Proof. Lemma 7.
The problem of the producer is
maxx(ω)βJ(ω)−a(ω) ˜τ(ω)x
pG(ω)
(7.20) subject tox(ω) =Hζ(ω)p(ω)σ−1σ ,whereJ(ω) =pG(ω)x
pG(ω)
−fM.The first order condition σ−1
σ βH1σζ(ω)σ−1σ x(ω)−1σ =a(ω) ˜τ(ω) (7.21) implies pG(ω) =a(ω) ˜τ(ω)/(ρβ)..
Proof. Lemma 8.
We need to establish the parameter restriction that ensures that for givenθensures a interior solution to the equilibrium sorting problem. We can write the flow profits associated to each mode of operation,mode∈ {D, SP, F} as the following set of equations:
δPVSP (A) = s(θ)βσB(¯τ A)1−σ−
s(θ)βfM + [1−s(θ)]cP (7.22)
πF(A) = B(¯τ A)1−σ−fF (7.23)
πD(A) = BA1−σ−fD, (7.24)
We establish a lower and an upper bound,f and ¯f ,respectively, to the expected fixed costs of the search modeSP.First, to pin downf, we search for the intercept ofδPVSP (A) that solves δPVSP(AD) = 0. That condition yields s(θ)βσB(¯τ A)1−σ−f= B AD1−σ
−fD. Recognizing from (7.9) that AD1−σ =fD/Bi,we find the lower bound
f =s(θ)βστ¯1−σfD.
The upper bound is found by finding the intercept ¯f for which δPVSP A˜
= 0 with ˜A determined by the conditionπF
A˜ one that appears in Lemma 8.
Proof. Corollary 8.
Consider how an increase inθ affects the δPVSP(A) locus (7.22): first, the locus becomes
steeper since s0(θ) >0; second, the locus shifts up (down) if βfM <(>)cP. Focusing on the case wherefM = 0,the locus always shifts up.
Using ‘hats’ to denote proportional changes, the cutoff levelsASPij andAFij change as follows:
AˆSPij = γ
σ−1ˆθij, (7.26)
where γ is the elasticity of the matching function with respect to the number of searching GIs. Similarly, we have
AˆFij =− γ σ−1
δ
δ+η(θ)βσˆθij <−AˆSPij , (7.27) where the inequality follows from the fact that bothδ/[δ+η(θ)] andβσ are strictly smaller than unity.
Proof. Lemma 10.
Consider again the GI’s share of the expected surplus. Using (7.7) and the Pareto assump-tion, we find an expression for the expected surplus
E[J(A)] = kσB τ β¯ −11−σ
k−(σ−1)
ASPk−(σ−1)
− AFk−(σ−1)
(ASP)k−(AF)k . (7.28) The independence of expected surplus of the demand level B and the homogeneous part of the trade costs ¯τ directly follows from inserting the cutoff profit conditions (7.9), (7.13), and (7.14) into (7.28). The in dependence of θ of B and ¯τ immediately follows from the free entry condition (7.17).
Chapter 8
On the Importance of Adjustment Dynamics For Bilateral Trade
Flows 1
8.1 Introduction
In the last fivty years, politicians have undertaken a huge effort to liberalize trade. For assessing the outcome of trade reforms it is important to know how quickly bilateral trade flows adjust. If adjustment is fast, potential gains from trade reforms are achieved quickly.
In the opposite case, however, it takes a long time to see the full beneficial impact.
Static gravity models implicitly assume trade volumes to be at their steady-state levels.
There is empirical evidence, however, for a dynamic relationship. Eichengreen and Irwin (1998) find cross-sectional evidence. De Grauwe and Skudelny (2000) and Egger (2001a) present first dynamic panel data evidence.
Recent years have witnessed an increasing number of dynamic gravity applications, e.g., Micco et al. (2003) and De Nardis et al. (2008) on the dynamic effect of the Euro on bilateral trade, or Moser et al. (2008) and Martinez-Zarzoso et al. (2009) on the effect of German export promotion. These studies, however, do not explicitly consider the speed of adjustment.2 Moreover, test statistics reveal misspecification problems, e.g. a significant Hansen test in De Nardis et al. (2008) signals invalidity of the instruments; see Roodman (2009).
Various theoretical explanations have been put forward for a dynamic trade relationship.
1This Chapter is based on a working paper, see Jung (2009).
2An important exception is Egger (2001b).
Baldwin (1988) and Dixit (1989) argue that sunk costs of market entry and exit lead to hysteresis in trade. Moreover, consumers and final good producers tend to prefer products and inputs they are already familiar with. Persistence in habits also result in highly path-dependent trade relationships.
Recent empirical work emphasizes the role of trust for economic activity. Using survey data on bilateral trust between European countries, Guiso et al. (2009) find that a one standard deviation increase in importer’s trust toward the exporter boosts exports by 10%.
The idea goes back to Arrow (1972), who argues that trust has first order economic effects.
More generally, De Benedictis and Vicarelli (2005) point out that “trade relationships be-tween countries are affected [...] by the accumulation of invisible assets such as political, cultural and geographical factors” (p. 9). The ‘invisible asset’, however, is not exogenously given, but created by repeated interactions between trading partners.3
In this paper, we offer the following contributions. First, drawing on the neoclassical growth model, we incorporate the endogenous accumulation of an ‘invisible asset’ into a standard Anderson and van Wincoop (2003) model of international trade. We do this to motivate a dynamic specification of the gravity equation. The notion of ‘invisible asset’
accommodates various interpretations. It can betrust that is created on the basis of what trading partners know about each other. Similarly, relational capital is nurtured by good trade relationships, and enhances future trade. One can also think of knowledge about the foreign market, which becomes, at least partly, known to all other firms. In either case, there arises a pure externality which positively affects trade through lower trade costs.
Second, we apply a dynamicgravity approach which differs from previous studies along the following lines. We account fortime-varying multilateral resistance terms by including country-and-time effects into our regressions.4 Moreover, as common in the growth litera-ture, we take data for every five years for the period 1980-2000 in order to tackle business cycle fluctuations. Our sample comprises information on potentially 96×95 country pairs rather than OECD countries only.
The estimated coefficient of the lagged endogenous variable lies in the expected range;
3The Economist concludes that “reciprocal ties become strongest between people who meet and trade frequently”. (October 18th-24th 2008, p. 84).
4See Anderson and van Wincoop (2003) for the theoretical explanation.