Simultaneous Estimation of Cost and Distance Function Share Equations

The study considers the simultaneous estimation of share equations using cost and distance functions. Simultaneous rather than single system estimation utilizes full as opposed to limited information. Econometric results exploit the nonstationary nature of the data and that variables are cointegrated. Under cointegration all variables are endogenous and so it is not necessary to undertake the somewhat ad hoc exercise of choosing instruments to achieve parameter consistency. Johansen's maximum likelihood estimator is applied to data from Central Canada and Western Canada (1935-2006). Symmetry and homogeneity restrictions are not rejected for either region. Monotonicity held for all data points and concavity held at 92% of the data points. Long-run constant returns and Hicks neutral technological change are rejected for both regions. Morishima elasticity estimates coming from the cost function in Western Canada indicate highly elastic long-run substitution between the land/fertilizer input pair and mildly elastic long-run substitution between land and both machinery and labor. In contrast, substitution for land and other inputs is inelastic for the land/machinery pair and the land/labor pair, with only the land/fertilizer pair being mildly elastic. The results indicate the limiting nature of land as a fundamental constraint on long-term agricultural production is a real possibility in Central Canada because other inputs are inelastic, or at best only mildly elastic, substitutes for land. In Western Canada, fertilizer is the only factor that is highly substitutable for land and, therefore, could mitigate the limiting nature of land in that region. However, given that fertilizer applications are often considered to be environmentally unfriendly, the long-run substitution of fertilizer for land as a fundamental mitigating factor to land scarcity in Western Canada is at a cost to the environment.