Exporter Dynamics, Firm Size and Growth, and Partial Year Effects in the next two years to 29 and 28 percent respectively. However, adjusting for the starting month of exporting produces dramatic changes as seen in the striped columns. These same firms now show average annual growth rates in the first three years of exporting of 25, 20 and 23 percent respectively. The unusually large growth rate between years 1 and 2 is completely eliminated. Instead of an anomalous first year, new, surviving exporters grow quickly but steadily after entry.<sup>18</sup> Again the numbers with and without partial year corrections are remarkably close to those in the simple example. Unadjusted first year growth rates are 90 log points in the data and 98 log points in the example. Adjusted first year growth rates are 22 and 20 log points in the data and the example respectively.

Adjusting for the month of entry eliminates the first year growth rate anomaly and raises initial export size. Similarly adjusting for the month of exit eliminates the last year growth rate anomaly and increases the relative size of first year exports to last year exports. The results suggest that the stylized facts on growth rates and levels for new exporters may be substantially different than are typically reported in the literature.

# **4.1 Productivity and Learning-by-exporting**

Our findings on the bias in initial export levels and growth rates have potential implications beyond the new literature on exporter dynamics. The relationship between exporting and productivity remains an ongoing question for research using micro-data on firms engaged in international trade. More productive firms select into exporting but the evidence is more mixed on the existence of learning-by-exporting or, more precisely, whether productivity growth is faster at a firm after it enters the export market.

To the extent that authors have found evidence of exporting effects on productivity, the higher productivity growth is often concentrated in the period just after export entry.<sup>19</sup> The results presented here suggest that output growth, domestic plus export revenue, measured on an annual basis will be biased around the years of entry into the export market. On average, the recorded level in the year of export entry will not reflect a full year of exports and the growth rate of total firm output will be biased. The bias will be negative for firm growth between year t-1 and year t and positive between years t and t+1.<sup>20</sup>

> 18Partial year adjustments for the month of exit also eliminate the unusually rapid decline in exports just before exit. Exiting exporters decline steadily for several years before leaving the export market entirely.

> 19De Loecker (2007) argues that Slovenian firms increase their productivity after entry into the export market and finds that almost all the productivity increase in the Slovenian data occurs between the first and second years in the export market. Delgado, Farina, and Ruano (2002) find that productivity growth is higher for new exporters. Many other authors, e.g. Lileeva and Trefler (2010), report average annual growth rates for a multi-year period after exporting which attenuates but does not eliminate the bias in total firm output. In Appendix 3.2, five year average output growth rates starting in the year of export entry remain on average 7 percent above the true underlying change in annual total output.

> 20As before the bias will be greatest for firms that enter the new market later in the year.

15