Three essays on exchange rate pass-throughs and pricing to market

Three Essays on Exchange rate Pass-Throughs and

Pricing to Market

Thèse

Nasreddine Ammar

Doctorat en économique

Philosophiæ doctor (Ph. D.)

Québec, Canada

Three Essays on Exchange rate Pass-Throughs and

Pricing to Market

Thèse

Nasreddine Ammar

Sous la direction de:

Bruno Larue, directeur de recherche Markus Herrmann, codirecteur de recherche

Résumé

Dans cette thèse, nous étudions comment les firmes ajustent leurs prix dans diffé-rents marchés pour répondre aux variations du taux de change (report de taux de change). En règle générale, l’incidence des mouvements de change sur les prix dé-pend des caractéristiques de chaque marché telles que la nature de la concurrence et l’élasticité de la demande. Le report de taux de change (RTC) et la tarification en fonction du marché sont analysés dans trois chapitres en utilisant les théories du commerce international et de l’organisation industrielle. Le RTC est complet lorsque les variations du taux de change sont pleinement transmises aux prix à l’exporta-tion. Le RTC est incomplet lorsque les variations de change ne se répercutent pas intégralement sur les prix à l’exportation. Un RTC est pervers si le prix varie plus proportionnellement que le taux de change.

Le premier chapitre examine la relation entre la durée de conservation des produits alimentaires et les RTC. Plusieurs produits agroalimentaires ont la caractéristique d’être vendus rapidement ou transformés en produits moins périssables, stockés et commercialisés dans des périodes ultérieures. Cette relation verticale entre produits frais et produits transformés a une incidence sur les RTC. Notre modèle prend en considération la capacité de traitement et de stockage. Nos résultats montrent que le degré de périssabilité du produit transformé diminue les RTC au prix des produits frais et transformés avant l’accumulation des stocks, et les augmente au cours de l’accumulation des stocks. Dans ce chapitre, nous constatons aussi une relation né-gative entre la persistance de l’appréciation du taux de change et l’accumulation des stocks. Nous y montrons également que des RTC pervers peuvent émerger à court terme si les coûts des intrants échangés couvrent une part significative des coûts totaux, même si les RTC à long terme sont toujours incomplets.

Le deuxième chapitre analyse les RTC aux prix à l’exportation en présence de la production conjointe. Plusieurs produits agricoles partagent certains intrants et sont

produits dans des proportions fixes (par exemple les épaules de porc et les reins de porc ou les pattes de poulet et la poitrine de poulet). Ainsi, l’augmentation de la pro-duction d’un produit s’accompagne d’une augmentation de la propro-duction d’autres produits. Il s’ensuit que le RTC au prix d’un produit est directement lié aux RTC aux autres produits joints. En conséquence, certains RTC peuvent être pervers, surtout lorsque les consommateurs du pays d’origine et des pays étrangers ont des préfé-rences non identiques ou que les produits joints partagent des proportions d’intrants asymétriques. Aussi dans ce chapitre, nous montrons que le degré de substitution entre les produits renforce les RTC pervers. Enfin, nous montrons que les firmes ont tendance à faire des ajustements de prix plus petits quand il y a moins de produits conjoints.

Le dernier chapitre généralise les fonctions de coût de production et de transfor-mation du modèle du premier chapitre et suppose que les fonctions coûts peuvent prendre des formes non linéaires. Dépendamment du degré de convexité de ces fonctions, la technologie de production et de transformation peut être caractérisée par des économies ou déséconomies de taille. Les RTC aux prix à l’exportation sont souvent incomplets, mais des répercussions perverses peuvent découler de diffé-rentes hypothèses concernant les coûts marginaux de production et de transforma-tion.

Abstract

This thesis outlines how firms adjust their prices in different markets in response to exchange rate variations (exchange rate pass-through). Generally, these price ad-justments depend on each market’s characteristics such as the degree of competition, demand elasticities, and product characteristics (pricing to market). We investigate the exchange rate pass-through (ERPT) and pricing to market (PTM) in three chap-ters employing concepts from international trade theory and industrial-organization (I/O) approach. The ERPT is complete when the export price just offsets the varia-tion in the exporting country’s currency. The ERPT is incomplete when the change in the exchange rate is not completely transmitted to the export price. The ERPT is perverse when the export price varies more proportionally than the exchange rate.

In the first chapter, we examine the relationship between the shelf life of food prod-ucts, the processing technology, and the ERPTs. Several food products have the char-acteristic of being sold quickly or being converted to less perishable products, stored and marketed in subsequent periods. Such coupling between fresh and processed products impacts on how their prices evolve in response to exchange rate shocks. Our model considers the capacity of processing and storage. Our results show that the rise in the perishability of the processed product decreases the short-run ERPTs for the fresh and processed product prices before the inventory accumulation and increases the short-run ERPTs during the inventory building. Moreover, we find a negative relationship between the persistence of the exchange rate appreciation and the inventory accumulation. We also show that perverse short-run ERPTs can emerge if the trade cost accounts for a significant proportion of the total costs even if the long-run pass-throughs are always incomplete.

In the second chapter, we analyze the ERPTs for export prices in the presence of jointness in production. Several agricultural products share some inputs and are produced in fixed proportions (e.g., pork shoulders and pork loins or chicken legs

and chicken breast). Thus, the increase in the production of one product is accom-panied by increases in the production of other products. It follows that the ERPT of one product is directly linked to the ERPT of jointly produced products. As a result, some ERPTs may be perverse, especially when consumers in the home and foreign countries have non-identical heterogeneous preferences or the joint products are produced in asymmetric proportions. We also show that the degree of substi-tutability between products enhances the perverse ERPTs. Finally, we show that the firm tends to make smaller price adjustments when there are fewer joint products.

In the last chapter, we develop a static version of the model developed that al-lows production and processing costs to take nonlinear forms. The latter lead to economies or diseconomies of scale depending on their convexity properties. The ERPTs of export prices are often incomplete but perverse ERPTs can be observed under different assumptions regarding marginal production and processing costs.

Table des matières

Résumé iii

Abstract v

Table des matières vii

Liste des tableaux ix

Liste des figures x

Remerciements xii

Introduction 1

1 Perishability and Exchange Rate Pass-Throughs for Fresh and

Proces-sed Products 5

1.1 Introduction . . . 6

1.2 Literature review on incomplete ERPTs along supply chains . . . . 10

1.3 The model . . . 12

1.4 Steady state ERPTs for prices of fresh and processed products . . . 21

1.5 Dynamic analysis of ERPT for prices of the fresh and processed products . . . 26

1.6 Further empirical evidence of the simulated ERPTs for prices of the fresh and processed products . . . 39

1.7 Conclusion . . . 42

2 Jointness and the Exchange Rate Pass-Through 44 2.1 Introduction . . . 45

2.2 The model . . . 48

2.3 Results . . . 53

2.4 Conclusion . . . 61

3 Nonlinear Costs, Vertically-Related Markets, and Exchange Rate Pass-Throughs 63 3.1 Introduction . . . 64

3.3 Discussion . . . 79 3.4 Conclusion . . . 80 Conclusion 81 A Appendix of chapter 1 83 B Appendix of chapter 2 87 C Appendix of chapter 3 94 Bibliographie 97

