Globalisation as a 'Good Times' Phenomenon: A Search-Based Explanation

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. --

: 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.
Trade growth based upon the expansion of traditional trading networks.(e) 7.
Growth especially concentrated in areas of the South or former Communist bloc entering the outsourcing trade. 9.
Reduction in protectionist barriers.

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.
(i) Wacziarg and K.H.Welch (2008). Kraay (2002 and. 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.
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 Helpman (2002 and2005), 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.

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 theory 3 -i.e. supplementing the models of Krugman, 1979 andHelpman, 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, 4 distribution 5 and the observed volatility of trade. 6 By 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 3 To use Srinivasan and Archana's (2009) terminology. 4 Melitz, 2003. 5 Feenstra andHanson, 1999. 6 Ishii and Yi (1997).
www.economics-ejournal.org 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, Pakistan 7 ). 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. 8 Search 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, 9 but 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.
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 u sells 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, µ i . 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 µ i before 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 u and d within 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.
Firms employ labour in the form of xed and variable elements. The cost of the latter is normalised at C = C N for North-North pairings, and at C = C S (C S < C N ) 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 i will equal where P is the CES aggregate price index. Pro ts of the pairing, before subtracting xed costs, will equal The model is driven by an assumed coordination cost which is inversely linearly related to the quality of the match µ i between 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 µ i , so that pro ts after subtracting xed cost, Note I am also assuming equal Nash bargaining weights between the upstream and downstream rms.

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, µ i , 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 d. For simplicity, I normalise the discount rate in terms of the contract period, de ning the discount rate and depreciation rate per contract period, Note that the depreciation rate re ects the probability of either rm in a pairing dying during the contract period. At the end of each contract period, the rm may either stick with its existing partner (which it will do if match quality µ i exceeds a reservation match quality, µ R ), or else seek a new partner (which it will do if µ i < µ R ). Note that, as we have assumed a uniform, rectangular ex ante probability distribution of match quality, the probability that search will be renewed, after the initial match period will equal µ R : However, over time, the probability of not having found a successful match will decline geometrically. By noting that, when µ i = µ R , a pair of rms will be indifferent between renewing search or staying together, we can derive the condition for equating discounted present value of searching and not searching, and so nd a value for the reservation match quality. This can be shown to satisfy which is declining as ρ or D increases. From (5), we can conclude that, with zero discount rates and zero probability of rm death (r = d = ρ = D = 0), rms will be in nitely patient in their search, so that the long-run equilibrium is for all rms to be equally and successfully matched. By contrast (and more realistically), with positive time preference, the long-run equilibrium has a uniform distribution of surviving matches, of quality ranging from µ R to 1, with pro ts likewise varying. A consequence is that rm pairings are heterogeneous in the long-run, both in terms of pro ts and trade volumes, with heterogeneity increasing when long-run interest rates are higher or contract periods are longer.

The Role of Monopolistic Competition
I assume there is free entry and exit into the industry. Consequently, the number of rm pairings will vary, with competition forcing the industry aggregate price, P up or down so as to make the marginal rm indifferent as to whether to enter or exit.
I focus rst on an expanding industry. In this case, the marginal rm is a new, searching rm. The condition for determining the reservation match quality means that the expected present discounted pro t of entering and engaging in a new search will equal that of a rm in a stable match of quality µ R : where C m is the unit cost of the marginal pairing (so it will equal C N during the pre-globalisation phase 1, and C S during phase 2). In phase 1, all rms have the same unit cost C m , and if we also note that the CES aggregate price where N is the number of pairings in the industry, then the initial number of pairings 2 The Stages of Development of North-South Inter rm Trade I discuss the three phases of the stylised time-scheme in turn.

