The Lumpiness of German Exports and Imports of Goods

This paper looks at a hitherto neglected extensive margin of international trade by investigating for the first time the frequency at which German exporters and importers trade a given good with a given country. Imports and exports show a high degree of lumpiness. In a given year about half of all firm-good-country combinations are recorded only once or twice for trade with EU-countries, and this is the case for more than 60 percent of all firm-good-country combinations in trade with non-EU countries. The frequency of recorded transactions tends to decline with an increase in the number of transactions per year. This is in accordance with the presence of per-shipment fixed costs that provide an incentive for trading firms to engage in cross-border transactions infrequently. Empirical models show that for Germany the frequency of transactions at the firm-good-country level tends to decrease with an increase in per-shipment costs when unobserved firm and goods characteristics are controlled for.


Motivation
International trade is costly.While tariff-type trade restrictions tend to play a diminishing role only today, other barriers to trade still matter.Hornok and Koren  (2015a) argue that some of these trade costs are not proportional to the value of the transaction.Hence, the assumption of iceberg-type trade costs used in most models of international trade is not appropriate here.There are fixed costs that come with every shipment across borders.These costs include paper work (filling in customs declarations and other forms) and the time and monetary costs related to having the cargo inspected.These fixed costs lead to a trade-off between per-shipment trade costs and shipping frequency.On the one hand, firms engaged in international trade would like to economize on these per-shipment costs by sending fewer and larger shipments.On the other hand, this comes at a cost due to timelags related to waiting to fill a larger shipment and because of the need to keep costly inventories between shipment arrivals.At the firm level, shipping frequency can be considered as an additional margin of trade besides the intensive margin (the volume of trade) and the extensive margins made of the number of goods traded and the number of countries traded with (see Békés et al. 2011).That said, per-shipment costs may make it optimal for traders to engage in cross-border transactions infrequently.If this is the case, trade flows at the microeconomic level -imports by one firm of one good from one country of origin, or exports by one firm of one good to one country of destination -are lumpy.Empirical evidence on the lumpiness of international trade has been reported in a small number of studies.Alessandria et al. (2010) use monthly data on the universe of US exports for goods in narrowly defined categories to six destination countries from January 1990 to April 2005 and find that goods are traded infrequently over the course of a year.Exports are lumpy, trade is highly concentrated in a few months.Békés et al. (2015) explore transaction level data for exports from France in 2007 at the firm-product-destination level and approximate the number of shipments by the number of months within a year in which a transaction is recorded for a given firm-product-destination.A large number of firms ship their products only in a few months.The authors report a high degree of lumpiness in exports -almost 45 percent of firms ship a given product to a given destination only once a year to EU markets and more that 60 percent do so to extra-EU markets.Hornok and Koren (2015a) examine disaggregated data on exports of the United States and Spain in 2009 and look at the lumpiness of trade transactions by documenting how frequently the same good is exported to the same destination country within a year.Trade transactions for a given product to a given destination show strong signs of lumpiness.Kropf and Sauré (2014) look at transaction level data for Swiss exports from 2007, a subset of which contains a firm identifier so that export data are at the firm-product-destination level.Exports are lumpy; the mean value of shipments per year is 3.5.Hornok and Koren (2015a) investigate how the frequency and the size of shipments vary with the level of per-shipment costs.They estimate a number of gravity-like regressions (that include variables for GDP and GDP per capita of destination countries, and distance to destination countries of exports, among others, as control variables) for exports of the US and Spain at the product-country level and find that the number of shipments decrease ceteris paribus when the time costs or the monetary costs per shipment increase.
Up to now, we have no evidence on the degree of lumpiness of international trade in goods by German firms and its relation to per-shipment costs.Given that Germany is one of the leading actors on the world market for goods (according to the WTO's World Trade Report, it was number three in both exports and imports in 2013; see World Trade Organization (2014, p. 34)), empirical evidence here is interesting in itself.This paper contributes to the literature by providing such evidence based on transaction data for complete German exports and imports at the firm-good-country level for the years 2009 to 2012.
To anticipate the most import results I document that imports and exports show a high degree of lumpiness.In a given year about half of all firm-goodcountry combinations are recorded only once or twice for trade with EU-countries, and this is the case for more than 60 percent of all firm-good-country combinations in trade with non-EU countries.Empirical models show that the frequency of transactions at the firm-good-country level tends to decrease with an increase in per-shipment costs when unobserved firm and goods characteristics are controlled for.
The rest of the paper is organized as follows.Section 2 introduces the data used and discusses measurement issues.Section 3 reports descriptive results for the lumpiness of German exports and imports of goods.Section 4 presents results from regressions of the number of shipments on per-shipment costs.Section 5 concludes.