Liste des tableaux

1.1 Effects of demand and cost parameters on the long-run ERPTs for

prices of fresh and processed products . . . 23

1.2 Marshallian and Hicksian Price Elasticities in Studies on Mexican Chi-cken Demand . . . 28

1.3 The replication of the average data of 2013 using the calibrated para-meters. . . 30

1.4 Estimation Results of equation (1.30) . . . 41

2.1 Parameter Values in the reference case . . . 54

2.2 The ERPTs for export prices sensitivity in relation to preference para-meters and capacity constraints . . . 55

A.1 Parameter conditions for corner and interior solutions . . . 83

A.2 Estimation Results for U.S. Chicken Exports to Mexico . . . 86

Liste des figures

1.1 Equilibriums in the case of the interior solution . . . 19

1.2 Exchange Rate Response to the Residual Shock . . . 31

1.3 The ERPTs for prices and quantities in the Reference Case. . . 32

1.4 The ERPTs for prices and quantities in response to rise in the traded input prices . . . 34

1.5 the ERPTs for prices in response to perishability degree . . . 35

1.6 The ERPTs for quantities in response to perishability degree . . . 36

1.7 The inventory adjustment in response to perishability degree . . . 36

1.8 the ERPTs for prices and quantities in Response to shock persistence . . . 37

1.9 The short-run ERPTs in the case of high costs ratio. . . 39

2.1 Export prices’ adjustment . . . 56

2.2 Export prices’ adjustment when wj >w−j . . . 58

2.3 The response of the ERPTs to the parameter of substitution θ . . . 59

2.4 The effect of number of joint products in ERPTs for export prices . . . 60

2.5 ERPTs in the case of production capacity adjustments . . . 61

3.1 Prices and quantities response to exchange rate appreciation when A> w_wy v ₂₍₁₋ θ2)+σ(σ−1)wzq2σ−2 1−θ  . . . 74

3.2 Prices and quantities response to exchange rate appreciation when . . 77

B.1 Effect of change in market size on production capacities . . . 91

B.2 Effect of the elasticity of substitution on production capacities . . . 92

Je dédie cette thèse à mes chers parents et à mes frères et sœurs

Remerciements

Tout d’abord, je remercie sincèrement mon directeur de thèse le professeur Bruno Larue pour sa disponibilité et tout ce qu’il m’a patiemment et généreusement ensei-gné. Je ne saurais oublier son soutien sans failles et l’appui considérable qu’il m’a accordé dans la rédaction de cette thèse, notamment pendant les moments difficiles. Sans son précieux soutien, cette thèse ne serait pas arrivée à ce stade.

Je remercie également le professeur Markus Herrmann pour avoir accepté de codi-riger cette thèse de doctorat. Merci pour son soutien, ses conseils, et son assistance technique amplement suffisante.

Merci énormément à mes parents, qui comptent plus que tout, sur qui j’ai pu m’ap-puyer, trouver réconfort et confiance. C’est de savoir que vous croyez en moi si fort qui m’a permis de relever ce défi particulier.

Merci à tous mes amis qui occupent une place si importante dans ma vie, spéciale-ment tous mes collègues économistes devenus ou en devenir ainsi que Safa, d’ex-ceptionnels supports intellectuels et moraux.

Je tiens à remercier les enseignants, les chercheurs et le personnel administratif du département d’économique de l’Université Laval.

Introduction

The aim of my Ph.D. thesis is to investigate the transmission degree of the exchange rate variations to import prices. This concept has been a popular topic of the inter-national trade literature over the past three decades since the papers of Krugman (1987) and Dornbusch (1987). These authors have called this transmission elasti-city the exchange rate pass-through (ERPT). Technically, ERPT is the elastielasti-city of local-currency import prices with respect to the local-currency price of foreign cur-rency. ERPTs have important implications for monetary policies. Cheikh and Lou-hichi (2016) argue that policymakers must be able to gage the impact of currency changes on domestic prices in order to determine the persistence of underlying in-flation pressures and, hence, the appropriate monetary policy responses to deal with them. Also, the ERPTs affects the strategies of exporting and importing firms in inter-national trade, and how they react to temporary and persistent exchange rate shocks. Thus, an optimal trade strategy presupposes that exporters firms have a good un-derstanding of the pass-throughs for the input and output prices.

A complete ERPT describes a full transmission of the change in the foreign coun-try’s currency exchange rate to import prices. In general, elasticities of import prices with respect to the exchange rate below unity (incomplete ERPTs) are the standard outcome of many theoretical and empirical studies (e.g.,Larue et al. (2010),Cheikh and Rault (2016), Li and Zhang (2016)). These results imply a deviation from the law of one price which posits that the price differences for the same product in dif-ferent markets reflect only the costs of marketing (comprising transport costs, tariffs, etc.). Many studies relate incomplete ERPTs to an adjustment in the markup (pricing to market) in a context of imperfect competition (see Krugman (1987) and Feens-tra(1989) for the primary references andAmiti et al. (2016) andAuer and Schoenle (2016) for recent references). if the demand in the importing country is more elastic than the demand in the home country, many firms reduce the margin on exported products in response to an importing country’s currency appreciation increase by

increasing their exports and decreasing their domestic sales which result in higher domestic prices and higher (lower) export prices when expressed in domestic (fo-reign) currency. This PTM strategy enhances the competitiveness of the exporting firms in the international market and allows to increase its market share relative to foreign competitors in the foreign market. However, markup variations cannot fully explain the incomplete ERPTs. Other factors to consider include market integration, cost structure (traded vs non-traded inputs), transaction costs (menu costs and swit-ching costs), and endogenous choice of invoicing currency (Aron et al.(2014)).

In the literature mentioned above, the analysis focuses on one product or many dif-ferentiated products (varieties) related Through a system of demand functions. The assumption of one-product exporter is adequate to analyze the relative importance of domestic non-traded cost components, markup adjustments, and nominal price rigidities in the incomplete transmission of exchange rate changes to prices. Ho-wever, Blanchard et al.(2012) argue that such a market structure prevents exports from being observed when trade costs (including production and/or transport costs and/or trade barriers) are high. Thus, the assumption of a one-product exporter is in contradiction with market reality which shows that many firms continue to ex-port after the appreciation of the imex-porting country’s currency even if the cost of imported inputs share a significant part of the production and distribution costs. Blanchard et al.(2012) explains this outcome by appealing to endogenous differentia-tion. A firm can continue to export when trade costs are high if it is a multi-product exporter. This endogenous differentiation can be easily observed in agricultural mar-kets. Many firms have the capacity to process many primary agricultural products into processed products (e.g. the fresh chicken meats can be processed to frozen ones or many fruits can be transformed into a juice, puree or paste). We model this supply chain as vertically-related products. Also, the agricultural products can be horizontally related because several sectors are characterized by joint production. Typical examples are the production of mutton and wool, meat and manure. . . Non-agricultural sectors can also be produced jointly, like naphta, gasoline, jet fuel, kero-sene, diesel, heavy fuel oil and asphalt. An important contribution of our research to the previous literature is to analyze the ERPTs for export prices in the case of vertically-related products (processing) and horizontally related products (joint pro-duction). The first concept is investigated through the first and the third chapter, while the second one is included in the second chapter.

mar-keted as fresh but highly perishable or be processed to acquire a longer product life. Products at different stages of processing likely face different ERPTs, but because of the demand substitution between these products, their ERPTs cannot be estimated in isolation from one another. Moreover, the extended life of many processed food products brings the issue of stock management in dynamic ERPT models.Teo(2011) shows that exchange rate changes can affect firms’ incentives to hold inventories and the changes in inventory holdings, in turn, can affect prices. In our case, the pro-cessed product is less perishable and it can be stored and marketed in subsequent periods. Thus, we analyze the perishability effect of the processed product on the monopolist’s pricing decision and we use the stock depreciation of the processed product as a measure of its perishability. Alessandria et al.(2010) document that a higher depreciation reduces inventories held by importers. Hence, importers order more frequently, incurring more trade costs, which affects the firms’ pricing decision. We evaluate the effect of the perishability of the processed product on the prices and quantities ERPTS for the fresh and processed products. This study is the first of its kind to put emphasis on a link between trade policies and output prices ERPTs via stock accumulation and product perishability. We calibrate the model using data from American exports of live and eviscerated chicken to Mexico.

