Abstract
The recent increase in farmland prices leads many to conjecture that a price bubble exists. A dataset of Iowa farmland prices for three grades of quality over the last 60 years is examined to address the question whether the conditions for a rational expectations bubble are evident. An abnormal component in the change in farmland prices is found during the most recent sub-period of the sample. A novel valuation model that measures the speculative component of farmland value as a function of cash rents shows no speculative component is present. An additional test of the time series characteristics of the data provides no evidence of negative duration dependence. However, analysis of transition probabilities shows asymmetry exists most notably in the low quality farmland data series. Finally, time irreversibility is shown to be present at different lags for only the lowest farmland quality grade. Overall, the results imply that the low quality grade farmland is the most likely candidate to exhibit the conditions necessary to support a rational expectations bubble. In general, however, the data offer weak support of a bubble in farmland prices.
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Notes
(Camerer 1989) provides a thorough review of asset bubbles and provides a more explicit definition of the rational speculative bubble model.
While it is theoretically possible to develop the appropriate hedging arguments to cast the pricing model presented here in the context of risk-neutral pricing, the approach used here opts for a simpler pricing model that does not depend on such assumptions.
Obtained from Ken French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
Details for the models for all three farmland quality data series are available from the authors.
Describing the time reversibility results, the order refers to i + j for γ i,j , and the degree refers to the maximum lag, which is 20.
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Acknowledgments
The authors wish to thank C.F. Sirmans (editor) and the reviewer for their helpful comments, as well as seminar participants at the University of Northern Iowa.
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Appendix
Appendix
Since only annual average cash rent is reported, an entropy-based model, based on (Golan 2006), is used to determine likely cash rents for low, medium, and high quality farmland using the most likely distribution of farmland by quality. Most of Iowa farmland is medium to high quality and, as a result, the simple average of farmland values is not the same as the reported average value. Therefore, the following optimization model is specified to recover the most likely proportion of farmland of each quality grade that would constitute the reported average. More clearly, the following framework is solved for each t:
s.t.
Where i is an index of farmland quality, and s it is the time t proportion or share of total Iowa farmland that is categorized by quality i. E(s) is the entropy of the distribution of the unobserved proportions. The first constraint is a moment matching equation wherein the weighted average farmland value is forced to equal the reported average, P t . The second constraint ensures that the proportions sum to one, while the third set of constraints ensures the proportions are non-negative. If the reported average appearing in the right-hand side of the first constraint is the simple average, the entropy would be maximized with a uniform distribution of proportions equal to one-third each.
Once the proportions are uncovered, they are applied to the reported average cash rent per acre. However, it is typically the case that cash rent for high (medium) quality farmland is about 20 % higher than cash rent for medium (low) quality farmland. Applying this simple rule allows for the development of cash rent data for each farmland quality that is consistent with the distribution of farmland prices by quality. One drawback of this construction is the fact that μ, the rate of growth in cash rents, will not vary by farmland quality even though it likely does in reality. However, the obvious advantage is that reported farmland values by quality can be fully utilized to construct excess abnormal returns.
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Olsen, B.C., Stokes, J.R. Is Farm Real Estate The Next Bubble?. J Real Estate Finan Econ 50, 355–376 (2015). https://doi.org/10.1007/s11146-014-9469-9
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DOI: https://doi.org/10.1007/s11146-014-9469-9