Resolved: That the United States should substantially change its federal agricultural policy.

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Source: American Journal of Agricultural Economics, Nov 1996 v78 n4
p1082(10).

Title: The effect of agricultural policies on land use and environmental
quality.
Author: Andrew J. Plantinga

Full Text COPYRIGHT 1996 American Agricultural Economics Association

Proponents of U.S. agricultural policy reform have emphasized the net surplus gains and taxpayer savings from removing or modifying provisions of the farm program (e.g., Council of Economic Advisors, Rausser). A recent analysis by Chang et al. estimates the net welfare gain from eliminating the U.S. farm program to be as high as $11 billion dollars.

In this paper, I examine potential gains in environmental quality resulting from program modifications, specifically, reductions in price support levels. Higher prices provide incentives for farmers to keep lower quality, or less productive, land in production. These lands tend to be susceptible to soil erosion, which can have substantial negative impacts on water and air quality. At lower prices, many low-quality lands would be put into forest, which reduces soil erosion and enhances wildlife habitat. Environmental quality improvements are a primary objective of the Conservation Reserve Program, which compensates farmers to plant marginal agricultural land in trees or other permanent vegetation. In this study I estimate the environmental benefits that may be achieved directly by lowering price supports.

A methodology is presented to estimate the shares of land devoted to different uses. The approach differs from those taken in earlier studies in that explicit distributions of land quality, derived from soil survey data, are incorporated into the empirical model. The land quality data allow a more general model of land use to be estimated than in previous analyses. Earlier studies place restrictions on the probability that land of a particular quality is put into a given use. Specifically, the probabilities are limited to the values zero or one or are assumed to be equal for each land use. For an application to Wisconsin these restrictions are rejected. The empirical results also reveal that price support reductions may provide environmental benefits comparable in scale to net gains to consumers and taxpayers. Thus, agricultural policy reforms may yield a significant environmental dividend, particularly in the case of policies which encourage the expansion of agricultural acreage. Moreover, policy reforms provide a more efficient method of achieving the environmental goals of land retirement programs.

The next section presents a taxonomy of earlier empirical analyses of land use. Then, an empirical model is specified which aggregates the allocation decisions of individual land managers and takes into account restrictions imposed by the available data. The following section presents an application of the model to a region of Wisconsin and a test of restrictions used in previous land use studies. Next, the effects of changes in support price levels on land use and environmental quality in the region are estimated and compared to related welfare gains. A final section presents conclusions.

Previous Empirical Studies of Land Use

Previous empirical analyses of land use measure how the extensive margin between two uses is influenced by land rents or variables influencing land rents. The models in these studies can be viewed in terms of restrictions on the following model:

(1) [Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the proportion of the land in county i in land use 1 in time t, [[Theta].sub.ij] is the proportion of land in quality class j in county i, J is the number of land quality classes, and [[Pi].sup.1]([X.sub.ijt]) is the probability that land of quality j in county i is put into land use 1 in time t. The probabilities are a function of the rents from different uses, denoted by the vector [X.sub.ijt]. The proportion of land in use 2 is given by [Mathematical Expression Omitted].

The model in Stavins and Jaffe follows from the restriction on equation (1):

(2) [Mathematical Expression Omitted]

where [j.sup.*]([X.sub.it]) defines the extensive margin between forestry and agriculture.(1) Forests are assumed to be found on the lowest-quality lands (low values of j) so the proportion of forested area is

(3) [Mathematical Expression Omitted]

where F is a particular continuous distribution function (e.g., log-normal). Lichtenberg and Parks and Murray use the logit specification [Mathematical Expression Omitted] and include measures of average land quality as regressors.(2) This approach is equivalent to equation (3), with the land quality distribution F specified as logistic and [j.sup.*]([X.sub.it]) = B[prime][X.sub.it]. Finally, a number of studies use the linear specification [Mathematical Expression Omitted] to approximate the relationship in equation (3) (White and Fleming; Alig; Plantinga, Buongiorno, and Alig). The linear model follows from the restriction [[Pi].sup.1]([X.sub.it]) = B[prime][X.sub.it] on equation (1), which is tantamount to restricting land in all quality classes to be put into use 1 with the same probability.