In the second chapter, we focus on horizontal-related products. Many food products are jointly produced, which means that they share some inputs and are produced in fixed proportions. Thus, the increase in the production of one product is accom-panied by increases in the production of other products. For example, beef can be divided into primal cuts or pieces of meat initially separated from the carcass, like chucks, ribs, briskets, plates. . . These joint products may be complements or sub-stitutes in consumption and have different income elasticities. It follows that the exchange rate pass-through of one product is directly linked to the exchange rate pass-through of jointly produced products. As a result, the ERPTs can move in op-posite directions, yielding perverse ERPTs (elasticities of import prices with respect the exchange rate more than one). Rancourt(2005) shows that perverse ERPTs can arise in part because of short-run capacity constraints of input in production be-cause primary inputs to be processed are contracted. We generalize the model of Rancourt (2005) by making preferences toward joint products to be country specific. For example, Canadian consumers prefer white poultry meat while dark meat is pre-ferred in India (Landes et al.(2004),Rafajlovic and Cardwell(2013)). The asymmetric preferences lead to asymmetric price elasticities between markets, which affects the

pricing behavior of exporters. In addition, we note that a firm can produce many joint products from an intermediate good and the number of this joint products may differ from one case to another. More joint products provide more substitution pos-sibilities for consumers which affect cross-price elasticities. We show that the ERPTs for the export prices depend on the number of joint products. We conceive a model in which a domestic firm can sell its products in the home country or export them to a foreign market where it competes with another firm.

In the third chapter, we return to the case of vertically-related products but we as-sume more general forms of the production and processing costs. We analyze the ERPTs for the primary and processed products when the technologies of produc-tion and processing are characterized by economies of size, diseconomies of size, or constant returns to scale. In our study, we analyze ERPT using only a static trade model. The dynamic model with quadratic costs is treated in the first essay. Few ERPT studies have allowed for non-linear costs (e.g., Hens et al. (1999) and Oku-guchi (2005)) but our study is the first of its kind to combine the non-linear costs with vertically integrated products. Okuguchi (2005) focuses on economies of scale and ignoring diseconomies and abstracting from product differentiation. Hens et al.(1999) consider economies of scope (not economies of scale) with firms producing a homogeneous commodity in segmented markets. Our aim is to examine the expor-ter’s pricing behavior in response to exchange rate variations with non-linear costs with treatable and local components as well as vertical integration in the production and marketing of primary and processed products. This analysis may help to explain why the effect of exchange rate changes on prices for multi-product exporters have been observed to be incomplete and even perverse.

Chapitre 1

Perishability and Exchange Rate

Pass-Throughs for Fresh and Processed

Products

Abstract

The exchange rate pass-through (ERPT) for import prices is the object of much controversy. Many Canadian consumers notice significant price differences for similar products sold on both sides of the Canada-US border. Several food products are perishable and must be sold quickly or be processed into less perishable products, stored and marketed in subsequent periods. Such coupling between fresh and processed products impacts on how their prices evolve in response to exchange rate shocks. Our model takes into account the capacity of processing and storage. Our results show that the rise in perishability of the processed pro-duct decreases short-run ERPTs for fresh and processed propro-duct prices before the inventory accumulation and increases the short-run ERPTs during inventory building. Moreover, we find a negative relationship between the persistence of an exchange rate appreciation and inventory accumulation. We also show that perverse short-run ERPTs can emerge if the cost of imported inputs accounts for a significant proportion of the total cost even if the long-run ERPTs are always incomplete.

Keywords :Exchange Rate Pass-Through, Pricing To Market, Vertical Integration, Stock

Ma-nagement, Monopoly, Intertemporal Optimization, .

1.1

Introduction

The exchange rate pass-through (ERPT), defined as the effect of exchange rate changes on export prices, and the closely related concept of pricing to market (PTM) have stimulated a voluminous body of research in economics since the seminal papers ofKrugman(1987) andDornbusch(1987). They impact on inflation and are respon-sible for the real effects of monetary policy and shocks to cost components like wages and commodity prices (Hong and Li, 2017). As a consequence, the degree of pass-through into imported prices affects the strategies of exporting and importing firms in international trade and how they react to temporary and persistent exchange rate shocks.

Krugman (1987), Dornbush (1987) and others have observed that a change in the ex-change rate is not always completely transmitted to the import price.1For example, Gopinath et al. (2009) report ERPTs for twenty American aggregate sectors that do not exceed 33%, a trade-weighted average ERPT across sectors of 21% and an overall trade-weighted average for inter-firm transactions across sectors of 22%. Ben Sheikh and Rault’s (2016) short-run ERPTs for the price of non-commodity imports vary between 31% and 58% for 12 euro area countries. For Canadian pork exports,Larue et al.(2010) estimate an ERPT of 70% for Quebec exports to the United States and an ERPT of 55% for Quebec sales to Japan, while the ERPTs for Ontario pork exports are 39% and 53%, respectively, for the same destinations.

These results differ from price adjustments in competitive markets and imply de-viations from the Law of One Price (LOP) which posits that the price differences for the same product in different markets reflect only the costs of marketing (transport costs, tariffs, etc.). Hence, LOP implies that changes in exchange rates have one-for-one effects on the price level. Under imperfect competition, an appreciation of the exporter’s currency does not generally induce a perfectly offsetting increase in the price in the importing country to keep the price constant when expressed in local currency.

Many studies have rationalized incomplete ERPTs by appealing to imperfectly com-petitive markets, product characteristics, demand elasticity, nominal price rigidities, intra-firm trade and the presence of nontraded inputs.2A particularity of many

agri-1. The depreciation of the foreign currency brings prices up in the importing country, but if the elasticity of demand is decreasing in price, sellers decrease the selling price to maintain or enlarge their market share. As a result, the ERPT can be small.

cultural products can be marketed as fresh and highly perishable or be processed to acquire a longer product life. Our study innovates by analyzing ERPTs for vertically related products. The capacity to transform fresh products for producers and pro-duct substitutions by consumers give rise to vertical ties between fresh and proces-sed products. Our setting covers several agrifood supply chains. For example, milk can be processed into cheese, yogurt, ice cream, skim milk powder, and modified milk substances used as ingredients in transformed dairy products, while live broi-lers can be eviscerated and further processed into chicken nuggets, canned soups, “ready-to-eat‘ chicken meals, etc. In most cases, processed products are less per-ishable than primary ones. For example, canned fruits and vegetables can be stored for long periods in comparison to fresh ones. Products at different stages of proces-sing likely face different ERPTs, but because of demand and production linkages, these ERPTs cannot be estimated in isolation from one another.

