Journal of International Economics 90 (2013) 337–347

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Technology adoption, government policy and tariffication Josh Ederington a,⁎, Phillip McCalman b a b

Department of Economics, University of Kentucky, 335 Gatton Building, Lexington, KY 40506, United States Department of Economics, University of Melbourne, Parkville, Victoria 3010, Australia

a r t i c l e

i n f o

Article history: Received 21 January 2009 Received in revised form 7 September 2012 Accepted 28 February 2013 Available online 15 March 2013 JEL classification: F12 F13 030

a b s t r a c t We integrate trade policy into an open-economy model of technology adoption to investigate the impact of alternate trade barriers on the equilibrium diffusion of a cost-saving technology. It is shown that even when ad-valorem tariffs have a neutral impact on technology adoption, non-tariff barriers such as quotas can be used to affect the speed of technology diffusion in both the home and foreign countries. In addition, we demonstrate how, in an open-economy setting, tariffication (i.e., the conversion of quotas to ad-valorem tariffs) can lead to faster technology adoption world-wide. © 2013 Elsevier B.V. All rights reserved.

Keywords: Technology adoption Tariffs Quotas

In addition to the conventional welfare gains induced by allocative efficiency and exploitation of economies of scale, it is often claimed that trade liberalization can lead to dynamic gains as well. Indeed, a common argument is that the increased foreign competition created by trade liberalization forces firms to modernize and adopt new costsaving technologies and advanced production techniques to remain competitive in the world marketplace. These claims are often based on empirical evidence that episodes of trade liberalization are correlated with subsequent productivity gains by both firms and industries (e.g., see Harrison (1994), Krishna and Mitra (1998), and Pavcnik (2002)). However, the majority of these papers fail to distinguish between a reduction in tariff levels and a relaxation of quantitative import restrictions (indeed, trade liberalization episodes are often captured simply through the use of time dummy variables). The exceptions are Lee (1996) and Kim (2000), both of which find that liberalization of quota

protection has a more significant impact on productivity growth than liberalization of tariff protection.1 This differential impact raises questions about the mechanism behind which quota protection could have a more significant influence on a firm's technology decisions and hence productivity growth. Indeed, while the literature on the nonequivalence of different trade policy instruments in static models is extensive, there is very little understanding of the respective effects of different trade policy instruments in dynamic models of productivity growth and technology adoption. Thus, in this paper, we integrate trade policy into an open-economy model of technology adoption to investigate how various trade policy instruments impact the equilibrium diffusion of a new cost-saving innovation. The key question addressed in this paper is how different trade policies (i.e., tariffs relative to quotas) can affect firm productivity by altering the rate at which both home and foreign firms adopt new cost-saving technologies. Our basic model is one in which an endogenous number of firms, located in two different countries and engaged in monopolistic

⁎ Corresponding author. E-mail addresses: [email protected] (J. Ederington), [email protected] (P. McCalman).

1 Both papers analyze an episode of trade liberalization across Korean manufacturing industries which included a gradual reduction in both Korean tariffs (following reforms in 1962) and quotas (following reforms in 1967). Lee (1996) uses panel data covering 38 Korean manufacturing industries over the years 1963–1983 while Kim (2000) uses panel data covering 36 industries over the period 1966–1988. Both papers find that while tariff protection failed to have a statistically significant impact on productivity growth, quota protection did have a (statistically significant) negative impact on both labor and total factor productivity growth.

1. Introduction

0022-1996/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jinteco.2013.02.007

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J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

competition, make decisions about when to invest in a cost-reducing productivity innovation. 2 We show that, in such a dynamic model of technology diffusion, a quota acts as an impediment to the adoption of cost-saving technology improvements since it has a disproportionately negative impact on high-productivity foreign firms as their relative price advantage is reduced. Basically, non-tariff barriers such as import quotas have an effect similar to a specific price increase, raising the relative price of foreign high-productivity (low-cost) firms, and thus impeding the desire of foreign firms to adopt new cost-saving innovations. 3 We demonstrate that this adoption-reducing effect can result in quotas influencing the technology adoption choices of both home and foreign firms, even in situations where an ad-valorem tariff has no effect. In addition, we show that in a dynamic model, the marginal impact of a quota on adoption decisions can vary across time periods. As an application of this result, we consider the non-equivalence of reciprocal tariff and quota protection within a dynamic setting of technology adoption. A primary component of recent GATT/WTO negotiations has been the promotion of tariffication (i.e., the conversion of non-tariff barriers such as quotas to ad-valorem tariffs). Indeed, one of the central achievements of the Uruguay Round was the widespread conversion of quantitative import restrictions and other forms of protection into equivalent ad-valorem trade barriers. As was mentioned before, in standard static models of perfect competition, tariffs and quotas are perfect substitutes and thus tariffication has no impact on the overall efficiency of the trade regime. Indeed, the typical justification for tariffication in WTO agreements is the increased transparency that ad-valorem custom duties provide (thus facilitating future negotiations). In this model, we show that quotas also tend to decrease the speed of technology diffusion (relative to ad-valorem tariff barriers) since they have a disproportionately negative impact on high-productivity firms. This result has the policy-relevant implication that tariffication, in addition to increasing the visibility of trade protection, can lead to faster technology adoption world-wide. There is an extensive literature in the field of international trade on the relative efficiency of different forms of trade barriers, specifically the relative efficiency of tariff versus quota protection. 4 This literature demonstrates that, while tariffs and quotas are equivalent under conditions of perfect competition, they can have differing impacts when the market is characterized by imperfect competition (see Bhagwati (1965) and Bhagwati (1968)). More recent contributions to this literature analyze trade policy instruments under different forms of competition (e.g., see Jorgensen and Schröder (2005)) as well as various market frictions (e.g., see Matschke (2003) and Herander (2005)). However, in considering the effect of different forms of trade protection on technology adoption decisions, our paper is most closely related to that of Miyagiwa and Ohno (1995) which considers the effects of unilateral protection on the adoption decisions of a single import-competing domestic firm engaged in Cournot competition with a foreign exporter (whose level of technology is held constant).5 In their model, the nonequivalence between tariffs and quotas rests on the lack of a strategic effect on technology adoption in the presence of a quota. Intuitively, under a tariff regime one of the benefits of adopting a cost-saving 2 This framework is similar to that employed in Ederington and McCalman (2008); however, this paper extends that model to analyze the relative productivity impact of different trade policy instruments. 3 The intuition for this result parallels that of the classic Alchian–Allen conjecture that specific transportation costs lead firms to export high-quality goods since per-unit transportation costs lower the relative price of high quality goods. This logic is central to the literature on how quotas can lead to an increase in the average quality of imports (e.g., see Falvey (1979), Krishna (1987) and Krishna (1990)). The applicability of this result became apparent in the 1980s with the voluntary export restraints applied to Japanese auto exports by the United States. Several studies have noted that in response to this quota, Japanese auto firms shifted toward higher-quality models (e.g., see Feenstra (1988)). 4 An analogous question concerns the relative efficiency of specific vs. ad valorem tariffs (for a review see Helpman and Krugman (1989)). 5 Also see Crowley (2006), which analyzes the different effects of multi-country versus country-specific tariffs on technology adoption.

technology is that it reduces the exports of the foreign firm and thus increases home firm profits. This strategic benefit to adoption is absent under a quota regime and thus Miyagiwa and Ohno (1995) conclude that home firms will adopt new technology earlier under tariff protection than under an equivalent quota. In contrast, our paper models the technology adoption decisions of an endogenous number of firms engaged in monopolistic competition and thus the strategic effects of Miyagiwa and Ohno (1995) do not arise. Rather, the non-equivalence in our paper rests on a distinction between trade policies that have a specific (per-unit) impact on marginal costs versus policies that have an ad valorem (percentage) impact. As a result of our different mechanisms, sufficiently restrictive unilateral trade protection, which unambiguously advances home-firm adoption in the Miyagiwa and Ohno (1995) framework, has a much richer effect in our framework (some firms adopt later while others adopt earlier). In addition, our approach, which endogenizes foreign adoption decisions, also allows us to consider the effects of unilateral trade policy changes on foreign firm productivity, as well as the effects of reciprocal policy changes and the issue of tariffication. In the following analysis, Section 2 lays out the model of technology adoption and solves for the equilibrium rate of diffusion of a new technology within an open economy. In Section 3 we investigate the impact of ad-valorem tariffs on technological progress while in Section 4 we consider the case of a quota. Section 5 concludes. 2. Model To study the effects of trade barriers on cost-reducing technological improvements, we must specify the process by which firms endogenously choose to adopt new technologies. Here we employ a standard model of technology adoption in a closed economy initially proposed by Reinganum (1981) and Fudenberg and Tirole (1985) and extended to a monopolistically competitive environment by Götz (1999). This framework has the advantage of fitting the empirical evidence on technology adoption in that the cost-saving technological innovation will only gradually diffuse through the industry. 6 This model of technology adoption has been previously extended to an open economy by Ederington and McCalman (2008) and here we use a simplified version of that model to investigate the differing effects of tariffs versus quotas on the rate of technology adoption. 7 2.1. Demand We assume two identical countries, a home country and a foreign country. Each country has two sectors: one sector consists of a numeraire good, x0, while the other sector is characterized by differentiated products. The preferences of a representative consumer are defined by the following intertemporal utility function: ∞

