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Welfare effects of technological convergence in processed food industries.


by Ruan, Jun^Gopinath, Munisamy^Buccola, Steven

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.

As Samuelson (2004) noted, a follower's technical progress can lower the leader's relative wage and living standards. We first address the change in the leader's wage rate relative to the follower's. The constant mark-up in each country can be used to derive this relative wage, which depends, as in Krugman (1980), on relative price and relative marginal cost. In our model, however, relative price depends on relative global supply, which in turn depends upon the technological convergence rate. While a 1% increase in follower's relative (labor) productivity brings a 1% increase in relative global supply, the corresponding terms-of-trade changes by less than 1% (equation A.2, Appendix A). Convergence therefore has a net positive (negative) effect on the follower's (leader's) relative wage, so that factor prices tend to equalize, a frequent result in traditional and new trade models. (2)

Result 2. Both for leader and follower, relative wage is proportional to relative productivity Technological convergence leads to factor price equalization.

Both countries allocate national income between domestic and imported goods. Because technological convergence raises the follower's output, and in each variety reduces its relative price, the leader's relative demand for the follower's products rises. Likewise, the decline in the follower's terms of trade reduces the imported share of its consumption (TR/[w.sup.*] [L.sup.*]).

Result 3. Technological convergence increases (decreases) the leader's (follower's) imported share of consumption.

Results 1 and 3 have received much attention in the convergence literature. Claims that the leader's comparative advantage or competitiveness erodes in the presence of convergence have been based on measures of global production and import share (Baumol, Nelson, and Wolff 1994; Keller 2001). However, the leader's welfare depends not on such shares, but on changes in its real income and terms of trade. In our setting, the leader's real income (w/p) is unchanged because we treat 13 as given. But the leader's terms of trade do improve. Hence, contrary to popular claims, the leader's welfare unambiguously improves when the follower catches up to the leader's technology (equation A.6, Appendix A). At the same time, convergence is not necessarily a win-win outcome for the follower, because the follower's welfare depends on the relative strength of terms-of-trade and income effects. (3)

Result 4. Real-income and terms-of-trade are both welfare-improving. Technological convergence unambiguously benefits the leader by increasing its terms of trade. The follower's welfare change depends upon convergence's positive real-income impact relative to its negative terms-of-trade impact.

Results 1 through 4 are derived under the assumption that one monopolistically competitive sector, with an increasing-returns-to-scale technology, operates in each country. Labor is the only production factor. To examine the sensitivity of Results 1-4 to these assumptions, we also assessed convergence in the context of a traditional trade model, employing a specific-factors model as in Jones and Scheinkman (1977). Outcomes were similar to those in Results 1-4. See Appendix B for details.

Empirical Framework for Technological Convergence

In our empirical application, we represent technology by total factor productivity, estimated from an econometric specification of a value-added function (Bernard and Jones 1996a; Harrigan 1999; Miller and Upadhyay 2002). (4) Details of the assumed value-added structure, which permits variable returns-to-scale, are provided in Appendix C. The approach in Appendix C allows, consistent with the convergence literature (Miller and Upadhyay 2002; Bernard and Jones 1996a; Baumol, Nelson, and Wolff 1994; Ark and Pilat 1993), hypothesis tests about the robustness of cross-country TFP measures. (5) The internationally comparable database described below permits cross-country comparisons of both TFP level and rate.

Industry- and country-specific time-series data on TFP levels permit us to measure each follower's TFP relative to that of the leader. To examine industry-specific [beta]-convergence, the relationship between followers' relative TFP growth rates and followers' initial relative TFP levels is specified as:

(4) [DELTA] ln([RTFP.sub.ci]) = [[delta].sub.0] + [[delta].sub.i][D.sub.i]ln([RTFP.sub.ci0]) + [[epsilon].sub.1ci]

where [DELTA]ln ([RTFP.sub.ci]) denotes, in industry i and over T periods, the average growth rate of country c's productivity relative to the leader; ln([RTFP.sub.ci0]) denotes country c's relative TFP level in industry i during the base year; [D.sub.i] is the industry-specific dummy variable; [[delta].sub.i] is the industry-specific slope parameter; and [[epsilon].sub.1ci] is a disturbance term. When [[delta].sub.i] < 0, countries with lower relative TFP levels have faster relative TFP growth, which is evidence of followers' catch-up with the leader, i.e., productivity convergence (Bernard and Jones 1996a). Following Bernard and Jones (1996a), we derive the speed or rate of productivity convergence in industry i, [[lambda].sub.i], given the sample length T:

(5) [[delta].sub.i] = [-[1- (1-[[lambda].sub.i]).sup.T]/T.