The extended life of processed food products raises the issue of stock management and dynamics in their ERPT analysis. Nakamura and Zerom (2010) rely on a dy-namic model of oligopolistic competition with price rigidity to ascertain the impact of menu costs, demand elasticity, and imported and domestic inputs on the ERPT of export prices. Their empirical analysis on coffee prices reveals that local inputs and markup adjustments are responsible for low ERPTs. But few authors have stu-died the relationship between exchange rate changes and inventory accumulation in dynamic models. Teo (2011) states that exchange rate changes can affect firms’ incentives to hold inventories. As a result, an increase in mean export price can be amplified by costly accumulation of inventories to buffer against an unstable export demand because of exchange rate volatility.Copeland and Kahn(2012) use data on U.S. automobile sales and inventories by country of origin and find strong evidence that exchange rate movements affect inventory-sales ratios, which is consistent with changing markups. They argue that the inventory-sales ratio provides an indirect measure of the exchange rate pass-through. These models are quite similar to the one we develop in this paper.

Göcke and Fedoseeva(2016) address ERPT and PTM by proposing an optimal control model of dynamic monopolistic pricing on a foreign market, which accounts for dy-namic demand effects (such as diffusion or saturation) and learning curve effects. The intertemporal demand spillover effects are represented via the accumulated ca-pital stock, but they do not consider the inventory accumulation on the supply side.

They demonstrate that positive intertemporal demand spillover effects and cost re-ducing learning-by-doing act as an incentive to set low prices directly after a firm has entered a foreign market. Moreover, these dynamic effects result in incomplete ERPT and PTM-strategies even in the long run.

Our main goal is to characterize the ERPTs of vertically related products with dif-ferent degrees of perishability. Also, we characterize the relationship between the pass-through for the inventory unit value and the pass-through for input and output prices. Our paper is one amongst few studies considering stock management and uncertainty related to currency fluctuations in the price transmission of vertically related products. We construct a dynamic model with a primary product which can be exported as fresh or processed by a monopolist. Since there are large vertically-integrated involved in commodity production, processing and exports, the mono-poly assumption is adopted for convenience but it is not too heroic. The fresh duct must be consumed or processed in the current period, while the processed pro-duct can be marketed in the current period, or in subsequent ones. The monopoly assumption is convenient to analyze stock management, processing capacity, and the incidence of perishability on the ERPTs of fresh and processed products. Many agri-food processing industries are heavily concentrated and often sell fresh and fro-zen products. While most of the studies assume that the primary good is only used for processing and cannot be consumed as a final good, we assume that consumers buy both primary and processed products, regarding them as imperfect substitutes. This assumption allows us to characterize the role of the substitution effect between primary and processed products, when the former is used in the production process of the latter, in the magnitude of ERPTs. To the best of our knowledge, these issues have not been treated in the literature.

Our results can be summarized as follows. The perishability degree, in the case of high stock accumulation, affects negatively the short-run ERPTs3for fresh and pro-cessed products which induces inventory building. During stock accumulation, the more perishable the processed product, the larger the ERPTs. The intuition is that the increased perishability raises the storage cost which pushes the firm to increase the pass-through for the prices of both types of products. Moreover, the perishability de-gree affects the gap between the dynamic ERPT for the processed product price and the ERPT for the fresh product price positively. This outcome reflects the fact that the

3. The dynamic ERPTs measure the short-run effects around the steady state solution while the long run ERPTs are about the steady state solution which is characterized by the absence of invento-ries.

processed product can be stored while the fresh product must be sold or processed. Interestingly, we find that perverse ERPTs (i.e., ERPTs higher than 100%) can emerge if the share of the imported inputs (the local input) in the total cost is sufficiently high (low) : The short-run ERPTs for the fresh and processed product prices (quantities) are positively (negatively) affected by the stock accumulation.Kryvtsov and Midri-gan(2012) document a strong relationship between inventories and the dynamics of costs. Since the imported input prices are high, firms anticipate a major rise in the marginal cost in response to an exchange rate appreciation. Hence, firms find it op-timal to invest in inventories in response to an exchange rate appreciation, which in turn increases the price ERPTs. Also, the persistence of the exchange rate affects po-sitively the short-run price ERPTs for the fresh and processed products under local currency pricing (LCP). This result builds on studies linking large adjustments in ex-port prices to persistent4exchange rate variations (Goldberg and Hellerstein(2008), Gopinath and Itskhoki (2010)). Using a regime dependent model that captures the change in the regime of the ERPT behavior and relying on data about the American exported of the fresh and frozen chicken products to Mexico, we find an empirical evidence that the short-run pass-throughs are positively related to the persistence of the exchange rate.

Another interesting finding is that the exporter engages in a speculative behavior by producing more of both products and by investing more in processing and storage if he anticipates that these products will be temporarily less valuable from time to time. We also find that the effect of the willingness to pay for the fresh product on the long-run ERPT for the processed product is negative when the cost of processing is low or if the degree of substitution is high. Otherwise, a stronger demand for the fresh product increases the long run ERPT for the processed product.

The remainder of the chapter is organized as follows. The next section provides a survey about incomplete ERPTs and ERPTs along supply chains, while section 3 de-velops a model of vertical integration and stock management. Section 4 describes the analytical results at the steady state. Section 5 reports analytical dynamic ERPTs in the presence of a corner solution when processed product is not exported. The-reafter, we also provide a numerical model calibrated on 2013 data about the Ameri-can exported of poultry products to Mexico to analyze the relationship between the short-run ERPTs for the fresh and processed products. Section 6 concludes.

1.2

Literature review on incomplete ERPTs along

supply chains

Many studies have provided insights to explain incomplete ERPTs. The degree of competition and the demand structure on export markets are investigated in the pioneering studies of Krugman (1987) and Dornbusch (1987). These insights have been empirically validated (e.g. Gross and Schmitt (2000), Nakamura and Zerom (2010)).

Other factors to consider include the persistence of exchange rate shocks and tran-saction costs. For example, if the U.S. dollar appreciates temporarily and then qui-ckly returns to its initial level, exporters in the U.S. market have no incentive to change their prices especially in the presence of menu costs. However, if the shock is persistent and large, then exporters are likely to change their prices frequently over time to minimize transaction costs.Goldberg and Hellerstein(2008),Gopinath and Itskhoki (2010),Devereux and Yetman (2010), and Larue et al.(2010) have tes-ted this hypothesis. Larue et al. (2010) find empirical support for threshold effects in ERPTs while Gopinath and Itskhoki (2010) show that firms that change their price infrequently also have a tendency to have a lower pass-through. They also find si-gnificant differences in pass-through between firms within a sector which can be explained by menu costs and variable markups.Nakamura and Zerom (2010) find that menu costs play an insignificant role in reducing ERPTs, but that they are im-portant to explain delayed price adjustments in the coffee industry.

Klemperer (1995), Byoung-Ky (2001) andBussiere (2013) explain the partial ERPT by transaction costs or switching costs. In essence, buyers have to pay a fee when switching to a different supplier (Farrell and Klemperer,2007). Sellers typically offer low prices to attract new customers and “lock“ them in long-term relationships, with switching costs preventing consumers from leaving when prices increase. In these models, ERPTs are low because the demand faced by firms is inelastic.

Another reason behind partial ERPTs is the relation between the border effect and supply chain integration. Campa and Goldberg (2008), Gopinath et al. (2009), Go-pinath et al. (2011)) and Burstein and Jaimovich (2009) reported that border trans-mission depends on the degree of market segmentation between countries. They confirm that integrated production weakens the impact of exchange rates. The intui-tion is that the final product sold in an import market consists of imported inputs

and services such as distribution and transportation. If markets for inputs and out-puts are integrated, the exchange rate will have no effect on the cost of sales and the selling price will be less sensitive to fluctuations in the exchange rate.

