Reassessing the link between firm size and exports

This paper re-examines the link between firm size and exports. The new theories of international trade emphasize firm heterogeneity as the theoretical basis of export behavior. In the context of this heterogeneity, this paper uses the quantile regression methodology to analyze the effects of firm size on firm export propensity (percentage of exported sales). The paper confirms the existence of a positive relationship between firm size and export propensity but finds that the conventional estimates of the elasticity of export propensity with respect to firm size on the average of the export propensities’ distribution underestimate the effect at the bottom of the distribution and overestimate the effect on the rest. Consequently, policies aimed at increasing exports should focus their efforts on increasing the size of those firms with a lower export propensity.


Introduction
This paper analyzes the proposal that increasing a country's average firm size increases the national exports and studies this relationship at the firm level. The relationship between firm size and exports has been used in Spain in recent years to explain paradoxical behavior observed in the Spanish export share. Antràs (2011) indicates that although recent years have seen a decline in the competitiveness of Spanish firms and an increase in the export share of emerging countries (e.g., China and India), the Spanish export share has, surprisingly, remained constant. His explanation for the phenomenon is that only large firms have an important influence on the national total export share because the unit labor costs of large firms have progressed better than those of smaller companies. Therefore, the firm size of exporters is a crucial variable to explain and increase the firm export propensity (percentage of sales exported). The small average size of Spanish companies relative to the average size of European Union firms is a disadvantage in this respect. Therefore, proposals that have been put forward seek to increase the country's average firm size. This paper examines the merits of these proposals for increasing a country's export propensity using a new estimation technique of quantile regression for panel data with nonadditive fixed effects proposed by Powell and Wagner (2014) that allow that these estimates can be interpreted in the same manner as traditional cross-sectional quantile estimates. I find that not any kind of increase in firm size is equally effective. In particular, I demonstrate that policies aimed at increasing exports should focus on increasing the size of those firms with a higher elasticity of export propensity with respect to firm size. Such firms are precisely the ones that exhibit a lower export propensity. 1 The rest of the paper is organized as follows. Section 2 presents the literature review. Section 3 describes the data used. Section 4 presents the econometric specification used to estimate the mean of the elasticity of export propensity with respect to firm size. Section 5 presents the quantile regression estimates and the elasticity of value of exports with respect to firm size. The section also compares the mean estimates with the estimates along the distribution of export propensities and value of exports by using the quantile regression. Section 6 summarizes and concludes.

Literature review
The new theories of international trade emphasize firm heterogeneity to explain the export status (Melitz 2003 andGreenaway andKneller 2007). Firm size is a crucial variable for explaining firm productivity (García-Santana and Ramos 2013), and both variables are determinants of whether firms choose to export (Wagner 1995(Wagner , 2007. Several reports indicate that the small average size of Spanish firms is the main impediment to their international competitiveness. This small average size of Spanish firms appears to be the consequence of distortions in the tax system (Almunia and López-Rodríguez 2014) and factors related to the firms' organization and internal management (Huerta and Salas, 2012). Mañez et al. (2004) find that firm characteristics, such as age, size, productivity, corporation, foreign ownership, R&D and advertising intensity have a positive influence on the probability of exporting by Spanish manufacturers. In this same sector, Fariñas and Martín-Marcos (2007) suggest that indicators of economic performance such as productivity, size, wages and innovation are greater in exporting firms. In 1 While this result suggests several policy guidelines, I am not proposing a specific policy in the paper. There are, at least, three types of policies that can increase firm size: (i) policies aimed at removing tax and labor distortions; (ii) policies that subsidize merges between firms; and iii) policies that enhance firms' competition (those that reduce bureaucracy, increase transparency, and so on). However, I do not attempt to analyze these policies in detail in the paper.

