Exporter Dynamics, Firm Size and Growth, and Partial Year Effects Theoretical models in Luttmer (2007), Arkolakis (2011), and Eaton, Kortum, and Kramarz (2011) all incorporate specific elements to handle the large number of small firms. This general feature of firm size distributions is subject to bias if the share of entrants is large, entrants are disproportionately among the smallest firms and their sales or employment only reflect a partial year of activity. Correcting the partial year effect should decrease the share of the smallest firms and may result in firm size distributions that more closely resemble a Pareto.

Arkolakis (2011) develops an analytical framework that integrates aspects of the export dynamics and firm size literatures to study firm and export growth. He compares calibrations of the model both to the growth of sales of US firms as well as to Brazilian exports to the US. Among the stylized facts he uses to motivate and assess the model are the negative relationship between firm size and firm growth rates and their variance, the small size of entrants in a market, the parity of size between entrants and exits, the different distributions of growth rates for large (lognormal) and small (skewed high) exporters, and the relationship between firm growth and firm age conditional on size.

A related set of findings focuses on the distribution of growth rates conditional on firm size and age, in particular Cabral and Mata (2003). Arkolakis (2011) shows that the distribution of growth rates for smallest (quartile 1) and largest (quartile 4) Brazilian exporters to the US are starkly different. The distribution of growth rates of the smallest firms is heavily skewed towards higher growth rates while that of the largest firms is approximately lognormal and center around zero. If a large share of entrants is concentrated in the smallest firms, partial year effects may lead to growth rates and their variance being overstated for the smallest firms in the market.

In spite of the potentially pervasive nature of the problem, there has been almost no work examining the degree of bias induced by partial year effects nor any correction in empirical work using firm-level data. In large part this is due to the nature of the data that are available to researchers. Most detailed trade datasets have been aggregated to the exporter-destination-productyear level before being provided to the researchers. Eaton, Kortum, and Kramarz (2011) are typical when they report “All (customs record) data is aggregated first at the monthly level. In the analysis files accessible to researchers, these records are further aggregated by year ....” However even when the underlying monthly (or daily) data are available, the first step is usually to aggregate the data to the annual level, e.g. Bernard, Jensen, Redding, and Schott (2009). An exception is the recent paper by Berthou and Vicard (2013) who control for the month of entry of exporting in their study of the effect of export experience and export growth for French exporters.<sup>5</sup> The rest of this paper explores the magnitude of partial year bias in the stylized facts on export dynamics and firm size and growth using Peruvian data. The data on Peruvian exports are

> 5Although Berthou and Vicard (2013) do not focus on partial year effects, they report that initial year exports are reduced by 32 percent.

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