1989
DOI: 10.2307/1241595
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The Conditional Beta Distribution as a Stochastic Production Function

Abstract: The conditional beta distribution is proposed as a parametric model of the probability distribution of agricultural output. A two‐stage maximum likelihood estimation procedure is shown to produce consistent, asymptotically efficient and normal estimates of maximum output and the parameters of the conditional distribution. Application of the procedure to data on corn yield response to fertilizers shows that fertilizers have a significant impact on each of the first three moments of the distribution of corn yiel… Show more

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Cited by 169 publications
(87 citation statements)
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“…Out of the 38 distribution functions fitted, 12 were Weibull, 11 Triangular, 4 Gamma, 7 BetaGeneral, 2 Logistic and lastly, 2 Logistic distributions. Such distributions have been proposed in earlier literature for crop yield modelling in agricultural economics (Atwood et al, 2003;Gallagher, 1987;Nelson and Preckel, 1989;Sherrick et al, 2004;Tolhurst and Ker, 2015). Results of these density fits are available from the authors upon request.…”
Section: Asymmetric Informationmentioning
confidence: 99%
“…Out of the 38 distribution functions fitted, 12 were Weibull, 11 Triangular, 4 Gamma, 7 BetaGeneral, 2 Logistic and lastly, 2 Logistic distributions. Such distributions have been proposed in earlier literature for crop yield modelling in agricultural economics (Atwood et al, 2003;Gallagher, 1987;Nelson and Preckel, 1989;Sherrick et al, 2004;Tolhurst and Ker, 2015). Results of these density fits are available from the authors upon request.…”
Section: Asymmetric Informationmentioning
confidence: 99%
“…Thus, we assume that the random productive shocks ε follow a beta distribution. The beta distribution has the advantage of being empirically supported and popular in stochastic yield modeling at the local level (see, among others, Nelson andPreckel, 1989, Babcock andHennessy, 1996), and of having bounded support, which is computationally convenient. We assume the distribution to have shape parameters 2 and 2, which makes it unimodal at 0.5, and symmetric.…”
Section: Calibrationmentioning
confidence: 99%
“…In other words, the distribution is then "conditional" on the value of economic variables, shifting the distribution over time as economic variables change. I adopt the approach of Nelson and Preckel (1989), utilizing the conditional beta distribution to model the probability distribution of population density individually for each of the sixteen EPPA regions. Nelson and Preckel (1989) demonstrated the broad application of the conditional beta distribution by using it to model the probability distribution of agricultural output, estimating a stochastic production function and allowing the shape-parameters of the distribution of output to be functions of economic variables (i.e.…”
Section: Empirical Models and Datamentioning
confidence: 99%
“…As Nelson and Preckel (1989) point out, the functions α(Z) and β(Z) must be consistent with the regularity conditions for maximum likelihood estimation. In addition, "…arguments for simplicity and parsimony might justify linear or log-linear functions" (p. 372).…”
Section: Empirical Models and Datamentioning
confidence: 99%