Outsourcing and Optimal Trade Policy

Outsourcing and Optimal Trade Policy Emanuel Ornelas∗ London School of Economics

John L. Turner† University of Georgia

May 5, 2008

Abstract Outsourcing under incomplete contracts tends to generate too little investment that is specific to the bilateral relationship. In a model where there are otherwise no social motives for protection, we show that protection is helpful when the buyer trades customized inputs with a specialized domestic supplier while also buying standardized inputs from the world market. In that case, a tariff worsens the outside option of the buyer, thereby increasing the seller’s incentives to invest. The optimal tariff never "solves" the hold-up problem, however, as positive tariffs create costs as well as benefits. In contrast, protection is not helpful when the specialized supplier is abroad, as tariffs have no effect on investment in that case. This provides a ‘wedge’ to domestic suppliers over foreign ones: even if there are no transportation costs and the foreign supplier has a better technology, domestic outsourcing can still be socially optimal, given the appropriate tariff. As transportation costs fall or contracts become more enforceable, however, the advantage of domestic outsourcing (and protection) over offshoring (and free trade) diminishes. Once a critical level is reached, optimal trade policy “jumps” to free trade.

VERY PRELIMINARY AND INCOMPLETE COMMENTS AND SUGGESTIONS VERY WELCOME

Keywords: International trade, trade policy, hold-up problem, outsourcing, offshoring JEL codes: F13, L23, D23

1

Introduction

International trade in intermediate goods has become increasingly important worldwide, accounting for about a third of the increase in global trade flows in recent years (Hummels, Ishii and Yi 2001). Trade in intermediate goods is not just important quantitatively; it is ∗

Managerial Economics and Strategy Group, London School of Economics, Houghton Street, London WC2A 2AE. E-mail: [email protected]. † Department of Economics, University of Georgia, Brooks Hall 5th Floor, Athens, GA 30602-6254. E-mail: [email protected].

1

also qualitatively different from trade in final goods, in that it often involves tailor-made components that have a lower value for parties not involved in the transaction. This implies that, in an environment with incomplete contracts, relationship-specific investments will tend to be inefficiently low–i.e. the hold-up problem of underinvestment arises. We study how a government can use trade policy to alleviate this inefficiency, and the impact of optimal trade policy on outsourcing location–domestic or offshore. We consider an economic environment in which none of the standard reasons for active trade policy exist, yet we show that protection can sometimes be welfare improving by mitigating hold-up problems. This will be the case when the two parties in the relationship are domestic but the downstream firm can substitute generic imported inputs for the specialized domestic ones, after adapting the generic inputs to its needs. In contrast, when the specialized supplier is foreign, trade policy is incapable of affecting investment. As a result, under optimal trade policy a foreign specialized supplier is chosen only if she has, for given levels of investment, a cost advantage over the domestic specialized supplier, net of trade costs, that is large enough to outweigh her lower incentives to carry out relationship-specific investments. We establish these and other results in a very simple and standard setting.1 There is a buyer who chooses a specialized supplier to customize a certain input. The buyer is located in a small country (Home); the chosen supplier could be either in Home or abroad. The buyer can purchase inputs from the chosen specialized producer and from the world market, where generic (but customizable) inputs are available. The specialized supplier can make a relationship-specific investment to reduce her production cost. However, due to opportunism in the bilateral relationship with the buyer, she does not appropriate the full gains from her investment. Under free trade, then, she underinvests. If the chosen supplier is a domestic producer, the government can use trade policy to induce more investment. Essentially, a tariff worsens the outside option of the buyer, thus tilting the outcome of the negotiation between the buyer and the domestic specialized supplier toward the latter. This enhances the seller’s marginal incentives to invest, weakening the hold-up problem. Yet the tariff also creates an inefficiency, as it induces the replacement of cheaper imports with domestic production. Thus, a tariff in this case alleviates the problem of underinvestment while creating a problem of overproduction. The optimal tariff balances these two effects. Since at free trade there is underinvestment but no sourcing inefficiency, the optimal tariff is strictly positive except for extreme levels of seller bargaining power. And because the marginal benefit of just achieving the first-best level of investment is vanishingly low, while the marginal cost is strictly positive, the optimal tariff yields a level of investment strictly below the first-best, thus not “solving” the hold-up problem. 1

The economic environment of this paper is a variation of the setting employed in Ornelas and Turner (2008). There, however, our focus is entirely different; rather than studying optimal trade policy, in Ornelas and Turner (2008) we just analyze the impact of falling (exogenous) tariffs on international trade flows through changes in investment and organizational decisions.

2

Now, if the selected specialized supplier is instead located abroad, active trade policy is always ineffective at promoting investment. The reason is simple: a tariff in that case worsens both the buyer’s gain from trade within the relationship and his outside option. As a result, a tariff has no effect on the surplus from the negotiation between the buyer and the foreign specialized supplier, and hence no effect on the latter’s incentive to invest. This asymmetry in the effectiveness of trade policy gives a wedge to domestic outsourcing, vis-à-vis offshoring. Clearly, if for given levels of investment and tariff, the production cost of the foreign supplier, inclusive of trade costs, is at least as large as the production cost of the domestic supplier, it will be optimal to form a relationship with the latter. The government will then set the tariff to balance greater incentives to invest against greater sourcing distortions. As trade costs fall, however, it could eventually become profitable to form a relationship instead with the foreign supplier, provided that she has a sufficiently large cost advantage in the production of specialized inputs. Notice, however, that the cost advantage has to be large enough to compensate for the ineffectiveness of trade policy to mitigate the hold-up problem when the specialized supplier is abroad. In that case, we should then observe a strictly positive tariff and domestic outsourcing if trade costs are relatively high. As trade costs fall, the tariff decreases continuously while it remains efficient to carry out the relationship with the domestic supplier. If trade costs fall below a threshold, the tariff then drops to zero and the supplier starts to outsource offshore. When we allow for (imperfect) contract enforcement, we find that the optimal trade policy under offshoring (free trade) is unaltered, but the optimal tariff under domestic outsourcing is affected by the level of contract enforcement in the country: when some contracts are enforceable, the optimal tariff is unambiguously lower than when all contracts are unenforceable. Furthermore, as the level of contract enforcement increases, the wedge of domestic outsourcing over offshoring decreases, since the role of active trade policy under the former is weakened and the underinvestment under the latter becomes less acute. There is a burgeoning literature that studies optimal sourcing decisions and organizational structure in an international, incomplete contracts, context.2 That literature has, however, largely ignored the role of trade policies in alleviating the problem of underinvestment. Of course, the international trade literature yields numerous rationales for active trade policy3 : terms of trade manipulations by large countries; short-term liquidity constraints and other market imperfections that justify "infant-industry" protection; "strategic" motivations to shift profits from foreign to domestic firms in oligopolistic markets; as well as political/redistributive goals that can make protection privately optimal to a government even when free trade is socially optimal. None of those forces arise in our setting. The model is static, so there are no infant-industry considerations. The home country is "small," 2

See for example McLaren (2000), Antràs and Helpman (2004), Grossman and Helpman (2005), Schwartz and Ari Van Assche (2007), Grossman and Rossi-Hansberg (2008), Conconi, Legros and Newman (2008). Helpman (2006) surveys that literature. 3 See the excellent survey in Chapter 7 of Feenstra (2003).

3

so there are no terms-of-trade effects. We also shut down all strategic or political economy reasons for positive tariffs. Hence, our rationale for active trade policy is entirely novel in the literature. The exception is the recent independent work of Antràs and Staiger (2007). Building on the modeling framework developed by Antràs and Helpman (2004), Antràs and Staiger provide a rich, insightful study of trade policy in the context of international outsourcing. As we find in this paper, they also identify a role for active trade policy in correcting holdup problems. Both their main goal and modeling strategy are different from ours, however. While our focus is on understanding the choice between domestic and offshore outsourcing in the presence of hold-up problems and active trade policy, Antràs and Staiger are interested primarily in the role of international trade agreements in correcting inefficiencies generated by the hold-up problem and by unilateral trade policies. In that sense, the two papers can be viewed as complementary to each other. Antràs and Staiger (2007) and this paper differ also in terms of their modeling strategies. First, in the setting of Antràs and Staiger governments can use trade policy to shift surplus across countries (through taxes/subsidies on trade of intermediate as well as final goods), and this sets up the environment for the study of international trade agreements. In contrast, to focus on the effectiveness of trade policy in affecting hold-up problems, we develop our framework as to shut down all other motivations for active trade policy, including surplus shifting. But while we restrict our model in that sense, we also expand it in dimensions not explored by Antràs and Staiger. In particular, we permit the final good producer to establish a relationship with a specialized supplier that can be either domestic or foreign, while Antràs and Staiger consider only foreign outsourcing. Moreover, in our setting the buyer can also purchase generic inputs in the world market, which defines the buyer’s outside option.4 The two papers differ also in that we follow the tradition in the property rights literature (e.g. Grossman and Hart 1986) in distinguishing investment from production decisions. In this context, while the Coase theorem implies that ex post production decisions will always be efficient from the perspective of the negotiating parties, given the level of the ex ante (sunk) investment, the optimal tariff never eliminates the hold-up problem entirely, because doing so would generate excessively high domestic production. This trade-off does not arise in the setting of Antràs and Staiger, where there is a one-to-one correspondence between investment and production. As a result, (internationally) efficient trade taxes fully solve the hold-up problem in their setting. Our work relates also to the industrial organization/law and economics literature on hold-up problems. The primary focus of that literature has been on situations where either complete contracts cannot be written or investment specifications are not verifiable. Authors have identified several theoretical situations where efficiency can be achieved with simple contracts, but they usually require either a commitment to not renegotiate contracts or the 4

In the model of Antràs and Staiger, outside options are given by the outcome of a secondary market for customized inputs, where their value is a fraction of their value within the relationship.

