Exporter Dynamics, Firm Size and Growth, and Partial Year Effects described in Section 2. Section 3 outlines a simple model of market entry by month and generates benchmark predictions for the bias on firm size and growth. The magnitude of the bias in entry levels and growth rates for surviving exporters is estimated in Section 4. Section 5 examines the importance of partial year effects in estimates of the cross-section firm size distribution and firm growth conditional on firm size. The final section concludes.

# **2 Data**

The data employed in this paper come from Peruvian transaction-level customs data from 19932009. The source of the data is SUNAT and it was collected by the Trade and Integration Unit of the World Bank Research Department as part of the effort to build the Exporter Dynamics Database (see Cebeci, Fernandes, Freund, and Pierola (2012)). Although we have daily information on all shipments between years 1992 and 2009, we aggregate the data to the monthly level before any of our analyses. The data have the usual features of transaction-level trade data in that it is possible to create flows of exports by product and destination for all Peruvian exporters. We create two measures of “annual” exports for each firm and each firm-destination in the data. The first measure is a simple aggregation to the calendar year summing across months. This results in an annual data set that is directly comparable to annual firm level export data used by other researchers. The second data set contains annual export data adjusting for the month of entry into the market by the firm.<sup>6</sup> The first year of exports starts in the month of first entry and runs for the next 11 months. For the same firm and market the second year also starts in the same month.

# **3 Partial Year Effects - An Example**

In this section we work through a simple example to demonstrate the potential magnitude of the partial year effect on first year sales and growth in a market. We refer to export sales and output interchangably throughout this section as the partial year effects will distort both revenue and quantity-based measures of sales. In the subsequent empirical work, we use revenue based measures of exports.

We assume that firms enter the market uniformly across months during the year with identical initial exports. All firms subsequently grow at 22.6 percent per year corresponding to a 1.715 percent compound monthly growth rate and firms do not exit.<sup>7</sup> The firms that enter in January will record a full year’s initial exports and grow between year 1 and year 2 at 22.6 percent with or without a

> 6The market can be a particular export destination or the export market in general. The month of entry will typically differ for a firm across markets and the annual exports will be adjusted correspondingly.

> 7Table 1 shows that the uniform entry assumption is not a bad approximation for the distribution of Peruvian export entrants across months. The growth rate number is designed to match the Peruvian export data on surviving exporters. The assumption of no exits from the market is clearly at odds with the firm-level evidence on new exporters. However, this assumption is useful to facilitate comparisons with growth rates of surviving entrants.

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