Trade Prices and Wages with more than Minimal Inputs

Transcription

1 Trade Prices and Wages with more than Minimal Inputs Henry Thompson Auburn University November 2007 There is a common thread of the link between prices and wages in classical, neoclassical, factor proportions, specific factors, and monopolistic general equilibrium models of production and trade. The present paper focuses on the effect of a fall in the price of imports on the wage in high wage countries in these models with more than the minimal number of productive factors. JEL F10 Contact information: Economics, 202 Comer Hall, Auburn University, AL 36849, , fax 5639, thomph1@auburn.edu 1

2 Trade Prices and Wages with more than Minimal Inputs There may be a presumption from trade theory that wages fall with a move to free trade in countries with high wages. In classical trade theory with the single labor input, however, the wage increases along with income. Neoclassical trade theory stresses gains in utility or real income without separating the wage effect. In general equilibrium production theory, the focus shifts to factor markets and the wage in the high wage country falls in the two factor competitive model. The present paper focuses on the effect of a falling import price on the wage across a variety of production models with classical fixed unit inputs, neoclassical cost minimization, specific factors of production, and monopoly pricing. The issue is the robustness of the presumption of a falling wage when there is more than the minimal number of productive factors. The empirical literature relates wages to trade levels. Feenstra and Hanson (1995) attribute a third of the decline in the production wage relative to the non-production (mostly skilled) wage in US manufacturing during the 1980s to the increased trade volume, and Wood (1994), Slaughter (1998), and Leamer (2000) uncover larger effects. Mokhtari and Rassekh (1989), Rassekh (1992), Ben-David (1993), and Sachs and Warner (1995) find evidence of a positive link between the trade level and per capita income, and Rassekh and Thompson (1996) explore the theoretical link between per capita income and the wage. Batra and Slotje (1992, 1993, 1994) believe US trade with Japan was a fallacy during the 1980s due to the falling US production wage while Rassekh (1994) and Marjit (1994) disagree. Regarding the effect of trade prices on wages, Copeland and Thompson (2007) uncover a small negative link between the US import price index and production wages between 1964 and 1997, suggesting the declining tariffs had a positive impact on the wage. The average trade weighted US manufacturing tariff for 459 industries at the 6-digit SIC level has fallen to 4% but with a strong right skew toward a maximum of 19%. Other developed countries 2

3 are similar with average tariffs of 5% in the EU, UK, Australia, and Canada, and 2% in Japan. Effective protection rates are somewhat higher. Import competition in these developed countries continues promises to continue increasing with imports of manufactures from low wage countries making the effect on wages relevant. The present paper reviews models with two sectors facing exogenous world prices holding technology and factor endowments constant. The fall in the import price may be due world markets or lower tariffs. A few novel models fill gaps in the logical progression of models. 1. Prices and wages with classical fixed coefficients In the classical model the move to trade prices raises national income and the wage due to efficiency gains from specialization with fixed unit inputs implying constant opportunity costs for the single input. There is no presumption, however, about the link between prices and wages with more than the minimal single input as the following examples show. Jones (1973) presents the production model with two inputs in fixed proportions and inequality employment constraints. In the related model with full employment, input ratios must span the endowment point as in a KX /a LX > K/L > a KM /a LM. Changing prices do not affect outputs but wages adjust according to factor intensity. A decrease in the price of labor intensive imports lowers the wage, and the surprise in this fixed factor proportions model is that the size of the wage adjustment is identical to the model with substitution. The missing link model of Ruffin (1988, 1992) has fixed unit input coefficients for labor L and skilled labor S each producing either of two products independently. Factors are employed in their comparative advantage sector and factor proportions determine the direction of trade. Suppose labor has a comparative advantage in imports M relative to exports X with a SX /a SM < a LX /a LM. For a range of preferences in autarky, each factor is employed by its comparative advantage sector implying L = a LM q M and S = a SX q X where the q j are outputs. It follows that w L = p M /a LM and w S = p X /a SX with the 3

