Welfare effects of technological convergence in processed food industries.

We decomposed TFP growth into that arising from technological convergence and non-convergence factors. We then estimated convergence's effects on followers' global value-added share, relative wage, imported share of consumption, and follower and leader welfare. Estimates of technological convergence effects are robust across three alternative welfare-equation specifications.

Consistent with our analytical results, convergence increases followers' global production shares and relative wages. The implication is that follower competitiveness and relative wage would be substantially lower in the absence of technological convergence. On account of its positive income effect, technological convergence improves follower welfare. Convergence enhances leader welfare by boosting the leader's terms of trade. But any such terms-of-trade-induced gains would be less important to the leader than would its own technological progress.

Since the 1990s, deepening world trade liberalization has greatly facilitated technology transfers between high- and low-income economies, speeding followers' technological "catch-up." The present study shows convergence can improve both leader and follower welfare. That appears to recommend such liberalization policies as trade-barrier reductions and open foreign-investment regimes, which would bring long-run benefits to both leaders and followers. Yet economic factors that co-vary with technological convergence, for example public infrastructure and human capital, may also influence leader and follower welfare by way of income and terms-of-trade effects. Linkages between technology, trade, and economic growth likely are conditional on the quantity and quality of public-good investments. Future analysis employing longer productivity time series may improve our understanding of the relationships between technological convergence, public goods, and trade liberalization.

Appendix A. Proof of Results 1-4

Result 1. Proof: Technological convergence lifts the follower's global production share ([n.sup.*][x.sup.*]/nx+[n.sup.*][x.sup.*]):

(A.1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the hat indicates the proportional change in the corresponding variable (e.g., [n.sup.*][x.sup.*]/nx+[n.sup.*][x.sup.*]).

Result 2. Proof: Technological convergence reduces the leader's relative wage (w/[w.sup.*]). The relative wage is derived from the ratio of the two countries' equilibrium prices:

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

Result 3. Proof: Technological convergence raises the leader's imported share of consumption,

(A.3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

but reduces that of the follower,

(A.4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where m = [w.sup.*][L.sup.*]/wL is the ratio of country B's to country A's national income.

Result 4. Proof: The indirect utility of the leader's representative consumer is

(A.5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Technological convergence unambiguously improves the consumer's welfare by lifting the terms of trade:

(A.6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Equilibrium indirect utility of the follower's representative consumer is

(A.7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Technological convergence enhances the consumer's real income [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], but diminishes the follower's terms of trade [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Under the assumption of exogenous [beta], the positive income effect dominates the negative terms-of-trade effect,

(A.8)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Therefore, technological convergence raises the follower's welfare as well.

Appendix B. Technological Convergence in a Specific-Factors Trade Model

An alternative to using the Krugman monopolistic competition framework for analyzing technological convergence is to employ an extension of the Ricardo-Viner-type specific-factors model (e.g., Jones and Scheinkman 1977). In such a model, two countries (A and B) each produce two goods (i = 1, 2) under perfect competition. Capital [K.sub.i] is specific to the ith sector, while labor L is perfectly mobile between the two sectors. Let Country A's production function for the respective goods be:

(B.1) [Q.sub.1] = F([K.sub.1], [L.sub.1], [[psi].sub.1]) [Q.sub.2] = G([K.sub.2], [L.sub.2], [[psi].sub.2])

where [Q.sub.i] and [L.sub.i] are output and labor in the ith sector (i = 1, 2). Parameters [[psi].sub.1] and [[psi].sub.2], respectively, denote product-augmenting technical change in Sectors 1 and 2. Corresponding variables and production functions in Country B are denoted with an asterisk. We assume Country A has the technological advantage in Sector 1 while Country B has the advantage in Sector 2, i.e., [[psi].sub.1] > [[psi].sup.*.sub.1] and [[psi].sub.2] < [[psi].sup.*.sub.2]. Each production function is concave, strictly increasing, twice differentiable, and linearly homogeneous in K and L. Cost minimization, along with perfect labor mobility, implies the following factor price relationships:

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

where [p.sub.i] denotes price of the ith good (i = 1, 2), [r.sub.i] is return to the ith capital, w is the wage rate, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively, denote the marginal product of labor and specific capital in each sector. Given full factor employment, Country A exports Good 1 to, and imports Good 2 from, Country B. That is, inter-industry trade takes place.

