1. A National-Level Econometric Analysis of the Costs of Carbon Sequestration
Ruben Lubowski
John F. Kennedy School of Government
Harvard University
Andrew J. Plantinga
Department of Agricultural and Resource Economics
Oregon State University
Robert N. Stavins
and
Resources for the Future
Prepared for Presentation at the
Forestry and Agriculture Greenhouse Gas Modeling Forum Workshop National Conservation Training Center
Shepherdstown, WV
September 30 - October 3, 2001

2. Model Overview
·      Scale: National (U.S.)
·      Land Uses: Forest, Cropland, Pasture, Rangeland, CRP, Urban
·      Prices: Output Prices for Forest and Agricultural Commodities are Endogenous
·      Landowner Responses: Model Parameters Based on Observed Behavior
·      Greenhouse Gases: Carbon

3. A National Econometric Model of Land Use
·      Dynamic Optimization Problem Representing the Landowner’s Land Allocation Decision
 Decision Rule for the Landowner
·      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

4. A First-Order Markov Transition Matrix of Land Uses
Forest
Crop
Pasture
Range
CRP
Urban
PFF
PFC
PFP
PFR
PFCo
PFU
PCF
PCC
PCP
PCR
PCCo
PCU
PPF
PPC
PPP
PPR
PPCo
PPU
PRF
PRC
PRP
PRR
PRCo
PRU
PCoF
PCoC
PCoP
PCoR
PCoCo
PCoU
PUF
PUC
PUP
PUR
PUCo
PUU
 ...·      For example, the probability that pasture is converted to forest is expressed:

5. Data · Primary Data Set is the National Resources Inventory (NRI)
·      Primary Data Set is the National Resources Inventory (NRI)
 Plot-level Observations of Land Use for 1982,
1987, 1992, and 1997
 Six Land Uses (Forest, Cropland, Pasture,
Rangeland, CRP, Urban) and the Contiguous U.S. States
 Plot-level Land Characteristics Summarized
as a Land Capability Class Rating
·      Annual Net Returns to Alternative Uses Measured at the County Level

6. Mean and Standard Deviation
Table 1: Independent Variables for Estimating Land-Use Transition Probabilities with Plot-Level Data
Variable
Variable Description
Expression where appears
Mean and Standard Deviation
Regional Level
South region dummy for CRP
South census region dummy variable1
CRP profits
0.37 (0.48)
0.36 (0.48)
0.43 (0.49)
Midwest region dummy for CRP
Midwest census region dummy variable
0.41 (0.49)
0.40 (0.49)
0.35 (0.47)
West region dummy for CRP
West census region dummy variable
0.16 (0.37)
0.12 (0.33)
County Level
Crop profits
Annual net crop return per acre (with government payments)
66.75 (49.1)
70.11 (55.6)
75.74 (62)
Forest profits
Annual net forest return per acre
6.02 (6.30)
7.83 (8.49)
12.65 (14.05)
Urban profits
Annual net urban return per acre (based on value of land for single-family home development)
( )
( )
( )
Beef cow prices
Net beef cow price per head
Pasture and range profits
(132.88)
355.28
(122.24)
281.59
(111.53)
Plot to county land quality ratio
Ratio of plot-level land capability class (LCC) to county-level mean land capability class (LCC)
Crops, pasture, forest, urban, range profits
0.98 (0.40)
Plot to region land quality ratio
Ratio of county-level mean land capability class (LCC) to region-level mean forestland LCC
0.98 (0.47)
1.06 (0.25)
1.08 (0.26)
1Dummy for Northeast Region normalized to zero. 2All land-use returns are the means of five-year lagged values from the year land use observed and are expressed in 1990 US$ deflated using the Producer Price Index for all commodities. 3LCC land quality ratings range from 1 to 7 with higher numbers denoting worse land quality for crop production.

