metadata: authors: 0: author: Bernard, Andrew B.
1: author: Massari,Renzo
2: author: Reyes,Jose Daniel
3: author: Taglioni,Daria
count: World
docna: 0: docna: Exporter dynamics, firm size and growth, and
            partial year effects
docty: Policy Research Working Paper
subtopic: Consumption,Fiscal & Monetary Policy,Economic Conditions and Volatility,International Trade and Trade Rules,Trade and Services,Inequality
teratopic: Poverty Reduction,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Two otherwise identical firms that enter
            the same market in different months, one in January and one
            in December, will report dramatically different annual sales
            for the first calendar year of operations. This partial year
            effect in annual data leads to downward biased observations
            of the level of activity upon entry and upward biased growth
            rates between the year of entry and the following year. This
            paper examines the implications of partial year effects
            using Peruvian export data. The partial year bias is very
            large: the average level of first-year exports of new
            exporters is understated by 65 percent and the average
            growth rate between the first and second year of exporting
            is overstated by 112 percentage points. This paper
            re-examines a number of stylized facts about firm size and
            growth that have motivated rapidly expanding theoretical and
            empirical literatures on firm export dynamics. Correcting
            the partial year effect eliminates unusually high growth
            rates in the first year of exporting, raises initial export
            levels, and shifts 10 percent of market entrants from below
            to above the median size. Revisiting an older set of facts
            on firm size and growth, the paper finds that correcting for
            partial year biases reduces the number of small firms in the
            firm size distribution and weakens the negative relationship
            between firm growth and firm size.
repnme: repnme: Exporter dynamics, firm size and growth,
            and partial year effects
display_title: Exporter dynamics, firm size and
            growth, and partial year effects
listing_relative_url: /research/2013/11/18554162/exporter-dynamics-firm-size-growth-partial-year-effects
topicv3: Macroeconomic Vulnerability and Debt
            m1326057 1104,Poverty m1326687 695,Trade m1326924 698,Trade in Services m1326928 780,Macroeconomic and Structural Policies
            m1327380 439
publishtoextweb_dt: 2013-11-01T00:00:00Z
historic_topic: Poverty Reduction,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 34
author_keys: 0: author_key: 1201219
1: author_key: 941773
2: author_key: 1155075
model_extractions: WPS6711 Policy Research Working Paper 6711 _Andrew B. Bernard Renzo Massari Jose-Daniel Reyes Daria Taglioni_ The World Bank Poverty Reduction and Economic Management Network International Trade Unit November 2013
Policy Research Working Paper 6711

# **Abstract**

Two otherwise identical firms that enter the same market in different months, one in January and one in December, will report dramatically different annual sales for the first calendar year of operations. This partial year effect in annual data leads to downward biased observations of the level of activity upon entry and upward biased growth rates between the year of entry and the following year. This paper examines the implications of partial year effects using Peruvian export data. The partial year bias is very large: the average level of first-year exports of new exporters is understated by 65 percent and the average growth rate between the first and second year of exporting is overstated by 112 percentage points. This paper re-examines a number of stylized facts about firm size and growth that have motivated rapidly expanding theoretical and empirical literatures on firm export dynamics. Correcting the partial year effect eliminates unusually high growth rates in the first year of exporting, raises initial export levels, and shifts 10 percent of market entrants from below to above the median size. Revisiting an older set of facts on firm size and growth, the paper finds that correcting for partial year biases reduces the number of small firms in the firm size distribution and weakens the negative relationship between firm growth and firm size.

This paper is a product of the International Trade Unit, Poverty Reduction and Economic Management Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at jreyes2@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Exporter Dynamics, Firm Size and Growth, and Partial Year Effects<sup>_∗_</sup> Andrew B. Bernard<sup>_†_</sup> Jose-Daniel Reyes<sup>_§_</sup> Daria Taglioni<sup>_¶_</sup>

**Keywords:** firm size distribution, firm growth, variance of firm growth, export entry, export growth, heterogeneous firms **JEL codes:** F14, L11, C81, D22 **Sector Board:** Economic Policy (EPOL)

> _∗_ We thank Emily Blanchard, Teresa Fort, Ana Fernandes and seminar participants at the World Bank for helpful comments and discussions. Any opinions or conclusions expressed herein are those of the authors and do not necessarily reflect those of the IBRD/World Bank and its affiliated organizations, the Executive Directors of the World Bank or the governments they represent, the NBER or any other institution to which the authors are affiliated.