Data and measurement issues
The empirical investigation uses a tailor-made data set that combines high quality transaction level data on Germany's exports and imports of goods from official statistics with data on per-shipment costs in international trade plus other information for characteristics of the countries traded with.
In Germany information on goods 1 traded across borders and on the countries traded with is available from the statistic on foreign trade (Außenhandelsstatistik).This statistic is based on two sources.One source is the reports by German firms on transactions with firms from countries that are members of the European Union (EU); these reports are used to compile the so-called Intrahandelsstatistik on intra-EU trade.The other source is transaction-level data collected by the customs on trade with countries outside the EU (the so-called Extrahandelsstatistik). 2 The raw data that are used to build the statistic on foreign trade are transaction level data, i.e. they relate to one transaction of a German firm with a firm located outside Germany at a time.Published data from this statistic report exports and imports aggregated at the level of goods traded and by country of origin.
The data used in this paper are based on the raw data at the transaction level.The unit of observation in these raw data is a single transaction between economic agents located in two countries, e.g. the import of X kilogram of good A with a value of Y Euro from China to Germany. 3 For a given year, the sum over all transactions is identical to the figures published by the Federal Statistical Office for total exports or imports of Germany.

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1 Note that in Germany information on international trade in services is compiled by the German Central Bank (Deutsche Bundesbank) to build the balance of services trade (Dienstleistungsbilanz). 2 Note that firms with a value of trade with EU-countries that did not exceed 400,000 Euro in the previous year or in the current year per direction of trade do not have to report to the statistic on intra-EU trade.For trade with firms from non-member countries all transactions that exceed 1,000 Euro (or have a weight that exceeds 1,000 kilogram) are registered.For details see Statistisches Bundesamt, Qualitätsbericht Außenhandel, Januar 2011, Wiesbaden.3 Transaction level data of this type have been used in numerous empirical studies on international trade for many countries in recent years; see Wagner (2016) for a survey.
The record of the transaction usually includes a firm identifier (tax registration number) of the trading German firm. 4Using this identifier information at the transaction level can be aggregated at the level of the trading firm.These data show which firm trades how much of which good with firms from which country in a given month.Products are distinguished according to very detailed classifications.In the data used for this paper, the Harmonized System at 6-digit level (HS6) is used as the product classification system.
For the reporting years 2009 to 2012 the transaction level data at the monthfirm-product-country level were used to compute a proxy-variable for the frequency of export or import transactions by one firm for one HS6-good and one country in a year.This proxy-variable is given by the number of months in a year in which transactions of this firm-good-country combination are recorded.Note that within a month all exports or imports of a specific HS6-good to a specific country by a firm are aggregated and reported as one data point only.Therefore, the proxy for trade frequency used here may be biased for high frequency traders which trade the same good with the same country in (nearly) every month several times.For low frequency traders, however, the number of months with recorded transactions is a reliable approximation (see the discussion in Békés et al. 2015).
The transaction level data at the firm-good-country level were matched to country-specific information that is taken from two sources.
Information on two types of per-shipment trade costs is taken from the World Bank's Doing Business Data Base (see www.doingbusiness.org).Doing Business measures the time and cost (excluding tariffs) necessary to complete every official procedure that is needed for exporting and importing a standardized cargo of goods by ocean transport.Time is recorded in calendar days, costs are in U.S. dollars; for details see appendix. 5ote that the time and cost of ocean transport are not included in the cost indicators from the Doing Business data base.The time dimension of transport can _________________________ be considered as another per-shipment cost -it takes X days to ship a container from Germany to country Y, irrespective of the amount of goods in this container.Time for transport is closely linked to distance between countries.Therefore, distance is included as another trade cost variable.Data on distance between Germany and the countries of origin of imports, and the countries of destination of exports, are taken from the CEPII's GeoDist database (Mayer and Zignago 2011).The "distw" -measure is used that calculates the distance between two countries based on bilateral distances between the biggest cities of those two countries, those inter-city distances being weighted by the share of the city in the overall country's population (see Mayer and Zignago (2011, p. 11) for details).
The empirical models that link the number of international trade transactions at the firm-good-country level to per-shipment costs of trade include two control variables that are standard in gravity models of trade, namely Gross National Income and per capita Gross National Income (see Hornok and Koren (2015a) for a similar approach).Gross National Income per capita (measured in current US-Dollar) is taken from the Doing Business database directly, Gross National Income is calculated from the per capita values and the size of the population reported in the data base. 6n the empirical study two groups of trade partner countries are distinguished, namely countries that are members of the European Union (EU) and Non-EU countries.This controls for the cutoff-point used when imports from and exports to EU-members are recorded.Furthermore, information on per-shipment costs is not relevant for intra-EU trade._________________________ 6 Note that information whether a country is landlocked or not (that is available from CEPII's GeoDist database described in Mayer and Zignago (2011) and that has been used in the literature on the lumpiness of trade) is not used here because this country characteristic is closely related to the time and monetary costs of exports and imports.