7. Table 2.1
 Changes in Major Non-Federal Land Uses between 1982 and in the Lower Forty-Eight States* From National Resources Inventory (NRI) (in thousands of acres)
Land Use in 1987
Land Use in 1982
Cropland
CRP
Forest Land
Pastureland
Rangeland
Urban Land
1982 Total
388,802
12,783
1,763
10,708
1,017
1,720
416,793
93.28%
3.07%
0.42%
2.57%
0.24%
0.41%
100%
9,340 51
394,059
1,607
872
2,440
399,498
0.01%
98.64%
0.40%
0.66%
0.61%
8,253
608
5,197
116,371
984
132,285
6.24%
0.46%
3.93%
87.97%
0.74%
3,565
326
675
1,490
406,346
848
413,251
0.86%
0.08%
0.16%
0.36%
98.33%
0.21%
515,80 0%
1987 Total
401,560
13,768
401,695
130,176
408,636
57,573
1,413,408
28.41%
0.97%
28.42%
9.21%
28.91%
4.07%
*Percentages are of 1982 totals (far right column). Totals include only lands which remained non-federal and in the six listed uses between 1982 and Read the table horizontally to see how land that was under a particular land use in (row heading) was subsequently allocated in terms of land use in 1987 (column heading). Read the table vertically to see where land that that was in a particular land use in 1987 (column heading) was previously allocated in terms of land use in 1982 (row heading).

8. Table 2.2
Changes in Major Non-Federal Land Uses between 1987 and 1992 in the Lower Forty-Eight States* From National Resources Inventory (NRI) (in thousands of acres)
Land Use in 1992
Land Use in 1987
Cropland
CRP
Forest Land
Pastureland
Rangeland
Urban Land
1987 Total
369,953
18,749
1,207
7,853
990
1,862
400,615
92.35%
4.68%
0.30%
1.96%
0.25%
0.46%
100% 13
137,87
13,801
0.10%
99.9% 0%
484 52
396,113
989
702
2,920
401,262
0.13%
0.01%
98.72%
0.18%
0.73%
6,340
1,302
3,638
116,777
453
1,308
129,819
4.88%
3.83%
2.80%
92.32%
0.35%
1.01%
257
124
913
865
402,14
985
407,59
0.55%
0.03%
0.22%
0.21%
98.74%
0.24%
57,728
57,729
1992 Total
379,049
34,014
401,872
126,485
404,560
9,859
1,410,785
26.87%
2.41%
28.49%
8.97%
28.68%
4.59%
*Percentages are of 1987 totals (far right column). Totals include only lands which remained non-federal and in the six listed uses between 1987 and Read the table horizontally to see how land that was under a particular land use in (row heading) was subsequently allocated in terms of land use in 1992 (column heading). Read the table vertically to see where land that that was in a particular land use in 1992 (column heading) was previously allocated in terms of land use in 1987 (row heading).

9. From National Resources Inventory (NRI) (in thousands of acres)
Table 2.3
Changes in Major Non-Federal Land Uses between 1992 and 1997 in the Lower Forty-Eight States*
From National Resources Inventory (NRI) (in thousands of acres)
Land Use in 1997
Land Use in 1992
Cropland
CRP
Forest Land
Pastureland
Rangeland
Urban Land
1992 Total
360,349
2,049
1,886
9,289
1,522
2,754
377,849
95.37%
0.54%
0.50%
2.46%
0.40%
0.73%
100%
2,238
30,465
184
809
297 7
34,001
6.58%
89.60%
2.38%
0.87%
0.02%
393,224 23
1,883
1,163
4,526
401,556
97.93%
0.01%
0.47%
0.29%
1.13%
8,952
110
6,143
107,250
1,561
1,879
125,894
7.11%
0.09%
4.88%
85.19%
1.24%
1.49%
1,963 21
1,587
694
399,663
1,150
405,078
0.48%
0.39%
0.17%
98.66%
0.28% 2
65,015
65,020 %
1997 Total
374,239
32,668
403,026
119,926
75,331
1,409,398
26.55%
2.32%
28.60%
8.51%
28.68%
5.34%
*Percentages are of 1992 totals (far right column). Totals include only lands which remained non-federal and in the six listed uses between 1992 and Read the table horizontally to see how land that was under a particular land use in (row heading) was subsequently allocated in terms of land use in 1997 (column heading). Read the table vertically to see where land that that was in a particular land use in 1997 (column heading) was previously allocated in terms of land use in 1992 (row heading).