To summarize, the restrictions used in previous studies involve either binary or equal values of the probabilities [[Pi].sup.1]([X.sub.ijt]). The model developed in the next section is more general. It retains the form of equation (1) by restricting the probabilities only to the unit interval. This allows for land of a particular quality to be devoted to all uses, rather than being restricted to a single use as in equation (2). In addition, a particular use may take place on land of all qualities. Thus, in general, there is no single extensive margin between any two uses.

A Framework for Estimating Land Use Shares

In this section, a model of land use is specified which incorporates the optimization problems of individual land managers but which may be tested with commonly available aggregate data.(3) The model is developed in the context of two broadly defined land uses, forestry and agriculture, though the approach easily can be modified to include additional or more narrowly defined uses. We begin with the land manager's problem of allocating a uniform parcel of land to the two uses. For simplicity, only one use can be chosen each period, forests are even-aged, and land managers are assumed to be risk neutral.(4) Thus, a land manager maximizes the present discounted value of expected net benefits, as follows:

(4) [Mathematical Expression Omitted]

subject to [u.sub.t] = {0, 1}; [v.sub.t] = {0, 1}; [a.sub.t + 1] = [a.sub.t][u.sub.t](1 - [v.sub.t]) + [u.sub.t]; [u.sub.t] = 0 is feasible only if [v.sub.t] = 1; [a.sub.t] [greater than or equal to] 0, [Mathematical Expression Omitted]; [a.sub.0] given; where [v.sub.t] indicates the decision to harvest ([v.sub.t] = 1) or not harvest ([v.sub.t] = 0) an existing stand at the start of period t, [u.sub.t] indicates the decision to put or keep the land in forest ([u.sub.t] = 1) or agriculture ([u.sub.t] = 0) for period t, [a.sub.t] is the age of the forest stand at the start of period t, [Mathematical Expression Omitted] ([a.sub.t]) is the expected net benefit from harvesting a forest stand of age [a.sub.t] in period t, [Mathematical Expression Omitted] is the expected net benefit from agriculture in period t, [Delta] is the constant discount factor, and [V.sub.T + 1]([a.sub.T + 1]) is the expected salvage value. Expected net benefits from the land include private nonmarket amenities such as recreation in addition to marketable commodities. When forestry is chosen, the optimal harvest age maximizes the discounted sum of market and nonmarket benefits (Hartman). The expected net benefits are also assumed to reflect costs of converting from one use to the other. The condition on [u.sub.t] = 0 requires the land to be bare before it is put into agriculture.

The dynamic programming solution to the problem is given by

(5) [Mathematical Expression Omitted]

for t = 0, 1, ..., T and subject to the above constraints. Expression [V.sub.t]([a.sub.t]) is the expected value of the optimally managed parcel. Since [V.sub.t]([a.sub.t]) is linear in the control [u.sub.t], land managers choose either forestry or agriculture each period. The period t allocation decision depends on [Mathematical Expression Omitted] and [Mathematical Expression Omitted], defined as follows:

(6) [Mathematical Expression Omitted]

(7) [Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the optimal harvesting decision. Expressions [Mathematical Expression Omitted] and [Mathematical Expression Omitted] equal the expected values of optimally managed parcels conditional on the choice of forestry and agriculture in period t, respectively. The land manager chooses forestry in period t if [Mathematical Expression Omitted] and agriculture if [Mathematical Expression Omitted]. Expansion of [V.sub.t + 1]([a.sub.t + 1]) implies that [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are linear functions of discounted expected net benefits from forestry and agriculture.

Data on the net benefits derived by individual land managers are typically unavailable and too expensive to obtain on a scale large enough to draw general policy conclusions. Instead, county-level data representing average net benefits across land managers and parcels of varying quality are available, though some benefits may be unobservable. Recognizing these data limitations, [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are specified as follows:

(8) [Mathematical Expression Omitted]

(9) [Mathematical Expression Omitted].

Expressions [Mathematical Expression Omitted] and [Mathematical Expression Omitted] denote vectors of observable average net benefits in county i which influence the allocation decision in time t. These benefits are adjusted by unobservable coefficients, in vector form [Mathematical Expression Omitted] and [Mathematical Expression Omitted], to account for discounting and the effect of land quality, indexed by j. For instance, average net returns to forestry and agriculture are adjusted downward on land with relatively low yields. Factors specific to individual land managers are measured by the random variables [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. These terms account for unobservable benefits such as nonmarket amenities and deviations from observable average net benefits due to factors such as the location of individual parcels.

