How are econometrics and stream flow connected?
Hydraulic geometry describes the relations between a stream's discharge and its width depth and velocity as a system. A continuity equation implies two cross-equation constraints, one of which is that the hydraulic exponents should sum to one. The 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) which is a common technique in Econometrics, 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(OLS). 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.
Sandy's background in Economics allowed her to see this connection between these seemingly unrelated areas of research. This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact her supervisor Carl Schwarz (cschwarzstat.sfu.ca), Department of Statistics and Actuarial Science.