10. ln(ratio of plot to county LCC)1 0.0071** (0.0009) 0.0056** 0.0095**
Table 3.1: Estimated Elasticities Evaluated at Sample Means from the Multinomial Logit Model of Land-Use Transitions: Arrival State is Forest
Dependent variable is the probability of the specified transition from the starting state. Elasticities reported with standard errors in parentheses.
Variable
Transition
Forest to Forest
Crops to Forest
ln(forest profits)
(0.0002)
0.0002
(0.0004)
1.248**
(0.148)
0.990**
(0.109)
1.096**
(0.0787)
ln(crop profits) ** ** **
(0.0001)
-0.124**
(0.040) **
(0.023)
ln (urban profits) ** ** **
(0.0008)
(0.000) **
(0.0003) **
( )
ln(beef cow price) **
( )
( ) **
( )
1.646**
(0.094)
0.302**
(0.097)
0.098**
(0.0258)
ln(ratio of plot to county LCC)1
0.0071**
(0.0009)
0.0056**
0.0095**
0.566**
(0.122)
0.720**
(0.161)
0.716**
(0.127)
ln(ratio of county to region LCC) 1 **
0.0045**
(0.0014)
0.0070**
(0.0025)
1.969**
(0.167)
-0.385
(0.554)
1.105**
(0.305)
Midwest region dummy for CRP
( )
(0.0005)
-0.043**
(0.010) **
(0.0055)
South region dummy for CRP
(0.0006)
-0.037**
(0.009) **
(0.0018)
West region dummy for CRP
( )
-0.041** **
(0.0023)
1 Higher land capability class (LCC) values indicate worse quality land for agriculture.
*Significant at 10% level. ** Significant at 5% level.

11. Elasticities reported with standard errors in parentheses.
Table 3.2: Estimated Elasticities Evaluated at Sample Means from the Multinomial Logit Model of Land-Use Transitions: Arrival State is Forest
Dependent variable is the probability of the specified transition from the starting state.
Elasticities reported with standard errors in parentheses.
Variable
Transition
Pasture to Forest
Range to Forest
ln(forest profits)
0.335**
(0.050)
0.280**
(0.061)
0.227**
(0.037)
0.285**
(0.042)
0.302** (0.057)
0.057**
(0.032)
ln(crop profits)
-0.031
(0.022)
-0.101**
(0.030)
-0.117**
(0.021)
-0.792**
-0.044**
(0.013)
-4.32e-09
(0.0000)
ln (urban profits)
(0.002)
-0.031**
(0.008)
-0.022**
(0.004)
-0.012**
(0.006)
-0.015**
(0.0049)
-3.64e-06
( )
ln(beef cow price)
0.095
(0.104)
-0.159**
(0.014)
-0.088**
(0.017)
-0.064
(0.062)
-0.034
(0.043)
1.937**
(0.538)
ln(ratio of plot to county LCC) 1
0.841**
(0.072)
0.816**
(0.066)
0.602**
(0.071)
0.721**
(0.069)
0.768**
(0.068)
1.751**
(0.361)
ln(ratio of county to region LCC) 1
0.502**
(0.094)
1.383**
(0.310)
0.583**
(0.275)
0.252**
(0.091)
1.31**
(0.186)
-0.449
(0.596)
Midwest region dummy for CRP
-0.027
(0.018)
-0.079**
(0.031)
(0.0013)
n/a
South region dummy for CRP
-0.026
-0.047*
(0.0014)
West region dummy for CRP
-0.081**
(0.034)
1 Higher land capability class (LCC) values indicate worse quality land for agriculture.
*Significant at 10% level. ** Significant at 5% level.

12. Elasticities reported with standard errors in parentheses.
Table 3.3: Estimated Elasticities Evaluated at Sample Means from the Multinomial Logit Model of Land-Use Transitions: Starting State is Forest
Dependent variable is the probability of the specified transition from the starting state.
Elasticities reported with standard errors in parentheses.
Variable
Transition
Forest to Forest
Forest to Crops
ln(forest profits)
(0.0002)
(0.0004)
0.0153
(0.022)
(0.0334)
(0.028)
ln(crop profits) ** ** **
0.880**
(0.078)
0.611**
(0.122)
0.821**
(0.087)
ln (urban profits) ** ** **
(0.0008) ** **
ln(beef cow price) **
( )
( ) **
( )
ln(ratio of plot to county LCC)1
0.0071**
(0.0009)
0.0056**
0.0095**
-1.292**
(0.116)
-1.160**
(0.161)
-1.151**
(0.147)
ln(ratio of county to region LCC) 1 **
0.0045**
(0.0014)
0.0070**
(0.0025)
0.222**
(0.083)
-0.556**
(0.188)
-0.485**
(0.187)
Midwest region dummy for CRP
( )
( )
(0.0005)
( )
South region dummy for CRP
( )
(0.0006)
West region dummy for CRP
1 Higher land capability class (LCC) values indicate worse quality land for agriculture.
*Significant at 10% level. ** Significant at 5% level.