Since [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are random variables from the researcher's standpoint, only probabilistic statements can be made about the allocation choices of land managers. Following Judge et al., the probability that an owner in county i puts a parcel of quality j in forest in time t may be written [[Pi].sub.ijt] = F([B[prime].sub.jt][X.sub.it]) where [Mathematical Expression Omitted] and F is a symmetric distribution function. The average probability that a parcel of land in county i is forested in time t may then be written

(10) [Mathematical Expression Omitted]

where [[Theta].sub.ij] and J are defined above. The discrete land quality density given by [[Theta].sub.ij], j = 1, ..., J, is observable and assumed to be constant over time.

The unobservable coefficients [B.sub.jt] may be estimated with plot-level land use observations, together with the economic and land quality information discussed above. For each county in time t, the number of forested plots [y.sub.it] from a sample of [n.sub.it] plots may be observed. Each plot sample is assumed to be a random draw from the Bernoulli distribution [Mathematical Expression Omitted], where x = 1 if the plot is forested and x = 0 if the plot is in agriculture. It follows that [y.sub.it] is distributed as a binomial random variable with parameters [n.sub.it] and [Mathematical Expression Omitted]. Maximum likelihood estimates of the [[Beta].sub.jt] may be obtained using cross-sectional data on I counties at T points in time. The log-likelihood function is

(11) [Mathematical Expression Omitted]

where

[c.sub.it] = [n.sub.it]!/[y.sub.it]!([n.sub.it] - [y.sub.it])!.

Function F is parameterized as a logistic function, yielding(5)

(12) [Mathematical Expression Omitted].

Coefficient estimates are obtained by substituting equation (12) into equation (11), and by applying a nonlinear estimation algorithm to the resulting log-likelihood function.

The model presented above is flexible in that the probabilities that land quality classes are forested (the [[Pi].sub.ijt]) may take any value on the unit interval. This allows land use decisions to be influenced by unobservable factors such as private nonmarket benefits, skills, and knowledge of individual land managers, and the location of individual parcels. The model also allows observable variables such as land rents to have different effects on land of different quality since separate [[Beta].sub.jt] are estimated. Finally, the model accounts explicitly for heterogeneous land quality within and across counties.

Application of the Model to Southwestern Wisconsin

The model developed in the previous section is applied to a fourteen-county region in southwestern Wisconsin.(6) Dairy farming is the primary agricultural enterprise in the region and most of the agricultural land, predominantly cropland and pasture, is used to provide feed for dairy herds. The forests are dominated by hardwood forest types, particularly oak-hickory and maple-birch, and the local forest products industry consists of sawmills which manufacture hardwood lumber and related products. Most of the forest land is held by nonindustrial private owners. The most important factor influencing land use decisions in the region is hypothesized to be the net returns to forestry and dairy farming. Factors such as urbanization pressures and federal and state land use policies (e.g., forestry incentive programs, agricultural land retirement programs) are found to have a limited influence during the period of analysis.

Net returns to forestry and dairy farming depend on the prices received by farmers for timber and milk, physical yields of these outputs, and inputs costs. Time-series data are available on timber prices by species and average milk prices across grades. Consistent yield data are unavailable, particularly for timber and forage yields on lower-quality land. It is hypothesized that the yield of timber relative to milk declines as land quality improves. However, on the poorest-quality land the magnitude of the relative yield is uncertain since timber and milk yields are very low or even zero. Input costs are likely to vary greatly across lands of different quality. On lower-quality land used for pasture and forestry, input costs are negligible. Seeding and other improvements are typically uneconomical on low-quality pasture and trees tend to be established through natural regeneration (Spencer et al.). On higher-quality land, there are considerable costs associated with growing feed crops (fertilizer, energy, etc.). However, since crop returns tend to be much larger than forestry returns on high-quality land, these costs are not likely to have a significant effect on decisions to put land in forest.(7) Finally, the conversion of forest to agricultural uses is assumed to be uneconomical since forests in the region tend to be found on lower-quality land (Hexem and Krupa). Thus, land use changes in the region involve only shifts from agricultural land to forest.(8)