> _†Tuck School of Business at Dartmouth, CEPR & NBER_ , 100 Tuck Hall, Hanover, NH 03755, USA, _tel:_ +1 603 646 0302, _email:_ andrew.b.bernard@tuck.dartmouth.edu

> _‡World Bank_ , 1818 H Street NW, Washington, DC 20433, USA, _tel:_ +1 202 473 8519 , _email:_ rmassari@worldbank.org

> _§World Bank_ , 1818 H Street NW, Washington, DC 20433, USA _tel:_ +1 202 458 7052, _email:_ jreyes2@worldbank.org

> _¶World Bank_ , 1818 H Street NW, Washington, DC 20433, USA _tel:_ +1 202 458 5264, _email:_ dtaglioni@worldbank.org
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).

1
Exporter Dynamics, Firm Size and Growth, and Partial Year Effects using transaction-level export data on Peruvian exports from 1992-2009. The partial year bias is found to be very large, causing the level of first-year exports of all new exporters to be understated by 65 percent on average and overstating the average growth rate between the first and second year of exporting by 112 percentage points. Similar partial year effects are found in the year of exit from the market.

Empirical work using annual firm-level export data by Eaton, Eslava, Kugler, and Tybout (2008) and others has documented a set of strong empirical regularities about the performance of exporters over time. These regularities include the fact that new market entrants, either new exporters or continuing exporters in new markets, have small levels of exports upon entry, a large fraction of entrants export for only a single year before exiting the market, and surviving entrants have extremely rapid export growth between years one and two with more modest growth rates subsequently. These facts have been taken as evidence against models of high sunk costs of entry into export markets as in Roberts and Tybout (1997) and have generated a growing literature on learning and experimentation in export markets.

Correcting for the partial year bias in the calendar year exports of new market entrants eliminates or dramatically mitigates most of these stylized facts. Surviving new entrants still have smaller initial levels than ongoing exporters but on average their adjusted first year sales are increased by more than 76 percent. Surviving entrants have adjusted exports in their first year that are 160 percent greater than those recorded in the annual data. Extremely rapid growth rates in the first year of exporting, average rates well over 100 percent are typical, are completely eliminated for surviving entrants. Growth rates in the first year are no different on average from those in subsequent years after adjusting for the month of entry.<sup>2</sup> In addition, we examine the implications of the partial year bias for an older set of facts on firm size and growth that have been the focus of substantial research in industrial organization. A large fraction of firms are new to the market in each year; from 1994 to 2007, 45.8 percent of Peruvian exporters were new to the US market each year. New entrants are a sizable fraction of firms even in developed economies. Over the same period, an average of 10.5 percent of active US firms (513,000) began operations each year. Correcting for partial year biases increases the average size of new entrants into exporting, reduces the number of small firms in the market, and shifts the overall structure of the firm size distribution of exporters. More than 10 percent of new Peruvian exporters move from below to above the median firm size after adjusting for the partial year bias with commensurate adjustments to their first year growth rates. The adjustments also weaken the negative relationships between firm growth and its variance and firm size as the level and dispersion of growth rates for the smallest quintile of market participants are reduced.

The empirical approach of this paper is heavily influenced by Arkolakis (2011) who develops

> 2Firm exit rates remain very high for new entrants in export markets.

2
Exporter Dynamics, Firm Size and Growth, and Partial Year Effects an analytical framework to study firm and export growth and evaluates the model by comparing results of calibration exercises with the growth of sales of US firms as well as with Brazilian export sales to the US. His argument that the same processes are at work within an economy and in export markets as firms search for customers motivates us to use export data to analyze the impact of partial years for new entrants in a market.

# **The characteristics and performance of new exporters**

The empirical literature on the dynamics of firm-level exports was initiated by the work of Eaton, Eslava, Kugler, and Tybout (2008) on Colombian exporters. Eaton, Eslava, Kugler, and Tybout (2008) set out to generate a new set of stylized facts on export dynamics and destination-specific flows for the same set of producers using annual trade transaction data for Colombian firms. In the abstract to the paper, they state “that nearly half of all Colombian exporters were not exporters in the previous year. These new exporters tend to be extremely small in terms of their overall contribution to export revenues, and most do not continue exporting in the following year.... Nonetheless, out of each cohort of new exporters, a fraction of firms go on to expand their foreign sales very rapidly....” Empirical work on annual firm-level export data that confirms some or all of these facts for other countries includes Lawless (2009) for Irish exporters and Buono and Fadinger (2012) for French exporters.

