アロー『やってみて学習』から学習:経済成長にとっての教訓 Learning from `Learning by Doing': Lessons for Economic Growth

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1 Learning from Learning by Doing : Lessons for Economic Growth M *1 * Version *1 c 2010 MIT *2 c

2

3 i MIT 1991

4 ii R.M.S. * 1 *1

5 iii i

6

7 1 1 (1962) * *1 :middlebrow theory.

8 /3 RAND

9 (Solow, Tobin, von Weizsäcker, and Yaari, 1965 ) ( ) product

10 g(t) t G(t) t 1 a G bg n n 1/3 ) ) G G L = b g n dg (1.1) G G x = a(g G ) (1.2) (1.1) G (1.2) x = ag [ 1 ( ) 1/(1 n) ] 1 L cg 1 n (1.3) n 1 c = b/(1 n) n = 1 (1.3) G G

11 5 n < 1 n > 1 G L n > 1 n 1 n = 1 n > 1 k k n n = 1/3 k 1/1 + 1/2 n + 1/2 n + 1/2 n /k n n > 1 k=1 k n n > 1 n 1 n > 1 n > 1 L n = 1/3 (1.3) n 1 ( n = 0 ) 0 < n < 1 L cg 1 n cg 1 n L n > 1 c = b/(1 n) 1 G ( ) n/(1 n) x G = 1 1 L cg 1 n (1.4) n 1 ) ( ) 2n 1 2 x G 2 = nl c Gn 2 1 L 1 n cg 1 n (1.5) n < 1 n > 1 G G

12 6 1 n > 1 () L L G 1 n γ γ/(1 n) n < 1 (s ) 1962 n < 1 (1.3) G L 1/1 n 1 n < 1 n > 1 1 n > 1 n > 1 1 1

13 7 n = 1 (1.3) n = 1 c = b/(1 n) (1.1) (1.2) (1.3) 1962 x = ag ( 1 e L/b) (1.6) G 1 s (1.6) G sa(1 e L/b ) G s sa 50 n = 1 AK 1962

14 8 1 (1.6) n = 1 n 1 n n < 1 n < 1 n = 1 n > 1 AK 1 1 1

15 9 1 n AK

16 10 1 AK

17 11 dh dt dh dt = khf(l H) = kh m f(l H ) m < 1 m > 1 L H m = 1 H kf(l H ) L H H AK AK MIT

18

19 13

20

21 15 2

22 16 2 G bg n B + bg n a a/b B = 0 B 1.3

23 17 n = 1/2 1 0 n n G L = b (B + bg 1/2 dg G (2.1) x = a(g G ) (2.2) n = 1/2 2.1 G 2.2 x = a (2.3) d = 2b/B 2.3 L 2.1 B(G G ) < L 2.2 x < al/b 2.3 B-17

24 18 2 B q < 1 k B q k B 0 B 0 q q q q 1 m h mh 1 mh m a k

25 19 k + 1 (q k q k+1 )B 0 k G q k+1 B 0 + bg 1/2 k k G G B q 1 i G a/(q i B 0 + bg 1/2 ) G

26 20 2 m q G n

27 21 factor share drift bg n

28 22 2 q k B 0 + = r nr B + bg n nr B q m 1/m 1/5 5 1 q m(1 q) nr m(1 q) q k B 0 bg n )

29 23 (m) (1 q) T k mt T t 0 t 0 + T x B t 0 t 0 + T B x ln q xt 1 ln q m ln q ln q = ln[1 (1 q)] (1 q) x mt mt 1 (ln q) 2 m(1 q) 2 /T

30 24 2 (n) (1 q) t k t t k+1 > t > t k [G(t) G(t k )] n > G(t) n **************************** 30

31 25

32

33 B = B 0 q k B 0 q k m a[bg n + B 0 q k ] 1 B 0 a 1 [bg n + q k ] 1 b t G(t) G(t) G t = G t 1 + x t (1 + r) t x t 1 r 0.03

34 28 3 G 1a 1b b = 1, n = 0.33, m = 0.2, q = /3 5 1a 1b

35 29 q b m G m q r 2a 2b 1a 1b b 1 2 3a 3b b = 1 n = 0.33 m = 0.5 q = 0.98 m(1 q)

36 (1 q) 1a 1b 2a 2b q = 0.95 q q , 0.2, 0.5, 0.2 q q = q 4a, 4b q

37 31 b = 1 m = 0.2 5a, 5b m = 0.5q = (n) G(t) 5c

38 32 3

39 33 m 0 = 0.5 t t 1 m t = (1 + u) m t 1 t 1 m t = (1 + u) 1 m t 1 u 0.05, 0.1, 0.15 b = 1, n = 0.33, q = a, 6b, 6c u = 0.05, 0.1, a 6b 6c t = 20 t = 35 t = (1 + u) (1 + u) 1 (1 + u) (1 + v) 1 m t n b

40 34 3

41 35-1 n 1 1 n < b = 1, n = 0.33, m = 0.2, q t = 10 7a b a 7c a 7c

42 36 3

43 b 2 n 0.5 m 0 = 0.5 v = u = m t () () b = 1, n = 0.33, q = 0.98 m(1 q) ,2 4, a,b,c,d,e g

44 38 3 t = 100 t =

45 39 t = 50 t = 100 8c a

46 (35 25)/35 ( )/1.10 8b 2 8a 8c 8e d 8c 8e 8c

47 41 2

48

49 43 4

50 Energizer Bunny. Still going and going and going... * GNP USD37, GNP Summers and Heston *1

51

52 OPEC 1 1

53 47 GNP 20 25

54 48 4 1

55 49 GDP x y GNP 2

56

57 51

58 A D

59 53 GDP GDP GDP )

60 ky

61 55 GDP 40 30

62

63 57 Kenneth Arrow The Economic Implications of Learning by Doing, Review of Economic Studies 28 (1962): David Levhari Further Implications of Learning by Doing, Review of Economic Studies 33 (1967): Extensions of Arrow s Learning by Doing, Review of Economic Studies 33 (1967): Eytan Sheshinski Tests of the Learning-by-Doing Hypothesis, Review of Economics and Statistics 49 (1967): Werner Hirsch, Manufacturing Progress Functions, Review of Economics and Statistics 34 (1952): Armen Alchian, Reliability of Progress Curves in Airframe Production, Econometrica 31 (1963): RAND Linda Argote and Dennis Epple, Learning Curves in Manufacturing, Science 247 (1990): Sherwin Rosen, Learning by Experience as Joint Production, textitquarterly Journal of Economics 86 (1972): Drew Fudenberg and Jean Tirole, Learning by Doing and Market Performance, Bell Journal 14 (1983): Alwyn Young, Learning by Doing and the Dynamic Effects of International Trade, Quarterly Journal of Economics 106 (1991): Young, Invention and Bounded Learning by Doing, Journal of Political Economy 101 (1993): Philippe Aghion and Peter Howitt, A Model of Growth Throught Creative Destruction, Econometrica 60 (1992): ; Robert Solow, James Tobin, Christian von Weizäcker, and Menachem Yaari, Neoclassical Growth with Fixed Factor Proportions, Review of Economic Studies 33 (1965): ; Robert Summers and Alan Heston, The Penn World Table (Mark 5): An Expanded Set of International Comparisons, , Quarterly Journal of Economics 106 (1991):

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