Ghosh (2009) tries to evaluate cross-border production sharing on ERPTs. He stu-dies three input market structures : the first one assumes that the reference market is the completely integrated. The exporter uses only local inputs to produce. The second case is the two-country production sharing and the third one is the three-country production case. For the last two cases, the firm imports an intermediate good from another market. Ghosh finds that the imported input plays an important role in reducing the ERPT when the currency in the exporting country appreciates, which means that the higher the PTM at the intermediate good level, the lower the pass-through.Gopinath et al.(2011) studied the prices of products in a large grocery chain in the United States and Canada. They find that the retail prices change from 0 to 24% when comparing Canadian and U.S. stores, but that they do not change across outlets within a country.

Aksoy and Riyanto(2000) evaluate the ERPT along supply chains. They compare the ERPT in vertically separated markets to the ERPT in a vertically integrated market. They use a duopoly model with intermediate and final good markets. Both firms sell their products in the domestic and foreign markets. In the symmetric case, there is a duopoly competition in both the final and intermediate goods market, but only the foreign firm is vertically integrated in the asymmetric case. In the symmetric case, the depreciation of the domestic currency pushes down the input price charged by the domestic firm in the foreign market, which means that the cost of producing the final good for the foreign firm is reduced. As a result, the PTM incentives are less pronounced and the degree of ERPT for the price of the final good set by the foreign firm in the domestic market rises. In the asymmetric case, the foreign vertically in-tegrated firm produces the final good at marginal cost because the domestic final good producer has to sell imported inputs at prices fixed by the foreign firm. This cost advantage for the foreign firm gives it an incentive to charge a higher price for its final goods when the domestic currency depreciates. Relative to the symmetric case, the foreign firm maintains a low production cost, contrary to the domestic firm which has a much higher production cost. Consequently, the positive effect of input prices on the ERPTs for final good prices will be more pronounced in the vertical integration case than in the vertical separation case.

Our model is close to the vertical integration model ofAksoy and Riyanto(2000) be-cause it features a vertically integrated firm which exports an intermediate good (the fresh product) and a final good (the processed product) and we evaluate the pass-through for both products. However, our theoretical model differs from the model of Aksoy and Riyanto in important ways. Firstly, we assume that the processed good can be stored for many periods, which gives a dynamic dimension to our model. This assumption allows us to characterize the relationship between the lifespan of the product and the ERPTs. Secondly, we assume that the consumers in the impor-ting country consume both fresh and final products and that these products are im-perfect substitutes for one another. In contrast, Aksoy and Riyanto assume that the consumers consume only the final good which uses the intermediate good as an in-put. The substitutability of the products affects the ERPTs for both products. Finally, our exporter uses local and imported inputs to produce the intermediate product, in contrast with Aksoy and Riyanto (2000) who assume that the intermediate good is made from a local input.

1.3

The model

The theoretical model below accounts for the dynamic processing and storage de-cisions made by an exporting firm facing uncertain prices for fresh and processed products due to exchange-rate fluctuations. We assume that the exchange rate fol-lows a mean reverting process, as it is subject to various shocks in real and monetary markets in short-run, but it converges to absolute purchasing power parity (PPP) in the long term :

et+1=h(et, e, ρ, et), (1.1)

where et is the exchange rate at time t, e is the long run PPP rate, 0<ρ<1 measures

the speed of reversion to e, and et is the random part of the exchange rate, normally distributed with a zero mean and a standard deviation σ. The exchange rate is defi-ned in terms of units of local currency per unit of foreign currency. Accordingly, an increase in et implies the depreciation of the local currency.

Many empirical studies have demonstrated that PPP holds in the long run.Wallace (2017) suggests that long-run PPP holds for the Mexico–US exchange rate and the evidence for PPP is stronger when structural breaks are allowed in the real exchange rate. Likewise, Yee and Ramirez(2016) present indirect evidence that absolute PPP

may hold in the long-run between Mexico and the US but due to data limitations, the relationship could not be tested directly.Lothian(2016) shows that PPP as a long-run proposition is a very useful approximation for exchange rates in a floating exchange rate regime as well as prices in a fixed exchange rate regime.5

Consumption

In our model, a single firm in country A exports primary and processed agricultu-ral products to country B where consumption decisions are made by a representative consumer. For simplicity, it is assumed that the whole production is exported.Göcke and Fedoseeva(2016) use the same assumption to analyze ERPTs in a dynamic mo-del.6Furthermore, we can believe that the foreign market is separated from the do-mestic market in the case of vertical intra-industry trade between farmers, food pro-cessors and retailers. As a result, the firm exercises noncompetitive pricing across markets. No et al.(2015) identify two conditions under which an exporter has the ability to exercise noncompetitive pricing across markets. "First, the markets must be separated in space, time, form or some other dimension. This separation must be maintained so that there is no possibility for arbitrage. Secondly, the response of de-mand to price changes must differ between markets so that the link between prices and marginal revenues varies in the different markets”. The authors mention that these assumptions may well be met in the U.S. broiler export trade.7

At period t, the consumer purchases a quantity of fresh produce q_tf at price p_tf ,m, a quantity of processed product q_tp at price p_tp,m and a numeraire good q0_t at a price normalized to one.8 Mt is the disposable income of the consumer at time t. We as-sume that there is no intertemporal budget transfer (no savings) and that the prefe-rences are stationary. These assumptions are reasonable given that there are lower and upper bounds for food consumption in any period and that food is essential for survival.

5. While our interest in PPP between the US and Mexico is motivated by our empirical applica-tion,He et al.(2014) also find support for PPP between 15 Latin American countries while Huang and Yang(2015) arrive at a similar conclusion for Norway, Sweden, Switzerland and the UK.

6. This assumption makes it easier to intuitively interpret the relationship between the ERPTs for the fresh and processed products, the perishability of the latter and the effect of the persistence of an exchange rate appreciation on inventory and price adjustments.

7. In our dynamic analysis of ERPTs, we rely on data about US exports of broilers and eviscerated chicken to Mexico.

8. p_tf ,mand p_tp,mare expressed in the currency of the importing country. We also assume that p_tf ,ex and pp,ex_t are the prices of the fresh product and the processed product expressed in the currency of the exporting firm. Consequently we have p_tf ,ex=etptf ,mand p

p,ex

We use the formulation ofEdgeworth(1924) to represent consumer preferences cha-racterized by a quasi-linear utility function with a quadratic component. This form of utility function is often used in international trade (e.g.,Ottaviano et al.(2002), Me-litz and Ottaviano(2008),Bertoletti and Epifani(2014)) because it allows for flexible markups.9The consumer’s maximization problem is given by :

max U(q_tf, q_tp, Zt) = αfq f t +αpq p t − 1 2(q f t)2− 1 2(q p t)2−θq f tq p t +q0t, (1.2) s.t. p_tf ,mq_tf +p_tp,mqp_t +q0_t ≤ Mt, (1.3)

where αf and αp measure consumer preferences towards fresh and processed ducts respectively. They also reflect the market sizes of the fresh and processed pro-ducts respectively. θ ∈ [0, 1) is a parameter of substitutability between the two pro-ducts. The consumer prefers the fresh product to the processed one when αf > αp and vice versa when αf < αp. The solution of the consumer’s optimization problem leads to a system of linear inverse demands :

pj,m_t =αj−qjt−θq −j

t , for all j ∈ {f , p} (1.4)