These stylized facts in turn have been used and extended by others to motivate dynamic models of exporting and learning. In Albornoz, Pardo, Corcos, and Ornelas (2012), firms experiment in a market to learn about export profitability and then expand to new destinations. In their empirical work on Argentine exporters, they confirm the small size, low survival and rapid growth of new exporters. They report that growth rates between the first and second years in a market range from 104 to 190 percent. In every case, they find that second year growth rates in export markets are much lower and are not substantially different from growth rates in subsequent years.

Eaton, Eslava, Jinkins, Krizan, and Tybout (2012) develop a model of search and learning to explain the dynamic pattern of entry and survival by Colombian exporters and to differentiate between the costs of finding new buyers and maintaining relationships with existing ones. Aeberhardt, Buono, and Fadinger (2012) and Araujo, Mion, and Ornelas (2012) model exporter dynamics in the context of contracting, learning and institutional quality, again confirming the small size upon entry of new exporters and their subsequent rapid growth conditional on survival, using annual firm-level French and Belgian data, respectively.

Akhmetova and Mitaritonna (2012) develop a model of experimentation and learning to explain the fact that new exporters exhibit different patterns in a given market than old exporters. They emphasize the facts of Eaton, Eslava, Jinkins, Krizan, and Tybout (2012) for Colombia and Eaton, Kortum, and Kramarz (2011) for France - many new exporters ship very small quantities and 3
Exporter Dynamics, Firm Size and Growth, and Partial Year Effects surviving exporters expand rapidly.

Timoshenko (2013) focuses on a different dimension of exporter behavior, the margin of product switching. A model of learning by exporters in new markets is motivated by the fact that Brazilian exporters in their second year in the market have disproportionately greater shares of sales from new products and greater shares of new products in their product mix. Partial year effects potentially play a role in these stylized facts as well, understating the number of products sold abroad in the first year of exporting and in turn overstating the growth in number of exported products and their share in sales between years one and two.<sup>3</sup>

# **Extensive margins in trade**

A related body of work has been attempting to understand the underlying sources of aggregate export growth and the importance of the extensive margins of trade. These extensive margins include new exporters and new destinations and products by existing exporters. Typically annual export growth is decomposed into the contribution of these extensive margins and the intensive margin, i.e. the change of sales of existing products by continuing exporters to previous destinations. Bernard, Jensen, Redding, and Schott (2009) find that the annual variation in aggregate trade is dominated by the intensive margin. The small role for the extensive margin is due primarily to the small size of new entrants relative to incumbents. Related analyses have been conducted by Lawless (2009) (Ireland); Amiti and Freund (2010) (China); Van Beveren, Bernard, and Vandenbussche (2012) (Belgium); and Cebeci and Fernandes (2013) (Turkey). The conclusion in all these papers that new exporters, new export destinations and newly exported products contribute only a small fraction to overall annual export growth is subject to potential downward bias from partial year

# **Firm size distribution**

Beyond the literature on export dynamics, the issues raised in this paper relate to the extensive body of work on the firm size distribution as exemplified by Axtell (2001) and Luttmer (2007) for the domestic economy and by Eaton, Kortum, and Kramarz (2011) for exporters by destination market.<sup>4</sup> All of these papers, and many others, find that the distributions of sales, or employees, closely approximate a Pareto distribution except in the region with the smallest firms. In every case, the smallest firms are present in greater numbers than suggested by a pure Pareto distribution.

> 3Freund and Pierola (2010) focus on exporter entry and survival in products not previously exported by Peruvian firms. As most of their analysis is on entry and the duration of export spells it is not directly affected by the partial year effects discussed here. However, it remains unknown how adjusting the date of the firm’s export year to reflect the initial month of entry would affect the probability of the frequently observed pattern of entry, exit and subsequent re-entry into the export market.

> 4Related work on firm size and growth includes Evans (1987b,a), Dunne, Roberts, and Samuelson (1989, 1988), Cabral and Mata (2003), and the survey by Sutton (1997).

4
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.

5
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.