−rt

U ¼ ∫ ðx0 ðt Þ þ logC ðt ÞÞe 0

dt

ð1Þ

where x0(t) is consumption of the numeraire good in time t and C(t) represents an index of consumption of the differentiated product. For C(t) we adopt the CES specification which reflects tastes for variety in consumption and also imposes a constant (and equal) elasticity of substitution between every pair of goods: h n˜ i1=ρ ρ C ðt Þ ¼ ∫0 yðz; t Þ dz

ð2Þ

where y(z,t) represents consumption of brand z at time t and n˜ represents the number of available varieties in a representative country. It 6

For a survey of the empirical evidence see Karshenas and Stoneman (1995). Ederington and McCalman (2008) were concerned with the relative impact of trade on the adoption decisions of exporting versus importing firms. However, it did not consider the relative impact of different policy instruments, which is the subject of this paper. 7

J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

is straightforward to show that, with these preferences, the elasticity of substitution between any two products is σ = 1/(1 − ρ) > 1 and aggregate demand in each country for good i at any point in time is given by: yði; t Þ ¼

pði; t Þ−σ E n˜

∫0 pðz; t Þ1−σ dz

as the foreign equivalents. Then the price index in the home country is given by: ∫

nþnf 0

¼

ð3Þ

where p(i,t) is the price of good i in time t and E represents the total number of consumers in the country. 2.2. Production

2.3. Price, profit and ad-valorem tariffs

1−σ

pði; t Þ dz  σ 1−σ h σ−1

pL ¼

σ σ ;p ¼ : σ −1 H φðσ −1Þ

0

pf ði; t Þ1−σ dz  σ 1−σ h   i   σ −1 σ −1 1−σ : ¼ qf φ þ 1−qf nf þ qφ þ ð1−qÞ nbf σ −1 ð7Þ

Finally, the operating profits for home firms using the lowproductivity technology (πL) and the high-productivity technology (πH) respectively are given by: πL ðt Þ ¼ π H ðt Þ ¼

ðσσ−1Þ1−σ E

nþn σ ∫0 f pði; t Þ1−σ dz σ 1−σ σ −1

ðσ −1Þ

nþnf

σ ∫0

F

σb σb F ;p ¼ : σ −1 H φðσ −1Þ

φ

E

pði; t Þ1−σ dz

þ þ

ðσσ−1Þ1−σ b1−σ E f nþnf

σ ∫0

pf ði; t Þ1−σ dz

1−σ

σ

ðσ −1Þ

nþnf

σ ∫0

φ

σ −1 1−σ : bf E

ð8Þ

pf ði; t Þ1−σ dz

Operating profits for foreign firms (πLF and πHF) are defined analogously. 2.4. Adoption decision In determining when to adopt the new technology, a firm takes the evolution of adoption by both home and foreign firms, q(t) and qf(t) respectively, as given. In this situation a firm in the home country chooses its adoption date, T, to maximize the discounted value of total profits: Π¼∫ e 0

    ∞ −rt πL qðt Þ; qf ðt Þ dt þ ∫T e πH qðt Þ; qf ðt Þ dt−X ðT Þ−F

where X(T) = e − rTx(T). As can be seen, these profits depend on both the firm's own adoption date, T, and the adoption decisions of rival firms (which are summarized by q(t) and qf(t)). Differentiating with respect to T yields the first-order condition: −rT

e

h    i ′ π H qðT Þ; qf ðT Þ −π L qðT Þ; qf ðT Þ ¼ −X ðT Þ:

ð9Þ

ð4Þ

Likewise prices set in the foreign market are given by: pL ¼

ð6Þ

nþnf

T −rt

In this section, we investigate international trade between two symmetric countries. As is typical in monopolistic competition models of trade, we assume iceberg transport costs where b > 1 units of a good need to be shipped for one unit to arrive. These iceberg transport costs can reflect a combination of standard shipping costs as well as any ad-valorem tariff barriers. Thus, prices set in the domestic market are defined by:

   i  qφσ −1 þ ð1−qÞ n þ qf φσ−1 þ 1−qf nf b1−σ

and the price index in the foreign country is given by: ∫

All goods are produced using constant returns to scale technologies and a single factor of production, labor. Thus, production of any good (or brand) requires a certain amount of labor per unit of output. For simplicity, we assume that production of the numeraire good is defined by l = x0, which ensures that the equilibrium wage is equal to unity. We assume that varieties of the differentiated good can be produced using two types of technology. A low-productivity technology is always available to any firm and is purchased at a cost F upon entering the industry. Production using the low-productivity technology is defined by l(t) = y(t). A high-productivity technology is also available at time t = 0, but requires an additional fee of X(t), which is defined in present value terms, where X(0) = ∞, X ð∞Þ ¼ — X, X′ b 0, and X″ > 0. In particular, we assume that the adoption cost is falling faster than the interest rate (i.e., − e rtX′ is declining over time).8 Intuitively, this gives firms an incentive to wait to adopt even when the adoption costs are not prohibitive. With this adoption cost function, earlier adoption is more expensive; however, the decreasing costs of technology adoption implies that eventually all firms will adopt the high-tech process. Production using the high-productivity technology is defined by l(t) = y(t)/φ, where φ > 1.

339

ð5Þ

Define b as the total shipping costs (freight costs plus any ad-valorem tariff barriers) of exporting to the home country and bf as the total shipping costs of exporting to the foreign country. Likewise, let [0,nq] be the range of firms that have adopted the high-productivity technology in the home country, where n is the number of home firms and q is between 0 and 1 and represents the fraction of home firms that have already adopted at a point in time. Let nf and qf have analogous interpretations

8 These assumptions on the behavior of X(t) are standard in the literature; see for example Fudenberg and Tirole (1985). Also see Saggi and Lin (1999) which motivates similar assumptions in an FDI setting. The assumption that adoption costs are bounded from below is made for expositional clarity so as to avoid late entry (i.e., entry after the last firm adopts).

An equivalent condition holds for adoption by foreign firms. This first-order condition demonstrates the tradeoff faced by firms in the choice of when to adopt. The left-hand side term is the gain in profits from adopting the high productivity technology while the right-hand side term gives the decrease in adoption costs from delaying adoption another period. Substituting Eqs. (6) and (7) into the profit functions (and dropping the time subscripts for notational convenience) it is direct to derive that:

πH −πL ¼

  " φσ −1 −1 E σ

bf1−σ 1 þ nq^ h þ nf q^ f b1−σ nf q^ f þ nq^ h b1−σ f

#

  where q^ i ¼ 1 þ φσ −1 −1 qi . Note that the profit differential (πH − πL) is decreasing as the number of firms producing with the high-tech production process (q) increases. This is because adoption by rival firms reduces the market share of other firms and, thus, the gain to adopting a cost-saving innovation. It is this property of the model that leads to the gradual diffusion of the new technology through the industry as the initial adoption by the early-adopting firms delays adoption by

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the remaining firms. By substituting the derived profit differentials into the first-order condition (for both home and foreign firms), one can solve for the Nash equilibrium: the equilibrium diffusion path in both the home (q ∗(t)) and foreign (qf∗(t)) countries9: 8 0 for t ∈ ½0; T L Þ >  1−σ > > 1−σ > < −rt 1 þ b b −2b f −e E 1   − σ−1 q ðt Þ ¼ for t ∈ ½T L ; T H    ′ > 1−σ 1−σ ð t Þnσ X −1 φ > 1−b 1−b > f > : 1 for t ∈ ðT H ; ∞Þ ð10Þ h  8 > for t ∈ 0; T fL > >0 >  1−σ > > > < h i −2b1−σ f −e−rt E 1 þ bf b 1    − σ −1 qf ðt Þ ¼ for t ∈ T fL ; T fH :   ′ > 1−σ 1−σ X ðt Þnf σ 1−b −1 φ > 1−bf > > >   > > f :1 for t ∈ T H ; ∞ ð11Þ As shown in Götz (1999), the equilibrium distribution function, q(t), is a Nash equilibrium distribution as it: (i) results in equivalent profits for all firms on dates where density is positive and (ii) results in lower profits on dates with zero density. This is the usual condition for a Nash equilibrium as it implies that the equilibrium strategy of any firm is not dominated by another strategy. Note that the equilibrium derived is one in which the rate of adoption during the diffusion phase results in all firms making the same profits (i.e., while the timing of adoption of an individual firm is not uniquely determined, the fraction of firms that have adopted at any time period is unique).10 The above functions describe the diffusion of the new production process through the industry for each country. Since adoption costs are initially very high, no firm will adopt earlier than TL. However, as adoption costs fall, more firms adopt the new technology so that all firms have adopted the new technology after TH. Finally, for TL ≤ t ≤ TH there exists a mix of low-tech and high-tech firms in equilibrium, and the distribution of firms is defined by q∗(t) and qf∗(t). 2.5. Present value of profits The model can be closed by solving for the equilibrium number of firms in the industry in each country, n and nf. Given perfect foresight, firms will enter the industry until the present value of profits is equal to zero. 11 Since the present value of profits is the same for every firm within a country, it is arbitrary which profit function is used to identify n. The following calculation is done for the last firm to adopt the technology (let TL be the adoption date for the first adopter and TH be the adoption date of the last adopter). Calculating the present value of profits for such a firm, the zero profit condition is given by:     T T Π ¼ ∫ L e−rt πL q ¼ 0; qf ¼ 0 dt þ ∫ H e−rt πL qðt Þ; qf ðt Þ dt 0 T L   ∞ þ∫ e−rt πH q ¼ 1; qf ¼ 1 dt−X ðT H Þ−F ¼ 0:

ð12Þ

TH

An equivalent condition holds for foreign firms. Substituting the respective profit functions into Eq. (12), one derives a zero-profit condition for home firms (П = 0) as a function of n. A straightforward application of the envelope theorem verifies that equilibrium 9

This calculation is conducted under the assumption that the number of firms is positive in each country. 10 Thus, the Fudenberg and Tirole (1985) critique in which preemptive adoption can occur does not apply. 11 Ederington and McCalman (2008) provide a proof that, in the context of this model, all entry occurs at t = 0. Intuitively, the combination of positive per-period profits and rational, forward-looking firms implies that firms have little incentive to delay entry, so all firms enter at t = 0.

profits are declining in n and, thus, n⁎ is defined by where П = 0. Similarly, nf∗ is defined by where П f = 0. These zero-profit conditions along with q ∗(t) and qf∗(t) (defined in Eqs. (10) and (11)) characterize the trade equilibrium. 3. Ad-valorem tariffs and technology adoption In this section we address the question of how the introduction of ad-valorem tariff protections affects technology adoption decisions. 12 First we will look at the unilateral imposition of a tariff and then we will look at the reciprocal imposition of symmetric tariffs. 3.1. Unilateral tariffs and technology adoption First, starting off with an initially symmetric equilibrium where b = bf, consider the case where the home country imposes an additional unilateral tariff on imports from the foreign country (i.e., an increase in b). As can be seen from the discussion in the previous section, the timing of technology adoption decisions is largely a function of the size of the profit differential between high-tech and low-tech firms at the time of adoption. From the profit functions, one can derive that the profit differential at time TL (i.e., when q = 0, qf = 0) is given by: πH −πL ¼

  " σ −1 φ −1 E σ

# 1−σ bf 1 þ : n þ nf b1−σ nf þ nbf1−σ

ð13Þ ∂ðπ −π Þ

From Eq. (13) it is direct to derive that, at time TL, H L > 0. Intu∂b itively, holding the number of firms constant, the direct impact of such a tariff will be to increase the market-share of home firms (while decreasing the market-share of foreign firms in the home country). The expanded scale accruing to domestic firms from protection would increase their incentive to adopt cost-saving innovations (i.e., they are more willing to pay a fixed adoption cost in order to reduce their marginal costs of production). It is direct to see from the first-order condition (9), that the increased profit differential to adoption when q = 0 and qf = 0 results in TL occurring earlier. Similar calculations reveal that TH occurs earlier as well. Thus, we can state Proposition 1 13: Proposition 1. Without free entry, the unilateral imposition of an ad-valorem tariff by the home country increases the speed of technology diffusion by domestic firms (i.e., both TL and TH occur earlier for the home country). However, countering this direct effect is the fact that a home tariff encourages the entry of new firms into the home market, endogenously increasing the number of home firms. The increase in the number of home firms would in turn decrease the market share of each individual home firm and thus tend to reduce the incentives for adoption. We refer to the ability of tariffs to impact entry and exit decisions as the indirect effect of a tariff change, and, as we show in the following proposition, for an ad-valorem tariff the indirect effect completely cancels out the direct effect. That is, starting from a case of initial symmetry, a unilateral increase in the ad-valorem tariff by the home country will not affect the adoption decisions of either home or foreign firms: Proposition 2. With free entry, the unilateral imposition of an ad-valorem tariff by the home country has no effect on the speed of technology diffusion 12 Since the focus of our paper is on the effect of trade protection on technology adoption, in the interests of simplicity we will ignore tariff revenue (and any differences between tariffs and quotas in the potential generation of government revenue). Note that, from the point of view of the firm, a governmental trade barrier (which generates government revenue) and a generic trade cost are equivalent and thus, for the purposes of calculating their effects on technology adoption, we treat them as equivalent. 13 A similar result to Proposition 1 can be found in Miyagiwa and Ohno (1995) and Crowley (2006). Both papers employ an oligopolistic framework in which the number of firms is automatically held constant.

J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

by either home or foreign firms (i.e., an increase in b will not impact either TL or TH for either the home or the foreign country). Proof. See Appendix A.1. Proposition 2 is the result of the ad-valorem nature of our tariff which ensures that the relative price of high-tech versus low-tech firms is unchanged in both the foreign and domestic markets. Given constant relative prices, an ad-valorem tariff only affects technology adoption by influencing the overall size of the firm. However, the zero-profit condition and the first-order condition for optimal adoption ensure that firm profits and output are also constant and, thus, an ad-valorem tariff has no effect on the adoption decisions of either home or foreign firms. 14 Given that a unilateral tariff does not impact technology diffusion in either the home or the foreign country, one would intuitively expect a similar result for the reciprocal imposition of import tariffs by both the home and the foreign country (i.e., b = bf). As we derive in the following section, this intuition is correct. 3.2. Symmetric tariffs and technology adoption Assume both countries impose a symmetric ad-valorem tariff on imports (i.e., b = bf). Substituting Eqs. (6) and (7) into the profit functions, Eq. (8), and analyzing at the symmetric equilibrium, one derives that profits for high-tech and low-tech firms (in both countries) are given respectively by:

πH ¼

φ

σ−1

E 1 E ; πL ¼ σ −1 : þ ð1−qÞ nσ þ ð1−qÞ nσ qφ

ð14Þ

341

4. Quotas and technology adoption In this section we address the issue of tariffication (i.e., the conversion of quotas and other non-tariff barriers into ad-valorem tariffs). Tariffication was a major negotiating point in the Uruguay Round of GATT, where the main objective was to make border protection more transparent and, hence, facilitate future negotiations. We argue in this section that an unnoticed benefit of tariffication is its potential to facilitate dynamic productivity improvements. First, we examine the effect that an import quota imposed at time t = 0 has on the speed of technology adoption. Assume that, at time t, firm i is allocated Q(i,t) number of quota licenses. Note that while the profit-maximizing price for the firm in its domestic market is still given by Eq. (4), the profit-maximizing price for the firm in the foreign market satisfies the following constrained maximization: max½pði; t Þ−cði; t Þyði; t Þ þ λi;t ½Q ði; t Þ−yði; t Þ

ð15Þ

where c(i,t) is the marginal cost of good i in year t and λi,t represents the shadow cost of the quota constraint (i.e., the extra profit that would be generated by relaxing the quota constraint one unit). Assuming that this quota is binding, from the first-order condition of the above maximization one can derive that prices in the foreign market for low-tech and high-tech firms respectively are: F

pL;t ¼

   σ  σ b F b þ λL;t ; pH;t ¼ þ λH;t : ðσ−1Þ φ σ−1

ð16Þ

We do not claim that the above propositions are a complete description of the effects of tariffs on the diffusion of new technologies. Indeed, it should be apparent that different assumptions about the demand or cost structure of the economy could allow tariffs to have a non-negligible impact on adoption decisions.16 However, they will serve as a useful benchmark to compare the relative effects of ad-valorem tariffs to quotas. Specifically, in the following sections we analyze the question of whether, given conditions where ad-valorem tariffs are an ineffective means of affecting adoption decisions, quantitative restrictions on trade could have a different effect.

