Globalisation as a 'good times' phenomenon: A search-based explanation

Edwards, T. Huw Article Globalisation as a 'good times' phenomenon: A searchbased explanation Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Edwards, T. Huw (2010) : Globalisation as a 'good times' phenomenon: A searchbased explanation, Economics: The Open-Access, Open-Assessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 4, Iss. 2010-24, pp. 1-48, https://doi.org/10.5018/economics-ejournal.ja.2010-24 This Version is available at: https://hdl.handle.net/10419/39690 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Vol. 3, 2010-24 | August 31, 2010 | http://www.economics-ejournal.org/economics/journalarticles/2010-24 Globalisation as a ‘Good Times’ Phenomenon: A Search-Based Explanation T.Huw Edwards CSGR, Warwick, and Loughborough University Abstract Globalisation is associated with long periods of sustained economic growth and credit expansion, whereas major recessions tend to lead to falling trade and protectionism. The sensitivity of trade to global economic conditions is not simply driven by policy: rather, in a model of costly search, firms who are engaged in a searching process are very sensitive to changing economic circumstances. In turn, this causes protectionism to be partly endogenous, since optimal noncooperative tariffs can be high during periods when the sensitive, searching firms have exited the market. JEL F15, F43 Keywords Globalisation; trade; search Correspondence T. Huw Edwards, Economics, Loughborough University, Epinal Way, LE113TU Loughborough, United Kingdom; e-mail: [email protected] © Author(s) 2010. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany conomics: The Open-Access, Open-Assessment E-Journal Introduction `Good times dampen anti-globalization attitudes, while bad times deepen them.' —Jagdish Bhagwati.1 Why do periods of prolonged global growth, such as 1980–2007, tend to be accompanied by even faster growth of World trade, particularly inter-rm, interindustry trade? Why is the stalling of such growth traditionally associated with protectionism? In addressing these questions, I wish particularly to stress the two-way nature of the relationship between globalisation and worldwide growth. Some characteristics of the boom years of the 1980s, 1990s and 2000s, which were associated with the integration of India, China and Eastern Europe into the World economy, are summarised in Table 1. Some of these features (though not the vertical fragmentation of production) replicate those of the pre-1929 globalisation boom. By contrast, the 1930s saw most of these trends go into sharp reversal (Crafts, 2004). Some of the features in Table 1 deserve special comment. In particular, the (not uncontroversial) conclusion that more open, market-orientated economies experienced faster growth stands rather contrary to standard economic thinking. After all, standard textbooks would argue that, while trade is good for all economies taken together, in most circumstances it is in the individual interests of `large' countries to impose a protectionist set of `optimal' tariffs on imports and exports, in order to improve their terms of trade2, so that there is a prisoner's dilemma situation, whereby the noncooperative outcome of tariff-setting games is against the collective interest. By contrast, one might tentatively view the evidence of the last 20 years or so as suggesting that there is little evidence of a prisoner's dilemma: open trade policies, which favour a country's neighbours, also seem in many circumstances to serve its self-interest. This is a feature which I particularly wish to investigate: is there some characteristic of globalisation booms which leads to a convergence of country and global welfare-maximising policies, and, if so, does such a convergence break down during prolonged recessions or depressions? 1`In Defense of Globalization' (2004), OUP, p. 10. 2E.g. Gros (1987). www.economics-ejournal.org 1 conomics: The Open-Access, Open-Assessment E-Journal Table 1: Stylised characteristics of the recent globalisation phase 1. Relatively rapid growth of the global economy. 2. Fast credit expansion, international mobility of capital and ease of borrowing. 3. Trade growing much faster than global GDP (a), with a high income elasticity. (b) 4. A growing extensive margin of trade.(c) 5. Rapid churn of trading rms.(d) 6. Trade growth based upon the expansion of traditional trading networks.(e) 7. Interrm, inter-industry trade growing faster still.(f) Vertical FDI/outsourcing.(g) Fragmentation.(h) 8. Growth especially concentrated in areas of the South or former Communist bloc entering the outsourcing trade. 9. Reduction in protectionist barriers. 10. Countries which pursued open strategies outperformed less open economies.