(PDF) Empirical relationship between workers' remittances and financial development (an ARDL cointegration approach for Sri Lank

NBER WORKING PAPER SERIES IMPORTERS, EXPORTERS, AND EXCHANGE RATE DISCONNECT Mary Amiti Oleg Itskhoki Jozef Konings Working Paper 18615 http://www.nber.org/papers/w18615 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 December 2012 We gratefully acknowledge the National Bank of Belgium for the use of its research facilities and data, and in particular Valere Bogaerts for help with the data collection, and Emmanuel Dhyne and Catherine Fuss for comments and data clarifications. We thank Ariel Burstein, Elhanan Helpman, Doireann Fitzgerald, Ulrich Muller, Steve Redding, Esteban Rossi-Hansberg, David Weinstein, Hylke Vandenbussche and seminar participants at Belgian National Bank, Princeton, Georgetown, Columbia, UCLA, Yale, the Federal Reserve Bank of New York and the EIIT 2012 conference in Santa Cruz for insightful comments. We also thank Sydnee Caldwell, Stefaan Decramer, Diego Gilsanz, Cecile Gaubert and Mark Razhev for excellent research assistance. The views expressed in this paper are those of the authors and do not necessarily represent those of the Federal Reserve Bank of New York or the National Bank of Belgium. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2012 by Mary Amiti, Oleg Itskhoki, and Jozef Konings. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Importers, Exporters, and Exchange Rate Disconnect Mary Amiti, Oleg Itskhoki, and Jozef Konings NBER Working Paper No. 18615 December 2012 JEL No. F14,F31,F41 ABSTRACT Large exporters are simultaneously large importers. In this paper, we show that this pattern is key to understanding low aggregate exchange rate pass-through as well as the variation in pass-through across exporters. First, we develop a theoretical framework that combines variable markups due to strategic complementarities and endogenous choice to import intermediate inputs. The model predicts that firms with high import shares and high market shares have low exchange rate pass-through. Second, we test and quantify the theoretical mechanisms using Belgian firm-product-level data with information on exports by destination and imports by source country. We confirm that import intensity and market share are the prime determinants of pass-through in the cross-section of firms. A small exporter with no imported inputs has a nearly complete pass-through of over 90%, while a firm at the 95th percentile of both import intensity and market share distributions has a pass-through of 56%, with the marginal cost and markup channels playing roughly equal roles. The largest exporters are simultaneously high-market-share and high-import-intensity firms, which helps explain the low aggregate pass-through and exchange rate disconnect observed in the data. Mary Amiti Jozef Konings International Research Department of Economics Federal Reserve Bank of New York University of Leuven 33 Liberty St Naamsestraat 69 New York, NY 10045-0001 3000 Leuven

Belgium and National Bank of Belgium Oleg Itskhoki

Department of Economics Princeton University Fisher Hall 306 Princeton, NJ 08544-1021 and NBER

1 Introduction One of the central puzzles in international macroeconomics is why large movements in ex- change rates have small eects on the prices of internationally traded goods. This exchange rate disconnect has generated a vast literature, yet no empirical pass-through study has taken into account one of the most salient features of international trade, that is that the largest exporters are simultaneously the largest importers. In this paper, we show that this pattern is key to understanding the low aggregate pass-through, as well as the variation in pass-through across rms. Using detailed Belgium micro data, we nd that more import-intensive exporters have signicantly lower exchange rate pass-through into their export prices, as they face osetting exchange rate eects on their marginal costs. These data reveal that the distribution of im- port intensity among exporters is highly skewed, with the import-intensive rms being among the largest exporters, accounting for a major share of international trade. Consequently, the import-intensive rms also have high export market shares and hence set high markups and actively move them in response to changes in marginal cost, providing a second channel that limits the eect of exchange rate shocks on export prices. These two mechanisms reinforce each other and act to introduce a buer between local costs and international prices of the major exporters, thus playing a central role in limiting the transmission of exchange rate shocks across countries. The availability of rm-level data with imports by source country and exports by destination, combined with domestic cost data, enables us to estimate the magnitude of these two channels. To guide our empirical strategy, we develop a theoretical framework to study the forces that jointly determine a rm's decisions to source its intermediate inputs internationally and to set markups in each destination of its exports. The two building blocks of our theoretical framework are an oligopolistic competition model of variable markups following Atkeson and Burstein (2008) and a model of the rm's choice to import intermediate inputs following Halpern, Koren, and Szeidl (2011). These two ingredients allow us to capture the key patterns in the data that we focus on, and their interaction generates new insights on 1 the determinants of exchange rate pass-through. More specically, we allow for three forms of exogenous rm heterogeneityin produc- tivity, quality of their goods, and importing costs of their intermediate inputsthat jointly determine rms' import intensities and their market shares in each destination. With xed 1 The combination of these two mechanisms is central to our results, while the choice of a particular model of variable markups or of selection into importing is less important. 1 costs of importing, rms face the standard trade-o in choosing whether to import and how much to import, with larger-scale rms nding it optimal to import more varieties. In equi- librium, the more productive rms end up having greater market shares and choose to source a greater share of their inputs internationally, which in turn further amplies the productivity advantage of these rms. Therefore, the two sources of incomplete pass-throughoperating through the marginal cost and the markupamplify and reinforce each other in the cross section of rms. The theory suggests a rm's import intensity and export market share form a sucient statistic for its exchange rate pass-through in the cross-section of rms, with import intensity proxying for marginal cost sensitivity to the exchange rate and market shares proxying for markup elasticity. We test the predictions of the theory with a rich data set of Belgian exporters for the period 2000 to 2008. A distinctive feature of these data is that they comprise rm-level imports by source country and exports by destination at the CN 8-digit product codes (close to 10,000 distinct product codes), which we match with rm-level characteristics, such as wages and expenditure on inputs. This allows us to construct a measure of imported inputs as a share of a rm's total variable costs and a measure of rm's market share for each export destination, which are the two key rm characteristics in our analysis. Further, with the information on imports by source country, we can separate inputs from Euro and non-Euro countries, which is an important distinction since imported inputs from within the Euro area are in the Belgium rms' currency. We start our empirical analysis by documenting some new stylized facts related to the distribution of import intensity across rms, lending support to the assumptions and predic- tions of our theoretical framework. We show that in the already very select group of exporters relative to the overall population of manufacturing rms, there still exists a substantial het- erogeneity in the share of imported inputs sourced internationally, in particular from the more distant source countries outside the Euro Zone. The import intensity is strongly cor- related with rm size and other rm characteristics and is heavily skewed toward the largest exporters. Our main empirical specication, as suggested by the theory, relates exchange rate pass-through with the rm's import intensity capturing the marginal cost channel and the destination-specic market shares capturing the markup channel. We estimate this rela- tionship within industries and destinations. This allows us to estimate the cross-sectional relationship between pass-through and its determinants, holding constant the general equi- 2 librium forces common to all rms in a given industry and destination. 2 In particular, such common forces include the correlations of sector-destination-specic price index, 2 The results provide strong support for the theory. First, we show that import intensity is an important correlate of a rm's exchange rate pass-through, with each additional 10 percentage points of imports in total costs reducing pass-through by 5.3 percentage points. Second, we show that this eect is due to both the marginal cost channel, which import intensity aects directly, and the markup channel through the selection eect. Specically, when we control for a rm's marginal cost, the eect of the import intensity on pass-through is reduced by half, and when we further control for market share, proxying for the markup variability, it largely disappears. Last, including both import intensity and market share, we nd these two variables jointly to be robust predictors of exchange rate pass-through across dierent sub-samples, even after controling for other rm characteristics such as productivity and employment size. Quantitatively, these results are large. A rm at the 5th percentile of both import intensity and market share (both approximately equal to zero) has a nearly complete pass- through of over 91%. In contrast, a rm at the 95th percentile of both import intensity and market share distributions has a pass-through of 56%, with import intensity and market share contributing nearly equally to this variation across rms. These results have important implications for aggregate pass through. Given that both import intensity and market share distributions are skewed toward the largest exporters, these ndings imply an aggregate exchange rate pass-through of 64%. We further explore the underlying mechanisms leading to incomplete pass-through with a number of extensions. We verify that our results hold non-parametrically when we sort the rms into bins of market share and import intensity. We also show that import-intensive exporters have lower pass-through due to greater sensitivity of their marginal costs to ex- change rates, conrming the theoretical mechanism. Finally, we show that it is the share of imports from the non-Euro OECD countries that matters the most, while the share of imports from within the Euro Zone has no eect on pass-through and imports from the non- 3 OECD countries have only a statistically marginal eect on exchange rate pass-through. Our paper is related to three strands of recent literature. First, it relates to the recent and growing literature on the interaction of importing and exporting decisions of rms. Earlier work, for example, Bernard, Jensen, and Schott (2009), has documented a large overlap in sector-specic productivity and cost index with the exchange rate. 3 Indeed, we expect to nd no eect of imports from within the Euro Zone since they are priced in the same currency and hence are not subject to exchange rate movements. The nding of little eect of imports from the non-OECD countries is consistent with low pass-through from these countries into import prices even when exchange rates move. We verify this hypothesis by estimating a pass-through regression of the exchange rate into import prices and nding a much larger coecient from the OECD import-source countries. 3 4 the import and export activity of rms. Indeed, major exporters are almost always major importers, and this is also true in our dataset. We focus exclusively on the already select group of exporters, most of whom are also importers from multiple source countries. We instead emphasize the strong selection that still operates within the group of exporters and in particular the heterogeneity in the intensity with which rms import their intermediate inputs. Our paper is the rst to empirically link the importing activity of the rms with the incomplete pass-through into export prices. Second, our paper is related to the recent empirical and structural work on the relation- ship between rm import intensity and rm productivity. Although we base our model on Halpern, Koren, and Szeidl (2011), who estimate the eects of import use on total factor productivity for Hungarian rms, similar models were developed in Amiti and Davis (2012) to study the eects of import taris on rm wages and in Gopinath and Neiman (2012) to study the eects of the Argentine trade collapse following the currency devaluation of 2001 5 on the economy-wide productivity. Amiti and Konings (2007) provide an empirical analysis of the micro-level eects of imports on rm productivity. In our study, the focus centers on the interplay between import intensity and markup variability, and the productivity eect of imported intermediate inputs contributes to the relationship of these two channels. Third, our paper contributes to the vast literature studying exchange rate disconnect (see Obstfeld and Rogo, 2001; Engel, 2001) and more specically the incomplete pass-through of exchange rate shocks into international prices. In the past decade, substantial progress 6 has been made in the study of this phenomenon, both theoretically and empirically. This literature has explored three channels leading to incomplete pass-through. The rst channel, as surveyed in Engel (2003), is short-run nominal rigidities with prices sticky in the local currency of the destination market, labeled in the literature as local currency pricing (LCP). Under LCP, the rms that do not adjust prices have zero short-run pass-through. Gopinath and Rigobon (2008) provide direct evidence on the extent of LCP in the US import and export prices. The second channel pricing-to-market (PTM)arises in models of variable markups in which rms optimally choose dierent prices for dierent destinations depending on local market conditions. Atkeson and Burstein (2008) provide an example of a recent quantitative investigation of the PTM channel and its implication for international aggregate 4 Other related papers include Kugler and Verhoogen (2009), Manova and Zhang (2009), Feng, Li, and Swenson (2012), and Damijan, Konings, and Polanec (2012). 5 Blaum, Lelarge, and Peters (2010) document stylized facts about import behavior of French rms and provide another related model. 6 For the survey of earlier work, see Goldberg and Knetter (1997), who in particular emphasize that [l]ess is known about the relationship between costs and exchange rates. . . (see p. 1244). The handbook chapter by Burstein and Gopinath (2012) provides a summary of recent developments in this area. 4 7 prices. Finally, the third channel of incomplete pass-through into consumer prices often considered in the literature is local distribution costs, as for example in Burstein, Neves, and Rebelo (2003) and Goldberg and Campa (2010). Our imported inputs channel is similar in spirit to the local distribution costs in that they make the costs of the rm more stable in 8 the local currency of export destination. A related line of literature identies the PTM channel by structurally estimating industry demand to back out model-implied markups of the rms. Goldberg and Hellerstein (2008) 9 provide a summary of the ndings in this literature, in particular that markup variation accounts only for a portion of exchange rate incompleteness, implying an important residual role for the marginal cost channel, for example, due to local distribution costs or imported intermediate inputs. Our work is complementary in that we provide direct measures of both markup and marginal cost variability, and conrm the importance of imported intermediate inputs in moderating exchange rate pass-through. Our paper is closely related to Berman, Martin, and Mayer (2012) in that we also study the variation in pass-through across heterogeneous rms. While they focus on the role of rm productivity and size, we emphasize the role of imported inputs and destination-specic 10 market shares. Some previous studies have acknowledged the potential role of imported inputs in limiting exchange rate pass-through (e.g., see Gopinath, Itskhoki, and Rigobon, 2010), but none has empirically estimated its impact. Our paper is the rst to incorporate 7 Gopinath and Itskhoki (2011) show the importance of PTM in matching patterns in the international aggregate and micro price data. Fitzgerald and Haller (2012) provide the most direct evidence on PTM by comparing the exchange rate response of prices of the same item sold to both the domestic and the international market. Gopinath, Itskhoki, and Rigobon (2010) and Gopinath and Itskhoki (2010) show that the PTM and LCP channels of incomplete pass-through interact and reinforce each other, with highly variable-markup rms endogenously choosing to price in local currency as well as adopting longer price durations. 