How Multi-Destination Firms Shape the Effect of Exchange Rate Volatility on Trade: Micro Evidence and Aggregate Implications 

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Descriptive Statistics

Summary statistics of key variables are given in Tables 2.1 and 2.2. They are consistent with previous evidence about French firms: exporting firms are highly heterogeneous in their performance and size, implying a large variance in our dataset. The average firm-country exported value is slightly above 520,000 thousand euros, whereas the average number of employees and value of assets are also quite small: the average exporter is a small firm, with modest values of exports. Performance indicators distributions, that are reported in Table 2.2, deliver a similar message: only a small number of highly performing firms, exporting towards a significant number of destinations. Half of the French firms export towards at most 2 destinations, which is consistent with previous studies on the subject (Eaton et al., 2011 or Mayer and Ottaviano, 2007) and supports the representativeness of the sample.
Note: The summary statistics are computed on the 2,260,149 firm-country-year observations that make up our final regression sample used in Table 2.3 to study the intensive margin.

French Firms and RER Volatility: Some Facts

Using these datasets, we start to explore how French firms cope with RER volatility. We report in Figure 2.1 the cumulative distribution of exports with respect to the bilateral RER volatility.
We represent on the vertical axis the share of total exports P(x) that was exported subject to a RER volatility lower than x. We restrict our figure to RER volatility that is under .1 since more than 98% of French exports are concentrated under this value. A high share of total exports face a low RER volatility: around 60% of exports are directed towards destinations with a volatility equal or lower than 0.02. This should not be surprising since an important part of French exports are directed towards Euro Area countries, with a structurally close to zero RER volatility. At the other end of the spectrum, 10% of aggregate exports face a bilateral RER volatility equal or above 0.04. On the whole, there is an interesting heterogeneity for our analysis.
Finally, we represent in Figure 2.2 two types of mean RER volatility faced by firms when exporting to many markets. The line represents the simple average RER volatility across all destinations, while the points represent the exports-weighted average RER volatility faced by firms. We thus compare average RER volatility and effective aggregate RER volatility for each type of firm. The higher the number of destinations, the higher the average RER volatility is.
Yet, once firm choices are taken into account, we find that the average RER volatility increases but less than if no reallocation choices were made by the firm. This is a first, descriptive evidence that, when firms can allocate their exports across destinations, they face lower aggregate RER volatility.
where ExportPerfijt is a measure of the export performance of firm i for export destination j in year t. We consider two alternative measures of export performance: the intensive margin of exports is captured with the log of the free-on-board export sales to country j in year t while the extensive margin is apprehended as entry. The latter is defined as Pr(Xijt > 0 | Xijt−1 = 0)5.
Bil_volatjt is the standard bilateral RER volatility in destination j. Our empirical strategy presumes the exogeneity of real exchange rate volatility, since it is very unlikely that a firm shock translates into a change in country-level exchange rate variations. This is a very standard assumption in the related empirical literature, made among others by Berman et al. (2012), Cheung and Sengupta (2013) or Héricourt and Poncet (2015).
All our estimations include firm-year fixed effects, &it, allowing us to examine variations in export allocations across destinations for a given year. We complete this specification by adding a set of country dummies to account for unobserved heterogeneity. In some specifications, we replace this set of dummies by a a set of firm-country fixed effect, μij : it allows us to account simultaneously for variations in exports across years, even though it is not the main focus of our investigation.
We include the interactive term between bilateral RER volatility and the (lagged) number of destinations to account for a non-linear effect of RER volatility with firm size. Note that all unconditional firm-year variables, such as the number of served destinations, are by construction subsumed in the firm-year fixed effects. The key parameter of interest is ⌧ (interaction with the number of destinations): its sign and level of significance tells whether the amplifying effect of the number of destinations on trade mentioned in section 2.2 is at play. If firm-destination trade flows of multi-destination firms tend to exhibite a largerake advantage of reallocation possibilities, ⌧ should exhibit a negative sign, like ↵ (see Testable Relationship 2).
5In that set of regressions, our sample consists of a firm-country series of zeros followed by a decision to begin exporting. For a given firm-country, we can have several beginnings. For example, the subsequent export statuses 011001 becomes 010001 in our sample.
The conditioning set Zjt consists of destination-year specific variables. In standard models of international trade, exports depend on the destination country’s market size and price index.
Therefore, Zjt includes in our specifications destination j’s GDP and effective RER.
We include in some specifications a set of country-year fixed effects (+jt). However, since it is colinear with the bilateral RER volatility, including this set of fixed effect makes bilateral volatility unidentifiable. We thus introduce this fixed effect in specifications including solely interactive terms.
Finally, all regressions are performed with the linear within estimator for the intensive margin and the linear probability model6 for the extensive margin. Finally, Moulton (1990) shows that regressions with more aggregate indicators on the right-hand side could induce a downward bias in the estimation of standard errors. All regressions are thus clustered at the destination-year level using the Froot (1989) correction.