(i) Notes on Table 1: (a) See the gure on www.imf.org/external/np/speeches/2006/pdf/0502, 06.pdf. In the period 1950– 2005, only in 1958, 1953, 1982–1983 and 2001 did trade decline relative to GDP: in each case during a recession year. (b) Ishii and Yi (1997). (c) Bernard et al (2009). (d) Besedes and Prusa (2006). (e) Rauch and Trindade (2003). (f) Ishii and Yi (1997). Hummels, Ishii and Yi (2001). (g) Markusen (1995). (h) Feenstra and Hanson (1999). (i) Wacziarg and K.H.Welch (2008). Dollar and Kraay (2002 and 2003). These studies are not without their critics—for example, Luebker et al (2002). Winters, McCulloch and McKay (2004) give a more overall survey of the benets of trade liberalisation. www.economics-ejournal.org 2 conomics: The Open-Access, Open-Assessment E-Journal In this paper, I link this, in particular, with point 3—the high observed income elasticity of trade during the economic `good times'. The starting point is that this high elasticity represents a footloose element of supply, which is explicitly linked to the dynamics of a search process, and which may be the rst thing to be eliminated during an economic downturn. Once this footloose element is eliminated, the economics of trade protection are turned on their head—essentially, the prisoner's dilemma is returned. The structure of the paper is as follows. The rest of Section 1 and Section 2 build on the theoretical ideas of existing papers by Ishii and Yi (1997), Rauch and Trindade (2003) and Rauch and Casella (2003) and Grossman and Helpman (2002 and 2005), to develop a partial equilibrium model of a single industry with twostage production, outlining the difference between growing and declining sectors and that between matched and searching rm pairs. In Section 3, I then set up a three-phase time schema, whereby in phase 1 there is little trade, phase 2 sees globalisation and phase 3 sees an economic crisis. Section 4 discusses how either a demand crisis, a credit crisis or a prolonged period of demand stagnation can affect this model. Section 5 is perhaps the most important part of the paper, since it develops the model into an explanation of why optimal tariffs may be low during periods of economic growth, but high during periods of economic slowdown, particularly when credit shortage is a contributory factor. In particular, behaviour can switch from free-trade to protectionist, if there is a crisis, particularly if it is followed by growth resuming at below a critical threshold level. This is illustrated by a numerical simulation model, calibrated to a stylised data set. It is also important to ask whether search is, in fact, quantitatively important enough to inuence behaviour in the ways suggested in this paper. In this regard, Section 5.2 reviews the empirical evidence. This is still somewhat limited, due to the short timespan of most rm-level data sets, but evidence from Besedes and Prusa (2006) and Eaton et al.(2007) suggests fast entry and exit. Despite the small scale of rms on initial entry, during the search process, those new entrants who survive rapidly build up to account for perhaps 20–25% of trade volumes. Tentative evidence linking outsourcing to search is also discussed. www.economics-ejournal.org 3 conomics: The Open-Access, Open-Assessment E-Journal 0.1 Fixed Costs, Search Costs and Trade Elasticities It has become a commonplace that costs of market entry impede global trading patterns, such that economic integration, even in the good times of the 1990s and 2000s, falls far short of what neoclassical theory would predict (Treer, 1995; Obstfeld and Rogoff, 2000). Since this primarily reects limitations on the extensive margins of trade (in other words, the fact that most rms do not trade most products internationally), this is widely explained in terms of a xed cost of market entry (Tybout, 2002)—rms need to make a particular level of prot in order to justify market entry, there are both selection effects in favour of large and successful rms (Bernard et al., 2007) and threshold effects on entry. The latter, threshold effect can also be explained simply in terms of a Ricardian model of comparative advantage (Yi, 2003): once trade costs fall sufciently, the fragmentation of production becomes possible so that different stages can be carried out in different countries. Consequently, there is a rapid, nonlinear growth of market participation, particularly in terms of vertical tie-ups between rms (Yi, 2003). In addition, where tariffs are ad valorem, effective protection against individual stages of production is magnied (since a tariff may be paid more than once, as the goods cross and re-cross borders), and the same applies to transport costs—so exaggerating the apparent price-sensitivity of intermediates trade. Many of these arguments are often summarised as the `new, new' trade theory3—i.e. supplementing the models of Krugman, 1979 and Grossman and Helpman, 1992, with the incorporation of rm-level participation effects and production fragmentation. These elements are now acknowledged to have powerful implications for growth through rm selection,4distribution5and the observed volatility of trade.6By themselves, however, they offer only a partial explanation, containing no real evidence of the nature of the xed costs of market participation, and under what circumstances they may become sunken rather than just xed. To explain this, we need to turn to another branch of the literature—the evidence of informational barriers and a search process. This stems from stylised facts 5 and 3To use Srinivasan and Archana's (2009) terminology. 4Melitz, 2003. 5Feenstra and Hanson, 1999. 