR

SR

NC

NE

SC

SE

Industrial

0.440

.169

.436

.247

.784

.283

.340

.321

.193

Nonindustriala

0.416

.402

.145

.180

.513

.672

.310

.290

.288

a Sample periods for PNWW, PNWE OP, PSW OP, NR, SC, and SE

1951-89; PNWE Fl, SR, and NE Fl 1975-89; NC and NE Fl 1960-89;

SW Fl 1970-89

Significant strides have been made in recent years in assaying the Canadian timber

resource and modeling the costs of timber extraction (see for example, Messmer and

Booth 1993, Williams 1991). Although these new tools hold much promise for future

use in an expanded model, TAMM at present employs a highly simplified scheme for

modeling the cost of wood delivered to Canadian lumber mills. A log-linear regression

is used to link historical delivered wood cost and the volume of wood consumed at

lumber mills in each of the three Canadian regions (volumes are in cubic feet, log

scale, costs in real $C per MCF). In projections, these relations are shifted according

to externally generated scenarios of future Canadian allowable cut policies and cost

developments. The Canadian relations enter TAMM in the same way as do the private

U.S. timber supply equations, and delivered wood cost is determined simultaneously

with other endogenous prices and quantities. The elasticities for delivered logs in the

three Canadian regions (at lumber mills for the period 1980-90) are 1.217, 0.668, and

1.330 for CBCC, CINT, and CEST, respectively.

Hardwood Solidwood Hardwood lumber is the only hardwood solidwood market treated as priceSector endogenous in TAMM. Hardwood plywood is projected in the nonstructural panels

segment discussed below, and miscellaneous products are projected outside the

model. Timber requirements for these latter products are incorporated as fixed

demands in the hardwood sawtimber demand relations.

General hardwood lumber model—The general structure of the hardwood lumber

model is described in the following simplified relations:

23

 
where

D and De are total U.S. hardwood lumber demand and demand in end-use e in board

feet (export demand is also included here);

P and pr are national average lumber price (real dollars per thousand board feet

lumber tally) and regional sawtimber stumpage price (real dollars per thousand board

feet) in region r;

S and Sr are total U.S. supply and supply from region r in board feet (import supply is

also included here);

dr is sawtimber stumpage demand (in cubic feet) in region r;

cr is region r lumber recovery factor;

sr, sp

r and sGr are total, private and government sawtimber supply in region r, and

Or is output of other sawtimber products (plywood and miscellaneous products) in

region r; .

The model is nonspatial with a single U.S. demand relation (the aggregate of all end

uses and exports) and price-sensitive supply relations for each of the Eastern regions

(supply from Western regions and external trade flows are fixed and projected outside

the model). We retain the fixed coefficients stumpage conversion assumption of the

softwood segment, so regional lumber supply is converted directly to sawtimber

stumpage demand. Total regional sawtimber supply is the sum of a price-sensitive

private component and a fixed public component.

Although hardwood lumber was estimated to comprise some 20 to 25 percent of total

U.S. lumber production and is the principal lumber species in some portions of the

Eastern states, econometric modeling of the market has been limited.18 Data limitations are a primary reason for this lack of research. Binkley and Cardellichio (1986)

and, more recently, Luppold and Dempsey (1989) have demonstrated the problems

in basic hardwood lumber-production data as reported by the Department of Commerce. In addition, there is little information on production and logging costs, and

stumpage price data of acceptable quality are available only for recent years in the

South. Given this paucity of data, most past studies have employed markedly

simplified structures of the market and a similar tack is taken in TAMM.

18

 Binkley and Cardellichio (1986) describe the most recent

publicly reported effort and summarize previous research.

24
Hardwood lumber demand—Eight end-use categories (or industries) are recognized

for hardwood lumber consumption: furniture, flooring, millwork, ties, pallets, mining,

containers and dunnage, and miscellaneous (all other categories). We treat use in

mining and containers and dunnage as exogenous. Demand relations for the remaining six categories use an "end-use factor" form as described by Adams and

others (1992):

where

De is hardwood lumber consumption in end-use category e;

Ae is the level of output (or activity) in end-use category (industry) e;

P

C

 L,e and is PCs,e are the prices of hardwood lumber and substitute composite

products used in industry e, and

t is a time trend representing technological change in the end-use industry.

Prices of the composite products, also termed "cost put-in-place," include wherever

possible, both materials (such as lumber or substitutes) and labor.

Estimated lumber price elasticities are shown in table 4. For ties and pallets, hardwood lumber consumption is derived in a two-step process. In the demand equations

(for which price elasticities are shown in table 4), consumption is expressed as number of hardwood pallets or ties produced, and end-use industry output is measured

as total ties or pallets produced. Thus the end-use factor in the equation is the fraction of total ties or pallets that is made from hardwood lumber.19

 The volume of lumber consumption is then computed as the fraction of total units that are hardwood

multiplied by the total number of units produced and then multiplied by a factor giving

lumber use per unit.

In two cases (furniture and millwork), the estimation sample was split between 1979

and 1980, recognizing the somewhat more price elastic consumption response in the

period since 1979. This shift coincides with the sharp, sustained drop in the relative

price of the lumber-using composite for these end uses and a reversal of historical

trends toward declining consumption per unit of end-use output. The elasticity differences are not great, but the coefficient shifts do improve the statistical properties of

the equations. Although variations in relative price trends do not constitute structural

changes in the usual sense, these coefficient shifts are effective because our demand models are too simple to capture the consumer behavior associated with the

large trend reversals observed in the early 1980s.

