Nested logit architecture

The strategy for nesting competing land uses and nesting nests of competing land uses has involved some expert judgment, as does the choice of logit exponents that govern substitution within each of the level of the nesting structure. Note that calibration and reproduction of historical results does not depend on the nesting strategy or the logit exponents used. Instead, these assumptions affect future period results as conditions or policies change from history.

Nesting strategies

Before discussing our nesting approach, it is useful to consider the space of possible nesting strategies. One approach is that of a single nest: the assumption that the land regions are small enough that all competing options are equally substitutable. This assumption implies that it is just as easy to switch from forest to wheat as it is to switch from corn to wheat. However, this conversion would not happen unless wheat was more profitable than forest or corn. With a high enough logit exponent for this single nest, the land sharing approaches an optimal “winner-take-all” result in that all land within a region will be dedicated to the most profitable product in that region. A single nest with a high exponent represents the extreme end of unconstrained optimization in which there is no transition cost or other hurdle for switching from one land type to another.

The other extreme is that of no substitution. This would be accomplished with near zero or zero logit exponents, whether in a single nest or multiple nests. This implies that either it is physically impossible or the transition costs are too high to allow switching from one land type to another. Currently, in GCAM, we use zero logit exponents in a very limited number of situations, where we do not want any substitution (e.g., we do not allow cropland to expand into desert or tundra). However, in most situations, we employ positive logit exponents and allow economics to dictate the land allocation within a region.

As a point of reference, we have compared the logit approach used in AgLU with the approach used in FASOM^[1], an optimization model of agriculture and forest in the United States. FASOM uses a mix of substitution strategies very different from our approach. FASOM divides the U.S. into a number of small regions. Within each of their regions, the model does not allow the mix of crops grown to change. However, they do allow total cropland to expand or contract in order to meet changing demand. They have also imposed a rule mapping potential biomass crops to marginal cropland outside their regular cropland category. This contrasts strongly with our approach where we allow easier substitution among crops within cropland but more difficult expansion or contraction of total cropland. The reason for the difference lies in the linear optimization approach. FASOM sets these cropland mix constraints as a way of calibrating future model behavior to history. Otherwise, in the first future period, the model would optimize and allocate land in a pattern very different from history. Our calibration approach also allows us to reflect history, but our logit sharing allows the future model periods to change the mix of crops as conditions change. For a reference case, the two approaches may give similar results. For a scenario with rapid change, the approaches may provide very different results.

Land nesting approach in GCAM

Our current approach is to use a nesting strategy that allows the logit exponents to reflect differences in substitutability across land categories. Figure 1 shows the nesting diagram of land with an AEZ subregion. At the top is all land, which is divided into two main types of nodes: agro-forestry land and the remaining categories of land that are not suitable for agriculture. This second category could be divided further if useful. The next node layer contains two further nodes: all agro-forestry, non-pasture land and all pasture land. The pasture land node contains two competing uses (land leaves in the code): managed pasture (that which feeds marketed livestock) and unmanaged pasture.

Figure 1: Competition for land in GCAM

The agro-forestry (non-pasture) node contains three competing nodes: shrub and grass lands, forest lands, and croplands. Shrublands and grasslands are separated from the rest as they are both classified as unmanaged land categories and we want to control their substitutability between each other separately. Finally, the forestland node competes with the total cropland node. Within forestland, there are managed and unmanaged forest leaves, and we have added a woody biomass option there in some regions and scenarios. Under cropland are all food and other agriculture products (e.g., corn, wheat, sugars, etc.), including biomass crops, along with an unmanaged land category called other arable land. Note that several crops are included explicitly in the CropLand node, and the grouping of “AllOtherCrops” is simply a convenience for this figure.

With the specification above, we can make substitution across categories more or less difficult by choosing lower or higher logit parameters. We can also effectively combine nests by making the logit exponents the same. For example, if we assign the same logit exponent for each level, this is equivalent to putting all uses under one nest. One implication of having equal exponents is that it would not matter in which node we placed new crop options like biomass.

References

[1] Beach, R.H., & McCarl, B.A. (Jan 2010). U.S. agricultural and forestry impacts of the Energy Independence and Security Act: FASOM results and model description. Final Report. Research Triangle Park, NC: RTI International. Prepared for the U.S. Environmental Protection Agency, Office of Transportation and Air Quality. RTI Project Number 0210826.003.