The two products are substitutes when θ > 0 : the demand for the fresh product is increasing in the price of the processed product and vice versa. For the fresh and processed product j ∈ {f , p}, we define εqpjj = −

1 1−θ2 pj,m_t qj_t and ε qj p−j = θ 1−θ2 p−j,m_t q_tj respec-tively as the direct and the indirect demand elasticity of product j, which vary along the inverse demand curves. Thus, we define the super-elasticities as the response of these elasticities to percentage variations in the prices of the fresh and processed products. Sijpf = ∂εqpij ∂ p_tf ,m p_tf ,m εqpij ∀{i, j} ∈ {f , p} (1.5) Sijpp = ∂εqpij ∂ p_tp,m p_tp,m εqpij ∀{i, j} ∈ {f , p} (1.6)

As pointed out by Nakamura and Zerom(2010), the super-elasticities are quantita-tive measures of the curvature of demand for each product, which can help to un-derstand the directions of the ERPTs. Equations (1.5) and (1.6) show that the demand

9. The marginal utility of income is equal to 1 as any additional income will be allocated to Z. The income elasticities for fresh and processed products are zero, which implies that the Marshallian and Hicksian demands are identical for these two products. As a result, consumer surplus is an unbiased measure of consumer welfare.

elasticity for each product depends on both prices, p_tf ,mand p_tp,m, because of the sub-stitution possibilities for a consumer between the fresh product and the processed product as measured by the the substitution parameter θ.

Production

At period t, the firm produces a quantity of fresh product Qt. A part of this produc-tion, q_tf, is sold, while the rest (Qt−q_tf ≥0) is processed into a storable product at a one-for-one rate contributing to total inventory It+1at the subsequent period. Given that current inventory It depreciates at rate 0 ≤ δ ≤ 1 and that the quantity of the

processed product q_tpto removed and sold at period t, the inventory’s law of motion is :

∆It+1= It+1− (1−δ)It =Qt−q_tf −q_tp. (1.7) We assume that a imported input Xt and a domestic input Yt are used in fixed pro-portions for different levels of production of the fresh product :

Qt =min √ Xt,Yt d  , (1.8)

where d >0 is a technology parameter.10

The monopolist uses imported input Xtat cost etwxand a domestic input at cost wy. With this functional form, the production cost function is given by :

C_tF =dwyQt+etwxQt2. (1.9)

For processing the fresh produce, we assume that the monopolist uses a unit of the fresh product and another imported input Ztat cost etwz. In the same way, as for the fresh product, we define a Leontief processing function :

Q_tp =min√Zt, Qt −qtf 

. (1.10)

Accordingly, the processing cost function, which does not take into account the cost of the fresh product,11 is given by :

CtP =etwz(Qtp)2 =etwz(Qt−qtf)2. (1.11) 10. In the short run, the input-mix to produce primary agricultural products can be assumed constant because the amount of capital, land, and even labor are basically fixed.

11. The fresh product used for processing is free of charge for the producer. However, the oppor-tunity cost is non-zero.

Furthermore, we assume that input prices are exogenous and constant. C_tF and C_tP are increasing and convex in the price of the imported inputs and this has interesting effects on ERPTs, as will soon become apparent. The convexity in output of proces-sing cost function implies increaproces-sing average costs. It can be justified on the ground that imported inputs need to be sourced further away as more is demanded.

We assume that trade in inputs Xt and Zt and output of fresh and processed pro-ducts occurs in the same currency. This hypothesis can be motivated by asymmetry in the size of trading partners, which is the case of the trade between Canada and the United States. It can also be motivated by the presence of a dominant trading currency : The US dollar is considered as a vehicle currency, a currency commonly used for transactions between firms from different foreign countries (Wang and Zou, 2015). Finally, the separation between imported inputs (Xt and Zt) and local inputs Yt allows us to evaluate the relation between the PTM at the intermediate good level and ERPTs for output prices.12

Taking into account the law of motion of the inventory (equation (1.7)) and the ex-change rate (equation (1.1)), the producer maximizes the expected present value of intertemporal profits. As in Goldberg and Hellerstein (2013) andGöcke and Fedo-seeva (2016), we assume that the firm is a risk neutral and has the following objec-tive : : max E0 " _∞

∑

with Π(Qt, q_tf, q_tp) = Rt(q_tf, q_tp) −C_tF −C_tP and where E0is the expectation operator given information at time 0 and 0 ≤ β ≤ 1 is the discount factor. Rt(q_tf, q_tp) = etp_tf ,mq_tf +etp_tp,mqp_t is total sales revenue from fresh and processed goods at time t, to covert to local currency. We rely on a sequential formulation of the problem in order to characterize the profit-maximizing production and sales decisions and we write the Lagrangian function :

L= E0 " _∞

∑

where λt+1is the Lagrange multiplier associated to the stock management constraint and represents the shadow value of a unit of inventory. Unknowns of this problem

12. Our analysis can be compared with the work byGhosh(2009),Nakamura and Zerom(2010) andGoldberg and Hellerstein(2013) who also investigate the relationship between ERPTs for output and input prices.

are the choice variables {Qt, q_tf, qp_t} and the state variables {It, et} (t = 0, 1...), the necessary Kuhn Tucker conditions for an optimum are given by :

∂C_tF ∂Qt + ∂C P t ∂Qt −βEtλt+1 ≥0, Q∗t ≥0 and  ∂C_tF ∂Qt + ∂C P t ∂Qt −βEtλt+1  Qt =0, (1.14) ∂Rt ∂q_tf −∂C P t ∂q_tf −βEtλt+1≤0, qf ∗ t ≥0 and " ∂Rt ∂q_tf − ∂C P t ∂q_tf −βEtλt+1 # q_tf =0, (1.15) ∂Rt ∂q_tp −βEtλt+1 ≤0, qf ∗ t ≥0 and " ∂Rt ∂qp_t −βEtλt+1 # q_tp =0, (1.16)

(1−δ)βEt[λt+1] −λt ≤0, It∗ ≥0 and[(1−δ)βEt[λt+1] −λt]It =0, (1.17) ∆It+1−Qt +qtf +q

p

t =0. (1.18)

Optimality conditions allow for many cases of corner solutions that can arise at per-iod t. The firm can choose not to sell a specific product or none at all or not to produce under specific market conditions (parameters affecting demand and cost functions) and for specific anticipations of the shadow value of a unit of inventory (λt+1) at the end of period t. In TableA.1in Appendix 1, we report the conditions supporting cor-ner and interior solutions in the case where current inventory is equal to zero at the beginning of the period (It =0). The latter could emerge when the firm is in the long-run equilibrium state which is characterized by no inventory accumulation.13 Our assumption of no current inventory is convenient to analyze the short-run ERPTs as it also captures a small perturbation around the steady state (the long-run equili-brium). Also, It =0 holds if the expected value of the inventory at the end of period t−1 is lower than the one at the beginning of the period. A numerical simulation of a shock on the long-run exchange rate is investigated further in section 5 of the dynamic analysis of ERPT for prices of the fresh and processed products.