Hardwood lumber supply—Hardwood lumber supply relations employ a form used

in earlier versions of TAMM:

19

 We ignore the recovery and other differences associated

with mills that produce pallets directly from logs rather than

purchasing hardwood lumber.

25
Table 4—Characteristics of hardwood lumber demand relations and lumber

price demand elasticities by end-use

Enduse

Furniture

Flooring

Millwork

Ties

Pallets

Miscellaneous

<1980

-0.62

-.942

Demand elasticity

for period:

1980+

-0.69

-.978

All

years

-1.865

-.12

-.287

-1.235

End-use

activity

measure

IIP-fumiturea

Floor area of

single-family homes

IIP-millwork

Total U.S. tie

production

Total U.S. pallet

production

IIP

Proportion of

total hardwood

lumber

consumption

1958-88

Percent

24.2

; 4.7

5.7

8.9

25.2

16.4

a

 IIP the index of industrial production, 1982 = 1.0, IIP-FURNITURE is the index of industrial production

for furniture, 1982 = 1.0. Lumber consumption shares for end-use categories treated as exogenous: mines

3.9 percent and containers and dunnage 11.0 percent.

where

P, Pw,and Po are normalized product, wood, and other input prices;

rw and r0 are output-input coefficients for w and o;

and K-1 is the level of fixed capital at the start of the period.

Other than the fixed conversions between inputs and output, this form does not correspond to any specific underlying technology assumption (form of the production

function). As discussed by Cardellichio and Kirjasniemi (1987), changes in either pw

or po in this form (like the Leontief production function) shift the aggregate marginal

cost by the inverse of the output-input coefficients.20 Unlike the Leontief model, however, marginal cost per unit of output rises with output and declines with the level of

fixed capital (a1 and a2 are both positive). This form assumes that marginal cost at

some fixed base level of output is consistent with the Leontief model but then rises

more rapidly than the sum of the converted input prices as output expands beyond

this level.

20

 The Leontief production function is characterized by the

use of productive factors in fixed proportions: one unit of

output requires x units of factor a, y units of factor b, etc., n

units of output require nx units of a, ny units of b, and so on.

With this production process, the marginal costs of production

are constant as long as factor prices are constant, because

each additional unit of output requires an identical increment

in all the factors and hence variable costs.

26
Supply relations of the form in equation (31) were estimated for the four Eastern production regions (NC, NE, SC, and SE). Estimated supply elasticities with respect to

product and stumpage prices are shown in table 5. Elasticities for the Southern regions are nearly four times those in the North, reflecting the stability of Northern output over the past two decades despite widely fluctuating prices and costs.

Capacity is projected over time by using a partial adjustment procedure similar to

that described by Cardellichio and others (1989). Target capacity utilization rates

(UT) are established for each region based on historical data. Desired capacity is

then defined as

where

St-1 is last period's output.

If actual capacity at the end of the previous period is Kt-1, then for

where

K is the projected change in capacity and

μ and δ are preset fractions of the difference between target and actual capacity by

which capacity is allowed to change in a period.

Hardwood stumpage demand and supply—Treatment of hardwood stumpage demand and supply is generally the same as in the softwood sector. Stumpage demand

is derived from product output by using conversion coefficients that differ over time

according to external projections and scenarios. Estimates of residue production are

derived as previously described for softwoods. Public supply in all regions is treated

as fixed and insensitive to price (supply is equal to harvest, which is assumed to

equal the volume sold). Private stumpage supply relations for industrial and nonindustrial owners have the same forms as in the softwood sector but are estimated

only for the Eastern regions. Private supplies in the West are assumed to equal the

quantities demanded. A summary of estimated private stumpage supply elasticities

for the eastern regions is given in table 6. As was the case for product supply,

elasticities in the North are consistently lower than those for the South.

Nonstructural panels—Nonstructural panels include four broad groups: hardwood

plywood, particleboard, hardboard, and insulating board. Domestic consumption and

production of these products are determined in TAMM by using a mechanical accounting procedure that is not sensitive to product price or the prices of substitutes.

Roundwood and residues used in the production of these products are estimated by

using prespecified (externally projected) conversion factors and enter TAMM's materials balance accounting together with the volumes for all other wood and fiber

products.

27
Table 5—Hardwood lumber supply elasticities for Eastern production regions

Hardwood

Lumber

Stumpage

North-central

0.189

-.042

Price per region

Northeast

0.244

-.057

South-central

0.813

-.121

Southeast

1.011

-.127

Table 6—Estimates of the elasticity of private hardwood stumpage supply with respect to stumpage

price in the Eastern regions

Region

North-central

Northeast

South-central

Southeast

Ownership

Forest industry

0.346

.076

.407

.454

Nonindustrial

0.214

.264

.480

.509

Ten end-use categories are identified for each panel group: single-family residential

construction, multifamily residential construction, mobile home production, residential

upkeep and improvement, nonresidential construction, manufacturing, pallets, containers, dunnage, and other (comprising all other unspecified uses). End-use factors,

the ratio of consumption to a measure of output in the end-use category, are computed for each category and projected outside of TAMM.21

 Projections of consumption by end-use category and panel group are then computed as in equations (2a)

and (2b) by using externally generated projections of output in the end-use categories.