4

ability of courts to punish contract breach.5 But if renegotiation cannot be prevented and courts cannot always enforce contracts, as we consider to be the case, then the standard underinvestment problem remains. The timing of the game we analyze is as follows: Period 1. The government sets a tariff on intermediate goods. Period 2. A final goods producer–the buyer–chooses a domestic or a foreign specialized supplier, specializes toward the chosen supplier, and requests a transfer from her. Period 3. The specialized supplier makes a relationship-specific investment. Period 4. The buyer and the specialized supplier bargain over price and quantity of customized inputs. Period 5. The buyer trades customized inputs with and pays the specialized supplier, while also buying generic inputs in the world market. We first consider the case where the buyer is specialized towards a domestic supplier (section 2). In section 3 we consider the case where the buyer is specialized toward a foreign supplier. In section 4 we then study the buyer’s choice between specializing toward either a domestic or a foreign supplier, which allows us to characterize the wedge that optimal trade policy provides to the former over the latter. In section 5 we allow for imperfect but possible enforcement of contracts. In section 6 we discuss the robustness of our results to modifications in our economic environment. We conclude in section 7.

2 2.1

Domestic Sourcing Basic Structure

A risk-neutral firm (B) located in the Home country needs to buy inputs. The inputs provide a gain of V (Q) to B, where Q is the quantity of inputs purchased, V  > 0, and V  < 0. Firm B has two sourcing options. It can purchase standardized inputs in the world market at price (including transportation and adaptation costs) pw . In that case, it also has to incur in a (specific) tariff t, so the cost of each imported unit of the input is pw + t. Alternatively, B can purchase specialized inputs from a risk-neutral manufacturer (S). In this section we assume the supplier is also located in Home; in section 3 we study the case where the supplier is in a foreign country. The cost of production of firm S’s specialized inputs is represented by the function C(q, i), where q denotes the quantity produced and i represents a cost-reducing investment. Firm 5 For example, Rogerson (1992) shows that the hold-up problem may be solved with properly specified initial contracts as long as it is possible to prohibit renegotiation, whereas Spier and Whinston (1995) and Edlin and Reichelstein (1996) show that well-tuned fixed-price contracts may solve the investment problem depending on the breach remedy enforced by courts.

5

S can also produce and sell standardized inputs in the world market, but under a different technology, affected neither by the relationship-specific investment i nor by the production of specialized inputs q. If S cannot affect the world price of the standardized input, as we consider to be the case, then S’s outside option is unaffected by its decisions regarding i and q. We normalize the value of that outside option for S to zero. Using subscripts to denote partial derivatives, we assume that Cq > 0, Ci < 0, and Cqi < 0 for any level of i and q. Furthermore, Cq (0, 0) < pw and Cqq > 0, so firm S has a cost advantage relative to the world market at low levels of q, but its specialized inputs technology displays increasing marginal costs. For now we take i as given; we return to the choice of i in the next subsection. We study first an environment where the parties are unable to use contracts to ensure efficient decisions (in section 5 we consider the case where contract enforcement is imperfect, but possible). Thus, as is standard in the theory of the firm literature, we consider that investment is observed by both B and S, but is not verifiable by an outside observer such as a court; hence, it is non-contractible. Furthermore, B and S cannot use contracts to affect their trade decision. This would be the case, for example, if S could produce either high quality or low quality specialized inputs, with low-quality inputs entailing a negligible production cost for the seller but being useless to the buyer. Similar assumptions have been used by several authors studying the impact of incomplete contracts on international trade–e.g. Grossman and Helpman (2002), Antràs (2003), Antràs and Staiger (2007). To avoid a taxonomy, we restrict the analysis to cases in which efficient sourcing requires dual sourcing, where B buys both specialized inputs from S and standardized inputs from abroad. When S is located in Home, as assumed in this section, dual sourcing is efficient when the tariff is sufficiently low, relative to the marginal cost of the domestic supplier. In the next subsection we provide a sufficient condition for this. Whenever B purchases at least some inputs from abroad, his total demand for inputs is given by Q∗ , which is defined implicitly by the condition that equalizes B’s marginal gain and marginal cost from acquiring an extra unit of input: V  (Q∗ ) = pw + t.

(1)

Of this total, privately efficient sourcing requires that B purchases quantity q∗ from the local supplier, where q ∗ is defined implicitly by Cq (q ∗ , i) = pw + t.

(2)

Hence, S produces up to the point where her marginal cost of production equalizes the world price, inclusive of the tariff. Now, because firm B cannot commit, ex ante, to purchase any quantity of standardized or specialized inputs, the two parties have to bargain ex post over their terms of trade.

6

Since at that point S’s investment is sunk, this allows B to "hold up" S by negotiating a price that takes advantage of the lower production cost due to S’s investment, but without compensating S for the cost of her investment. The quantity and price at which B and S trade are therefore determined by a bargain between the two parties in light of S’s post-investment cost structure. If bargaining is successful, the parties implement the efficient sourcing decision described by (1) and (2), trading q ∗ units between themselves while B purchases the remaining Q∗ − q ∗ units from abroad. The bargaining price p divides the surplus generated by S selling q∗ units to B (instead of B importing all Q∗ units) according to bargaining powers. We assume the generalized Nash bargaining solution applies, with α and 1 − α denoting S’s and B’s bargaining powers, respectively, where α ∈ [0, 1]. If B does not buy any specialized input from S, then S does not produce any specialized input and obtains a payoff of zero. Thus, if negotiation bargaining breaks down, ex post payoffs are


u0b = V (Q∗ ) − (pw + t)Q∗ u0s = 0.

By contrast, if the two parties agree in their negotiation, ex post payoffs are


u1b = V (Q∗ ) − (pw + t)(Q∗ − q ∗ ) − pq ∗ u1s = pq ∗ − C(q ∗ , i).

(3)

Thus, B’s the net gain from negotiating is his savings from purchasing q∗ units of inputs at a price lower than the world price, inclusive of the tariff: u1b − u0b = q ∗ (pw + t − p). For S, the net gain (relative to selling no specialized input) is her profit from the transaction: u1s − u0s = pq ∗ − C(q ∗ , i). Total negotiation surplus (NS) is therefore NS ≡ (u1b − u0b ) + (u1s − u0s ) = (pw + t)q ∗ − C(q∗ , i).

(4)

According to the Nash bargaining solution, the renegotiation price p(t) satisfies p(t) = (1 − α)C(q ∗ , i)/q ∗ + α(pw + t),

(5)

so that p(t) is a weighted average of S’s average cost of production and of the imported input unit cost. Clearly, if α = 1, S absorbs all the negotiation surplus and therefore all the saving costs from its ex ante cost-reducing investment. Conversely, if α = 0, B captures all the negotiation surplus and the transaction’s price equals S’s average cost.

7

2.2

Investment

The production cost of the local manufacturer can be reduced by an investment i ∈ [0, i], carried out and paid for by S in anticipation of future trade. The investment costs I(i), with I(0) = 0. Function I(i) is increasing for positive i and strictly convex in i, so that I  (0) = 0, I  > 0 for i > 0, and I  > 0. Thus, firm S’s total cost function is Γ(q, i) ≡ C(q, i) + I(i). To ensure that it is efficient to import at least some inputs, we assume that A1 : t < tp (i), where tp (i) is the tariff that (just) forecloses international trade when i = i. This tariff is defined implicitly by Cq (Q∗ (tp ), i) ≡ pw + tp . Therefore, for any t < tp (i) and for any i ∈ [0, i], Cq (Q∗ (t), i) > pw + t and it is efficient to import some standardized inputs. Henceforth we assume as well that Γ is convex: A2 : Γ(q, i) is convex in q and i. Assumption A2 ensures that the second-order necessary condition for S’s investment choice is always satisfied. Anticipating the outcome of the bargaining process, the domestic supplier knows that she will sell to B at price p(t). The seller’s profit is given by the revenue that she receives minus her cost of production, C(q ∗ , i), and the cost of her investment, I(i). Thus, using (5), the seller obtains us (i, t) = α [(pw + t)q ∗ − C(q ∗ , i)] − I(i), (6) where α defines the share of the negotiation surplus that is absorbed by the seller. We can define analogously the payoff of the buyer, ub (i, t). Using (3) and (5), we have ub (i, t) = V (Q∗ ) − (pw + t)Q∗ + (1 − α) [(pw + t)q∗ − C(q ∗ , i)] .

(7)

And we can employ (6) and (7) to define also total profit as the sum of B’s and S’s payoffs: U(i, t) = V (Q∗ ) − (pw + t)(Q∗ − q ∗ ) − C(q ∗ , i) − I(i).

(8)

Notice that, for given i, the distribution of bargaining power does not affect U(i, t), since α only redistributes profit between B and S. It does matter for the realized level of total profit, however, as they change S’s incentive to invest.

8

2.2.1

First-best investment

To serve as a benchmark for the subsequent analysis, it is appropriate to calculate the firstbest level of investment. To do so, we need to define first national surplus. We define national surplus as W (i, t) ≡ U(i, t)+tM(t), where M (t) = Q∗ −q ∗ represents B’s imports of inputs.6 The difference between U(.) and W (.) is that the latter concept recognizes that the tariff duties paid by B do not constitute a social loss. Using (8), we can rewrite national surplus as W (i, t) = V (Q∗ ) − pw (Q∗ − q ∗ ) − C(q ∗ , i) − I(i).

