Product quality at the plant level: Plant size, exports, output prices and input prices in Colombia
This paper uses uniquely rich and representative data on the unit values of "outputs" (products) and inputs of Colombian manufacturing plants to draw inferences about the extent of quality differentiation at the plant level. We extend the Melitz (2003) framework to include heterogeneity of inputs and a complementarity between plant productivity and input quality in producing output quality and we show that the resulting model carries distinctive implications for two simple reduced-form correlations - between output prices and plant size and between input prices and plant size - and for how those correlations vary across sectors. We then document three plant level facts: (1) output prices are positively correlated with plant size within industries, on average; (2) input prices are positively correlated with plant size within industries, on average; and (3) both correlations are more positive in industries with more scope for quality differentiation, as measured by the advertising and R&D intensity of U.S. firms. The correlations between export status and input and output prices are similar to those for plant size. These facts are consistent with our model of quality differentiation of both outputs and inputs, and difficult to reconcile with models that assume homogeneity or symmetry of either set of goods. Beyond recommending an amendment of the Melitz (2003) model, the results highlight shortcomings of standard methods of productivity estimation, generalize and provide an explanation for the well-known employer size-wage effect, and suggest new channels through which liberalization of trade in output markets may affect input markets and vice-versa.
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