Thus, the introduction of an import quota (or a voluntary export restraint) acts in the same way as a specific price increase, not a proportional price increase. To discuss the full implications of a quota regime on the diffusion of new technologies we must make some assumptions about the allocation of quota licenses. Specifically, we assume that a perfectly competitive market for quota licenses exists in which the licenses can be traded.17 Given this assumption, the price of a quota license (and thus the shadow price of the quota constraint) will be equalized over all firms at any point in time (i.e., λL,t = λH,t = λt). In addition, for reasons of expositional simplicity and consistency, we consider the case where the home country imposes a quota on foreign imports, but adjusts the number of quota licenses over time so that the marginal cost of the quota remains constant. Typically in administering quota systems, the number of quota licenses is adjusted over time in response to changes in demand and supply conditions. In addition, many quota systems provide additional flexibility by allowing firms to transfer quota licenses intertemporally.18 Thus, in this section, we assume that the number of licenses available increases as aggregate supply in the industry grows due to technological diffusion. We make this assumption for two reasons. First, as stated previously, it mimics a realistic quota system in which the quota level is adjusted to changing market conditions. Second, it allows for a more direct comparison between a tariff system (where the marginal cost is automatically time-invariant) and the quota system. In Appendix B, we show that results are similar if one assumes the volume of quota licenses is held constant over time. Operationally, given this assumption, the price of a quota license (and thus the shadow price of the quota constraint) will be equalized over

14 An interesting corollary to the proposition below is that foreign firms, despite having different costs, are equal in size to home firms. This is due to the fact that it is the number of firms, n, not the size of individual firms, which adjusts to ensure that the zero-profit condition is satisfied. This is a standard feature of models with monopolistic competition and CES preferences; see e.g. Krugman (1980). 15 The invariance of profits to symmetric ad-valorem tariffs also implies that asymmetric multilateral trade liberalization will behave similar to the case of unilateral trade liberalization. 16 Indeed, in Ederington and McCalman (2008) we provide a model in which the imposition of ad-valorem tariffs can affect the rate of technology adoption.

17 This assumption has no impact on the baseline results of the paper that quotas tend to reduce the speed of technology adoption. Indeed, as we show in the appendix (Section A.1), the rate of technology adoption is reduced even further when quota licenses are symmetrically distributed to firms and cannot be transferred. Intuitively, fixed, non-transferable quota licenses deter adoption as they prevent adopting firms from expanding the scale of their production. 18 For example, see the European Union's quota system for imports of clothing, footwear and steel (available at http://trade.ec.europa.eu/sigl). In that system, not only are the quota levels adjusted from year to year, but there are additional flexibility provisions which allow quota licenses to be transferred intertemporally.

qφ

σ −1

Note from Eq. (14) that symmetric ad-valorem tariffs do not impact the profit functions and thus do not affect the profit differential from adopting new technologies. The invariance of profits to reciprocal ad-valorem tariffs implies that such tariffs do not affect the equilibrium rate of technology diffusion (even when the equilibrium number of firms is held constant).15 This result is due to the fact that, the increase in domestic market share generated by the domestic tariff is countered by the loss of foreign market share due to the foreign tariff. Thus, we can state the following proposition: Proposition 3. The imposition of a symmetric ad-valorem tariff by both the home and the foreign country has no effect on the speed of technology diffusion (with or without free entry).

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all firms over time (i.e., λL,t = λH,t = λ). Thus, while prices of domestic firms are unchanged, and defined by Eq. (4), prices of foreign firms in the domestic market are now defined by: F pL

  σ σ b F ðb þ λÞ; pH ¼ þλ : ¼ σ −1 ðσ−1Þ φ

ð17Þ

Note that the presence of a binding quota affects the relative price of high-technology versus low-technology firms in the foreign market. Specifically, as the shadow price of the quota increases, the relative price of the two firms tends toward equality (i.e., the high-technology firms lose their relative price advantage overseas). It should be apparent that this reduction in the price advantage for high-technology firms will have a disproportionately negative impact on their overseas operating profits. We analyze the implications of this result in the following two sections when first we look at the unilateral imposition of a quota and then we look at the reciprocal imposition of a quota. 4.1. Unilateral quotas and technology adoption Given symmetric iceberg transport costs (b = bf), the profits for a home firm are defined by Eq. (8). However, now the price index in the home country is given by: nþnf

∫

0

pði; t Þ1−σ dz   σ −1     σ 1−σ  b ¼ qφσ −1 þ ð1−qÞ n þ qf þ 1−qf ðb þ λÞ1−σ nf þλ σ −1 φ

ð18Þ while the price index in the foreign country is given by: nþnf

∫

0

pf ði; t Þ1−σ dz   1−σ     σ 1−σ  b qf φσ −1 þ 1−qf nf þ q þ ð1−qÞb1−σ n : ¼ σ−1 φ

ð19Þ Note that a unilateral quota by the home country affects home firms by increasing the prices of their foreign competitors (and thus increases the domestic market share of home firms). As with the ad-valorem tariff, this increase in market share corresponds to an increased incentive to adopt the cost-saving technology: Proposition 4. Without free entry, the unilateral imposition of an import quota by the home country increases the speed of technology diffusion by domestic firms (i.e., both TL and TH occur earlier for the home country). Proof. Let λ be the marginal cost of the quota constraint. From the profit functions, one can derive that the profit differential at time TL (i.e., when q = 0, qf = 0) is given by:

πH −πL ¼

  " φσ −1 −1 E σ

# 1 b1−σ þ : n þ nf ðb þ λÞ1−σ nf þ nb1−σ

From Eq. (20) it is direct to derive that, at time TL,

ð20Þ

increases the rate of diffusion so that the final adoption date occurs earlier. Proposition 5. With free entry, the unilateral imposition of a time-varying quota by the home country results in the initial adoption by home firms, TL, occurring later, but the last adoption, TH, occurring earlier. Proof. See Appendix A.2. Proposition 5 requires more discussion as it may appear counterintuitive that a quota regime will result in faster adoption at the point in time when the number of quota licenses are the most numerous (i.e., at the end of the diffusion phase) and slower adoption at the point in time when the quota is the most restrictive (i.e., at the beginning of the diffusion phase). However, Proposition 5 simply reflects the fact that, even if the marginal cost of a quota license is being held constant over time, the overall protectionist impact of the quota system is increasing over the diffusion phase. Specifically, recall that a quota has a greater impact on high productivity firms than low productivity firms (as it reduces their cost advantage overseas). Correspondingly, a quota regime has a greater protectionist impact at the end of the diffusion phase (when foreign firms are high-tech) than at the beginning of the diffusion phase (when foreign firms are low-tech). As a result, since the direct effect of the quota increases over time, it reduces incentives to adopt at the beginning of the diffusion phase, while increasing incentives to adopt at the end of diffusion. Of course, a second question of interest is how the unilateral imposition of a quota by the home country impacts the technology adoption decisions of foreign firms. Not surprisingly, given the intuition of the model, a quota, which reduces the competitive cost advantage of high-tech firms overseas, delays the adoption of new technologies by foreign exporting firms. Specifically, starting from a case of initial symmetry, the unilateral imposition of a quota by the home country will delay both TL and TH in the foreign country: Proposition 6. With free entry, the unilateral imposition of a quota by the home country results in delayed adoption by foreign firms (i.e., both TL and TH occur later for the foreign country). Proof. See Appendix A.3. Proposition 6 reflects the fact that a quota delays the adoption of cost-saving technologies by foreign firms since the benefits of such technology adoption are diminished. In this sense, it is instructive to compare Propositions 5 and 6 (that concern the impact of a unilateral quota) with Proposition 2 (that concerns the impact of a unilateral tariff). As can be seen, allowing endogenous entry and exit decisions, governments have no ability to influence the rate of technology adoption by unilaterally imposing ad valorem tariff protection. However, governments can influence the rate of technology adoption (by both domestic and foreign firms) by unilaterally imposing a comparable quota. In the next section we consider the case where both countries impose a symmetric quota on imports. 4.2. Symmetric quotas and technology adoption

∂ðπH −πL Þ ∂λ

> 0.