Positive [[lambda].sub.i] implies followers are catching up to the leader's productivity level and the rate of convergence is inversely related to the magnitude of [[delta].sub.i] (Bernard and Jones 1996a). In equation (4), [[delta].sub.i][D.sub.i] ln([TFP.sub.ci0]) captures the proportion of followers' TFP growth rate attributable to technological "catch up," while TFP growth induced by factors other than convergence is given by [delta].sub.0] + [[epsilon].sub.1ci].

Empirical Specification of Welfare Effects

To empirically examine our Results 1-4 regarding convergence effects, we first estimate the welfare impacts of followers' relative TFP growth, then, based on equation (4), decompose welfare changes into those attributable to convergence as opposed to nonconvergence factors.

Result 1 shows that convergence raises the follower's and reduces the leader's global production share. We therefore use a first-order linear approximation of equation (A.1) in Appendix A to estimate convergence effects on followers' share in global production:

(6) [DELTA][S.sub.ci] = [[phi].sub.0c] + [[phi].sub.1] [DELTA] ln([RTFP.sub.ci]) + [[phi].sub.2] [[DELTA]K[s.sub.ci] + [[phi].sub.3][DELTA][Ls.sub.ci] + [[epsilon].sub.2ci]

where [DELTA][S.sub.ci] denotes, in industry i and over T periods, the average growth rate of follower-country c's share in global value-added, and [[epsilon].sub.2ci] is the disturbance term. To control for unobserved heterogeneity across countries, we introduce a country fixed effect, [[phi].sub.0c]. Given equation (A.1), we expect a positive sign on [[phi].sub.1]. Equation (4)'s decomposition of follower's relative TFP growth would then identify the impact of technological convergence on the growth rate of follower's share of global value-added. All else constant, any gain to follower's production share due to convergence is also a measure of the erosion of leader's competitiveness. Control variables in equation (6) are [DELTA][Ks.sub.ci] and [DELTA][Ls.sub.ci], respectively, denoting the average growth rate of country c's global capital and labor share. Parameters [[phi].sub.2] and [[phi].sub.3] are expected to take a positive sign because relative factor accumulation increases a country's value-added.

According to Result 2, convergence reduces the wage gap between the leader and followers. Similar to equation (6), a first-order linear approximation of equation (A.2) is

(7) [DELTA][Wage.sub.ci] = [[gamma].sub.0c] + [[gamma].sub.1][DELTA] ln([RTFP.sub.ci]) + [gamma].sub.2] [DELTA][Cap.sub.ci] + [[epsilon].sub.3ci]

where [DELTA][Wage.sub.ci] denotes, in industry i, the average growth rate of country c's relative wage over T periods and [[epsilon].sub.3ci] is the disturbance term. As before, [[gamma].sub.0c] represents country-specific intercepts. We expect [[gamma].sub.1] to be positive because higher relative TFP growth increases followers' relative wages. The control variable in the relative wage equation (7), is [DELTA][Cap.sub.ci], which denotes the average growth rate of country c's capital-labor ratio in industry i. The coefficient [[gamma].sub.2] is expected to capture the positive impact of the growth of the capital-labor ratio on the marginal product of labor and wages. The impact of technological convergence again can be derived from the decomposition of relative TFP growth in equation (4).

To identify convergence's effects on a follower's imported share of consumption (Result 3), we specify:

(8) [DELTA][Ims.sub.ci] = [[omega].sub.0c] + [[omega].sub.1][DELTA]ln([RTFP.sub.ci]) + [[omega].sub.2][DELTA][Kr.sub.ci] + [[omega].sub.3][DELTA][Lr.sub.ci] + [[epsilon].sub.4ci]

where [DELTA][Ims.sub.ci] denotes, in industry i and over T periods, the average growth rate of country c's imported share of consumption. Imports only from the leader are considered in equation (8). A follower's total consumption equals its domestic output plus imports from the leader less exports to the leader. Result 3 and equation (A.4) suggest [[omega].sub.1] should be negative. The intercepts, [[omega].sub.0c], account for country-specific effects. Control variables [DELTA][Kr.sub.ci] and [DELTA][Lr.sub.ci], respectively, denote follower-country c's average capital and labor growth relative to those of the leader. Both should reduce the follower's imported share of consumption since an increase in the follower's relative factor accumulation improves its relative supply of each of the consumption goods in world markets.