(9)

The first-best level of investment maximizes expression (9) conditional on the tariff. Differentiating (9) with respect to i, we obtain dW (i, t) dq ∗ dq ∗ = pw − Cq (q ∗ , i) − Ci (q ∗ , i) − I  (i). di di di From equation (2) we know that privately optimal sourcing requires Cq = pw + t. Thus, equating dW (i, t)/dt to zero defines the first-best level of investment, if b : −Ci (q∗ , if b ) = I  (if b ) + t

dq ∗ . di

(10)

To guarantee that if b corresponds indeed to a maximum, we assume the following condition is satisfied: A3 : Ciq /Cqq is constant. Since dq ∗ /di = −Ciq /Cqq by (2), condition A3 is equivalent to assuming that a marginal increase in investment always increases domestic sourcing by the same amount. Under A3, the second-order necessary condition associated with if b being a maximum of (9) is satisfied, 2 /C − C − I  < 0, where the negative sign follows from as it corresponds to SONC f b ≡ Ciq qq ii A2. A marginal increase in investment lowers the cost of production by Ci . On the other hand, the extra investment costs I  . Furthermore, the increase in investment raises domestic production at the expense of imports. This has no social cost in the absence of tariffs. However, if t > 0, society saves pw to spend Cq on the marginal imported unit that is replaced by domestic production. Since equation (2) implies that Cq > pw when t > 0, this is inefficient and therefore lowers the socially optimal level of investment. 6

In the trade policy literature, it is traditionally assumed that tariff revenue is rebated back to consumers in a lump sum fashion. Of course, ours is a partial equilibrium model where consumers are left in the background. Still, the government will presumably not waste the revenue from tariffs, but use it in some socially beneficial way. This presumption seems particularly appropriate here, since we are analyzing how a government can mitigate a market imperfection optimally. Accordingly, we add tariff revenue to our measure of social surplus. Entering it additively in W (i, t) is consistent as long as the marginal value of income for (the background) consumers is one, as it is for the firms in the model.

9

Predictably, if b is independent of α. Under A3, it is independent also of the tariff, as the following lemma shows. All the proofs are in the Appendix, unless they are very short. Lemma 1 Under A3, the first-best level of investment, if b , is unaffected by the tariff. As the tariff increases, for each level of investment the wedge between S’s marginal cost and the cost of imports widens, thus raising the social marginal cost of investment. On the other hand, since the tariff increases q ∗ for each level of investment, the benefit from lowering the seller’s cost is greater, raising the social marginal gain of investment. When the ratio between the effect of investment on marginal cost and the slope of marginal cost does not vary with q, as it is the case under A3, the increase in the social marginal gain and cost of investment are of the same magnitude, and as a result the first-best level of investment does not change with the tariff.7 2.2.2

Investment choice

When contracts are unenforceable, the domestic supplier chooses investment to maximize her payoff, as described in equation (6). Thus, using equation (2), S’s choice of investment, id , is characterized by −αCi (q ∗ , id ) = I  (id ), (11) where subscript d indicates that the seller of specialized inputs is a domestic producer. The left-hand side of (11) denotes the fraction of the reduction in the cost of production induced by a marginal increase in i that is absorbed by S, whereas the right-hand side represents the cost of this extra unit of investment. The second derivative of (6) with respect to i is SONC α ≡ α



2 Ciq − Cii Cqq



− I  .

(12)

Assumption A2 ensures that SONC α < 0, so that id denotes indeed a maximum of (6). Expression (11) is familiar from studies of the hold-up problem. If α = 0, the hold-up problem is extreme and S does not have any incentive to invest. As α rises, the level of investment increases. A direct comparison between if b and id makes clear that, under free trade, the seller underinvests relative to the socially optimal level whenever α < 1. When t = 0 and α = 1, S’s investment is perfectly protected from opportunism and therefore there is no underinvestment problem. Under import protection (t > 0), however, S’s investment can be either too little or too large, relative to the first best. While weak protection of supplier’s investment (α < 1) induces underinvestment, import protection fosters over investment, because when investing the seller does not internalize the social inefficiency from the displacement of imports caused by the subsequent increase in domestic production. The next proposition proves these points. 7

If A3 were not imposed, sgn(dif b /dt) = sgn(Cqq Ciqq − Ciq Cqqq ), and the tariff would affect if b . The subsequent analysis would remain unaltered, however.

10

Proposition 1 If α = 0, id = 0. If α > 0, id > 0 and is strictly increasing in α and in the tariff. Moreover, id (td ) < if b (td ) if and only if t <  t, where  t ≡ (1 − α)Ci Cqq /Ciq ≥ 0.

The possibility of hold up implies that the marginal benefit of S’s investment is dampened whenever her investment is not fully protected (i.e. she has less than full bargaining power in the negotiation with B). As Proposition 1 shows, greater protection of supplier’s investment lowers the hold-up problem. But while α is generally exogenous, Proposition 1 also shows that, for α ∈ (0, 1), a tariff could solve the hold-up problem as well, potentially raising investment to its first-best level. This is possible because the tariff increases the negotiation surplus (4) by worsening B’s outside option. Since S’s outside option is unaffected by the tariff, the higher NS unambiguously raises her incentive to invest, attenuating the hold-up problem unless it is insoluble–i.e., unless S has no bargaining power, in which case S obtains none of the NS. Figure 1 illustrates the effects of the tariff. It shows the supplier’s marginal cost curve and optimal sourcing decisions under free trade and under a strictly positive tariff. [Ignore for now the letters a-e in the figure.] Under free trade, the negotiation surplus NS is given by the area between the horizontal line that represents pw and the marginal cost curve Cq (q, id (0)). Any further investment would push the Cq curve down, increasing NS, but would also be costly for the supplier. The supplier choice of investment, id , is defined when α times the increase in NS equals the additional cost of investment: α [dNS(id , t = 0)/di] = I  (id ). Once a tariff is introduced, foreign inputs become more expensive, thus worsening the outside option of the buyer. As a result, at the initial level of investment NS jumps to the area between the pw + t line and the curve Cq (q, id (t)). Clearly, then, S’s marginal gain from increasing investment also jumps, unlike her cost, which is unrelated to the tariff. As a result, the supplier increases her investment, until the point where marginal gain and marginal cost of investment are equalized again. Naturally, this effect is present only when α > 0. Notice, however, that a tariff can also induce too much incentive for investment: if t >  t, the seller invests more than is optimal. Moreover, the tariff itself generates distortions. For that reason, a tariff that "solves" the hold-up problem is inefficiently high. We show this and other results in our characterization of optimal trade policy in the next subsection.

2.3

Trade Policy

The Home government can impose an import tariff before the supplier makes her investment. To rule out time inconsistency considerations from our analysis, we assume that the government cannot alter the tariff between the supplier’s investment and production decisions. While we recognize the importance of time consistency in policy decisions in general, our goal here is to study optimal trade policy in an environment where this is not a concern. We return to this issue in our concluding remarks. In line with the normative goal of this paper, we assume that the government sets trade policy seeking to maximize national surplus. Thus, the government’s optimal tariff weighs 11

Figure 1: The Effects of a Tariff under Domestic Outsourcing the benefits from raising S’s incentives to invest, moderating the hold-up problem, against the cost of creating inefficiencies in B’s sourcing decisions. Since under free trade sourcing decisions are socially efficient but the seller’s investment is inefficiently low, there could be room to increase national surplus with a positive tariff. Taking into account how S chooses her investment as a function of the tariff, the objective function of the government is W (id (t), t) = V (Q∗ (t)) − pw [Q∗ (t) − q ∗ (id (t), t)] − C(q ∗ (id (t), t), id (t)) − I(id (t)), where we write S’s optimal investment as a function of the tariff, id (t). We want to know, first, whether there is scope for active trade policy in this context. Assuming concavity of W in t,8 the optimal tariff, td , is defined implicitly by differentiating W (id (t), t) with respect to t and equating it to zero: td

 dMd (td ) did (td )  − Ci (q ∗ , id (td )) + I  (id (td )) = 0, dt dt

(13)

where Md denotes imports of inputs and where we have used equation (1) and (2) to simplify (13). For given investment, the tariff inefficiently reduces imports. This distortion of sourcing 8

This assumption allows us to restrict attention to a unique interior, td . We provide sufficient conditions on C, I and V for concavity of W in the Appendix. Note that Proposition 2 does not depend on concavity.