Thus, TL occurs earlier. Similar calculations reveal that TH occurs earlier as well. Q.E.D. However, given endogenous entry and exit decisions, such a change in market share results in corresponding changes in the number of home (and foreign) firms. The question is whether, as was the case for the ad-valorem tariff, these indirect effects cancel out the direct effect. As we show in the following proposition, they do not. Specifically, starting from a case of initial symmetry, a unilateral imposition of a quota by the home country delays the date of initial adoption but

In this section, we consider the case in which symmetric quotas are placed on trade. In such a situation, profit functions of firms in each country are defined symmetrically. For expositional purposes we will assume the absence of transport costs (i.e., b = 1). The symmetric price index in the open economy equilibrium is then given by: nþnf

∫

0

pði; t Þ1−σ dz  σ 1−σ h    i  qφσ −1 þ ð1−qÞ n þ qf φσ−1 ð1 þ λφÞ1−σ þ 1−qf nf ð1 þ λÞ1−σ : ¼ σ−1

ð21Þ

J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

The symmetry of the model implies that, in equilibrium, q = qf and n = nf. Thus, imposing symmetry between the two countries and substituting Eq. (21) into the profit functions give operating profits (from both domestic and foreign markets) as: σ −1

φ

1−σ

1 þ ð1 þ λφÞ

i 1−σ

E nσ

ð1 þ ð1 þ λφÞ1−σ qφσ −1 þ ð1−qÞð1 þ ð1 þ λÞ1−σ

E nσ

πH ¼ πL ¼

h

σ −1

þ ð1−qiÞð1 þ ð1 þ λÞ ð1 þ ð1 þ λφÞ h qφ 1−σ 1 þ ð1 þ λÞ 1−σ

:

ð22Þ

Substituting the above profit functions into the first-order condition for the adoption decision and solving for q(t), one derives that: 8 0 > h i > > 1−σ > > 1 þ ð1 þ λÞ < −e−rt E 



 − q ðt Þ ¼ X ′ ðt Þnσ ð 1 þ ð1 þ λÞ1−σ − 1 þ ð1 þ λφÞ1−σ φσ −1 > > > > > : 1

for t ∈ ½0; T L Þ for t ∈ ½T L ; T H  for t ∈ ðT H ; ∞Þ:

ð23Þ We are interested in how this rate of adoption compares to the open-economy rate of diffusion with an ad-valorem tariff. First, note that when λ = 0 the equilibrium rate of diffusion is the same as that in the open-economy cases. Taking the partial of q(t)with respect to λ gives: ∂qðt Þ ∂λ

j

λ¼0

h i σ σ−1 2ð1−σ Þ φ −φ ¼ b 0 for T L ≤ t ≤ T H :  2 4 1−φσ −1

ð24Þ

So holding n constant, the imposition of symmetric quotas by each country decreases the speed of technology adoption below that of the open economy case (i.e., at any time TL ≤ t ≤ TH a smaller fraction of firms will have adopted the new technology). This implies that the presence of a quota regime slows the rate of technology diffusion relative to an ad-valorem tariff regime. The reason is simple. Specific transport costs change the relative prices of the differentiated good in favor of the low technology (high cost) firms in the foreign markets, reducing the relative profitability of the high technology firms and the incentive to adopt the new technology. Note that this is in contrast to the reciprocal ad-valorem tariff case where, even when the number of firms was held constant, reciprocal tariffs had no impact on profit differentials and, thus, the equilibrium rate of adoption. While the preceding analysis held the number of firms in the industry constant, the imposition of reciprocal quotas is also likely to have an impact on the number of firms in an industry. Thus, in deriving the complete impact of a quota regime on the rate of technology adoption, we must also take into account its indirect effect (i.e., how it may affect q(t) indirectly through n). However, as we verify in the following proposition, even allowing n to be endogenous, it is still the case that the presence of reciprocal quotas reduces the rate of technology adoption. Proposition 7. With free entry, the reciprocal introduction of a quota will delay the adoption of new cost-saving technologies (i.e., both TH and TL will occur later for both countries). Proof. See Appendix A.4. Propositions 3 and 7 have a direct implication for the question of tariffication in international trade agreements. Assume two open economies impose symmetric quotas on each other. The above propositions imply that a reciprocal trade agreement to convert these quota constraints into equivalent ad-valorem tariff constraints will increase the rate of technology adoption in both countries. Thus, this paper implies that the preference in GATT/WTO negotiations for the conversion on non-tariff barriers into tariff barriers actually has a potential dynamic

343

rationale in that it tends to have a positive effect on the diffusion of new technology. 4.3. Welfare implications of technology adoption The final issue addressed in this paper is the welfare implications of the above result. It is well-known that in imperfectly and monopolistically competitive markets the welfare ranking of tariff and quota protection is a complex issue with ambiguous results (see e.g., Helpman and Krugman (1989), Miyagiwa and Ohno (1995), Collie and Su (1998) and (Jorgensen and Schröder (2005)). Thus, in this section we do not attempt a full welfare ranking of the different policy instruments or attempt to calculate optimal policies. However, it is possible to derive an unambiguous welfare ranking with respect to the effect of protection on technology diffusion (what Miyagiwa and Ohno (1995)) refer to as the indirect welfare effect). Specifically, as we show in the following proposition, reciprocal tariff protection results in a technology diffusion path closer to the socially efficient diffusion path than does reciprocal quota protection: Proposition 8. The diffusion path with reciprocal tariff protection, q τ(t) is closer to the constrained socially-efficient diffusion path, q s(t), than is the diffusion path with reciprocal quota protection q λ(t). That is qs ðt Þ ¼ qτ ðt Þ ¼

−e−rt X ′ ðt Þnσ

!

σ 1 − σ −1 φσ −1 −1

! −e−rt 1 − σ−1 X ′ ðt Þnσ φ −1

h i 1 þ ð1 þ λÞ1−σ −e−rt E λ 

 q ðt Þ ¼ ′ −

X ðt Þ n˜ σ 1 þ ð1 þ λÞ1−σ − 1 þ ð1 þ λφÞ1−σ φσ−1

ð25Þ

where q s(t) ≥ q τ(t) ≥ q λ(t). Proof. See Appendix A.5. The intuition behind the above proposition is direct. As we derive in the proof to Proposition 8, the rate of technology diffusion in the market equilibrium is slower than is socially optimal since firms do not fully appropriate the social gains to adopting new technologies (note that a portion of the gains are shared with consumers in the form of lower prices). Thus, since the reciprocal tariff rate of technology diffusion is equal to the market rate, it is direct to show that reciprocal tariff protection is slower than would be socially efficient (i.e., qs(t) ≥ qτ(t)). However, as we show in Proposition 7, reciprocal quota protection delays the process of technology adoption even longer resulting in an equilibrium rate of diffusion further from what would be socially optimal (i.e., qs(t) ≥ qτ(t) ≥ qλ(t)). Thus, with respect to the impact of trade protection on technology diffusion, the welfare ranking is unambiguous: reciprocal tariff protection is superior to reciprocal quota protection. 5. Conclusion This paper has examined the linkage between policy instruments and the speed at which firms adopt a cost-saving innovation. We argue that the form of trade barriers has important implications for this question. Specifically, while ad-valorem tariffs have a neutral effect on technology adoption, non-tariff barriers such as import quotas tend to delay adoption of new cost-saving technologies. This is due to the fact that, since a quota constraint has effects similar to a specific price increase, the imposition of quota protection changes relative prices in favor of high cost firms and thus tends to delay the adoption of new, productivity-improving technologies. This result has important policy implications since it implies that the conversion of current non-tariff barriers into equivalent ad-valorem tariffs (i.e., tariffication) has a positive impact on the diffusion of new cost-saving technologies.

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Note that the basic intuition behind our story is that quotas have a disproportionately negative impact on low-price (low-cost) differentiated product goods in overseas markets. In this paper we concentrate on the adoption of a cost-improving technology to clarify the link between a country's trade barriers and firm/industry productivity. However, it should be apparent that this story does not translate to the case of a quality-improving technology since higher quality goods tend to be correlated with higher prices. Notice that, in this case, there might be a positive effect to reciprocal quota protection on the adoption of quality-improving technologies (at least to the extent that the quality improvement results in higher prices and not simply in greater scale). Our findings also suggest that distinguishing between tariffs and quotas is important in understanding the effects of trade barriers on technology adoption and firm productivity. It is common in the empirical literature on trade liberalization and productivity to use time dummy variables to capture episodes of trade liberalization (e.g., see Harrison (1994), Krishna and Mitra (1998), and Pavcnik (2002)). While this approach is intuitively attractive, it has the unfortunate side effect of lumping together quotas and tariffs in estimating the productivity effects of trade liberalization. One of the implications of our paper is that the effect of changes in tariff protection on productivity growth is different from the effect of a change in quota protection since the policy instruments affect the decision to adopt new cost-saving innovations differently. Thus, our findings suggest a benefit in distinguishing between quota protection and tariff protection in attempts to estimate the productivity effects of trade barriers. In this sense, it is instructive that empirical studies which do disaggregate trade protection into tariffs and non-tariff barriers (specifically Lee (1996) and Kim (2000)) find that reductions in quotas have much larger effects on total factor productivity than do equivalent reductions in tariffs. Appendix A

and taking derivatives one can cancel out lines 3 and 4. Using the first-order condition, and evaluating the derivatives, one can cancel out line 5. Thus one derives     T T dΠ ¼ δ0 dπ0 þ ∫T L dπL q; qf e−rt dt þ ∫T H dπH q; qf e−rt dt þ δ1 dπ1     T T −rt −rt þ∫T L dπL q ¼ 0; qf ðt Þ e dt þ ∫T HH dπH q ¼ 1; qf ðt Þ e dt: L