Phase 1: The Pre-Globalisation, Northern Economy
I start by concentrating on the initial phase 1 of our time-scheme, when trade costs are suf cient to ensure that there are no matches between Northern and Southern partners. I consider an equilibrium, where the industry in the North is initially static, with demand and prices constant.
I start by characterising rm pairs on this initial equilibrium growth path as established' or`matched', if they are already in a settled match (µ i > µ R ) at the start of a contract period-otherwise, we de ne them as`searching'.
The basic situation is shown in Figure 1. Since unit variable cost with Northern pairings is 1, rm pairs will supply at a price of Searching rms will only engage in search if the price is at least P 1 : free entry will keep the price to this level, as long as the industry is not shrinking. Matched rm pairings will also supply at this price, though most of these are intramarginal matches, which would continue to produce if the price were to fall (hence the upward-sloping supply curve for matched rms). The number of rms in the industry will satisfy (8), and also balance demand and supply at the price P 1 : I will denote this initial demand level for the industry's products as Y 1 .
If rms were in nitely-lived, the economy would tend towards a steady-state equilibrium where all rms were matched (µ i > µ R ). However, if proportion D of rm pairings suffer in a given contract period from one or both rms randomly expiring, then there will be some new rms entering and searching. In equilibrium, I denote the number of matched rms in period 1 as N m1 and the number of searching rms as N s1 . In the next contract period, proportion D of existing matched pairings will expire, while proportion (1 µ R ) of searching pairings will nd established partners. In a static equilibrium, where N m is constant over time, this implies If the number of rms in the industry were growing at rate G, this would become This situation is shown in Figure 1. The price in equilibrium, P 1 , is given by the entry price for new, searching pairings. However, there is a kink in the supply conomics: The Open-Access, Open-Assessment E-Journal Figure 1: Equilibrium in the pre-globalisation, Northern economy curve, since searching pairings will all enter or leave the market at P 1 = P 1 , while matched rms are heterogeneous in the price at which they would exit the market. The most ef cient rm pairing would potentially leave the market at P 1 = P 1 , as given in equation (9). The ratio of searching to matched rms in equilibrium is given by equation (10) or (10a).

Phase 2: The Globalising Economy
Now assume that trade costs fall, so that upstream production in the South becomes more competitive. In particular, assume that unit variable costs, including trade costs, for a North-South pairing are C S , as opposed to 1 for a North-North pairing (C S < 1). However to enter the market, foreign rms of type u have to engage in a costly search process, and so will only do so at a World reference price of www.economics-ejournal.org at which a rm in a reservation-quality pairing breaks even. The effect on existing North-North pairings is variable. The N S1 searching Northern pairings would not expect to break even at the new, lower price, and consequently will exit the market, except for a fraction who nd their existing partners pro table and become matched.
The N m1 existing matched North-North pairings are heterogeneous, since they vary in match quality between µ R and 1. The price at which a matched pairing of quality µ i will exit the market is given by The last rm will exit when (See Figure 1). I assume North-South pairings are not suf ciently low-cost to drive the price down to this level. At price P 2 ; the proportion of rms in existing North-North pairings which will continue in the market is which is declining as C S falls. Output of these pairings will also be lower than before the start of globalisation by proportion ( P 2 P 1 ) ε , since the industry aggregate price has fallen. However, total industry output will be higher, due to the fall in prices: I denote the own-price demand elasticity for the industry's output as η; so that The residual will be made up by new, North-South pairings. Initially, these will be searching, but over time, in a model with static overall demand, the proportion of conomics: The Open-Access, Open-Assessment E-Journal Figure 2: Demand and supply in the globalising economy these still searching will decline, as some gain matches, until eventually the ratio of searching to matched pairs among the North-South pairings will equal that in equation (10). Figure 2 shows the situation in an economy during the globalisation phase. Searching North-South (foreign) pairings are prepared to enter the market at price P 2 , which is lower than P 1 ; but assumed to be above P 0 1 . Consequently, all North-North (domestic) searching pairings exit the market, as do some matched North-North pairings. Once some North-South pairings nd successful matches, the result is a supply curve with three segments (i.e. two kinks). First, between P 0 2 and P 0 1 (the left segment), only the most successful North-South pairings will be prepared to supply. Between P 0 1 and P 2 we are summing horizontally the supply curves of North-North and North-South matched pairings, so the gradient is somewhat less steep. Finally, when the industry aggregate price, P = P 2 , there is a horizontal segment made up of searching North-South pairings. 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. 3 The Impact of a Negative Economic Shock

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 µ R ; 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. 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

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 ρ 0 > ρ: www.economics-ejournal.org 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 However, since the reservation price which overseas rms type u will demand in order to enter into search is 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.
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.
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.

