Dual Profit Function Research Articles

Abatement costs of alternative tax systems to regulate agricultural nitrogen loss

Nitrogen emissions from agriculture are considered an important environmental problem in Denmark, motivating consideration of different tax schemes as regulatory instruments. In this article, input/output behavior of Danish pig farms is estimated with farm-level panel data using the dual profit function approach, and emission functions for nitrogen loss are derived. With the estimated model, we are able to compare cost effectiveness of a comprehensive Pigouvian tax on nitrogen loss with simpler tax schemes that focus on nitrogen use. We find that both a fertilizer tax and a feed tax generate substantially higher abatement costs than Pigouvian incentives. A tax on nitrogen in all inputs will, on the other hand, only generate a marginal increase in abatement costs. These results are of interest because a tax on all nitrogen inputs is easier to implement than a comprehensive nitrogen loss tax. Our result implies that even a limited administrative cost advantage may make the input tax preferable to implementing Pigouvian incentives through a nitrogen loss tax.

Nitrogen Fertilizer Demand from Danish Crop Farms: Regulatory Implications of Heterogeneity

This paper estimates nitrogen fertilizer demand elasticities for Danish crop farms using the dual profit function approach on micro panel data. The model includes several farm‐specific parameters, allowing us to estimate the mean demand elasticity and test for homogeneity of elasticities across panel farms. The mean own‐price elasticity for nitrogen is −0.45, and there is a significant standard deviation from this mean for individual farms of 0.24.Heterogeneity of demand elasticities implies that regulating fertilizer application through mandated uniform percentage reductions, as is currently used in Danish nitrogen regulation, increases abatement costs relative to tax regulation. Somewhat surprisingly, this causes the abatement costs of quota regulation to be only 8% larger than with tax regulation. Simulation results indicate that the primary threat to the efficiency of uniform reduction schemes comes from inaccurate estimation of baselines rather than from heterogeneity of elasticities.L'auteur estime les élasticités de la demande d'engrais azotés pour l'agriculture danoise en appliquant la fonction du double profit aux données issues de microgroupes de consultation. Le modèle inclut plusieurs paramètres spécifiques à l'agriculture, ce qui permet d'estimer l'élasticité moyenne de la demande et de vérifier l'homogénéité des élasticités pour les agriculteurs consultés. On constate qu'il existe une élasticité‐prix moyenne de −0,45 pour l'azote et que cette moyenne présente un écart‐type significatif de 0,24 par exploitation agricole.Les élasticités hétérogènes de la demande supposent que si on régule les engrais azotés par une réduction uniforme du volume employé en pour cent, ainsi que l'exige présentment le règlement danois, on accroît le coût des mesures de lutte, comparativement à ce qui se produit avec les mesures fiscales. Il est un peu surprenant de voir que la régulation par quota n'augmente le coût des mesures de lutte que de 8%, par rapport aux mesures fiscales. Les résultats de la simulation révèlent que l'efficacité des programmes de réduction uniforme est surtout menacée par une estimation inexacte des valeurs de base et non par l'hétérogénéité des élasticités.

A comparison of proxy variable and stochastic latent variable approaches to the measurement of bias in technological change in south african agriculture*

Technical change is inherently unobservable and has conventionally been represented by proxy variables, from simple time trends to more sophisticated knowledge stock variables. This paper follows Lambert and Shonkwiler (1995) in modelling technical change as a stochastic unobservable variable and tests this formulation against the alternative of using R&D and patent indices. This is done by fitting a system of share equations, derived from the dual profit function, to production data for South African agriculture. Each equation includes both unobserved technical change components and technical proxy variables. Variable deletion tests show that conventional proxy variables fail to explain the biases of technological change, while cointegration tests show that technical change is both stochastic and biased. The latent variables provide estimates of biases that are consistent with past studies and the historical record and can be explained by policy change in South Africa following WWII. The demonstration of high rates of return to R&D is not sufficient to justify R&D activity when biased technological change exacerbates input use and welfare distortions within and without the sector. * We thank the University of Pretoria for funding the study and the referees and delegates for many useful comments.

