Econometric Estimation of The
National Carbon Sequestration
Supply Function
Ruben N. Lubowski
USDA Economic Research Service
Andrew J. Plantinga
Oregon State University
Robert N. Stavins
Harvard University and
Resources for the Future
Derivation of the Carbon
Sequestration Supply Function
• Econometric national land-use model used to
simulate baseline land use changes and effects
of carbon sequestration policy.
– Incentives (e.g. annual per acre forest subsidies)
modify land-use patterns
• Partial equilibrium model of agricultural
commodity and timber markets used to model
endogenous price effects.
• Baseline and simulated land use changes are
mapped into changes in carbon storage.
Changes in Major Non-Federal Land Uses between 1992 and
1997 in the Contiguous 48 United States (in thousands of acres)
Land Use in 1997
Land Use
in 1992
Crops
Pasture
Forest
Urban
Range
CRP
1997
Total
Crops
Pasture
Forest
Urban
Range
1992
Total
CRP
360,349
9,289
1,886
2,754
1,522
2,049
377,849
95.37%
2.46%
0.50%
0.73%
0.40%
0.54%
100%
8,952
107,250
6,143
1,879
1,561
110
125,894
7.11%
85.19%
4.88%
1.49%
1.24%
0.09%
100%
736
1,883
393,224
4,526
1,163
23
401,556
0.18%
0.47%
97.93%
1.13%
0.29%
0.01%
100%
2
0
2
65,015
0
0
65,020
0%
0%
0%
100%
0%
0%
100%
1,963
694
1,587
1,150
399,663
21
405,078
0.48%
0.17%
0.39%
0.28%
98.66%
0.01%
100%
2,238
809
184
7
297
30,465
34,001
6.58%
2.38%
0.54%
0.02%
0.87%
89.60%
100%
374,239
119,926
403,026
75,331
404,207
32,668
1,409,398
26.55%
8.51%
28.60%
5.34%
28.68%
2.32%
100%
National Econometric Model of
Land Use
• Dynamic Optimization Problem Representing the
Landowner’s Land Allocation Decision
 Landowner chooses land use that maximizes present
discounted stream of future expected net benefits.
• Random Utility Framework
 Probability that land in current use is converted to each
alternative use.
• First Order Markov Transition Matrix
 Transition probabilities are parametric functions of
economic decision variables.
 Maximum likelihood procedures are used to recover
parameter estimates.
Data for Land-Use Model
• Primary data set is USDA National
Resources Inventory (NRI)
– Plot-level observations of land use for 1982, 1987,
1992, 1997
– 800,000 plots in all counties in the 48 contiguous U.S.
states
– Six land uses (Crops, Pasture, Forests, Urban,
Range, and CRP)
– Plot-level land quality
• Annual net returns for the different uses
measured at the county level
Estimation Approach for
Land-Use Model
• Estimate separate parameters for five
starting land uses (crops, pasture, forest,
range, CRP).
• Estimate model with pooled data from
three transition periods (1982-87, 1987-92,
1992-97).
• Discrete choice model: Nested Logit
Econometric Specification Issues
 Nested logit model allows for differences in
substitutability among land-use choices.
 Profit variables available only at county level.
- Interact county-level profits for each land use with
dummy variables for plot-level land quality,
measured by Land Capability Class (LCC) rating.
Summary of Estimation Results
 Plot-level land quality important in determining
size of effect of county-level profits.
 Lands starting in crops responsive to profits from
all land uses.
 Lands starting in forests and pasture responsive
to crop and urban profits.
 Lands starting in range only responsive to urban
profits.
 Land starting in all uses responsive to urban
profits.
Endogenous Price Algorithm
• Crop and timber prices are endogenous.
• Prices of pasture and range outputs and
urban prices are exogenous.
• Transition probabilities and other variables
are specified at the county-level.
Supply
• Supply is inelastic and determined by
acres and yields.
• Timber Supply
– Lagged for new forests
– Existing forests assumed to be “fully
regulated”
Demand
• Constant Elasticity Demand Curves
• Demand Elasticities
– Estimates from econometric studies
– Commodity specific
– Regional or national
Endogenous Price Simulations
Initial Acres by Use
Initial Transition
Probabilities
Change in Acres
Change in Output
Change in Prices
Updated Transition
Probabilities
Updated Acres
Repeat until
convergence
Endogenous Price Simulations
Equilibrium Prices
Initial Transition
Probabilities
Initial Acres by Use
Updated Acres
Repeat
Carbon Model
Cropland and Pasture into Forest
• Carbon flows vary by species, region, and
initial land use.
• All land is assumed to go into timber
production (for results presented here).
• All carbon data from 1999 version of
FORCARB tables (U.S. Forest Service).
Carbon Model
Carbon Flows from Timber Harvests
• After harvest, carbon in non-merchantable
wood, understory, and floor litter is emitted.
Soil carbon assumed constant for land that
remains in forest.
• Carbon flows in merchantable wood vary by:
– Tree Species
– Region
– End Products
Carbon Model
Forest into Other Uses
• Timber harvests
– Timber inventory assumed to be “fully
regulated.”
– Timber into pulpwood or sawtimber depending
on age.
• Soil carbon adjusts immediately to
equilibrium level for new use.
Carbon Model
Land Remaining in Forest
• All land in timber production (for results
presented here).
• Timber inventory assumed to be “fully
regulated.”
• Oldest age class is harvested.
Carbon Model
Cropland into Pasture (and vice-versa)
• Carbon flows vary by region.
• Initial soil carbon from FORCARB tables.
• Carbon adjustment equations derived by
Richard Conant (CSU Nat. Resource
Ecology Lab) for this study.
Alternative Estimates of the Marginal Costs of
Carbon Sequestration in the U.S.
Marginal
Cost ($/ton)
200

150

100

50



 



 

 


0


 
0
200



 

 




400
600

800
Carbon (Million Tons)
This Study
Stavins (1999)
Adams et al. (1993) Callaway and McCarl

Richards et al. (1993)

Future Research Directions
• Revise preliminary marginal cost estimates.
• Explore different economic, policy, and
biophysical scenarios.
• Further refine econometric model:
-Option values (uncertainty).
-Greater spatial resolution.
• Integrate changes in management
practices in simulations.
• Examine other environmental impacts.