Uncertainty, duality and perversity: an empirical test of the Schultz-Baron hypothesis

It has been suggested that supply curves may be negatively sloped under conditions of output price uncertainty and risk aversion if the effect of an increase in expected price is offset by the effect of an associated increase in uncertainty/risk. This hypothesis, first articulated by Schultz and given a more rigorous theoretical exposition by Baron, is tested using aggregate time series data to estimate a stochastic model of US agriculture based on a generalized Leontief certainty equivalent profit function. Evidence of risk aversion and a positive correlation between mean output price and its variance are found; however, these factors are not strong enough to generate perversity. Thus the own-price elasticity of supply of agricultural output is found to be positive with a value of 0.25. Although no evidence of perversity is found, the empirical results suggest that ignoring price uncertainty may bias estimates of aggregate supply response downwards by between 5% and 47%. As well as testing the Schultz - Baron hypothesis, the paper demonstrates how the dual approach to applied production analysis can be extended to cover production under output price uncertainty.