Production risk in multi-output industries: estimates from Norwegian dairy farms

Abstract

Farmers who produce multiple outputs are portfolio managers in the sense that they use inputs to balance expected economic return and variance of return. This article estimates the structure of the stochastic multioutput production technology in Norwegian dairy farming, allowing for a more flexible specification of the technology than previous studies. We find that an increase in input levels leads primarily to higher output variability, and that inputs also influence the covariance of shocks between outputs. Risk reducing effects of inputs on outputs are primarily present in the covariance functions. Technical change leads to shifts in the profit distribution over the data period, but no welfare improvement for risk averse farmers.

Acknowledgements

Comments from participants at a seminar at the Norwegian Agricultural Economics Research Institute, J. Brian Hardaker, Subal C. Kumbhakar and an anonymous referee are gratefully acknowledged. This research was funded by the Research Council of Norway.

Notes

¹ Econometric studies of production risk in agriculture using a primal model approach include Just and Pope (1979), Griffiths and Anderson (1982), Antle (1983), Antle and Goodger (1984), Nelson and Preckel (1989), Wan and Anderson (1990), Wan et al. (1992), Kumbhakar (1993), Traxler et al. (1995), Regev et al. (1997), Roberts et al. (2004), Di Falco et al. (2007), Groom et al. (2008), Serra et al. (2006, 2009) and Shankar et al. (2008), while aquaculture has been studied by Asche and Tveteras (1999) and Tveteras (1999, 2000).

² The state contingent approach (Chambers and Quiggin, 2001) has been introduced as an alternative to the traditional parametric stochastic production function approaches such as the JP specification belongs. Full application of the state contingent approach is very data demanding (Just, 2003), and empirical study based on this approach has only recently appeared in the agricultural economics literature (O’Donnell and Griffiths, 2006; Chavas, 2008).

³ See Just and Pope (1978) for other requirements for a risky production technology.

⁴ Examples of multi-output technology estimation in the absence of production risk is given in Nehring et al. (2005).

⁵ An input is allocable when the amount of the input used in producing output y_j can be distinguished from the amount of the same input used in producing y_k (j ≠ k) (Beattie and Taylor, 1985).

⁶ However, the subjective weighting of the marginal effects is determined by the producer's degree of risk aversion, i.e. the size of dU*/dVar(π).

⁷ Driscoll et al. (1992) compare the flexibility properties of the TL and GL. Tveteras (1999, 2000) estimate both translog and GL mean production functions. Several studies have employed the more restrictive CD specification for the mean function, e.g. Hallam et al. (1989) and Wan et al. (1992) in their multi-output JP functions. They were then forced to estimate the CD nonlinearly in order not to violate the JP postulates.

⁸ The first element of z, z ₀, is taken as unity. This implies that Var(ε) = exp(β ₀).

⁹ 5.10 NOK ≈ 1 USD.

¹⁰ The estimated parameters are not reported here due to space considerations, but are available from the authors upon request.