Estimating productivity with multi-product firms, pricing heterogeneity and the role of international trade

In this paper, we analyze the relationship between exports, imports and firm productivity taking into account pricing heterogeneity and multi-product firms. We use a rich firm–product level dataset providing both revenue and quantities of all products produced, exported and imported for a large panel of Danish manufacturing firms over the period 1999–2006. With this detailed information, we compute a firm level price index to deflate our measure of output and compare our productivity measures when we deflate output with an industry-level deflator. We find that firms only importing have a large productivity premium, but not firms only involved in exporting, while firms involved in both importing and exporting are the most productive. The international trade premia are found to be significantly larger when output is deflated with our firm-specific price index rather than the traditional sector-level PPI, suggesting that pricing heterogeneity plays an important role in productivity measurement. We also find evidence of a self-selection into exporting but not into importing. Finally, we detect the presence of learning by exporting only when we control for pricing heterogeneity; when looking at learning by importing, we find a positive effect in the long run, but the effect is lower when we deflate revenue with a firm-specific price index. These results suggest that pricing heterogeneity can significantly affect the way we measure productivity and our assessment about the link between productivity and trade.