A-1 Trade And Inequality With Limited Labor Mobility: Theory And Evidence From China Muqun Li Ian Coxhead Contents: APPENDIX A.1. Proof of lemma 1... 1 A.2. Relative labor dem... 2 A.3. Trade balance conditions... 3 A.4. Proof of Lemma 2... 4 A.5. Proof of Proposition 1... 4 A.6. Proof of Proposition 2... 9 A.7. Property of skill labor share... 9 A.8. Trade balance condition rewriting 2... 10 A.9. Proof of Proposition 3... 11 A.10. Proof of Proposition 4... 15 Table A.1: Products used in calculating skill-intensity of exports... 16 Table A-2: Unit root test results... 17 A.1. Proof of lemma 1 Define, as homogenous of degree one in both wages.. Differentiating w.r.t we get by Shephard's lemma. So we have therefore
A-2 When,. From inequality 3.a, So Intra-South inequality can be proved in similar fashion. A.2. Relative labor dem In Inl, consider some from, zero profits, where is the optimal amount of skilled labor relative to unskilled labor for producing z, given the labor endowment. Hence Similarly, In equilibrium the excess dem for skilled labor relative to unskilled should be zero:. In a similar fashion, for,
A-3. A.3. Trade balance conditions Since so similarly,, similar equations hold for. Therefore So now these trade balance conditions can be rewritten as:
A-4 A.4. Proof of Lemma 2 Dem for unskilled labor in the Inl is Take derivative of it w.r.t, similarly A.5. Proof of Proposition 1 We need to prove that when the Coast catches up with the North, i.e.,, with the Southern economy has unbalanced technological progress, more specifically,, but the sign of is ambiguous. For the Northern trade balance condition:
A-5 totally differentiating, we have since, the average skill intensity to produce goods in the North, is higher than, the skill intensity to produce the marginal product of the North. Similarly, we also have
A-6 Totally differentiating North s labor dem: Similarly,
A-7 These yield (A.1) where Finally, the signs of the imply that the sign of is positive. We can rewrite trade balance as so In similar fashion,
A-8 We restrict our focus to Hicks neutral technological change, which implies Inverting equation A.1 yields (A1.1) The coefficients on those of are negative, which, together with a positive sign of the determinant of, implies faster technological progress in the Coast relative to those of the North the Inl helps the Northern least skill-intensive good productions migrate to the Coast. (A 1.2) Coefficients on both are positive, which means faster Coast technical progress relative to the rest of the world induces more production in Coast. (A 1.3) The coefficients on are negative. So faster Coast technical progress increases the skill premium in the North. (A 1.4) The coefficients on are all negative. So the Coast's catch-up with the North, i.e.,, boosts Coastal wage inequality. On the other h, Inl's slow technological progress relative to the Coast reduces Coastal wage inequality. When the effect from international trade dominates the intranational trade effect, wage inequality in the Coast should increase.
A-9 (A 1.5) All coefficients of of are positive, which indicates that as Coast catch-up with the North leaves the Inl lagging, Inl's wage inequality decreases overtime. A.6. Proof of Proposition 2 If we abstract from the change in z, faster technological progress in Coast relative to Inl induces faster wage growth of both types of labor from Coast relative to those of Inl. Then we know,, by lemma 2,,,,. Taken together,. A.7. Property of skill labor share where Therefore
A-10 therefore A.8. Trade balance condition rewriting 2, total output of the North, can be rewritten as. Similarly therefore Revised trade balance conditions:
A-11 A.9. Proof of Proposition 3 We need to prove that when the Coast catches up with the North, i.e.,, with still ambiguous.,we have,., but the sign of is Now with the free mobility of skilled workers, we have, so So the trade balance condition for the North becomes
A-12 therefore that of the Inl takes the form of so As for the labor market clearing conditions in each region,
A-13 Similarly relative dem in the l then Now we have
A-14 (A.2) Equation A.2 yields Comparing with equation A1.1, we have couple of extra terms that come from this partial labor migration. The extra terms on those of on all have negative signs, which indicates that allowing skilled labor to move makes the Coast s adoption of skill-intensive production easier. Similarly, comparing the following equation A2.2 with A1.2 (A2.2) Similarly, faster technological progress in Coast attracts skilled labor from Inl, Inl therefore loses its most skill-intensive production to the Coast. (A2.4) The extra terms on both are all positive. So skilled labor mobility helps to reduce the wage inequality in the more dynamic region of the South. (A 2.5)
A-15 The additional terms on all have negative signs, which indicating that faster Coast technological progress increases the Inl's wage inequality. A.10. Proof of Proposition 4 Abstracting from change of z, faster technological progress in Coast relative to Inl induces faster wage growth of unskilled labor in Coast relative to Inl. Then we know Δz₂>0, Δz₁<0, by lemma 2,,. Taken together,. Dem for skilled labor in the South is: Taking derivative w.r.t Thus.
A-16 Table A.1: Products used in calculating skill-intensity of exports High Skill Intensive Products Product by Skill Intensity Aircraft spacecraft Pharmaceuticals Office, accounting computing machinery Radio, TV communications equipment Medical, precision optical instruments Medium-High Skill Intensive Products Other electrical machinery apparatus Motor vehicles, trailers semi-trailers Chemicals excl. pharmaceuticals Railroad equipment other transport equip. Other machinery equipment Medium-High Skill Intensive Products Coke, refined petroleum product nuclear fuel Rubber plastics products Other non-metallic mineral products Building repairing of ships boats Basic metals Fabricated metal products, excl. machinery Low Skill Intensive Products Other manufacturing recycling Wood, pulp, paper printed products Food products, beverages tobacco Textiles, textile products, leather footwear Source: United Nations Conference on Trade Development (UNCTAD) World Investment Report 2005: Internationalization of R&D Activities, New York, United Nations
A-17 Table A-2: Unit root test results Variable Average manufacturing wage Bottom 20% income 1* 2** 1* 2** Coefficient -0.072-0.212-0.581-0.916 t-value -2.756-7.032-7.681-9.024 t-star 0.105-3.858-4.180-5.362 P-value 0.5419 0.0001 0.0000 0.0000 Obs 319 319 203 203 Groups 29 29 29 29 * no lag is allowed ** 1 order lag is allowed