Estimation of the elasticity of substitution in the presence of errors of measurement

Under certain circumstances an estimate of the elasticity of substitution for competitive exports in international trade may be bracketed when prices are not directly measured. Often only value and quantity data are available. In this case regressing value ratios on quantity ratios and vice versa will bracket the estimate as the asymptotic biases will have opposite signs. If values are divided by quantities to generate a price series, and then regressions are run, both estimates will be biased towards zero and not provide the bounds sought.