13. Elasticities reported with standard errors in parentheses.
Table 3.3: Estimated Elasticities Evaluated at Sample Means from the Multinomial Logit Model of Land-Use Transitions: Starting State is Forest
Dependent variable is the probability of the specified transition from the starting state.
Elasticities reported with standard errors in parentheses.
Variable
Transition
Forest to Pasture
Forest to Urban
ln(forest profits)
0.0153
(0.022)
(0.0334)
(0.028)
ln(crop profits) **
(0.0002) **
(0.0001) **
ln (urban profits) **
(0.0004) ** **
(0.0008)
0.459**
(0.051)
0.499**
(0.040)
0.587**
(0.044)
ln(beef cow price)
0.188**
(0.189)
0.0569**
(0.126)
0.417**
(0.085) **
( )
( ) **
( )
ln(ratio of plot to county LCC) 1
-0.509**
(0.094)
-0.511**
(0.121)
-0.656**
(0.102)
-0.529**
(0.071)
-0.612**
(0.061)
-0.584**
(0.052)
ln(ratio of county to region LCC) 1
0.222**
(0.083)
-0.556**
(0.188)
-0.485**
(0.187)
Midwest region dummy for CRP
( )
( )
( )
South region dummy for CRP
( )
West region dummy for CRP
1 Higher land capability class (LCC) values indicate worse quality land for agriculture.
*Significant at 10% level. ** Significant at 5% level.

14. Elasticities reported with standard errors in parentheses.
Table 3.5: Estimated Elasticities Evaluated at Sample Means from the Multinomial Logit Model of Land-Use Transitions: Starting State is Forest
Dependent variable is the probability of the specified transition from the starting state.
Elasticities reported with standard errors in parentheses.
Variable
Transition
Forest-Range
Forest-CRP
ln(forest profits)
0.0153
(0.022)
(0.0334)
(0.028)
ln(crop profits) **
(0.0002) **
(0.0001) **
ln (urban profits) **
(0.0004) ** **
(0.0008)
ln(beef cow price)
1.072**
(0.215)
1.632**
(0.264)
1.020**
(0.183) **
( )
( ) **
( )
ln(ratio of plot to county LCC) 1
-0.460**
(0.084)
-0.233**
(0.111)
-0.389**
(0.106)
-0.307
(0.499)
-1.369**
(0.392)
-1.448
(1.203)
ln(ratio of county to region LCC) 1
0.222**
(0.083)
-0.485**
(0.187)
-0.556**
(0.188)
Midwest region dummy for CRP
( )
( )
( )
1.025
(1.114)
23.194**
(1.107)
20.317
(.)
South region dummy for CRP
( )
1.288
(1.044)
22.994**
(1.104)
22.19**
(1.257)
West region dummy for CRP
-0.425
(1.236)
20.348
22.504**
(1.442)
1 Higher land capability class (LCC) values indicate worse quality land for agriculture.
*Significant at 10% level. ** Significant at 5% level.

15. Derivation of the Carbon Sequestration Supply Function
·      Baseline Land Use
·      Simulation of Effects of Carbon Sequestration Policy
 Example: Subsidies for Converting Cropland
and Pasture to Forest
 Incentives Modify Transition Probabilities
and Land-Use Patterns
·      Partial Equilibrium Model of Agricultural
Commodity and Timber Markets Used to Model Endogenous Price Effects
 Output Price Elasticities by Region for Major
Commodities

16. Derivation of the Carbon Sequestration Supply Function
·      Baseline and Simulated Land-Use Changes Mapped into Changes in Carbon Storage
 Dynamic Carbon Budget Model for the U.S.
Agricultural and Forest Lands
 Three Land-Use Categories (Forest,
Cropland, Pasture)
 Soil Carbon Dynamics for all Transitions
Forest Carbon Dynamics and Post-Harvest
Product Pools