Rulon D. Pope

Stochastic specification of production functions and economic implications

Abstract The stochastic specification of input-output response is examined. Postulates are set forth which seem reasonable on the basis of a priori theorizing and observed behavior. It is found that commonly used formulations are restrictive and may lead to inefficient and biased results. A function which satisfies the postulates is suggested. Two- and four-stage procedures for estimation of the resulting function are then outlined. The estimators are shown to be consistent and, in the latter case, asymptotically efficient under normality.

Production Function Estimation and Related Risk Considerations

There has been considerable interest in estimations of input effects on the probability distribution of output. Most empirical and theoretical analyses utilize multiplicative stochastic specifications which are analyzed and found unduly restrictive, particularly since inputs that marginally reduce risk are not allowed. A more general stochastic specification is proposed, free of these a priori restrictions. The proposed functional form estimation is discussed and demonstrated with nitrogen-response data and common log-linear production functions. Though nitrogen is risk-increasing, the marginal variance contribution is smaller when compared to estimates based upon multiplicative specification. Finally, stochastic specification error effects are analyzed.

On Testing the Structure of Risk Preferences in Agricultural Supply Analysis

Risk preferences broadly affect many economic decisions when markets are incomplete. Common representations of risk preferences are constant absolute, relative, and partial relative risk aversion. Each of these preference classes has distinct impacts on choice. An econometric test for distinguishing the class of preferences is proposed and implemented for potato supply response in Idaho. The data reject constant absolute and partial relative risk aversion and are congruent with constant relative risk aversion.

Modeling Farm-Level Crop Insurance Demand with Panel Data

A random-effects, binomial probit model is applied to data for a panel of Kansas wheat farms to examine Multiple Peril Crop Insurance demand. A theoretical model is developed which suggests inclusion of the moments of both market return and the return to insurance. Empirical results indicate that the first and second moments of both market return and the returns to insurance are significant. The price elasticity of demand is estimated to be −0.65. Preseason weather variables when included in the models were not found to be significant, failing to support the hypothesis of intertemporal adverse selection. Copyright 1996, Oxford University Press.

An Expected-Indemnity Approach to the Measurement of Moral Hazard in Crop Insurance

A definition of moral hazard in multiple peril crop insurance is proposed that focuses on expected indemnities rather than input use. Five years of production and insurance data for a panel of Kansas wheat farms is used to empirically test for this type of moral hazard. Results suggest that moral hazard affects multiple peril crop insurance indemnities in poor production years but that no significant moral hazard occurs in years when growing conditions are favorable. Copyright 1997, Oxford University Press.

Allocatable Fixed Inputs and Jointness in Agricultural Production: Implications for Economic Modeling

Allocatable fixed inputs, such as land, are a potentially important source of jointness in agriculture. As with other causes of jointness, they necessitate multiple-product systems for modeling product supply and input demand. In other important ways, however, their analytical implications are very different from other causes of jointness. Model specification differs. Demand functions for the quantities of each input used in the production of individual commodities can be derived if a primal approach is used, but such allocation equations cannot in general be identified from a dual specification. Available allocation data are not even useful in such dual estimations.

Participation in Farm Commodity Programs: A Stochastic Dominance Analysis

The net benefits of participation in farm commodity programs are analyzed with a normative risk model based on stochastic dominance theory. Utilizing entire probability distributions of participation and nonparticipation net returns, the impacts of alternative program features and farm size are investigated. Small changes in program parameters are found to affect participation decisions. It also is demonstrated that farm size can influence participation choices.

Diversification in Relation to Farm Size and Other Socioeconomic Characteristics

Interest by agricultural economists in farm diversification is evident in published research. Since the early work of Markowitz and Heady, attention has focused mainly on mean-variance portfolio approaches (Johnson; Stovall; Carter and Dean: Greve, Plaxico, Lagrone). These studies generally focus on the normative issue of optimal diversification under uncertainty. In the present paper, a positive examination of diversification using detailed microdata is undertaken.

Aggregate Productivity Measures

The essence of productivity calculation is aggregation. Cast in its simplest possible terms, measuring productivity growth is about measuring how the ratio Y/X changes over time, where Y measures an aggregate output and X measures an aggregate input. So, productivity measures essentially tell us whether input utilization is growing faster than output production. There are a number of ways to calculate productivity measures. One can estimate a representation of the technology (a distance function, cost, or revenue function) and calculate productivity measures from the estimated representation. Another alternative is to use programming methods to envelop the data and calculate productivity measures relative to a bestpractice frontier. But by far the most frequently encountered method is the index-number approach which measures productivity only using data on observed prices and quantities without the need for econometric estimation or the solu-

Empirical implementation of ex ante cost functions

Abstract Conventional dual methods ignore production risk. Under production risk, estimation of the cost function is complicated even with risk neutrality because the observed actual output is not the decision-relevant expected output. The decision-relevant cost function is not directly observed. An ex ante cost function approach is proposed by embedding the dual distance function computation of expected output within the estimation process. The resulting estimator is consistent and asymptotically efficient. Monte Carlo results indicate that biases and mean squared errors from conventional ex post methods are substantial whereas this approach approximates the efficiency of the directly observable case. An empirical application to U.S. agriculture also produces more plausible estimates than conventional methods.