The foregoing discussion suggests a simple specification of the net returns to forestry and agriculture, in particular, [Mathematical Expression Omitted] and [Mathematical Expression Omitted], where [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are timber and milk prices in county i in time t and [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are yields of timber and milk from land of quality j in time t. Expectations of future prices and yields are assumed to be static.(9) In particular, land managers expect future prices to equal an average of prices in the preceding three years, implying that a sustained change in price must be observed before the change is expected to continue in the future. With static expectations, an infinite time horizon, and bare land,(10) the time t allocation decision is based on a comparison of discounted infinite streams of returns to forestry and agriculture (appendix A). Specifically, the benefit functions in equations (8) and (9) become

(13) [Mathematical Expression Omitted]

(14) [Mathematical Expression Omitted]

where [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are averages over the preceding three years. Expressions [Mathematical Expression Omitted] and [Mathematical Expression Omitted] measure unobservable yields and discounting expressions.

Observations of [y.sub.it] and [n.sub.it] are available for fourteen counties at two points in time, 1968 and 1983, providing twenty-eight county-level observations (see appendix B for details on the data). Since decisions to convert agricultural land to forest are observable only after trees have become established, the price variables [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are lagged four years to allow for forest establishment. Land quality densities are constructed from county-level soil surveys. Quantity [[Theta].sub.ij] is defined as the proportion of land in county i in quality class j where j = l, 2, 3, 4 indicates the grouped LCCs I-II, III-IV, V-VI, and VII-VIII, respectively.(11)

For the application to southwestern Wisconsin, the time-series observations are pooled and a more parsimonious specification of equation (12) is used. Namely, each [[Pi].sub.ij] is specified as a [TABULAR DATA FOR TABLE 1 OMITTED] function of an intercept term, [[Beta].sub.0], plus the ratio of returns to forestry and agriculture, yielding

(15) [Mathematical Expression Omitted]

where [Mathematical Expression Omitted]. Maximum likelihood estimates of the [[Beta].sub.j] are obtained by substituting equation (15) into equation (11) and applying the nonlinear estimation algorithm in White. The estimates of [[Beta].sub.1] through [[Beta].sub.4] are expected to be positive and, as discussed above, increasing in j. However, the relative magnitude of [[Beta].sub.4] is uncertain since yields from class VII and VIII land may be very low or even zero.

The estimation results indicate a good model fit, conform to prior expectations, and have intuitively appealing interpretations (table 1). The asymptotic t-ratios indicate that three of the five coefficient estimates are significantly different from zero at the 99% confidence level. In addition, the coefficient estimates have the expected signs (the estimate of [[Beta].sub.1] is negative, but not significantly different from zero) and the estimates of [[Beta].sub.1] through [[Beta].sub.3] are increasing in j. Thus, as expected, the yield of timber relative to milk is found to be higher on lower-quality land. The relative yield is found to be lower on the lowest-quality land. The [R.sup.2] measure (Chow) indicates that the explanatory variables provide a considerably better prediction of the forest land shares ([y.sub.it]/[n.sub.it]) than the mean of ([y.sub.it]/[n.sub.it]). Likelihood ratio tests (not reported here) reject all equality restrictions on [[Beta].sub.1] through [[Beta].sub.4] except [[Beta].sub.1] = [[Beta].sub.2].

The estimates of the [Beta]'s are used to estimate the average probability (across counties) that land quality classes are forested and the elasticities of the probabilities with respect to the price ratio (table 1). The results indicate that high-quality land has a low probability of being forested ([Mathematical Expression Omitted] and [Mathematical Expression Omitted]), reflecting the relatively high return from agriculture on productive land. On lower-quality land where forestry is a competitive use, the probability is higher ([Mathematical Expression Omitted]). For very poor quality land, which in some cases may not be able to support vegetation, the probability is somewhat lower ([Mathematical Expression Omitted]). Ninety-five percent confidence intervals for the probabilities are estimated using the Delta Method [ILLUSTRATION FOR FIGURE 1 OMITTED].(12) For the most part, the probabilities are different from each other and different from either zero or one. Finally, the elasticity estimates indicate an approximately unit-elastic effect of the price ratio on the probability that land in the region is forested.

