This paper proposes an estimation of an augmented Tornqvist price-index - featuring demand shifters - which is exact for homothetic translog preferences. Contrary to previous work based on a constant elasticity of substitution across varieties, this demand system allows for changes in markups even when the number of products is large. We then propose a structural decomposition of this index in terms of changes in markups, productivity, variety and demand shocks. We illustrate our approach using sample data from ACNielsens Homescan Panel. For instance, our results are consistent with competition effects where a decrease in per-product demand translates into lower markups.