In our exercise to evaluate the dynamic ERPTs for the fresh and the processed pro-ducts, we illustrate the interior solution characterized by positive trading of the fresh and processed products at time t. The resulting equilibrium is shown in Figure 1.1. Our analysis of this equilibrium is motivated by the calibration and simulation of the production and marketing of the two product types in section 5. Both products are exported in all of the years covered by the sample. Unless stated otherwise, it is as-sumed that variations in the exchange rate are small enough to maintain the control and state variables inside the interior solutions boundaries as shown in Figure1.1.14

13. We describe the long-run equilibrium in section 4.

me-In Figure1.1a, the solid lineC₁represents the inverse demand function for the fresh product p_tf(q_tf, q_tp). The dashed line C2, defined as : ∂Rt

∂q_tf

− ∂CtP

∂q_tf , represents the fresh product’s margin. Regarding Figure 1.1b, the solid line C₃ defines the inverse de-mand function for the frozen product p_tp(q_tf, q_tp). The dashed lineC₄, ∂Rt

∂q_tp, defines the frozen product’s margin. Finally, we represent the total marginal cost of production in Figure 1.1c by the dashed line C5. The initial equilibrium for the fresh and fro-zen products (q_tf∗, p_tf∗) and (q_tp∗, p_tp∗), and total production Q∗_t, "Equilibrium 1", are determined by the intersection of C2, C4, and C5 with the horizontal line C6 which defines the shadow value of the inventory.

After the importing country’s currency appreciation, lines C2 in Figure1.1a and C4 in Figure 1.1bpivot to the right, as shown by the dotted lines, because the margins of the fresh and processed products increase in response to the increase of the export prices (etpf

∗

t and etpp ∗

t ). Furthermore, in response to the rise in the margin of the processed product, we anticipate an increase in the shadow price of stocking for this product for the future period , as displayed by the upward shift of the line C₆.15 These changes yield larger equilibrium q_tf∗ and q_tp∗, as displayed in Figures1.1aand 1.1b.

thods” of the equations system around its long-run equilibrium. 15. From equation (1.16),∂Rt

(a) Equilibrium for q f t (b) Equilibrium for q p t (c) Equilibrium for Qt F IG U R E 1.1 – Equilibriums in the case of the interior solution C1 and C3 ar e respectively the inverse demand curves for the fr esh and pr ocessed pr oducts (p f (t q f ,qt p )t and (p p (t q f ,qt p )t . C2 is the fr esh pr oduct’s mar gin ( ∂ Rt ∂ q f t − ∂ C P t ∂ q f t ) and C4 defines the fr ozen pr oduct’s mar gin ( ∂ Rt ∂ q p t ). C5 repr esents the total mar ginal cost of pr oduction ( ∂ C f t ∂ Qt + ∂ C p t ∂ Qt ). Line C6 defines the shadow value of the inventory (β Et [ λt+ 1 ] ). • is the initial equilibrium (Equilibrium 1) and M is the equilibrium after the exchange rate shock (Equilibriun 2). ↑ defines the response of curves to the exchnage rate appr eciation.

Because of the substitution between the fresh and proccessed products, the rise of the consumption of one product leads to the reduction of the willingnesses to pay for the other one. These effects are represented by the movements of lines C₁ and

C3to the left as shown by the dashed lines. Line C5 in Figure1.1c pivots to the left, resulting in a steeper slope because of the rise in the imported inputs prices in the currency of the exporting country (etwx and etwz). The new equilibrium becomes "Equilibrium 2", yielding a larger Q∗_t, q_tf∗, and q_tp∗and a lower p_tf∗and pp_t∗.

As seen in figure 1.1c, a rise in the production Qt is conditioned by a small rise of the marginal cost of production (line C5). The latter could be the result of small in-creases in the imported inputs prices in the currency of the exporting country (etwx and etwz), which could be in turn ensured by a small positive perturbation of the exchange rate around its initial equilibrium state. In this illustrative case, the combi-ned rise in q_tf, and q_tpdoes not exceed the rise in the total supply Qt. The residual is added to the inventory which is in accordance with our conjecture that its expected implicit value increases. Also, we can observe that the latter is positively related to its shadow price βEtλt+1. If the firm anticipates a higher shadow price, curveC6moves upward, yielding reductions in q_tf, and q_tpand an increase in Qt, and so It+1>0.

Equation (1.14) shows that the expected shadow value of inventory at t+1 equals the sum of the marginal cost of producing fresh produce and processing it. Substi-tuting equation (1.14) into (1.15) shows that the sum of marginal costs of production and processing is equal to the marginal net revenue from selling the fresh product. Equations (1.14) and (1.16) provide a similar interpretation for the processed pro-duct. The marginal net revenue from selling this product must equal the marginal cost of production and processing. Equation (1.17) shows that the marginal benefit of an additional unit of the processed product in inventory in period t equals the ex-pected marginal benefit that this unit will convey in the subsequent period. Equation (1.18) is the law of motion also described by (1.7).

We first explore the steady-state solutions of the model to analyze the long-run ERPTs. The deterministic steady state characterizes the long-run values of the mo-del’s variables. These values are stable (and hence independent of time).

1.4

Steady state ERPTs for prices of fresh and

processed products

The exchange rate in the long run converges to a value that maintains the purcha-sing power parity. From the necessary conditions for optimality (equations (1.14), (1.15), (1.16), (1.17) and (1.18)) evaluated at the steady state, we derive the following equations for interior solutions :

2ewz(Q−qf) +dwy+2ewxQ = βλ (1.19)

e(2pf ,m−αf) +2ewz(Q−qf) = βλ (1.20)

e(2pp,m−αp) = βλ (1.21)

λI = 0 (1.22)

δI−Q+qf +qp = 0 (1.23)

From equation (1.22), we have two candidate solutions : λ = 0 and I ≥ 0 or λ > 0 and I = 0. In the first case, the shadow value of inventories is zero, but inventories are positive. Equation (1.19) becomes :

2ewz(Q−qf) +dwy+2ewxQ =0.

The solution to this equation implies Q <0 and can be ruled out. As a result, λ >0 and I =0, in which case there is no appreciation in the value of commodity stocks, and optimal inventories are zero. The intuition behind this result is that the firm does its best in the long run to avoid inventory costs and adjusts production of fresh and processed products to match sales. The model turns into a deterministic one and the results can then be compared to results derived from static models.

Recall that it is assumed that the exporting monopolist chooses the foreign country’s currency for invoicing purposes. Thus, the ERPT for product j∈ {f , p}at period t is defined as the percentage change in its export price expressed in the home country’s currency after the depreciation :

ERPTj = ∂ pj,ex_t ∂et et pj,ex_t ∗100= 1+∂ p j,m t ∂et et pj,m_t ! ∗100 (1.24)

We define ERPTj,SS as the ERPT of the product j ∈ {f , p} at the steady state. The expressions below represent the ERPTs for good j in function of the demand

elasti-cities : ERPT_j,SS =1− A αj  1− 1 1−θ2((ε qj pj) −1₋ θ2(εqp−jj ) −1₎  (1.25) with, A = dwy(1−θ 2₊ θwz) 2e(−θ2+wx(−2θ+wz+2)+wz+1) >0

The long-run price ERPTs (defined in (1.25)) depend on the own-price and cross-price elasticities of demand because the two products are substitutes in the foreign country. From equations (1.4), for all j ∈ {f , p}, we know that the own-price elas-ticities εqpjj are negative and the cross-price elasticities ε

qj

p_−j are positive. Therefore, ERPT_{f ,SS} and ERPTp,SS are generally incomplete (< 1). Based on equation (1.25), we can analyze some special cases :

- If the share of the domestic input in the production of the fresh product is too small (d → 0), then the prices ERPTs for the fresh and processed products are almost complete (ERPTj,SS →1) as A →0. A low share of the domestic input in production and processing processes means that the export prices depend almost entirely on the imported inputs, which implies ERPTs close to 100%. - Given that the firm uses a positive quantity of the local input (d > 0) and

its price is much lower than the price of the imported inputs (_wxw₊y_wz → 0), the price ERPTs for the fresh and processed products are almost complete as A →0. Again, in this case, export prices depend almost entirely on the prices of imported inputs.16