The estimates of the probabilities and associated confidence intervals (table 1 and [ILLUSTRATION FOR FIGURE 1 OMITTED]) can be used to test the restrictions used in previous empirical analyses of land use. As indicated above, restrictions used in earlier studies involve either equal or binary probabilities. However, the probabilities estimated above are mostly different from each other and, in three out of four cases, lie between 0 and 1, indicating that the restrictions used in previous studies are rejected at the 95% confidence level. An important qualification is that the restrictions are shown to be invalid only with respect to the application considered here. It is another matter whether or not the restrictions are valid for the particular applications considered in other studies.

Environmental Effects of Milk Price Supports

Changes in the support price for milk affect the relative returns to forestry and dairy farming and thus, according to the results of the previous section, the amount of land allocated to these uses. The increase in forest area in southwestern Wisconsin, by land quality classes, is estimated for 5%, 10%, and 15% increases in the timber-to-milk price ratio. These changes correspond to declines in the average mid 1980s milk price of $0.62, $1.18, and $1.70, respectively. No further price declines are considered since Whipple, Powe, and Gray estimate that the competitive market price is $1.74 below the support price. The long-term gains in forest area, accounting for expectations formation and forest establishment (see above), are 85, 167, and 245 thousand acres, respectively, corresponding to approximately 5%, 9%, and 14% increases in forest area (table 2). Most of the increase takes place on lower-quality lands, where forestry is a relatively competitive use. Following historical trends, it is assumed that the former agricultural uses of the land are predominantly pasture and wooded pasture (Spencer et al.).

Declines in the support price primarily affect land use decisions on low-quality lands which tend to be susceptible to soil erosion when used for grazing or crop production. Soil erosion increases levels of water-borne sediment, pesticides, and fertilizers, which may impair the operation of water conveyance and storage systems, lower water quality, and degrade recreational resources. Afforestation of marginal agricultural land tends to reduce rates of soil erosion and therefore improves environmental quality.(13) Numerous estimates have been made of the benefits of reduced soil erosion (e.g., Holmes; Palmquist and Danielson; Van Kooten, Weisensel, and de Jong). For the purpose of estimating the environmental quality improvements associated with lower support prices, off-site benefits (e.g., improved water quality) are the primary concern. In principle, land managers can capture the on-site benefits. For instance, improved land productivity is reflected in land values (Palmquist and Danielson), and land managers can lease the land for recreation (Ribaudo et al.). In this case, the value of on-site benefits will be accounted for in the estimated land use elasticities.

Water quality improvements associated with reduced soil erosion are estimated for each of the milk price declines (table 2). The damage from soil erosion in the Lake States region is estimated to range from $2 to $6 per ton [TABULAR DATA FOR TABLE 2 OMITTED] (Ribaudo). Annual soil erosion rates are taken from the 1982 National Resources Inventory (USDA 1987).(14) The rates for the grouped Land Capability Classes I-II, III-IV, V-VI, and VII-VIII are 0.0, 0.7, 1.4, and 3.6 tons per acre per year, respectively. A thirty-year time horizon is considered to allow for long-run adjustments in the forestry and dairy sectors.(15) The erosion rates are long-term averages and, thus, provide a reasonable estimate of the annual soil loss over a thirty-year period. A 10% increase in the timber-to-milk price ratio (a $1.18 decline in the average milk price) is estimated to yield between $8.1 and $24.3 million in water quality benefits, in present value terms (5% discount rate). Five percent and 15% increases yield benefits ranging from 4.1 to 12.3 million dollars and from 12.0 to 35.9 million dollars, respectively.

To provide a basis for comparison, some rough estimates are made of the net gains in consumer surplus and the taxpayers' savings resulting from milk price support declines (table 2). Estimates have been made over the years of the welfare effects of lowering milk price supports (e.g., Buxton and Hammond; Heien; Whipple, Powe, and Gray; Chang et al.). For this study, estimates are derived from Council of Economic Advisors, which summarizes the findings of other studies and conforms to the period of analysis. Consumer and taxpayer losses range from $8.00 to $14.00 per thousand pounds of milk produced.(16) Milk supply elasticities are used to estimate the decline in milk production in southwestern Wisconsin resulting from support price declines. Estimates of short- and long-run elasticities specifically for the Lake States region are taken from Chavas and Kraus. As above, a thirty-year time horizon and a 5% discount rate are used. A 10% increase in the price ratio is estimated to decrease the burden on consumers and taxpayers by between $8.2 and $13.3 million, in present value terms. The burden is lessened by 4.3 to 7.0 and 11.8 to 19.1 million dollars for 5% and 15% increases, respectively.

