Markov Chain Monte Carlo (MCMC) methods are used to estimate a seemingly un
related regression (SUR) system of input demand functions for U.S. agricult
ure. Our demand functions have flexible forms and allow for nonrandom techn
ical inefficiency. Concavity constraints are imposed at individual data poi
nts, and the distributions of measures of relative technical efficiency are
constrained to the unit interval. Results are evaluated in terms of charac
teristics of the posterior distributions of parameters, measures of relativ
e technical efficiency, and other nonlinear functions of the parameters.