Technological convergence occurs when [[psi].sup.*.sub.1] approaches [[psi].sub.1] and/or [[psi].sub.2] approaches [[psi].sup.*.sub.2], following the respective approach functions [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

RESULT 1. In the presence of technological convergence, the return to the follower's specific capital rises, and the return to the leader's specific capital declines, in each sector. Wages in both countries rise, but the change in the relative wage depends upon the relative rates of convergence in the two sectors. A higher convergence rate in a country's lagging industry boosts its relative wage.

RESULT 2. In the presence of technological convergence, the two countries become more similar in their cross-sector labor allocations, i.e., d[L.sub.1] - d[L.sup.*.sub.1] < 0. In each sector, the follower's global production share rises and the leader's share falls.

RESULT 3. Changes in terms of trade depend upon the relative rates of convergence in the two sectors. Quicker convergence reduces relative product price in that sector, impairing the leader's terms of trade.

Similar to the monopolistic competition model, technological convergence in the specific-factors model increases the follower's relative factor returns and global production share. Terms-of-trade effects depend upon the two sectors' relative rates of technological convergence. Welfare effects require additional assumptions about those relative convergence rates. In particular, when convergence rates are equal across sectors, both countries' welfares improve because of rising incomes. When convergence rates instead differ across sectors, the country with the faster technological convergence in its lagging industry will gain on account of both rising incomes and rising terms-of-trade. The other country's net welfare change depends upon whether its rising income effect dominates its declining terms-of-trade effect. Hence, we continue to employ a monopolistically competitive framework in the body of this article, abstracting from factor substitution and utilization changes but maintaining scale economies, love of variety, and intra-industry trade.

Appendix C. Estimation of Cross-Country and Cross-Industry TFP

For country c in industry i at time t, consider real value-added, [y.sub.cit], as a function of real capital stock [k.sub.cit] and employment level [l.sub.cit]:

(C.1) [y.sub.cit] = [Z.sub.cit] x [g.sub.cit]([k.sub.cit], [l.sub.cit])

where [Z.sub.cit] is an index of TFP (Hicks-neutral technological change). Assume that function [g.sub.cit] ([k.sub.cit], [l.sub.cit]) has a Cobb-Douglas form, so that an estimable form of equation (C.1) is

(C.2) ln([y.sub.cit]/[l.sub.cit]) = [a.sub.0cit] + [a.sub.1] ln([k.sub.cit]/[l.sub.cit]) + p ln [l.sub.cit]

where [rho] = [a.sub.1] + [a.sub.2] - 1. Equation (C.2) indicates that value added per worker is a function of capital per worker and total employment. The scale elasticity in equation (C.2) is given by 1 + [rho], where [rho] indicates how far the value-added function deviates from constant returns to scale.

Since TFP generally varies across countries, industries, and time, the analysis of cross-country and cross-industry variation in value added per worker should allow for country-, industry-, and time-specific effects. The fixed-effect specification of equation (C.2) with country, industry, and time dummies is thus given by (Miller and Upadhyay 2002):

(C.3) ln([y.sub.cit]/[l.sub.cit]) = [b.sub.0c] + [b.sub.0i] + [b.sub.0t] + [a.sub.1] ln([k.sub.cit]/[l.sub.cit]) + p ln [l.sub.cit] + [[mu].sub.cit]

where [b.sub.0c] is a country-specific intercept, [b.sub.0i] is an industry-specific intercept, [b.sub.0t], is a time-specific intercept, and [[mu].sub.cit] denotes a disturbance term. As a result, the logarithm of TFP of country c in industry i at period t is given as

(C.4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].