3
The lumpiness of German exports and imports: Descriptive evidence The degree of lumpiness of trade is measured by the number of import or export transactions at the firm-product-country level.In the German trade data used here trade frequency is measured by the number of months in a year in which transactions of this firm-good-country combination are recorded.Note that within a month all exports or imports of a specific HS6-good to or from a specific country by one single firm are aggregated and reported as one data point only.Therefore, the proxy for trade frequency used here may be biased for high frequency traders which trade the same good with the same country in (nearly) every month several times.For low frequency traders, however, the number of months with recorded transactions is a reliable approximation (see the discussion in Békés et al. 2015).
That said, information on the lumpiness of German trade in goods is reported in Table 1 to Table 8.All data are for the reporting year 2012. 7Information is provided for trade with EU-countries and non-EU-countries separately.
To begin with imports, Table 1 shows a high degree of lumpiness.About half of all firm-good-country combinations are recorded only once or twice for imports from EU-countries, and this is the case for 70 percent of all firm-good-country combinations in imports from non-EU countries.The frequency of recorded transactions tends to decline with an increase in the number of transactions per year.This is in accordance with the presence of per-shipment fixed costs that provide an incentive for importers in engage in cross-border transactions infrequently.However, there is a remarkable increase in the frequency of the number of transactions when it comes to twelve transactions per year.This might be due to the fact (mentioned above) that within a month all imports of a specific HS6-good from a specific country by one single firm are aggregated and reported as one data point only.Therefore, the proxy for trade frequency used here may be biased for high frequency traders which trade the same good with the same country in (nearly) every month several times.Table 2 and Table 3 report more detailed information by looking at four of the most important countries of origin for German imports of goods, namely the Netherlands and France from the EU, and the US and China from outside the EU.The big picture is highly similar if results for these countries are compared to results reported for the EU as a whole, or for all non-EU countries, in Table 1.Appendix Table 1 reports the average number of import transactions per year by firm-good-country of origin for countries of origin with more than 5,000 recorded import transactions in 2012.The degree of lumpiness varies widely over the countries.Within the EU, the average number of transactions is 3.31 for Luxembourg and 4.63 for the Czech Republic.Outside the EU, imports from the United Arab Emirates (1.82), Hong Kong (1.98) and Australia (2 (4.00) and Switzerland (2.67), or Sweden (3.98)  and Norway (2.16).Table 4 illustrates that the degree of lumpiness of imports differs between goods (classified by section at the HS2 level) when EU membership is controlled for.For example, live animals and animal products (HS2-section 1) have the lowest degree of lumpiness in imports for both EU-members and non-members.This does not come as a surprise -it is obvious that an importer will only rarely trade all the beef he intends to import over the year from Poland or Brazil in one deal.Other figures in the table are more difficult to understand -for example, why is the extra-EU trade with "Pulp, paper, paperboard and articles thereof" (HS2section 10) so lumpy?Is this due to trade costs related to the countries of origin?This will be investigated empirically in the next section of the paper.But before this, we will look at exports.Table 5 shows that the big picture for exports is very much the same as the one for imports (documented in Table 1) -exports are lumpy, the degree of lumpiness is much larger for trade with non-EU countries than for trade with EU-countries, and there is a remarkable increase in the frequency of the number of transactions when it comes to twelve transactions per year.Compared to imports, exports tend to be less lumpy, but the difference is small.Table 6 and Table 7 report more detailed information by looking at four of the most important destination countries for German exports of goods, namely the Netherlands and France from the EU, and the US and China from outside the EU.The big picture is highly similar if results for these countries are compared to results reported for the EU as a whole, or for all non-EU countries, in Table 5. Appendix Table 2 reports the average number of export transactions per year by firm-good-destination country for destination countries with more than 5,000 recorded export transactions in 2012.The degree of lumpiness varies widely over the countries.Within the EU, the average number of transactions is 5.29 for Austria and 2.85 for Malta.Outside the EU, imports from Syria (1.67), Ethiopia (1.71) and Libya (1.78) show a high degree of lumpiness compared to countries Table 8 illustrates that the degree of lumpiness of exports differs between goods (classified by section at the HS2 level) when EU membership is controlled for.Similar to the case of imports discussed above, some of these differences are easily explained by the characteristics of the goods traded (e.g., the low degree of lumpiness in exports of "Live animals; animal products" -HS2-section 1 -and in exports of "Prepared foodstuffs; beverages; tobacco" -HS2-section 4) while  others are not (e.g., the high degree of lumpiness in exports of "Footwear, headgear, umbrellas" -HS2-section 12-in trade with non-EU members).