4 wage w L tied to the import price. Moving to world prices at p X * > p X and p M * < p M the wage w L falls to p M */a LM unless the increase in p X * is large enough to attract labor to that sector. The condition for a fall in the wage is a LX /a LM > p X */p M *. Reversing that inequality, the economy specializes with labor moving to the export sector and w L increasing to p X */a LX. Fixed labor coefficients can be combined with other cost minimizing inputs. Suppose labor is employed in the protected import competing sector with w M = (1+t)p M */a LM greater than the potential export sector wage w X = p X */a LX. Trade prices lower the wage to the higher of p M */a LM or w X. Labor remains in the import sector if the relative price of imports is greater than its opportunity cost of producing exports, p M */p X * > a LM /a LX. Percentage changes in both w M and the domestic price of imports then equal -t/(1+t) and the real wage falls. If p M */p X * < a LM /a LX labor moves to the export sector and the percentage fall in the wage %Δw = [(a LM p X /a LX (1+t)p M ) 1] is greater than the percentage fall in the import price -t(1+t) and the effect on the real wage depends on consumption shares. In summary, classical fixed labor input coefficients imply a necessary effect of trade prices on the wage only if there is a single factor of production. 2. Prices and wages with cost minimization Neoclassical production theory introduces cost minimization requiring a minimum of two inputs. As the neoclassical economy adjusts along its concave production frontier to trade prices, factor demands and prices adjust as the value of consumption rises and the value of production falls at autarky prices. Stolper and Samuelson (1941) show a falling relative price of labor intensive imports lowers the relative wage in the 2x2 model as both sectors become more labor intensive. The price taking import sector faces a lower price and production falls. The magnification effect of Jones (1965) implies a decline in the real wage regardless of consumption shares. 4

5 Moving beyond the minimal number of inputs, there is a wide range of potential wage adjustments. In the 3x2 model, factor intensity and substitution jointly determine wage adjustment as developed by Suzuki (1982), Jones and Easton (1983), Ruffin (1981), and Thompson (1985). Suppose labor L is the most intensive input in the import sector and skilled labor S the most intensive in exports in the ranking a LM /a LX > a KM /a KX > a SM /a SX. Trade prices might lower the wage but a low degree of labor intensity would imply little wage pressure. If labor is a strong substitute for skilled labor, a rising skilled wage would increase labor demand. Also a falling capital return would increase labor demand if labor and capital were complements. Cost in the labor intensive import sector would fall in spite of the potentially higher wage. The array of potential 3x2 wage adjustments is illustrated in the 13 magnification effects of Thompson (1993). Reasonably realistic models of production and trade are much more complicated. The typical assumption of only two skilled labor groups is questioned by Leamer (1994). In fact, Clark, Hofler, and Thompson (1988) show there are at least 8 separate labor skill groups in US manufacturing. Aggregation can lead to various distortions discussed by Thompson (2005). If the basic paradigm is a model with various labor inputs as well as natural resources and capital, little can be said about the effects of a falling import price on the wage. The literature includes the high dimensional models of Chipman (1979), Chang (1979), Ethier (1984), and Thompson (1987). Falling import prices in neoclassical factor proportions models lead to an unambiguous wage effect only when there are two factors of production. 3. Prices and wages with specific factors of production In the specific factors model of Jones (1971) and Samuelson (1971) each sector employs its own capital K j along with shared labor. The effects of prices on the wage depend on factor intensity and substitution as well as magnitudes of price changes. A falling import price lowers the wage, and 5

6 the effect on the real wage depends on consumption shares in the neoclassical ambiguity examined by Ruffin and Jones (1977). Even if labor were specific to the import competing sector, a falling import price would necessarily lower the wage only if there is a single shared factor. Suppose the export sector employs shared capital and shared skilled labor as in Thompson (1989). There is a presumption a falling import price would lower the wage of import specific labor but it may rise given the flexibility afforded by the third input. If labor is a complement with capital and the capital return falls, the demand for labor increases. Consider a model not in the literature with specific capital K X and K M for each sector and shared inputs of labor L and skilled labor S. The presumption with labor intensive imports a LM /a SM > a LX /a SX is that a falling import price would lower the wage but it may not. Aggregate substitution terms S hk describe the input of factor h with respect to the price of factor k, and a positive (negative) S hk indicates substitutes (complements) as developed by Jones and Scheinkman (1979). Constant returns imply Σ h w h S hk = 0 and rescaling factors to w h = 1 implies Σ h S hk = 0. The comparative static model in (1) is derived with full employment in the first four equations and competitive pricing in the last two. Returns to capital are r X and r M in the system S LL S LS S LX S LM a LX a LM dw dl 0 S LS S SS S SX S SM a SX a SM ds ds 0 S LX S SX S XX 0 a XX 0 dr X = dk x = 0 (1) S LM S SM 0 S MM 0 a MM dr M dk m 0 a LX a SX a XX dq X dp x 0 a LM a SM 0 a MM 0 0 dq M dp m dp m. 6

