Innovation and Inequality

1. Innovation and Inequality Gilles Saint-Paul Gerzensee, August 20-24 2007

2. I. Introduction

3. What is this course about? • Our aim is to analyze when technical progress can make some workers worse-off • The “standard” view is that technical progress raises wages: workers produce more, and wages = productivity • Historically, episodes of revolt against technical change • Furthermore, rise in wage inequality since the 1970s

4. Why do we believe that wages increase with technical progress? • Kaldor’s « stylized facts » of growth • Output per capita grows, and share of wages is constant • Therefore wage per capita grows • And, according to Neo-classical models, technical progress is the ultimate engine of growth

5. Where do these stylized facts come from? • Empirical approximation over the very long run • Theoretical property of balanced growth paths in NC growth models • But: • the economy is on a BGP only in the long run • BGP exists only under special conditions

6. A first research direction • A natural route is to re-examine the conditions under which a BGP exists • What happens in the short-run? • What happens if technical progress is not multiplicative in labor and the production function is not Cobb-Douglas? • By challenging these conditions, we may get that technical progress harms wages in general

7. Heterogeneity • In growth models, labor is a homogeneous input • Thus, all wages go up, or all wages go down • One may extend this model by introducing heterogeneous labor • Technical progress may them harm some workers and benefit others

8. Sources of heterogeneity • Just different endowments won’t do it • Multidimensional labor input • Multisectors with costly reallocation • Heterogeneity with respect to learning/reallocation costs

9. A second research direction • Introduce different kinds of labor in the standard neoclassical model • Presumably, the results will depend on whether technical progress is complement or substitute with a given kind of labor

10. Individuality • In NC classical models, people own abstract quantities of factors of production which they sell. • For the market for human time (= labor), that is problematic • People can’t do two things at the same time • They can’t be at two different places at the same time

11. Why does individuality matter? • An individual’s contribution to a firm may be unique and not reducible to the sum of the contributions of homogeneous factors. • Individuals may reap rents out of that uniqueness • Individuals also cooperate, exerting spillovers over each other’s productivity • And these effects are all affected by technical progress

12. Pricing • The neo-classical model assumes competitive pricing • But firms may have monopoly power, which reduces consumption wages • And if all is not homothetic, that power may be affected by technical change • Thus, pricing is another factor through which productivity may have unconventioonal effects on wages

13. II. Models of the distribution of income

14. An individual’s labor income is the sum of the value of all the labor inputs he supplies to the market:

15. But what he can supply to the market depends on time, space, and our modelling strategy… • I can be beautiful and clever, but not a beauty model and a scientist at the same time. • But if I’m a beautiful executive, that may help me in negotiating contracts…

16. Three basic models • The unbundling model • The specialization model • The bundling model

17. The unbundling model • Each characteristic is supplied anonymously to a single market • Each characteristic has a unique price • This price is equal to its marginal product

18. Example • Two characteristics, raw labor l and human capital h • Prices w = FL’ and ω = FH’ • z(l,h) = wl + ωh • People may be ranked by skill s, dl/ds > 0, dh/ds > 0. • The skill premium ω/w is « inegalitarian » if h is more elastic to skill than l

19. The specialization model • Each characteristic is supplied anonymously to a single market • But workers can only supply one characteristic • They elect the one which maximizes their income

20. An interpretation • Characteristics = productivity at different tasks • Fixed time endowment • One may only perform one task at the same time

21. Example • Two characteristics, raw labor l and human capital h • Prices w = FL’ and ω = FH’ • z(l,h) = max(wl,ωh) • People may be ranked by skill s, dl/ds > 0, dh/ds > 0.

22. Example (ctd) • People specialize according to their comparative advantage: • That leads to sorting by skills • The most skilled supply human capital

23. z(s) z = wl(s) z = ωh(s) Specialize in H Specialize in L s Figure 1.2: occupational choice and the wage schedule

24. An increase in the skill premium increases inequality • We consider any pair of workers s, s’ • Assume s’ > s • There are five possible cases depending on their specialization before and after the increase in the skill premium

27. The unbundling model • People supply their whole vector of characteristic to a single employer • Therefore, they cannot unbundle their characteristics and supply them to different employers • Nor can they specialize in a single characteristic

28. Each employer treats each characteristic as a homogeneous input • While employers offer a single price for each characteristic, this price may differ across employers • People elect the employer which yields the maximum income • There exist results about whether or not prices are equalized across employers • If not, we expect sorting by skills across employers

29. III. Productivity and wages in the standard neo-classical growth model

30. The balanced growth path • Output grows at a constant rate • This rate is determined by the growth rate of total factor productivity • The share of wages in total income is constant • Therefore, wages grow at the same rate as output • This rate goes up with that of TFP

31. A BGP exists and the economy converges to it if • TFP is multiplicative in labor • The production function has constant returns in labor and capital • The utility function is isoelastic

32. Reconsidering the predictions • We look at three possibilities: • Output-augmenting TP • Labor-augmenting TP • Capital-augmenting TP • And at two time horizons: • The short-run, with fixed K • The Ramsey long run, such that

33. III.1. The short run

34. Output-augmenting TP • With A multiplicative in F, the marginal product of labor goes up unambiguously with A

35. Capital-augmenting TP • An increase in A is equivalent to an increase in K • As F’’KL > 0, the marginal product of labor unambiguously goes up

36. Labor-augmenting TP • Wages fall iff

37. Interpretation • Each worker has more efficiency units  wages go up • But MP product of efficiency units fall  wages go down • Latter effect strong if capital/labor complementarity strong, i.e. F’’/F’ large in absolute value

38. Example • With a CES production function wages fall with A iff

39. III.2 The long-run

40. The adjustment of capital • Output-augmenting: upon impact, MPK goes up, more capital in the LR, wages go up even more • Capital-augmenting: MPK may fall, less capital in the LR, can this lead to falling wages? • Labor-augmenting: MPK goes up, more capital in LR, can this overturn lower wages in the SR?

41. In the LR, wages cannot fall • Otherwise, firms would face the same interest rate, lower labor costs, and would produce more • That would lead to strictly positive profits, which cannot be in equilibrium • In other words, the economy must lie on the factor-price frontier.

42. r FPF ρ w w Figure 2.1: long-run determination of wages in the Ramsey model

43. FPF’ r FPF ρ w w w’ Figure 2.2: long-run impact of technical progress on wages in the Ramsey model

44. Other models of accumulation • Technical progress may induce little more or less accumulation • This may lead to higher ROR on capital in the LR • Therefore, wages may fall in the LR • But that rests on strong income effects in savings

45. r r’ r FPF’ FPF w’ w w Figure 2.3: wages may fall if the marginal product of capital goes up by a lot.

46. Wages can only fall in two cases • In the short run, if TP is labor augmenting, and complementarities between K and L are strong • In the long run, if income effects are so strong that the capital stock is reduced by enough.

47. IV. Heterogeneous labor

48. The 3-factor model • There are now 3 factors, H,K,L • The Ramsey condition no longer determines wages • It just pins down a partial factor-price frontier • Technical change may twist that frontier so that the wage of one kind of labor falls • If w falls we have skilled-biased technical progress

49. Determination of factor prices • Production function • Factor-price frontier • Ramsey condition • Supply=demand • These 3 conditions determine the 3 factor prices

50. r ω w Figure 3.1: The factor price frontier with 3 factors