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The big picture on the lumpiness of trade reported for Germany is in line with the empirical evidence (summarized in Section 1 above) for exports from the U.S., France, Spain and Switzerland.The role of differences in trade costs between the destination countries of exports or the countries of origin of imports for an explanation of differences in the degree of lumpiness of exports or imports will be investigated in the next section.

Per-shipment costs and the lumpiness of German exports and imports: Econometric results
One empirical fact documented in Section 3 is the large difference in the degree of lumpiness of imports and of exports in trade with EU-members on the one hand and with non-EU countries on the other hand.This might be due to the much lower per-shipment costs in trade with EU-countries, because there are no costs related to customs' procedures in intra-EU trade.However, this might be due to different concepts used to record the trade with EU-countries and non-EU countries (see Footnote 2), too.Given that information on per-shipment costs (detailed below) is relevant for extra-EU trade only we will focus on trade with countries outside the EU for the rest of this section.

Empirical strategy
Information on two indicators of per-shipment trade costs is taken from the World Bank's Doing Business Data Base (see www.doingbusiness.org).Doing Business measures the time and cost (excluding tariffs) necessary to complete every official procedure that is needed for exporting and importing a standardized cargo of goods by ocean transport.Time is recorded in calendar days, costs are in U.S. dollars.The data used here (that are discussed in detail in the appendix) are taken from the report for 2013 and refer to June 2012.8Note that the time and cost of ocean transport are not included in the cost indicators from the Doing Business data base.The time dimension of transport can be considered as another per-shipment cost -it takes X days to ship a container from Germany to country Y, irrespective of the amount of goods in this container.Time for transport is closely linked to distance between countries.Therefore, distance is included as another trade cost variable (for details, see Section 2 above).
The value of an indicator of per-shipment costs varies widely between countries.The figures for the 151 non-EU countries included in the econometric investigation are reported in Appendix Table 3.The time necessary to complete every official procedure that is needed for exporting and importing a standardized cargo of goods by ocean transport is between 5 days (Hong Kong) and 81 days _________________________ (Kazakhstan) for exports, and between 4 days (Singapore) and 101 days (Chad) for imports.Cost (excluding tariffs) necessary for this is between 435 US-Dollar (Malaysia) and 8,450 US-Dollar (Tajikistan) for exports, and between 420 US-Dollar (Malaysia) and 9,800 US-Dollar (Tajikistan) for imports.Distance between Germany and the country of origin of imports or the destination country of exports varies between 543 kilometers (Switzerland) and 18,220 kilometers (New Zealand).
To see how these per-shipment costs are related to the degree of lumpiness of imports and exports in German trade with goods with non-EU countries in 2012, empirical models are estimated with the number of transactions for firm-HS6goodcountry combinations as the endogenous variable and trade-cost variables measured at the level of the country of origin (for imports) or destination country (for exports) plus data on other characteristics of the country.Some of the empirical models include fixed effects for the firms engaged in international trade and the goods traded (discussed in detail below).
In the econometric investigation six variants of empirical models are estimated that include different sets of exogenous variables.Model 1, Model 3 and Model 5 include the time to export (for imports to Germany) or the time to import (for exports from Germany), Model 2, Model 4 and Model 6 include the costs of exports (for imports to Germany) or the costs of imports (for exports from Germany).Note that both indicators of per-shipment costs of trade are highly positively correlated with a correlation coefficient of +0.79 for export costs and +0.77 for import costs; therefore, the two indicators are included in the empirical models alternatively.