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Eurasian Business Review (2020) 10:207-223 the service sector, Minondo (2013) finds that trading firms exhibit premia relative to non-traders with respect to size, labor productivity and average wages. Mañez-Castillejo et al. (2010) indicate that productivity seems to be a barrier to entry into export markets, particularly for small firms. However, Díaz-Mora et al. (2015) find that if these small firms are both importers of intermediate inputs and exporters, they have a higher likelihood in continuing to export.
A positive relationship between firm size and export propensity has long been generally accepted. Wagner (1995) finds a non-linear relationship between firm size and exporting and that this impact is positive but decreasing. Majocchi et al. (2005) suggest that the simple linear relationship is the most plausible one for the data used.
However, there are studies that point in other directions. Wolf and Pett (2000) and Bonaccorsi (1992) find that firm size has little or no influence, and Patibandla (1995) finds a negative relationship between firm size and export propensity. More recently, Pla-Barber and Alegre (2007) do not find this relationship in a sample from the French biotechnology industry, and Iyer (2010) finds that firm size has a negative effect on export propensity in New Zealand's agriculture and forestry sectors. With this wide range of findings, Verwaal and Donkers (2002) refer to the relationship as an empirical puzzle.
The new international trade theories emphasize firm heterogeneity as an explanation for many of the behaviors observed in international markets (Bernard et al. 2007(Bernard et al. , 2012Redding 2011). According to these theories, not only are exporting firms very different from non-exporters (Bernard and Jensen 1995), but there is also high heterogeneity within the firms in each group (Powell and Wagner 2014). In the context of this heterogeneity, the differences in the mean of a distribution of some variables or econometric estimates that only obtain valid results at this average are incomplete. Hence, empirical analyses along the distribution of a given variable are replacing those that only look at the mean. Wagner (2011) recommends this type of analysis along the entire distribution of a given variable when the theoretical framework is firm heterogeneity and suggests using quantile regression for such an analysis.
Thus, several studies have examined the impact of certain plant characteristics, including firm size, on export propensity along the export propensity distribution (Piccardo et al. 2014;Wagner 2006;Yasar et al. 2006). Wagner (2006) finds that firm size is statistically significant at a conventional level for the 0.25 quantile only. However, Wagner does not include firm fixed effects and uses a dataset with few observations: a Germany dataset with only 458 firms. The main difference of this paper from Wagner's (2006) is the use of the quantile regression model for panel data with non-additive firm fixed effects (Powell and Wagner 2014). Moreover, I use two datasets: (i) The Encuesta Sobre Estrategias Empresariales (Survey on Business Strategies, hereafter, ESEE), for the period 1990-2010, which is an unbalanced panel of Spanish manufacturing that includes 3249 firms and 23,083 observations in the subsample used, and (ii) the EFIGE dataset (project European Firms in a Global Economy: internal policies for external competitiveness supported by the European Commission), which is a cross-sectional dataset in seven European countries, with 7807 firms in the subsample used. The use of these two datasets allows more precise estimates to be obtained.