Domestic production is found as the sum of projected consumption and net trade (the

latter also projected externally).

21

 End-use activity measures are total floor area of new

dwelling units for the three residential construction categories, total real expenditures for residential upkeep and

improvement, total value of nonresidential construction,

value of manufacturing shipments, total U.S. pallet production for pallets, and value of wooden container shipments for

containers. Dunnage consumption is projected directly, and

consumption in other uses is computed as a percentage of

use in the sum of the explicitly identified uses.

28
Fiber Products Sector Projections of volumes, prices, and trade flows in the markets for pulp, paper, and

paperboard are provided by the NAPAP model (see Ince 1994). NAPAP is a spatial

market model of the North American fiber products sector that uses three regions in

the United States and two in Canada and accounts as well for offshore trade.22

NAPAP provides TAMM with projections of pulpwood consumption by roundwood and

mill residue categories and of roundwood and residue prices by region and species.

Roundwood and residue volumes enter TAMM's materials balance accounting, and

roundwood demands are cumulated with other harvest requirements as input to timber

inventory projections. Residue prices are used in the supply processes for lumber and

plywood as described in an earlier section.

Roundwood pulpwood supply in NAPAP is the sum of a price-sensitive private component (aggregated across all private owner classes) and a fixed public harvest. Private supply is represented by stumpage supply relations that depend in part on

growing-stock inventory and prices of sawtimber. To implement these supply relations,

projections of sawtimber prices and growing-stock inventory are provided by TAMM.

Residue supply is treated as a fixed-coefficients production process (consistent with

the assumptions regarding its generation used in TAMM) with marginal costs constant

for volumes up to the amount generated (a "right angle" supply curve). Marginal residue production cost estimates are derived in part from timber harvest and log transportation cost projections provided by TAMM. Projections of total available residues

generated at mills also are derived from TAMM.

Given the contemporaneous interdependence between the two models, an iterative

(Gauss-Seidel) solution scheme is used to seek an overall equilibrium in the two

(solidwood and fiber) sectors. An initial TAMM solution is found with input from

NAPAP. Inventory, sawtimber price, and residue data are then transferred to NAPAP,

which is re-solved with the resulting pulpwood consumption and residue prices being

returned to TAMM. The process continues until solutions in both models stabilize. In

the 1993 assessment update, acceptable convergence generally was achieved in

three to five iterations, with more iterations needed for scenarios depicting extreme

departures from baseline conditions.

Timber Inventory Timber inventories on private ownerships only are projected in TAMM by using a

Projection modified version of the ATLAS model (Mills and Kincaid 1992). Basic inventory data

are derived from the Forest Service's periodic forest surveys.23 Because the dates of

these inventories differ with region (for example, some are circa 1985 and others

1990), the simulation structure allows staggered "starting" times in the projection process. Lands include only those classed as "timberland," meeting a minimum standard

of productivity and not reserved from timber harvesting. Timberland is stratified by

22

 The NAPAP regions are North (TAMM's NE and NC

regions), South (TAMM's SE and SC regions), West (the

remainder of TAMM's U.S. regions), West Canada (TAMM's

Coastal British Columbia and Interior Canada regions), and

East Canada (corresponding to TAMM's Eastern Canada

region).

23

 Summary inventory data for the United States are

contained in Powell and others (1993).

29
region, owner, (representative) age class, site productivity group, management intensity (Ml) class, and forest type. No quality descriptors are available. Average diameter

at breast height is projected and reported together with stand yields, but the inventory

cannot be disaggregated by diameter class.

General management regimes—ATLAS uses both even-age and partial cutting

modes to describe the broad type of management regime applied to forest lands. For

lands classed under even-age management, ATLAS uses a "model II" format (following Johnson and Scheurman's [1977] terminology). Acres shift through time by

age class, and once harvested and regenerated, cannot be readily linked back to the

acres in the original (starting) inventory. Lands classed under partial cutting are harvested according to preset removals regimes by using a process that adjusts average

stand age to reflect the impact of removals and ingrowth on stand-age composition,

volumes per acre, and growth. Assignment of areas to even-age and partial cutting

classes is based on data derived from field measurements and judgments of Forest

Service inventory analysts. Lands grouped in either even-age or partial cutting categories remain in these classes throughout a projection.

Elements of inventory projection—

Ml classes and Ml class shifting—A (Ml) class is defined by a combination of silvicultural activities including, but not limited to, regeneration, precommercial and commercial thinning, and fertilization. These actions are depicted in ATLAS through the

use of a specific age-dependent yield function for even-age-strata (or yield process

for partial cutting) that reflects the growth and yield impacts of the regime. Yield relations used in the 1993 timber assessment update are summarized by Mills.24

 Lands

classified under even-age management can shift among Ml classes over time to reflect changes in timber management investment. At present, the extent and timing of

these shifts are determined outside of the TAMM-ATLAS model and occur only after

an acre is harvested.

Area change—Over time, the timberland base is adjusted for the movement of land

between forest (timber production) and nonforest (including, agricultural, urban, and

reserved) uses. Projections of these shifts are developed outside of the model. When

land shifts to a nonforest use, a portion of its volume at the time of shifting is assumed to be harvested and is counted in the current aggregate cut from its stratum.

This reflects the process of land clearing or volume reduction associated with most

land use changes in the private sector.