8 The dierence with the distribution cost channel is that the use of imported inputs results in incomplete pass-through not only into consumer prices, but also into the at-the-dock export prices of the producers. 9 See structural evidence on PTM in Goldberg and Verboven (2001) for the European car market, and in Nakamura and Zerom (2010) and Goldberg and Hellerstein (2011) for the coee and beer markets respectively, where the latter two papers explicitly incorporate price stickiness. De Loecker, Goldberg, Khandelwal, and Pavcnik (2012) apply an alternative structural methodology to identify markups, and estimate the pass- through from import taris into domestic prices, marginal costs and markups. 10 A number of earlier papers have linked pass-through with market share of exporters. Feenstra, Gagnon, and Knetter (1996), Alessandria (2004), and Garetto (2012) emphasize the U-shape relationship between market share and pass-through. The Atkeson and Burstein (2008) model can in general produce such a non-monotonic relationship, however when the price index is held constant, consistent with our empirical strategy, pass-through monotonically decreases in market share. Empirically, we also nd no evidence of a U-shape relationship between market share and pass-through (see footnote 33). A recent paper by Auer and Schoenle (2012) shows that greater sector-level market share of exporters from a particular country contributes to higher pass-through. We instead focus on the rm-level interaction between market share and pass-through, and nd a negative relationship. These seemingly contradictory ndings are consistent with each other in a model of strategic complementarities due to counteracting general equilibrium eects operating at the sectoral level and held constant in our analysis (see Burstein and Gopinath, 2012). 5 the endogenous choice of importing within an exchange rate pass-through model, as well as to construct a theoretically consistent empirical measure of import intensity at the rm level and estimate its impact on pass-through. In addition, the focus of our paper is on the interaction between the imported inputs and the PTM channels, which, as we show, reinforce and amplify each other. We further build on the previous literature by quantita- tively decomposing the contribution of the marginal cost and variable markup channels to 11 incomplete exchange rate pass-through. The rest of the paper is structured as follows. Section 2 lays out the theoretical frame- work and provides the theoretical results that motivate the empirical analysis that follows. Section 3 describes our main empirical ndings. It also provides information on the dataset, highlights the stylized patterns of cross-sectional variation in the data, and reports the results of the robustness tests. Section 4 concludes. 2 Theoretical Framework In this section, we develop a theoretical framework linking a rm's exchange rate pass- through to its import intensity and export market shares, all of which are endogenously determined. We use this framework to formulate testable implications and to derive an empirical specication, which we later take to the data. We start by laying out the two main ingredients of our frameworkthe Atkeson and Burstein (2008) model of strategic complementarities and variable markups and the Halpern, Koren, and Szeidl (2011) model of the rm's choice to import intermediate inputs. We then show how the interaction of these two mechanisms generates new theoretical insights on the determinants of exchange rate pass-through. The key predictions of this theory are that a rm's import intensity and market shares are positively correlated in the cross-section and together constitute prime determinants of incomplete exchange rate pass-through at the rm level, with import inten- sity proxying for marginal cost sensitivity to the exchange rate and market shares proxying for markup elasticity. All the technical derivations are provided in the appendix. We develop the model in partial equilibrium and focus on the equilibrium cross-sectional variation between rms within industries and export destinations. This approach allows us to derive sharp predictions for cross-sectional variation, holding constant the general 11 Burstein and Jaimovich (2008) emphasize the importance of discriminating between the marginal cost and the markup channels in order to assess the welfare implications of pass-through incompleteness. We return to this issue in the concluding section, where we also discuss the implications of our ndings for the misallocation literature (see Hsieh and Klenow, 2009). 6 equilibrium environment of the rms within industry-destinations, without imposing any exogeneity assumptions for exchange rate shocks. To focus our analysis on the relationship between import intensity and pass-through of the rms, we make a number of simplifying assumptions. First, we condition our analysis on the subset of exporting rms, and hence we do not model entry, exit, or selection into exporting (as, for example, in Melitz, 2003), but rather focus on the import decisions of the rms. Similarly, we do not model the decision to export to multiple destinations, but simply take this information as exogenously given. These additional sources of endogenous selection would only reinforce the cross-sectional patterns predicted by the model and leave the qualitative predictions for pass-through unchanged. Furthermore, we assume all rms are single-product, but as we explain below, within this framework one can think about multi-product rms in a similar way as multi-destination rms. Second, we assume exible price setting as in Atkeson and Burstein (2008) and hence do not need to characterize the currency choice (i.e., local versus producer currency pricing). This modeling choice is motivated by the nature of our dataset in which we use unit values as proxies for prices. Empirically, incomplete pass-through is at least in part due to price stickiness in local currency, and in light of this we provide a careful interpretation of our 12 results in the discussion section (see Section 4). Last, while the marginal cost channel emphasized in the paper is inherently a mechanism of real hedging, in modeling rms' import decisions we abstract from choosing or switching import source countries to better hedge their export exchange rate risk. Empirically, we nd that the positive correlation between a rm's destination specic exchange rate and its import-weighted exchange rate does not vary with the main rm variables that are the focus 13 of our analysis (see Section 3). 12 It is useful to keep in mind that, as shown in Gopinath, Itskhoki, and Rigobon (2010), the exible-price pass-through forces shape the currency choice of the rms, i.e. rms with a low pass-through conditional on a price change choose to price in local currency, which further reduces the short-run pass-through of these rms. In this paper, we focus on the endogenous determinants of exible-price (or long-run) pass-through in the cross-section of rms, which in the sticky price environment would also contribute to the prevalence of local currency pricing, yet the two forces work in the same direction. 13 Note that under the assumption of risk neutrality of the rm and in the absence of liquidity constraints (for example, of the type modeled in Froot, Scharfstein, and Stein, 1993), nancial hedging constitutes only a side bet to the rm and does not aect its import and pricing decisions. Fauceglia, Shingal, and Wermelinger (2012) provide evidence on the role of imported inputs in natural hedging of export exchange rate risk by Swiss rms and Martin and Méjean (2012) provide survey evidence on the role of currency hedging in international transactions of the Euro Zone rms. 7 2.1 Demand and markups Consider a rm producing a dierentiated good i in sector s and supplying it to destination market k in period t. Consumers in each market have a nested CES demand over the varieties of goods, as in Atkeson and Burstein (2008). The elasticity of substitution across the varieties within sectors is ρ, while the elasticity of substitution across sectoral aggregates is η, and we assume ρ > η ≥ 1. Under these circumstances, a rm i faces the following demand for its product: −ρ ρ−η Qk,i = ξk,i Pk,i Pk Dk , (1) where Qk,i is quantity demanded, ξk,i is a relative preference (quality) parameter of the rm, Pk,i is the rm's price, Pk is the sectoral price index, and Dk is the sectoral demand shifter, which the rm takes as given. Index k emphasizes that all these variables are destination specic. For brevity, we drop the additional subscripts s and t for sector and time, since all of our analysis focuses on variation within a given sector. 1−ρ 1/(1−ρ) P The sectoral price index is given by Pk ≡ i ξk,i Pk,i , where the summation is P across all rms in sector s serving market k in time period t, and we normalize i ξk,i = 1. As a convention, we quote all prices in the local currency of the destination market. An important characteristic of the rm's competitive position in a market is its market share given by: 1−ρ Pk,i Qk,i Pk,i Sk,i ≡P = ξk,i ∈ [0, 1], (2) i0 Pk,i0 Qk,i0 Pk where market share is sector-destination-time specic. The eective demand elasticity for the rm is then d log Qk,i σk,i ≡ − = ρ(1 − Sk,i ) + ηSk,i , (3) d log Pk,i since ∂ log Pk /∂ log Pk,i = Sk,i . In words, the rm faces a demand elasticity that is a weighted average of the within-sector and the across-sector elasticities of substitution with the weight on the latter equal to the market share of the rm. Larger market share rms exert a stronger impact on the sectoral price index, making their demand less sensitive to their own price. When rms compete in prices, they set a multiplicative markup Mk,i ≡ σk,i /(σk,i − 1) over their costs. Firms face a demand with elasticity decreasing in the market share, and hence high-market-share rms charge high markups. We now dene a measure of the markup 8 elasticity with respect to the price of the rm, holding constant the sector price index:14 ∂ log Mk,i Sk,i Γk,i ≡ − = > 0. (4) ∂ log Pk,i ρ − Sk,i 1 − ρ−η S ρ−η ρ−1 k,i A lower price set by the rm leads to an increase in the rm's market share, making optimal a larger markup. Furthermore, the markup elasticity is also increasing in the market share of the rm. We summarize this discussion in: Proposition 1 Market share of the rm Sk,i is a sucient statistic for its markup; both markup Mk,i and markup elasticity Γk,i are increasing in the market share of the rm. The monotonicity of markup and markup elasticity in market share is a sharp prediction of this framework. Although this prediction is not universal for other demand structures, it emerges in a wide class of models, as surveyed in Burstein and Gopinath (2012). In Section 3, we directly test this prediction and nd no evidence of non-monotonicity in the data. 2.2 Production and imported inputs We build on Halpern, Koren, and Szeidl (2011) to model the cost structure of the rm and its choice to import intermediate inputs. Consider a rm i, which uses labor Li and intermediate inputs Xi to produce its output Yi according to the production function: Yi = Ωi Xiφ L1−φ i , (5) where Ωi is rm productivity. Parameter φ ∈ [0, 1] measures the share of intermediate inputs in rm expenditure and is sector specic but common to all rms in the sector. Intermediate inputs consist of a bundle of intermediate goods indexed by j ∈ [0, 1] and aggregated according to a Cobb-Douglas technology: ˆ 1 Xi = exp γj log Xi,j dj . (6) 0 The types of intermediate inputs vary in their importance in the production process as ´1 measured by γj , which satisfy 0 γj dj = 1. Each type j of intermediate good comes in two 14 We choose this partial measure of markup elasticity (holding price index Pk constant) because in what follows we focus on the dierences in price response across rms within sectors, hence facing the same sector- destination price index. Note that the monotonicity result in Proposition 1 does not in general apply to other measures of markup elasticity without further parameter restrictions. 9 varietiesa domestic and a foreignwhich are imperfect substitutes: ζ 1 ζ 1+ζ ζ 1+ζ 1+ζ 1+ζ Xi,j = Zi,j + aj Mi,j , (7) where Zi,j and Mi,j are respectively the quantities of domestic and imported varieties of the intermediate good j used in production. The elasticity of substitution between the domestic and the foreign varieties is (1 + ζ) > 1, and aj measures the productivity advantage (when aj > 1, and disadvantage otherwise) of the foreign variety. Note that since home and foreign varieties are imperfect substitutes, production is possible without the use of imported inputs. At the same time, imported inputs are useful due both to their potential productivity advantage aj and to the love-of-variety feature of the production technology (7). A rm needs to pay a rm-specic sunk cost fi in terms of labor in order to import each type of the intermediate good. The cost of labor is given by the wage rate W ∗ , and the prices of domestic intermediates are {Vj∗ }, both denominated in units of producer currency (hence starred). The prices of foreign intermediates are {Em Uj }, where Uj is the price in foreign currency and Em is the exchange rate measured as a unit of producer currency for one unit 15 ´1 of foreign currency. The total cost of the rm is therefore given by W ∗ Li + Vj∗ Zi,j dj + ´ 0 Em Uj Mi,j + W ∗ fi dj , J0,i where J0,i denotes the set of intermediates imported by the rm. With this production structure, we can derive the cost function of the rm. In partic- ular, given output Yi and the set of imported intermediates J0,i , the rm chooses inputs to minimizes its total costs subject to the production technology in equations (5)(7). This results in the following total variable cost function net of the xed costs of importing: C∗ T V Ci∗ (Yi |J0,i ) = Yi , (8) Biφ Ωi 16 where C∗ is the cost index for a non-importing rm. The use of imported inputs leads to a n´ o 1/ζ ≡ 1+aj (Em Uj /Vj∗ )−ζ cost-reduction factor Bi ≡ B(J0,i ) = exp γ log bj dj J0,i j , where bj is the productivity-enhancing eect from importing type-j intermediate good, adjusted for the relative cost of the import variety. We now describe the optimal choice of the set of imported intermediate goods, J0,i , in the absence of uncertainty. First, we sort all intermediate goods j by γj log bj , from highest to lowest. Then, the optimal set of imported intermediate inputs is an interval J0,i = [0, j0,i ], 15 We denote by m a generic source of imported intermediates, and hence Em can be thought of as an import-weighted exchange rate faced by the rms. 16 This cost index is given by φ 1−φ ´1 C ∗ = V ∗ /φ W ∗ /(1 − φ) V ∗ = exp γj log Vj∗ /γj dj . with 0 10 with j0,i ∈ [0, 1] denoting the cuto intermediate good. The optimal choice of j0,i trades o the xed cost of importing W ∗ fi for the reduction in total variable costs from the access to 17 an additional imported input, which is proportional to the total material cost of the rm. This reects the standard trade-o that the xed cost activity is undertaken provided that the scale of operation (here total spending on intermediate inputs) is suciently large. With this cost structure, the fraction of total variable cost spent on imported intermediate inputs equals: ˆ j0,i γj 1 − b−ζ ϕi = φ j dj, (9) 0 where φ is the share of material cost in total variable cost and γj (1 − b−ζ j ) is the share of material cost spent on imports of type-j intermediate good for j ∈ J0,i . We refer to ϕi as the import intensity of the rm, and it is one of the characteristics of the rm we measure directly in the data. Finally, holding the set of imported varieties J0,i constant, this cost structure results in the following marginal cost: M Ci∗ = C ∗ / Biφ Ωi . (10) The partial elasticity of this marginal cost with respect to the exchange rate Em equals the expenditure share of the rm on imported intermediate inputs, ϕi = ∂ log M Ci∗ /∂ log Em , which emphasizes the role of import intensity in the analysis that follows. We summarize these results in: Proposition 2 Within sectors, rms with larger total material cost or smaller xed cost (i) of importing have a larger import intensity, ϕi . (ii) The partial elasticity of the marginal cost of the rm with respect to the (import-weighted) exchange rate equals ϕi . 2.3 Equilibrium relationships We now combine the ingredients introduced above to study the optimal price setting of the rm, as well as the equilibrium determinants of the market share and import intensity of the rm. Consider rm i supplying an exogenously given set Ki of destination markets k. The 17 The marginal imported input satises γj0,i log bj0,i · T M Ci = W ∗ fi , where the left-hand side is the ∗ φ incremental benet proportional to the total material cost of the rm T M Ci ≡ φC Yi / Bi Ωi and the cost-saving impact of additional imports γj0,i log bj0,i . 