6Ishii and Yi (1997). www.economics-ejournal.org 4 conomics: The Open-Access, Open-Assessment E-Journal 6 in Table 1: the high turnover of trading rms (Besedes and Prusa, 2006) and the evidence of network effects (Rauch and Trindade, 2003), taken with strong evidence that clusters of low-cost producers can go unnoticed by traders for long periods (the noted example being surgical steel production in Sialkot, Pakistan7). Informational barriers can generate a search process, and I argue that this process is a primary cause of threshold effects, which in turn helps explain the dynamics of trade.8Search takes time and requires condence and the availability of credit. Critically, rms need to incur a series of ongoing xed costs during the search process, but once they eventually achieve a satisfactory match, the cost of the past search is sunken. This means that searching rms will indeed be very sensitive to price movements, as in Ishii and Yi (1997), but that, as the search process goes on, rms achieve matches and become more heterogeneous and less subject to threshold effects. This process indicates a sensitivity of trade during the process of globalisation to international traded prices, global aggregate demand and capital availability,9but the trading patterns of long-established rms, which are likely to be much less sensitive,10 and it is this nonlinearity—missed by the existing literature—which may underlie the danger of policy shifts during and after economic crises. 1 An Illustrative Model of Firm-Level Trade I set up a simple, stylised, partial equilibrium model of a monopolistically competitive industry in a two-country world—the two countries being the North and the South, the former being characterised by higher skill endowments per head. 7Schmitz, 1999. 8Ishii and Yi (1997) use xed costs of vertical specialization to explain the high observed income elasticities of trade—which they argue cannot plausibly reconciled with more orthodox models. 9In terms of a macroeconomic model, market search has elements of capital formation, and so it should be no surprise that it has many of the characteristics of investment demand—in terms of cyclical sensitivity. 10This reects in part the heterogeneity both of rms (Melitz, 2003) and of trading match quality (Rauch and Casella, 2003). www.economics-ejournal.org 5 conomics: The Open-Access, Open-Assessment E-Journal The main market for nal goods is in the North. Production requires two stages, which I name upstream (u)and downstream (d). Typically these are carried out by a pairing of rms (which may or may not be vertically integrated by merger), where usells a semi-nished good to d, who then completes the manufacture and sells it on to nal consumers. The two rms are of equal size and ex ante expected efciency: however, productivity varies depending on the goodness of t of the match, µi. As in Rauch and Casella (2003) or Rauch and Trindade (2003), µ;potentially follows a uniform, rectangular distribution between 0 and 1, and rms do not know µibefore entering a match i, though they know its overall distribution.11 (See Appendix 1 for more details on the derivation.) Trade between the North and South develops over time. The historical setup takes three phases. In phase 1, trade costs are high, so that there is little trade, and most goods are produced by pairings of rms type uand dwithin the North. However, the South is assumed to have a potential comparative advantage in upstream production, while the North has a comparative advantage in downstream production. We then enter phase 2: a period of growth and global integration, spurred by a technological or policy change reducing trade costs. Some Northern, downstream rms (though not all) will now search for upstream partners in the South. For example, garments might be manufactured by an upstream rm in China, but according to designs from the downstream rm in a Western economy, which then completes the marketing and distribution worldwide. Phase 3 represents an unanticipated crisis, where credit ceases to be available and growth stalls for a protracted period. Concentrating on phase 2, the period of globalisation, the growth of the outsourcing trade is impeded by search friction deriving from an assumed need for at least one rm to make a relationship-specic investment: in order to avoid a potential hold-up problem,12 this generally requires a contractual relationship for at least some minimum period, which I characterise by a xed contract period, t, during which the two rms have an exclusive relationship. 11This setup is derived from Salop's circular cylinder, and is standard in rm-level matching models. Note that Grossman and Helpman's (2002) model is similar, except that rms know with certainty the location of potential partners, and always match with the nearest. 