Welfare effects of technological convergence in processed food industries.

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 adopt country-specific import and export price indexes from WDI and convert them to constant 2000 U.S. dollars. (10)

Our use of cross-country and cross-industry data suggests groupwise heteroskedasticity may impair efficient estimation of welfare equations (6)-(10). We therefore estimate three specifications of each welfare equation: ordinary least squares (OLS), feasible generalized least squares (FGLS) with cross-country heteroskedasticity, and FGLS with cross-industry heteroskedasticity. Likelihood ratio tests are employed to check for group-wise heteroskedasticity across country and industry.

Cross-Country/Industry Productivity Estimates and Convergence

Estimates of the determinants of country-level TFP, equation (C.3) in Appendix C, are presented in table 1. Log of capital per unit labor is significant at the 1% level and indicates the elasticity of value added with respect to capital is 0.226. The statistically significant coefficient of the log of employment (-0.045) suggests food industries exhibit (marginally) decreasing returns to scale. Earlier studies have found mixed evidence of scale economies in processed food industries. For instance, focusing on aggregate processed-food industry data, Chan-Kang, Buccola, and Kerkvliet (1999) find modest scale economies in the U.S. food processing industry, while Gopinath (2003) finds significant scale diseconomies in thirteen OECD countries. The elasticity of value-added with respect to employment, implicit in the coefficients of employment and capital per unit labor in table 1, is 0.729 (equation C.3). Processed food industries appear to be labor intensive, consistent with earlier analysis (Melton and Huffman 1995; Gopinath 2003).

Cross-country and cross-industry TFP estimates are derived for each year with the estimates in table 1, using equation C.4 in Appendix C. An F-test rejects, at the 1% level, the null hypothesis of identical technologies across countries [F(29, 2972), 148.55]. Thus, TFP estimates show significant variation in level and growth rate across countries, among which the United States is the technological leader in eleven of seventeen processed food industries (see table 2, drawn). (11) Previous studies have found U.S. TFP levels in most processed foods to be high as well (Harrigan 1997; Chan-Kang, Buccola, and Kerkvliet 1999; Gopinath 2003). Other leaders include Japan, Korea, Mexico, and Spain. Because our results are based on four-digit industries, the United States may not necessarily be the productivity leader in certain subsectors (e.g., sugar). Table 2 shows that the leader's average TFP growth rate has been generally higher than that of followers. (12)

Table 3 gives results of the [beta]-convergence tests specified in equation (4), where a negative coefficient on the log of initial (relative) TFP suggests productivity convergence. (13) In thirteen food industries--ISIC 1511-13, 1520, 1531, 1533, 1541, 1543, 1549, 1551-54--the coefficient on the log of initial (relative) TFP is negative and significant at least at the 10% level. That is, countries with lower relative TFP levels have higher relative TFP growth, evidence of their catch-up with the leader, that is of productivity convergence. The convergence regression explains about 22.5% of the variation in the dependent variable; the rest likely is explained by R&D and technological opportunity and appropriability conditions (Cohen and Levin 1989).