11 rm sets destination-specic prices by solving ( ) X C∗ max Ek Pk,i Qk,i − Yi , Yi ,{Pk,i ,Qk,i }k k∈Ki Biφ Ωi P subject to Yi = k∈Ki Qk,i and demand equations (1) in each destination k. We quote the destination-k price Pk,i in the units of destination-k local currency and use the bilateral nominal exchange rate Ek to convert the price to the producer currency, denoting with ∗ Pk,i ≡ Ek Pk,i the producer-currency price of the rm for destination k. An increase in Ek corresponds to the depreciation of the producer currency. The total cost of the rm is quoted 18 in units of producer currency and hence is starred. Note that we treat the choice of the set of imported goods J0,i and the associated xed costs as sunk by the price setting stage. The problem of choosing J0,i before the realization of uncertainty is dened and characterized in the appendix and Section 3 provides empirical evidence supporting this assumption. Taking the rst order conditions with respect to Pk,i , we obtain the optimal price setting conditions: ∗ σk,i ∗ C∗ Pk,i = M Ci = Mk,i φ , k ∈ Ki , (11) σk,i − 1 Bi Ωi where M Ci∗ is the marginal cost as dened in (10) and Mk,i = σk,i /(σk,i − 1) is the mul- tiplicative markup with the eective demand elasticity σk,i dened in (3). This set of rst order conditions together with the constraints fully characterizes the allocation of the rm, given industry-level variables. In the appendix we exploit these equilibrium conditions to derive how relative market shares and import intensities are determined in equilibrium across rms, and since these results are very intuitive, here we provide only a brief summary. We show that other things equal and under mild regularity conditions, a rm with higher productivity Ωi , higher quality/demand ξk,i , lower xed cost of importing fi , and serving a larger set of destinations Ki has a larger market share Sk,i and a higher import intensity ϕi . Intuitively, a more productive or higher-demand rm has a larger market share and hence operates on a larger scale which justies paying the xed cost for a more comprehensive ac- cess to the imported intermediate inputs (larger set J0,i ). This makes the rm more import intensive, which through the cost-reduction eect of imports (larger Bi in (8)) enhances the productivity of the rm and, in turn, results in higher market shares. We refer to this feed- back mechanism as the amplication eect of import intensity of the rm. This discussion implies that market shares and import intensities are likely to be positively correlated in the 18 We do not explicitly model variable trade costs, but if they take an iceberg form, they are without loss of generality absorbed into the ξk,i Dk term in the rm-i demand (1) in destination k. 12 cross-section of rms, a pattern that we document in the data in Section 3. 2.4 Imported inputs, market share, and pass-through We are now in a position to relate the rm's exchange rate pass-through into its export prices with its market share and import intensity. The starting point for this analysis is the optimal price setting equation (11), which we rewrite as a full log dierential: ∗ d log Pk,i = d log Mk,i + d log M Ci∗ . (12) Consider rst the markup term. Using (2)(4), we have: Γk,i d log Mk,i = −Γk,i d log Pk,i − d log Ps,k + d log ξk,i , (13) ρ−1 ∗ where converting the export price to local currency yields d log Pk,i = d log Pk,i − d log Ek , and we now make explicit the subscript s indicating that Ps,k is the industry-destination- specic price index. The markup declines in the relative price of the rm and increases in the rm's demand shock. From Proposition 1, Γk,i is increasing in the rm's market share, and hence price increases for larger market-share rms are associated with larger declines in the markup. Next, the change in the marginal cost in equation (10) can be decomposed as follows: Em Ūs Cs∗ d log M Ci∗ = ϕi d log + d log + M i C . (14) V̄s∗ Ω̄s This expression generalizes the result of Proposition 2 on the role of import intensity ϕi by providing the full decomposition of the change in the log marginal cost. Here Ūs and V̄s∗ are the price indexes for the imported intermediates (in foreign currency) and domestic intermediates (in producer currency), respectively. The subscript s emphasizes that these indexes can be specic to sector s in which rm i operates. Finally, d log C̄s∗ /Ω̄s is the log change in the industry-average marginal cost for a rm that does not import any interme- diates, and M i C is a rm-idiosyncratic residual term dened explicitly in the appendix and assumed orthogonal with the exchange rate. In deriving (14), we maintain the assumption that the set of imported intermediates J0,i is sunk, yet this can be relaxed without qualitative consequences for the results. Combining and manipulating equations (12)(14), we prove our key theoretical result: 13 Proposition 3 The rst order approximation to the exchange rate pass-through elasticity into producer-currency export prices of the rm is given by ∗ d log Pk,i Ψ∗k,i ≡E = αs,k + βs,k ϕi + γs,k Sk,i , (15) d log Ek where (αs,k , βs,k , γs,k ) are sector-destination specic and depend only on average moments of equilibrium co-movement between aggregate variables common to all rms. We now provide the interpretation of this result. The pass-through elasticity Ψ∗k,i mea- sures the equilibrium log changes of the destination-k producer-currency price of rm i relative to the log change in the bilateral exchange rate, averaged across all possible states of the world and shocks that hit the economy. Under this denition, the pass-through elasticity is a measure of equilibrium co-movement between the price of the rm and the exchange rate, rather than a partial equilibrium response to an exogenous movement in the exchange rate. Proposition 3 shows that, independently of a particular general equilibrium environment, we can relate rm-level pass-through to market share and import intensity of the rm, which form a sucient statistic for cross-section variation in pass-through within sector-destination. Under mild assumptions on equilibrium co-movement between exchange rate and aggregate variables (price and cost indexes), we show that βs,k and γs,k are positive. For example: d log Em d log(Em Ūs /V̄s∗ ) 1 βs,k = E · , (16) 1 + Γ̄s,k d log Ek d log Em where Γ̄s,k is the markup elasticity evaluated at some average measure of market share S̄s,k . Intuitively, βs,k depends on the co-movement between export and import exchange rates and the pass-through of import exchange rate into the relative price of imported intermediates, as can be see from (16). Empirically, we expect both of these elasticities to be positive, and hence βs,k > 0. When βs,k > 0 and γs,k > 0, the rms with a higher import intensity (ϕi ) and larger destination-specic market share (Sk,i ) adjust their producer prices by more. This in turn implies that these rms have lower pass-through into destination-currency prices (equal to 1 − Ψ∗k,i ). Intuitively, the high import intensity of a rm reects its marginal cost sensitivity to exchange rate changes, other things equal. Firms with marginal costs strongly co-moving with devaluations against the destination currency respond with a bigger adjustment to their producer-currency prices and hence a lesser change in their destination-currency prices. The larger destination market share of the rm reects its greater markup elasticity. Hence, these 14 19 rms choose to absorb a larger portion of their marginal cost uctuations into markups. Consequently, larger market share rms have lower pass-through into destination-currency export prices (or, equivalently, higher Ψ∗k,i ). In the next section we test these hypotheses, as well as estimate the average magnitudes of β and γ in (15) to quantify the extent of cross-sectional variation in pass-through. 3 Empirical Evidence This section provides our empirical results starting with a description of the dataset and the basic stylized facts on exporters and importers, proceeding with our main empirical results, and concluding with a battery of robustness tests. 3.1 Data description and construction of variables Our main data source is the National Bank of Belgium, which provided a comprehensive panel of Belgian trade ows by rm, product (CN 8-digit level), exports by destination, and imports by source country. We merge these data, using a unique rm identier, with rm level characteristics from the Belgian Business Registry, comprising information on rms' inputs, which we use to construct total cost measures and total factor productivity estimates. Our sample includes annual data for the period 2000 to 2008, beginning the year after the euro was introduced. We focus on manufacturing exports to the OECD countries outside the Euro Zone: Australia, Canada, Iceland, Israel, Japan, the Republic of Korea, New Zealand, Norway, Sweden, Switzerland, the United Kingdom and the United States, 20 accounting for 58 percent of total non-Euro exports. We also include a robustness test with the full set of non-Euro destinations. We provide a full description of all the data sources in the data appendix. The dependent variable in our analysis is the log change in a rm f 's export price of good i to destination country k at time t, proxied by the change in a rm's export unit value, 19 Consider the destination-currency price, Pk,i = Mk,i M Ci∗ /Ek . Changes in Ek aect M Ci∗ /Ek , and rms partially pass them through into their destination-currency price Pk,i and partially absorb them in their markups Mk,i , with the relative strength of the markup adjustment increasing in Γk,i (and hence in Sk,i ). 20 The Euro Zone was formed on January 1, 1999, in Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, and Spain. Greece joined on January 1, 2001, Slovenia joined in 2007, Cyprus and Malta joined in 2008, and Slovakia joined in 2009. We also exclude Denmark from the set of export destinations because its exchange rate hardly moves relative to the Euro. 15 dened as the ratio of export values to export quantities: Export valuef,i,k,t ∆p∗f,i,k,t ≡ ∆ log , (17) Export quantityf,i,k,t where quantities are measured as weights or units. We use the ratio of value to weights, where available, and the ratio of value to units otherwise. We note that unit values are an imprecise proxy for prices because there may be more than one distinct product within a CN 8-digit code despite the high degree of disaggregation constituting close to 10,000 distinct manufacturing product categories over the sample period. Some price changes may be due 21 to compositional changes within a product code or to errors in measuring quantities. To try to minimize this problem, we drop all year-to-year unit value changes of plus or minus 200 percent. A distinctive feature of these data that is critical for our analysis is that they contain rm-level import values and quantities for each CN 8-digit product code by source country. We include all 242 source countries and all 13,000 product codes in the sample. Studies that draw on price data have not been able to match import and export prices at the rm level. In general, many rms engaged in exporting also import their intermediate inputs. In Belgium, around 80 percent of manufacturing exporters import some of their inputs. We use these import data to construct two key variablesthe import intensity from outside the Euro Zone ϕf,t and the log change in the marginal cost ∆mc∗f,t . Specically, Total non-euro import valuef,t ϕf,t ≡ , (18) Total costsf,t where total costs comprise a rm's total wage bill and total material cost. We often average this measure over time to obtain a rm-level average import intensity denoted with ϕf . The change in marginal cost is dened as the log change in unit values of rm imports from all source countries weighted by respective expenditure shares: X X ∆mc∗f,t ≡ ∗ ωf,j,m,t ∆ log Uf,j,m,t , (19) j∈Jf,t m∈Mf,t 21 This is the typical drawback of customs data (as, for exmaple, is also the case with the French dataset used in Berman, Martin, and Mayer, 2012), where despite the richness of rm-level variables, we do not observe trade prices of individual items. As a result, two potential concerns are, one, aggregation across heterogeneous goods even at the very ne level of disaggregation (rm-destination-CN 8-digit product code level) and, two, aggregation over time of sticky prices. In particular, we cannot condition our analysis on a price change of a good, as was done in Gopinath, Itskhoki, and Rigobon (2010) using BLS IPP item-level data, which however is limited in the available rm characteristics and hence not suitable for our analysis. We address these two caveats by conducting a number of robustness tests and providing a cautious interpretation of our ndings in Section 4. 16 ∗ where Uf,j,m,t is the euro price (unit value) of rm f imports of intermediate good j from country m at time t, the weights ωf,j,m,t are the average of period t and t−1 shares of respective import values in the rm's total costs, and nally Jf,t and Mf,t denote the set of all imported goods and import source countries (including inside the Euro Zone) for the rm at a given time period. Note that this measure of the marginal cost is still a proxy since it does not reect the costs of domestic inputs and rm productivity. We control for estimated rm productivity separately; however, data on the prices and values of domestic inputs are not available. Nonetheless, controlling for our measure of the rm-level marginal cost is a substantial improvement over previous pass-through studies that typically control only for the the aggregate manufacturing wage rate or producer price level. Furthermore, our measure of marginal cost arguably captures the component of the marginal cost most sensitive to exchange rate movements. Ideally, we would like to construct ϕf,t and ∆mc∗f,t for each of the products i a rm produces; however, this measure is available only at the rm-f level, which may not be the same for all of the products produced by multi-product rms. To address this multi-product issue, we keep only the rm's main export products, which we identify using Belgium's input- output table for the year 2005, comprising 56 IO manufacturing codes. For each rm, we identify an IO code that accounts for its largest export value over the whole sample period and keep only the CN 8-digit product codes within this major-IO code. The objective is to keep only the set of products for each rm that have similar production technologies. This leaves us with 60 percent of the observations but 90 percent of the value of exports. We also present results with the full set of export products and experiment with dening the major product using more disaggregated product lines, such as HS 4-digit. [MA: please include this footnote - "This approach also deals with the potential problem of including carry-along trade (Bernard, Blanchard, Van Beveren, and Vandenbussche, 2012) i.e. products that rms export but do not produce themselves since these would not be the rms core products" Further, it is possible that some of the rm's imports might be nal goods rather than intermediate inputs. We attempt to identify imported intermediate inputs using a number of dierent approaches. First, we omit any import from the construction of ϕf,t that is 22 dened as a nal product using Broad Economic Codes (BEC). Second, we construct ϕf using only the intermediate inputs for a given industry according to the IO tables. The last key variable in our analysis is a rm's market share, which we construct as 22 See http://unstats.un.org/unsd/cr/registry/regcst.asp?Cl=10. We dene intermediate inputs as including codes 111, 121, 2, 42, 53, 41, and 521. 17 follows: Export valuef,s,k,t Sf,s,k,t ≡ P , (20) f 0 ∈Fs,k,t Export valuef 0 ,s,k,t where s is the sector in which rm f sells product i and Fs,k,t is the set of Belgian exporters to destination k, in sector s at time t. Therefore, Sf,s,k,t measures a Belgium rm's market share in sector s, export destination k at time t relative to all other Belgium exporters. Note that, following the theory, this measure is destination specic. The theory also suggests that the relevant measure is the rm's market share relative to all rms supplying the destination market in a given sector, including exporters from other countries as well as domestic competitors in market k. But, since our analysis is across Belgian exporters within sector-destinations, the competitive stance in a particular sector-destination is common for all Belgian exporters, and hence our measure of Sf,s,k,t captures all relevant variation for our 23 analysis (see below). We dene sectors at the HS 4-digit level, at which we both obtain a nontrivial distribution of market shares and avoid having too many sector-destinations 24 served by a single rm. 3.2 Stylized facts about exporters and importers A salient pattern in our data set is that most exporters are also importers, a pattern also present in many earlier studies cited in the introduction. As reported in Table 1, in the full sample of Belgian manufacturing rms, the fraction of rms that are either exporters or importers is 33%. Out of these rms, 57% both import and export, 28% only import and 16% only export. That is, 22% of manufacturing rms in Belgium export and 78% of 25 exporters also import. We show that this empirical regularity turns out to be important in understanding why there is incomplete exchange rate pass-through. This high correlation between exporting and importing reects the fact that selection into both of these activities is driven by rm characteristics such as productivity and scale of operation. Interestingly, the data reveal a lot of heterogeneity within exporting rms, which are an 23 In an extension of the theory (not provided due to space constraints), a multiproduct rm sets the same markup for all its varieties within a sector, as in (11), where its markup depends on the cumulative market share of all these varieties. Therefore, Sf,s,k,t is indeed the appropriate measure of market power for all varieties i exported by rm f to destination k in sector s at time t. 24 The median of Sf,s,k,t is 7.8%, yet the 75th percentile is over 40% and the export-value-weighted median is 55%. 24% of Sf,s,k,t observations are less than 1%, yet these observations account for only 1.4% of export sales. 