Transcript WELFARE STATE: GENERAL TRANSFER

Politics and growth
Advanced Political Economics
Fall 2011
Riccardo Puglisi
Main Question
Are political factors and institutions
correlated to economic growth?
Stylized facts
• Inequality in the distribution of income (or wealth) is
significantly and negatively correlated with subsequent growth
• mixed evidence of the effects of growth on income distribution
(Kuznets curve)
•Political instability (social unrest, violence, frequent regime
change) is significantly and negatively correlated with growth
•Better protection of property right is positively correlated with
growth
•No robust evidence on the correlation between democracy and
growth
Literature
1. Inequality is harmful for growth because it promotes fiscal policy
which decrease capital accumulation; PERSSON –TABELLINI
(1994), ALESINA-RODRIK (1994)
2. Social conflicts and lack of protection of property right reduce
capital accumulation and thus growth: poverty trap; BENHABIBRUSTICHINI (1996)
3. Inequality induces more human capital accumulation through
public education and thus promotes growth; SAINT PAULVERDIER (1993)
Persson-Tabellini (AER 1994)
QUESTIONS
•Why do growth rates differ among countries and time?
•What’s the role of income distribution on growth?
IDEA: Inequality is harmful, because it leads to
economic policies that reduce growth, that is
high taxation on physical and human capital
accumulation
PT94: The Model
• 2 period OLG with constant population growth
• utility of an agent i born at time t-1
vt  u(ci t 1, d i t )
i
with u is concave, well-behaved and homothetic
• agents are heterogeneous in their endowments y
• budget constraints
c i t 1  k i t  y i t 1

d i t  r (1   t )kt   t K t
i

with y i t 1 income of type i and r (exogeneous) rate of return of
capital
PT94: The Model
• Fiscal policy: θ is the tax rate on capital accumulation, which is
i
redistributed lump-sum to the old. Notice that kt is the capital
accumulation of individual i, and Kt is the average capital accumulated
in the economy
• Income
y t 1  (w  e )k t 1
i
i
i
where w is the basic endowment and e is the idiosyncratic component,
such that E(e)  0 and emedian  0
NOTE: K is the average stock of capital accumulated from the previous
period. Interpretation: knowledge spillover as in Romer (1986). Capital
creates an externality for the next period income
PT94: Voting game
t-1
t
t+1
 t 1
kt
y t  ( w  e )k
i
i
kt 1
i
(1
i
)
k
t 1  t 1Kt 1
t 1
t
Timing: Taxation is decided at the beginning of the period in order
to avoid credibility or time inconsistency problems.
Old, thus, do not vote since they will not be around when the policy
is implemented.
Young are the only voters

PT94: Economic Equilibrium
From homoteticity:
d it
 D( r ,  t )
i
c t 1
with
Dr  0 and D  0
The share of income consumed does not depend on wealth, just on
intertemporal price.
Every individual has the same Saving Rate:
More wealth
More capital
PT94:Solution
Consumption levels:

i
rD
(
1


)
y
t 1   t K t
i
t
t
dt
Dt  r (1  t )

i
d
t
i
c t 1 
Dt
Growth rate of the economy ( growth rate of K or y)
gt  G( w, r ,t ) 

?

Kt
wD(r ,t )
1 
1
Kt 1
r  wD(r ,t )
Notice: growth depends on the externality or the model would not
display growth
PT94: Political equilibrium
Recall that
vt  u (c i t 1 , d i t )
i
i
d
t
i
c t 1 
D
i
d i t  r (1   t )kt   t K t


Thus, type i maximizes his utility w.r.t.  and, by the envelope
theorem, we obtain:

vi t
Kt 
i
 ud () ( Kt  k t )  t

t


t 

If ( Kt  k t )  0
i
Benefit from
redistribution
Cost for
distortion
PT94: Political equilibrium
Notice that
Hence
DKt 1
Kt  k  
ei
D  r (1   )
i
t
if e  0
Kt  k i t
if e  0
Kt  k t
i
Individual preferences can be indexed by e, thus median voter theorem
applies. The equilibrium policy:
D (r, )wr
D(r , )em


0
2
D(r , )  r (1   ) r  D(r , )
PT94: Political equilibrium
 0 if e  0
equilibrium tax rate  
and e  0
 0 if e  0
 0 if e  0
w 
 0 if e  0
Equilibrium Growth Rate g *  G ( w, r , * ( w, r , e m )
g *
 G  e  0
m
e
g *
 Gw  G  w  0
w
PT94: Predictions & Evidence
Theoretical Predictions
(1) More equal distribution of income implies higher growth
(2) The higher average level of basic skills, the higher is growth
Empirical Evidence (Historical data on 9 countries)
More Inequality & Lower Growth (highly significant)
More Schooling & More Growth (not sign)
More Political Participation & More Growth (not sign)
Empirical Evidence (Post-war data on 56 countries)
More Inequality & Lower Growth (but only in democracies)
Saint Paul-Verdier (JDE 1993)
Idea: Inequality does not need to lead to lower growth.
Why? More unequal societies promote more public
education to redistribute from rich to poor. Yet, more
public education leads also to more human capital
accumulation, and hence to higher growth.
Moreovoer, growth is associated with a decrease in
inequality.
SPV93: The model
• Infinite sequence of non-OLG, each living one period
• Dynasty: each person generates a kid
• Preferences: people cares about their own current consumption
and their children human capital (joy of giving model)
u (ci ,t , hi ,t 1 )
u ' c  0 and u '' cc  0
'
hi ,t 1
u
h
Utility is homotetic,
 F(
)x
'
uc
ci ,t
with F '  0
SPV93: The model
Define
 ( x)  F ()
1
'

