1、Journal of International Economics 53 (2001) 445461www.elsevier.nl/locate/econbaseQuasi-specific factors: worker comparative advantage inthe two-sector production modela,b,*Roy J. RuffinaDepartment of Economics, University of Houston, Houston, TX, USAbFederal Reserve Bank of Dallas, Dallas, TX, USAR
2、eceived 7 April 1999; accepted 6 December 1999AbstractThis paper integrates the HeckscherOhlin, specific factors, and the Ricardian models ofproduction with applications to international trade and labor economics. The modeleconomy exhibits both HeckscherOhlin and specific factors properties, but nev
3、er at thesame time. In international trade, the wage skill premium across countries can move indifferent directions and has natural limits within countries. In labor economics, we showthat the earning of economic rents is not inconsistent with competitive markets in generalequilibrium and that proce
4、ss and skill-based innovations have contrasting effects on wageinequality. 2001 Elsevier Science B.V. All rights reserved.Keywords: HeckscherOhlin; Ricardian; Specific factors; WagesJEL classification: F11; D331. IntroductionThe skewed distribution of earnings is strong evidence of comparative advan
5、-tage in individuals (Sattinger, 1978). Thus, individuals with comparative advan-tages earn economic rents in their favored industries. Ironically, perhaps, thestandard HeckscherOhlin model of trade ignores the comparative advantage ofindividuals or factors, because economic rents are zero. This pap
6、er augments the*Tel.: 11-713-743-3827; fax: 11-713-743-3798.E-mail address: rruffinuh.edu (R.J. Ruffin).0022-1996/01/$ see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0022-1996(00)00072-6446 R.J. Ruffin / Journal of International Economics 53 (2001) 445 461standard HeckscherOhl
7、in model by supposing one of the factors is produced bytwo labor types with Ricardian comparative advantages (Ruffin, 1988). Thisallows each industry to have a distinctive factor-intensity, but labor may earnrents. The model implies that the tension between comparative advantages andfactor intensiti
8、es is resolved with specific-factors and HeckscherOhlin properties,but never at the same time.The assumptions of the model contrast sharply with Mussa (1974) and Neary(1978) who assume that labor is mobile in the short-run, but capital is only mobilein the long-run. This paper assumes that at every
9、moment the economy is inlong-run equilibrium.The model sheds some fresh light on the impact of changes in prices ortechnology on factor prices. For example, much attention has been lavished onrecent changes in wage inequality (Juhn et al., 1993; Davis, 1998a,b; Welch,1999), and this paper is no exce
10、ption. The present model has refutable implica-tions that can be compared to alternative hypotheses.Leamer (1995) examines a model in which each good has a different Leontiefproduction function for each type of labor; and Jones and Ruffin (1975) present amodel in which each good has a different neoc
11、lassical production function for eachcountry. While the visions are similar, the present model has more Ricardianfeatures and can be analyzed more easily. The Ricardian model is about aparticular characterization of technology differences.Section 2 presents three stylized empirical observations that
12、 motivate the model.Section 3 previews the model and Section 4 specifies the detailed equilibriumconditions. Section 5 examines the StolperSamuelson and factor price equaliza-tion theorems. Section 6 investigates the Rybczynski theorem. Section 7 summa-rizes the impact of different kinds of technolo
13、gical change. Section 8 sketches howto include the case of many types of labor. Finally, Section 9 concludes the paper.2. Empirical motivationsThe theoretical model can account for three stylized facts about labor markets.The first is that ratio of skilled to unskilled wages does not behave the same
14、 in allnational markets. While the ratio of skilled to unskilled wages was rising sharply inthe United States and the United Kingdom during the 1980s (Juhn et al., 1993;Freeman and Katz, 1995, p. 28), the same was not true in Japan, France, and1Germany (Freeman and Katz, 1995, p. 28 and p. 372). Thi
15、s divergent behaviorcannot be explained by a standard HeckscherOhlin model of production; forchanges that drive factor prices in one economy also drive them in all economies1See Butler and Dueker (1999) for some convenient charts showing wage inequality acrosscountries, but using wages in high-tech
16、and low-tech industries. The results are similar, except for theUnited Kingdom.R.J. Ruffin / Journal of International Economics 53 (2001) 445 461 447in an integrated world. Thus, if the world economy is favoring goods that useskilled workers, skilled workers around the world would experience an impr
17、ove-ment in their relative incomes. In a paper that complements the present one, Davis(1998a,b) shows that even fixed European wages cannot be used to explain thedivergence in global trends because free trade in commodities equalizes factorprices, forcing Europe to bear the brunt in unemployment.The