3% of Sf,s,k,t observations are unity, yet they account for less than 2.5%. Our results are robust (and, in fact, become marginally stronger) to the exclusion of observations with very small and very large market shares. We depict the cumulative distribution function of Sf,s,k,t in Figure A1 in the appendix. 25 These statistics are averaged over the sample length, but they are very stable year-to-year. In the subsample of exporters we use for our regression analysis in Section 3.3, the fraction of importing rms is somewhat higher at 85.5%, reecting the fact that data availability is slightly biased toward larger rms. 18 Table 1: Exporter and importer incidence Exporters All and/or importers exporters Fraction of all rms 32.6% 23.7% of them: exporters and importers 57.0% 78.4% only exporters 15.8% 21.6% only importers 27.2% Note: Manufacturing rms sample. Average frequencies over the years 20002008. already very select subsample of rms. The large dierences between exporters and non- exporters are already well-known and are also prevalent in our data. The new stylized facts we highlight here are the large dierences within exporters between high and low import- intensity exporting rms. We show in Table 2 that these two groups of exporting rms dier in fundamental ways. We report various rm-level characteristics for high and low import-intensity exporters, splitting exporters into two groups based on the median import 26 intensity outside the Euro Zone (ϕf ) equal to 4.3%. For comparison, we also report the available analogous statistics for non-exporting rms with at least 5 employees. From Table 2, we see that import-intensive exporters operate on a larger scale and are more productive. The share of imported inputs in total costs for import-intensive exporters is 37% compared to 17% for nonimport-intensive exporters, and similarly for imports sourced outside the Euro Zone it is 17% compared to 1.2%. And of course, these numbers are much lower for non-exporters at 1.6% for imports outside Belgium and 0.3% for imports outside the Euro Zone. Import-intensive exporters are 2.5 times larger in employment than nonimport- intensive exporters and 13 times larger than non-exporters; they pay a 15 percent wage premium relative to non-import-intensive rms and a 40 percent wage premium relative to non-exporters. Similarly, import-intensive exporters have much larger total material costs, total factor productivity, and market share. These rms also export and import on a much larger scale, in terms of export and import values, number of export destinations, and import source countries and in numbers of exported and imported varieties of goods. Specically, import-intensive rms import on average a total of 80 varieties of intermediate inputs (at the CN-8-digit level) from 14 countries, of which 9 countries are outside the Euro Zone. Compare this with the lower numbers for nonimport-intensive rms that import 53 varieties from 9 countries, of which 4 countries are outside the Euro Zone. These numbers highlight 26 The unit of observation here is a rm-year. If we split our sample based on rm-product-destination-year (which is the unit of observation in our regression analysis), the median import intensity is higher at 8.2%, however, this has no material consequences for the patterns we document in Table 2. 19 Table 2: Exporting rms with high and low import intensity ϕf Exporters Import Not import Non-exporters intensive intensive Share of total imports in total cost 0.368 0.173 0.016 Share of non-Euro imports in total cost (ϕf ) 0.166 0.012 0.003 Employment (# full-time equiv. workers) 270.9 112.1 20.7 Average wage bill (thousands of Euros) 48.8 42.3 34.9 Material cost (millions of Euros) 103.5 28.1 3.0 Total Factor Productivity (log) 0.36 0.07 Market share (rmdestinationHS-4) 0.19 0.12 Export value 49.6 9.4 # of products exported 28.5 12.0 # of non-Euro export destinations 18.8 9.4 # of non-Euro export destinations by HS-8 8.1 5.0 Import value 49.3 6.9 # of import source countries 14.5 9.2 # of import source countries by HS-8 2.7 2.0 # of HS 8-digit products imported 79.8 53.4 # of HS 8-digit-country products imported 131.0 75.1 Import value outside EZ 20.8 0.5 # of import source countries outside EZ 8.7 4.3 Producer-price pass-through coecient 0.25 0.14 Note: The exporter sub-sample is split at the median of non-Euro import intensity (share of non-Euro imports in total costs) equal to 4.3%. The non-exporter subsample is all non-exporting manufacturing rms with 5 or more employees. All import and export values are in millions of Euros. 33% of low import intensity rms do not import at all, and 48% of them do not import from outside the Euro Zone. The construction of the measured TFP follows standard procedure and is described in the data appendix. that both types of exporting rms are active in importing from a range of countries both within and outside the Euro Zone but that the two types of rms dier substantially in import intensity, consistent with the predictions of our theoretical framework. We exploit the large dierences between these two groups of exporters to show that import-intensive rms have a higher exchange rate pass-through into producer prices which we report in the last row of Table 2 and further explore in Section 3.3. We now provide more details on the distribution of import intensity outside the Euro Zone (ϕf ) among the exporting rms and its relationship with other rm-level variables. We see that the distribution of import intensity among exporters in Table 3, although somewhat skewed toward zero, has a wide support and substantial variation, which we exploit in our regression analysis in Section 3.3. Over 24% of exporters do not import from outside the Euro Zone; yet they account for only 1% of Belgian manufacturing exports. For the majority 20 Table 3: Distribution of import intensity ϕf among exporters fraction fraction of # rms of rms export value ϕf =0 716 24.9% 1.2% 0 < ϕf ≤ 0.1 1,478 51.3% 38.5% 0.1 < ϕf ≤ 0.2 348 12.1% 23.8% 0.2 < ϕf ≤ 0.3 154 5.4% 8.9% 0.3 < ϕf ≤ 0.4 95 3.3% 22.7% ϕf > 0.4 89 3.1% 4.9% Note: Import intensity, ϕf , is the share of imported intermediate inputs from outside the Euro Zone in the total cost of the rm, averaged over the sample period. of rms, the share of imported inputs in total costs ranges between 0 and 10%. At the same time, the export-value-weighted median of import intensity is 12.7% and nearly 28% of export 27 sales are generated by the rms with import intensity in excess of 30%. We further depict the cumulative distribution function of import intensity ϕf in Figure A1 in the appendix, which also provides a cumulative distribution function for our market share variable Sf,s,k,t . Table 4 displays the correlations of import intensity with other rm-level variables in the cross-section of rms. Conrming the predictions of Section 2.3, import intensity is positively correlated with market share, as well as with rm TFP, employment, and revenues. The strongest correlate of import intensity is the total material cost of the rm, consistent with the predictions of Proposition 2. Overall, the correlations in Table 4 broadly support the various predictions of our theoretical framework. At the same time, although import intensity and market share are positively correlated with productivity and other rm performance measures, there is sucient independent variation to enable us to distinguish between the determinants of incomplete pass-through in the following subsections. We close this section with a brief discussion of the patterns of time-series variation in import intensity for a given rm. Import intensity appears to be a relatively stable char- acteristic of the rm, moving little over time and in response to exchange rate uctuations. Specically, the simple regression of ϕf,t on rm xed eects has an R2 of over 85%, imply- ing that the cross-sectional variation in time-averaged rm import intensity ϕf is nearly 6 times larger than the average time-series variation in ϕf,t for a given rm. When we regress the change in ϕf,t on rm xed eects and the lags of the log change in rm-level import- weighted exchange rates, the contemporaneous eect is signicant with the semi-elasticity 27 While the unweighted distribution (rm count) has a single peak, the export-value-weighted distribution has two peaks. This is due to the fact that one exporter with ϕf = 0.33 accounts for almost 14% of export sales. Our results are not sensitive to the exclusion of this largest exporter, which accounts for only 134 observations out of a total of over 90,000 rm-destination-product-year observations in our sample. 21 Table 4: Correlation structure of import intensity Import Material intensity TFP Revenues Empl't cost Market share 0.16 0.20 0.28 0.25 0.27 Material cost 0.23 0.70 0.99 0.83 Employment 0.10 0.60 0.86 Revenues 0.21 0.72 TFP 0.15 Note: Cross-sectional correlations of rm-level variables averaged over time. Material costs, employment, revenues and TFP are in logs. Import intensity is the share of imported intermediate inputs from outside the Euro Zone in the total cost of the rm. of only 0.056, and with osetting, albeit marginally signicant, lag eects. That is, a 10% depreciation of the euro temporarily increases import intensity by 0.56 of a percentage point. Furthermore, we nd that the rm hardly adjusts its imports on the extensive margin in 28 response to changes in its import-weighted exchange rate. All of this evidence provides support for our assumption in Section 2 that the set of imported goods is a sunk decision at the horizons we consider, and hence the extensive margin plays a very limited role in the response of a rm's marginal cost to exchange rate movements, justifying the use of ϕf as a time-invariant rm characteristic in the empirical regressions that follow. To summarize, we nd substantial variation in import intensity among exporters, and this heterogeneity follows patterns consistent with the predictions of our theoretical framework. Next, guided by the theoretical predictions, we explore the implications of this heterogeneity for the exchange rate pass-through patterns across Belgian rms. 3.3 Main empirical ndings Empirical specication We now turn to the empirical estimation of the relationship between import intensity, market share and pass-through in the cross-section of exporters (Proposition 3). The theoretical regression equation (15) cannot be directly estimated since pass-through Ψ∗k,i is not a variable that can be measured in the data. Therefore, we step back to the decomposition of the log price change in equations (12)(14), which we again linearize in import intensity and market share. After replacing dierentials with changes over time ∆, we arrive at our main empirical specication, where we regress the annual change in log export price on the change in the exchange rate, interacted with import intensity and market 28 We measure the extensive margin as the change in rm imports due to adding a new variety or dropping an existing variety at CN 8-digit level. 22 share: ∆p∗f,i,k,t = αs,k + βϕf,t−1 + γ̃Sf,s,k,t−1 ∆ek,t + δs,k + bϕf,t−1 + cSf,s,k,t−1 + ũf,i,k,t , (21) where p∗f,i,k,t is the log Euro producer price to destination k (as opposed to local-currency price) and an increase in the log exchange rate ek,t corresponds to the bilateral depreciation 29 of the Euro relative to the destination-k currency. In our analysis we focus on estimating parameters β and γ̃ with values averaged across sector-destinations. We emphasize that regression (21) is a structural relationship emerging from the theoretical model of Section 2, and Sf,s,k,t−1 corresponds to our measure of market share dened in (20). Under a mild assumption that ∆ek,t is uncorrelated with (ϕf,t−1 , Sf,s,k,t−1 ), we prove in the appendix: Proposition 4 The OLS estimates of β and γ̃ in identify the weighted averages across (21) sector-destinations of βs,k and γs,k ·Ss,k,t−1 respectively, where Ss,k,t−1 is the sector-destination- time-specic cumulative market share of all Belgian exporters and (βs,k , γs,k ) are the theoret- ical coecient in the pass-through relationship (15). This result shows that, despite the fact that we cannot directly estimate the theoretical regression (15), we can nonetheless identify the theoretical coecients in the relationship between pass-through, import intensity and market share. Furthermore, it formally conrms the validity of our measure of the market share relative to other Belgian exporters. Equation (21) is our benchmark empirical specication. Note that it is very demanding in that it requires including sector-destination dummies and their interactions with exchange rate changes at a very disaggregated level. Therefore, we start by estimating equation (21) with a common coecient α for the group of non-Euro OECD countries within the man- ufacturing sector. Later we allow for α to be country-industry specic at a much higher degree of industry disaggregation, as well as estimate (21) for exports to a single destination (US) only. In our main regressions we replace ϕf,t−1 with a time-invariant ϕf to reduce the measurement error, and also to maximize the size of the sample since some of the lagged ϕf,t−1 were unavailable. This has little eects on the results since, as we show, ϕf,t is very persistent over time. In the main specications we also replace Sf,s,k,t−1 with the contem- 30 poraneous Sf,s,k,t , as both give the same results. In the robustness section we report the estimates from the specication with the lagged ϕf,t−1 and Sf,s,k,t−1 . 29 The exchange rates are average annual rates from the IMF. These are provided for each country relative to the US dollar, which we convert to be relative to the Euro. 30 We do not use the time-averaged market share as rms move in and out of sector-destinations over time. 23 Table 5: Import intensity, market share, and pass-through Dep. var.: ∆p∗f,i,k,t (1) (2) (3) (4) (5) (6) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∆ek,t 0.214 0.149 0.129 0.136 0.077 0.088 (0.029) (0.030) (0.028) (0.038) (0.028) (0.031) ∗∗∗ ∗∗∗ ∗ ∗∗∗ ∆ek,t · ϕf 0.526 0.285 0.375 0.178 0.397 (0.097) (0.104) (0.202) (0.108) (0.091) ∗∗∗ ∗∗∗ ∆ek,t · Sf,s,k,t 0.225 0.262 (0.054) (0.059) ∆mc∗f,t 0.582 ∗∗∗ 0.577 ∗∗∗ (0.034) (0.033) FPY FE no no no yes no no Note: Observations unweighted at the rm-destination-product-year level; number of observations in each regression is 92,693. ∆ corresponds to annual changes. All regressions include country xed eects. FPY FE stands for rm-product-year xed eects. Regressions (2)(3) and (6) include a control for the level of ϕf , and regression (5)(6) also include a control for the level of the market share, Sf,s,k,t . ∗ and ∗∗∗ correspond to 10% and 1% signicance levels respectively. Standard errors are clustered at the country-year level, reported in brackets. Alternative clustering at the rm level and at the country-HS 4-digit level yield the same conclusions. Estimation results To explore the underlying mechanisms behind the equilibrium rela- tionship between pass-through, import intensity, and market shares, we begin with a more simple specication and build up to the specication in equation (21). Table 5 reports the results. First, in column 1, we report that at the annual horizon the unweighted average exchange rate pass-through elasticity into producer prices in our sample is 0.21, or, equiva- lently, 0.79(= 1 − 0.21) into destination prices. We refer to it as 79% pass-through. In column 2, we include an interaction between exchange rates and a rm's import intensity. We see that the simple average coecient reported in column 1 hides a considerable amount of heterogeneity, as rms with dierent import intensities have very dierent pass- through rates. Firms with a high share of intermediate inputs relative to total variable costs exhibit lower pass-through into destination-specic export pricesa 10 percentage point higher import intensity is associated with a 5.3 percentage point lower pass-through. A typical rm with zero import intensity has a pass-through of 85%(= 1 − 0.15), while a rm with a 38% import intensity (in the 95th percentile of the distribution) has a pass-through of only 65%(= 1 − (0.15 + 0.53 · 0.38)). Next, we explore whether import intensity operates through the marginal-cost channel or through selection and the markup channel. In columns 3 and 4, we add controls for the marginal cost of the rm to see whether the eect of import intensity on pass-through per- sists beyond the marginal cost channel. In column 3, we control for the change in marginal 24 cost ∆mc∗f,t , measured as the import-weighted change in the rm's import prices of material inputs (see (19)), which is likely to be sensitive to exchange rate changes if the rm relies heavily on imported intermediate inputs. Comparing columns 2 and 3, we see that the coef- cient on the import intensity interaction nearly halves in size once we control for marginal cost, dropping from 0.53 to 0.29, but still remains strongly signicant with a t-stat of 2.74. We conrm this nding with an alternative control for marginal cost changes, by including rm-product-year xed eects (FPY FE) in column 4. In this specication, the only vari- ation that remains is across destinations for a given rm and hence, among other things, 31 arguably controls for all components of the marginal cost of the rms. The coecient on the import intensity interaction in column 4 is somewhat larger compared to column 3, but still about a third smaller compared to column 2 without the control for marginal cost. The coecient in column 4 is much less precisely estimated, yet it remains marginally signicant with a t-stat of 1.86. This result is impressive, given that this specication is saturated with xed eects, and the similarity of the results in columns 3 and 4 provides condence in our measure of marginal cost. The results in column 3 and 4 suggest that, although the marginal cost is an important channel through which import intensity aects pass-through (see Proposition 2), there is still a considerable residual eect after conditioning on the marginal cost that is operating through the markup channel. This eect is consistent with theoretical predictions, since import intensity correlates with market share in the cross-section of rms and market share determines the markup elasticity (hence, omitted variable bias). To test this, in column 5 we augment the specication of column 4 (controlling for ∆mc∗f,t ) with a market share in- teraction with the log change in exchange rate to proxy for markup elasticity, as suggested by Proposition 3. Given that we now control for both marginal cost and markup, we expect import intensity to stop having predictive power. Indeed, the coecient on import inten- sity interaction further nearly halves in size (from 0.29 to 0.18) and becomes statistically 32 insignicant. Finally, column 6 implements our main specication in equation (21) by including the import intensity and market share interactions, without controlling for marginal cost. Propo- 31 Although FPY FE arguably provide the best possible control for marginal cost, the disadvantage of this specication is that it only exploits the variation across destinations and thus excludes all variation within industry-destinations that is the main focus of our analysis. Consequently, we cannot use our measure of market share in a specications with FPY FE since our market share measure only makes sense within industry-destinations, as we discuss in Section 3.1. 