Harvest allocation and harvest order—All strata have externally set minimum harvest ages below which timber cannot be cut. This age is intended to represent a lower

bound of merchantability under current and foreseeable processing standards. The

sum of all volume in age classes above minimum harvest age in a given stratum is

termed the "available volume," or the volume that can be cut.

24

 Mills, John R. Data files 1993. Timberland inputs to the

1993 RPA assessment. Portland, OR: Pacific Northwest

Research Station. Unpublished report. On file with: U.S.

Department of Agriculture, Forest Service, Pacific Northwest

Research Station, Portland, OR 97208-3890.

30
Once the market clearing harvest volumes are determined for a given period in the

market portion of TAMM-ATLAS, they must be allocated in some way to the several

strata in the timber inventory. At the market level, products are divided into two broad

species classes: softwoods and hardwoods. In ATLAS, forest types also are grouped

into hardwood and softwood fiber types depending on the preponderant source of

volume in the type (hardwood types generally have some softwood volume and softwood types some hardwood volume). The allocation process is begun at the fiber type

level (combinations of forest types) by using the following simple simultaneous solution scheme, where we seek S and H:

where

P

i

j are the proportions of available volume of species type i (S = softwood, H =

hardwood) in the total volume in fiber type j (either S or H);

S and H total harvest volumes (all species combined) in the softwood and hardwood

fiber types; and

SR and HR total softwood and hardwood cut requests from the market portion of the

TAMM-ATLAS model.

The resulting split of harvests between the softwood and hardwood fiber types from

solving equations (34) is,

Within a given fiber type, harvest is then allocated across forest types, sites, and Ml

classes in proportion to available volumes in these classes. Harvest is allocated to

age classes in proportion to an externally established "preferred harvest order." If the

cut request cannot be fully satisfied under this order, the remainder of the request is

filled by using the "oldest first" rule.25 This approach has proven to be reasonably

effective in practice, but final harvest volumes can differ slightly from requests. This

results from the allocation of cut to age classes in a manner that is not proportional

to available volume. Hence the P'j fractions for the fiber type are not identical to the

fractions observed in the strata that are actually cut.

25

 This approach does not guarantee nonnegative S and H.

In cases where one of S or H is negative, the smaller of the

two harvest requests (SR or HR) is first allocated to strata in

both fiber types in proportion to available volumes in the

strata. The larger request, adjusted for volumes already

generated from the first allocation, is then allocated to strata

in proportion to their available volumes.

31
Other Model Elements External trade—Canadian softwood lumber and OSB are the only endogenous non11.S. markets in TAMM. All remaining external trade links are exogenous. Export demands and all other import supplies of both logs and products are assumed to be perfectly inelastic at externally established levels over time. In general, trade volumes (for

both imports and exports) are set at the national (U.S. total) level and allocated to

U.S. producing or consuming regions by using exogenous proportions. Options exist

in the TAMM-ATLAS model to employ export demand and import supply relations

with some price elasticity if estimates of these relations are available. Given the

endogenous link to Canadian solidwood markets, TAMM also requires projections of

future Canadian-U.S. currency exchange rates and levels of any tariffs on softwood

lumber and OSB.

Transport costs—As part of the analysis of spatial equilibrium, TAMM requires estimates of transportation costs associated with the shipment of products from producing

to consuming (demand) regions. Initial data for these costs were derived from available public and industry association reports on rail and truck shipments. In strictest

terms, however, competitive spatial equilibrium requires that goods classed in any

given product category (such as softwood lumber) be relatively homogeneous in quality. If this were the case, the difference in mill (FOB) prices between any two supply

regions shipping to the same demand region would equal the difference in transport

costs to this market. Similarly, differences among prices in demand regions served by

a given supply region would be no larger than the transport cost differential to the

two markets.

For most of the products treated in TAMM, the quality mix of production differs

markedly across regions. At the same time, TAMM uses a high level of product aggregation, and regional prices are volume-weighted averages across all quality classes.

Thus, differences among the average regional supply prices for any two regions

serving a given market may be substantially different from the average transport cost

difference. This is but one of many examples of the quality aggregation problem discussed by Brooks (1987). In TAMM projections, we have adjusted average interregional transport costs so as to preserve the correspondence between observed and

projected prices at the supply region level.

Model Solution Contemporaneous price linkages between the hardwood and softwood solidwood

sectors in TAMM are limited. The current period hardwood lumber price appears only

in the railroad tie end-use demand relation for softwood lumber, whereas softwood

lumber price appears in the hardwood lumber end-use demand for ties and pallets

(pallet end-use factor projections are exogenous for softwoods). Technically, this

would require the simultaneous solution of both sectors to find market equilibrium.

To simplify the solution process, we solve the hardwood sector first by using the

one-period lagged price of softwood lumber and then solve the softwood sector by

using the resulting hardwood lumber price.

32
Hardwood sector—As illustrated in equation (29), the hardwood sector is a

nonspatial system of simultaneous equations, though some of the end-use

demand relations are nonlinear in variables. We solve the system by using a

simple Newton-Raphson gradient method26 structured to find the price solution that

minimizes the difference between aggregate demand and supply quantities at the

product and stumpage levels.

