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

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

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

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:

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

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 1982-87 1987-92 1992-97 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) 2157.92 (2134.25) 2526.11 (3279.51) 2341.87 (2567.85) Beef cow prices Net beef cow price per head Pasture and range profits 403.07 (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.

      Table 2.1  Changes in Major Non-Federal Land Uses between 1982 and 1987 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 1987. Read the table horizontally to see how land that was under a particular land use in 1982 (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).

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 1992. Read the table horizontally to see how land that was under a particular land use in 1987 (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).

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 1997. Read the table horizontally to see how land that was under a particular land use in 1992 (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).

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 1982-87 1987-92 1992-97 ln(forest profits) -0.0001 (0.0002) 0.0002 -0.00003 (0.0004) 1.248** (0.148) 0.990** (0.109) 1.096** (0.0787) ln(crop profits) -0.0021** -0.0007** -0.0016** (0.0001) -0.124** (0.040) -0.0761** (0.023) ln (urban profits) -0.0029** -0.0034** -0.0072** (0.0008) -0.000001 (0.000) -0.0015** (0.0003) -0.0004** (0.00047) ln(beef cow price) -0.0002** (0.00006) -0.00002 (0.00002) -0.0001** (0.00004) 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 -0.0022** 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 (0.00007) (0.0005) -0.043** (0.010) -0.0055** (0.0055) South region dummy for CRP (0.0006) -0.037** (0.009) -0.0054** (0.0018) West region dummy for CRP 0.00004 -0.00005 (0.00003) -0.041** -0.0077** (0.0023) 1 Higher land capability class (LCC) values indicate worse quality land for agriculture. *Significant at 10% level. ** Significant at 5% level.

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 1982-87 1987-92 1992-97 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) -0.0031 (0.002) -0.031** (0.008) -0.022** (0.004) -0.012** (0.006) -0.015** (0.0049) -3.64e-06 (0.00001) 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) -0.0021 (0.0013) n/a South region dummy for CRP -0.026 -0.047* 0.00002 (0.0014) West region dummy for CRP -0.081** (0.034) -0.0016 1 Higher land capability class (LCC) values indicate worse quality land for agriculture. *Significant at 10% level. ** Significant at 5% level.

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 1982-87 1987-92 1992-97 ln(forest profits) -0.00015 (0.0002) 0.00021 -0.00003 (0.0004) 0.0153 (0.022) -0.0267 (0.0334) -0.0021 (0.028) ln(crop profits) -0.0021** -0.0007** -0.0016** 0.880** (0.078) 0.611** (0.122) 0.821** (0.087) ln (urban profits) -0.0029** -0.0034** -0.0072** (0.0008) -0.0028** -0.0071** ln(beef cow price) -0.0002** (0.00006) -0.00002 (0.00002) -0.0001** (0.00004) 0.00002 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 -0.0022** 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 -0.00012 (0.00014) (0.00007) (0.0005) -0.00007 (0.00005) South region dummy for CRP (0.00013) (0.0006) -0.00008 West region dummy for CRP 0.00004 1 Higher land capability class (LCC) values indicate worse quality land for agriculture. *Significant at 10% level. ** Significant at 5% level.

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 1982-87 1987-92 1992-97 ln(forest profits) 0.0153 (0.022) -0.0267 (0.0334) -0.0021 (0.028) ln(crop profits) -0.0021** (0.0002) -0.0006** (0.0001) -0.0015** ln (urban profits) -0.0028** (0.0004) -0.0034** -0.0071** (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) -0.0002** (0.00006) 0.00002 (0.00002) -0.0001** (0.00004) 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 -0.00012 (0.00014) (0.00007) -0.00007 (0.00005) South region dummy for CRP -0.00015 (0.00013) -0.00008 West region dummy for CRP 0.00004 1 Higher land capability class (LCC) values indicate worse quality land for agriculture. *Significant at 10% level. ** Significant at 5% level.

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 1982-87 1987-92 1992-97 ln(forest profits) 0.0153 (0.022) -0.0267 (0.0334) -0.0021 (0.028) ln(crop profits) -0.0021** (0.0002) -0.0006** (0.0001) -0.0015** ln (urban profits) -0.0028** (0.0004) -0.0034** -0.0071** (0.0008) ln(beef cow price) 1.072** (0.215) 1.632** (0.264) 1.020** (0.183) -0.0002** (0.00006) 0.00002 (0.00002) -0.0001** (0.00004) 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 -0.00012 (0.00014) (0.00007) -0.00007 (0.00005) 1.025 (1.114) 23.194** (1.107) 20.317 (.) South region dummy for CRP -0.00015 (0.00013) -0.00008 1.288 (1.044) 22.994** (1.104) 22.19** (1.257) West region dummy for CRP 0.00004 -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.

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

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