32 Importantly, the coecient ∆mc∗f,t in both specications of columns 3 and 5 is remarkably stable at 0.58. The theory suggests that this coecient should be 1/(1 + Γ̄), that is the average pass-through elasticity of idiosyncratic shocks into prices, corresponding to an average markup elasticity of Γ̄ ≈ 0.7, close to the estimates provided in Gopinath and Itskhoki (2011) using very dierent data and methods. 25 0.4 0.25 Unconditional ∆mc∗f,t on ∆ek,t Producer price pass-through, Ψ∗ Cond’l on ∆mc∗f,t only Condl’l on ∆mc∗f,t and Sf,s,k,t 0.2 ∆mc∗f,t on ∆eM Marginal cost sensitivity f,t 0.3 Cond’l on Sf,s,k,t only 0.2 0.1 0.1 Bin 1 Bin 2 Bin 3 Bin 4 Bin 1 Bin 2 Bin 3 Bin 4 0 0 0 0.03 0.09 0.18 0.82 0 0.03 0.09 0.18 0.82 Import intensity bins, ϕf Import intensity bins, ϕf Figure 1: Pass-through by quartile of ϕf distribution Note: Equal-sized bins in terms of rm-product-year-destination observations. The means of ϕf in the four bins are 1.3%, 5.5%, 13.1% and 30.1% respectively. The left panel reports pass-through coecients of ∆p∗f,i,k,t on ∆ek,t within each ϕf -quartile, where the regressions include additional controls in levels and interacted with ∆ek,t , as indicated in the legend of the gure. The right panel reports the pass-through coecients from regressions of the log change in our measure of the marginal cost of the rm ∆mc∗f,t on both bilateral export exchange rates ∆ek,t and rm-level import-weighted exchange rate ∆eM f,t , by quartiles of the ϕf -distribution. Additional information is reported in Table A1 in the appendix. sition 3 suggests that import intensity and market share are two prime predictors of exchange rate pass-through, and indeed we nd that the two interaction terms in column 6 are strongly statistically signicant. Interpreting our results quantitatively, we nd that a rm with a zero import intensity and a nearly zero market share (corresponding respectively to the 5th percentiles of both distributions) has a pass-through of 91.2%(= 1 − 0.088). Although com- plete pass-through for such rms is statistically rejected, a 97% pass-through coecient falls within a 95% condence interval around our point estimate. A hypothetical non-importing rm with a 75% market share relative to other Belgian exporters (corresponding to the 95th percentile of the rm-level distribution of market shares) has a pass-through of 71.5%, that is 19.7 percentage points (= 0.262 · 0.75) lower. Holding this market share constant and increasing the import intensity of the rm from zero to 38% (corresponding again to the 95th percentile of the respective distribution) reduces the pass-through by another 15.1 per- centage points (= 0.397 · 0.38), to 56.4%. Therefore, variation in market share and import 33 intensity explains a vast range of variation in pass-through across rms. 33 Additionally, we have also looked for possible non-monotonic eects of market share on pass-through by augmenting the main specication in column 6 of Table 5 with a quadratic term in market share and its interaction with the exchange rate change. The coecient on the squared market share interaction is negative, but insignicant and small, so even taking its point estimate, the estimated relationship between pass-through and market share remains monotonically increasing throughout the whole range [0, 1] of the market share variable. This conrms the theoretical prediction in Proposition 1. 26 Deciphering the mechanism Our main empirical ndings in Table 5 provide strong support for the theoretical predictions developed in Section 2. However, we want to ensure that these results are smooth and not driven by outliers, as well as to isolate the partic- ular mechanism through which import intensity aects pass-through. We re-estimate the specications in Table 5 nonparametrically, by splitting the distribution of import intensity ϕf into four quartiles. Specically, we estimate a separate pass-through coecient for each quartile of the import intensity distribution, including additional controls, and plot these coecients in the left panel of Figure 1. All estimated coecients, standard errors, and p-values are reported in Table A1 in the appendix. The graph shows that the coecient is estimated to be monotonically higher (thus lower pass-through) as we move from low to higher import intensity bins when we do not include both marginal cost and market share controls. The steepest line corresponds to the unconditional regression (a counterpart to column 2 of Table 5), and is somewhat atter with controls for marginal cost (column 3), and it is much atter after controlling jointly for the change in the marginal cost and the market share interaction (column 5). The dashed line corresponds to our main specication (column 6), which controls for both market share and import intensity, but not marginal cost, and it also exhibits a considerable slope across the import intensity bins. Furthermore, in all of these cases the dierence between the pass-through coecient in the rst and fourth quartiles is signicant with a p-value of 1%, with the exception of when we control for both marginal cost and market share. Consistent with our ndings in column 5 of Table 5, when controlling for market share and marginal costs, the prole of pass-through coecients across the bins of the import intensity distribution becomes nearly at with the dierences between the pass-through values in dierent bins statistically insignicant. A key mechanism that the theory highlights is that import intensity aects exchange rate pass-through by increasing the marginal cost sensitivity to exchange rates (Proposi- tion 2). In the right panel of Figure 1, we test this by regressing our measure of the change in the marginal cost ∆mc∗f,t on the change in the destination-specic exchange rate ∆ek,t and separately on the change in the rm-level import-weighted exchange rate ∆eM f,t , within each 34 quartile of the import-intensity distribution. Indeed, we nd a very tight monotonically in- creasing pattern of marginal cost sensitivity to the destination-specic exchange rates across the bins with increasing import intensity. Quantitatively, an increase in import intensity from 1% on average in the rst quartile to 30% on average in the fourth quartile leads to an increase in marginal cost sensitivity to the exchange rate from 0.03 to 0.17. Consistent 34 The import-weighted exchange rate ∆eM is a weighted average of bilateral exchange rates with weights f,t equal to the import expenditure shares from outside the Euro Zone at the rm-level. 27 Table 6: Pass-through by import-intensity and market-share bins Low import intensity High import intensity ∗∗∗ Low market share 0.114 0.146∗∗∗ Fraction of observations 30.0% 20.0% Share in export value 8.8% 9.3% High market share 0.235∗∗∗ 0.388∗∗∗ Fraction of observations 19.9% 30.1% Share in export value 21.2% 60.7% Note: Coecients from regression of ∆p∗f,i,k,t on ∆ek,t within respective bins. Firms are sorted by market share Sf,s,k into below and above the median equal to 9.8%; and by import intensity ϕf into below and above median equal to 8.2%. All coecients are signicantly dierent from each other at least at a 5% level, with the exception of 0.114 and 0.146 which are statistically distinguishable only at 10.6% level. The reported fraction of observations is at the rm-product-destination level. with the theory, the response of the marginal cost to the import-weighted exchange rate is also monotonically increasing in ϕf and lies strictly above the response to the destination- specic exchange rate, ranging from 0.05 to 0.21. Table A1 reports the coecients from these regressions in columns 6 and 7. Column 8 of Table A1 also reports the projection coecients of rm-level import-weighted exchange rates ∆eM f,t on destination-specic exchange rates ∆ek,t across the quartiles of import-intensity distribution. This link is important for our mechanism since we expect import intensity to aect pass-through into export prices only to the extent that import and export exchange rates correlate with each other (see (16)). We nd these projection coe- cients to be stable at around 0.45, with no systematic and little overall variation across bins of import intensity. In particular, the coecients across the range of import intensity cannot be distinguished statistically from each other. For our results it is unimportant whether real hedging is prevalent, that is, if rms align their import sources and export destinations to hedge their exchange rate risks; however, what is important is the absence of a systematic relationship between real hedging and import intensity. To summarize, we conclude that the marginal cost channel through which import intensity aects pass-through, as emphasized in the theory, is indeed at play empirically and that import intensity does not appear to proxy for other omitted characteristics of the rm, such as the extent of real hedging. Finally, given the importance of the interaction eects between import intensity and market share highlighted in the theory, we explore it further nonparametrically in Table 6 by creating four bins based on whether a rm's market share and import intensity are above or below their respective medians. Within each bin, we estimate a simple pass-through 28 regression of the change in producer export prices on the change in the exchange rate. Consistent with results in column 6 of Table 5, we nd that pass-through into destination- specic export prices decreases signicantly either as we move toward the bin with a higher market share or toward the bin with a higher import intensity. The lowest pass-through of 61%(= 1 − 0.388) is found in the bin with above median market share and above median import intensity, compared with the pass-through of 89%(= 1 − 0.114) for rms with below median import intensity and market share, quantitatively consistent with the results in Table 5. Furthermore, we report in Table 6 the fraction of observations and the share in total export value that fall within each of the four bins. Although we split the sample at the medians along both dimensions, we end up with more observations along the main diagonal (around 30% in each bin) relative to the inverse diagonal (around 20% in each bin). This nding reects the positive correlation between the market share and the import intensity in the cross-section of rms. This notwithstanding, the share of export value in the rst bin with both low market share and low import intensity is only 9%. The fourth bin with both above median import intensity and market share accounts for the majority of export values, namely, over 60%. Table 6 also suggests that the pass-through coecient into destination prices from an unweighted regression as in column 1 of Table 5 should be substantially higher than from a regression in which observations are weighted by respective export values. Indeed, when weighting by export values, we nd a pass-through coecient of 64.5% as opposed to 78.6% 35 in the unweighted specication, consistent with our earlier calculations. Our evidence further shows that part of this dierence is due to greater markup variability among the large exporters, but of a quantitatively similar importance is the higher import intensity of these rms. 3.4 Extensions and robustness In this section, we provide some additional evidence on the particular mechanism at play behind our main empirical ndings, as well as report results from an extensive series of robustness tests. Which imports matter? We rst explore whether imports from all countries are equally important for exchange rate pass-through. Our main results in the previous section focused 35 This dierence also largely helps close the gap in the pass-through estimates between rm-level trade datasets nding larger pass-through (as, for example, in Berman, Martin, and Mayer, 2012) and product-level datasets nding substantially lower pass-through (as, for exmaple, in Gopinath and Itskhoki, 2010). 29 Table 7: Euro-area imports and imports from OECD vs non-OECD countries Euro Area imports OECD vs non-OECD ∗ Dep. var.: ∆pf,i,k,t (1) (2) (3) ∆ek,t · ϕf 0.534*** 0.394** (0.099) (0.094) ∆ek,t · ϕEZ f 0.103 0.027 0.025 (0.122) (0.120) (0.121) ∆ek,t · ϕOECD f 0.485*** (0.156) ∆ek,t · ϕnon−OECD f 0.272 (0.193) ∆ek,t · Sf,s,k,t 0.261*** 0.261*** (0.059) (0.060) Note: ϕEZ f is the share of rm's imports from within the Euro Zone in total variable costs, so that ϕf + ϕEZ f is the share of total imports in variable costs. ϕOECD f and ϕnon−OECD f are the cost shares of imports from non-Euro OECD and non-OECD countries respectively, so that ϕOECD f + ϕnon−OECD f = ϕf . All regressions additionally include ∆ek,t without interactions, as well as controls for levels of all variables included as interaction terms. The coecients on ∆ek,t range closely around 0.088 estimate in column 6 of Table 5 and hence are not reported for brevity. Other details as in Table 5. on the measure of imports from outside the Euro Zone as a share of total variable costs of the rm. Hence, although this measure fully excludes all imports of Belgian rms from other members of the common currency area, it treats symmetrically all source countries outside the currency union. We now ask whether imports from within the Euro Zone play a separate role in aecting pass-through, and whether imports from OECD and non-OECD countries outside the Euro Zone have dierent eects on pass-through. This is a possibility since what matters for marginal cost changes, beyond the exchange rate variation, is the pass-through of shocks into the prices of imported inputs, and this may well vary across import source countries. Table 7 reports the results when we estimate our main empirical specications with additional measures of import intensity. In columns 12, alongside our measure of import intensity from outside the Euro Area ϕf , we include ϕEZ f the share of imports from within the Euro Area in total variable costs. Column 1 has no additional controls, analogous to specication (2) in Table 5, while column 2 also controls for the market share interaction, as in our main specication (6) in Table 5. We nd that imports from within the Euro Area have no additional eect on pass-through once we control for import intensity from outside the Euro Area. Indeed, we do not expect imports from within the Euro Zone to 30 aect marginal costs dierentially from inputs sourced inside Belgium. However, what is also interesting is that importing from within the Euro Zone does not appear to be a strong indicator of rm selection, since this variable does not have predictive ability even when we do not control for market share. In column 3 of Table 5 we re-estimate our main empirical specication but partition the non-euro import intensity ϕf into import intensity from non-OECD and OECD coun- tries outside the Euro Zone, as well as controlling for import intensity from within the Euro Zone, which still turns out inconsequential. We nd that only imports from non-Euro OECD countries have a statistically signicant eect on pass-through, while the eect of imports from non-OECD countries is half as big in its point estimate but is imprecisely estimated. To gain further understanding of these results, we estimate pass-through regres- sions of import-country exchange rates into the price of imported inputs from each country, pooling separately the coecients on all OECD and all non-OECD countries, and weighting the observations by their import shares. We nd the import pass-through coecient to be 48% from OECD countries and only 15% from non-OECD countries. Therefore, despite substantial uctuations in Euro exchange rates with non-OECD countries, the pass-through from these countries into the prices of intermediate goods is very low, which explains why a high import intensity of a rm from these countries has little bearing on the rm's pass- 36 through into export prices. Finally, we nd that larger importers in our sample import more from non-OECD countries, apparently another dimension of rm selection in the data. Specically, the share of non-OECD imports monotonically increases from 24% to 45% as we go from the lowest to the highest quartile of import intensity. This pattern explains the somewhat moderated slope of the marginal cost pass-through across import-intensity quartiles reported in the right panel of Figure 1, and acts to diminish the strength of the export-price pass-through eects that we nd, which are nonetheless large. To ensure that our results are not sensitive to our denition of ϕf , we experimented extensively with alternative denitions. We report these robustness checks in Table A2 in the appendix, where we estimate our main empirical specication using dierent denitions of import intensity. First, in column 1, we verify that our results are unchanged when as in specication (21) we use lagged time-varying ϕf,t−1 and Sf,s,k,t−1 , as suggested by Proposition 4, instead of ϕf and Sf,s,k,t respectively. Remarkably, the coecient on the 36 This dierential pass-through from rich and poor countries has been documented in many previous studies (e.g., see discussion in Gopinath and Itskhoki, 2011). One possible reason for this is low dierentiation of products coming from poor countries. Another potential reason is volatile macroeconomic policies in the poor countries leading to swings in exchange rates, which do not aect foreign-currency prices of international transactions of these countries. 