Lionel Artige Laurent Cavenaile H E C - U n i v e r s i t y o f L - PowerPoint PPT Presentation

I n t r o d u c t i o n M o d e l G r o w t h I n e q u a l i t y E m p i r i c a l R e s u l t s Q u a n t i t a t i v e E x e r c i s e C o n c l u s i o n A p p e n d i x oo oooooooo ooo oo ooo ooo o ooooo P u b lic E d u c a t io n E x p e n d it u r e s , G r o w t h a n d In c o m e In e q u a lit y Lionel Artige Laurent Cavenaile H E C - U n i v e r s i t y o f L ie g e U n i v e r s i t y o f T o r o n t o CEPR Conference Growth and Inequality: Long-Term Effects of Short-Term Policies T e l A v i v U n iv e r s i t y M a y 1 6 t h 2 0 1 8

I n t r o d u c t i o n Model Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix • O O O O O O O O O O O O OO O O O O O O O O O O O O I n t r o d u c t io n a P u b li c e d u c a t io n r e p r e s e n t s a la r g e s h a r e o f G D P in m o s t c o u n t r ie s ( 5 . 6 % in t h e U S in 2 0 1 2 ) a T w o p o t e n t i a l e f f e c t s o f p u b lic e d u c a t io n Q I n c r e a s e g r o w t h Q D e c r e a s e i n e q u a l i t y a M ix e d e m p ir ic a l r e s u lt s a R e c e n t r e s e a r c h e m p h a s iz in g t h e r o le o f q u a l i t y v s . q u a n t i t y o f e d u c a t io n ( e . g M a n u e l li a n d S e s h a d r i ( 2 0 1 4 ) , H a n u s h e k a n d W o e s s m a n n ( 2 0 1 2 , 2 0 1 5 ) )

I n t r o d u c t i o n Model Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix 0 • O O O O O O O O O O O OO O O O O O O O O O O O O W h a t W e D o R e v is it t h e r e l a t i o n s h ip b e t w e e n p u b lic e d u c a t io n , g r o w t h a n d i n e q u a l i t y in a 9 m o d e l w i t h e n d o g e n o u s e d u c a t io n q u a l i t y (supply side) a n d o c c u p a t i o n a l c h o ic e 9 W e s h o w t h a t : Q T h e e f f e c t i v e n e s s o f p u b l i c e d u c a t i o n p o l i c y a t r a i s i n g g r o w t h d e p e n d s o n t h e H C d i s t r i b u t i o n Q T h e r e l a t i o n s h i p b e t w e e n p u b l i c e d u c a t i o n a n d i n e q u a l i t y is p o t e n t i a l l y n o n - m o n o t o n e ( U - s h a p e d ) 9 W e p r o v id e e m p ir ic a l e v id e n c e f o r t h o s e p r e d ic t io n s Q u a n t i t a t i v e e x e r c is e : t r a d e - o f f b e t w e e n g r o w t h a n d i n e q u a l i t y t h r o u g h p u b lic 9 e d u c a t io n p o lic ie s f o r s o m e c o u n t r ie s

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O •O O O O O O O O O O OO O O O O O O O O O O O O M o d e l S t r u c t u r e 9 T w o - p e r i o d O v e r la p p i n g G e n e r a t io n s M o d e l o f E n d o g e n o u s G r o w t h 9 Y o u n g a g e n t s g o t o ( p u b l i c ) s c h o o l w h e n y o u n g a n d a c c u m u l a t e h u m a n c a p i t a l M a s s o n e o f o ld a g e n t s w o r k a n d c o n s u m e 9 H e t e r o g e n e i t y in h u m a n c a p i t a l ( d i s t r i b u t i o n F ( h ) ) a n d o c c u p a t i o n a l c h o ic e 9 Q W o r k e r Q T e a c h e r Q M a n a g e r H u m a n c a p i t a l a c c u m u l a t i o n d e p e n d s o n i n v e s t m e n t in p u b lic e d u c a t io n a n d 9 t h e e n d o g e n o u s q u a l i t y o f t e a c h e r s

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O 0 * 0 0 0 0 0 0 O O O O O O O O O O O O O O O O O S t a t ic P r o b le m : F ir m s 9 A f i r m m a t c h e d w i t h a m a n a g e r w i t h h u m a n c a p i t a l h p r o d u c e s y ( h ) = h na , w h e r e n a r e u n i t s o f la b o r . P r o d u c t i o n is t a x e d a t a r a t e r t o f in a n c e p u b lic e d u c a t io n 9 9 W o r k e r s a r e p a id a w a g e w p e r u n i t o f la b o r / \ Q 1 M a n a g e r s r e c e iv e t h e p r o f i t o f t h e i r f i r m s : 7 r ( / 7 [ ( 1 — r ) / 7 ) = ( 1 — a ) ( ^ ) ] 1־״ 9

M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix 0 0 * 0 0 0 0 0 O O O O O O O O O O O O O O O O O P u b lic E d u c a t io n E x p e n d it u r e s , T e a c h e r s ’ W a g e a n d E d u c a t io n Q u a lit y 9 G o v e r n m e n t c o lle c t s t a x e s e q u a l t o r f M y ( h ) d F ( h ) , w h e r e M is t h e s e t o f m a n a g e r s T a x e s a r e u s e d t o f i n a n c e t h e w a g e o f t e a c h e r s a n d b u d g e t is b a la n c e d 9 9 W a g e o f t e a c h e r s : w T = T . w h e r e T is t h e s e t o f t e a c h e r s E d u c a t i o n q u a l it y : S = f T h d F ( h ) 9