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).
conomics: The Open-Access, Open-Assessment E-Journal Figure 7: Effect of a low tariff, τ 1 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 conomics: The Open-Access, Open-Assessment E-Journal Figure 8: Effect of a higher tariff, τ 2 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 Total expenditure on the product M 1000: 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.

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: 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 insufcient 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. For growth rates below about 5% per annum, countries will choose noncooperative tariffs of around 4% on trade. By contrast, above this threshold growth rate, there is a sudden, nonlinear shift to a zero noncooperative tariff, as countries prefer free trade, in order to attract the more footloose, searching rms.
Again, this result is dependent upon the substitution elasticity assumed, and upon the initial import share (a lower substitution elasticity and/or lower import share would raise the growth threshold needed to make tariffs unattractive, while a higher substitution elasticity or higher import share would do the reverse). 14 The evidence that there is a threshold growth rate required to induce countries to maintain open markets is signi cant. As long as G + D > 0, new rm entry into trade will eventually resume following a crisis. However, many economic shocks-such as Latin America in the early 1980s, Japan in the early 1990s and the Asian Tigers in 1997-tend to be followed by either stagnation (a`lost dec-ade') or at least reduced growth for a prolonged period. If growth falls below a critical trigger, the analysis of this section suggests that open trade policies may be harder to sustain.

Is Search Suf cient to Trigger a Policy Switch?
While the model in the preceding section is somewhat sensitive to parameter choices, it does indicate certain important properties: in particular, a prolonged period of high global trade growth will favour little or no protectionism, but only if the growth rate exceeds a critical threshold (maybe around 5% per annum). Linked to this is the question of how much trade, in practice, can be considered to be searching. Evidence on this is somewhat hard to come by, partly because most rm-level trade databases have until recently covered timespans too short to assess long-run industry dynamics thoroughly. Nevertheless, Besedes and Prusa's (2006) study of US imports suggests a 1 year average turnover for new products entering the market. In a model of industry dynamics, these would then be replaced by other new entrants in a repeating cycle. Eaton et al.'s (2007) study of Colombian exporters shows even faster exit rates (83% of entrants in 1997 left after a year), but continuing high exit rates in the second year (38%) and third year (10%) after entry. The number of rms entering in any one year is very large compared to the overall number of rms in the market (for example, in 2005, there were 5060 rms which had been exporting for less than a year, out of 11; 720 exporters): however, rms exporting in the rst year tend to export very small amounts. The scale of survivors each year then increases steadily over at least a decade, as they expand their networks of customers. The share of total sales by rms of different age vintages is shown in Figure 10-given the high exit rates for the rst 3 4 years we can certainly argue that at least 5 10% of sales should be considered searching exports, but given the continuing build-up of customers per rm over 10 years, we could also view all rms with less than ten years in the market as being searchers (which would imply nearly 25% of total sales). A slight caution here: Colombian exports tend to be dominated by small ower-growers, who can enter foreign markets easily and are less tied to a single customer (e.g. by blueprints) than exporters from other countries in other industries might be.  Eaton et al., 2007) An alternative argument that search is quantitatively signi cant is given in Edwards and Ferrett (2009), based upon the idea that merger with a downstream supplier usually gives better coordination and security, whereas inter-rm trade bene ts from exibility, and so is associated with search or experimentation. This is supported by evidence from Spencer (2005), showing that outsourcing in China preceded the growth of FDI, but that perhaps 20% of rm-level trade is still accounted for by outsourcing rather than FDI.
Both the Eaton et al. (2007) and Edwards and Ferrett (2009) estimates of search would suggest values (during the growth cycle) quite close to that required on our parameter assumptions to trigger a switch to zero protectionism. This may indicate that countries would be likely to favour free trade in faster-growing industries, while maybe not in others. Following the crisis of 2008-2009, it is likely that few industries would still have enough search to make unilateral free trade attractive.
It is worth bearing in mind that, in a CES demand formulation, the pro tshifting effect (which makes tariffs more attractive) is higher in industries with a lower import share.