31 import-intensity interaction decreases only marginally, while the coecient on market share interaction is completely unchanged. Next, in columns 2 and 3 of Table A2, we respectively restrict the denition of imports to exclude consumer goods and capital goods. In the subsequent columns, we use IO tables to identify a rm's intermediate inputs. In column 4, we include only imports identied as intermediate inputs in the IO tables for all of the rm's exports, and in column 5 we only include IO inputs for a rm's IO major exports. Finally, in column 6, we exclude any import at the CN 8-digit industrial code if the rm simultaneously exports in this category. In all cases, the results are essentially unchanged, except that in the last case the coecient on the import intensity substantially increases, but it should be noted that the average import intensities here are much lower as we drop a large share of imports from the import intensity calculation. Within destination-industry We now check whether the empirical relationship between pass-through, market share, and import intensity documented in Table 5 is driven largely by within industry-destination variation, as suggested by Propositions 3 and 4. Table A3 reports the results from estimating equation (21) with exchange rate changes interacted with industry-destination xed eects (that is, allowing for sector-destination specic αs,k ). Columns 14 of this table replicate the main specications in Table 5 augmented with destination-industry (SITC 1-digit) xed eects both in levels and interacted with exchange rate changes, hence identifying the pass-through relationship within destination and 1-digit manufacturing industries. The results are nearly identical to those in Table 5, in which we restricted αs,k to be the same across 12 non-Euro OECD destinations and all manufacturing exports. This suggests that the relationship between pass-through, import intensity and market share that we uncover is almost entirely a within industry-destination relationship. We further conrm this in column 5 of Table A3 by controlling for industry interactions at a higher degree of disaggregation (specically, 163 3-digit SITC manufacturing industries), but dropping the destination xed eects. Alternative samples We further check the robustness of our results within alternative subsamples of the dataset, both in the coverage of export destinations and in the types of products. Table A4 in the appendix provides the results from estimates of the main specication from column 6 of Table 5 in eight alternative subsamples. By and large, it reveals the same qualitative and quantitative patterns we nd in our benchmark sample. Columns 13 of Table A4 report the results for three alternative sets of export destinations 32 all non-Euro countries, non-Euro OECD countries excluding the US, and the US only. It is noteworthy that for the US subsample we estimate both a lower baseline pass-through (for rms with zero import intensity and market share) and a stronger eect of import intensity on pass-through, than for other countries. Specically, small non-importing rms export- ing to the US market pass-through on average only 80% of the Euro-Dollar exchange rate changes, while the largest rms with high import-intensity (at the 95th percentile) pass- through only 39%. This is consistent with previous work on low pass-through into the US. The remaining columns in Table A4 consider a dierent set of products and rms. So far, all of the specications have been restricted to the subsample of only manufacturing rms because our ϕf measure is likely to be a better proxy of import intensity in manufac- turing than for wholesalers, who may purchase nal goods within Belgium to export them 37 or alternatively import nal goods for distribution within Belgium. In column 4, which adds in all wholesale rms to our baseline sample, we see that although the import intensity and market share interactions are still positive and signicant, their magnitudes and t-stats are smaller. The wholesalers represent around 40 percent of the combined sample. Next, in column 5, we drop all intra-rm transactions from our baseline sample (around 15 percent 38 of observations), and this has little eect on the estimated coecients. Finally, our sample has included only the rm's major export products, based on its largest IO code, in order to address the issue of multi-product rms. In columns 68, we show that the results are not sensitive to this choice of main products. In column 6, we include all of the rm's manufacturing exports rather than restricting it only to IO major products. In column 7, we adopt an alternative way to identify a rm's major products, using the HS 4-digit category, which is much more disaggregated than the IO categories. And in column 8, we only include a rm if its HS 4-digit major category accounts for at least 50 percent of its total exports. In all three cases, we nd the magnitudes on the import intensity and market share interactions very close to our main specication. Additional controls Our theory provides sharp predictions that market share is a su- cient statistic for markup variability and that import intensity is an important predictor of 37 Another related concern is that even some non-wholesale rms may import their intermediate inputs through other Belgian rms, which we cannot see in our data, and hence cannot adjust accordingly our measure of import intensity. Note, however, that this would work against our ndings since some of the fun- damentally import-intensive rms would be wrongly classied into low import-intensity. This measurement error should cause a downward bias in our estimates of the import-intensity eects on pass-through, which we nd to be large nonetheless. 38 Using data from the Belgium National Bank, we classify intra-rm trade as any export transaction from a Belgium rm to country k in which there is either inward or outward foreign direct investment to or from that country. 33 Table 8: Robustness with additional controls Dep. var.: ∆p∗f,i,k,t (1) (2) (3) ∆ek,t · ϕf 0.326*** 0.353*** 0.387*** (0.095) (0.098) (0.098) ∆ek,t · Sf,s,k,t 0.199*** 0.235*** 0.265*** (0.060) (0.061) (0.060) ∆ek,t · log Lf,t 0.043*** (0.012) ∆ek,t · log T F Pf,t 0.054** (0.023) ∗ ∆ log Wf,t -0.008 (0.013) ∆ log T F Pf,t 0.037*** (0.006) # observations 91,891 91,424 86,958 Note: The same specication as in column 6 of Table 5, augmented with additional controls. Lf,t is rm employment, Wf,t ∗ is rm average wage rate, and T F Pf,t is the estimate of rm total factor productivity. marginal cost sensitivity to exchange rate changes. Therefore, together they form a sucient statistic for pass-through (Proposition 3). We test this prediction by including additional controls, which could be viewed as alternative proxies for markup elasticity and marginal cost sensitivity to exchange rates. Specically, Table 8 re-estimates the main empirical specication in column 6 of Table 5 with additional controlsrm's employment size and measured TFP interactions with the exchange rate change. Consistent with theory and with the empirical correlations in Table 4, market share and import intensity are both positively correlated with employment and measured TFP in the cross-section of rms. As a result, it is possible that the market share or import intensity variables are picking up variation in 39 one of these other variables. Columns 1 and 2 of Table 8 show that our empirical ndings are robust to the inclusion of additional interaction terms. Controlling for employment and TFP interactions reduces 39 In theories where productivity is the only source of heterogeneity, market share, employment, and productivity itself are all perfectly correlated. However, when there is more than one source of heterogeneity, these variables are correlated less than perfectly. The modeling framework that we use makes a sharp prediction that market share is the sucient statistic for markup. Alternative theories may emphasize rm productivity as the sucient statistic for markup variability, as for example in Berman, Martin, and Mayer (2012). Specications in columns 12 of Table 8 are counterparts to some of their regressions with the exception that we include both the import intensity and market share interactions. Overall, our empirical results are consistent with their ndings in that more productive rms have lower pass-through, but we split this eect into the markup and marginal cost eects by controlling separately for market share and import intensity, and show that these two controls are at least as strong as employment and productivity, consistent with our theoretical model. 34 slightly the estimated coecients on import intensity and market share interactions, but they remain large and strongly statistically signicant. The coecients on employment and TFP interactions, although signicant, are in turn quantitatively very moderate. Finally, column 3 of Table 8 controls for the local component of the marginal cost by including the change in the measure of the rm-level wage rate and the log change in rm TFP to isolate the eect of import intensity through the foreign-sourced component of the marginal cost of the rm. These controls have essentially no eect on the estimated coecients of interest. 4 Conclusion In this paper, we show that taking into account that the largest exporting rms are also the largest importers is key to understanding the low aggregate exchange rate pass-through and the variation in pass-through across rms. We nd that import intensity aects pass- through both directly, by inducing an osetting change in the marginal cost when exchange rates change, and indirectly, through selection into importing of the largest exporters with the most variable markups. We use rms' import intensities and export market shares as proxies for the marginal cost and markup channels, respectively, and show that variation in these variables across rms explains a substantial range of variation in pass-through. A small rm using no imported intermediate inputs has a nearly complete pass-through, while a rm at the 95th percentile of both market share and import intensity distributions has a pass- through of only 56%. Around half of this incomplete pass-through is due to the marginal cost channel, as captured by our import intensity measure. Since import intensity is heavily skewed toward the largest exporters, our ndings help explain the observed low aggregate pass-through elasticities, which play a central role in the study of exchange rate disconnect. Finally, we show that the patterns we document emerge naturally in a theoretical framework, which combines standard ingredients of oligopolistic competition and variable markups with endogenous selection into importing at the rm level. Our ndings suggest that the marginal cost channel contributes substantiallyreinforcing and amplifying the markup channelto low aggregate pass-through and pass-through vari- ation across rms. The decomposition of incomplete pass-through into its marginal cost and markup components is necessary for the analysis of the welfare consequences of exchange rate volatility and the desirability to x exchange rates, for example, by means of integra- tion into a currency union. Furthermore, price sensitivity to exchange rates is central to the expenditure switching mechanism at the core of international adjustment and rebalancing. A sign of ineciency is when exchange rate movements aect mostly the distribution of 35 markups across exporters from dierent countries, leading to little expenditure switching. However, if the lack of pass-through is largely due to the complex international web of in- termediate input sourcing, incomplete pass through of exchange rates into prices may well be an ecient response. A complete analysis of the welfare consequences requires a general equilibrium model disciplined with the evidence on the importance of marginal cost and markup channels of the type we provide, and we leave this important question for future research. Even after controlling for the marginal cost channel, our evidence still assigns an im- portant role for the markup channel of incomplete pass-through. In particular, we nd that large high-market-share rms adjust their markups by more in response to cost shocks. This is consistent with a model in which larger rms also choose higher levels of markups, a pattern that can rationalize the evidence on misallocation of resources across rms, as, for example, documented in Hsieh and Klenow (2009). The markup interpretation of this evidence on misallocation diers from the conventional cost-side frictions interpretation (an exception in the literature is Peters, 2011). Our evidence, therefore, is useful for calibration and quantitative assessment of the models of misallocation at the rm-level. Finally, we briey comment on the interpretation of our results in an environment with sticky prices, where exporters choose to x their prices temporarily either in local or in producer currency. Since we cannot condition our empirical analysis on a price change or split the sample by currency of pricing, our results confound together the change in the desired markup with the mechanical changes in markup induced by the exchange rate movements when prices are sticky in a given currency. Therefore, one should keep in mind that our results suggest that import intensity and market share contribute either to exible-price pass-through incompleteness or to the probability of local currency pricing, which in turn leads to low pass-through before prices adjust. In reality, our results are likely to be driven 40 partly by both these sources of incomplete pass-through. Indeed, Gopinath, Itskhoki, and Rigobon (2010) show that the two share the same primitive determinants and provide evidence that the choice to price in local currency is closely correlated in the cross-section of rms with the pass-through incompleteness conditional on price adjustment. Nonetheless, we favor the exible-price interpretation of our results, as we focus on a relatively long horizon using annual data. 40 Our data do not allow us to do a decomposition into these two sources, but one can make such inference by taking a stand on a particular structural model of incomplete pass-through with sticky prices, and using outside information to calibrate its parameters related to price stickiness and currency of pricing. We do not attempt this exercise in the current paper. 36 A Appendix A.1 Theoretical Appendix A.1.1 Cost function and import intensity For brevity, we drop the rm identier i in this derivation. Given output Y and the set of imported intermediate goods J0 , the objective of the rm is ˆ 1 ˆ ∗ ∗ Vj∗ Zj dj ∗ T C (Y |J0 ) ≡ min W L+ + Em Uj Mj + W f dj , L,X,{Xj ,Zj },{Mj } 0 J0 Denote by λ, ψ and χ the Lagrange multiplier on constraints (5), (6) and (7) respectively. The rst order conditions of cost minimization are respectively: W ∗ = λ(1 − φ)Y /L, ψ = λφY /X, χ = ψγj X/Xj , j ∈ [0, 1], Vj∗ = χ(Xj /Zj )1/(1+ζ) , j ∈ [0, 1], 1/(1+ζ) Em Uj = χ(aj Xj /Mj ) , j ∈ J0 , with Mj = 0 and Xj = Zj for j ∈ J˜0 ≡ [0, 1]\J0 . Expressing out ψ and χ, taking the ratio of the last two conditions and rearranging, we can rewrite: W ∗ L = λ(1 − φ)Y, Vj∗ Xj = λφγj Y (Xj /Zj )1/(1+ζ) , j ∈ [0, 1], −ζ Em Uj Mj Em U j = aj , j ∈ J0 . Vj∗ Zj Vj∗ 1+ζ aj (Em Uj /Vj∗ )−ζ Substituting the last expression into (7), we obtain Xj = Zj 1 + ζ for j ∈ J0 , which together with the expression for Vj∗ Xj above yields: λφγj Y bj , j ∈ J0 , Vj∗ Xj = λφγj Y, j ∈ J˜0 , where 1/ζ bj ≡ 1 + aj (Em Uj /Vj∗ )−ζ . (A1) Based on this, we express L and Xj for all j ∈ [0, 1] as functions of λY and parameters. Substituting these expressions into (5)(6), we solve for  n´ V ∗ o φ 1 j 1  exp 0 γj log γj dj  1−φ W∗ C∗ λ= n´ o = φ , (A2) Ω φ exp J0 γj log bj dj 1−φ B Ω 37 where ˆ B = exp γj log bj dj (A3) J0 ∗ ∗ ∗ and C is dened in footnote 16. Finally, we substitute the expression for W L, Vj Zj = Vj∗ Xj · (Zj /Xj ) and Em Uj Mj = Vj∗ Zj · (Em Uj Mj /(Vj∗ Zj )) into the cost function to obtain ´ T C ∗ (Y ; J0 ) = λY + J0 W ∗ f dj. (A4) Choice of J0 without uncertainty minJ0 T C ∗ (Y |J0 ), given output Y . Consider solves adding an additional variety j0 ∈ / J0 to the set J0 . The net change in the total cost from this is given by ∂λ Bγj0 log bj0 + W ∗ f = −φλY · γj0 log bj0 + W ∗ f, Y ∂B since γj0 log bj0 is the increase in log B from adding j0 to the set of imports J0 . Note that ´1 ´ φλY = 0 Vj∗ Zj dj + J0 Em Uj Mj dj is the total material cost of the rm. Therefore, the optimal choice of J0 must satisfy the following xed point:   ∗  C /Ω  J0 = j ∈ [0, 1] : φ n ´ o Y · γj log bj ≥ W ∗ f .  