12

decisions is represented by the first term in the left-hand side of (13), which is negative. But a tariff also helps to mitigate the inefficiency in investment decisions. For a given level of imports, more investment is socially beneficial as long as α < 1, because S invests too little due to the fear of hold up (equation 11). And a tariff stimulates investment unless α = 0 (Proposition 1). The second term in the left-hand side of (13) represents the net social gain from a marginal increase in investment. This effect is strictly positive unless α = 1 or α = 0. Balancing these two effects yields td . Proposition 2 If the hold-up problem is insoluble (α = 0) or there is no hold-up problem (α = 1), then td = 0. Otherwise, td > 0. For sufficiently low α, the optimal tariff is strictly increasing in α. For sufficiently high α, the optimal tariff is strictly decreasing in α. Proposition 2 shows that, unless hold-up problems are either non-existent (α = 1) or completely insoluble (α = 0), there is a rationale for active trade policy in our environment. To our knowledge, this motivation for protection is entirely novel in the literature.9 Here, the country is "small," in the sense that it does not affect the world price pw , infant industry issues are not present, and imperfect competition in the final goods market is not considered. Still, the country can gain with a strictly positive tariff because it alleviates S’s underinvestment caused by the fear of hold up. The inefficiency is such that, at least for a small enough tariff, the social gain from the lower production costs that a tariff induces more than compensates for the social cost from inefficient sourcing that the tariff brings about. Figure 1 shows the social gains and (part) of the social losses from a tariff. With a tariff, as we have seen, the supplier anticipates earning rents from her investment on more sold units, so she increases her investment. This causes Cq to fall, which further increases her supply, to q ∗ (id (t)). As a result, national surplus increases by area a due to the supplier’s lower marginal cost for the units she already produced. Because the supplier now produces more, national surplus increases also by area b, which corresponds to the cost savings relative to the country’s cost of imported inputs, pw , on the extra units produced by S. But national surplus falls by area c due to the wedge that the tariff drives between the social cost of foreign and domestic inputs in equilibrium. The tariff also causes the aggregate purchase of inputs, Q∗ (t), to fall, producing the additional deadweight loss to total surplus shown in area e. Area d represents the tariff revenue collected by the government.10 Proposition 2 further shows that, in cases where td is vanishingly small (α near 0 or 1), it is possible to characterize the relationship between supplier protection and optimal tariffs quite generally. An increase in supplier protection exerts two opposing forces. First, the tariff becomes more effective in promoting investment because the supplier absorbs a larger fraction of the surplus brought about by her investment. This effect induces a higher tariff 9 The exception being Antràs and Staiger (2008), whom, as we indicate in the introduction, independently study trade policy in the presence of hold up problems. 10 There is also the cost of the increased investment, not shown in the figure, as investment rises from id (0) to id (t).

13

when α rises. On the other hand, because S operates at a higher level of i, the net social gain due to the increase in investment is smaller under a higher α. That is, the hold-up problem is less severe, making the motivation for active trade policy weaker. The first force dominates when α is very low, while the second dominates when α is very high. Now, although we have shown that a strictly positive import tariff can be socially helpful whenever the hold-up problem is not extreme, this does not imply that the tariff should be designed to induce the first-best level of investment, eliminating the hold-up problem. Instead, the optimal tariff ameliorates the underinvestment problem, but without "solving" it, because doing so would generate too much inefficiency in sourcing decisions. Proposition 3 id (td ) < if b (td ) for any α < 1. Thus, while incomplete contracts provides an efficiency rationale for protection in environments where relationship-specific investments matter, the government would not want to use trade policy to induce the first-best level of investment. The reason is that the "remedy" that could solve the hold-up problem brings its own distortions. First, the tariff inefficiently reduces B’s total purchases of inputs (area e in figure 1). In addition, the tariff promotes excessive domestic production (area c in figure 1). Both of these imports-reducing effects of the tariff work as ‘brakes’ on how far the government can use trade policy to mitigate the hold-up problem.

3 3.1

Offshoring Basic Structure

We consider now a model that is analogous to the one considered in section 2, but where the supplier with whom the buyer forms a relationship is located abroad (S f ). We assume the Home country is a member of the World Trade Organization and has to abide by the principle of non-discrimination across different sources of imports. Thus, any tariff the Home government applies has the same effect on the cost of specialized and standardized inputs. Firm B’s total demand for inputs is still defined by equation (1). On the other hand, privately efficient sourcing, which is also socially efficient in this case, requires now that Cqf (qf∗ , i) = pw ,

(14)

where we use f as either a subscript or a superscript from now on to indicate variables related to the foreign specialized supplier. Since B has no sourcing option in the domestic market, he must pay the tariff regardless of how many specialized inputs he purchases. Thus, B and S f will trade up to the point where S f ’s marginal cost of production equalizes the world price, not including the tariff. At the bargaining stage between B and S f , if bargaining breaks down, ex post payoffs are just as they were for B and S under domestic outsourcing. By contrast, if the two parties 14

agree in their negotiation, ex post payoffs are


∗ w ∗ w ∗ u1f b = V (Q ) − (p + t)Q + (p − p)qf ∗ f ∗ u1f s = pqf − C (qf , i).

(15)

Thus, for B the net gain from negotiating is his savings from purchasing qf∗ units of inputs 0 ∗ w f at a price lower than the world price, net of the tariff: u1f b − ub = qf (p − p). For S , the net gain (relative to selling no specialized input) is her profit from the transaction: 0 ∗ f ∗ f u1f s − us = pqf − C (qf , i). Total negotiation surplus (NS ) is therefore NS f = pw qf∗ − C f (qf∗ , i).

(16)

According to the Nash bargaining solution, the renegotiation price pf (t) satisfies pf (t) = (1 − α)C f (qf∗ , i)/qf∗ + αpw ,

(17)

so that pf (t) is a weighted average of S f ’s average cost of production and of the world price of the input. As before, if α = 1, the supplier absorbs all the negotiation surplus and therefore all the saving costs from its ex ante cost-reducing investment. Conversely, if α = 0, B captures all the negotiation surplus and the transaction’s price equals S f ’s average cost.

3.2

Investment

We consider that the foreign supplier has access to the same investment technology presented before, I(.), but to a (potentially) different technology C f (.), which nonetheless displays the same general properties of C(.). Thus, firm S f ’s total cost function is Γf (q, i) ≡ C f (q, i) + I(i), which we assume to be convex as well: A2f : Γf (q, i) is convex in q and i. Assumption A2f ensures that the second-order necessary condition for S f ’s investment choice is always satisfied. Anticipating the outcome of the bargaining process, the foreign supplier knows that she will sell to B at price pf (t). The seller’s profit is given by the revenue that she receives minus her cost of production, C f (q ∗ , i), and the cost of her investment, I(i). Thus, using (17), the seller obtains   ufs (i, t) = α pw qf∗ − C f (q ∗ , i) − I(i). (18) Analogously, the payoff of the buyer in this case, ufb (i, t), is given by

  ufb (i, t) = V (Q∗ ) − (pw + t)Q∗ + (1 − α) pw qf∗ − C f (qf∗ , i) .

15

(19)

Using (18) and (19), we can define also total profit as the sum of B’s and S f ’s payoffs: U f (i, t) = V (Q∗ ) − (pw + t)Q∗ + pw qf∗ − C f (qf∗ , i) − I(i). 3.2.1

(20)

First-best investment

In this case, the first-best level of investment, from a global perspective, is not the investment level that maximizes Home’s national surplus, because that measure does not incorporate the payoff of the foreign supplier. But once we add S f ’s payoff to Home’s national surplus, we obtain an expression that becomes identical to equation (9) once we replace q ∗ with qf∗ and C(.) with C f (.). When the supplier is abroad, the first-order necessary condition that characterizes firstbest investment is therefore w

p

dqf∗ di

− Cqf (qf∗ , i)

dqf∗ − Cif (qf∗ , i) − I  (i) = 0. di

From equation (14) we know that privately optimal sourcing requires Cqf = pw . Thus, the first-best level of investment in this case, iff b , satisfies −Ci (qf∗ , iff b ) = I  (iff b ).

(21)

The convexity of Γf ensures that iff b corresponds to a maximum. 3.2.2

Investment choice

The foreign supplier chooses investment to maximize her payoff, as described in equation (18). Thus, using equation (14), S f ’s choice of investment, if , is characterized by −αCif (qf∗ , if ) = I  (if ),

(22)

where subscript f indicates that the seller of specialized inputs is a foreign producer. The second derivative of (18) with respect to i is  2  f  Ciq  SONCfα ≡ α  − Ciif  − I  . f Cqq

(23)

Assumption A2f ensures that SONCfα < 0, so that if denotes indeed a maximum of (18). Equation (22) resembles equation (11), and in fact if shares some characteristics of id – e.g. it is increasing in α. However, if is unaffected by the tariff. The reason is that, when the specialized supplier is abroad, a tariff affects B’s payoff in precisely the same way regardless of whether bargaining between the two parties breaks down or not. As a result, B’s net gain from negotiation is unaffected by the tariff, and so is the negotiation price and negotiation 16

surplus. As a result, S f ’s payoff is also unaffected by the tariff, implying that in this case a tariff is incapable of promoting investment. Proposition 4 If α = 0, if = 0. If α > 0, if > 0 and is strictly increasing in α, with if < iff b unless α = 1. However, if is independent of the tariff. Proof. The proof of the statements in the first two sentences of the proposition is entirely analogous to the proof of Proposition 1. To see that if is independent of the tariff, notice that, by (14), qf∗ is unaffected by the tariff. It then follows from (22) that if is also unaffected by the tariff.

3.3

Trade Policy

We have just seen that, under offshoring, the Home government cannot affect investment or the gains from negotiation of either party. Thus, since standard motivations for active trade policy are absent in our setting, under offshoring a tariff would inefficiently lower imports and do nothing else. It follows that the best the Home government can do is to follow a policy of free trade. Corollary 1 Under offshoring, Home’s optimal trade policy is free trade. Figure 2 shows, for a fixed supplier’s investment, the effective marginal cost curves under free trade (t = 0) and a positive tariff t > 0. Because the tariff affects the cost of purchasing specialized inputs from S f in the same way it affects the cost of purchasing standardized inputs in the world market, it does not affect B and S f negotiation surplus: the area below pw and above the curve Cq is identical to the area below pw + t and above the curve Cq + t. Hence, the tariff does not affect investment incentives. It does, however, reduce Q∗ and create the standard deadweight loss shown by area e. The optimal trade policy avoids this loss by establishing tf = 0.