Implications: Return of the Prisoner's Dilemma in Trade Liberalisation?
Trade liberalisation is often portrayed as a prisoner's dilemma situation: liberalisation bene ts countries collectively, but large countries, individually, have an incentive to cheat and impose optimal (terms-of-trade-improving) tariffs. The argument of this paper is that, in a rapidly changing, globalising world, the incentives to impose protection in this way would be greatly reduced by the presence of a relatively large share of footloose trade, associated with searching rms. In such circumstances, the incentives of individual countries are not far out of line from those of the global economy, which bene ts from free trade.
This conclusion might raise some eyebrows: few involved in trade negotiations over recent decades would argue that they were pushing on an open door (as the failure of the Doha Round talks indicates). Nevertheless, trade liberalisation has undoubtedly made substantial strides-particularly with respect to developing countries abandoning previous autarkic developmental strategies, but also in terms of successive rounds of tariff reduction by the advanced countries. Perhaps most signi cantly, where protection has been maintained, or liberalisation has been resisted, the reasons have tended to be argued in terms of distributional impact, or in terms of damage to countries within trade blocs which were dependent on trade diverted from poorer countries outside the bloc (for example, Portugal or Italy resisting EU liberalisation of textiles and footwear industries). In general, the argument that high tariffs bene t national income-at least, when based upon terms of trade arguments-has rarely been used. An exception may be in agricultural commodities.
Part of the reason may be a trend towards accepting that the price elasticity of demand for traded commodities is perhaps higher than we used to think-for example, Anderson and van Wincoop's (2004) survey cites elasticities of between 5 and 10 for many commodities: a far higher number than traditionally used in Armington CGE models of the 1980s and 1990s. 15 These higher trade elasticities are seen as tting the data because of Ricardian, xed-factor elements in trade, 16 including rm heterogeneity, which mean that supply elasticities are reduced. However, a search-based interpretation would say that supply elasticities differ considerably ex ante and ex post, and that expanding supply may be more elastic than contracting supply.
In addition, the recent wave of globalisation has essentially involved connecting a large workforce in China, India, Asia and Eastern Europe to global markets from which they were previously isolated by autarkic policies and/or by their location in pre-industrial societies. The supply of labour to the globalising cities of Asia has been elastic at a low wage, so ensuring that, once search and other capital costs are met, there is an elastic supply of unskilled labour-intensive goods, meaning that optimal tariffs for large, advanced countries are likely to be much less than at some other stages of global development. 17 A prolonged global recession-perhaps especially one where credit is shortis likely to change this situation for the worse (as memories of the 1930s indicate). 18 In terms of the very schematic analysis of this paper, we are moving from the situation in Figure 6, where there is a substantial volume of footloose trade, to that in Figure 8, where the supply of price-elastic, searching trade is insuf cient to maintain the incentive to keep tariffs low. In such a situation, the interests of individual countries (which may wish to try to manipulate their terms of trade by protection) and those of the global economy are no longer aligned, hence raising the risks of triggering a round of beggar-thy-neighbour policies. Given the recent advances in understanding the interaction between trade integration and growth, 19 there must be a danger that protection could trigger a self-perpetuating circle, whereby trade growth is reduced, increasing incentives to protect.
A secondary element, which must be of particular concern when countries are credit constrained, is the potential effect on the stability of existing agreements, where these are sustained by the threat of retaliation in a trigger strategy. Such a strategy depends upon people weighing the loss of future welfare, from the collapse of trade agreements, more highly than the short-term gain from imposing a terms-of-trade-improving tariff. Again, if credit constraints shorten national timehorizons, the prisoner's dilemma will be restored.
In sum: the recent wave of globalisation has been sustained and strengthened by the coming-together of national and global interests, when trade is relatively footloose and credit is available. The removal of those conditions, once a shock drives out the more price-elastic elements of trade, creates a totally new set of incentives, where national interests are to protect, yet the global interest still requires a liberal trade regime. If cooperation is allowed to fall, it may be very dif cult to restore global trade to its recent Golden Age. 19 Not just the standard comparative advantage effects, but the pro-competitive, choice-widening and scale-exploiting effects identi ed by the New Trade Theory (Krugman, 1979), as well as the rm selection effects of the New New Trade Theory (Melitz, 2003). The starting premises of this paper-that search costs, even in phase 2 of our time-schema, maintain trade at below the level which would be favoured in the presence of full information, rather emphasise that trade-impeding policies will push the World further from optimality.

