Abstract
A spatial-temporal autocorrelation consistent covariance matrix is suggested for estimating the standard errors of a first-order Markov process model depicting aggregate land use dynamics. Particular attention is given to covariance estimation robust to temporal and spatial dependence. An empirical example compares the adjusted covariance estimators by examining cropland dynamics, revenue, and the corresponding own-price area supply elasticities with a Monte Carlo analysis. The relative precision of own-price elasticities increased in most cases, suggesting gains in efficiency when the covariance estimator of transition probabilities is adjusted for temporal and spatial dependence and cross-equation correlation. In this example, adjusting for temporal-spatial dependence moderates the absolute magnitude of elasticity point estimates. The approaches suggested in this letter will be of interest to researchers modeling land use transitions with aggregate data.
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Notes
The model estimates 3 by 95 = 285 sets of transition probabilities. These results are available on request.
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Acknowledgments
This research was supported by the United States Department of Agriculture National Institute of Food and Agriculture Grant # 2014-51130-22493. We thank two anonymous reviewers for their helpful comments and suggestions. We are grateful to Dr. Andrew Griffith and Tammy McKinley for assistance with beef cattle prices. Remaining errors are those of the authors.
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Lambert, D.M., Boyer, C.N. & He, L. Spatial-temporal heteroskedastic robust covariance estimation for Markov transition probabilities: an application examining land use change. Lett Spat Resour Sci 9, 353–362 (2016). https://doi.org/10.1007/s12076-015-0164-0
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DOI: https://doi.org/10.1007/s12076-015-0164-0