Systems of equations comprising cost functions and ¢rst-order derivative equations are often used to estimate characteristics of production technologies. Unfortunately, many estimated systems violate the regularity conditions implied by economic theory. Sampling theory methods can be used to impose these conditions globally, but these methods destroy the £exibility properties of most functional forms. We demonstrate how Bayesian methods can be used to maintain £exibility by imposing regularity conditions locally. The Bayesian approach is used to estimate a system of cost and share equations for the merino wool-growing sector. The e¡ect of local imposition of monotonicity and concavity on the signs and magnitudes of elasticities is examined.

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