Conclusions

This study demonstrates that lowering support prices for milk will reduce incentives for farmers to keep marginal agricultural land in production. At lower prices, the land will be put into forest, thereby reducing soil erosion and enhancing environmental quality. For the application considered, the gains in environmental quality are at least as large as the consumer and taxpayer gains. If the high estimate of the environmental benefits applies, the value of environmental quality improvements may be two or three times as large as the welfare benefits. It should be emphasized that not all of the potential effects of afforestation are included in these estimates. In addition to reducing soil erosion, forests provide a number of public goods such as wildlife habitat, scenery, and carbon sequestration. On the other hand, use of the additional wood fiber in forest products manufacturing may reduce environmental quality, implying lower benefit estimates than those presented in this study.

This study has two main policy implications. First, the finding that price support reductions may yield a significant environmental dividend indicates a central role for environmental quality considerations in motivating agricultural policy reforms. If the benefits estimated for Wisconsin are similar for other dairy regions, the elimination of price supports may yield over $0.5 billion in environmental quality gains. More broadly, afforestation of marginal agricultural land may be expected in many parts of the U.S. when agriculture no longer holds a competitive advantage (Clawson). The environmental benefits from policy reforms may be largest in the case of programs such as price supports which encourage the expansion of agricultural acreage. Benefits would likely be less for programs already modified to reduce these incentives (e.g., deficiency payment programs) (Council of Economic Advisors). A second policy implication is that the environmental goals of land-retirement programs like the CRP may be achieved more efficiently through policy reforms. Reductions in price supports will make forestry competitive on marginal agricultural land, eliminating the need to compensate farmers for converting the land to forest.

This study presents a general framework for estimating land use shares. The empirical model benefits from the use of explicit distributions of land quality, which permits a flexible model to be estimated. The model allows unobservable variables, such as private nonmarket benefits and particular skills and knowledge of individual land managers, to influence land use decisions. The estimation results support the more general specification used here. In most cases, the probability that land of a particular quality is forested or put into agriculture is found to lie between 0 and 1. Thus, the restrictions used in previous studies, which involve binary or equal probabilities, are rejected for the application considered. Future research will determine if the general specification is warranted for other regions and uses of the land.

This article is based on the author's dissertation work at the tee members, Peter Berck, Anthony Fisher, Keith Gilless, Michael Hanemann, William McKillop, and David Zilberman, for their suggestions and assistance. The author also wishes to thank Ralph Alig, Gordon Rausser, Marc Ribaudo, Robert Stavins, and anonymous AJAE referees for comments on earlier versions of this paper. Maine Agricultural Experiment Station Publication No. 2024.

1 Stavins and Jaffe also allow for a range of land quality above [j.sup.*]([X.sub.it]) in which land is kept in its current use (possibly forestry) due to conversion costs. For ease of exposition, these forest lands are not included in the following discussion.

2 Lichtenberg considers more than two land uses, which involves a simple extension of equations (1)-(3).

3 The objectives of land managers and landowners are assumed to be the same, so no attempt is made to distinguish between them.

4 Many empirical analyses of the risk preferences of farmers find some degree of risk aversion (e.g., Antle; Chavas and Holt; Saha, Shumway, and Talpaz). If land managers are risk averse, then some (homogeneous) parcels may be allocated to forest and agricultural uses, rather than to a single use. However, Brink and McCarl find that the best prediction of actual crop acreages in the Corn Belt is made under the assumption of risk neutrality. In addition, the empirical model specified below is flexible to allow for departures from allocations implied by risk neutrality.

5 An alternative functional form is the standard normal, which gives

[Mathematical Expression Omitted].

6 The region corresponds to the U.S. Forest Service's Southwest Survey Unit (Spencer et al.).

7 Costs of improving pasture of moderate quality may influence the decision to put land in forest; however, data are not available to measure these costs.

8 Spencer et al. indicate that the natural regeneration of forests on pasture land has been the dominant land use change in the region during the past several decades.

9 Just and Miranowski test a model of farmland price changes under alternative assumptions about expectations formation. The naive expectations model in which future values equal lagged values performs better than models with forward-looking expectations.

