# **1 Introduction**

A small proportion of firms generate the bulk of export revenue in each nation (Bernard et al., 2007; Mayer and Ottaviano, 2007). Richer countries tend to have more and larger exporters, with greater concentration in the top 5% (Fernandes, Freund, and Pierola, 2015). These large exporters help define specialization patterns and play a key role in shaping the impact of trade liberalization on macroeconomic volatility (Freund and Pierola, 2015; di Giovanni and Levchenko, 2012). To understand how and why (some) firms eventually become successful exporters, the heterogeneous-firm trade literature is paying growing attention to dynamics. While the increased availability of customs records has made it possible to study firms’ export behavior over time, we still have a limited understanding of the mechanisms underlying the evolution of export performance over the firm life cycle.

In this paper, we use rich micro data to document new facts about the joint evolution of firm performance and prices over the life cycle, and develop a theory of firm dynamics emphasizing the interaction between learning about demand and quality choice to explain the observed patterns. Drawing on transactions-trade and firm-level census data from the Portuguese manufacturing sector, we document that: (1) within narrow product categories, firms with longer spells of activity in export destinations tend to ship larger quantities at similar prices, thus obtaining larger export revenue; and (2) older or more experienced exporters tend to import more expensive inputs. In line with prior research, we also find that the positive relationship between export revenue and market experience reflects growth, not just market selection based on initial size; and that revenue growth within destinations (conditional on initial size) tends to decline with the length of activity there (Eaton et al., 2008; Berthou and Vicard, 2013; Ruhl and Willis, 2014).

To account for the joint observation of these patterns in the data, we introduce quality choice of outputs and inputs (Verhoogen, 2008; Kugler and Verhoogen, 2012) and learning about demand (Jovanovic, 1982; Arkolakis, Papageorgiou, and Timoshenko, 2015) into a Melitz (2003) model of monopolistic competition and firm heterogeneity. In the model, firms supply products of varying quality based on their beliefs about idiosyncratic expected demand. Through the life-cycle, an average surviving firm updates its demand expectations upwards, grows, and, as a result, finds it optimal to upgrade the quality of outputs, which requires using higher quality inputs. Since inputs of higher quality are more expensive, average input prices rise with export experience. The evolution of output prices is less clear-cut. On the one hand, quality upgrading leads to a higher price. On the other hand, an increase in demand expectations increases profitability and causes a price reduction. Hence the model is able to rationalize the varying behavior of input and output prices over the firm life cycle observed in the data.

We explore the quantitative implications of our theory by calibrating it to match crosssectional and dynamic moments of the distributions of sales, exports and prices observed in the Portuguese data. Calibrated to match the observed age-dependence of exports growth 2