All models include the distance to the country of origin (for imports to Germany) or the distance to the destination country (for exports from Germany).Distance is closely related to the time necessary to transport a good from the country of origin or to the country of destination, and to the costs of transport.For the countries included in the empirical investigation distance is negatively correlated with the time and cost indicators, but the correlation is small (-0.17 for time to export and -0.18 for time to import; -0.24 for cost to export or import).Furthermore, all models include two standard variables from gravity models of trade, Gross National Income and per capital Gross National Income, as control variables. 9he indicators for trade costs and the control variables are included in Model 1 and Model 2 (where Model 1 includes the time to trade, and Model 2 includes the costs of trade from the Doing Business Database detailed above).All these variables are constant for a given country of destination (for exports) or origin (for imports).Descriptive evidence reported in Table 3 and Table 7 (for import and export transactions with the United States and China) demonstrates that the number of transactions per year by firm-good-country is not constant.For a given country of destination or origin with given values for trade costs (and control variables) the number of transactions varies widely between one and twelve.
This illustrates that for some firms trading some goods with a specific country the same measured trade costs lead to a high degree of lumpiness in trade, and for others they lead to a low degree of lumpiness.This might be caused by differences between firms with respect to productivity, size, or other characteristics.Unfortunately, the data available have no information on the trading German firm (besides the firm identifier).To control for unobserved firm characteristics in the link between trade costs and lumpiness of trade Model 3 and Model 4 include firm fixed effects.Identification of the role of trade costs for the number of transactions per year by firm-good-country here comes from the within-firm variation over goods and countries.
Descriptive evidence reported in Table 4 (for imports) and Table 8 (for exports) shows that the average number of transactions per year by firm-goodcountry differs between different groups of goods.This variation is expected to be related to the differences in the fixed costs of trade with the different countries of destination or origin of these goods, but it might as well be related to the characteristics of the goods itself (irrespective of the countries traded with).To control for these unobserved characteristics of goods in the link between trade costs and _________________________ 9 Gross National Income per capita (measured in current US-Dollar) is taken from the Doing Business database directly, Gross National Income is calculated from the per capita values and the size of the population reported in the data base.Information for 2012 used here is taken from the 2014 edition.lumpiness of trade, and to take care of the role of unobserved firm characteristics discussed above, Model 5 and Model 6 include fixed effects at the firm-good level.Identification of the role of trade costs for the number of transactions per year by firm-good-country here comes from the within-firm within-good variation over countries.
Following the literature on the lumpiness of trade all variables are included in logs.The regression coefficients, therefore, are estimates for the elasticity of the number of trade transactions per year by firm-good-country with respect to an indicator of trade costs (or a control variable). 10f higher per-shipment costs make it optimal for traders to engage in crossborder transactions more infrequently and if the degree of lumpiness is positively related to fixed costs of trade this means that the number of transactions per year at the firm-good-country level decreases with an increase in trade costs.In the empirical models this implies a negative sign of the estimated elasticity of the number of transactions with respect to a variable that measures trade costs.

