The value of the elasticity of substitution between labour and capital (σ) is a ‘crucial’ assumption in understanding the secular decline in the labour share of income and long-run growth. This paper develops and implements a new strategy for estimating σ by combining a low-pass filter with panel data to identify the low-frequency/long-run relations appropriate to production function estimation. Using spectral analysis, we assess the extent to which our choices of the critical periodicity and window defining the low-pass filter are successful in emphasising long-run variation. We document that standard estimation methods, which do not filter-out transitory variation, generate downwardly biased estimates. After correcting for this bias, our preferred estimate of σ is 0.40, substantially below the Cobb-Douglas assumption of σ =1 , which implies that the secular decline in the labour share of income cannot be explained by secular increases in the capital/income ratio or secular decreases in the relative price of investment or capital taxation.