Welfare effects of technological convergence in processed food industries.

In the past few decades, the composition of global agricultural trade has shifted decidedly toward processed foods. For instance, processed exports rose an average annual 6% between 1981 and 2004, compared with an annual 3% rise in primary exports. Two-thirds of globally traded agricultural products, with a value above $783 billion in 2004, have in recent years undergone some form of value addition before shipment (International Trade Statistics 2005; U.S. Department of Agriculture 2005). At the same time, the structure of global food production and consumption has changed significantly. Rapid income growth in emerging markets--for example, in Asian countries--has expanded the supply and demand for processed foods, in turn altering the regional composition of global trade. China alone has become the third largest destination for exports and fourth largest source of imports of U.S. processed foods (U.S. Department of Commerce 2006).

The literature on global trade patterns has demonstrated that technology is a key source of comparative advantage in food processing and that technological level and growth vary by country (Trefler 1993; Bernard and Jones 1996a; Harrigan 1997; Chan-Kang, Buccola, and Kerkvliet 1999; Morrison Paul 2000). In the wake of the 1990s globalization wave, a number of analysts have asked whether technological convergence has eroded such comparative advantage (Baumol, Nelson, and Wolff 1994; Coe and Helpman 1995; Bernard and Jones 1996b; Keller 2001; Gopinath 2003). Indeed, the nature and rate of technological convergence between high- and low-income economies, and its consequence for both leaders and followers, have become the core of a new literature (Krugman 1990; Coe, Helpman, and Hoffmaister 1997; Keller 2001; Samuelson 2004; Bhagwati, Panagariya, and Srinivasan 2004).

Yet convergence's welfare impacts, and production and trade consequences, have remained contentious. Krugman's (1990) technology-gap model suggests that when a follower catches up with a leader, the follower's real wages rise but the leader's welfare may decline through terms-of-trade effects. Samuelson (2004) argues that if a less-developed country improves technology in its export industries, all countries benefit from the global output rise. Yet if the same improvement is in a good exported from an advanced country, the latter loses on account of falling terms of trade. These analyses, however, are limited to the traditional, inter-industry trade context. In a response to Samuelson (2004), Bhagwati, Panagariya, and Srinivasan (2004) point out gains from growing intra-industry trade would alleviate the advanced country's losses due to declining trade terms.

The objective of this article is to analyze technological convergence and its consequences for processed food industries in the presence of intra-industry trade. Indeed global trade including processed foods is increasingly intra-industry in nature, where Krugman's (1980) monopolistic competition model has been the basis of extensive gravity-type modeling of trade structure and patterns (Anderson and van Wincoop 2003; Feenstra 2004). We extend Krugman's (1980) monopolistic competition setting to model technological convergence as the source of narrowing inter-country gap in fixed or marginal costs of production. Our comparative statics results suggest convergence raises the follower's relative wage and global production share, a result consistent with Samuelson's (2004) claim. However, convergence also improves the leader's terms-of-trade, unambiguously improving its welfare. This is consistent with Bhagwati, Panagariya, and Srinivasan's argument that leaders can benefit from technological convergence when trade is intra-industry. Unlike in previous studies, the follower's welfare depends on the relative strength of its technology enhancement and terms-of-trade decline.

Our empirical analysis includes 1993-2001 data from thirty countries (10 high-income, 20 low-income) on seventeen processed food industries, defined on the basis of ISIC (Revision 3) four-digit classification. We employ a value-added function allowing for country-, industry-, and time-specific effects to estimate total factor productivity (TFP) levels and growth rates, assuming variable returns to scale (Harrigan 1999). Technological or productivity convergence is identified by regressing TFP growth rates on initial TFP levels ([beta] convergence) in each food industry (Bernard and Jones 1996a). We then estimate welfare impacts of productivity convergence, including effects on the follower's global value-added share, relative wage, imported share of consumption, and welfare of both leader and follower. To our knowledge, this is the first study of the welfare implications of cross-country TFP convergence in disaggregated (ISIC four-digit) food industries.

Conceptual Framework

Our economic setting considers two countries, A and B, each of which produces a series of differentiated goods under monopolistic competition (Krugman 1980). Labor is the only input in production, which involves fixed ([alpha]) and variable ([beta]) costs. Technology is expressed in unit labor requirements: [l.sub.i] = [alpha] + [[beta][x.sub.i], where [x.sub.i] denotes the output of the ith good. As in Krugman's (1980) framework, an asterisk denotes the corresponding variable in country B. For example, country B's technology is given by [l.sup.*.sub.i] = [[alpha].sup.*] + [[beta].sup.*][x.sup.*.sub.i]. International trade is costless, and consumers in either country consume all varieties produced by both countries.

The representative consumer's utility takes a CES form over a number of goods: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], denotes the elasticity of substitution, [c.sub.i] is consumption of the ith good, and n ([n.sup.*]) is the number of goods in country A (B). The ith good's demand function is:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where w and [p.sub.i] denote country A's wage rate and the price of the ith good, respectively.

Consistent with monopolistic competition, each firm produces a unique good in equilibrium. Profit maximization implies all firms charge a price equal to a constant markup over marginal cost ([p.sub.i] = [beta]/[theta]w). Consequently, all goods produced within a country have the same price. Free entry leads to zero profit, yielding the equilibrium output of each good:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Equation (2) indicates all goods produced in the same country have identical output. Full labor employment generates the equilibrium number of varieties in each country:

(3) n = L(1-[theta]/[alpha], [n.sup.*] = [L.sup.*](1 - [theta])/[[alpha].sup.*].

Note that country size (L or [L.sup.*]) positively affects, and fixed cost ([alpha] or [[alpha].sup.*]) negatively affects, the number of varieties (n or [n.sup.*]). In each country imports equal exports, given by TR = wL[w.sup.*][L.sup.*] / wL + [w.sup.*][L.sup.*], where TR denotes trade.

To model technological convergence, we assume country A has a technological advantage over country B, i.e., [alpha] < [[alpha].sup.*], [beta] < [[beta].sup.*]. Convergence is defined as a narrowing inter-country gap in fixed or marginal production costs, captured by a decline in [[alpha].sup.*]/[alpha] or [[beta].sup.*]/[beta]. Alternatively, convergence can be thought of as a narrowing difference between countries A and B in labor productivity (x/l and [x.sup.*]/[l.sup.*]). Our focus below is on marginal cost convergence, holding fixed costs constant. (1) We will refer to country A and B as leader and follower, respectively. Suppose the leader's marginal cost [beta] is given, while the follower's marginal cost [[beta].sup.*] is endogenously determined. In particular, [[beta].sup.*] approaches [beta] according to [[beta].sup.*] = [beta]/(1 - [e.sup.-[lambda]), where [lambda] is rate of convergence in marginal costs. The faster the technological convergence, the lower is the follower's marginal cost, i.e., [partial derivative][[beta].sup.*]/[partial derivative][lambda] < 0. We now outline our key comparative static results and testable hypotheses. Technical derivations and proofs are in Appendix A.

Our first result pertains to the leader's and follower's global production share. In the presence of technological convergence, the leader's output will remain unchanged because its fixed and marginal costs remain the same. Since labor endowments and fixed costs do not change, the number of varieties in each country remains constant. However, as shown in equation (2), the follower's output of each variety increases with the decline in its marginal cost. As a result, the follower's relative supply increases, inducing an expansion in global supply. This is consistent with Krugman (1990) and the arguments of Bhagwati, Panagariya, and Srinivasan (2004).

Result 1. Technological convergence will increase (decrease) the follower's (leader's) global production share.