However, note that the symmetry of the initial equilibrium implies that the second line is zero (i.e., in the symmetric equilibrium TL∗ = TL and TH∗ = TH prior to the imposition of the tariff), which gives us:     T −rt T −rt dΠ ¼ δ0 dπ 0 þ ∫ dπL q; qf e dt þ ∫ H dπH q; qf e dt þ δ1 dπ 1 : ð26Þ TL

From the profit conditions, Eq. (8), one derives that the profit differential for a firm is given by:   σ −1 πH −πL ¼ φ −1 πL :

  πL q ¼

    T −rt π L q ¼ 0; qf ðt Þ dt þ ∫T L e πL qðt Þ; qf ðt Þ dt L     T T þ∫T H e−rt πH qðt Þ; qf ðt Þ dt þ ∫T HH e−rt π H q ¼ 1; qf ðt Þ dt T

−rt

Π ¼ δ0 π0 þ ∫T L e

þδ1 π1 −e

−rT

Note, the above expression assumes that TL∗ ≤ TL and TH∗ ≥ TH, which is satisfied given our assumption of symmetry across countries (i.e., in the symmetric equilibrium TL∗ = TL and TH∗ = TH prior to the imposition of the tariff). The total differential is equal to:     T −rt T −rt dΠ ¼ δ0 dπ 0 þ ∫T L dπ L q; qf e dt þ ∫T H dπ H q; qf e dt þ δ1 dπ 1     TL −rt T H −rt þ∫T  dπ L q ¼ 0; qf ðt Þ e dt þ ∫T H dπ H q ¼ 1; qf t e dt L     T −rt dT  −rt þdδ0 π0 þ ∫dTL  π L q ¼ 0; qf e dt þ ∫T HH π H q ¼ 1; qf e dt L

dT

−rt

T

−rt

dT

−rt

dt

Note that lines 3–5 account for changes in TL, TL∗, TH, TH∗ and T holding instantaneous profits constant, while lines 1 and 2 account for the impact of the change in the instantaneous profit functions holding adoption dates constant. Using δ0 π 0 ¼

  1−e−rT L π L ð0Þ r

and δ1 π1 ¼

ð28Þ

    T −rt T −rt ∫ πL q; qf e dt þ ∫T H π H q; qf e dt 1 ½X ðT L Þ−X ðT H Þ−X ðT H Þ: φσ −1 −1

ð29Þ

Note that profits during the diffusion phase are completely independent of b. Since πH(q = 1, qf = 1) = πL(q = 0, qf = 0), δ0π0 and δ1π1 are proportional (i.e., their derivatives with respect to policy must have the same sign). Since the differential in the present value of profits must equal zero in equilibrium, from Eq. (32): δ0 dπ 0 δ1 dπ1 ¼ ¼ 0: db db

X ðT Þ−F 0 ¼ 0:

þdδ1 π 1 þ ∫T  L π L ðqÞe dt þ ∫dT L π L ðqÞe dt þ þ∫T H π H ðqÞe  L   T −rt dT −rt þ∫dTH π H q ¼ 1; qf e dt þ ∫T L π L ðqÞe dt H   T −rt −rT þ∫dTH π H ðqÞe dt−d e X ðT Þ :

  1 −X ′ ðT Þ φσ −1 −X ′ ðT Þ ; π H q ¼ σ−1 φ −1 e−rT φσ−1 −1 e−rT

which implies that:

¼

Assume we begin in the symmetric equilibrium where b = bf. Let ⁎ denote the foreign country. Note that the zero profit condition for a domestic firm that adopts at T ∈ [TL,TH]:

ð27Þ

Thus, during the diffusion phase, the first-order condition, Eq. (9) fixes low-tech profits and thus high-tech profits at:

TL

A.1. Proof of Proposition 2

T



e−rT H πH ð1Þ r

ð30Þ   dπ L q ¼ 0; qf ¼ 0

δ0 dπ0 db

¼ 0 implies that i

 h  δ0 π0 ¼ 1−e−rT L =r πL q ¼ 0; qf ¼ 0 . Thus, from

Finally, note that

     d π H q ¼ 0; qf ¼ 0 −π L q ¼ 0; qf ¼ 0 db

db

Eq.

¼ 0 as

(27),

¼ 0. Since an ad-valorem tariff has

no impact on the profit differential prior to the diffusion phase (i.e., before TL), it will have no impact on the timing of TL. The fact that ad valorem tariffs do not affect TH is similarly established. Thus, the unilateral imposition of an ad-valorem tariff by the home country will not affect either TL or TH (i.e., the speed of technology diffusion). With respect to the effect of a home tariff on the adoption decisions of a foreign firm, note that profits for a foreign firm, given a home tariff of b, are given by:

π Lf ðt Þ ¼

ðσσ−1Þ1−σ b1−σ E σ∫

nþnf

0

π Hf ðt Þ ¼

σ

pði; t Þ1−σ dz

1−σ

ðσ −1Þ σ∫

nþnf

0

σ −1 1−σ

φ

b

þ

ðσσ−1Þ1−σ E nþnf

σ∫

0

E

pði; t Þ1−σ dz

þ

pf ði; t Þ1−σ dz

ðσ−1Þ1−σ φσ −1 E σ

σ∫

nþnf

0

pf ði; t Þ1−σ dz

:

ð31Þ

J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

From these the profit differential for a foreign firm is given by: πHf −πLf

  σ −1 ¼ φ −1 π Lf :

ð32Þ

Canceling out terms and applying the envelope condition, one can derive the equivalent of Eq. (26) for the foreign firm and the remainder of the proof is equivalent to that given above for the home firms. Q.E.D.

dΠ ¼ δ0 dπ 0 þ δ1 dπ1 ¼ 0:

ð33Þ

However, given the presence of a quota, πH(q = 1, qf = 1) > πL(q = 0, qf = 0) for home firms (reflecting the increased protectionist impact of the quota over the diffusion period). Thus, δπ0 is not proportional to δπ1     dπ H q ¼ 1; qf ¼ 1 dπ L q ¼ 0; qf ¼ 0 and, since > , from Eq. (33) it dλ

dλ

λ¼0

implies that TL is delayed, similar calculations show that

dλ δ1 dπ 1 > 0 imdλ

plies that TH will occur earlier. Q.E.D.

T

TL

ð35Þ Note that profits for a foreign firm in both the foreign country market, πf ∗, and the home country market, πh ∗ are given by: ðσσ−1Þ1−σ ðb þ λÞ1−σ E nþnf

σ∫ ðσ −1

pði; t Þ

1−σ

σ Þ1−σ E ðσ−1

f

; πL ðt Þ ¼

pði; t Þ1−σ dz 0 σ Þ1−σ φσ −1 ðb þ λφÞ1−σ E 0

dz

σ∫

nþnf

0

f

; πH ðt Þ ¼

pf ði; t Þ1−σ dz ðσσ−1Þ1−σ φσ−1 E σ∫

nþnf

0

pf ði; t Þ1−σ dz

    σ −1 f πH ðt Þ−πL ðt Þ ¼ φ −1 πL ðt Þ φσ −1 ðb þ λφÞ1−σ −ðb þ λÞ1−σ h π L ðt Þ: ðb þ λÞ1−σ

ð37Þ

Note that, from the first-order condition for optimal adoption,

  d π H −π L dλ

dλ

b0 which implies that

one can derive that



λ¼0

dπ H

, from Eq. (38) it must be the case

  q ¼ 1; qf ¼ 1



b0. Thus, from Eq. (37),

λ¼0 dλ      d π H q ¼ 1; qf ¼ 1 −π L q ¼ 1; qf ¼ 1



dλ

λ¼0

b0 which implies

  dπ H q ¼ 1; qf ¼ 1



λ¼0

dλ

b 0,one

can derive that

     d πH q ¼ 0; qf ¼ 0 −πL q ¼ 0; qf ¼ 0 dλ



λ¼0

b0

which implies that TL occurs later as well. Q.E.D. A.4. Proof of Proposition 7 As in the proof to Proposition 2, totally differentiating the zero profit condition, canceling out terms and applying the envelope condition, one derives Eq. (26). From the profit conditions for reciprocal quotas, Eq. (22), one derives that the profit differential is given by: h i 1−σ 1 þ ðb þ λφÞ

1 þ ðb þ λÞ1−σ πL ðt Þ:

ð39Þ

Thus, during the diffusion phase, the first-order condition fixes low-tech profits at: ð1 þ ðb þ λÞ1−σ −X ′ ðt Þ

   φσ −1 1 þ ðb þ λφÞ1−σ − 1 þ ðb þ λÞ1−σ e−rt

πL ðt Þ ¼

ð40Þ

σ −1

φ

ð1 þ ðb þ λÞ

   ½X ðT L Þ−X ðT H Þ−X ðT H Þ 1 þ ðb þ λφÞ1−σ − 1 þ ðb þ λÞ1−σ

ð41Þ     T T −rt −rt where Π 2 ¼ ∫T L dπL q; qf e dt þ ∫T H dπH q; qf e dt. From the dΠ 2 above it is direct to derive that λ¼0 > 0. Since δ0π0 and δ1π1 are dλ