4 4.1

Offshoring versus Domestic Outsourcing Choice of Specialized Supplier

So far we have assumed that the buyer can purchase specialized inputs either from a domestic producer (section 2) or from a foreign one (section 3), but cannot choose between them. We now allow the buyer to choose between S and S f . To do so, we add a stage after the government’s choice of tariff but before the seller’s investment decision. We assume B has to make an adaptation in his technology toward the specialized inputs of either S and S f . If B chooses to adapt toward S, the specialized inputs of S f become worthless to B; if B chooses to adapt toward S f , then the specialized inputs of S become worthless to B. The specialized inputs of supplier j ∈ {S, S f }, have nonetheless 17

Figure 2: The Effects of a Tariff under Offshoring the same value to B provided B had adapted its production technology toward j, regardless of who j is. We assume the cost of the adaptation is independent of the supplier, and we normalize it to zero. Now, since B has the option to pick either S and S f , before specializing he will ask for a transfer from the chosen supplier. Since neither supplier has an alternative (besides selling standardized inputs in the world market), they would be willing to pay up to their total profit within the relationship. This is given by (6) for S and by (18) for S f , each evaluated at the suppliers’ choices of investment. Suppose then that B chooses to adapt toward S and requires a transfer of us (id , t). S makes the transfer and the buyer obtains a total payoff of U(id , t), where U(i, t) is defined in equation (8). Analogously, if B adapts toward S f , he requires a transfer of ufs (if , t), obtaining a total payoff of U f (if , t), where U f (i, t) is defined in equation (20). Assuming that B chooses the domestic supplier when indifferent, B specializes toward the domestic supplier if U(id (t), t) − U f (if , t) ≥ 0, (24) and toward the foreign supplier otherwise.

18

4.2

Trade Policy

When the buyer chooses his supplier, the Home government sets trade policy taking into account also its effect on B’s sourcing choice. To understand how this affects trade policy, we note first that B’s criterion to pick the domestic supplier (condition 24) is different from the socially optimal outsourcing criterion whenever t > 0. The latter corresponds to W (id (t), t) − W f (if , t) ≥ 0. This condition is equivalent to U(id (t), t) − U(if , t) − t [Mf (t) − Md (t)] ≥ 0,

(25)

where Mf (t) denotes total imports when the specialized supplier is foreign. In particular, firm B chooses the domestic supplier "too often," in a sense made clear by the next lemma. Lemma 2 If national surplus is higher under domestic outsourcing than under offshoring, B chooses to outsource domestically. However, if t > 0, B chooses domestic outsourcing even in some circumstances where offshoring would produce a higher national surplus. The buyer’s sourcing decision need not be socially optimal because it disregards the benefit from tariff revenue. For a given tariff, imports and tariff proceeds are lower under domestic outsourcing, implying that the difference between firm B’s total payoff and Home’s national welfare is smaller under domestic outsourcing than under offshoring; this is why B tends to choose the domestic supplier "too often." This distinction between the buyer’s and the socially optimal criteria for supplier’s selection suggests a source of inefficiency beyond that produced by the hold-up problem, and which could potentially limit the effectiveness of trade policy. But as it turns out, this is not the case: the Home government will always set trade policy optimally, assuming the buyer’s organizational choice will be socially optimal–and the buyer will indeed make that choice. More specifically, the government will compare national welfare under domestic outsourcing and tariff td with national welfare under offshoring and free trade. Denote the former by d (td ) and the latter by W f (t = 0). The next proposition states the result. W d (td ) ≥ W f (t = 0), the government sets t = td and firm B specializes Proposition 5 If W d (td ) < W f (t = 0), the government follows a free toward the domestic supplier. If instead W trade policy and firm B specializes toward the foreign supplier.

Thus, even though the buyer tends to outsource domestically too often for any strictly positive tariff, this bias is never decisive in B’s organizational choice. The reason is that, when the government wants to induce domestic outsourcing, the buyer’s bias is ineffectual. The government can then set the optimal tariff assuming that organizational choice, knowing that B will indeed follow the domestic outsourcing route. When the government wants to 19

induce offshoring, B’s domestic bias could become a problem. However, the bias arises only when t > 0, and optimal trade policy under offshoring calls for free trade. The government can then set t = 0 as it wishes, knowing that B will indeed follow the offshoring route. Now, since tariffs are effective at promoting domestic investment but ineffective at promoting foreign investment, optimal trade policy favors domestic outsourcing over foreign outsourcing, given equal cost functions. Corollary 2 If C f (q, i) = C(q, i), the government sets t = td and firm B specializes toward the domestic supplier. Proof. Suppose C f (q, i) = C(q, i). Then the optimality of td and the symmetry of S and d (td ) > W d (t = 0) = W f (t = 0). S f under free trade imply that W

It follows immediately that it is also possible to have a situation where C f (q, if (t = 0)) < C(q, id (t = 0)), but the government chooses t = td and induces domestic outsourcing. Such d (td ) > W f (t = 0) > W d (t = 0), i.e. the original cost disadvantage of the a case requires W domestic supplier is overcome by the optimal tariff, td , under domestic outsourcing. In that sense, under optimal trade policy domestic outsourcing has a ‘wedge’ over offshoring. To fix ideas about this wedge, assume that marginal cost under C f (.) is lower than marginal cost under C(.) by a constant: A5 : C f (q, i) = C(q, i) − δq, δ ∈ [0, δ) and δ = Cq (0, i). Under A5, Cqf (q, i) = Cq (q, i) − δ. Thus, δ provides the extent to which the marginal cost of the foreign supplier, perhaps because of lower labor costs abroad, is lower than the marginal cost of the domestic supplier, for given level of investment. The following proposition summarizes the discussion above under A5. Proposition 6 Under A5, the government sets t = 0 and firm B specializes toward the foreign supplier if and only if δ >  δ, where  δ ∈ (0, δ). Hence, the tariff-induced wedge is effective for δ ∈ (0,  δ].

4.3

Transportation Costs

It is straightforward to incorporate also exogenous trade costs (e.g. transportation or communication costs) in the model. To avoid any confusion with tariffs, we call such exogenous costs simply "transportation" costs. Suppose then that the buyer has to incur a transportation cost of τ ≥ 0 for each unit of imported good, customized or not, he purchases. The direct effect of lower transportation costs on organizational choice is unambiguous: when transportation costs fall, offshoring becomes relatively more attractive than domestic outsourcing. But there are also indirect 20

effects through investment decisions and optimal trade policy, since both are affected by transportation costs. The effect of τ on sourcing, production and investment decisions is entirely analogous to the effect of the tariff. However, since transportation costs correspond to a pure loss to society, whereas the tariff produces revenue for the government, tariffs and transportation costs have a different effects on the first-best level of investment. In particular, it can be shown that, under domestic outsourcing, the difference between the privately chosen and the first-best levels of investment increases when τ rises.11 Thus, even though investment rises with transportation costs under domestic outsourcing, the hold-up problem emerges for any τ . As a result, active trade policy is potentially useful regardless of the level of transportation costs. The effect of transportation costs on the optimal tariff td is nevertheless ambiguous in general. The optimal tariff is still determined by dW (id (t), t)/dt = 0, as in equation (13). Note, however, that q ∗ and id are now affected by τ . Letting SONC t ≡ d2 W (id (t), t)/dt2 , using (13) we can calculate dtd /dτ using the implicit function theorem:  2   dtd 1 d Md d2 id did dq ∗ did   did =− t − (Ci + I ) − Ciq + Cii +I , dτ SONC t dtdτ dtdτ dt dτ dτ dτ

(26)

where we omit the arguments of the functions for brevity. It is not difficult to see that ∗ did  did (Ciq dq dτ + Cii dτ + I dτ ) < 0. Intuitively, a larger transportation cost increases the number of units of output produced by S for given investment i, increasing the marginal benefit of investment. This increases the gains to mitigating the hold-up problem through tariff protection. Under a quadratic specification (where the V  and Cq curves from figures 1 and 2 would be linear), the dead-weight-loss triangles increase with τ and t at the same constant 2M d2 id d rate, so the two high-order derivatives, ddtdτ and dtdτ , vanish. Therefore, in that case the optimal tariff under domestic outsourcing rises with τ , implying a complementarity between 2M d transportation costs and the optimal tariff.12 But because the two second derivatives, ddtdτ 2 d id , depend on the curvature of the V  , Cq and I  functions (i.e. on third derivatives), and dtdτ the sign of (26) is generally indeterminate. Hence, under domestic outsourcing the optimal tariff and transportation costs could be strategic substitutes. Now, while the endogeneity of td with respect to τ may suggest that the relative appeal of offshoring could even decrease after a small fall in τ , this is not really possible, because at the optimal tariff under domestic outsourcing, changes in td do not produce a first-order effect on national welfare. Thus, only the direct effect of τ on welfare remains. Proposition 7 As transportation costs fall, the benefits from offshoring relative to those from domestic outsourcing unambiguously increase. If the technology of the foreign supplier is sufficiently better than the technology of the domestic supplier, then for low levels of τ offshoring is preferred, with the opposite happening 11 12

Proof available from the authors upon request. Proof available from the authors upon request.

21

Figure 3: Transportation Costs and Optimal Organizational Choice under a higher τ . Under assumption A5, transportation costs function the same way as δ, the fundamental cost advantage of the foreign supplier. It follows immediately from Proposition 6 that if τ = δ, so that transportation costs just offset the foreign supplier’s advantage, then the government sets t = td and B specializes toward the domestic supplier. In fact, we can state the following: Lemma 3 Under A5, the government sets t = 0 and firm B specializes toward the foreign supplier if and only if δ − τ >  δ, where  δ ∈ (0, δ).

