Estimating High-Dimensional Demand Systems in the Presence of Many Binding Non-Negativity Constraints Daniel L. Millimet  Southern Methodist University Rusty Tchernis Indiana University Abstract Two econometric issues arise in the structural estimation of consumer or producer demand systems in the presence of many binding non-negativity constraints. First, most existing methods entail the evaluation of multivariate probability integrals. Second, the issue of statistical coherency must be addressed. We cir- cumvent both of these issues using Gibbs Sampling, along with data augmentation and rejection sampling. We illustrate our method using several simulated data sets. JEL: C11, C31, D12, L66 Keywords: demand systems, translog, coherency, data augmentation, Markov Chain Monte Carlo, Gibbs Sampling  The authors are grateful for comments from an anonymous referee. Corresponding author: Daniel Millimet, Department of Economics, Box 0496, Southern Methodist University, Dallas, TX 75275-0496. Tel: (214) 768-3269. Fax: (214) 768-1821. E-mail: millimet@mail.smu.edu.