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, µ i ; is measured by the circumference distance between the two rms. Firms only have a single partner at any time. 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, µ R : The decision process of the rm is shown in Figure  A2.
Any match with a circumference length greater than µ R will yield a pro t great enough for the rms to choose to continue. This gives a probability of acceptance of 1 µ R . However, of these pairings, proportion D will naturally expire anyway during the rst contract period, so any surviving rm will have to renew search. By contrast, proportion µ R of initial pairings will be unsatisfactory, and be dropped after one contract period. We note that the pro t of a reservation quality match (µ i = µ R ) is zero. Pro t increases linearly with respect to match quality, so that the expected pro t of a successful match (where µ R < µ i < 1) is 1+µ R 2 minus the pro t of a reservation quality match. This yields an expected pro t of 1 µ R 2 : Likewise, an unsatisfactory match qill have an expected pro t of µ R 2 : Finally note that a renewed search will yield a present discounted value of zero.
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 since only the negative root lies between zero and unity.
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 i is sales by rm pairing i. ε is the elasticity of substitution in consumption and Ω is a scale parameter, which we can set at 1 without loss of generality, since utility is basically ordinal. Hence we derive The rst order condition for an optimum is where P is the aggregate CES price of utility. We can replace the term in brackets by rearranging (24), so that Or, by rearranging, De ning A = Y , this is equation (1) in the main paper. When the number of rms, N, is large, then a change in Y i will have negligible impact upon U, in which case Applying the standard pro t-maximising formula for a rm with constant demand elasticity and a constant marginal cost, C i , rm pairing i will charge a price of Substituting from (1) into (23) When all rms are identical, P j = P 8 j: Consequently, which is decreasing with respect to N for ε > 1; demonstrating the love of variety effect.

Firm Pro ts
Taking (26), we note that pro t of rm i, before taking account of xed cost, is We assume the rm's xed costs µ i is a random match quality parameter, where 0 6 µ i 6 1 .Hence, pro t after xed cost Where all rms have identical marginal costs

Monopolistic Competition with Free Entry and Exit and Search
In the monopolistically competitive model, a rm pairing with the reservation match quality, µ i = µ R ; will just break even after its xed costs. Hence, in an equilibrium where all rms have the reservation match quality, Substituting into (29), we obtain P ; 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

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 where υ > 0: Hence, substituting into (33), 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