Imports
Results for the empirical models for the lumpiness of imports are reported in Table 9. 11 Here Model 5 and Model 6 are the preferred models because the unobserved characteristics of both firms and goods are controlled for by including fixed effects at the firm-good level.
From Model 6 we see that the costs of exports in the country of origin and the distance between Germany and the country of origin are negatively related to the number of transaction per year at the firm-good-country level.Both variables can be regarded as indicators of per-shipment trade costs (see the discussion in Section 4.1).These results, therefore, are in line with the expectations regarding the link between per-shipment costs and the degree of the lumpiness of trade, because fixed costs lead to a trade-off between per-shipment trade costs and shipping _________________________ frequency.On the one hand, firms engaged in international trade would like to economize on these per-shipment costs by sending fewer and larger shipments.On the other hand, this comes at a cost due to time-lags related to waiting to fill a larger shipment and because of the need to keep costly inventories between shipment arrivals.
A negative impact of costs of exports in the countries of origin and of distance to Germany is found in all other models listed in Table 9 (including models without fixed effects, 12 and with firm fixed-effects only), too.The exception is the time to export in the country of origin.The estimated regression coefficient of this indicator of per-shipment costs is statistically insignificant at a conventional level in the preferred Model 5 (and positive and significant in Model 1 and Model 3). 13egarding the estimated size of the elasticities of the number of transactions with respect to trade costs, from Model 6 we see that a one hundred percent increase in the cost of export in the country of origin leads to a reduction in the number of import transactions by 15.3 percent.Doubling the distance between Germany and the country of origin reduces the number of transactions by 11 percent according to Model 5 and by 14.5 percent according to Model 6.As is documented in Appendix Table 3 trade costs vary considerably between the countries of origin; therefore, the estimated elasticities can be considered to be significant from an economic point of view (and not only from a statistical point of view), too.
It was pointed out in Section 3 that within a month all imports of a specific HS6-good from a specific country by one single firm are aggregated and reported as one data point only.Therefore, the proxy for trade frequency used here may be biased for high frequency traders which trade the same good with the same country in (nearly) every month several times.The large increase in the frequency of the _________________________ 12 As suggested by a referee, the models without fixed effects were estimated using the sample that is used to identify the estimated coefficients in the models with firm-HS6 fixed effects, too, i.e. after dropping 1,100,883 singletons in firm-good groups from the estimation sample.Results did not change qualitatively; details are available on request.13 Note that both GNI and GNI per capita in the country of origin are included as control variables in the empirical models only.Therefore, we do not discuss the results for the estimated coefficients of these variables here and in the next section.number of import transactions per year from 11 to 12 reported in Table 1 to Table 3 illustrates this.As a robustness check, therefore, all empirical models were estimated using a restricted sample that excludes cases with a calculated number of 12 transactions (see the discussion in Békés et al. 2015).The big picture from this robustness check is identical to the one reported in Table 9; details are available on request.

Exports
Results for the empirical models for the lumpiness of exports are reported in Table 10.From Model 5 and 6, which are again the preferred models because the unobserved characteristics of both firms and goods are controlled for, we see that all three indicators of trade costs are negatively related to the number of transaction per year at the firm-good-country level.As in the case of imports these results are in line with the expectations regarding the link between per-shipment costs and the degree of the lumpiness of trade, and this holds for results reported for the other models (without fixed effects, 14 and with firm fixed-effects only), too.
Regarding the estimated size of the elasticities of the number of transactions with respect to trade costs, from Model 5 we see that a one hundred percent increase in the time to import in the country of destination leads to a reduction in the number of import transactions by 6.7 percent.According to Model 6, doubling the costs of imports in the destination country reduces the number of export transactions by 2.4 percent.This estimated elasticity is considerable smaller than the value for import transactions.Doubling the distance between Germany and the destination country reduces the number of transactions by ca.18 percent according to Model 5 and Model 6.As is documented in Appendix Table 3 trade costs vary considerably between the countries of destination; therefore, the estimated elasticities can be considered to be significant from an economic point of view (and not only from a statistical point of view), too._________________________ 14 As suggested by a referee, the models without fixed effects were estimated using the sample that is used to identify the estimated coefficients in the models with firm-HS6 fixed effects, too, i.e. after dropping 750,615 singletons in firm-good groups from the estimation sample.Results did not change qualitatively; details are available on request.
Like in the case of import transactions, as a robustness check all empirical models were estimated using a restricted sample that excludes cases with a calculated number of 12 transactions.Again, the big picture from this robustness check is identical to the one reported in Table 10; details are available on request.