12See Hart (1995). www.economics-ejournal.org 6 conomics: The Open-Access, Open-Assessment E-Journal Firms employ labour in the form of xed and variable elements. The cost of the latter is normalised at C=CNfor North-North pairings, and at C=CS (CS<CN) for North-South pairings. The elasticity of substitution between nal goods varieties is ε, which will also closely approximate the own-price elasticity for the output sold by rm pairings, at least as long as the number of rms, N, is large. Sales by pairing iwill equal Yi=A(εCi (ε1)P)ε;i2 fN;Sg;(1) where Pis the CES aggregate price index. Prots of the pairing, before subtracting xed costs, will equal πi=A ε(εCi (ε1))1εPε=kC1ε iPε:(2) The model is driven by an assumed coordination cost which is inversely linearly related to the quality of the match µibetween rms in pairing i. For simplicity, I concentrate on a rather stylised model where quality of match affects xed cost, rather than unit variable costs. More precisely, I assume that xed costs are Fµi, so that prots after subtracting xed cost, Πi=kC1ε iPεF+µi:(3) Note I am also assuming equal Nash bargaining weights between the upstream and downstream rms. 1.1 The Matching Process We now want to look at the matching process in more detail. Appendix 1 explains the matching process in more detail. I assume rms take a series of blind matches, where match quality, µi, varies according to a uniform rectangular distribution between 0 and 1. Further, assume that rms are stuck with an existing partner for a xed contract period, t, during which time rms face a discount rate r. Firm pairings are also subject to sudden, random death with a constant probability of www.economics-ejournal.org 7 conomics: The Open-Access, Open-Assessment E-Journal Figure 3: Evolution of different types of pairings after a reduction in trade costs starts a globalisation phase, related to the underlying growth of demand per annum The kinks in this supply curve are an important element in explaining the differential effects of economic shocks, and the potential change in policy following such shocks—as explained in the subsequent sections. Figure 3 summarises some simulations on the evolution of the proportions of different types of rm pairings over time, following a 10% reduction in the cost of North-South pairings. These are based upon the parameter assumptions in Table 2. Simulations are carried out for underlying demand growth rates of 2%, 5% and 8%. After 20 periods, the proportions of searching NS pairings vary between 1530%, depending on demand growth, while matched NS pairings are 5662% and NN pairings 829% per cent of the market. www.economics-ejournal.org 14 conomics: The Open-Access, Open-Assessment E-Journal Table 2: Parameter assumptions for simulations Time preference per contract period ρ0.08 Death rate of one rm in pairing D0.02 Basic xed cost of market participation F1 Subs elasticity between rms ε5 Own price elasticity for industry output η-1 Implied reservation match quality µR0.768. 3 The Impact of a Negative Economic Shock 3.1 A Demand Shock We now want to consider the effect of shocks to an economy which has been undergoing the process of globalisation (in the sense of entry by searching foreign upstream rms, and the gradual development of successful, importing partnerships). Take the situation in Figure 2, and assume that there is a sudden inward shift in the demand curve, caused by a recession. The situation is shown in Figure 4: essentially, searching foreign rms are footloose, and will simply exit the market at the end of their existing contracts (except for the minority who nd profitable contracts). This is a component of import supply which is very sensitive to demand changes. Consequently, unless the demand shock is very large, it can be accommodated simply by the exit of these rms: the remaining foreign and domestic rms see very little change in their demand or prices. Only larger shocks will force established rm pairings back down their supply curves. Note that, at the point where searching North-South pairings have been eliminated, the elasticity of imports with respect to the industry aggregate price falls from innite to ε µR;and continues to rise thereafter, as more rms are driven out. The situation with a larger negative demand shock is that, only after seaching rms have been eliminated will prices be driven down. At this point, existing domestic pairings, as well as established importing pairings will be faced with falling prices, and the least efcient will be eliminated (so driving the rms down their supply curves). This is shown in Figure 5. www.economics-ejournal.org 15 conomics: The Open-Access, Open-Assessment E-Journal Figure 4: A negative demand shock which wipes out searching rms, leaving matched rms unchanged Note that an implication is that the rst rm pairings to exit the market are searching, North-South pairings, so that trade is especially vulnerable to a medium shock. In the larger shock in Figure 4, matched North-North pairings will exit at the margin faster than matched North-South pairings in the ratio σN3 σS3 =P 2P0 1 P 2P0 2 <1:(15) 3.2 A Credit Shock A credit shock is somewhat harder to model—particularly where it results in shortages of cash, rather than a rise in headline interest rates. Nevertheless, I will assume that rms suddenly face a rise in risk premia on their interest rates, so that the interest rate per contract period rises to ρ0>ρ: www.economics-ejournal.org 16 conomics: The Open-Access, Open-Assessment E-Journal Figure 5: A larger negative demand shock I consider the unlikely phenomenon of a pure credit shock (one which affects supply, but does not result in a recession shifting the demand curve inwards). It is worth noting that this type of shock hits different rms disproportionately. In particular, by raising the de facto interest rate facing rms, a credit shortage will make the search process costly. As