Softwood sector—Considering only the product and stumpage quantities and prices,

the softwood sector model can be represented with the following set of matrix equations where matrices are denoted by capital letters and lower case names denote

vectors:

where

sp and sq are vectors of prices and volumes in the product markets;

hp and hq are vectors of prices and volumes in the stumpage markets;

rhd, rhs, rhb, and rhh are vectors computed from exogenous and predetermined

variables and their associated coefficients in the four blocks of equations.

Trade in logs among domestic U.S. regions is extremely small and is ignored in

TAMM. Consequently, the product supply, stumpage demand and stumpage supply

relations in each region can be solved simultaneously to yield expressions for stumpage price that depend solely on the regional product supply quantities (sq) and the

exogenous and predetermined variables in the several equations. These expressions

appear as,

Equation (37) is then used to replace stumpage prices in the product supply relations.

The resulting product supply equations are partially reduced form expressions that

depend only on the prices of other products, recognizing price and output adjustments in the stumpage market.

26

 The Newton-Raphson approach involves the use of

derivatives or gradients of sets of equations characterizing

the solution of the model system to locate that solution. In

this case, the equations are simply the difference between

demand and supply equations in the product and stumpage

markets. We want these equations or differences to equal

zero at the solution point; that is, supply should equal

demand. We find the prices that bring about this equality by

using an iterative process, beginning with "guesses" of the

solution. We repeatedly examine the price slopes of the

demand and supply functions to determine the best directions in which to change our guesses to find the equality

points.

33
The product demand functions and the partial reduced form product supply relations

comprise a spatially disaggregated system, where the product demand relations in

each demand region are (in general) interdependent in product prices and the product

supply curves are interdependent in regional supply prices. This system is solved for

equilibrium values of the product prices and volumes by using the reactive programming algorithm (Brooks and Kincaid 1987). Stumpage prices and volumes are then

retrieved from equation (37) and the stumpage supply relations.

Model Behavior in To illustrate the performance of the model, and to provide some qualitative basis for

Simulations of a judging its adequacy in tracking market behavior, figures 6-11 show model simulation

Historical Period results and actual data for 34 selected concepts for 1977 through 1992. Reliable historical hardwood data were available only through 1988. Table 7 provides a summary

of average absolute percentage error (AAPE) measures for these same series. In this

simulation, historical rather than model-simulated data are used for timber inventories

in the SE and SC regions through 1985 and in all other regions through 1990. In most

cases, behavioral equations were estimated with data through 1989 (exceptions used

a shorter sample).

Of the 34 series in table 7, 10 have AAPEs less than 5 percent, 26 are less than

10 percent, and 29 are less than 15 percent. TAMM errors tend to be largest in those

regions with limited solidwood output and sawtimber harvest, such as the NC, NE,

and SR. This results in some cases from low-quality and limited data for costs, recoveries, product, and stumpage prices. Large errors for OSB volumes result from

the inability of TAMM to track the rapid increases in output over the 1977-92 period

in some regions. In all cases, the model reproduces the general pattern of growth

but underestimates actual levels in several years. Larger errors also arise in TAMM

projections of sawtimber stumpage prices in the PNWW and Southern regions.

Southern projections seem to exaggerate all the peaks and troughs relative to actual

levels. PNWW projections have the more common mixture of underestimated peaks

and troughs, excepting that the model overestimates the sharp rise in prices beginning in 1987-88. In considering TAMM's performance in these and other price projections, it should be remembered that, unlike most other widely used models of forest products markets, there are no explicit behavioral relations to explain price.

Rather, prices are determined by the interaction of supply and demand relations

at the stumpage and product levels.

Projections, Policy To illustrate the application of TAMM, this section presents a set of alternative

Simulations, and scenarios of the future development of the U.S. forest sector under different assumpModel Evaluation tions on forest resource policies. We examine a "base" case and four variants derived

from the 1993 timber assessment update (Haynes and others 1994): (1) reduced harvest from public lands in the United States, (2) increased rates of paper and paperboard recycling, (3) the adoption of more stringent public regulations on private forest

practices, and (4) limited harvests from provincial forest lands in Canada. A concluding section presents some general criticisms of the policy simulation behavior of

TAMM .

Text continued on page 42

34
Figure 6—Softwood and hardwood sawtimber stumpage prices,

actual and projected values for selected regions

35
Figure 7—Softwood and hardwood sawtimber harvest volumes, actual and projected values for

selected regions

36
Figure 8—Softwood lumber, OSB, and softwood plywood production,

consumption and imports, actual and projected values.

37
Figure 9—Indexes of real prices for softwood lumber, hardwood

lumber, softwood plywood, and price of OSB, actual and projected

values.

38
Figure 10—Production of softwood lumber and plywood, actual and

projected values for selected regions

39
Figure 11—Production of softwood lumber, softwood plywood, OSB,

and hardwood lumber, actual and projected values for selected

regions

40
Table 7—Average absolute percentage errors, TAMM projections for historical period 1977-92

Concept per region

Softwood lumber:

Consumption

Production

Imports

Price per index

Softwood plywood:

Consumption

Production

Price per index

OSB:

Consumption

Production

Imports

Price per index

Hardwood lumber:

Consumption

Production

Price per index

Stumpage sector:

Softwood cut

Hardwood cut

Softwood price

Hardwood price

U.S. total

1.88

3.06

6.68

7.89

2.95

9.47

28.96

14.93

14.64

6.44

5.19

6.70

PNWW

5.59

6.53

2.94

18.89

NR NC

Percent

6.00

6.30

4.69

8.73

32.02

26.36

North

4.45

3.57

5.70

South

4.58

5.03

14.41

6.22

3.85

5.45

21.61

8.29

Canada

3.49

41
Base Scenario As a datum for comparison in policy simulations, the timber assessment process develops a base projection. This scenario is to be interpreted as the results of a specific

macroeconomic projection and continuation of past trends in all of the key land base,

timber management investment and policy elements of the forestry sector. For the

1993 timber assessment update, the several assumptions underlying the base projection are described in Haynes and others (1994). The associated TAMM base projections for selected market elements are shown in figures 12-17.