Short and long‐run returns to agricultural R&D in South Africa, or will the real rate of return please stand up?

AbstractThis paper briefly presents the results of a total factor productivity (TFP) study of South African commercial agriculture, for 1947‐1997, and illustrates some potential pitfalls in rate of return to research (ROR) calculations. The lag between R&D and TFP is analyzed and found to be only 9 years, with a pronounced negative skew, reflecting the adaptive focus of the South African system. The two‐stage approach gives a massive ROR of 170%. The predetermined lag parameters are then used in modeling the knowledge stock, to refine the estimates of the ROR from short‐ and long‐run dual profit functions. In the short run, with the capital inputs treated as fixed, the ROR is a more reasonable 44%. In the long run, with adjustment of the capital stocks, it rises to 113%, which would reflect the fact that new technology is embodied in the capital items. However, the long‐run model raises a new problem since capital stock adjustment takes 11 years, 2 years longer than the lag between R&D and TFP. If this is assumed to be the correct lag, the ROR falls to 58%, a best estimate. The paper draws attention to the possible sensitivity of rate of return calculations to assumed lag structure, particularly when the lag between changes in R&D and TFP is skewed.

Short and long-run returns to agricultural R&D in South Africa, or will the real rate of return please stand up?

This paper briefly presents the results of a total factor productivity (TFP) study of South African commercial agriculture, for 1947-1997, and illustrates some potential pitfalls in rate of return to research (ROR) calculations. The lag between R&D and TFP is analyzed and found to be only 9 years, with a pronounced negative skew, reflecting the adaptive focus of the South African system. The two-stage approach gives a massive ROR of 170%. The predetermined lag parameters are then used in modeling the knowledge stock, to refine the estimates of the ROR from short- and long-run dual profit functions. In the short run, with the capital inputs treated as fixed, the ROR is a more reasonable 44%. In the long run, with adjustment of the capital stocks, it rises to 113%, which would reflect the fact that new technology is embodied in the capital items. However, the long-run model raises a new problem since capital stock adjustment takes 11 years, 2 years longer than the lag between R&D and TFP. If this is assumed to be the correct lag, the ROR falls to 58%, a best estimate. The paper draws attention to the possible sensitivity of rate of return calculations to assumed lag structure, particularly when the lag between changes in R&D and TFP is skewed.

Effects of N-surplus taxes: Combining technical and historical information

Technical information on the production of an externality can be included in a dual profit function to yield insight into the effects of a tax on the externality. The methodology is applied to a tax on nitrogen surplus in the context of future mineral policies for Dutch arable farms. In future policy, N surplus will probably be calculated using an accounting relationship that relates inputs and outputs to N surplus. The simulation model used to determine the effects of the tax on N surplus is based on equations that have been estimated with panel data. Copyright 1997 by Oxford University Press.

Using the quadratic Box-Cox for flexible functional form selection and unconditional variance computation

A quadratic Box-Cox methodology is presented for choice of flexible functional form that includes consistent computation of variance estimates. Empirical viability of the procedure is investigated by specifying a dual profit function using highly aggregated U.S. agricultural data. Conditional and unconditional variance estimates for the parameters are compared and contrasted. Like-lihood ratio tests are utilized to discriminate among the generalized Leontief, normalized quadratic, translog, and square-rooted quadratic functional forms. Statistical results indicate that the squarerooted quadratic is the preferred choice of functional form for these data, followed by the normalized quadratic.

Measurement of profit efficiency using behavioural and stochastic frontier approaches

The objectives of this study are to estimate profit inefficiency of farms in the North-west Frontier Province of Pakistan using stochastic frontier and the behavioural profit functions. The derived measure of inefficiency, based on a half-normal distribution of the stochastic error term, is related to socio-economic variables; and of these, the size of holding, fragmentation of land,subsistence needs the higher age of farmers contribute positively to inefficiency. The behavioural approach satisfies most of the assumptions of the dual profit function and the likelihood ratio test rejects the market efficiency hypothesis. It is also shown that use of manures, labour and fertilizers is below the optimum. Small farms seem to have higher productive efficiency than large farms and, therefore small farm ownership needs to be encouraged.