3 3 The data
The data used in this paper are the Encuesta Sobre Estrategias Empresariales (ESEE) and the EFIGE dataset. The ESEE for the period 1990-2010 is an unbalanced panel of Spanish manufacturing firms. This survey originates from an agreement in 1990 between the Ministry of Industry and the SEPI Foundation, formerly the Fundación Empresa Pública (Public Firm Foundation). The database contains the following information for each year over the period 1990-2010 for a sample of approximately 1800 firms: activities, products, manufacturing processes, customers and suppliers, costs and prices, markets covered, technological activities, income statements, accounting balance sheets, employment and foreign trade. Firms with fewer than 10 employees are excluded from the survey. The survey contains information on 70% of all Spanish manufacturing firms with more than 200 employees, together with a random sample that covers 5% of the remaining firms (firms with 10-200 employees).
The EFIGE is a cross-sectional dataset that has recently been collected within the EFIGE project (European Firms in a Global Economy: internal policies for external competitiveness), supported by the European Commission. Altomonte and Aquilante (2012) describe this dataset in detail. This database, which is available for the first time in Europe, combines measures of firms' international activities (e.g., exports, outsourcing, FDI, imports) with quantitative and qualitative information on some 150 items, ranging from R&D and innovation, labor organization, financing and organizational activities, and pricing behavior. The data are a representative sample (at the country level, for the manufacturing industry) of almost 15,000 surveyed firms (above 10 employees) in seven European economies (Germany, France, Italy, Spain, the United Kingdom, Austria, and Hungary). It was collected in 2010, spanning the years from 2007 to 2009. Special questions related to the behavior of firms during the crisis were also included in the survey, but the sample is built to be representative for 2008.
The ESEE and EFIGE datasets are not methodologically homogeneous surveys because they have different objectives. The main reason for using the EFIGE dataset is not to replicate again the results for Spain but to check whether these results occur in other countries.
Appendix Table 6 shows the export growth for Spanish manufacturing firms, as measured by its extensive margin (percentage of firms that report having exported) and intensive margin (average percentage of sales exported of each company), based on ESEE data. It should be mentioned that this increase has not occurred evenly across all firms, and if we analyze the behavior according to size, we note that there is high heterogeneity. For the EFIGE dataset, Table 6 shows that Spain has the lowest extensive and intensive margins. Table 7 shows the average percentage of sales exported by industries on ESEE data. Table 1 shows the export propensity distribution by firm size. The export propensity is the percentage of exported sales measured as a percentage of the average value of percentage of sales exported in the 20 industries considered and for each of the 21 years included in the ESEE dataset  and in the 11 NACE-CLIO industries and 166 regions (at the NUTS-1 level of aggregation) included in EFIGE dataset. For example, if the average value of percentage of sales exported in an industry and a year is 30% and a firm has exported 60% of its sales, the export propensity for this firm is 200%. 2 Table 1 shows that the average export propensity is higher in firms with more than 50 employees. However, the export propensity values reported by percentiles show that for the three groups of firms categorized by size, companies with high export propensity coexist with others whose percentage of export sales is relatively small.
In the ESEE data for 2010, there are firms with fewer than 50 employees whose propensity to export in the 95th percentile reaches 231.4% of the mean. Similar percentages are obtained in larger companies: 280.8% in those with more than 50 and fewer than 250 employees and 258.6% in those with more than 249 employees. At the same time, the export propensity of the largest companies is very similar to that of the smaller ones in the 5th percentile: 2.6% for those with more than 249 employees and 1.6% for those with fewer than 50 employees. In the EFIGE dataset, there are more differences in the 5th percentile, but the percentages obtained in the 95th percentile are quite similar across the three firm sizes considered. In many cases, Table 1 shows that the export propensity of medium-size firms is larger than that of large firms. Large firms may thus be sufficiently productive that they use direct investment to reach foreign markets, thereby reducing the need for exports. The percentage of firms by size along the distribution of export propensities is shown in Table 2. The number of firms is in brackets. The percentage of companies with over 249 employees located in the first quintile of the distribution of export propensities stands at approximately 25% for the considered period in the ESEE dataset, although there is a clear downward trend (39.4% achieved in 1990 and 13.7% in 2010). At the top of the distribution, the percentage of firms with fewer than 50 employees located in the fifth quintile of the distribution stands at approximately 21% throughout the period considered, and in this case, there is no clear downward trend. In the EFIGE dataset, there are a few large firms in the first quintile, but the 56.6% of firms in the 5th quintile are small (fewer than 50 employees).
Annual data in ESEE are treated as a different cross-sectional dataset. The same firm could be in different size ranges, depending on the year. This could explain the increasing share of medium size firms in the 5th quintile: successful firms increase their size, and doing so positively affects their movement toward higher quintiles.
In short, high firm heterogeneity is clear. Although there is a positive correlation between firm size and export propensity for any firm size considered, among firms with high export propensity, we can find both small and large companies. Among firms that do not export much, there is also considerable diversity in firm size. Consequently, in this context of high heterogeneity, analysis of the differences in distribution means is an incomplete exercise. As a result, this paper proposes an analysis along the distribution of export propensities using the quantile regression approach.

Mean estimates
To analyze the effect of firm size on export propensity in the average of the distribution, I estimate Eq. (1) with the ESEE dataset: where P jt is the log of export propensity of firm j in year t and S jt is the log of firm size, as measured by the number of employees in firm j in year t. With the ESEE dataset, both firm fixed effects (α j ) and time fixed effects (δ t ) are included. With the EFIGE dataset, it is not possible to include these fixed effects, so I include other controls (Z j ) available in the data and estimate Eq. (2): (1) These controls are the countries, industries, firm age and other firm characteristics, such as importer of materials, importer of services, active outsourcer, passive outsourcer, foreign direct investor, global exporter, active abroad, the number of employees engaged in R&D activities, product innovation, process innovation, market innovation, organizational innovation, human capital, labor flexibility, credit request, credit obtained, family managed, family chief executive officer, foreign group, decentralized management, bonus for managers, quality certification, and competition from abroad.