18、 second stylized fact is that there is no long-run trend in the ratio of skilledto unskilled wages. Juhn et al. (1993) report that from 1960 to 1989, the ratio ofskilled to unskilled wages rose by 45%. However, in the first half of the century,the skilled wage premium fell. Keat (1960) estimated tha
19、t from 1900 to 1949 theratio of skilled to unskilled wages fell by roughly 33%. Thus, taking the entireperiod 1900 to 1989 into account, there is remarkable stability in the ratio ofskilled to unskilled wages. Skill premiums in the 1990s appear to have once againstabilized in the face of large chang
20、es in technology and growth in international2trade. My model shows that permanent trends in relative commodity prices orprocess innovations even in industries in which skilled workers have a compara-3tive advantage will only result in temporary changes in relative wages.The third is the commonplace
21、fact that there is a distribution of wages withinindustries and some workers earn economic rents, sharing those rents with otherfactors. In the labor economics literature, this sharing of economic rents has beeninterpreted as indicating non-competitive labor markets (Blanchflower et al.,1996). If wo
22、rkers share comparative advantages with other factors, their economicrents will move together even in a competitive market-clearing model.3. PreviewA specific factor is one that is always used in a particular industry and has avalue of zero in any other industry. I define a quasi-specific factor as
23、one that has apositive value in another industry and, thus, can be induced to leave the industry ifits economic rents vanish.Now consider a standard two-sector model in which there are two goods (1 and2) and three productive factors: capital and quasi-specific effective labor for eachsector. Capital
24、 is perfectly mobile. Both kinds of effective labor are producedunder constant returns by either type 1 labor or type 2 labor. However, type i laborhas a comparative advantage in producing effective labor for industry i, or, moresimply, a comparative advantage in industry i.Fig. 1 shows the producti
25、on-possibility curve for the economy. In the ranges ABand CD, the model works as the HeckscherOhlin model; and in the middle range,2I am indebted to Chinhui Juhn for 1990s observations on the skill premium.3For the view that the rise in wage inequality will continue as long as present trends continu
26、e, seeGregg and Manning (1997).448 R.J. Ruffin / Journal of International Economics 53 (2001) 445 461Fig. 1. In the BC range of the production-possibility curve the model works as specific-factors model,and in the AB and CD ranges as HeckscherOhlin where large sector uses labor with a comparativedis
27、advantage.BC, it works as the specific-factors model. When production is in the specific-factors range, both labor types earn an economic rent. Raising the relative price ofany good then increases the rent of the labor type with a comparative advantage inthat sector and lowers the rent on the other
28、labor type, precisely as in thespecific-factors model (Jones, 1971a; Samuelson, 1971). In this region, wageinequality is changing. Eventually, the economic rent of a labor type with acomparative advantage in the good with the falling price disappears. At this pointproduction moves out of the specifi
29、c factors range into either ranges AB or CD asa no-rent labor type now competes with the favored labor type. In either of theseHeckscherOhlin regions, the relation between commodity and factor prices isgoverned by the usual factor intensity conditions. In these regions the effectivewage ratio will b
30、e fixed, because wage inequality will then simply reflect fixedproductivity differences in the sector using both types of labor, exactly as in theRicardian model when two factors or countries produce the same good.Clearly, the model implies absence of StolperSamuelson effects when wageinequality is
31、changing.The fact that there are divergent changes in the ratio of skilled to unskilledwages around the world can be explained in the present model by countries beingin different regions of their production-possibility curves. These production setsR.J. Ruffin / Journal of International Economics 53
32、(2001) 445 461 449can differ simply because factor endowments differ. Thus, temporary changes incommodity prices will cause the wage structure to change in the country in thespecific factors range but not to change in the country in the HeckscherOhlinrange. But a permanent trend in commodity prices
33、will eventually push allcountries into the same HeckshcherOhlin range. In other words, it should be nosurprise to find the skill premium rising in one country, and then stabilizing aboutthe same time another country finds the skill premium starting to rise! Of course,in any uneven HeckscherOhlin mod