10 This condition is satisfied in the case of land-use shifts from agriculture to forestry (see above text).

11 The classes are grouped to conserve degrees of freedom and avoid estimation problems related to zero acreage in some LCCs. A natural grouping is implied by the description of the LCCs given in USDA (1973).

12 In general, if [Mathematical Expression Omitted] is a vector of estimated parameters and [Mathematical Expression Omitted] is a function of those parameters, then an estimate of the variance of [Mathematical Expression Omitted] is [Mathematical Expression Omitted] where [S.sub.i] is the derivative of S(B) with respect to [[Beta].sub.i] and [Mathematical Expression Omitted] is the estimated covariance matrix for [Mathematical Expression Omitted].

13 In the long term, afforestation is likely to increase the volume of wood fiber used by the forest products industry in the region, possibly resulting in adverse environmental impacts (e.g., declines in water quality from more paper production). Inclusion of these effects would decrease the benefit estimates reported here.

14 The average of the erosion rates for pasture and wooded pasture, net of the erosion for forest, is used.

15 The price changes take three years to be fully incorporated into expectations about future prices and benefits are delayed four years to allow for forest establishment. Milk supply responses depend on factors such as long-term adjustments in herd sizes.

16 Second-order effects of lowering the price support on per unit consumer and taxpayer losses are ignored. Consequently, the estimates overstate the consumer and taxpayer gains.

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Appendix A

Proof that time t allocation decision depends on the relative magnitudes of [Mathematical Expression Omitted] and [Mathematical Expression Omitted] equations (13) and (14)

Static expectations imply stationary expected net benefits or, formally, [Mathematical Expression Omitted] and [Mathematical Expression Omitted] for s = t + 1, ..., T. Define [Mathematical Expression Omitted] as the optimal rotation length from the standpoint of time t and let T [approaches] [infinity]. Then, assuming it is optimal to choose forestry in all periods and starting with bare land ([a.sub.t] = 0), the value of the optimal program equation (5) may be specified as

(A1) [Mathematical Expression Omitted].

When the land is put into agriculture for all periods, the analogous expression is

(A2) [Mathematical Expression Omitted].

In the special case of stationary expected net benefits, infinite time horizon, and bare land, the period t allocation decision is based on a comparison of [Mathematical Expression Omitted] and [Mathematical Expression Omitted], as stated in the following proposition.

PROPOSITION. It is optimal to allocate land to (a) agriculture in period t if [Mathematical Expression Omitted] and (b) forestry in period t if [Mathematical Expression Omitted].

Proof. Part (a). Suppose not. Then it is optimal to put the land into forestry up to some age [Mathematical Expression Omitted] before switching to agriculture. This implies

(A3) [Mathematical Expression Omitted]

where V(0) is the continuation value after the stand is harvested at age [Mathematical Expression Omitted]. But (A3) can be rearranged to yield

(A4) [Mathematical Expression Omitted]

which contradicts [Mathematical Expression Omitted] since by definition

(A5) [Mathematical Expression Omitted]

for all [Mathematical Expression Omitted]. Part (b) is the converse of part (a) and follows from a similar proof.

Appendix B

Data Sources

Plot-level data on land use decisions are from U.S. Forest Service inventories of Wisconsin. Observations for public and reserved forest land (2% of the total forest area) are excluded. Timber prices ($ per thousand board feet) are from the University of Wisconsin Extension Service's Forest Products Price Reviews. Prices for each county are a weighted average of stumpage prices for the dominant species (white oak, red oak, basswood, hard maple, soft maple, elm, aspen), with the weights given by county-level species composition. Milk prices ($ per cwt) are from Wisconsin Agricultural Reporting Service publications and represent a state-level average of the prices received by farmers for grade A and grade B milk. Prices reflect the influence of federal price support and marketing order programs. The land-quality densities are constructed from U.S. Soil Conservation Service county-level soil surveys. Soil surveys report the acreage of land in each of eight Land Capability Classes (LCCs). The capability rating (denoted I through VIII, where I indicates the most productive or highest-quality land) is an index based on twelve soil characteristics (USDA 1973).

Andrew J. Plantinga is assistant professor in the Department of Resource Economics and Policy at the University of Maine.

 
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