Modelling disaggregated lumber demand and supply by constrained estimation techniques

Abstract

Constrained estimation techniques were used to estimate a 12-equation demand and supply system for Douglas-fir and hemlock–fir (true fir) lumber by clear and common grades. Such techniques combine sample information with nonsample information and produce estimates with smaller variances than those based only on sample data. Conventional econometric estimation was compared with a quadratic programming technique with regression coefficients constrained to their a priori correct signs. A goal programming technique that minimized the sum of the absolute deviations was rejected because of its substantially different results and lack of information on the statistical properties of its estimates. The quadratic programming technique had the advantages of statistical efficiency, objectivity, and speed. The conventional estimation technique excluded fewer variables from the system and thus was less susceptible to omission of variables bias. Elasticity estimates for most key variables were similar. Quadratic programming versus conventional estimates of demand elasticity were, respectively, −0.95 and −0.88 for Douglas-fir clears, −2.83 and −2.91 for Douglas-fir commons, and −2.13 and −2.27 for all Douglas-fir; whereas supply elasticities for hemlock–fir commons were 1.35 and 1.37, and for all hemlock–fir, −1.76 and −1.42.