Model I n t r o d u c t i o n E m p i r i c a l R e s u l t s Q u a n t i t a t i v e E x e r c is e A p p e n d i x 00 0 *0 0 0 0 O O O O O O O O O O O O O S t a t ic P r o b le m : O ld A g e n t s O ld - a g e u t i l i t y is g iv e n b y : u = c — ! 7 7 ( /? ) 9 17 = 1 f o r t e a c h e r s ( > ( < 7׳)/7 0 , 7 " ) / 7 0 l i m /,^0 7 ( h ) = 00 a n d l i m / , ^ , ^ 7 ( h ) = 0 . 7 ( / 7 ) , 7 r ( / 7 9 M a x [ w , w T ) ] —

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O 0 0 0 0 * 0 0 0 O O O O O O O O O O O O O O O O O O c c u p a t io n a l C h o ic e : C u t o f f R u le F i g u r e : O c c u p a t i o n a l c h o i c e ׳ y ( x ) = i׳ o : = r = 0 . 1 , A = 1 a n d F is a l o g - n o r m a l d i s t r i b u t i o n w i t h m e a n a n d v a r i a n c e e q u a l t o o n e .

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O 0 0 0 0 0 * 0 0 O O O O O O O O O O O O O O O O O C o m p a r a t iv e s t a t ic s : r

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O 0 0 0 0 0 0 * 0 O O O OO O O O O O O O O O O O O D y n a m ic M o d e l E m b e d t h e s t a t i c m o d e l in a n O L G f r a m e w o r k w i t h t w o p e r io d s 9 9 Y o u n g a g e n t s : g o t o s c h o o l a n d a c c u m u l a t e H C 9 O l d a g e n t s : o c c u p a t i o n a l c h o i c e a s in s t a t i c m o d e l E a c h o ld a g e n t h a s o n e c h ild 9 a g e n t in f a m i l y / a t t i m e t + 1 : H u m a n c a p i t a l o f o ld 9 u , _ / . f t e f t ׳ V + 1 — f t , t״! t t G ( a ) w h e r e a , j t

Introduction M o d e l Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix OO O O O O O O O • OOO OO OOO OOO O OOOOO H u m a n C a p it a l D is t r ib u t io n 9 A s s u m p t io n s : t ( h ) = ^ 7 lo g (h o ) ~ A f(n o ,a Z ) lo g (a t ) ~ N { n a, a 2 a) !3! = 1 — [32 H u m a n C a p it a l d i s t r i b u t i o n a t t i m e t + 1 : 9 lo g {h t+ 1) ~ A f ( p a + /?!/it + lh lo g { S t ), a l + j3 la 2 t )

Introduction Model Growth Inequality Empirical Results Quantitative Exercise Conclusion Appendix O O O O O O O O O O • O O OO O O O O O O O O O O O O B a la n c e d G r o w t h P a th Balanced Growth Path Definition: A b a la n ce d g ro w th p a th is a d y n a m ic e q u ilib riu m in w h ic h : O h w ,t, hfj! t , S t, Y t = p y t (h ) d F t (h ), w t a n d w j a ll g ro w a t th e sam e ra te g . Q ( P — 1 1 A 2 • !־ ־ ״ Q The m ass o f w orkers, te a ch e rs a n d m a n a g e rs are c o n s ta n t.

I n t r o d u c t i o n M o d e l E m p i r i c a l R e s u lt s Q u a n t i t a t i v e E x e r c is e OO OOOOOOOO O O O O O O P u b lic E d u c a t io n a n d G r o w t h I Growth rate Inequality

M odel Growth Inequality Empirical Results Q uantitative Exercise C o n c l u s i o n A p p e n d i x 0 O O O O O O O O O O O O • O O O O O O O O O O O O O P u b lic E d u c a t io n a n d G r o w t h II t = 1 % a s a f u n c t i o n o f a a . F i g u r e : C o m p a r a t i v e s t a t i c s a t t h e s t e a d y s t a t e : G r o w t h e f f e c t o f A c n = 0 . 2 , = 0 . 4 , tp = 0 . 0 1 , /j,a = 3 a n d r = 0 . 0 5 . » P u b li c e d u c a t io n m o r e e f f e c t i v e a t r a is in g g r o w t h i f f a t t e r r i g h t t a i l o f H C d i s t r i b u t i o n

Introduction Model Growth I n e q u a l i t y Empirical Results Quantitative Exercise Conclusion Appendix O O O O O O O O O O O O O • O O O O O O O O O O O O O P u b lic E d u c a t io n a n d I n e q u a lit y I d F t ( h ) ( 1 - a ( l - T ) ) ( ^ 1 ) 1״“־ /- x 1 0 /lO r a tio t = ל — —- 0.1 w t ( 1 — q(1 — t))(q(1 — r))1^ ip9■ 0) 1־) ^ l a d F t {h ) 1 = קזר — r t { h w , t ) ! ( q ( I - t ) ) 1 -״ / C . x־1׳׳“ d F t( h ) d ( 1 0 / 1 0 r a t / 'o ) Q jr e c t p r o f j f e ffe c t + D ir e c t la b o r d e m a n d e ffe c t _ d r < 0 >° L a b o r s u p p ly e ffe c t + M a n a g e r d is trib u tio n e ffe c t +