δ0 dπ0 δ dπ b 0 and 1 1 b 0. dλ dλ δ dπ dπ ðq ¼ 0Þ Finally, note that 0 0 b0 implies that L ¼ 0 . Thus, from λ¼0 dλ dλ dðπH ðq ¼ 0Þ−π L ðq ¼ 0ÞÞ Eq. (39), one can derive that b 0 which implies λ¼0 dλ δ dπ that TL occurs later. Similar calculations show that, since 1 1 b 0, TH dλ

proportional, from Eq. (26), one derives that

will occur later as well. Q.E.D. : ð36Þ

Thus, the profit differential for a foreign firm is given by:

þ

  dπ L q ¼ 0; qf ¼ 0

1−σ

       T  −rt T  −rt   dΠ ¼ δ0 dπ0 þ ∫  dπL q; qf e dt þ ∫ H dπH q; qf e dt þ δ1 dπ1 ¼ 0:

σ∫

λ¼0

b

that TH occurs later. Finally, using Eq. (37) and the fact that

Π2 ¼

Once again, let ⁎ denote the foreign country. As in the proof to Proposition 2, totally differentiating the zero profit condition, canceling out terms and applying the envelope condition, one derives that:

nþnf

dλ



which implies that:

A.3. Proof of Proposition 6

π h H ðt Þ ¼

that

δ1 dπ1

ð34Þ

in the time periods preceding diffusion, which implies that the diffuδ dπ sion phase will be delayed (i.e., TL will occur later). Just like 0 0 b0

h π L ðt Þ ¼

ð38Þ

σ −1

  dπ L q ¼ 0; qf ¼ 0 δ0 dπ0 b0. Thus, dðπH −πL Þ b0 b0 implies that Finally, λ¼0 λ¼0 dλ dλ dλ

> 0 during diffusion which implies,

Given the presence of a quota, πH∗ (q = 1, qf = 1) b πL∗(q = 0, qf = 0) for foreign firms, and thus δ∗π0∗ is not proportional to δ∗π1∗ . Since

φ πH ðt Þ−πL ðt Þ ¼ 

δ0 dπ 0 δ dπ b 0 and 1 1 > 0: dλ dλ

λ¼0

δ0 dπ 0 δ1 dπ1 þ b0: dλ dλ

λ¼0

must be the case that:



dλ

from Eq. (35) that:

dλ

As in the proof to Proposition 2, totally differentiating the zero profit condition, canceling out terms and applying the envelope condition, one derives Eq. (26). From the profit conditions, one finds that πH − πL = (φ σ − 1 − 1)πL. Thus, by similar reasoning as that in the proof to Proposition 2, one derives that profits during the diffusion phase are completely independent of λ and:

  f d π h L þ πL

can derive that

  dπ H q ¼ 1; qf ¼ 1

A.2. Proof of Proposition 5

345

¼ 0, during the diffusion phase. Thus, from Eq. (37), one

A.5. Proof of Proposition 8 Assume the social planner takes the number of firms and their pricing behavior as given (i.e., we restrict ourselves to solely considering the welfare impact of trade barriers on technology diffusion). In that case, the free-trade equilibrium is defined by Eqs. (1), (2), (3), (4) and (6) defined where b = bf = 1. Substituting Eqs. (4) and (6) into Eq. (3), the demand for low and high tech goods can be rewritten as: ρ yL  ; yH ¼ σ −1 yL ¼  σ−1 : þ ð1−qÞ n ϕ qφ

ð42Þ

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J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

Using Eq. (2), the index for the differentiated sector can be written as:

ρ ρ 1 C ðt Þ ¼ nð1−qðt ÞÞyL þ nqðt ÞyH h i1 1 σ −1 ¼ ρn qðt Þφ þ ð1−qðt ÞÞ : ρ

ð43Þ

σ −1

σ−1

which implies:   σ −1 1 −1 e−rt σ−1 φ ∂H ′   þ nX ðt Þ ¼ 0: ¼ ∂qðt Þ qðt Þ φσ−1 −1 þ 1 Solving for q s(t) yields:

This gives an objective function for the social planner of: V ¼∫

∞

0

   h i  σ −1 −rt sðt Þ e dt c0 ðt Þ þ log ρn qðt Þφ þ ð1−qðt ÞÞ 1 σ −1

1 σ−1

ð44Þ

where the social planner chooses c0(t), q(t) and s(t) = the rate of expenditure on the differentiated good in period t. However, expenditure must equal income — which includes net profits. The industry's net profits are given by:   ∞ −rt ∞ ′ n ∫ ½ð1−qðt ÞÞπL ðt Þ þ qðt ÞπH ðt Þe dt−∫ q ðt ÞX ðt Þdt : 0

ð45Þ

0

Note that q′(t) is the fraction of firms that adopt at time t, therefore nq′(t)X(t) is the expenditure on new technology at t. The net profit expression can be simplified in two ways. First note R that πH = ϕσ − 1πL and πL ¼ L . Therefore at any point in time, total σ   R industry profits are: n ϕσ −1 qðt Þ þ ð1−qðt ÞÞ L . Furthermore, RL ¼ σ

sð t Þ nðϕσ−1 qðt Þþð1−qðt ÞÞÞ

s

q ðt Þ ¼

−e−rt X ′ ðt Þnσ

!

σ 1 − : σ −1 φσ −1 −1

From the second order conditions it is direct to show that the Hamiltonian is concave in q(t) ∈ [0,1] and thus the “socially efficient” rate of diffusion represents a maximum with welfare increasing monotonically as the rate of diffusion approaches the “socially efficient” rate. Note that, compared to the reciprocal tariff solution, q τ(t), defined by Eq. (10) where b = bf: τ

q ðt Þ ¼

! −e−rt 1 − σ−1 X ′ ðt Þnσ φ −1

and the reciprocal quota solution, q λ(t), defined by Eq. (23) implies q s(t) ≥ q τ(t) ≥ q λ(t). Q.E.D.

, which implies that at any point in time total industry

profits are:

Appendix B. Non-transferable and time-invariant quotas

sðt Þ . σ

To simplify the adoption cost expression, assume that the social planner chooses beginning and end adoption dates; T1 and T2. Therefore T ′ ∫T 2 q ðt ÞX ðt Þdt 1

T T T ′ ′ ¼ X ðt Þqðt Þ T 2 −∫T 2 qðt ÞX ðt Þdt ¼ X ðT 2 Þ−∫T 2 qðt ÞX ðt Þdt: 1

1

1

This gives the present value of net profits as:   ∞ sðt Þ −rt T ′ e dt−n X ðT 2 Þ−∫ 2 qðt ÞX ðt Þdt : ∫ T1 0 σ Therefore the budget constraint can be written as:   sðt Þ −rt T ′ ∞ −rt e dt−n X ðT 2 Þ−∫ 2 qðt ÞX ðt Þdt ¼ ∫ ðc0 ðt Þ þ sðt ÞÞe dt T1 0 σ   ∞ ð1−σ Þsðt Þ −rt T ′ ∞ −rt e dt−n X ðT 2 Þ−∫ 2 qðt ÞX ðt Þdt −∫ c0 ðt Þe dt ¼ 0: ⇒I þ ∫ T1 0 0 σ ∞ 0

Iþ∫

The constrained optimization program is then:    ∞ ð1−σ Þsðt Þ −rt T ′ ∞ −rt e dt−n X ðT 2 Þ−∫ 2 qðt ÞX ðt Þdt −∫ c0 ðt Þe dt : L¼V þω Iþ∫ 0 0 T1 σ

One particularly useful feature of this program is that c0, s(t) and q(t) are additively separable and therefore maximization can proceed sequentially. −rt