6
<!-- Start of picture text --> Size of Initial Year Exports<br>Y<br>= os Yj<br>: j<br>000<br>5cTihin-<br>0 j<br>TnYj<br>Oo<br>PEELE,<br><!-- End of picture text -->
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Exporter Dynamics, Firm Size and Growth, and Partial Year Effects example above, the first year size of new entrants is underestimated on average by 80 percent. This will cause the number of small firms to be overestimated and will lead to a corresponding distortion in the firm size distribution. Of course the extent of the bias in the firm size distribution depends on the share of new entrants in the overall number of firms but the potential magnitudes are large: in Peru more than 45 percent of firms are new to exporting each year, while in the US more than 10 percent of firms are new to the domestic market in each year.<sup>8</sup> In addition, the bias can affect attempts to understand the relationship between firm size and firm growth. Entrants are disproportionately small in the unadjusted data and thus the growth rates of the smallest firms is likely to be subject to greater overstatement.<sup>9</sup>

# **3.1 Bias Approximation**

In Table 1, we report the distribution of new Peruvian exporters across months based on their first month of exporting. There is some systematic variation over months; March, April and June have higher shares of entrants while May, July and December have lower shares. However, the monthly averages are reasonably close to what would be expected if entry were uniform across days during the year. This finding suggests both that partial-year bias is likely to be important in the Peruvian export data and that for aggregate or market-specific measures of exporting a relatively simple adjustment might be possible.

The relationship between the firm’s exports in its first full year in the market, _Xs_<sup>_true_</sup> , and the observed first year exports, _Xs_<sup>_obs_</sup> , is given by _Xs_<sup>_true_</sup> = _θsXs_<sup>_obs_</sup> , where _s_ is the month of entry into exporting. The adjustment factor for the levels of exports in the first year for each month of an entering cohort is where _r_ is a common constant compound monthly growth rate and average entry levels across months are assumed to be identical. We can also sign the partial year bias in log difference growth rates, _β_ = ∆ _log_ � _X_ 0<sup>_true_</sup> � _−_ ∆ _log_ � _X_ 0<sup>_obs_</sup> �, for a cohort of firms entering the market in year 0 as where _N_ is the total number of entrants and _N_<sup>_s_</sup> is the number of entrants in month _s_ . If shares of entering firms are constant across months, the bias in log differences can be closely approximated by

> 8The US numbers are the average share of entrants per year from 1994-2007 tabulated by the authors from the Business Dynamics Statistics database, http://www.census.gov/ces/dataproducts/bds/data.html.

> 9In the raw data, more than 76 percent of the bottom decile of Peruvian exporters to the US are new entrants.

9
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Exporter Dynamics, Firm Size and Growth, and Partial Year Effects

## 18.1 percent for January entrants.<sup>11</sup>

If calendar years corresponded with the start of exporting, as they do for the January entrants, then growth rates for these firms should be constant except for the year of entry into exporting. The growth rate of total output between year t-1 and year t will be twice as large as any other year as the exports are added to domestic sales. With the assumption that exports and domestic sales grow at the same rate, growth rates for earlier periods and subsequent periods should be identical. However, partial year effects bias the total output growth for entrants after January in both the year of entry and in the first year of exporting.

Figure 3 shows the four annual total output growth rates for firms entering in each month. For all firms, the growth rates before entry and after the first year of exporting are identical. Partial year effects bias the measures of total firm growth both between the last year without exports and the year of entry into exporting and between the first and second years in the export market. Except for January entrants, other monthly export cohorts have total output growth rates biased downwards between years t-1 and t and growth rates biased upwards between the first and second years in the export market. Firms that enter later in the year show higher growth rates between t and t+1 without adjustments for the month of export entry. On average, total output growth in between years t-1 and t is biased down by 13.1 percentage points or 36 percent, while total output growth in the first year after the start of exporting is biased up by 7.9 percentage points or 37 percent without partial year adjustments.

The magnitude of the bias in total firm growth depends on the level of domestic sales (the export to sales ratio) upon export entry and the underlying growth of domestic and export outputs.<sup>12</sup>

# **4 Growth and Levels of Surviving Peruvian Exporters**

In this section, we turn our focus to the two main stylized facts from the literature on firm export dynamics: the small levels of exports in the initial year in the market and the very high average growth rate for surviving firms between years one and two. We examine the levels and growth rates of continuing Peruvian exporters using both raw, calendar years (covering twelve months from January through December) and years adjusted for the initial month of exporting (covering twelve months from the first month _m_ of exports in year _t_ through month _m-1_ in year _t+1_ ).<sup>13</sup> The goal in this section is to estimate the log level of exports for new exporters during their initial years in the market. From the estimated levels, we can calculate the associated growth rates with and without

> 11Initial domestic sales are assumed to be 300 in month 1 of year t-2. Initial export sales are assumed to be 100 in the month of entry in year t. The differences in the export to sales ratios come from the greater size of domestic sales for firms that start exporting later in the year.