Proof. ...

Figure 3 illustrates the quadratic case, when td and τ are complements. For high transportation costs, the tariff is also high and domestic outsourcing prevails. As τ falls, the tariff falls monotonically. Once τ reaches δ −  δ, td drops to zero and domestic outsourcing gives room to offshoring. This threshold contrasts to δ, which would be the threshold for distinct organizational choices if the government always followed a free trade policy.

5

Partial Contract Enforcement

So far we have assumed away the possibility of enforcement of any contract. That assumption is helpful in that it allows us to highlight the central forces in play under outsourcing and incomplete contracts. But assuming that contracts of any kind are unenforceable is probably too extreme even in our context of relationship-specific investments. Thus, we now allow some contracts to be enforceable. This will permit us to analyze the relationships between

22

the level of contract enforcement in a country and both organizational structure (domestic or offshore outsourcing) and optimal trade policy. Thus, we consider now that, with probability λ ∈ (0, 1), B and his chosen specialized supplier can write an efficient, enforceable complete contract covering investments, terms of trade, etc. With probability 1 − λ, they cannot. Uncertainty about contract enforceability is resolved after the government chooses tariffs, but before the supplier investment is sunk.13 The remaining structure remains unaltered. We consider how investment decisions change under enforceable contracts and how trade policy is affected by this possibility, under domestic outsourcing and under offshoring. We then study how partial enforcement affects the buyer’s organizational choice.

5.1

Domestic outsourcing

When contracts are enforceable and B chooses the domestic specialized supplier, B and S can induce the level of investment that maximizes their joint surplus, which we denote by ied . Mathematically, this is equivalent to the case where S chooses i individually and has full bargaining power, α = 1. This yields the first-order necessary condition −Ci (q ∗ , ied ) = I  (ied ), which equates the marginal private benefits of investment to the marginal private costs, eliminating the hold-up problem. In general this investment is different from the first-best unless t = 0, because B and S do not factor in tariff revenue into their investment decision. Taking into account how S chooses her investment as a function of the tariff, and the probability λ that contracts are enforceable, the objective function of the government is now Eλ {W } = λ {V (Q∗ (t)) − pw [Q∗ (t) − q ∗ (ied (t), t)] − C(q∗ (ied (t), t), ied (t)) − I(ied (t))} +(1 − λ) {V (Q∗ (t)) − pw [Q∗ (t) − q ∗ (id (t), t)] − C(q ∗ (id (t), t), id (t)) − I(id (t))} . The optimal tariff, tλd , is defined implicitly by differentiating Eλ {W } with respect to t and equating it to zero: tλd

   dMde did (tλd )  dMd λ + (1 − λ) − (1 − λ) Ci (q ∗ , id (tλd )) + I  (id (tλd )) = 0, dt dt dt

(27)

where we have used equation (1) and (2) to simplify (27) and where Mde denotes imports under enforceable contracts. Again, for given investment, the tariff inefficiently reduces imports, with this distortion of sourcing decisions being represented by the first bracketed 13

If one were to resolve uncertainty about contract enforceability after S’s investment is sunk, then it would be possible, in some circumstances, to write initial contracts in ways that could guarantee first-best investments, regardless of λ ∈ (0, 1) (the reason is similar to that developed by Edlin and Reichelstein 1996). Our interest is in situations where complete contracts are sometimes impossible, so we model enforceability in the simplest possible way that yields this outcome.

23

term on the left-hand side of (27). The second bracketed term on the left-hand side of (27) represents the net social gain from a marginal increase in investment, weighted by the (1−λ) probability that this gain is achieved. This effect is strictly positive unless α = 1 or α = 0. Balancing these two effects yields tλd . Proposition 8 Suppose contracts are sometimes but not always enforceable, λ ∈ (0, 1), and bargaining power is not extreme, α ∈ (0, 1). Then td > tλd > t1d = 0. The possibility of contract enforceability reduces the expected losses due to the hold-up problem. As a result, the government chooses a tariff strictly beneath td when λ > 0. Hence, moving from unenforceable contracts to partially enforceable contracts, we find that contract enforceability "crowds out" the need for tariff protection in mitigating the hold-up problem. Contract enforceability and tariffs are in that sense strategic substitutes.

5.2 5.2.1

Offshoring Investment and trade policy under enforceable contracts

When contracts are enforceable under offshoring, B and S f will induce an investment level that is entirely analogous to ied , and which we refer to as ief : −Cif (q ∗ , ief ) = I  (ief ). This investment is identical to the first-best under offshoring, ief = iff b , yet the relationship between tariff and investment is just as it is in the absence of contracts: nil. Since under offshoring the Home government cannot affect investment or the gains from negotiation of either party, regardless of the level of contract enforcement, the best the Home government can do is to follow a policy of free trade. Corollary 3 For any level of contract enforcement, under offshoring Home’s optimal trade policy is free trade. Hence, tariffs and contract enforceability are neither substitutes nor complements in the case of offshoring.

5.3

Choice of Specialized Supplier

Consider then the buyer’s choice of supplier. Under assumption A5, this does not depend on whether contracts are enforceable. Lemma 4 Under A5, for any trade cost T , if domestic outsourcing is preferred when contracts are not enforced, domestic outsourcing is also preferred when contracts are enforced.

24

This result means that, for any tariff and level of enforcement, expected national welfare k (t)}, where k ∈ {d, f} is the location of the specialized supplier chocan be written as Eλ {W sen by B. Hence, analogous to section 4, the government chooses its trade policy by compard (tλ )}, ing expected national welfare under domestic outsourcing with optimal tariffs, Eλ {W d f (0)}. If the former is to national welfare under foreign outsourcing with free trade, Eλ {W at least as large as the latter, then it sets t = tλd , and otherwise chooses free trade. Hence, under assumption A5, partial contract enforceability does not change the qualitative nature of the government’s trade policy. d (tλ )} and Eλ {W f (0)}, The level of contract enforcement λ affects the relative sizes of Eλ {W d however, and determines the size of the wedge favoring domestic outsourcing.

Proposition 9 Under A5, it is optimal to outsource offshore if and only if δ >  δ(λ), where   δ(λ) > 0 for any λ < 1 and δ(1) = 0. Proof. ...

Hence, as contracts become perfectly enforceable, the wedge shrinks to zero. Intuitively, there is no hold-up problem under perfect enforcement, so trade policy is unnecessary. Since free trade is optimal, the optimal pattern of outsourcing considers only direct cost functions (net of transportation costs).

5.4

An Example

To summarize our findings and clarify the relationship between contract enforcement and 2 optimal tariffs, consider the following specification. Let V (Q) = 100Q− Q2 and let production 2 costs be given by C(q, i) = (C0 − i)q + q2 , with C0 < pw , and where i ∈ [0, C0 ]. This yields linear "supply" (Cq ) and "demand" (V  ) curves. Moreover, let investment cost I(i) = i2 , so 2 that Γ(q, i) = (C0 − i)q + q2 + i2 . Then we have q ∗ = i + (pw + t − C0 ), Q∗ = 100 − (pw + t), as long as t < tp (i = C0 ). This holds as long as t < 50 − pw . It is also easy to check that assumption A2 is satisfied in this case. Under no contract enforcement, the seller’s payoff (equation 6) can be written in this case as
  (q∗ )2 w ∗ ∗ us (i, t) = α (p + t)q − (C0 − i)q + − i2 . 2 We can use (11) to find S’s investment choice and her corresponding production level: α (t + pw − C0 ) , 2−α 2 = (t + pw − C0 ) . 2−α

id (t, α) = q∗

25

The corresponding investment and production under enforceable contracts is ied (t) = (t + pw − C0 ) , q∗ = 2 (t + pw − C0 ) . Equation (27) then gives us the optimal tariff: tλd =

2α(1 − α)(1 − λ) (pw − C0 ) . 4(2 + λ)(1 − α) + 3α2

As Proposition 2 shows, tλd = 0 when either α = 0 or α = 1. In this linear example, tλd is in fact an inverted U with respect to α, reaching its highest level at an intermediate level of investor protection. It is also clear that tλd = 0 when λ = 1, and that tλd is strictly decreasing in λ for any α ∈ (0, 1). Hence, in this case contract enforceability and tariffs are always strategic substitutes. [Specify C f and introduce τ ] Consider now the case where trade costs fall. For τ > 5, it is clear that domestic outsourcing is optimal, as the domestic technology is superior to the effective foreign technology even without optimal tariffs. For τ < 5, effective foreign technology is better, but due to imperfect enforcement optimal trade policy may create the possibility that domestic outsourcing is preferred to foreign outsourcing. The "threshold" value of τ is an increasing function of λ, as figure 4 illustrates.

6

Extending the Model/Sensitivity

... • Ad valorem tariffs • Discriminatory tariffs • Tariffs on final good • Export policy by Foreign • Single sourcing (if i is sufficiently high or pw is sufficiently low) • Competition between specialized suppliers at the production level (i.e. both invest) • Different bargain structure in first stage, in which B does not get S’s full surplus: no effect on trade policy when S is in Home, but (possibly) when S is abroad • Fringe of producers of standardized inputs is present both abroad and in Home (which can be either an exporter or an importer of standardized inputs)

26

Figure 4: Free Trade "Thresholds" • It would be interesting to extend this analysis to the case of a "large" country. The key questions surround whether the presence of a terms-of-trade effect would exacerbate or mitigate the incentives to use active trade policy to promote relationship-specific investments.