Our final empirical specification deals with leaders' and followers' welfares. The leader's welfare is represented by its total consumption, which equals the leader's output plus its imports from follower c less its exports to country c. Equation (A.6) shows that technological convergence improves the leader's national welfare by improving its terms of trade. The leader's welfare also is enhanced by its own TFP growth and factor accumulation. Controlling for country-specific fixed effects, the leaders' welfare is specified as:

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

where [DELTA]L[welfare.sub.ci] denotes, in industry i over T periods, the average growth rate of the leader's welfare; [DELTA] ln([LTFP.sub.i]) is the leader's average TFP growth in industry i; and control variables [DELTA][Lk.sub.i] and [DELTA][Ll.sub.i] are, respectively, the leader's average capital and labor growth in the ith industry. As improvement in the leader's terms of trade comes solely from technical convergence, the follower's comparative average productivity growth, [DELTA] ln([RTFP.sub.ci]), represents the terms-of-trade effect. All variables in (9) should have a positive coefficient.

Recall from Result 4 (equation A.7) that convergence has two opposite influences on followers' welfare: a positive real-income effect and a negative terms-of-trade effect. As shown in equation (A.7), real income is determined only by technology growth, so that convergence's real-income effect is reflected empirically by the follower's TFP growth rate. The terms-of-trade effect, however, is captured by the follower's relative TFP growth. Thus, we can estimate convergence's effect on followers' welfare with country-specific intercepts as

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

[DELTA][Fwelfare.sub.ci] is follower c's average welfare growth rate--where welfare is the follower's domestic output plus imports from the leader less exports to the leader; [DELTA]ln([TFP.sub.ci]) is average growth rate of country c's TFP; and [DELTA][K.sub.ci] and [DELTA][L.sub.ci] are country c's average capital and labor growth rates. Coefficients of all variables except [DELTA]ln([RTFP.sub.ci]) in (10) should be positive. Following (5), we can decompose the real-income effect in equation (10) into those attributable to convergence and nonconvergence factors. (6) A similar decomposition can also be made for the terms-of-trade effect in equations (9) and (10).

Data and Econometric Procedure

The United Nations Industrial Development Organization's (UNIDO) Industrial Statistical Database (INDSTAT4 2005) provides cross-country data on manufacturing industry value-added, employment, gross fixed capital formation, wages, and output. Data on seventeen processed food industries, based on ISIC (Revision 3) four-digit classifications in thirty countries from 1993 to 2001, are taken from INDSTAT4. Among the thirty countries, ten are developed (Austria, Denmark, Finland, Italy, Japan, Norway, Portugal, Spain, United Kingdom, United States), and twenty are developing economies (Columbia, Cyprus, Ecuador, Eritrea, Ethiopia, India, Indonesia, Iran, Jordan, Korea, Malawi, Malaysia, Malta, Mexico, Mongolia, Oman, Panama, Singapore, Thailand, Turkey).

Data for some countries are available only in selected years, so data classified at ISIC Revision 2 are used to complete the series. In U.S. industries, correspondence between ISIC Revision 2 and Revision 3 is taken from U.S. Bureau of Census; we assume this correspondence is applicable to every nation. (7) As data availability varies by country and industry, we have an unbalanced data panel. Except for employment, which is expressed in labor units, production data are measured in INDSTAT4 in current local currencies. To render them internationally comparable, we first convert cross-country and cross-industry data to constant 2000 local currencies by using the corresponding price index from the World Bank's 2005 World Development Indicators (WDI). We then convert them to constant 2000 U.S. I dollars by using the purchasing power parity (PPP) conversion factors from 2005 WDI. (8)

With data on annual gross fixed capital formation, we construct capital stock as a function of past investment flows, following the standard perpetual inventory equation with declining-balance depreciation (Crego et al. 1998; Hall et al. 1988):

(11) [K.sub.t] = (1 - d) [K.sub.t-1] + [I.sub.t]

where [I.sub.t] is gross fixed capital formation in year t, [K.sub.t] is capital stock at end of year t, and d is depreciation rate. (9)

Bilateral trade data, expressed in nominal U.S. dollars, come originally from the COM-TRADE database (United Nations) and are reclassified into ISIC (Revision 3) four-digit-level industries. We ado