a result, the reservation match quality will fall (rms will accept lower-quality reservation matches than previously, when they were more patient). The implication of this is that the reservation match quality falls to µ0 R=1+ρ0+Dp(ρ0+D)(1+ρ0+D)<µR:(16) However, since the reservation price which overseas rms type uwill demand in order to enter into search is P =µR µ0 R P 2;(17) this will now be higher than previously. However, while the supply price of searching rms is raised, the supply curves of established rms are unchanged. www.economics-ejournal.org 17 conomics: The Open-Access, Open-Assessment E-Journal Figure 6: Effect of a credit shock increasing the cost for searching rms Figure 6 shows a pure credit shock, just sufcient to drive searching foreign rms out of the market, while raising prices at home (hence leading to established domestic and foreign rms supplying marginally more than before). Note that the price does not rise as far as P, so that search is halted entirely in the short/medium run.13 Existing rms can supply somewhat more than previously, as the market price, P;rises, in accordance with equation (1). However, new rms cannot enter unless the price rises to P, so below that level supply is relatively inelastic. In reality, we should perhaps consider that, at least in their initial stages, credit shocks are usually associated with demand shocks as well. However, in both cases we should note that it is the searching importing rms (and their domestic partners) which are the most sensitive to macroeconomic shocks: established pairings, whether domestic or international, are far more robust. 13In the longer run, depreciation of the stock of existing matched rms at rate Dwill gradually raise the supply cost and price, until it reaches P and new rms start to enter and search again. www.economics-ejournal.org 18 conomics: The Open-Access, Open-Assessment E-Journal The conclusion should be that, in the event of a combined credit and demand shock hitting an economy which had been undergoing a process of steady growth and increasing trade openness, there will be a relatively large proportion of trading rms and their partners—as implied by equation (15)—which will exit the market relatively quickly. One should perhaps not be surprised by this nding. Trade search can be viewed as a kind of capital formation, with rms prepared to undergo losses in the early years of search, in order to make an expected positive return thereafter, once they are established. Like any form of capital formation, we would expect search capital formation to be sensitive, both to changes in the cost and availability of credit, and to accelerator-type changes in overall demand growth. That is what this model indicates. 4 Endogenous Policy Responses to a Boom, a Shock or Stagnation We have so far established that, during a globalisation boom, where demand and imports are rising fast, there should be at any one time a relatively high proportion of trade which is accounted for by searching rms, whose presence in the market is footloose, and who are vulnerable to either demand and/or credit shocks. This, by itself, implies that the globalisation process can be suddenly halted by unexpected shocks, regardless of any policy response. Moreover, since search is necessary for the long-run growth of trade, a shock may have a prolonged negative impact upon trade. We now want to consider how trade policy might respond to economic circumstances, given a search model, where various components of foreign supply differ greatly in terms of their price sensitivity. In this context, it is worth bearing in mind that, where trade is between rms who are specically matched, all countries can be considered `large' from the point of view of trade policy, since trade with a matched partner is differentiated from trade with any other potential partner, yielding potential monopsony power to the importing country (and monopoly power to the exporting country). We will follow a modied version of the standard `large country, partial equilibrium' exposition of optimal tariff policy (see, for example, van Marrewijk, 2007, Section 8.3). www.economics-ejournal.org 19 conomics: The Open-Access, Open-Assessment E-Journal Figure 7: Effect of a low tariff, τ1 Figure 7 shows schematically the effects of imposing a tariff on an economy with a large amount of initial importers who are searching (and hence pricesensitive). It has been drawn slightly differently to Figures 1, 2, 4, 5 and 6, since domestic supply is now subtracted from consumers' demand, to give a demand curve for imports. (Note that the domestic supply curve increases less quickly above P, since a rise in price does not affect the number of domestic rms, while a fall in price will cause further exit). The elastic portion of the supply curve, accounted for by the initial searching importers, means that a tariff has to be substantial before it can begin to lower the import price. The welfare effects of this are that there is a rise in consumer prices (causing a welfare loss), and no fall in import costs. There is, however, some tariff revenue from the higher price paid by consumers (though there is still a deadweight loss). Since the model is monopolistically competitive, and prices exceed marginal costs, there is also