34、el there need not be factor price equalization;but the present model specifies conditions under which factor price equalizationdoes or does not obtain.The absence of long-run trends in the ratio of skilled to unskilled wages occursbecause any permanent trend in, say, commodity prices eventually caus
35、esproduction to move into the HeckscherOhlin region of the economy in whichwages move together. For example, around mid-century, after unskilled wages hadbeen rising relative to skilled, one would then expect to find more skilled workersin blue-collar industries, as neatly documented by Goldin and K
36、atz (1998) for1940.In a StolperSamuelson world all workers would want to protect the labor-intensive industry, whether working in that industry or not. Magee (1980) showshow coalitions in favor of protection are formed along industry lines. The presentmodel is compatible with that observation, since
37、 in the specific factors range eachRicardian factor (and there may be many) will want to protect the industry inwhich it has a comparative advantage.4. The model: formal treatment4.1. The specific factors modelAssume industry i (i 5 1, 2) has the constant-returns-to-scale productionfunction with all
38、 the usual concavity properties:x 5 F (K , E ), (1)iiiiwhere K is mobile capital and E is the quasi-specific effective labor used inindustry i.With constant-returns we can let a and a denote the amounts of capital andKi Eieffective labor per unit of good i. The price of each good, p , must equal the
39、 uniticost of production; thus,ar1 aw5 p (2)Ki Ei i iwhere r and w are the prices of mobile capital and specific effective labor. Good 2iserves as numeraire, so p 5 p /p . To keep the notation simple we suppress the12dependence of the a s on the factor prices w and r. The two equations in (2), forji
40、 i450 R.J. Ruffin / Journal of International Economics 53 (2001) 445 461given commodity prices, are not sufficient to determine the three factor prices. Asin Jones (1971a), we must add the full employment conditionsax1 ax5 K (3)K11 K22ax5 E (i 5 1, 2) (4)Ei i iThe five Eqs. (2)(4) suffice to determi
41、ne the two x s, the two wages, and r forigiven values of the p s, the E s, and K (Jones, 1971a).ii4.2. Ricardian comparative advantageEffective labor is produced by the Ricardian production function (Ruffin, 1988):E 5 L /b 1 L /b , (5)i 1i 1i 2i 2iwhere L is the amount of type j labor employed in th
42、e production of effectivejilabor of type i. Of course, effective labor can be interpreted as any intermediateproduct; and labor can be interpreted as any Ricardian factor. The b s are thejifixed Ricardian production coefficients; and, of course, represent the amount ofraw labor required to produce a
43、 unit of effective labor. We could assume anynumber of such Ricardian factors (even a continuum); however, in the interests ofsimplicity, we will restrict our present analysis to only two such labor types. Laterwe shall indicate the implications of adding more Ricardian factors.We assume the familia
44、r condition thatb /b , b /b . (6)11 12 21 22We are here assuming that type i labor has a comparative advantage in industry i.We cannot solve the model as in the specific factors model because thequantities L are not yet determined. However, in the range BC of Fig. 1 eachjilabor type is specialized i
45、n the industry in which it has a comparative advantage,that is L 5 L 50. We can then solve for the factor prices by appending the12 21equationE 5 L /b (7)jjjwhere L is the supply of type j labor to the economy. The resulting effective wagejrates (the w s) can now be determined.jThis solution will in
46、 fact prevail (for a given p) provided no worker has anincentive to work in another industry. Let w denote the wage type j worker earnsjiin industry i. Of course, workers earn the value of their marginal product inproducing effective labor. Given (5), it is easy to see thatw 5 w /b . (8)ji i jiIn ge
47、neral, however, we cannot have workers of both types earning higher wagesR.J. Ruffin / Journal of International Economics 53 (2001) 445 461 451in the same industry if both industries are to be viable. Type 1 workers cannot earnhigher wages in industry 2, that is:w /b $ w /b . (9)111 212Similarly, ty
48、pe 2 workers cannot earn higher wages in industry 1, that is:w /b $ w /b . (10)222 121The differences between the two sides of the above inequalities simply measurethe economic rents earned by each type of labor. Both (9) and (10) will holdprovidedb /b $ w /w $ b /b . (11)21 22 1 2 11 12This, of cou
49、rse, is exactly the same as the link between commodity prices and costratios in the Ricardian theory of international trade, with effective labor pricesreplacing commodity prices. It is impossible for the effective wage ratio to beoutside the range depicted in (11); for, otherwise, all labor would be in oneindustry.4.3. The specific-factors regionWhen the commodity price ratio is such that strict inequalities prevail in (11),the model will work exactly like the specific factors model. Recall that p 5 p /p .12In the open range defined by (11) replacing the weak