Product and stumpage price trends (fig. 12) provide a useful summary illustration of

general developments in the base scenario. Softwood lumber prices rise in two major

steps over the projection. The 1990s increase derives from reduced public harvest in

the West. The step-up beginning just before 2010 reflects the limitation on private harvests in the South, which becomes most pronounced in that period. After 2015, softwood lumber prices remain roughly stable as growth in demand and supplies are

more nearly in balance. Hardwood lumber prices rise steadily over the projection,

thereby reflecting the steady growth in demand and stable to declining hardwood

inventories and private supply. Prices of OSB remain essentially stable after the

mid-1990s, despite rapid growth in consumption, as capacity expands and wood and

other costs are stable in real terms. Softwood plywood prices are at first held in check

by the substitution prospects of OSB. Once these use changes have played out, and

as prices of timber force up costs, plywood prices rise slowly through 2040.

In the softwood stumpage sector, prices in Western regions show cyclical peaks early

in the projection as public cut drops and "excess" processing capacity is eventually

forced out of operation. Stumpage prices then resume growth following trends in product prices and demand. Southern prices catch up with those in the PNWW some time

after 2000 and remain roughly aligned thereafter. The greatest rates of stumpage

price growth occur in the Rockies and the North as a result of declining public cut,

in the former, and rising lumber output, in the latter.

Figure 13 provides an aggregate view of softwood timber harvest for broad classes of

products (sawtimber includes lumber and plywood, nonsawtimber includes pulpwood,

fuelwood and reconstituted panels) by region. The effects of declining public harvest

and limited private inventories in the West are clear from the drop in the Western

sawtimber curve. Virtually all the substitution observed for Western public harvest

reductions, and nearly all the future growth in harvest for both sawtimber and nonsawtimber products, comes from the East.

The macroeconomic forecast underlying the base projection includes limited growth

in aggregate U.S. economic activity (only 2- to 3-percent growth in GNP) and little

change in new housing construction relative to levels in the mid-1980s. This results

in only limited growth in lumber demand in manufacturing uses and a steady decline

in its use in new residential construction (despite increased house size). Rather than

these traditional sources of demand, the rising trends in softwood lumber consumption

shown in figure 14 derive from residential upkeep and alteration, as the housing stock

ages, and to a lesser extent from nonresidential construction and miscellaneous uses.

Imports from Canada provide about half the growth through 2020, then fall, supplanted by increased domestic production as young-growth timber stocks in the West

and South reach merchantable ages.

Text continued on page 48

42
Figure 12—Projected real producer price indices and softwood stumpage prices for selected

products and regions: base case.

43
Figure 13—Projected softwood sawtimber and nonsawtimber

harvests for selected regions base case

Figure 14—Projected softwood and hardwood lumber production,

consumption, and imports base case

44
Figure 15—Projected softwood plywood and OSB production, consumption, and imports:

base case.

45
Figure 16—Projected softwood and hardwood growing-stock removals from timberland

for selected regions and owners: base case.

46
Figure 17—Projected softwood and hardwood growing-stock

inventory for selected regions and owners base case

47
Hardwood lumber demand, in contrast, rises almost entirely because of growth in

pallet consumption and use of hardwoods in millwork (though the increment in total

consumption, less than 4 billion board feet over 50 years, is not large relative to softwoods). Growth in output is projected to come entirely from the Southern regions.

Consumption and production of softwood plywood falls slowly over the projection

(fig. 15) due to substitution by OSB and other materials. OSB consumption, in contrast, rises nearly fivefold. Some of this increase, roughly 6 billion square feet, comes

from substitution for softwood plywood. The remainder derives from the capture of

virtually all of the growth in the residential upkeep and repair market and to a lesser

extent from the growth in nonresidential construction as well.

Figure 16 shows TAMM projections of future regional and ownership sources of softwood and hardwood timber removals. As suggested by previous results, Southern

private lands will provide the bulk of any growth in softwood removals. Removals on

Western private lands are projected to return just to the levels of the late 1980s by

2040. For hardwoods (removals here include both sawtimber and nonsawtimber products), largest growth is again projected to occur in the Southern private sector,

whereas Northern private lands show a less rapid but steady increase.

Reversing the trend of the past 30 years, TAMM projects a steady decline in Southern

nonindustrial softwood and hardwood inventories after 2000 (fig. 17). This results in

part from the shifting of Western harvest to Eastern sources (as Western public cut

and private inventories decline), continued low levels of timber management activity

on Southern nonindustrial lands, and loss of these lands to other uses and other

classes of private owners. Southern forest industry inventories expand sharply,

thereby reflecting continued intensification of management and growth in their land

base. This growth supports much of the increased Southern cut seen in other charts.

Western and Northern nonindustrial private inventories rise, as growth outpaces harvest even in the face of rising prices.

