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

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

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

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

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

51. w ω Figure 3.2: The partial factor-price frontier: relationship between w and ω for a given r. slope = -L/H

52. Technical progress without conflict If the slope of the partial FPF does not change too much, then both H and L gain That means that TP has little impact on the MRS between H and L In other words, it is not particularly more complementary with one factor than the other

53. w ω Figure 3.3: Technical change with little bias: Both wages increase

54. Neutral technical progress The MRS between H and L is unaffected if they enter through a homogenous aggregate unaffected by A The slope ratio of the partial FPF is given by the derivatives of the cost function of the aggregate, independent of A

55. Skilled-biased technical progress The MRS between skilled and unskilled sharply falls The partial FPF flattens I can now use 1 skilled instead of many unskilled To maintain equilibrium in the labor market, the wage of the unskilled has to fall

56. w ω Figure 3.4: Technical progress with a strong bias against Unskilled workers: w falls

57. Capital-skill complementarity

58. Capital-augmenting TP harms the unskilled and benefits the skilled The same is true of capital accumulation Thus, an investment boom (in IT) triggered by a fall in the price of capital goods (e.g. computers) is inegalitarian In the long-run, w = r/A, wages fall proportionally to TP

59. Estimating KSC Krusell et al estimate the following: Their estimates are ε = -0.5 and σ = 0.4 Their model does well at tracking the skill premium

60. Figure 3.5: Actual vs. Matched skill premium in the Krusell et al. model. Source: Krusell et al. (1999)

61. V. Unbalanced growth

62. The basic idea Several sectors Labor immobile between sectors in the short run Technical progress asymmetrical between sectors In the LR, technical progress benefits workers In the SR, wage dispersion goes up

63. The substitutability case If goods are substitute, demand increases a lot for the more productive sectors Labor needs to be reallocated to those sectors Wages go up in these sectors in the short run

64. The complementarity case If goods are complements, demand increases little in the more productive sectors Labor has to be reallocated away from these sectors Wages fall in the sectors where technical progress happens

65. A simple model Continuum of goods Isoelastic utility Linear production In the short run, allocation of labor frozen In the long run, it adjusts to equalize wages

66. The equilibrium conditions FOC for utility maximization Zero profits Relative labor demand Aggregate price level

67. The long run Labor adjusts so as to equalize wages Equilibrium wage necessarily goes up

68. The short run If technical change homothetic, all wages go up proportionally Assume TP takes place only in a few sectors Under substitutability, people gain from TP in their sector They lose under complementarity They always gain from TP in other sectors