Optimal Location and Production: A Profit Function Analysis in Cartesian Space

This paper specifies a dual profit function which facilitates the generalization and extension of the analysis of the Hoover–Isard–Moses problem of integration of optimal location and production decisions. The optimal location of a multi-input, multi-market firm in two-dimensional space is analyzed. The central question is, which combinations of the economic characteristics will be sufficient to induce concavity in the dual profit function with respect to the Cartesian coordinate space over which it is defined? We show that for any configuration of input and market sites which are not all collinear, concavity of the dual profit function depends upon a sufficiently small elasticity of input substitution. The model is sufficiently general so that previous results derived under restrictive conditions of zero substitution, city-block metric, or one-dimensional space can be obtained as special cases. The use of vectors and Cartesian coordinates facilitate not only the straightforward generalization to multiple inputs and markets but also allow an intuitively appealing representation of the location optimality condition. Furthermore, we demonstrate how our approach simplifies and facilitates comparative static analysis, the introduction of the profit-improving location direction, and the economic and geometric interpretations of the results.

The Effects of Suburbanization on Agriculture

AbstractThis article conceptualizes the effects of suburban population density and land speculation on agricultural production choices, prices, and profits. A dual profit function model and a system of reduced‐form price equations are used to estimate these effects for New Jersey. Results show that vegetable production is the only subsector to benefit from suburbanization, while livestock is the most adversely affected. Suburbanization reduces responsiveness to agricultural prices and discourages capital and land use. The overall impact on profits is positive when capital gains on land are included. Policy implications for farmland preservation and “right to farm” legislation are discussed.

Usefulness of Pretests for Estimating Underlying Technologies Using Dual Profit Functions

Translog and generalized-linear approximating forms are used to estimate dual profit functions from stochastically simulated data generated from a known, relatively complex technology under profit-maximizing conditions. The hypotheses of monotonicity, convexity, and equality of parameters common to the profit function and demand equations are tested. This last hypothesis is always rejected and monotonicity is never rejected. Convexity is rejected for about a third of the translog models and fewer than 5 percent of generalized-linear models. Neither approximating form strongly dominates the other for accuracy in estimating the underlying elasticities of substitution. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Testing Efficiency Hypotheses in Joint Production: A Parametric Approach

N recent years a great deal of research has been directed to the modelling and measurement of technical and allocative efficiency in production. With few exceptions this research has been restricted to single-product firms.' However, recent developments in duality theory have facilitated the extension of this research to multi-product firms. The main purpose of this paper is to develop a model of the multiproduct firm in which the possibilities of both technical and allocative inefficiency are incorporated in an econometrically useful way. The first model we develop includes a nonneutral2 type of technical inefficiency and three distinguishable types of allocative inefficiency-output mix, input mix, and scale. Each type of inefficiency is costly to the firm, in the sense that each causes a reduction in profit beneath the maximum value attainable under full efficiency. The cost of each type of inefficiency depends on the magnitude of the inefficiency and the structure of the underlying production technology. In the second model we develop, technical inefficiency remains nonneutral, but allocative inefficiency is not generally decomposable into output mix, input mix and scale components. However, both technical and allocative inefficiency remain costly to the firm, the cost of each type of inefficiency depending on its magnitude and the structure of the underlying production technology. We model the technology of a competitive profit maximizing multi-product firm with the dual profit function. This enables us to use Hotelling's Lemma to generate a system of profit maximizing output supply and input demand equations. These equations are then modified to allow for the possibility of technical and three types of allocative inefficiency. A virtue of using the profit function to represent production technology is that it permits a straightforward comparison of maximum profit under full efficiency with actual profit, and with the profit that would result from any combination of the four types of inefficiency. This enables us to allocate the cost of inefficiency to each of four components. Our model of inefficiency is parametric, and is embedded in a Generalized Leontief profit function, although any flexible specification of the profit function can be used. The model is developed in sections II-IV. Estimation of the model is considered in section V. An empirical example designed to illustrate the workings of the model is discussed in section VI. Section VII concludes.