A constrained joint-equation estimation of at-a-station hydraulic geometry

Hydraulic geometry describes the relations between a stream's discharge and its width, depth and velocity as a system. The continuity equation implies two cross-equation constraints, one of which is that the hydraulic exponents should sum to one. Traditional literature, using one-at-a-time estimation methods, have either ignored the constraints, or force the exponents to sum to unity by arbitrarily manipulating the estimates. By using a systematic approach called Seemingly Unrelated Regression(SUR), we are able to jointly estimate the relations and impose the constraints. The unrestricted and restricted estimates are computed from SUR method and Ordinary Least Squares(0LS). It is found that SUR and OLS yield identical unrestricted results when the sets of regressors are identical. Although SUR estimates are asymptotically at least as efficient as OLS, due to the finite sample sizes of our data, the restricted estimates from SUR generally have larger standard errors than the restricted OLS.