a protshifting effect from the increase in market share borne by domestic producers (see Brander and Krugman, 1983). (This effect will only be enough to outweigh the www.economics-ejournal.org 20 conomics: The Open-Access, Open-Assessment E-Journal Figure 8: Effect of a higher tariff, τ2 loss of consumer surplus when the elasticity of substitution, ε, is low enough to generate high prot margins, yet still large enough for domestic sales to increase signicantly.) Figure 8 shows a larger tariff, which begins to lower import prices (c.f. the large, open economy partial equilibrium model in many trade textbooks). The fall in import prices (by driving out the less efcient importers) means that some of the tariff revenue is at the expense of importers rather than consumers. However, the presence of the at segment (the threshold effect) means that this effect (when combined with the prot-shifting effect) needs to be large to offset the loss of consumer surplus, since only sizeable tariffs will begin to reduce traded prices. By contrast, where there are few initial searching rms, a tariff begins much more quickly to impact upon traded prices. The implication is that there is likely to be a discontinuity in tariff-setting: when the sector is shrinking, or growing www.economics-ejournal.org 21 conomics: The Open-Access, Open-Assessment E-Journal Table 3: Parameters for numerical simulation Discount per contract period ρ0:08 Fixed cost F1 Elasticity of substitution between rms ε10 Share of non-trading rm pairs (base) SD0:5 Death rate of rms per contract period D0:02 Marginal cost of NN pairing CN1 Marginal cost of SN pairing CS1 1:1 Total expenditure on the product M1000: slowly, optimal tariffs are positive, while, when the sectoral rate of import growth exceeds a threshold rate, optimal tariffs fall to zero. The analysis here is somewhat simplied, since in reality one needs to consider tariffs in a dynamic setting. In due course, even with a tariff, the natural death of existing matched rms will lead the economy back to a position where searching rms begin to reenter the market—under some circumstances, we would expect this to lead to a cycle of optimal tariffs over time. Nevertheless, the situation with stalled growth indicates a signicant difference between eras of prolonged trade growth, where protection is not favoured, and eras of stagnation, where it is. 4.1 Numerical Simulation Analysis (see Appendix 3) To examine the effects of a crisis and/or a period of stalling of growth, I set up a numerical simulation of the partial equilibrium model outlined in Figures 7 and 8. The model is static only. Key parameters chosen are as shown in Table 3. An elasticity between rms of ε=10 is consistent with many recent studies of trade elasticities (Anderson and van Wincoop, 2004). The model is calibrated to a series of equilibrium starting growth paths for a variety of growth rates between 2% and +9% per annum. The former case corresponds to the situation where G+D=0, and so is a situation where in equilibrium there are no searching rms. The higher the initial growth rate, the more searching rms there will be. To summarise the results of the simulations: www.economics-ejournal.org 22 conomics: The Open-Access, Open-Assessment E-Journal Given the parameter assumptions, a tariff that eliminates searching rms reduces national welfare. This is because, while the tariff is not large enough to remove more than the price-sensitive, searching component of supply, import prices do not fall. Consequently, the tariff revenue plus prot-shifting are insuf- cient at the margin to outweigh the loss of consumer surplus. The results are shown in Appendix 1, Table A1. Note that, where the elasticity of substitution is lower, or the initial share of domestic production is higher, then the prot-shifting effect will be larger, and may outweigh the loss of consumer surplus. Driving searching rms out is costlier to welfare, the higher is the initial growth rate of trade. This is seen in Appendix 3, Figures A3–A5, and should not be seen as surprising, since a higher tariff is required when there are more searching rms to start with. Once searching rms have been driven out, a further rise in the tariff rst increases and then reduces welfare. This can be seen in Appendix 3, Figures A3–A5. It is worth remembering that, once searching rms have been driven out, the analysis is closer to the typical large country model of trade, where a tariff is initially welfare-improving, by reducing import prices. Only later do the marginal costs of a tariff outweigh the benets. This result is important in the immediate aftermath of a crisis, where a fall in demand or a collapse of credit have resulted in the exclusion of searching rms. In this case, as in Appendix 1, Figure A1, there are no initial searching rms, and welfare will always benet from some tariff (in this case, reaching a noncooperative `optimal tariff' of around 4%, reducing trade by around 32% in total. Whether or not a tariff can improve national welfare depends on the initial number of searching rms. This is seen by comparing Appendix 3, Figures A3–A5 The faster the initial growth rate of the economy, the more searching rms have to be driven out before a tariff can start to improve the country's terms of