∂L e −rt −ωρe ¼0 ¼ ∂sðt Þ sðt Þ ∂L −rt −rt ¼0 ¼ e −ωe ∂c0 ðt Þ which imply ω = 1 and sðt Þ ¼ ρ1. Using these optimal values the Hamiltonian involving q(t) can be simplified to: H¼

h   i 1 σ−1 −rt ′ log qðt Þ φ −1 þ 1 ÞÞe þ nqðt ÞX ðt Þ σ −1

First, consider the case where Q quota licenses are distributed to each firm and these quota licenses are non-transferable. In that case, assuming the quota binds, each firm sells Q ¼

pði; t Þ−σ E

∫n0 pði; t Þ1−σ dz

units

in the foreign country. From Eq. (16) this implies that in each period: 1 þ λL ¼

1 þ λH : φ

ð46Þ

Note that Eq. (46) implies that symmetric allocated quota licenses impose greater costs on high-tech firms than they do on low-tech firms (i.e., λH > λL). Basically, in this framework, quotas act as a conditional tariff, where the trade tax is increased on those firms which choose to adopt the new technology. Thus, a non-transferable quota results in an even greater delay in adoption than a transferable quota (since firms which adopt the cost-saving technology cannot purchase additional licenses from the low-tech firms). Intuitively this result is not surprising as the main benefit of adopting a productivityimproving technology is that one can sell a greater volume of goods at a lower price (i.e., a scale effect). Thus, quantity constraints (such as a quota) which prevent the expropriation of these scale effects by firms tend to deter the adoption of such technologies in a dynamic setting. Second consider the case where quota licenses are tradable, but where Q represents the per-period quantity of quota licenses provided to firms by the home country and Q is time invariant. Given the presence of a perfectly competitive market for quota licenses the prices of domestic firms will be unchanged and defined by Eq. (4), while prices of foreign firms in the domestic market are defined by Eq. (16) where λL,t = λH,t = λt. Note that a reduction Q results in an increase in λt for any time period t. Given iceberg transport costs of b = bf = b, the profits for a home firm are defined by Eq. (8). However, now the price index in the home country is given by: nþnf

∫0

pði; t Þ1−σ dz  1−σ   σ 1−σ     b þ λt qφσ −1 þ ð1−qÞ n þ qf þ 1−qf ðb þ λt Þ1−σ nf ¼ σ −1 φ

ð47Þ

J. Ederington, P. McCalman / Journal of International Economics 90 (2013) 337–347

while the price index in the foreign country is given by Eq. (19). As with the time-varying quota it is direct to derive the equivalent of Propositions 4 and 5 for the case of a time-invariant quota: Proposition 9. Holding n and nf constant, the unilateral imposition of a time-invariant import quota by the home country will increase the speed of technology diffusion by domestic firms (i.e., both TL and TH occur earlier). However, with free entry the unilateral imposition of a time-invariant quota by the home country results in the initial adoption by home firms, TL, occurring later, but the last adoption, TH, by home firms occurring earlier. Proof. First, we derive that without free entry the unilateral imposition of a time-invariant import quota by the home country will result in both TL and TH occurring earlier. Let λT L be the marginal cost of the quota constraint prior to technological diffusion (i.e., prior to TL). From the profit functions, one can derive that the profit differential at time TL (i.e., when q = qf = 0) is given by:   2 3 1−σ φσ −1 −1 E 1 b 4 5:  þ πH −πL ¼ σ nf þ nb1−σ n þ nf b1−σ þ λT L From Eq. (48) it is direct to derive that, at time TL,

ð48Þ

∂ðπH −πL Þ ∂λT L

> 0.

Thus, TL occurs earlier. Similar calculations reveal that TH occurs earlier as well. Second, we derive that with free entry the unilateral imposition of a time-invariant quota by the home country results in TL occurring later but TH occurring earlier. As in the proof to Proposition 2, totally differentiating the zero profit condition, canceling out terms and applying the envelope condition, one derives Eq. (26). From the profit conditions, one finds that πH − πL = (φσ − 1 − 1)πL. Thus, by similar reasoning as that in the proof to Proposition 2, one derives that profits during the diffusion phase are completely independent of Q. However, given the presence of a time-invariant quota, δ0π0 and δ1π1 are no longer proportional. Specifically, once again let λT L be the marginal cost of the quota prior to diffusion and λT H be the marginal cost of the quota following diffusion. It is direct to derive that, for the aggregative level of foreign imports to be held constant over time (since the quota is time-invariant), it must be the case that λT H > λT L . However, it can be shown that this increase in the marginal cost of the quota results in the quota increasing home firm profits following diffusion (iH(q = 1, qf = 1)) relative to profits prior to diffusion (πL(q = 0, qf = 0)). Thus, from Eq. (26), it must be the case that: δ0 dπ 0 δ dπ b 0 and 1 1 > 0: dQ dQ Finally,

δ0 dπ0 b0 dQ

implies that

ð49Þ   dπ L q ¼ 0; qf ¼ 0 dQ



λ¼0

b0.

Thus,

dðπH −π L Þ b0 λ¼0 dQ

in

the time periods preceding diffusion, which implies that the diffusion phase will be delayed (i.e., TL will occur later). Just like that TL is delayed, similar calculations show that

δ1 dπ 1 dQ

δ0 dπ0 b0 dQ

implies

> 0 implies that

TH will occur earlier. Q.E.D. Proposition 9 reflects the fact that the marginal cost of the quota is increasing over the diffusion phase. Specifically, recall that the aggregate number of quota licenses is held constant over time. However, as

347

the high-productivity technology diffuses through the industry, production levels and the desired volume of trade will increase. Thus, the quota will have a greater protectionist impact at the end of the diffusion phase than at the beginning of the diffusion phase (i.e., λT H > λT L ). As the direct effect of the time-invariant quota is weaker prior to diffusion and stronger following diffusion, it will reduce incentives to adopt at the beginning of the diffusion phase, while increasing incentives to adopt at the end of diffusion. It should be apparent that the increase in the magnitude of the direct effect over time is a function of the fact that the level of quota licenses is time-invariant even while the desired volume of trade is increasing over time (as technology adoption improves the productivity of firms in the industry). However, as we show in the body of the paper, we derive similar results even when the quota is relaxed over time so the marginal impact of the quota remains constant. References Bhagwati, J., 1965. On the equivalence of tariffs and quotas. In: Baldwin, Robert E., et al. (Ed.), Trade, Growth and the Balance of Payments: Essays in Honor of Gottfried Haberler. Rand McNally, Chicago. Bhagwati, J., 1968. More on the equivalence of tariffs and quotas. American Economic Review 58, 142–146. Collie, D., Su, Y., 1998. Trade policy and product variety: when is a VER superior to a tariff? Journal of Development Economics 55, 249–255. Crowley, M.A., 2006. Do safeguard tariffs and antidumping duties open or close technology gaps? Journal of International Economics 68, 469–484. Ederington, J., McCalman, P., 2008. Endogenous firm heterogeneity and the dynamics of trade liberalization. Journal of International Economics 74, 422–440. Falvey, R., 1979. The composition of trade within import-restricted product categories. Journal of Political Economy 87, 1105–1114. Feenstra, R., 1988. Quality change under trade restraints in Japanese autos. Quarterly Journal of Economics 103, 131–146. Fudenberg, D., Tirole, J., 1985. Preemption and rent equalization in the adoption of new technology. Review of Economic Studies 52, 383–401. Götz, G., 1999. Monopolistic competition and the diffusion of new technology. The Rand Journal of Economics 30, 679–693. Harrison, A., 1994. Productivity, imperfect competition and trade reform: theory and evidence. Journal of International Economics 36, 53–73. Helpman, E., Krugman, P., 1989. Trade Policy and Market Structure. MIT Press, Cambridge, MA. Herander, M., 2005. The (Non)equivalence of Tariff and Quota Policy in the Presence of Search Costs Manuscript. Jorgensen, J., Schröder, P., 2005. Welfare-ranking ad valorem and specific tariffs under monopolistic competition. Canadian Journal of Economics 38, 228–241. Karshenas, M., Stoneman, P., 1995. Technological diffusion. In: Stoneman, P. (Ed.), The Economics of Innovation and Technological Change. Basil Blackwell. Kim, E., 2000. Trade liberalization and productivity growth in Korean manufacturing industries: price protection, market power and scale efficiency. Journal of Development Economics 62, 55–83. Krishna, K., 1987. Tariffs versus quotas with endogenous quality. Journal of International Economics 23, 97–113. Krishna, K., 1990. Protection and the product line: monopoly and product quality. International Economic Review 31, 87–102. Krishna, P., Mitra, D., 1998. Trade liberalization, market discipline and productivity growth: new evidence from India. Journal of Development Economics 56 (2), 447–462. Krugman, P., 1980. Scale economies, product differentiation, and the pattern of trade. American Economic Review 70, 950–959. Lee, J.-W., 1996. Government interventions and productivity growth. Journal of Economic Growth 1, 391–414. Matschke, X., 2003. Tariff and quota equivalence in the presence of asymmetric information. Journal of International Economics 61, 209–223. Miyagiwa, K., Ohno, Y., 1995. Closing the technology gap under protection. American Economic Review 85, 755–770. Pavcnik, N., 2002. Trade liberalization, exit, and productivity improvements: evidence from Chilean plants. Review of Economic Studies 69, 245–276. Reinganum, J., 1981. On the diffusion of new technology: a game theoretic approach. Review of Economic Studies 48, 395–405. Saggi, K., Lin, P., 1999. Incentives for foreign direct investment under imitation. Canadian Journal of Economics 32, 1275–1298.