Increased Public The Increased Public Harvest scenario envisions a return to National Forest harvest

Harvest Scenario levels as proposed in the final land management plans developed by each forest in

1990 and to levels of cut on other government lands as planned in the late 1980s.

Over the period from 1995 to 2040, this combination of changes would lead to an

increase in total public cut of some 0.8 billion cubic feet per year relative to the base

scenario. This increase in public cut leads to a rapid drop in Western stumpage

prices (fig. 18) and a gradual decline in other regions such as the South. These

declines in stumpage prices reduce timber harvests in the South (fig. 19), but the

increased public cut raises harvest in the West. In product markets, stumpage price

reductions yield a decline in softwood lumber prices, a reduction in U.S. softwood

lumber imports, and a net expansion in softwood lumber consumption.

Increased Recycling This scenario examines the impacts of further increases in the use of wastepaper as

Scenario raw material for paper and board production. In Forest Service assessment projections before 1988, it generally was assumed that wastepaper usage rates would

remain relatively constant at around 20 percent. Little change was expected because

chip-pulpwood prices were projected to experience only modest growth (no growth

was expected for hardwood pulpwood and chip prices in some regions). Projections

for the 1989 assessment abandoned this view in recognition of growing national concerns about waste management. The usage projections in this scenario rise still more

48
Figure 18—Projected sawtimber stumpage prices and sawtimber harvests for

selected regions: BASE case and increased public harvest scenarios.

49
Figure 19—Projected softwood lumber producer price index and U.S. production, consumption, and

imports: BASE case and increased public harvest scenarios.

50
rapidly, reflecting major recent gains in actual levels of usage and marked revisions

in projections of future relative fiber costs. Ince (1994) discusses the technical basis

for continued expansion in the use of recycled fibers and provides the motivation for

this scenario.

The following tabulation gives recent historical rates of wastepaper use,27 projections

from the 1993 assessment update and past assessments. The increased recycling

scenario calls for usage rates of about 60 percent beginning in 2020.

Year

1986

1991

1993

2000

2010

2020

2030

2040

Actual

24.7

29.2

33.0est

Wastepaper usage

Base

1989 1993

Percent

21

22

25

27

28

37.5

41.2

42.5

43.7

45.4

Increased

recycling

45.3

56.5

60.6

60.8

59.5

As shown in fig. 20, the effect of greater use of recycled fiber is to lower nonsawtimber demand and aggregate growing-stock removals for both softwood and

hardwood in all regions. Particularly large reductions occur in Eastern softwoods,

because the largest share of U.S. pulpwood harvest occurs in the East. Over time,

this yields some expansion in timber inventories, reduces softwood sawtimber stumpage prices, raises sawtimber demand for lumber and plywood, and allows an expansion in softwood sawtimber harvest. Given this chain of interactions, and recognizing

that all elements of private timber management intensity are fixed in the scenario at

their base levels or trends, high recycling could be seen as having some potential to

compensate for other policies that act to reduce timber supply.

Increased Public In a recent study, Greene and Siegel (1994) obtained judgmental estimates of the

Regulation of Private potential timber supply impacts of current and potential future changes in State and

Practices Federal regulation of private forest practices from panels of forestry experts in various

U.S. regions. The results of this process were a set of average percentage reductions

in private timber "supply" by region associated with the two levels of regulation (current and potential future). We examine the more stringent "potential future change"

category here by multiplying the stumpage supply functions in both TAMM and

NAPAP by (one minus) the appropriate fixed regional percentage.

27 Wastepaper usage rate is the ratio of recovered

wastepaper used in domestic paper and board mills to

domestic production of paper and board.

51
Figure 20—Projected softwood and hardwood growing-stock removals and softwood

sawtimber harvest: BASE case and high recycle scenarios.

52
The results, as illustrated in figure 21, run somewhat counter to intuition because of

substitution of fiber sources in the pulp sector. Reduced private supply lowers U.S.

average annual softwood growing-stock removals by some 4.7 percent relative to the

base scenario. The largest impact is on pulpwood harvest, however, with a substantial

shifting of pulp fiber demand to nonroundwood and nonwood (recycled fiber) sources.

This shift occurs rapidly and frees enough additional inventory to allow sawtimber

harvest to rise relative to the base. Expanded inventories and private supply lead to

reduced sawtimber stumpage prices in all regions.

Canadian Lumber There has been some discussion in recent years of possible reductions in allowable

Output Restriction cut levels on Crown lands in virtually all Canadian provinces (examples from British

Columbia include, Government of British Columbia 1994 and Reed 1993). Restrictions

would result from a combination of land withdrawals for natural preserves and from

lagging regeneration on lands harvested in the past. The extent of such restrictions

is, at present, highly uncertain as is the distribution of any reductions across the solidwood and fiber products sectors. To obtain some preliminary idea of the potential impacts of such changes on U.S. markets, we examined a case in which harvest restrictions are limited to the solidwood sector and act to constrain output in the future to

levels no higher than those observed in the peak periods of the late 1980s.

In Canada, the hypothetical restriction reduces total softwood lumber output by an

average of 3.6 billion board feet per year between 2000 and 2040 relative to the base

(see fig. 22). Because Canadian domestic and non-U.S. export demands are insensitive to price in TAMM, exports to the United States fall by a similar amount. Net U.S.

consumption falls by an average of 0.8 billion board feet per year (relative to a total

of roughly 52 billion board feet) as U.S. domestic output rises by 2.8 billion board feet

per year. Softwood lumber prices are on average 4.8 percent higher than the base.

