Unraveling firms: demand, productivity and markups heterogeneity

We develop a novel framework that simultaneously allows recovering heterogeneity in demand, quantity TFP and markups across firms while leaving the correlation between the three dimensions unrestricted. We accomplish this by explicitly introducing demand heterogeneity and systematically exploiting assumptions used in previous productivity estimation approaches. In doing so, we provide an exact decomposition of revenue productivity in terms of the underlying heterogeneities, thus bridging the gap between quantity and revenue productivity estimations. We use Belgian firm's production data to quantify TFP, demand and markups and show how they are correlated with each other, across time and with measures obtained from other approaches. In doing so, we find quantity TFP and demand to be strongly negatively correlated with each other so suggesting a trade-off between the quality of a firm's products and their production cost. We also show how our framework provides deeper and sharper insights on the response of firms to increasing import competition from China. In particular, we find that changes in revenue productivity materialise as the outcome of complex, and sometimes offsetting, changes in quantity TFP, demand, markups and production scale.