Exporter Dynamics, Firm Size and Growth, and Partial Year Effects

# **1 Introduction**

The past two decades have seen an explosion of research on the microeconomic determinants of exporting and the complicated relationship between participating in foreign markets and firm performance. This new perspective on international trade has been fostered by access to increasingly detailed data, starting with census data on whether or not an establishment, or firm, exports in a given year, and continuing with panel data at the transaction level from individual customs records with information on exports at the level of the firm-product-destination-year. The most recent round of research is now matching individual sellers to individual buyers by destination, product and year.<sup>1</sup> A growing literature, both empirical and theoretical, is considering the firm-level evolution and dynamics of exports over time by examining the process of entry and growth.

This paper focuses on one specific issue that touches on most of the existing empirical work on export entry and performance and suggests caution when approaching the disaggregated data. The concept is quite simple, almost trivial, yet the implications for the existing stylized facts on export levels and growth rates are profound. Consider two otherwise identical firms that enter the same market in different months, one in January and one in December. These two firms, starting at the same initial size and growing at the same rate per month, will report dramatically different annual sales for the first calendar year of operations. The January entrant will record a full 12 months of sales and its growth rate from its first to second year will reflect the true underlying annual growth rate of the firm in the market. The December entrant, in contrast, will only record one month of sales for its first year so the calendar, or annual sales, of the December firm will be biased downwards relative to its actual sales during its first year in the market. Similarly the recorded first year growth rate of the December firm will be biased upwards as one month of sales will be compared to as many as 12 months of sales in the second calendar year.

This “partial year” effect contaminates all the statistics about market entrants that depend on the first year of activity. For example, the average level of exports for entering firms will contain a downward bias, depending on the distribution of entry months over the year, and the average first year growth rate of entrants will be biased upward. Measures that flow from these averages will, in turn, contain the same bias. There is, of course, a comparable bias in the last year of exporting when the firm totals are based on calendar years. Exiting firms will appear to have annual sales that are lower than the total for their last 12 months of operations and their growth rates just before exit will be biased downward.

This partial year effect in annual data has the potential to lead to large downward biased observations of level of activity upon entry as well as to large upward biased growth rates between the year of entry and the following year. This paper examines the implications of partial year effects

> 1See Blum, Claro, and Horstmann (2011), Eaton, Eslava, Jinkins, Krizan, and Tybout (2012), Bernard, Moxnes, and Ulltveit-Moe (2013), and Carballo, Ottavianio, and Martincus (2013).

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