Why are estimates of agricultural supply response so variable?

Abstract

JEL Classification Codes: C1, C2, C4, C5Key words: Agricultural supply response, Bayesian estimation, MELO estimation Abstract: Estimates of the response of agricultural supply to movements in expected price display curiously large variation across crops, regions and time periods. We argue that this anomaly may be traced, at least in part, to the statistical properties of the commonly-used econometric estimator, which has infinite moments of all orders and may have a bimodal distribution. We propose an alternative minimum-expected-loss estimator, establish its improved sampling properties, and argue for its usefulness in the empirical analysis of agricultural supply response.Acknowledgements: We thank the Co-Editor and referees for constructive suggestions, but we alone should be blamed for remaining inadequacies. Parts of this work were completed at the University of Chicago, whose hospitality is gratefully acknowledged. Particular thanks go to Arnold Zellner, who provided exceptionally useful input. Participants at meetings of the Econometric Society and the American Agricultural Economics Association provided helpful comments, as did Ed Leamer, Doug McManus and Marc Nerlove on a long-ago draft. Asad Zaman brought the problem treated in this paper to our attention. We are grateful for support from the National Science Foundation, the Sloan Foundation, the International Food Policy Research Institute, and the University of Pennsylvania Research Foundation.See for example Braulke (1982), Gardner (1993), Just (1993, and Tomek and Myers 1 (1993).A related paper, of which we became aware after completing ours, is Bewley and Fiebig 2 (1990). As will become clear shortly, however, the two papers are very different. Ours, in particular, focuses entirely on the agricultural supply question and treats it in depth.

Maximum entropy and Bayesian approaches to the ratio problem

“…5 and thus does not possess finite moments. As Zellner (1978Zellner ( , 1985Zellner ( , 1986, Zellner and Park (1979), Zaman (1981), and Diebold and Lamb (1997) observe, ratios or reciprocals of unbounded random variables do not have finite moments. Marsaglia (1965) shows that, if two random variables are normally and independently distributed, their ratio can be expressed as a function of several bivariate normals or as a Nicholson's V function.…”

“…Doing so may not be appropriate because of the potentially serially-correlated disturbance and lagged dependent regressors. As OLS is virtually the only approach actually used, we follow Diebold and Lamb (1997) and use the OLS approach as the "straw man" base case.…”

“…The ratio problem arises when one estimates market power (Bresnahan, 1982), the dose-response relationship (Zellner and Rossi, 1984), the Keynesian savings rate in Haavelmo's model of long-run supply response (Bewley and Fiebig 1990), the willingness-to-pay in contingent valuation studies (Shen 1999), and the Nerlove model of agricultural supply response (Nerlove and Addison 1958;Nerlove 1979;Diebold and Lamb 1997).…”

The Impact of Lehmann’s Work in Applied Probability

“…As we note above, the impact of the Lehmann and Shaffer [20] article has been limited, perhaps due to its focus on these curious aspects of (inverted) distributional theory. A few applications have appeared for selected econometric problems-see, e.g., Diebold and Lamb [8] and ten Raa and Steel [29]-but these have generally been confined to calculations on inverse moments and not to the more general features of the inverted distribution. An interesting, hierarchical modeling effort is given by Peng [22], who estimates an inverse moment via Bayesian methods in an engineering reliability analysis.…”

Improved interval estimation of long run response from a dynamic linear model: A highest density region approach

“…As we will later demonstrate, this bootstrap distribution can be heavily skewed, with extreme values on the longer tail of the distribution. This is mainly because the estimator typically takes a ratio form and does not possess finite sample moments, as has also been noted by Bewley and Fiebig (1990) and Diebold and Lamb (1997). In this case, the usual percentile interval (Efron and Tibshirani, 1993) can often be excessively wide and uninformative.…”