7 Consider a comparative static decrease in the import price p M in the vector of exogenous variables holding the export price p X and factor endowments constant as in the last column of (1). Chang (1979) shows the system determinant is positive with neoclassical production. Cramer s rule leads to the solution δw/δp M. With no loss of generality, rescale products to unit capital inputs a MM = a XX = 1. For simplicity also assume a SM = a SX = a LX = S LS = S LX = S SX = S SM = 1 with skilled labor a substitute for other inputs and labor a substitute with export capital. The focus is then on the a LM term for factor intensity, and on the S LM term for substitution between labor and import capital. If a LM = 1.1 the import sector is labor intensive. Suppose also S LM = -0.1 with labor and import capital complements. It follows that δw/δp M = -0.02, an elasticity with the scaling. The decrease in the import price p M then unambiguously raises the real wage. The expanding export sector substitutes toward labor as its capital price rises. As the price of import capital falls, the declining import sector demands complementary labor. If S LM = 1 it follows that δw/δp M = 0.18 making the effect of a lower p M on the real wage ambiguous. The real wage then falls if labor spends less than 18% of its income on the import. In specific factors models, the only necessary effects of a falling import price on the real wage occurs if labor is specific to the import competing sector and there is only one shared factor. 4. Prices and wages with monopolistic pricing Monopoly price searching introduces demand and optimal pricing. Melvin and Warne (1973) and Casas (1989) analyze the aggregate utility effects of trade with monopoly pricing by domestic monopolies on world markets. Thompson (2002) shows monopolistic pricing can be modeled as a parametric relaxation of competitive pricing in comparative static analysis, and the wage effect of a fall in the import price is weaker but in the same direction as the competitive model. Consider an import competing monopoly in a small open economy facing the exogenous international price p M. 7

8 Introducing demand, imports are the difference between quantity demanded q D (p M, Y) and the optimal output q 0. When the tariff is eliminated, q 0 falls and q D rises implying increased imports. The wage falls with the lost tariff but by less than with competitive pricing. A falling import price raises domestic income and the income effect on demand for the import can be included. Monopoly profit π falls as well. In summary, a falling import price lowers the wage in models with monopolistic pricing but by less than with competition given the minimal number of inputs. There is no presumption of any wage effect beyond the minimal number of inputs as in the previous sections. Similar conclusions hold with monopolistic competition in the import competing sector with average cost equal to the import price. Game theoretic competition in the import sector leads to no general prediction for prices much less wages. 5. Conclusion Various strands in the literature show that the link between the price of imports and the wage is broken by relaxed sufficient conditions such as elastic factor supply, full employment, perfect factor markets, competitive pricing, and constant returns. The link between trade prices and the wage with two factors and two goods is robust to parametric relaxations of these assumptions, however, as shown by Thompson (2003). The present paper stresses that the link is not robust to more than the minimal number of factors of production. Empirical studies asserting evidence against the Stolper-Samuelson theorem examining the relative wage of two labor groups implicitly assume a two input model disregarding capital and natural resource inputs. There are various theoretical outcomes possible between trade prices and the wage with more than the minimal two inputs. The competitive factor proportions theory of production and trade provides a foundation to examine the link between trade prices and the wage but there are no shortcuts to learning more about factor substitution and intensity. 8