> 12We reiterate that partial year effects in total output should appear in measures based on either revenue or quantity.

> 13We adjust for the final month of exporting in a similar fashion. The last year of exports covers twelve months from month _l+1_ in year _t-1_ through the last month _l_ of exports in year _t_ .

11
Exporter Dynamics, Firm Size and Growth, and Partial Year Effects adjusting for partial year effects. Our focus on continuing exporters matches that of the empirical literature on exporter dynamics that explores the growth pattern of surviving exporters.<sup>14</sup> To conduct the exercise we first select a sample of firms with enough data to be able to compare the levels of exports in the initial three years after export entry to export levels in subsequent (nonexit) years. Similarly we examine exports in the final three years of exporting. The sample includes all firms who export for at least four years and have just one change in their export status (entry or exit but not both) for measures of calendar year exports and exports adjusted for the initial month.<sup>15</sup> These criteria mean that firms with gaps in their annual exports (by either method) are excluded, as are all firms who export for brief spells, defined as fewer than 4 consecutive years. The number of firms in the sample is reduced from the overall population of Peruvian exporters because many firms enter and then exit, a large number of firms in the data enter after 2005, and a smaller number of firms have multiple spells of exporting with a gap of at least one calendar year. After limiting our sample in this manner we are left with 2352 firms and 10,580 firm export-years.

For the sample of “continuing” exports we estimate the following regression, where _lnYit_ is the log exports of firm _i_ in year _t_ , _δi,t_<sup>_entry_</sup> _−n_<sup>isanindicatorthatequalsoneiffirm</sup><sup>_i_</sup> started exporting in year _t − n_ , i.e. _Yi,t−n−_ 1 = 0, _Yi,t−n >_ 0, and _δi,t_<sup>_exit_</sup> + _x_<sup>isanindicatorthatequals</sup> one if the firm stopped exporting in year _t_ + _x_ , i.e. _Yi,t_ + _x−_ 1 _>_ 0, _Yi,t_ + _x_ = 0. The regression is run on the same set of firms, once using the raw calendar year data and once using the data adjusted for the initial export month. Standard errors are clustered at the firm level.<sup>16</sup> Table 2 reports coefficients on dummy variables for the first, second and third year of exporting and the last, second to last, and third to last year of exporting. Firm and year fixed effects are included so all coefficients give log levels relative to average firm exports in years outside the first three and last three.

Figure 4 shows the average within-firm deviations in percentages for new exporters in their first three years and exiting exporters in the last three years. The baseline is the within-firm average over the period of active exporting. The red series of circles is calculated from the raw data without any partial year corrections. These numbers correspond to the often-reported facts about exiting and especially entering exporters. New exporters are small at entry, 75 percent below their within sample average. However within several years most of the difference is erased, in their third year of exporting these firms are just 22 percent below their average. Similarly firms contract in the years

> 14We also estimate levels and growth rates for exiting firms in their last years in the market.

> 15It is important to make sure there are no 12 months gaps in either the annual calendar data or the data adjusted for initial months as no gaps in one series does not necessarily mean no gaps in the other.

> 16This specification means that we lose several years of data at the beginning and end of the sample period so that all the dummies are correctly specified for every firm.

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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.

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Exporter Dynamics, Firm Size and Growth, and Partial Year Effects some exports in the following calendar year t+1. The solid columns are the average first year growth rates by month of entry for all firms using the raw calendar data. The growth rates are given as the deviation from the average across all months and years. As expected, partial year effects cause the growth rates based on the calendar year data to rise systematically across the months with the lowest for January entrants (81 log points below the mean) and the highest for December entrants (108 log points above the mean). The striped columns show the same growth rates relative to the mean for first year export growth adjusting for the month of entry. The systemic relationship between entry month and export growth is eliminated and the pattern partly reverses.<sup>21</sup> On average the growth rates of all new exporters is 112 percent higher using calendar year data instead of the adjusted data.

# **5.2 Export Levels of Entrants**

Table 3 reports the average size of all new exporters in their first year relative to continuing exporters by year for the entire set of firms. As emphasized in the exporter dynamics literature, entrants are indeed much smaller than continuing exporters. However, adjusting for partial year effects increases entrant size by 65 percent.<sup>22</sup> In addition there is a noticeable downward trend over time in the relative size of entrants, calculated by either method. This decline is due to the systematic increase in the size of continuing exporters rather than a decline in the size of entrants. Table 4 shows that adjusting for partial year effects varies systematically across months. Entrants in December on average have a 599 percent increase in the measured first year exports.