trade. Consequently, the inverted-U curve of welfare starts from a lower point. Beyond some threshold rate of growth (in this case, approximately G=5%), a country will switch from charging an `optimal tariff' to free trade. This is also summarised in Figure 9, which shows the simulated `optimal tariff' for different initial growth rates. www.economics-ejournal.org 23 conomics: The Open-Access, Open-Assessment E-Journal Appendix 1: The Matching Setup The paper follows Rauch and Trindade (2003) and Rauch and Casella (2003) in using a matching framework based upon Salop's circular cylinder (note that Grossman and Helpman, 2002, use a similar setup). This is shown in Figure A1. Position on the circle refers to some rm-specic characteristics. The essence of the Salop model is that rms are ex ante equal in efciency, but that rm performance is determined by the degree of t with the match partner: the aim is to match with a rm directly opposite on the cylinder. Hence, match quality, µi;is measured by the circumference distance between the two rms. Firms only have a single partner at any time. Figure A1: The Salop matching framework The key difference between the match-searching model employed here and the models in the earlier papers is the ability of a rm in an unsatisfactory match to renew search, after a given contract period. This determines the generation of a reservation match quality, µR:The decision process of the rm is shown in Figure A2. www.economics-ejournal.org 30 conomics: The Open-Access, Open-Assessment E-Journal Any match with a circumference length greater than µRwill yield a prot great enough for the rms to choose to continue. This gives a probability of acceptance of 1 µR. However, of these pairings, proportion Dwill naturally expire anyway during the rst contract period, so any surviving rm will have to renew search. By contrast, proportion µRof initial pairings will be unsatisfactory, and be dropped after one contract period. Figure A2: The match-searching decision setup We note that the prot of a reservation quality match (µi=µR) is zero. Prot increases linearly with respect to match quality, so that the expected prot of a successful match (where µR<µi<1) is 1+µR 2minus the prot of a reservation quality match. This yields an expected prot of 1µR 2:Likewise, an unsatisfactory match qill have an expected prot of µR 2:Finally note that a renewed search will yield a present discounted value of zero. Table A1: Expected returns for the matching process Match Probability Expected prot above reservation Satisfactory Both rms survive (1µR)(1D)1+µR 2µR=1µR 2 One or more dies (1µR)D0 Unsatisfactory µR µR 2µR=µR 2 www.economics-ejournal.org 31 conomics: The Open-Access, Open-Assessment E-Journal We wish now to solve this problem, based upon the knowledge that monopolistic competition will equate the expected return from entering a search process to zero. Discounted prot with a successful match = one period expected loss with a poor match (1µR)2 2Φ=µ2 R 2(1+Φ);where Φ=ρ+D; (18) (1+Φ)(12µR+µ2 R) = Φµ2 R; (19) µ2 R2(1+Φ)µR+(1+Φ) = 0; (20) µR=2(1+Φ)p4(1+Φ)24(1+Φ) 2; =1+ΦpΦ(1+Φ);(21) since only the negative root lies between zero and unity. www.economics-ejournal.org 32 conomics: The Open-Access, Open-Assessment E-Journal Appendix 2: The Thick Industry `Love of Variety' Partial Equilibrium Model with Match-Searching The industry is described as `thick' in the sense that the number of rms producing differentiated goods is large. Competitive Structure The industry is assumed to be monopolistically competitive, on the lines of Krugman (1979). There are both xed and variable costs. Subject to these, rms can enter or exit the market, although they need a partner (existing or new) in order to produce saleable goods. The elasticity of substitution between nal goods varieties is ε(>1)20, which closely approximates the own-price elasticity for the output sold by rm pairings, at least as long as the number of rms, N, is large. To summarise the love of variety model, we start with a Dixit-Stiglitz utility function for utility from consumption of the industry's good: Y=Ω N ∑ i=1 Y ε1 ε i!ε ε1 :(22) Yiis sales by rm pairing i.εis the elasticity of substitution in consumption and Ωis a scale parameter, which we can set at 1 without loss of generality, since utility is basically ordinal. Hence we derive Y= N ∑ i=1 Y ε1 ε i!ε ε1 :(23) The rst order condition for an optimum is ∂Y ∂Yi = N ∑ j=1 Y ε1 ε j!1 ε1 Y 1 ε i=Pi P;i2j;(24) 20The restriction ε>1 is associated with consumers' assumed `love of variety', and also helps ensure nite pricing by rms. www.economics-ejournal.org 33 conomics: The Open-Access, Open-Assessment E-Journal where Pis the aggregate CES price of utility. We can replace the term in brackets by rearranging (24), so that ∂Y ∂Yi =Y 1 εY 1 ε i=Pi P; (25) Or, by rearranging, Yi=Y(Pi P)ε:(equation 1) Dening A=Y, this is equation (1) in the main paper. When the number of rms, N, is large, then a change in Yiwill have negligible impact upon U, in which case ∂lnYi ∂lnPi =ε:(26) Applying the standard prot-maximising formula for a rm with constant demand elasticity and a constant marginal cost, Ci, rm pairing iwill charge a price of Pi=ε ε1Ci:(27) Substituting from (1) into (23) Y=YPε ∑ j P1ε j!