The analytical explicit expressions of ERPTs for the fresh and the processed products’ prices are respectively :

ERPT_{f ,SS} = αfeΦ+αpeχ

αfeΦ+αpeχ+Γ+dwy(1−θ)wz, (1.26) ERPTp,SS = αfeΨ+αpe(Φ+wz) αfeΨ+αpe(Φ+wz) +Γ, . (1.27) where Φ= 3wx(1−θ) +2wxwz+wz+1−θ2
,

16. The positive (negative) impact of the imported (domestic) input share could be also observed in Figure 1.1. In the case of a high (low) share of inported (domestic) inputs, the production and processing marginal costs increase much more in response to the exchange rate shock. Thus, holding inventories becomes efficient, which is defined by the movement of C6more upward. Also, line C5

pivots more to the left resulting in a steeper slope because of the rise in the imported inputs prices. These combined effects yield a lower increase in Q∗_t, q_tf ∗, and qp∗_t and a lower decrease in p_tf ∗and p_tp∗ in response to the exchange rate shock.

χ= (1−θ)wx,

Ψ= ((1−θ)wx−θwz), Γ=dwy(1−θ2+θwz).

Table1.1summarizes the response of the prices ERPTs to different values of demand parameters and imported and domestic input prices.17

TABLE1.1 – Effects of demand and cost parameters on the long-run ERPTs for prices of fresh and processed products

Parameters traded VS local Fresh VS processed Effect on ERPTFSS Effect on ERPTPSS

wy Local fresh -

-wx traded fresh + +

wz traded processed - +

α_f n.a. fresh +

+/-αp n.a. processed + +

The price ERPTs for both fresh and processed products decrease (increase) with the share of the domestic (imported) input used in the production of the fresh product (∂ERPT_∂wyj,ss < 0, for all j ∈ {f , p}). This finding is in line with the result of previous studies about ERPTs and vertical integration (e.g.,Gopinath et al. (2009), Gopinath et al.(2011), andAhmed et al.(2015)). A depreciation of the monopolist’s currency is akin to positive demand shocks for both products. However, the depreciation makes imported inputs costlier. At the steady state, there is no inventory and the adjust-ment operates on the quantity of the fresh product and the fraction that is to be processed. The increase in the production of the fresh product is larger and the price increases smaller when there are no imported inputs to offset the demand-increasing effects of depreciation. If the costs of production and marketing depend more on local inputs (imported inputs), the output prices are less (more) affected by the ex-change rate fluctuation and the ERPT is low (high). We find the same positive rela-tionship between the relative importance of imported inputs in processing cost and the price ERPT for the processed product (∂ERPT_∂w p,ss

z > 0). However, this cost has an

opposite effect on the price ERPT for the fresh product (∂ERPT_∂wzf ,ss <0) because these two products are strategic substitutes on the demand side. The monopolist adjusts the price ERPT for the processed product upward and the one for the fresh product downward in response to an increasing value of wzto incite consumers to substitute the less profitable product by the more profitable one.

Regarding the effects of the demand parameters on long-run ERPTs, we note that the long-run price ERPT for the product j is increasing in its willingness to pay (∂ERPT_∂α j,ss

j > 0, for all j ∈ {f , p}). An increase in αj, at a given quantity consumed,

increases the price, the demand elasticity of product j and magnifies the price effect of a devaluation in the exporter’s currency.

Regarding the cross effects, the relationship between the demand elasticity’s para-meter αp and the long-run ERPT for the fresh product is positive (

∂ERPT_{f ,ss}

∂αp > 0).

This result can be explained by the fact that the firm does not build an inventory in steady state and that all processed products must be sold. As a result and due to the substitutability of the two products, the firm increases the pass-through of the fresh product to push the consumer to buy less of this product and more of the processed product. Therefore, ERPTf ,SSis increasing in the preference parameter αp.

However, the effect of the willingness to pay for the fresh product αf on the long-run ERPT for the processed product is ambiguous (∂ERPT_∂α p,ss

f ≷ 0). At first glance,

we expect that the effect of αf on the ERPTp,ss is the same as the effect of αp on the ERPT_{f ,ss}because of substitutability of the two products. The firm increases the pass-through of the processed product to push consumers to buy less of this product and more of the fresh product. However, the result in table1.1shows that this effect can be negative under a specific condition characterized in the following proposition. We explain the ambiguous effect of αf on ERPTp,ssby the difference in use of the fresh and processed products and the convexity of cost functions. The processed product is the final stage of vertically integrated products that should be sold to consumers. However, the fresh product could also be used as an input for processing rather as a final product. Also, the marginal processing cost is increasing in the imported input Z.

Proposition 1. The relationship between the long-run ERPT for the processed

product and the willingness to pay for the fresh product is ambiguous : (∂ERPT_∂α p,ss f <

0 if wz > wx(1_θ−θ) and ∂ERPT_∂αfp,ss >0, otherwise).

Using the super-elasticities expressions (1.5) and (1.6), we find that the rise in the fro-zen product price makes the demand for the frofro-zen product more elastic, Spppp > 0,

but the demand for the fresh product less elastic, Spf fp <0. Furthermore, we note that

the higher the processing cost and/or the higher the substitution between fresh and processed products (wz > wx(1_θ−θ)), the higher the processed product price.

There-fore, increasing ERPTp,ssin response to αf when wz > wx(1_θ−θ) can result in a signi-ficant loss in frozen product market share (Spppp > 0) without necessarily increasing

the consumption of the fresh product at the same rate (because Spf fp <0). With these

conditions, the firm could choose to decrease the long-run ERPTp,ssinstead of rising it. This result delivers a new insight on the ERPTs in the case of vertical integrated products and non-linear costs.

Corollary. When the two products have independent demands (i,e., θ →0), the

long-run ERPT for the processed product price is increasing in response to the willingness to pay for the fresh product (∂ERPT_∂α p,ss

f ). Nevertheless, if the two pro-ducts are strongly substitutable (i.e., θ →1), the long-run price ERPT for the

pro-cessed product is decreasing in response to an increase in the market size for the fresh product (i.e., parameter αf).

The firm can increase the ERPT for the processed product without having to be concerned about a cross-price effect transferring demand from the processed duct to the demand for the fresh product. In the case of strongly substitutable pro-ducts, the monopolist protects his sales of processed products by reducing the price increase for its processed products.

Recall that at the steady state, the inventory is zero because the firm has complete information about the long-run state variables. In the short-run, the firm may take a “precautionary strategy” because of the exchange rate volatility. Teo(2011) men-tions that exchange rate changes can affect firms’ incentives to hold inventories and that these changes in inventory holdings can, in turn, affect prices. In our case, the processed product is less perishable and can be stored and marketed in subsequent periods. The dynamic analysis described in the next section allows us to shed light on the relationship between the exchange rate variations and inventory accumula-tion. Also, we analyze the perishability effect of the processed product on the mo-nopolist’s pricing decision in the short-run and we use the stock depreciation of the processed product as a measure of its perishability. Alessandria et al. (2010) show that a large depreciation reduces inventories held by importers, make them order more frequently and incur higher trade costs, which affects the firms’ pricing deci-sion. Thus, we evaluate the effect of the perishability of the processed product on the short run prices and quantities ERPTS for the fresh and processed products.