6.1

Time consistency

In our analysis, we set time consistency issues about trade policy aside. However, if the government could eliminate the tariff after the seller’s investment has become sunk, the government would want to do so to guarantee efficient sourcing. But if the supplier anticipated the government’s motivation and knew that the policy could be altered, the tariff would then become irrelevant for her investment decisions. The time inconsistency of protectionist programs has been studied before. The nature of the time inconsistency here shares similarities but displays also some interesting differences vis-à-vis much of that literature. For example, in the analyses of Matsuyama (1990) and Tornell (1991), protection is supposed to be temporary, aimed at providing breathing room for the domestic industry until it “catches up” with the foreign competition. Thus, the domestic industry invests only if it expects free trade in the future, but it might choose not to invest to induce the government to keep protection longer. In that context, an ex post deviation from the government’s proposed policy benefits the domestic industry. By 27

contrast, in our setting protection is supposed to be permanent, to ensure enough return for the domestic supplier’s investment. Accordingly, the supplier invests only if she expects protection in the future–i.e., at the production stage–and she does not want to induce any change in the government’s original policy, but rather hopes that the government will honor its promise. Thus, here an ex post change in the government’s ex ante policy hurts the domestic supplier.14 Still, it is clear that active trade policy can be effective to ameliorate hold-up problems in our setup only if the government can credibly commit to keep the tariff unchanged after investment decisions have become sunk. Assuming that the government has such a commitment power, as we do here, we uncover a new motivation for active trade policy. However, the general validity of the argument requires also a thorough assessment of the government’s ability to commit. Such a commitment could be achieved, for example, if changing trade laws were sufficiently costly, as seems to be the case in many circumstances.15 Alternatively, one could extend the analysis to a truly dynamic, infinite-horizon setting, where reputational concerns affect as well the time consistency of trade policy. This constitutes a challenging but interesting topic for future research. here, political economy forces work to keep promised policy ex post, in contrast with the time consistency literature; if alignment with political economy forces is important to keep government’s promises, then time consistency issues are less important here.

7

Conclusion

We study in this paper the role of trade policy when outsourcing takes place under incomplete contracts. In an environment where there are otherwise no reason for active trade policy, we show that some protection is socially desirable when outsourcing is domestic, because protection moderates hold-up problems. Tariffs are not helpful under offshoring, however, because in that case they affect the gains from trade inside and outside the relationship in the same way. And even when protection is helpful (i.e. under domestic outsourcing), the optimal tariff does not ‘solve’ the hold-up problem, because protection also distorts (ex post) sourcing decisions. Protection is less important also if some contracts can be enforced. Nevertheless, because tariffs can help under domestic, but not under offshore outsourcing, we find that optimal trade policy provides a ‘wedge’ to the former over the latter. This result indicates that, even when foreign labor costs are lower and/or foreign technology is better, domestic outsourcing could be socially preferable, given the appropriate level of protection. Now, even though our goal is mainly normative, i.e. to determine optimal trade policy 14 This is similar to the context in Eaton and Grossman (1985), where the social value of protection is greater ex ante (to promote risk sharing through sectoral reallocation) than ex post. 15 As Mayer (1999) points out, “trade laws [are typically held unaltered] unless fundamental shifts in an industry’s competitiveness occur” (p. 247). This regularity is possibly explained by the often-costly legislative procedures necessary to alter trade laws, which are generally both time demanding and hard to enact.

28

in an environment marked with relationship-specific investments and incomplete contracts, our analysis also offers a general lesson that applies regardless of how governments set trade policies. If protectionist policies are in place, motivated by reasons other than economic efficiency (e.g. politics), our results imply that they are likely to be less harmful (and perhaps even beneficial) from a social standpoint than standard trade theory suggests if applied on sectors where asset specificity and incomplete contracts are important, and outsourcing is mainly among domestic firms.

8

Appendix

Proof of Lemma 1. be rewritten as

Notice from (2) that dq ∗ /di = −Ciq /Cqq . Thus, equation (10) can t

Therefore, under A3

Ciq − Ci (q ∗ , if b ) − I  (if b ) = 0. Cqq

difd b [Ciq /Cqq − Ciq (∂q ∗ /∂t)] =− . dt SONC f b

Since ∂q∗ /∂t = 1/Cqq from (2), dif b /dt = 0. Proof of Proposition 1. If α = 0, it follows directly from (6) that investment is worthless for S, and therefore id = 0. Otherwise, id > 0 because I  (0) = 0, and satisfies (11). As α rises, the convexity of Γ ensures that id increases. Investment also increases with the tariff whenever α > 0: did αCqi /Cqq = > 0, dt SONC α

(28)

where we use the fact that ∂q ∗ /∂t = 1/Cqq , which follows from the definition of q ∗ in (2). Finally, from the first-order conditions that define if b and id (equations 10 and 11, respectively), it follows that id < if b if and only if −αCi > −Ci − t

Ciq dq ∗ = −Ci + t, di Cqq

or equivalently iff t> completing the proof.

(1 − α)Ci Cqq  = t ≥ 0, Ciq

To prove Proposition 2, we will need the following lemma, where we use the following 2 Ciq d(Ciq /Cqq ) d(χ) α α definitions: χ ≡ Cqq − Cii , ε1 ≡ dα (Ciq /Cqq ) and ε2 ≡ dα χ . Lemma 5

d2 id dtdα

=

Ciq /Cqq (SON C α )2

 −I  (1 + ε1 ) + χα ε1 − ε2 + 29

1 dI  χ dα

 .

Proof. Using the expression for did /dt in (28) and the definition of SONC α in (12), we obtain    d2 id Ciq /Cqq dχ dI   = − . (χα − I )(1 + ε1 ) − α χ + α dtdα dα dα (SONC α )2 After straightforward manipulation, we then obtain the expression in the lemma. Proof of Proposition 2. Using (11), we can write the effect of a marginal increase in the tariff on national welfare as dW (id (t), t) did (t) = tM  (t) − (1 − α)Ci (q ∗ , id (t)). dt dt

(29)

Suppose first that α ∈ (0, 1). Then, the second term of (29) is strictly positive, because did dW dt > 0 and Ci < 0. Hence, dt > 0 provided that the first term is non-negative. Since M  < 0, that term is nonnegative for any t ≤ 0. Hence, dW dt > 0 for any t ≤ 0, so it cannot be true that td ≤ 0. Hence td > 0. d ,0) = 0, so dW (iddt(t,0),t) = tM  (t). Since Next suppose that α = 0. By Lemma 1, did (t dt M  < 0, (29) is positive for t < 0, negative for t > 0, and zero for t = 0. Hence, td = 0. If α = 1, the second term of (29) vanishes and once again dW (iddt(t,0),t) = tM  (t). The same logic follows. d2 W/dtdα 2 2 d Now, from the implicit function theorem, dt dα = − d2 W/dt2 . Since d W/dt < 0 at td , then sign(dt/dα) = sign(d2 W/dtdα). To get sign(d2 W/dtdα), let us first rewrite dW/dt (dropping the arguments of all functions for brevity) as     Ciq 1 1 did dW  =t − − −t + Ci + I , dt V  Cqq dt Cqq using the definition of Q∗ (in equation 1) and of q ∗ (in equation 2) to substitute for M  . Taking the partial derivative of this expression with respect to α, and noticing that dq ∗ /di = −Cqi /Cqq from (2), we find     Cqi d2 id d2 W d 1 1 did d(Ciq /Cqq ) =t − + + dtdα dα V  Cqq Cqq dtdα dt dα

di di d2 id − Ci (1 − α) − d d dtdα dt dα



 2 Ciq − + Cii + I  , (30) Cqq

where we use the first-order necessary condition for id (equation 11) to obtain the second term above. Since td → 0 as α approaches 0 or 1, the first term in (30) goes to zero in both d ,0) of these limiting cases. Since did (t = 0, we then have that dt d2 id d2 W =− (α = 0)Ci . α→0 dtdα dtdα lim

30

Using Lemma 5, this expression becomes I  Ci Ciq /Cqq d2 W > 0. = α→0 dtdα (SONC α )2 lim

Hence, by continuity the optimal tariff and supplier protection are positively related as α approaches zero. Similarly, d2 W did did lim =− α→1 dtdα dt dα



2 Ciq − + Cii + I  Cqq



< 0,

where the negative sign follows because the expression in parenthesis corresponds to the determinant of the Hessian matrix of Γ, which is positive under A2, divided by Cqq > 0. Hence, by continuity the optimal tariff and supplier protection become negatively related as α approaches one. Proof of Proposition 3. From Proposition 1 we know that id (td ) < if b if and only if td <  t. Developing (13), one finds that td =

α(1 − α)Ci Ciq V  . Cqq SONC α + V  (αCii + I  )