Quantile regression
The effect on the mean of the distribution is incomplete in the presence of firm heterogeneity. Such heterogeneity involves differences beyond those observed in the mean of the distribution, extending the differences. To analyze the elasticity of export propensity with respect to firm size, considering firm heterogeneity, I use the quantile regression method to estimate the elasticity of export propensities at different percentiles of the distribution. For the ESEE dataset, I use the estimator for panel data with non-separable disturbance proposed by Powell and Wagner (2014) and developed by Powell (2016) in the context of the exporter productivity premium. According to these authors, we are interested in the structural quantile function (SQF): where β(τ) is the elasticity of export propensity with respect to firm size at the τ th quantile. With the Powell and Wagner (2014) Powell (2016) lists the differences between his estimator and quantile panel data estimators with additive fixed effects. The disadvantage of this estimator is that it limits one to a single explanatory variable, in addition to time fixed effects and firm fixed effects. This estimator maintains the nonseparable disturbance term that is commonly associated with quantile estimation. It estimates the impact of exogenous explanatory variables on the outcome distribution using within variation in the explanatory variables for identification purposes. Most quantile panel data estimators include additive fixed effects that separate the disturbance term and assume that the parameters vary based only on the time-varying components of the disturbance term. Another advantage is that the moment conditions are simple to interpret and implement. Because the individual fixed effects are never estimated or even specified, the number of parameters that need to be estimated is small.
Because the EFIGE dataset does not allow the inclusion of firm fixed effects, the structural quantile function is

Estimation results
Estimates of the elasticity of export propensity with respect to firm size (β) in the average of distribution are presented in Table 3; the values reach 0.146 in the ESEE dataset and 0.078 in the EFIGE dataset. That is, firm size has a positive effect on the export propensity, although this effect is inelastic. It has previously been determined that there is no selection bias when estimating the Heckman selection model (Heckman 1979) with the sample of exporting and non-exporting firms. This requires a first stage for estimating a probit model to assess the probability that a firm exports and a second stage that includes the Heckman correction term (the inverse Mill's ratio, lambda). The results of the estimation of the second stage of Heckman model show that the inverse Mill's ratio, the lambda variable, is not statistically significant. Vermeulen (2004) estimates this same model and obtains the same result. The estimates for the probit model of the first stage of Heckman model are available upon request. Table 4 shows the estimates of these elasticities from the quantile regressions with the two datasets. The estimated elasticities are positive, statistically significant and less than unity, but the values decrease as we move along the distribution Table 3 Mean estimates of the elasticity of export propensity with respect to firm size t statistics are in brackets. ***, **, and * indicate the statistical significance at the 1, 5, and 10%, respectively. The export propensity is the percentage of exported sales measured as a percentage of the average value of the percentage of sales exported in the 20 considered industries and the 21 years included in ESEE dataset and in the 11 industries and 166 regions included in EFIGE dataset. Other controls in the EFIGE estimates are countries, industries, age, importer of materials, importer of services, active outsourcer, passive outsourcer, FDI, global exporter, active abroad, employees to R&D activities, product innovation, process innovation, market innovation, organizational innovation, human capital, labor flexibility, credit request, credit obtained, family managed, family chief executive officer, family group, decentralized management, bonus, quality certification, and competition from abroad The probit equation includes the number of employees, age of the firm, year fixed effects and industries fixed effects in the ESEE dataset, and the number of employees, countries, industries, age, importer of materials, importer of services, employees to R&D activities, product innovation, process innovation, market innovation, organizational innovation, human capital, labor flexibility, credit request, credit obtained, family managed, family chief executive officer, family group, decentralized management, bonus, and quality certification in the EFIGE dataset 1 3 of export propensities. For the ESEE dataset, the elasticity of export propensity with respect to firm size is 0.201 at the 10th quantile and decreases to 0.099 at the 60th quantile. In the upper quantiles, this elasticity is not significantly different from zero. The elasticity estimated with the EFIGE dataset is 0.128 at the 10th quantile and 0.030 at the 90th quantile. In summary, the traditional estimate of this elasticity at the average of the export propensities' distribution Table 4 Quantile regression estimates of the elasticity of export propensity and the elasticity of value of exports with respect to firm size t statistics are in brackets. ***, **, and * indicate the statistical significance at the 1, 5, and 10%, respectively. The export propensity is the percentage of exported sales measured as percentage of the average value of the percentage of sales exported in the 20 considered industries and 21 years included in ESEE dataset and in the 11 industries and 166 regions included in the EFIGE dataset. Standard errors are estimated using bootstrap technique and are clustered by firm throughout in the ESEE dataset. Other controls in the EFIGE estimates are countries, industries, age, importer of materials, importer of services, active outsourcer, passive outsourcer, FDI, global exporter, active abroad, employees to R&D activities, product innovation, process innovation, market innovation, organizational innovation, human capital, labor flexibility, credit request, credit obtained, family managed, family chief executive officer, family group, decentralized management, bonus, quality certification, and competition from abroad Year underestimates the effect at the bottom of the distribution and overestimates the effect on the rest. Figure 1 shows the differences between the mean and quantile estimates for the elasticity of export propensity with respect to firm size, where the mean estimates are the straight lines in the figure and the quantile estimates are the discontinuous lines.
A plausible explanation for the result shown in the figure is the influence of transaction costs on the relationship between firm size and export propensity, as noted by Verwaal and Donkers (2002). According to these authors, firm size does not capture all of the economies in the context of export relationships, but it is necessary to include the size of the export relationship. They use the average annual value of transactions per foreign buyer as an explicative variable of export propensity and an interaction term between this variable and the firm size. The export relationship size variable has a positive influence on export propensity and a moderating effect on the relationship between firm size and export propensity because the coefficient of export relationship size is positive and significant and because the coefficient of that interaction term is negative and statistically significant. In my datasets, there is no information about the number of foreign buyers, and I cannot include a variable that measures the size of the export relationship. However, according to Verwaal and Donkers (2002), there is a positive correlation between the size of the export relationship and export propensity. Consequently, the moderating effect of export relationship size on the elasticity of export propensity with respect to firm size is greater in firms with higher export propensities.
However, the percentage of sales exported has an upper bound (although I use a relative measure of the export propensity by industry and year), and the firms that have a higher percentage of sales exported cannot increase it as much as firms with Fig. 1 Elasticity of export propensity with respect to firm size a smaller percentage of sales exported can. To check that this does not affect the previous result and to assess robustness, I estimate the elasticity of the value of exports with respect to firm size with the ESEE dataset. 3 With the EFIGE dataset, it is not possible to estimate this elasticity because the annual turnover is defined by ranges and because there is no upper bound. Column 4 of Table 4 shows this elasticity, and Table 5 shows the mean estimates of the elasticity of value of exports with respect to firm size. The mean estimate of elasticity is unitary, so the quantile regression estimates shown in Table 4 also confirm the previous results. Up to the 30th quantile, the estimated elasticity it is greater than unity, and after that point, it is less than unity. Therefore, it is shown that the effect of firm size on exports-export propensity or value of exports-is smaller as exports rise. Figure 2 shows the differences between the mean and quantile estimates for the elasticity of value of exports with respect to firm size. These differences show a very similar profile to that shown in Fig. 1.