ε ε1 ; P= N ∑ j=1 P1ε j!1 1ε :(28) When all rms are identical, Pj=P8j:Consequently, P=N1 1εP=N1 1εε ε1C;(29) which is decreasing with respect to Nfor ε>1;demonstrating the love of variety effect. www.economics-ejournal.org 34 conomics: The Open-Access, Open-Assessment E-Journal Firm Prots Taking (26), we note that prot of rm i, before taking account of xed cost, is πi= (PiCi)Yi=1 ε1CiYi=1 ε1CiY( ε ε1Ci P)ε; =1 ε1CiYPε(ε ε1Ci)ε=Y εPε(ε ε1)1εCi1ε;(equation 2) =kYPεCi1ε; where k=1 ε(ε ε1)1ε: We assume the rm's xed costs f c =Fµi;where F>1:(30) µiis a random match quality parameter, where 0 6µi61 .Hence, prot after xed cost Πi=kYPεCi1εF+µi:(equation 3) Where all rms have identical marginal costs Πi=kPεC1εF+µi; =kYN ε 1ε(ε ε1)εCF+µi; =Y ε1Nε 1εCF+µi:(32) www.economics-ejournal.org 35 conomics: The Open-Access, Open-Assessment E-Journal Monopolistic Competition with Free Entry and Exit and Search In the monopolistically competitive model, a rm pairing with the reservation match quality, µi=µR;will just break even after its xed costs. Hence, in an equilibrium where all rms have the reservation match quality, Y ε1Nε 1εCF+µR=0; N= ((ε1)(FµR) YC )1ε ε:(equation 8) Substituting into (29), we obtain P; P=N1 1εε ε1C;(equation 7) = ((ε1)(FµR) YC )1 εε ε1C; = ( Y (ε1)(FµR))1 εε ε1C ε1 ε:(33) Note that, in a model with constant and identical marginal cost, all rms will be of the same scale, so all will set prices and output at the level that a rm pairing with reservation match quality would set. Hence (7) and (8) describe the equilibrium with identical rms. Another way of writing (8) is to take πi=kYPεC1ε=FµR; P= ( FµR kYC1ε)1 ε:(equation 6) Higher-Level Demand Consumption of the industry good, at price P, leads to utility of Y(P). This is assumed to be isoelastic, so that Y=Y0Pυ;(34) www.economics-ejournal.org 36 conomics: The Open-Access, Open-Assessment E-Journal where υ>0:Hence, substituting into (33), P=Pυ ε(Y0 (ε1)(FµR))1 εε ε1C ε1 ε; Pευ=(ε1)(FµR) Y0 (ε ε1)εCε1; P= ((ε1)(FµR) Y0 )1 ευ(ε ε1)ε ευC ε1 ευ:(35) For utility to be decreasing with respect to C, we need the parameter restriction that ε>υ: Assuming a Cobb-Douglas higher-level nesting of the economy, then, as long as the industry is 'small' in proportion to the overall economy, we can take overall national income as given, and hence assume υ=1:Hence, (35) becomes P= ((ε1)(FµR) Y0 )1 ε1(ε ε1)ε ε1C:(36) Ranges of Firm Threshold Prices An existing, successfully-matched rm pairing will have a match quality µR< µi<1:The reservation market price for a rm with match quality µi;P0 i;is the value of Pat which a rm with match quality µiwill break even. From (3) this condition is kYPεCi1εF+µi=0; (37) P0= ( Fµi kYCi1ε)1 ε(38) When µi=µR;this is satised by Pas calculated in the previous section. By contrast, when µi=1;this corresponds to P0= ( F1 kYCi1ε)1 ε;(39) www.economics-ejournal.org 37 conomics: The Open-Access, Open-Assessment E-Journal which is lower than P, rstly because F1<FµR;and also because the term on the denominator, is an increasing function of Y;which should improve as P falls. The intuition is that the most efcient matched rm pairings will withdraw from the market at a lower price than the threshold for new rm entry, and this difference is greater the lower is µR, and hence the more heterogeneous are existing matched pairings. We really want to substitute for kin (39) as a function of P. Since k= 1 ε(ε ε1)1ε;assuming a top-level own price elasticity of unity for the aggregate industry produce, and substituting into (38), we can write P0 i= (Fµi kCi1ε)1 εY1 ε 0P01 ε; P0 i= (Fµi kCi1ε)1 ε1Y1 ε1 0= (Fµi kCi )1 ε1Y1 ε1 0Ci:(40) Hence, we have a situation where P0 iis proportional to Ci. Also note that the reservation prices for market withdrawal when µi=µRand µi=1;in the case where marginal cost, Ci=Care P= (FµR kCi )1 ε1Y1 ε1 0C; P0= (F1 kCi )1 ε1Y1 ε1 0C; P0 P= ( F1 FµR )1 ε1:(41) The Model with Alternative Supply Sources Phase 1 pre-globalisation: We start assuming the only pairings available are NN, who supply at a combined cost of C=1. Consequently, the entry price is given by substitution into equation (9): P 1= ((ε1)(FµR)) 1 ε1(ε ε1)ε ε1:(equation 9) www.economics-ejournal.org 38 conomics: The Open-Access, Open-Assessment E-Journal Phase 2 globalisation: SN pairings are now available, at a marginal supply cost of CS(<1). This means they will enter at any aggregate price greater than P 2, where P 2= ((ε1)(FµR)) 1 ε1(ε ε1)ε ε1CS=P 1CS:(equation 11) The price at which a given NN pairing of quality µi>µRwill withdraw from the market is given by P0 i1 P 1 = ( Fµi FµR )1 ε1;(equation 12) so that at price P 2, the critical match quality at which existing matched NN pairings which will withdraw is µi=F(P 2 P 1 )ε1(FµR)=(1Cε1 2)F+Cε1 SµR; µiµR= (1Cε1 S)(FµR): at which price the proportion of rms which will continue in the market is σN2=1µi 1µR =1µiµR 1µR ; =1(1Cε1 S)(FµR) 1µR :(z = equation (13)) Appendix 3: National Welfare Effects of a Tariff in the Presence of Search The economy is assumed to be in a steady-state growth equilibrium, with growth rate G, which can be varied between 2% and 9% per annum. Other key parameters are: www.economics-ejournal.org 39 conomics: The Open-Access, Open-Assessment E-Journal References Anderson, J. E., and E. van Wincoop (2004). 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