This paper addresses the crucial issue of estimating the elasticity of substitution between production factors in macroeconomic models, with a particular focus on overcoming measurement errors in the user cost of capital. We introduce a system estimator approach that combines the relative first-order conditions and the production function to mitigate bias caused by measurement errors. Through simulations, we demonstrate that this approach yields unbiased estimates, even in the presence of misspecified technical change. Applying our method to data from MAKRO, we find a range of elasticities across sectors and production nests, ranging between 0.5 and 1.7.