9 References Batra, Raveendra (1992) "The Fallacy of Free Trade," Review of International Economics 1, Batra, Raveendra (1994) "The Fallacy of Free Trade II," Review of International Economics 2, Batra, Raveendra and Daniel Slotje (1993) Trade Policy and Poverty in the United States: Theory and Evidence, , Review of International Economics 2, Chang, Winston (1979) Some Theorems of Trade and General Equilibrium with Many Goods and Factors, Econometrica 47, Chipman, John (1979) A Survey of the Theory of International Trade: Part 3, The Modern Theory, Econometrica 34, Copeland, Cassandra and Henry Thompson (2007) Lost Protection and Wages: Some Time Series Evidence for the US, International Review of Economics and Finance, forthcoming. Ben-David, Dan (1993) "Equalizing Exchange: Trade Liberalization and Income Convergence," Quarterly Journal of Economics 108, Clark, Don, Richard Hofler, and Henry Thompson (1988) Separability of Capital and Labor in US Manufacturing, Economics Letters 2, Ethier, Wilfrid (1984) Higher Dimensional Issues in Trade Theory, in Ron Jones and Peter Kenen (eds) The Handbook of International Economics, vol 1, New York: Elsevier. Feenstra, Robert and Gordon Hansen (1995) "Foreign Investment, Outsourcing, and Relative Wages," NBER Working Paper #5121. Jones, Ron (1965) The Structure of Simple General Equilibrium Models, Journal of Political Economy 73, Jones, Ron (1971) A Three Factor Model in Theory, Trade, and History, in Trade, Balance of Payments, and Growth, edited by J. Bhagwati, R. Jones, R. Mundell, and J. Vanek, Amsterdam: North-Holland. Jones, Ron (1973) World Trade and Payments, Chapter 8, Little, Brown, & Co. Jones, Ron and Stephen Easton (1983) "Factor Intensities and Factor Substitution in General Equilibrium," Journal of International Economics 15, Jones, Ron and José Scheinkman (1977) "The Relevance of the Two-Sector Production Model in Trade Theory," Journal of Political Economy 85, Leamer, Edward (1994) "Trade, Wages, and Revolving Door Ideas," NBER Working Paper #

10 Leamer, Edward (2000): "What s the Use of Factor Contents?" Journal of International Economics 50, Marjit, Sugata (1994) "The Fallacy of Free Trade: Comment," Review of International Economics 2, Markusen, James (1981) Trade and the Gains from Trade with Monopolistic Competition, Journal of International Economics 11, Melvin, James and R.D. Warne (1973) Monopoly and the Theory of International Trade, Journal of International Economics 3, Mokhtari, Monoucheur and Farhad Rassekh (1989) "Tendency toward Factor Price Equalization among OECD Countries, ," The Review of Economics and Statistics 70, Rassekh, Farhad (1992) "The Role of International Trade in the Convergence of per Capita GDP in the OECD: ," International Economic Review 6, Rassekh, Farhad (1994) "An Evaluation of Batra's 'Fallacy of Free Trade'," Review of International Economics 6, Rassekh, Farhad and Henry Thompson (1998) "Micro Convergence and Macro Convergence: Factor Price Equalization and Equality of Per Capita Income," Pacific Economic Review 3, 3-11 Ruffin, Roy (1981) "Trade and Factor Movements with Three Factors and Two Goods," Economics Letters 7, Ruffin, Roy (1988) "The Missing Link: The Ricardian Approach to the Factor Endowments Theory of Trade," American Economic Review 77, Ruffin, Roy (1992) First and second best comparative advantages and international trade, Economica 59, Ruffin, Roy and Ron Jones (1977) Protection and Real Wages: The Neoclassical Ambiguity, Journal of Economic Theory 14, Sachs, Jeffrey and Andrew Warner (1995) "Economic Convergence and Economic Policies," NBER Working Paper No Samuelson, Paul (1971) Ohlin was Right, Scandinavian Journal of Economics 4, Slaughter, Matthew (1998) "International Trade and Labour-Market Outcomes: Results, Questions, and Policy Options," Economic Journal, 108, Stolper, Wolfgang and Paul Samuelson (1941) "Protection and Real Wages," Review of Economic Studies 9,

11 Suzuki, Katsuhiko (1983) "A Synthesis of the Heckscher-Ohlin and the Neoclassical Models of International Trade: A Comment," Journal of International Economics 14, Thompson, Henry (1985) "Complementarity in a Simple General Equilibrium Production Model," Canadian Journal of Economics 18, Thompson, Henry (1987) A Review of Advancements in the General Equilibrium Theory of Production and Trade, Keio Economic Studies 24, Thompson, Henry (1989) "Do Tariffs Protect Specific Factors?" Canadian Journal of Economics 22, Thompson, Henry (1993) "The Magnification Effect with Three Factors," Keio Economic Studies 30, Thompson, Henry (2002) Price Taking Monopolies in Small Open Economies, Open Economies Review 13, Thompson, Henry (2003) Robustness of the Stolper-Samuelson Factor Intensity Price Link, in Handbook of International Trade, edited by Kwan Choi, Blackwell. Thompson, Henry (2005) Aggregation and Applied Trade Theory, Journal of Economic Integration. Wood, Adrian (1994) North-South Trade, Employment and Inequality: Changing Fortunes in a Skill-Driven World, Oxford: Clarendon Press. 11