exp φ J0 γ` log b` d`  This immediately implies that once j 's are sorted such that γj log bj is decreasing in j , the set of imported inputs is an interval J0 = [0, j0 ] for some j0 ∈ [0, 1]. Furthermore, the condition for j0 can be written as:   ∗  C /Ω  j0 = max j ∈ [0, 1] : φ n ´ o Y · γj log bj ≥ W ∗ f , (A5) j  exp φ 0 γ` log b` d`  and such j0 is unique since the LHS of the inequality is decreasing in j. Figure A2 provides an illustration. Proof of Proposition 2 The fraction of variable cost spent on imports is given by ´ ˆ J0 Em Uj Mj dj ϕ= = γj (1 − bζj )dj, λY J0 where we used the rst order conditions from the cost minimization above to substitute in for E m U j Mj . Note that ϕ J0 , and in particular when J0 = [0, j0 ], ϕ increases increases in in j0 . Therefore, from (A5) it follows that ϕ increases in total material cost T M C = φλY = φ[C ∗ Y ]/[B φ Ω] and decreases in xed cost W ∗ f . From the denition of total cost (A4), holding J0 constant, the marginal cost equals 38 M C ∗ (J0 ) = λ dened in (A2). We have: ˆ ∂ log M C ∗ (J0 ) ∂ log λ ∂ log B ∂ log bj = = −φ · γj dj = ϕ, ∂ log Em ∂ log B ∂ log Em J0 ∂ log Em since from (A1) ∂ log bj /∂ log Em = −(1 − bζj ). A.1.2 Price setting and ex ante choice of J0 Under the assumption that J0 is a sunk decision chosen before uncertainty is realized, we can write the full problem of the rm (bringing back the rm identier i) as: ( ( )) X max E max Ek Pk,i Qk,i − T Ci∗ (Yi |J0,i ) , J0,i Yi ,(Pk,i ,Qk,i ) k∈Ki P subject to Yi = k∈Ki Qk,i , with (Pk,i , Qk,i ) satisfying demand (1) in each market k ∈ Ki , and total cost given in (A4). We assume that J0,i is chosen just prior to the realization of uncertainty about aggregate variables, and for simplicity we omit a stochastic discount factor which can be added without any conceptual complications. Substituting the constraints into the maximization problem and taking the rst order condition (with respect to Pk,i ), we obtain: ∂Qk,i ∂T Ci∗ (Y |J0,i ) ∂Qk,i Ek Qk,i + Ek Pk,i − = 0, ∂Pk,i ∂Y ∂Pk,i which we rewrite as λi Ek Qk,i (1 − σk,i ) + σk,i Qk,i = 0, Pk,i where σk,i is dened in (3) and λi = M Ci∗ (J0,i ) is dened in (A2). Rearranging and using ∗ Pk,i = Ek Pk,i , results in the price setting equation (11). Now consider the choice of J0,i . By the Envelope Theorem, it is equivalent to min E {T Ci∗ (Yi |J0,i )} , J0,i where Yi is the equilibrium output of the rm in each state of nature. Therefore, this problem is nearly identical to that of choosing J0,i without uncertainty, with the exception that now we have the expectation and Yi varies across states of the world along with exogenous variables ∗ aecting T Ci . As a result, we can write the xed point equation for J0,i in this case as:     ∗   C /Ωi  ∗  J0,i = j ∈ [0, 1] : E φ o Yi · γj log bj ≥ E {W fi } .  exp φ ´ γ log b d` n (A6)    J0,i ` ` Therefore, J0,i still has the structure [0, j0,i ], but now we need to sort goods j in decreasing order by the value of the LHS in the inequality in (A6) (in expected terms). 39 A.1.3 Equilibrium Relationships To illustrate the implications of the model for the equilibrium determinants of market share 0 and import intensity, we study the following simple case. Consider two rms, i and i , in a given industry and both serving a single destination market k . The rms face the same industry-destination specic market conditions reected in Ek , Pk , Dk , C ∗ and φ. We allow the rms to be heterogeneous in terms of productivity Ωi , demand/quality shifter ξk,i and the xed cost of importing fi . For a single-destination rm we have Yi = Qk,i , and we drop index k in what follows for brevity. We want to characterize the relative market shares and import intensities of these two rms. In order to do so, we take the ratios of the equilibrium conditions (demand (1), market 41 share (2) and price (11)) for these two rms: −ρ 1−ρ Mi Biφ0 Ωi0 Yi ξi Pi Si ξi Pi Pi = , = and = , Yi0 ξi0 Pi0 S i0 ξi0 Pi0 Pi0 Mi0 Biφ Ωi where Mi = σi /(σi − 1) and σi = ρ(1 − Si ) + ηSi . Log-linearizing relative markup, we have: Mi Γ̄ Si log = log , Mi0 ρ−1 Si0 where Γ̄ is markup elasticity given in (4) evaluated at some average S̄ . Using this, we linearize the equilibrium system to solve for: Si 1 ξi ρ−1 Ωi Bi log = log + log + φ log (A7) Si0 1 + Γ̄ ξi0 1 + Γ̄ Ωi0 Bi0 and the interim variable (total material cost) which determines the import choice: T M Ci Yi Ωi Bi Γ̄ Si log = log − log − φ log = 1− log . (A8) T M C i0 Yi0 Ωi0 Bi0 ρ−1 Si0 Assumption A1 Γ̄ < (ρ − 1). This assumption implies that the (level of ) markup does not vary too much with the productivity of the rm, so that high-market-share rms are simultaneously high-material- 42 cost rms (as we document is the case in the data, see Table 4). Consequently, under A1, high-market-share rms choose to be more import intensive, as we discuss next. Denote χ(j) ≡ γj E log bj , where expectation is over aggregate equilibrium variables (i.e., 0 aggregate states of the world), and sort j so that χ (·) < 0 on [0, 1]. Assuming the choice of 41 Note that taking these ratios takes out the aggregate variables such as the price index. Intuitively, we characterize the relative standing of two rms in a given general equilibrium environment, and aggregate equilibrium variables such as the price index, which aect outputs and market shares of rms proportionately. 42 This assumption is not very restrictive for the parameters of the model, as for a moderate value of ρ = 4, it only requires S̄ < 0.8 (given the denition of Γ in (4) and η ≥ 1). 40 the import set is internal for both rms, we can rewrite (A6) as a condition for a cuto j0 (i): ( ) φC ∗ Yi E γj0 (i) log bj0 (i) = E{W ∗ fi }, Biφ Ωi and log-linearize it to yield: −χ0 j̄0 0 Yi Ωi Bi fi · j0 (i) − j0 (i ) = E log − log − φ log − log , χ j̄0 Y i0 Ωi0 Bi0 fi 0 where j̄0 is some average cuto variety. Finally, using denition (A3), we have Bi = χ j̄0 · j0 (i) − j0 (i0 ) . E log (A9) Bi0 Combining the above two equations with (A8), we have: −χ0 j̄0 Bi Γ̄ Si fi 2 φE log = 1− E log − log . φχ j̄0 Bi0 ρ−1 Si0 f i0 Combining with (A7), we solve for: " Γ̄ # 1 − ρ−1 Bi 1 ξi Ωi fi φE log = log + (ρ − 1) log − log , (A10) Bi0 κ̄0 − 1+ρ Γ̄ − 1 1 + Γ̄ ξi0 Ωi0 f i0 Si 1 κ̄0 ξi Ωi ρ−1 fi E log = log + (ρ − 1) log − log , (A11) S i0 κ̄0 − 1+ρ Γ̄ − 1 1 + Γ̄ ξi0 Ωi0 1 + Γ̄ f i0 2 κ̄0 ≡ −χ0 j̄0 /[φχ j̄0 ] > 0. where −χ0 j̄0 ρ Assumption A2 κ̄0 ≡ 2 > − 1. φχ j̄0 1 + Γ̄ The parameter restriction in A2 is a local stability condition: the function χ(j) = Eγj log bj must be decreasing in j fast enough, otherwise small changes in exogenous rm characteristics can have discontinuously large changes in the extensive margin of imports. We view it as a technical condition, and assume equilibrium is locally stable. Finally, we relate import intensity of the rm ϕi to Bi . From denition (9) it follows that ν j̄0 B 0 E log i , E ϕi − ϕi0 = ν j̄0 j0 (i) − j0 (i ) = (A12) χ j̄0 Bi0 where ν(j) = γj E{1 − bζj } and the second equality substitutes in (A9). Equations (A10)(A12) provide the log-linear characterization of (expected) relative mar- ket share and relative import intensities of the two rms as a function of their relative exoge- 41 nous characteristics. These approximations are nearly exact when the exogenous dierences between rms are small. In other words, one can think of those relationships as describing elasticities of market share and semi-elasticities of import-intensity with respect to exoge- nous characteristics of the rm (productivity, demand/quality and xed cost of importing), holding the general equilibrium environment constant. Therefore, we have: Proposition A1 Under Assumptions A1 and A2, (expected) market share and import inten- sity of the rm are both increasing in rm's productivity and rm's quality/demand shifter, and are both decreasing in rm's import xed cost, in a given general equilibrium environment (that is, holding the composition of rms constant). A similar result can be proved for rms serving multiple and dierent number of destinations. A.1.4 Pass-through relationship and proof of Proposition 3 Markup Given (2) and (3), we have the following full dierentials: σk,i (ρ − η)Sk,i d log Sk,i d log Mk,i ≡ d log = d log Sk,i = Γk,i , σk,i − 1 σk,i (σk,i − 1) ρ−1 d log Sk,i = d log ξk,i − (ρ − 1) d log Pk,i − d log Pk , where Γk,i is as dened in (4). Combining these two expressions results in (13). Marginal cost Taking the full dierential of (10), we have: C∗ d log M Ci∗ = d log − φd log Bi . Ωi Using denitions (A1) and (A3), and under the assumption that J0 is a sunk decision (that is, the set of imported goods is held constant), we have: Em Uj d log bj = −(1 − bζj )d log , Vj∗ ˆ φd log Bi = φ γj d log bj dj J0,i ˆ Vj∗ Em Ū Uj = −ϕi d log ∗ − φ γj (1 − bζj ) d log − d log ∗ dj, V̄ J0,i Ū V̄ ∗ ´1 = 0 γj d log Vj∗ djdj and similarly d log Ū = where ϕi is dened in (9), and d log V̄ ´1 0 γ j d log U j djdj . Substituting this expression into the full dierential of the marginal cost above results in (14), where the residual is given by: ˆ Vj∗ Uj Ωi M i C = γj (1 − b−ζ j ) d log − d log ∗ dj − d log , J0,i Ū V̄ Ω̄ 42 where d log Ω̄ is the sectoral average change in rm-level productivity. Combining (13) and (14) with (12), we have: ∗ C∗ Em Ū d log Pk,i = −Γk,i d log Pk,i − d log P̃k + d log + ϕi d log ∗ + k,i , (A13) Ω̄ V̄ where Γk,i M ξk,i k,i ≡ M i C + , M k,i ≡ d log ¯ , ρ − 1 k,i ξk d log ξ¯k is the sector-destination average change in demand/quality across rms, we denoted 1 with P̃k ≡ ξkρ−1 Pk the sector-destination price index adjusted for the average demand/quality shifter for Belgian rms. We make the following: Assumption A3 M k,i , k,i , and hence k,i , are mean zero and independent from d log Em C M and d log Ek . Note that k,i reects the rm idiosyncratic dierences in the change in input prices, produc- tivity and demand/quality shifter, and therefore Assumption A3 is a natural one to make. Essentially, we assume that there is no systematic relationship between exchange rate move- ment and rm's idiosyncratic productivity or demand change relative to an average rm from the same country (Belgium) serving the same sector-destination. This nonetheless al- lows the exchange rates to be correlated with sector-destination average indexes for costs ∗ and productivity (that is, Ω̄, Ū , V̄ , as well as P̃k ). ∗ Substituting d log Pk,i = d log Pk,i − d log Ek into (A13) and rearranging, we arrive at: ∗ Γk,i ϕi Em Ūs Γk,i d log P̃s,k + d log Ω̃Cs + k,i ∗ s,k d log Pk,i = d log Ek + d log + , (A14) 1 + Γk,i 1 + Γk,i V̄s∗ 1 + Γk,i where we have now made the sector identier s an explicit subscript (each i uniquely deter- mines s, hence we do not carry s when i is present). Note that Γk,i is increasing in Sk,i . We now linearize (A14) in ϕi and Sk,i : Lemma A1 Log price change expression (A14) linearized in ϕi and Sk,i is ∗ Γ̄s,k ḡs,k 1 Em Ūs d log Pk,i ≈ d log Ek + S̃k,i d log Ek + ϕi d log (A15) 1 + Γ̄s,k 1 + Γ̄s,k 1 + Γ̄s,k V̄s∗  ∗ ∗  Γ̄s,k d log P̃s,k + d log Ω̃Cs + ¯0k,i ḡs,k d log P̃s,k − ϕ̄s d log EmV̄ Ū∗ s − d log Ω̃Cs + ¯00k,i s,k s s,k + + S̃k,i  , 1 + Γ̄s,k 1 + Γ̄s,k where Γ̄s,k = Γk,i S̄s,k , ḡs,k ≡ ∂ log(1 + Γk,i )/∂Sk,i S̄s,k , S̄s,k is some average statistic of the Sk,i distribution, S̃k,i = Sk,i − S̄k,i , and ¯0k,i ≡ M , ¯00k,i ≡ . C Γ̄s,k M Γ̄s,k M i + ρ−1 k,i ρ−1 k,i − M i C 43 Proof: Given the denitions of Γ̄s,k and ḡs,k in the lemma, we have the following rst-order approximations: 1 1 − ḡs,k S̃k,i Γk,i Γ̄s,k + ḡs,k S̃k,i ϕi ϕi − ϕ̄s ḡs,k S̃k,i ≈ , ≈ and ≈ . 1 + Γk,i 1 + Γ̄s,k 1 + Γk,i 1 + Γ̄s,k 1 + Γk,i 1 + Γ̄s,k Substitute these approximations into (A14) and rearrange to obtain (A15). Proof of Proposition 3 Divide (A15) through by d log Ek and take expectations to char- acterize the pass-through elasticity: ∗ d log Pk,i Ψ∗k,i ≡E ≈ αs,k + βs,k · ϕi + γs,k · Sk,i , d log Ek where Γ̄s,k (1 + ΨPs,k ) + ΨCs,k αs,k = − γs,k S̄s,k , 1 + Γ̄s,k ΨM s,k ḡs,k (1 − ϕ̄s ΨM P C s,k ) + (Ψs,k − Ψs,k ) βs,k = and γs,k = , 1 + Γ̄s,k 1 + Γ̄s,k and with ( ) ( ) d log(Cs∗ /Ω̃s,k ) d log(Em Ūs /V̄s∗ ) d log P̃s,k ΨPk,i ≡E , ΨC s,k ≡E , ΨM s,k ≡E . d log Ek d log Ek d log Ek Note that the terms in k,i drop out since, due to Assumption A3, E k,i /d log Ek = 0. · Finally, note that Ψs,k≈ cov(·, d log Ek )/var(d log Ek ), that is Ψ-terms are approximately projection coecients. The expectations and the denitions of Ψ-terms are unconditional, and hence average across all possible initial states and paths of the economy. A.1.5 Empirical specication and proof of Proposition 4 We start from the linearized decomposition (A15) by replacing dierential d with a time lag operator ∆, making the time index t explicit, and rearranging: Γ̄s,k ∆p̃s,k,t + ∆cs,t + ¯0k,i,t ḡs,k ∆p̃s,k,t − ∆cs,t + ¯00k,i,t ∆p∗i,k,t ≈ + S̃k,i,t−1 (A16) 1 + Γ̄s,k 1 + Γ̄s,k Γ̄s,k ∆ek,t ϕi,t−1 Em,t Ūs,t ḡs,k S̃k,i,t−1 Em,t Ūs,t + + ∆ log ∗ + ∆ek,t − ϕ̄s,t−1 ∆ log ∗ , 1 + Γ̄s,k 1 + Γ̄s,k V̄s,t 1 + Γ̄s,k V̄s,t ∗ ∗ ∗ ∗ where ∆pi,k,t ≡ log Pk,i,t − log Pk,i,t−1 , ∆ek,t ≡ log Ek,t − log Ek,t−1 , ∆cs,t ≡ log(Cs,t /Ω̄s,t ) − ∗ log(Cs,t−1 /Ω̄s,t−1 ), and ∆p̃s,k,t ≡ log P̃s,k,t − log P̃s,k,t−1 . Note that we chose t − 1 as the point of approximation for S̃k,i,t−1 and ϕi,t−1 . We also chose the approximation coecients Γ̄s,k and ḡs,k not to depend on time by evaluating the respective functions (see Lemma A1) at a time-invariant average S̄s,k . 44 Next consider our main empirical specication (21) which we reproduce as: Sk,i,t−1 Sk,i,t−1 ∆p∗i,k,t = αs,k + βϕi,t−1 + γ̃ ∆ek,t + δs,k + bϕi,t−1 + c + ũk,i,t , (A17) Ss,k,t−1 Ss,k,t−1 where Ss,k,t is the cumulative market share of all Belgian exporters. Our goal is to estab- lish the properties of the OLS estimator of β and γ̃ in this regression, given approximate structural relationship (A16). To this end, we introduce two assumptions: Assumption A4 For every k, ∆ log ek,t is mean zero, constant variance and independent from (ϕi,t−1 , Sk,i,t−1 , Ss,k,t−1 ). Assumption A5 The variance and covariance of (ϕi,t−1 , Sk,i,t−1 /Ss,k,t−1 ) within (s, k, t−1) is independent from (βs,k , γs,k Ss,k,t−1 ), where βs,k and γs,k are dened in the proof of Propo- sition 3 above. Assumption A4 is a plausible martingale assumption for the exchange rate, which we require in the proof of Proposition 4. One interpretation of this assumption is that the cross- section distribution of rm-level characteristics is not useful in predicting future exchange rate changes. Assumption A5, in turn, is only made for convenience of interpretation, and qualitatively the results of Proposition 4 do not require it. Essentially, we assume that the cross-section distribution of rm-characteristics within sector-destination does not depend on the aggregate comovement properties of sectoral variables which aect the values of βs,k and γs,k . Before proving Proposition 4, we introduce the following three projections:  Em,t Ūs,t cov ∆ log ∗ V̄s,t ,∆ek,t ∆ log Em,t Ūs,t  ≡ ρM M s,k ∆ek,t + vs,k,t , ρM s,k = ,   ∗ V̄ var(∆ek,t )    s,t  cov(∆p̃s,k,t ,∆ek,t ) ∆p̃s,k,t ≡ ρPs,k ∆ek,t + vs,k,t P , ρPs,k = , (A18)   var(∆ek,t )  cov(∆cs,k,t ,∆ek,t )   ∆c∗s,t ≡ ρC C s,k ∆ek,t + vs,k,t , ρC s,k =   var(∆ek,t ) M P C and therefore (vs,k,t , vs,k,t , vs,k,t ) are orthogonal with ∆ek,t . Note that (ρM P C s,k , ρs,k , ρs,k ) are the M P C empirical counterparts to (Ψs,k , Ψs,k , Ψs,k ) dened in the proof of Proposition 3. Proof of Proposition 4 Substitute projections (A18) into (A16) and rearrange:    Γ̄s,k (1 + ρP ) + ρC ρM [(1 − ϕ̄s ρM P C s,k ) + (ρs,k − ρs,k )]ḡs,k Ss,k,t−1 Sk,i,t−1   s,k s,k s,k ∆p∗i,k,t ≈  + ·ϕi,t−1 + ·  ∆ek,t   1 + Γ̄s,k 1 + Γ̄s,k 1 + Γ̄s,k Ss,k,t−1  | {z } | {z } | {z } ≡αs,k ≡βs,k ≡γ̃s,k,t M P C − ϕ̄s,t−1 vm,k,t + ¯00k,i,t ḡs,k Ss,k,t−1 Sk,i,t−1 P C + ¯0i,t vs,k,t vs,k,t − vs,k,t Γ̄s,k vs,k,t + vs,k,t + ·ϕi,t−1 + · + . 1 + Γ̄s,k (1 + Γ̄s,k )2 Ss,k,t−1 1 + Γ̄s,k | {z } | {z } | {z } ≡bs,k ≡cs,k,t ≡δs,k +uk,i,t 45 Comparing this equation with the empirical specication (A17), the residual in the empirical specication is given by: h i Sk,i,t−1 k,i,t−1 S ũk,i,t = uk,i,t + (βs,k − β)ϕi,t−1 + (γ̃s,k,t − γ̃) Ss,k,t−1 ∆ek,t + (bs,k − b)ϕi,t−1 + (cs,k,t − c) Ss,k,t−1 , P Γ̄s,k vs,k,t C +vs,k,t 0i,t +¯ where from the price decomposition above it follows that 1+Γ̄s,k uk,i,t = − δs,k , where δs,k takes out the variation across sector-destination which is time-invariant. 