Thus, if α < 1, td <  t and id (td ) < if b if and only if

(1 − α)Ci Cqq α(1 − α)Ci Ciq V  < α   Cqq SONC + V (αCii + I ) Ciq 2  αCiq V   ⇐⇒ > Cqq SONC α + V  αCii + I  Cqq     2 C iq ⇐⇒ V  α − Cii − I  > Cqq SONC α Cqq ⇐⇒ V  < Cqq ,

which is always true. Proof of Lemma 2. For any tariff t ≥ 0, B chooses the domestic supplier if inequality (24) holds, whereas national surplus is higher under domestic outsourcing if inequality (25) holds. The right-hand sides of (24) and (25) are both zero, but the left-hand side of (24) is greater than the left-hand side of (25), since imports are obviously higher when B sources specialized inputs from the foreign supplier. Hence, if condition (25) is satisfied, condition (24) is satisfied as well for any t ≥ 0. On the other hand, if t > 0 there could be situations where U(id (t), t) − U(if , t) ≥ 0 > U(id (t), t) − U(if , t) − t [Mf (t) − Md (t)] , in which case firm B outsources domestically even though offshoring would be socially opti31

mal. d (td ) ≥ W f (t = 0). Since free trade is optimal under Proof of Proposition 5. Suppose W d (td ) ≥ W (f; td ). It then follows from Lemma 2 that, if offshoring, we also have that W t = td , firm B will outsource domestically. Since domestic outsourcing and t = td maximize national welfare by construction in this case, the government sets t = td . f (t = 0) > W d (td ). Since under domestic outsourcing t = td is Suppose now that W f (t = 0) > W (d; t = 0). Now, with free trade B’s criterion to optimal, we also have that W choose his supplier is equivalent to the socially optimal criterion (i.e., inequalities 24 and 25 are identical if t = 0). Thus, firm B will outsource abroad. Since offshoring and free trade maximize national welfare by construction in this case, the government sets t = 0. f (t = 0) > Proof of Proposition 6. It is optimal to outsource offshore if and only if W d (td ). This condition can be rewritten as W   V (Q∗ (t = 0))−pw Q∗ (t = 0) − qf∗ (if , t = 0) −C(qf∗ (if , t = 0), if )+δqf∗ (if , t = 0)−I(if ) > V (Q∗ (td )) − pw [Q∗ (td ) − q ∗ (id (td ), td )] − C(q ∗ (id (td ), td ), id (td )) − I(id (td )). (31)

If δ = 0, C f (q, i) = C(q, i) and inequality (31) is contradicted by the definition of td . Note now that, while the right-hand side of (31) is not affected by δ, the left-hand side is:  dqf∗ (if , t = 0) dlhs(31)  w = p − Cq (qf∗ (if , t = 0), if ) + δ dδ dδ   ∂i dq∗ (if , t = 0) f f f ∗ ∗  + qf (if , t = 0) − Ci (qf (if , t = 0), if ) − I (if ) . (32) ∂qf∗ dδ Since under A5 equation (14) becomes Cq (.) = pw + δ, the first term in (32) vanishes. Using (22), (32) then becomes ∂if dqf∗ (if , t = 0) dlhs(31) = qf∗ (if , t = 0) − (1 − α)Cif (qf∗ (if , t = 0), if ) ∗ . dδ ∂qf dδ It is straightforward to check that the two derivatives above are positive. Since Cif (.) < 0, if follows that the whole expression is positive. The first term represents the direct gain from lowering the marginal cost of the foreign supplier, for given qf∗ . The second term represents the indirect gain from increasing δ: at a higher δ, qf∗ is higher; while in itself the higher quantity has no first-order effect, it induces more investment, which provides a first-order gain because investment is too low. If δ is high, then the inequality is satisfied ........... ..... Proof of Proposition 7.

Notice first that the impact of τ and of t on B’s total surplus 32

and on imports is always the same. Thus, j (t) j (t) dW dW = − Mj , dτ dt

j = f, d. The impact of a reduction in τ on welfare under offshoring is then −

f (t = 0) f (t = 0) dW dW =− + Mf = Mf , dτ dt

since the first term is nil under free trade. Similarly, − We then find that −

d (td ) d (td ) dW dW =− + Md = Md . dτ dt

  d (td ) − W f (t = 0) d W dτ

= Mf − Md > 0,

since imports are always greater under offshoring. Proof of Proposition 8. Differentiating Eλ {W } with respect to t, we find    dMde dEλ {W } dMd did (t)  ∗  = (1 − λ) t − Ci (q , id (t)) + I (id (t)) + tλ . dt dt dt dt

(33)

Evaluating expression (33) at td (which is, of course, the optimal tariff for λ = 0), the term in the curly bracket vanishes, as it corresponds to the first-order necessary condition for td . Since Mde decreases with t, the expression above is unambiguously negative when evaluated at td . Given the concavity of Eλ {W }, it follows that tλd < td . Since [Ci (q ∗ , id (t)) + I  (id (t))] < 0 due to the hold-up problem, (expression 33 evaluated at t = 0 is strictly positive). It follows that tλd > 0. As λ → 1, the bracketed term vanishes. Hence, limλ→1 tλd = 0.   Proof of Lemma 4. We first show that, under dual sourcing, the expression U(id (t), t) − U f (if , t) is monotone increasing in t for any value of α > 0. Differentiating, we have       dV (Q∗f ) dufs (if , t) d U(id (t), t) − U f (if , t) dV (Q∗d ) dus (id , t) = + − + . dt dt dt dt dt Under dual sourcing, we have Q∗d = Q∗f , and the tariff has the same effect on both, so   d U(id (t), t) − U f (if , t) dus (id , t) dufs (if , t) = − . dt dt dt Since the tariff has no effect on ufs (if , t), we have from Proposition 1 that   d U(id (t), t) − U f (if , t) dus (ied , t) = > 0. dt dt 33

Hence, if domestic outsourcing is preferred for some  t, then it is preferred for any t >  t. Let the "cutoff" value of the tariff be t0 in the case contracts are not enforced and t1 in the case contracts are enforced. Next, we show that t0 = t1 . Consider first the case where τ > Cqd (q, i) − Cqf (q, i), so that the presence of trade costs means that the foreign supplier has a higher effective marginal cost. Then it is straightforward to show, using (2) and (14), that under free trade qd∗ > qf∗ if id = if . Since Cqi < 0, it is clear that S s optimal investment is increased above if . Hence, profit is higher under domestic outsourcing for t = 0. Given the monotonicity result above, we have that profit is higher under domestic outsourcing for any t ≥ 0. Now, consider the case where τ < Cqd (q, i) − Cqf (q, i) and define   tcut = Cqd (q, i) − Cqf (q, i) − τ . We now show that tcut = t0 = t1 . It is clear that, for id = if , it must be true from (2) and (14) that qd∗ = qf∗ , as the foreign supplier’s marginal cost is effectively the same as the domestic supplier’s marginal cost. Hence, for any α, (11) yields the same optimal investment as (22), and the same payoffs. Therefore, we have U(id (tcut ), tcut ) − U f (if , tcut ) = 0 for any α. Since U(id (t), t)−U f (if , t) is monotonic in t, we have that U(id (t), t)−U f (if , t) < 0 for any t < tcut and U(id (t), t) − U f (if , t) > 0 for any t > tcut . Thus, for any tariff t, if domestic outsourcing is preferred when contracts are not enforced, then domestic outsourcing is preferred when contracts are enforced.

References Antràs, Pol and Elhanan Helpman. "Global sourcing." Journal of Political Economy 112, 2004, 552—580. Antràs, Pol and Robert W. Staiger. "Offshoring and the Value of Trade Agreements." Mimeo, 2007. Conconi, Paola, Patrick Legros and Andrew F. Newman. “Trade Liberalization and Organizational Choice.” Mimeo, 2008. Eaton, Jonathan and Gene Grossman. "Tariffs as Insurance: Optimal Commercial Policy when Domestic Markets are Incomplete." Canadian Journal of Economics 18, 1985, 258-272. Edlin, Aaron and Stefan Reichelstein. "Holdups, Standard Breach Remedies and Optimal Investment." American Economic Review 86, 1996, 478-501. Feenstra, Robert. Advanced International Trade: Theory and Evidence. Princeton: Princeton University Press, 2003. Grossman, Sanford and Oliver Hart. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration." Journal of Political Economy 94, 1986, 691-719. 34

Grossman, Gene and Elhanan Helpman. "Outsourcing in a Global Economy." Review of Economic Studies 72, 2005, 135-59. Grossman, Gene and Esteban Rossi-Hansberg. "Trading Tasks: a Simple Theory of Offshoring." American Economic Review, forthcoming. Helpman, Elhanan. "Trade, FDI and the Organization of Firms." Journal of Economic Literature 44, 2006, 589-630. Hummels, David, Jun Ishii and Kei-Mu Yi. "The Nature and Growth of Vertical Specialization in World Trade." Journal of International Economics 54, 2001, 75-96. Matsuyama, Kiminori. "Perfect Equilibria in a Trade Liberalization Game." American Economic Review 80, 1990, 480-492. Mayer, Wolfgang. “The Political Economy of Administering Trade Laws,” in J. Piggott and A. Woodland (eds.), International Trade Policy and the Pacific Rim. London: Macmillan, 1999. McLaren, John. "Globalization and Vertical Structure." American Economic Review 90, 2000, 1239-1254. Ornelas, Emanuel and John L. Turner. "Trade Liberalization, Outsourcing, and the HoldUp Problem." Journal of International Economics 74, 2008, 225-241. Rogerson, William P. "Contractual Solutions to the Hold-up Problem." Review of Economic Studies 59, 1992, 777-793. Schwartz, Galina and Ari Van Assche. Input Specificity and Global Sourcing. Mimeo, 2007. Spier, Kathryn and Michael Whinston. "On the Efficiency of Privately Stipulated Damages for Breach of Contract: Entry Barriers, Reliance and Renegotiation." RAND Journal of Economics 26, 1995, 180-202. Tornell, Aaron. "Time Inconsistency of Protectionist Programs." Quarterly Journal of Economics 106, 1991, 963-974.

35