and input prices, the model accounts for about a third of the (conditional) size-dependence of growth rates that emerges from the data, and correctly predicts that the quantity of inputs increases with export-age.

Armed with the calibrated model, we assess the implications of regulations imposing minimum product quality standards on exports. We find that this policy reduces welfare through two distinct channels. First, it reduces firm entry in export markets, and hence lowers the number of export varieties available to consumers. Second, it distorts an intensive margin of adjustment. To participate in the export market, marginal exporters are forced to comply with the standard by choosing higher-quality inputs. This choice leads to a reallocation of productive resources from large and old towards small and young firms, which causes a further decline in welfare.

We contribute to several strands of existing research. A recent body of literature on firm dynamics offers variants of Melitz (2003) in which firms experience idiosyncratic shocks to their productivity, including Luttmer (2007), Impullitti, Irarrazabal, and Opromolla (2013), and Arkolakis (2015). If modified to allow for quality choice (as in Kugler and Verhoogen (2012)), this class of models would generate a positive relationship between input prices and export experience: as entrepreneurs become more capable (for exogenous reasons), firms grow and find it optimal to upgrade the quality of outputs and inputs. However, as emphasized by Arkolakis, Papageorgiou, and Timoshenko (2015) this class of models is unable to explain the age-dependence of growth rates (conditional on size) observed in the data.

A related class of models links firm dynamics in export markets to learning about unobserved demand (Albornoz et al., 2012; Chaney, 2014; Eaton et al., 2014; Ruhl and Willis, 2014; Timoshenko, 2015a,b; Arkolakis, Papageorgiou, and Timoshenko, 2015). While the microfoundations of the learning process vary across models, this body of work makes it possible to rationalize the age-dependence of export growth (conditional on size) observed in the data. Existing learning models are not well-suited, however, to explain the observed increase in wages and material input prices with export experience.<sup>1</sup> Our findings also contribute, therefore, to the literature on product quality and trade at the firm-level. We borrow from Verhoogen (2008) and Kugler and Verhoogen (2012) the theoretical ideas that in order to produce higher-quality outputs firms need to use higher-quality inputs; and that all else equal more capable entrepreneurs will choose to produce higher quality products. These hypotheses have found considerable support in the data. Using detailed firm-product records from the Colombian manufacturing sector,

> 1We also build on Cabral and Mata (2003) who show that the firm size distribution is significantly right-skewed and evolves over time toward a lognormal distribution largely because of firm growth (as opposed to selection based on initial size). A related body of evidence reveals that firm growth (in terms of employment, sales or export revenue) declines with age, conditional on initial size (Evans, 1987; Sutton, 1997; Haltiwanger, Jarmin, and Miranda, 2013; Arkolakis, 2015; Timoshenko, 2015a,b). While confirming that these patterns also hold in our data, we depart from previous work by examining the joint evolution of export performance and prices over the firm life cycle; and by providing theory and evidence that the interaction between learning about demand and quality choice is an important driver of firm dynamics.

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