The elasticities of long-run population growth rate with respect to vital rates are useful in studying selection on vital rates, and in evaluating management policy that aims to control vital rates. In temporally varying environments, elasticity is often calculated from simulations that assume a probability distribution for the environmental states. Here we develop a method to estimate elasticities directly from demographic data. Using a time-series of demographic matrices and age-structure we construct a consistent statistical estimator of elasticity that converges to the correct limiting value as the sample length increases. We also construct confidence intervals for elasticities from temporal data and suggest tools for testing hypotheses about the strength of selection. We use data on a natural population to show that our method can indeed accurately estimate elasticities using relatively short time series.