Concluding remarks
This paper looks at a hitherto neglected extensive margin of international trade by investigating for the first time the frequency at which German exporters and importers trade a given good with a given country over a year.Imports and exports show a high degree of lumpiness.In a given year about half of all firm-goodcountry combinations are recorded only once or twice for trade with EU-countries, and this is the case for more than 60 percent of all firm-good-country combinations in trade with non-EU countries.
The frequency of recorded transactions tends to decline with an increase in the number of transactions per year.This is in accordance with the presence of pershipment fixed costs that provide an incentive for trading firms to engage in crossborder transactions infrequently.Empirical models show that for Germany the frequency of transactions at the firm-good-country level tends to decrease with an increase in per-shipment costs when unobserved firm and goods characteristics are controlled for.
To put the findings for Germany reported in this paper into perspective we compare them to results reported in empirical studies on the lumpiness of trade for other countries.This, however, is not an easy task because these studies differ in details in the empirical approach used and as regards the type of data that are analyzed.That said, a high degree of lumpiness in exports is reported for the US (in trade with six destination countries) by Alessandria et al. (2010), for France by Békés et al. (2015), for the US and Spain by Hornok and Koren (2015a), and by Kropf and Sauré (2014) for Switzerland.The findings for the lumpiness of German exports, therefore, are in line with the big picture from empirical studies for exports from the US, France, Spain and Switzerland.Note that none of the studies on the lumpiness of trade for other countries looks at the degree of lumpiness of imports.
The finding that for Germany the frequency of export transactions at the firmgood-country level tends to decrease with an increase in per-shipment costs when unobserved firm and goods characteristics are controlled for is in line with results reported by Hornok and Koren (2015a) for exports of the US and Spain at the product-country level (without control for the exporting firms).Again, comparable results for imports are not available for other countries.
The bottom line, then, is that according to the empirical results presented in this paper for Germany and with a view on the results for other countries summarized above a reduction of per-shipment costs can be expected to lead to a decrease in the degree of lumpiness of trade and to a reduction of costly inventories.This will foster international trade by pushing a hitherto neglected extensive margin of international trade of firms -the number of transactions at the firm-good-country level.
.04) show a high degree of lumpiness compared to countries like Bangladesh (3.79), Tunisia (3.45) or Vietnam (3.27).The role of EU membership is nicely illustrated by comparing the neighbor countries Austria like the United States (3.84) or Switzerland (3.90).Like in the case of imports the role of EU membership is nicely illustrated by comparing the neighbor countries Austria (5.29) and Switzerland (3.90), or Sweden (4.60) and Norway (3.53).

Table 1 :
Number of import transactions per year by firm-good-country of origin in 2012 Note: Number of transactions refers to months with recorded import transactions at the firm-productcountry of origin level; goods refer to categories at the HS6 level.

Table 2 :
Number of import transactions per year by firm-good-country of origin in 2012 for imports from the Netherlands and France Note: Number of transactions refers to months with recorded import transactions at the firm-productcountry of origin level; goods refer to categories at the HS6 level.

Table 3 :
Number of import transactions per year by firm-good-country of origin in 2012 for imports from the United States and China

Table 4 :
Average number of import transactions per year by firm-good-country of origin for HS2-sections of goods in 2012 Note: Number of transactions refers to months with recorded import transactions at the firm-productcountry of origin level.For a detailed description of the HS2 classification by section see the web at: http://unstats.un.org/unsd/tradekb/Knowledgebase/HS-Classification-by-Section.

Table 5 :
Number of export transactions per year by firm-good-destination country in 2012 Note: Number of transactions refers to months with recorded export transactions at the firm-productdestination country level; goods refer to categories at the HS6 level.

Table 6 :
Number of export transactions per year by firm-good-destination country in 2012 for exports to the Netherlands and France

Table 7 :
Number of export transactions per year by firm-good-destination country in 2012 for exports to the United States and China Note: Number of transactions refers to months with recorded export transactions at the firm-productdestination country level; goods refer to categories at the HS6 level.

Table 8 :
Average number of export transactions per year by firm-good-destination country for HS2-sections of goods in 2012 Note: Number of transactions refers to months with recorded export transactions at the firm-productdestination country level.For a detailed description of the HS2 classification by section see the web at: http://unstats.un.org/unsd/tradekb/Knowledgebase/HS-Classification-by-Section

Table 1 :
Average number of import transactions per year by firm-good-country of origin for selected countries of origin in 2012

Table 2 :
Average number of export transactions per year by firm-gooddestination country for selected destination countries in 2012

Table 3 :
Trade cost data for 2012 www.economics-ejournal.org