0 0 0 Dene xk,i,t = (1s,k , ϕi,t−1 , S̃k,i,t−1 ) , so that we can write our regressors as zk,i,t = (x0k,i,t , x0k,i,t ∆ek,t ). From Assumptions A3 and A4 and properties of the projection (A18), 0 0 0 it follows that xk,i,t ∆ek,t is orthogonal with xk,i,t , and xk,i,t ∆ek,t is uncorrelated with uk,i,t . Therefore, the properties of the estimates of (αs,k , β, γ̃) are independent from those of (δs,k , b, c). OLS identies (αs,k , β, γ̃) from the following moment conditions: 0 = Ek,i,t {xk,i,t ∆ek,t ũk,i,t } = Ek,i,t {xk,i,t ∆ek,t (ũk,i,t − uk,i,t )} , where the second equality follows from Ek,i,t {∆ek,t xk,i,t uk,i,t } = 0 (due to Assumption A3 and projection (A18)). We now rewrite this moment condition in the form of summation (across the population of rms, sector-destinations, and time periods/states): X X 0 0= xk,i,t ∆ek,t (ũk,i,t − uk,i,t ) = ∆e2k,t xk,i,t x0k,i,t 00s,k , βs,k − β, γ̃s,k,t − γ̃ , k,i,t k,i,t where the second equality substitutes in the expression for ũk,i,t − uk,i,t and uses the fact that ∆ek,t is orthogonal with xk,i,t (Assumption A4). Using the same assumption further, we can rewrite the last expression as: X βs,k − β σk2 ns,k,t Σs,k,t = 0, (A19) s,k,t γ̃s,k,t − γ̃ where σk2 is the variance of ∆ek,t , Σs,k,t is the covariance matrix for (ϕi,t−1 , Sk,i,t−1 /Ss,k,t−1 ) within (s, k, t − 1), and ns,k,t is the respective number of observations. Equation (A19) already establishes the result of the proposition that β and γ̃ identify gen- eralized weighted averages of the respective coecients. Under additional Assumption A5, we have a particularly simple expressions for these weighted averages: X X 0 00 β= ωs,k,t βs,k and γ̃ = ωs,k,t γ̃s,k,t , s,k,t s,k,t 0 00 ωs,k,t ∝ σk2 ns,k,t vars,k,t−1 (ϕi,t−1 ) and ωs,k,t ∝ σk2 ns,k,t vars,k,t−1 (Sk,i,t−1 /Ss,k,t−1 ) with vars,k,t−1 (·) denoting the variance for observations within (s, k, t − 1). Finally, βs,k and γ̃s,k,t = γs,k Ss,k,t−1 are dened above, and (βs,k , γs,k ) provide rst order M P C M P C approximations to their analogs in Proposition 3 since (ρs,k , ρs,k , ρs,k ) ≈ (Ψs,k , Ψs,k , Ψs,k ). 46 A.2 Data Appendix Trade Data The import and export data are from the National Bank of Belgium, with the extra-EU transactions reported by Customs and the intra-EU trade by the Intrastat Inquiry. These data are reported at the rm level for each product classied at the 8-digit combined nomenclature (CN) in values and weights or units. Note that the CN code is a Europe-based classication with the rst 6-digits corresponding to the World Hamonized System (HS). We include all transactions that are considered as trade involving change of ownership with compensation (codes 1 and 11). These data are very comprehensive, covering all rms with a total extra-EU trade whose value is greater than 1,000 euros or whose weight is more than 1,000 kilograms. Since 2006, even smaller transactions are reported. However, for intra-EU trade, the thresholds are higher, with total intra-EU imports or exports above 250,000 euros in a year, and in 2006 this threshold was raised to 1,000,000 euros for exports and 400,000 for imports. Note that these thresholds result in changing cutos for countries that joined the EU during our sample period as their transactions move from being recorded by Customs to the Intrastat Inquiry. Firm-level data The rm-level data are from the Belgian Business Registry, covering all incorporated rms. These annual accounts report information from balance sheets, income statements, and annexes to the annual accounts. Only large rms are required to provide full annual accounts whereas small rms have to only provide short annual accounts so that some variables such as sales, turnover, and material costs may not be provided for small rms. A large rm is dened as a company with an average annual workforce of at least 100 workers or when at least two of the followhing three thresholds are met: (i) annual average workforce of 50 workers, (ii) turnover (excluding VAT) amounts to at least 7,300,000 euros, or (iii) total assets exceeding 3,650,000 euros. Note that the last two thresholds are altered every four years to take account of ination. Although less than 10 percent of the companies in Belgium report full annual accounts, for rms in the manufacturing sector these account for most of value added (89 percent) and employment (83 percent). Each rm reports a 5-digit NACE code based on its main economic activity. The key variable of interest is the construction of ϕ dened as the ratio of total non-Euro imports to total costs (equal to wages plus total material costs). These total cost variables are reported by 58 percent of exporters in the manufacturing sector. Combining this information with the import data, we can set ϕ equal to zero when total non-Euro imports are zero even if total costs are not reported, giving us a ϕ for 77 percent of manufacturing exporters, which account for 98 percent of all manufacturing exports. Product Concordances We use SITC one-digit product codes (5 to 8) to identify a man- uacturing export as it is not possible to do so directly from the CN 8-digit classications nor from its corresponding HS 6-digit code. We construct a concordance between CN 8-digit codes and SITC Revision 3 by building on a concordance between HS 10-digit and SITC 5-digit from Peter Schott's website, which takes into account revisions to HS codes up to 47 43 2006. We update this to take account of HS 6-digit revisions in 2007 using the concordance from the U.S. Foreign Census (see http://www.census.gov/foreign-trade/reference/ products/layouts/imhdb.html). We begin by taking the rst 6-digits of the 8-digit CN code, which is eectively an HS 6-digit code, and we include only the corresponding SITC code when it is a unique mapping. Some HS 6-digit codes map to multiple SITC codes, so that in those cases we do not include a corresponding SITC code. This happens mainly when we get to the more disaggregated SITC codes and rarely at the one-digit SITC code. Second, we need to match the CN codes to input-output (IO) codes. We use a 2005 Belgium IO matrix with 74 IO codes of which 56 are within the manufacturing sector. The IO codes are based on the Statistical Classications of Product by Activity, abbreviated as CPA, which in turn are linked to the CN 8-digit codes using the Eurostat correspondence tables.The matching of the IO codes to the CN 8-digit was not straightforward as we had to deal with the many-to-many concordance issues. We included an IO code only when the match from the CN code was clear. Sample Our sample is for the years 2000 to 2008, beginning with the rst year after the euro was formed. We keep all rms that report their main economic activity in manufacturing dened according to 2-digit NACE codes 15 to 36, thus excluding wholesalers, mining, and services. We restrict exports to those that are dened within the manufacturing sector (SITC one-digit codes 5 to 8). To address the multi-product rm issue, we keep only the set of CN 8-digit codes that falls within a rm's major IO export, which we identify as follows. We select an IO code for each rm that reects the rm's largest export share over the sample period and then keep all CN codes that fall within that IO code. For most of the analysis, we focus on exports to noneuro OECD countries that are dened as advanced by the IMF or high-income by the World Bank. We keep all import product codes and all import source countries. For some robustness checks, we limit the set of imports to intermediate inputs dened either according to Broad Economic Codes (BEC) by exluding any import that is classied as a consumer good or using the Belgium 2005 IO table to identify a rm's intermediate inputs. Total Factor Productivity Measures We measure total factor productivity (TFP) for each rm by rst estimating production functions for each 2-digit NACE sector separately. We note that a key problem in the estimation of production functions is the correlation between inputs and unobservable productivity shocks. To address this endogeneity problem we estimate TFP using two dierent methodologies. The rst approach is based on Levinsohn and Petrin (2003) (LP), who propose a modication of the Olley and Pakes (1996) (OP) estimator. OP uses investment as a proxy for unobservable productivity shocks. However, LP nds evidence suggesting that investment is lumpy and hence that investment may not respond smoothly to a productivity shock. As an alternative, LP uses intermediate inputs, such as materials, as a proxy for unobserved productivity. In particular, we assume a Cobb 43 See Pierce and Schott (2012). 48 Douglas production function, νf,t = β0 + βl lf,t + βk kf,t + ωf,t + ηf,t , (A20) where νf,t represents the log of value added, lf,t is the log of the freely available input, labor, and kf,t is the log of the state variable, capital. The error term consists of a com- ponent that reects (unobserved) productivity shocks, ωf,t , and a white noise component, ηf,t , uncorrelated with the input factors. The former is a state variable, not observed by the econometrician but which can aect the choices of the input factors. This simultaneity prob- lem can be solved by assuming that the demand for the intermediate inputs, xf,t , depends on the state variables kf,t and ωf,t , and xf,t = xf,t (kf,t , ωf,t ). (A21) LP shows that this demand function is monotonically increasing in ωf,t and hence the in- termediate demand function can be inverted such that the unobserved productivity shocks, ωf,t , can be written as a function of the observed inputs, xf,t and kf,t , or ωf,t = ω(kf,t , xf,t ). A two-step estimation method is followed where in the rst step semi-parametric methods are used to estimate the coecient on the variable input, labor. In the second step, the co- ecient on capital is estimated by using the assumption, as in OP, that productivity follows a rst-order Markov process. However, as pointed out by Ackerberg, Caves, and Frazer (2006), a potential problem with LP is related to the timing assumption of the freely available input, labor. If labor is chosen optimally by the rm, it is also a function of the unobserved productivity shock and capital. Then the coecient on the variable input cannot be identied. Wooldridge (2009) shows how the two-step semi-parametric approach can be implemented using a unied one- step Generalized Methods of Moments (GMM) framework. This is the second methodology that we adopt for estimating TFP. In particular ωf,t = ω(kf,t , xf,t ) is proxied by a lagged polynomial in capital and materials, which controls for expected productivity in t. We use a third-order polynomial in capital and material in our estimation. To deal with the potential endogeneity of labor, we use its rst lag as an instrument. A benet of this method is that GMM uses the moment conditions implied by the LP assumptions more eciently. The log of TFP measures are normalized relative to their 2-digit NACE sector mean to make them comparable across industries. The correlation between both measures is very high at 99 percent. 49 A.3 Additional Figures and Tables 1 1 0.95 0.95 0.9 0.9 Count of firms 0.75 0.75 Count of Export-value- observations weighted 0.5 0.5 Export-value- weighted 0.25 0.25 0.1 0.1 0.05 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 Import intensity, ϕf Market share, Sf,s,k,t Figure A1: Cumulative distribution functions of import intensity ϕf and market share Sf,s,k,t Note: Estimated cumulative distribution functions. In the left panel, the upper cdf corresponds to the un- weighted rm count, while the lower cdf weights rm observations by their export values. The unweighted distribution of ϕf has a mass point of 24% at ϕf = 0, while this mass point largely disappears in the value- weighted distribution, which in turn has a step ϕf = 0.33 corresponding to the largest exporter in our sample with an export share of 14%. In the right panel, the upper cdf corresponds to the count of rm-sector- destination-year observations, and it has small mass points at both Sf,s,k,t = 0 and Sf,s,k,t = 1, which largely correspond to small sectors in remote destinations. The lower cdf weights the observations by their export value, and this weighted distribution has no mass points, although the distribution becomes very steep at the very large market shares. 2 B(j ) 1.5 B(j0 ) FC 1 T M C(j) 0.5 Area = log B(j0 ) γj log bj 0 0 0.2 j 0 0.4 0.6 0.8 1 Figure A2: Import cuto j0 and cost-reduction factor B(j0 ) Note: F C = W ∗ fi is the xed cost of importing an additional type of intermediate input. T M C(j) = C Yi /[B(j)φ Ωi ] is the total material cost of the rm, decreasing in j holding output xed due to cost-saving ∗ eect of importing. The intersection between γj log bj and F C/T M C(j) denes the import cuto j0 , and the exponent of the area under γj log bj curve determines the cost-reduction factor from importing. 50 Table A1: Pass-through into producer prices and marginal cost by quartiles of import intensity Dep. variable: ∆p∗f,i,k,t ∆mc∗f,t ∆eM f,t (1) (2) (3) (4) (5) (6) (7) (8) ∆e`,t · δ1,f 0.117*** 0.102*** 0.163*** 0.054 0.062 0.026*** 0.053*** 0.415*** (0.036) (0.037) (0.055) (0.038) (0.038) (0.007) (0.006) (0.063) ∆e`,t · δ2,f 0.193*** 0.164*** 0.129*** 0.113*** 0.133*** 0.050*** 0.092*** 0.449*** (0.038) (0.035) (0.049) (0.035) (0.037) (0.017) (0.011) (0.066) ∆e`,t · δ3,f 0.234*** 0.177** 0.223*** 0.098* 0.142** 0.097*** 0.146*** 0.480*** (0.055) (0.050) (0.069) (0.050) (0.055) (0.022) (0.010) (0.069) ∆e`,t · δ4,f 0.314*** 0.217*** 0.222*** 0.135*** 0.217*** 0.167*** 0.213*** 0.438*** (0.037) (0.037) (0.055) (0.040) (0.035) (0.037) (0.018) (0.082) 51 ∆ek,t · Sf,s,k,t 0.350*** 0.416*** (0.070) (0.083) ∆mc∗f,t 0.580*** 0.575*** (0.034) (0.033) FPY FE no no yes no no no no no p-value Bin 1 vs 4 0.000*** 0.012** 0.403 0.082* 0.000*** 0.000*** 0.000*** 0.465 Note: 92,693 of rm-product-destination-year observations in each specication, unweighted, equally split into four bins according to the associated ϕf values; δi,f is a dummy for respective bins (corresponding to the quartiles of ϕf -distribution). All specications control for country xed eects. Specications (4) and (5) also control for the level of the market share Sf,s,k,t . In columns (1)-(6), ∆e`,t ≡ ∆ek,t is the destination-specic bilateral exchange rate; in column (7) ∆e`,t ≡ ∆eMf,t is the rm-level import-weighted exchange rate (excluding imports from the Euro Zone). Column (8) reports the regression of rm-level import-weighted exchange rate ∆eM f,t on the destination-specic exchange rate ∆ek,t by quartiles of ϕf -distribution. p-value for the F -test of equality of the coecients for quartiles 1 and 4. *, ** and *** corresponds to 10%, 5% and 1% signicance. Standard errors clustered at the destination-year level. Table A2: Robustness to the denition of import intensity Lagged Drop Drop Only Only Drop time-varying consumer capital IO-table IO-table re- (ϕf,t−1 , Sf,s,k,t−1 ) imports goods inputs inputs* exports Dep. var.: ∆p∗f,i,k,t (1) (2) (3) (4) (5) (6) ∆ek,t · ϕf,· 0.332*** 0.404*** 0.377*** 0.391*** 0.403*** 1.205*** (0.142) (0.115) (0.129) (0.097) (0.095) (0.385) ∆ek,t · Sf,s,k,· 0.264*** 0.265*** 0.263*** 0.265*** 0.264*** 0.257*** (0.060) (0.060) (0.057) (0.059) (0.059) (0.056) Note: The number of observations in column 1 is 87,173 and 92,693 in columns 26, with the dierence due to the use of lagged import intensity. Column 1 estimates (21) with lagged import intensity and market share variables. Specications in columns 26 are the same as in column 6 of Table 5, but with alternative measures of import intensity ϕf . The coecient on ∆ek,t varies very little with the alternative denitions of import intensity and is omitted. Columns 26 drop respective categories of imports from the denition of import intensity ϕf : column 2 and 3 exclude consumer and capital goods categories respectively according to the BEC classication; columns 45 keep only imports that correspond to intermediate input categories for the exports of the rm according to the input-output tables, where column 5 also focuses on the major export category of the rm; column 6 drops all imports in the same industrial codes as exports of the rm. Other details appear in the text and as in Table 5. Table A3: Robustness within destinations and industries Dep. variable: ∆p∗f,i,k,t (1) (2) (3) (4) (5) ∆ek,t · ϕf 0.569*** 0.306*** 0.177 0.411*** 0.477*** (0.105) (0.108) (0.108) (0.099) (0.125) ∆ek,t · Sf,s,k,t 0.252*** 0.298*** 0.138*** (0.050) (0.055) (0.059) ∆mc∗f,t 0.578*** 0.572*** (0.034) (0.034) Fixed eect interactions: ∆ek,t × country × SITC-1d yes yes yes yes no ∆ek,t × SITC-3d no no no no yes # of industries 4 4 4 4 163 Note: 92,693 observations. Columns 14 correspond to specications in columns 23 and 56 of Table 5, and additionally include destination-industry xed eect interacted with the change in the exchange rate. The number of destination is 12, and industries are dened at SITC 1-digit level (4 manufacturing industries). Column 5 repeats the specication in column 4, but replaces the destination-industry interactions with only industry interaction, but at a ner SITC 3-digit level (163 manufacturing industries). All specications include respective destination-industry xed eects in levels. Other details appear in the text and as in Table 5. 52 Table A4: Robustness with dierent samples Countries All rms Dropping Products all w/out only including intra-rm all HS 4-digit countries US US wholesalers trade products major major* Dep. var.: ∆p∗f,i,k,t (1) (2) (3) (4) (5) (6) (7) (8) ∆ek,t 0.065*** 0.055* 0.203*** 0.168*** 0.096** 0.081*** 0.128*** 0.132*** (0.014) (0.033) (0.059) (0.032) (0.037) (0.030) (0.041) (0.042) ∆ek,t · ϕf 0.240*** 0.352*** 0.567* 0.217** 0.390*** 0.529*** 0.368** 0.492*** 53 (0.068) (0.104) (0.328) (0.088) (0.096) (0.100) (0.177) (0.167) ∆ek,t · Sf,s,k,t 0.081*** 0.277*** 0.262** 0.119* 0.188*** 0.226*** 0.184*** 0.175** (0.027) (0.059) (0.120) (0.061) (0.067) (0.051) (0.057) (0.071) # countries 59 11 1 12 12 12 12 12 # observations 206,610 81,745 10,948 157,431 78,851 142,998 62,301 52,729 Note: Main specication from column 6 of Table 5 estimated with alternative subsamples of the data. All the details are as in Table 5. 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