Exporter Dynamics, Firm Size and Growth, and Partial Year Effects for the quintile of the smallest firms and the quintile of the largest firms are given in Table 5. The left-hand columns report statistics on growth rates for the smallest quintile of firms, first using the raw, calendar data and then adjusting levels and growth rates of new exporters for the initial month of entry. The right hand pair of columns reports the same statistics for the largest quintile of firms.

The Peruvian exporter growth rate distributions in the US vary across firm sizes in much the same way as the Brazilian growth rates reported in Arkolakis (2011). Growth in the smallest firms is high on average, is skewed towards higher values, and shows a large amount of dispersion. Growth rates in the largest firms are centered around zero, are skewed towards negative growth rates and have relatively compact support.

Performing the partial year adjustments for new exporters, we find large changes in the features of the distribution that vary systematically across the size groups. Figure 9 shows characteristics of the growth rate distribution for the smallest and largest size quintiles of firms. The partial year adjustments dramatically lower the mean and median growth for the group of the smallest firms and shift the distribution of their growth rates leftward over the entire range but particularly for the highest values. The dispersion and skewness also fall for these smaller firms. As expected, the largest quintile of firms shows relatively little change since there are many fewer new exporters in this part of the firm size distribution. The distribution of growth rates for the largest firms also shifts to the left but the changes are small.

Overall we have shown that partial year effects are responsible for some of the observed regularities in the firm size distribution and the growth rate distribution for firms of different sizes. These effects provide a partial explanation for the presence of large numbers of small firms. They also reduce the mean and dispersion of growth rates for the smallest firms in the market. However, it is important to recognize that, for Peruvian exporters to the US, adjusting for partial year effects does not overturn the stylized facts on overall firm size and firm growth.

# **5.5 Employment versus Sales**

The focus of the empirical work in this paper has been on export sales and the firm size distribution measured by exports. There is every reason to believe that the findings on exports will largely be replicated when looking at overall firm sales or sales in the domestic market.<sup>25</sup> However, most of the empirical work on firm size and growth has looked at the employment levels of firms in an economy. To the extent that employment is a variable factor of production and covaries systematically with sales levels, our findings should apply more broadly to the employment size distribution and growth rates. In contrast, if labor is a fixed factor that does not adjust with firm output growth, the biases documented here for exports will be less likely to distort the empirical results based on firm

> 25Obviously, exports do differ from domestic sales in a number of dimensions, particular the level of activity, the selection of firms into the market, and the duration of the market participation spells.

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