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
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