# **5.3 Firm Size Distribution**

The downward bias in levels for new exporters in a market has the potential to shift the export firm size distribution. In the raw data typically used to calculate the firm size distribution, new entrants are not measured with a full year’s sales in the market. Measuring their firm size with a full year of export sales would increase their size and since exporters are typically smaller firms these adjustments should have the biggest effects in the left tails of the distribution. We investigate the effects of partial year effects on the export size distribution of Peruvian firms in the US market.<sup>23</sup> As is the case in many exporting countries, a large fraction of Peruvian exporters are new to the market each year. The US market is no exception, fully 45.8 percent of Peruvian exporters in the US are new in each year. These new exporters vary substantially in initial size. Figure 7 shows the percentage of new exporters in the export size distribution for firms serving the US market. The

> 21The lower growth rates for entrants in later months comes from a truncation of the sample. Firms are included if they report exports in years t and t+1 whether or not they continue to export past December, t+1. The later months include a greater fraction of firms that no longer export to the US in year t+2 and thus have small exports in their second year in the market due to exit.

> 22This is twice as large as the size correction reported for new French exporters by Berthou and Vicard (2013).

> 23The patterns in other destinations market are largely unchanged.

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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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Exporter Dynamics, Firm Size and Growth, and Partial Year Effects employment. The extent to which partial year effects are important in analyses of employment levels and growth across firms remains a question for future research.

# **6 Conclusion**

This paper has taken a first step towards a deeper understanding of the performance of firms in their first years in a market. The motivation for the work is the rapidly growing literature on firm export dynamics that is heavily based on the twin stylized facts that exporters start small and grow very rapidly in their first year in the foreign market. This paper shows that these two facts are largely explained by the fact that exporters enter the market throughout the year and only part of their first year sales are recorded in the calendar year of entry.

Aggregated to the calendar year, the Peruvian data used in this paper match the stylized facts in the literature quite closely. Adjusting for the month of entry changes the findings dramatically. Exporters are larger upon entry, although still smaller than continuing exporters, and their growth in their first year in the market is no different from subsequent years. The motivating stylized facts on new exporter size and growth are not robust to partial year adjustments.

These findings have implications for a variety of research efforts using detailed micro-data on exports. A number of papers have examined the contributions of extensive and intensive margins to annual export growth and during specific events such as the Asian Crisis and the Great Recession. The use of annual data will understate the contribution of the extensive margins in annual export growth. New exporters will contribute less to overall growth in their year of entry because only part of their first year sales are recorded. Symmetrically their growth rates will be biased upwards between the year of entry and the following year and will be recorded as increases in the intensive margin of exporting.

Partial year effects also distort total firm growth in and after the year of export entry. The growth rates between year t-1 and t, the year of export entry, will be reduced and the growth rate between t and t+1 biased upward. Depending on the timing of input purchases this may lead to perceived higher productivity growth after entry and mistaken conclusions that there is learning-by-exporting.

The potential consequences of partial year effects go beyond firm export dynamics and include effects on the firm size distribution and the relationships between firm size and growth. We examine the implications for the firm size and growth distributions of Peruvian exporters in the US market. After adjusting for partial year effects the size distribution is shifted to the right (towards large firm sizes), albeit modestly, and the growth distribution of the smallest firms in the market is shifted to the left (towards lower growth rates). More work using data on firms active in the domestic market is needed to understand how important the partial year effect is for measures of output and employment growth and for the overall firm size distribution.

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Exporter Dynamics, Firm Size and Growth, and Partial Year Effects The consequences of partial year effects may extend to work on more aggregated data such as that assembled in the Exporter Dynamics Database at the World Bank and described by Cebeci, Fernandes, Freund, and Pierola (2012). Stylized Fact 1 in that paper states that more developed and larger countries have larger average exporter size and exhibit significantly lower exporter entry and exit rates. However, the findings reported here suggest that large shares of entrants and exits will by themselves be likely to induce downward bias in firm size as measured in unadjusted annual export flows. As a result, the cross-country correlation between average exporter size and GDP per capita may be driven in part by partial year effects. The importance of entry and exit in the exporting sector and the reliance on export value data for analysis means that such comparisons based on even aggregate data must be viewed with caution.

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