Future Modifications in Until recently, TAMM has been run exclusively on a mainframe computer. With

TAMM Structure and the advent of high-speed, high-capacity microcomputers, TAMM now has been

Solution adapted to the PC environment. Experimental systems have been developed to

run TAMM-NAPAP iterations with the bulk of the file transfer procedures between

models automated through spreadsheets and to link the models in their annual

solution cycles with only a one-period lag. Future efforts will continue to refine this

critical model interface.

The reactive programming algorithm used in TAMM since its inception has many

advantages as a solution procedure, including speed and compactness. It has proven

increasingly difficult, however, to adequately represent many types of policy scenarios

in this structure, particularly those that involve constraints on endogenous variables

such as interregional flows, levels of output in the stumpage sector, or limits on multiregional changes in capacity. Experimental versions of TAMM have been developed

in which the spatial market solution procedure uses a nonlinear programming framework following the "net revenue" maximization approach described by Takayama and

Judge (1971) and Martin (1981). This has also enabled simultaneous solution of the

softwood and hardwood sectors.

53
Figure 21—Projected softwood stumpage prices and growing-stock removals BASE case and

increased public harvest scenarios

54
Figure 22—Projected U.S. softwood lumber production, consumption and imports, softwood lumber price index, and Canadian

softwood lumber production: BASE case and restricted Canadian

harvest (REST) scenarios.

55
Product supplies in TAMM have always been represented by continuous functions

whose parameters have been estimated by econometric methods. Although useful in

many respects, this approach limits the types of future product supply scenarios that

can be simulated, particularly ones involving new or speculative production technologies not now widely used. Efforts are underway to develop an activity analysis representation of U.S. and Canadian lumber and plywood supply to supplant the continuous, aggregate form. This will involve specification of various existing technologies

by region with associated costs and conversion coefficients (as in the present version

of TAMM, there will be no product quality differentiation). Implementation of this approach also will entail an evaluation of the ability of the activity analysis form to track

historical market behavior.

The current structure of ATLAS involves periodic (5- to 10-year) inventory updates,

whereas TAMM operates on an annual cycle. As noted in figure 1, this disparity in

projection cycles requires an additional iterative process to ensure that the annual

inventory approximations generated in TAMM are "close enough" to the periodic projections developed by ATLAS. Work is now underway to allow ATLAS to employ an

annual cycle. This modification may increase the size of the ATLAS module and its

operating time. At the same time, it will dramatically simplify the overall projection

process (by eliminating the TAMM-ATLAS iteration) and improve the ability to control

simulations.

With the above modifications in place, it will be possible to directly merge much of the

solidwood market solution directly with the pulpwood sector in the same solver and

period-to-period update process, eliminating the need for the TAMM-NAPAP iteration.

As presently envisioned, implementation of this merger will use the programming solution package presently used with NAPAP operating under an expanded simulation

controller program that integrates other wood-using sectors and the timber inventory.

Acknowledgments We thank Jonna Kincaid, University of Washington, CINTRAFOR, and Eric Jensen,

University of Montana, School of Forestry for their efforts in computer programming.

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Spelter, H. 1985. A product diffusion approach to modeling softwood lumber demand

Forest Science 31 (3) 685-700

Spelter, H. 1992. Technology-driven substitution in the forest sector the variable price

elasticity model revisited In Lonnstedt, Lars, ed Forest sector analysis Proceedings

of P06 02 FORESEA, IUFRO centennial, 1992 August 4-September 30, Berlin,

Germany Uppsala, Sweden Swedish University of Agricultural Sciences,

Forest-Industry-Market Studies 24-29

Takayama, T.; Judge, G.G. 1971. Spatial and temporal price and allocation models

Amersterdam North-Holland Publishing Co

U.S. Department Agriculture, Forest Service. 1982. An analysis of the timber situation

in the United States, 1952-2030 Forest Resource Rep 23 Washington, DC 499 p

Williams, D.H. 1991. The price responsive timber supply model (PRTSM) concepts and

structure Working Pap Ottawa, Canada Forestry Canada, Policy and Economics

Directorate, Economics Studies Division 24 p

58

* U S GOVERNMENT PRINTING OFFICE 1997 589 353 / 63001 REGION NO 10
Adams, Darius M.; Haynes, Richard W. 1996. The 1993 timber assessment

market model structure, projections, and policy simulations Gen Tech Rep

PNW-GTR-368 Portland, OR U S Department of Agriculture, Forest Service,

Pacific Northwest Research Station 58 p

The 1993 timber assessment market model (TAMM) is a spatial model of the solidwood and timber inventory elements of the U S forest products sector The TAMM

model provides annual projections of volumes and prices in the solidwood products

and sawtimber stumpage markets and estimates of total timber harvest and inventory

by geographic region for periods of up to 50 years TAMM and its companion models

that project pulpwood and fuelwood use were developed to support the quinquennial

Resource Planning Act (RPA) timber assessments and assessment updates conducted by the USDA Forest Service This report summarizes the methods used to

develop the various components of TAMM and the estimates of key behavioral parameters used in the TAMM structure, and also illustrates the use of TAMM with a

base and several scenario projections

Keywords Forest sector models, supply, demand, prices, timber supply, RPA

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