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Baseline evidence

We study the joint effects of both bilateral RER volatility, firm performance and number of destinations on the two margins of trade separately: the size of export value per firm for the intensive margin, and the decisions to start exporting (entry) for the extensive margin.

Table of contents :

1 How Migrant Workers Foster Exports 
1.1 Introduction
1.2 Exports and migration
1.3 Data and stylised facts
1.3.1 Data
1.3.2 Stylised facts
1.4 Theoretical framework
1.4.1 Model set-up
1.4.2 Demand
1.4.3 Supply
1.4.4 First-order selection effects
1.5 Pro-trade effect of foreign-born workers
1.5.1 Endogeneity concerns
1.5.2 Propensity score matching and treatment effect estimation
1.5.3 Pro-trade effect of foreign-born workers: results
1.6 Disentangling the productivity from the trade-cost effect
1.6.1 Empirical strategy
1.6.2 Results
1.7 Conclusion
1.8 Additional Material
A Additional Information – Data
B Additional Results: The pro-trade effect of migrants
C Additional Results: The two channels
2 How Multi-Destination Firms Shape the Effect of Exchange Rate Volatility on Trade: Micro Evidence and Aggregate Implications 
2.1 Introduction
2.2 Real Exchange Rate Volatility, Firm Heterogeneity and Exports: Theoretical Background
2.2.1 How should the average firm react to bilateral RER volatility?
2.2.2 How should firm performance impact this relationship between bilateral RER volatility and exports?
2.2.3 Key testable relationships
2.3 Empirics
2.3.1 Data
2.3.2 Descriptive Statistics
2.3.3 French Firms and RER Volatility: Some Facts
2.4 Export Performance and Bilateral RER Volatility
2.4.1 Baseline evidence
2.4.2 Robustness analysis
2.5 Investigating Reallocation Behavior
2.5.1 Firm-year fixed effects and export shares
2.5.2 External RER volatility and Reallocation
2.5.3 Selection effects
2.5.4 The Product Margin of Trade
2.6 Aggregate Implications
2.7 Conclusion
2.8 Additional Tables
D Alternative Definitions of Key Variables
E Alternative Measures of Firm Performance
F Alternative Definitions of the Extensive Margin
G Omitted Variables
H Alternative Samples
I Additional results on reallocation
3 Trade Costs and Current Accounts 
3.1 Introduction
3.2 Literature Review
3.3 Theory
3.4 Empirical Strategy
3.4.1 Translating the Predictions into Empirics
3.4.2 Specifications and Econometric Issues
3.4.3 Data Sources and Stylized Facts
3.5 Results
3.5.1 Prediction 1: Trade Costs and Current Accounts
3.5.2 Prediction 2: Institutional Integration, Trade Costs and Current Accounts
3.6 Robustness
3.6.1 Alternative Treatment for Unobserved Individual Heterogeneity
3.6.2 Lagged Effects
3.7 Conclusion
Conclusion

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