Ranges of Firm Threshold Prices
An existing, successfully-matched rm pairing will have a match quality µ R < µ i < 1: The reservation market price for a rm with match quality µ i ; P 0 i ; is the value of P at which a rm with match quality µ i will break even. From (3) this condition is When µ i = µ R ; this is satis ed by P as calculated in the previous section. By contrast, when µ i = 1; this corresponds to which is lower than P , rstly because F 1 < F µ R ; 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 µ R , and hence the more heterogeneous are existing matched pairings. We really want to substitute for k in (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 Hence, we have a situation where P 0 i is proportional to C i . Also note that the reservation prices for market withdrawal when µ i = µ R and µ i = 1; in the case where marginal cost, C i = C are 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): Phase 2 globalisation: SN pairings are now available, at a marginal supply cost of C S (< 1). This means they will enter at any aggregate price greater than P 2 , where The price at which a given NN pairing of quality µ i > µ R will withdraw from the market is given by so that at price P 2 , the critical match quality at which existing matched NN pairings which will withdraw is at which price the proportion of rms which will continue in the market is (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: Discount per contract period ρ 0:08 Fixed cost  The rst scenario is that a tariff is applied suf cient to remove all searching SN pairings (but no other ones). The tariff required to do this is derived by numerically solving two simultaneous equations: M = P N N D P X P S ε + (P S + τ)N SN S S1 ; M P X = Ψ N D S η N1 P X P S εη + N SN S η S1 1 η

:
The rst equation derives from the assumption of unit elastic demand for the product as a whole (so expenditure, M, is constant, while the CES aggregate price, price P X changes. P X will equal average cost of domestic and imported goods.). The second equation derives real-terms CES aggregate consumption. The assumption of both equation is that the tariff is applied to SN pairings only, and drives out the searching (but not the non-searching) pairings. The industry aggregate price facing domestic producers, P X , is raised, but that facing SN pairings is unchanged. Welfare calculations are as follows:

Consumer surplus loss
Tariff revenue gain T = τN SN S S1 Domestic pro t gain (pro t shift) 21 Π = (P N C N ) N D S N1 ( P X P S ε 1): Domestic welfare loss W = V T Π: Table A2 shows the key results of the numerical simulation of this scenario. 21 Although the bargaining process between the rms in SN pairings has not been modelled in depth, it is expected that an unanticipated tariff on imports would be borne primarily by the foreign rm in the pairing (by shifting the threat point). The faster the economy is growing in steady-state, the higher the equilibrium share of searching rms, the larger the tariff needed to eliminate them, and the greater the net loss of welfare from doing so.
Second scenario: a tariff to maximise welfare in steady-state growth The model in this case is somewhat more complicated (as Figure 7 in the paper would indicate). We estimate the following equations simultaneously: 120mmYY Price recieved by SN pairings, P 2 P 2 = P T τ: Total expenditure M relating to CES aggregate price level P D M = P N N D S S1 PD PS ε + P T N 0 S S S1 Tariff revenue gain T = τN 0 S S S1 P 2 PS ε : Domestic pro t gain (pro t shift) Π = (P N C N ) N D S N1 ( P D P S ε 1): Domestic welfare loss W = V T Π:

Results:
Figures A3 A5 plot national welfare change against the tariff level. Note that simulations have been carried out for a series of tariffs, starting from the tariff level needed to exclude searching rms (so the starting tariff for the simulations varies according to the growth rate). Critically, once the growth rate rises above 5% per annum, the curve never crosses zero, so there is no longer any optimal tariff rate which is preferable to a zero tariff.
It is worth noting that in all cases the national welfare curve peaks at a tariff rate of about 4%. However, when growth is faster, the curve is shifted downwards (because there is a larger initial loss from applying a tariff to the searching rms). Beyond a point (approximately 5% annual trade growth), no positive tariff will yield a higher national welfare than free trade. The results of these simulations are summarised in Figure 9, in the main text. Figure A3: Welfare gain plotted against tariff with a growth rate of -2%, plotted for tariff rates over and above that required to exclude searching rms Figure A4: Welfare gain plotted against tariff with a growth rate of +2%, plotted for rates over and above that required to exclude searching rms www.economics-ejournal.org Figure A5: Welfare gain plotted against tariff with a growth rate of +5%, plotted for rates over and above that required to exclude searching rms Third scenario: initial searching rms are wiped out This scenario is analytically equivalent to our scenario where G = 2%, since in that case G + D = 0 and hence there are no initial searching rms. Consequently, in our numerical example, a tariff of around 4% would maximise national welfare.