Conclusions
The elasticity of export propensity with respect to firm size is found to be positive, statistically significant and less than unity along the distribution of export propensities. However, this elasticity decreases as export propensity increases. Thus, the traditional estimate of this elasticity on the average of the export propensities distribution underestimates the effect at the bottom of the distribution and overestimates the effect on most of it. The quantile regression estimates include non-additive firm Table 5 Mean estimates of the elasticity of value of exports with respect to firm size ESEE t statistics are in brackets. ***, **, and * indicate the statistical significance at the 1, 5, and 10%, respectively. The export propensity is the percentage of exported sales measured as a percentage of the average value of the percentage of sales exported in the 20 considered industries and the 21 years included in the ESEE dataset. fixed effects by using the Powell and Wagner (2014) estimation technique for panel data, which means that the estimates can be interpreted in the same manner as traditional cross-sectional quantile estimates. Consequently, the positive effect of firm size on export propensity is found to be relatively more important in companies with less export propensity. I also estimate the elasticity of value of exports with respect to firm size to check the robustness of the results and obtain similar results.
The study findings may have important policy implications, given that export growth is being promoted in Spain and other countries as a way to emerge from the current economic crisis. The aim is for the increase in foreign demand to counter the reduced domestic demand. According to the results obtained in this paper, policies aimed at increasing exports should concentrate their efforts on increasing the size of the firms with lower export propensity. The rationale is that it would be more efficient to direct public funds to increasing firm size for these companies: doing so would generate a greater increase in overall export propensity (or value of exports) because the increase in export propensity would be higher in these firms than it would be in others.  Table 8 Mean and quantile regression estimates of the elasticity of percentage of sales exported with respect to firm size t statistics are in brackets. ***, **, and * indicate the statistical significance at the 1, 5, and 10%, respectively. Standard errors are estimated using bootstrap technique and are clustered by firm throughout in the ESEE dataset. Other controls in the EFIGE estimates are countries, industries, age, importer of materials, importer of services, active outsourcer, passive outsourcer, FDI, global exporter, active abroad, employees to R&D activities, product innovation, process innovation, market innovation, organizational innovation, human capital, labor flexibility, credit request, credit obtained, family managed, family chief executive officer, family group, decentralized management, bonus, quality certification, and competition from abroad