x

( x)
and assume that
1
 ( x)
This condition is sufficient to ensure that poor people will vote
for more redistribution (t decreasing in h)
• People are heterogenous in the endowment of human capital:
hi ,t 1  (1  z)hi.t  gt
where (1-z) constant exogenous fraction of time devoted to
transfer human capital, δ is the coefficient of productivity of
human capital inheritance and g is public education provided
SPV93: The model
• Aggregate productivity is
1
Yt  H t  z  hi ,t di  zht
0
• Public (and private) education have the same production function
for human capital:
'
gt  ht
where h’ is the share of resources devoted to public education
• Therefore, for a generic type-i, consumption is
ci ,t  z(1 t t )hi ,t
•and public education
gt  zt t ht
SPV93: Political equilibrium
Type i maximizes (for τ≥0):
t i ,t  arg maxU hi ,t z(1  t t ); (1  z)hi ,t  zt t ht 
*
The F.O.C. is
hence
U ' h hit

'
U c ht
t i ,t  max0,t (hi ,t / ht )
*
SPV93: Political equilibrium
The previous assumption on the utility implies that
t i ,t *
 ( hi ,t / ht )
0
Intuition: poorer wants more public education
Moreover, preferences are single-peaked and median voter applies.
Optimal tax level is:
t t
*
m,t
 max0,t (hm,t / ht )
SPV93: Income distribution and growth
The dynamics of the average human capital is:
1
ht 1   (1- z) hi ,t di  zt t ht 
0
  1  z  zt t ht
therefore the growth rate is:
 t   (1  z  t t z)
Hence, the higher is taxation the higher is growth.
SPV93: Income distribution and growth
How does income distribution evolves over time?
hi ,t 1
ht 1
hi ,t
zt t ht
(1  z )



(1  z  zt t ) ht  (1  z  zt t )ht
zt t
(1  z ) hi ,t


(1  z  zt t ) ht (1  z  zt t )
If τ>0, the income dispersion is shrinking overtime
1. Dynasties that are initially poorer than the mean grow faster
than the economy
2. This convergence is quicker the larger is expenditure in public
education
SPV93: Evolution
1. Initially, as the meadian voter is far from the average human
capital, the tax rate, human capital accumulation and thus
growth are high
2. At the time evolves inequality decreases, and so does the tax
rate…. and growth
3. Eventually…
SPV93: Evolution
• If for ht , m
U 'h
h  '
Uc

t 0
1

then we still
have positive spending on education
'
U
1
h
Eventually, we will have
g t : '      (1  z  ztˆ)
Uc 
• If for
ht ,m
U 'h
h  '
Uc

t 0
1

then we have no
educational spending once we reach an equilibrium with no growth
Benhabib-Rustichini (JEG 1996)
Question: Why do (some) poor countries grow at a lower
rate than rich countries?
Idea: There are organized social group that try to capture a larger
share of income. This fact reduces accumulation and thus growth.
Under particular conditions on the utility and production function, we
have slow growth at low level of wealth and rapid growth at high
level of wealth.
Organized groups play trigger strategies and take into account current
benefits from redistributing against future consumption losses
The model
• 2 groups of player with concave, strictly increasing utility, having β
as discount factor
• production is concave and increasing, with f(0)≥0
• we define that a feasible path of consumption must satisfy:
f (kt )  c1t  c2t  kt 1 and ci t  0
• The first best solution gives utility
vˆ(k )  max u (c i t )  vˆ( y  2c)
0 c 
f (k )
2
What happens if the two groups play Nash in deciding their
current consumption?
We can see how consumption is regulated for any given attempted
consumption. For any given capital k, and attempted or planned
consumption c, the actual allocation is:
f (k )
c1 if c1  c2  f (k ) or c1 
2
A1 (c1 , c2 k ) 
thus if
f (k )
f (k )  c2 if c1  c2  f (k ) and c1 
 c2
2
f (k )
f (k )
if c1 , c2 
2
2
f (k )
c2 
 A1 (c1 , c2 , k )  minc1 , f (k )  c2 
2
The model
Notice that FAST CONSUMPTION STRATEGIES constitutes a
S.P.E. for all values of capital:
c1 (k )  c2 (k )  f (k )
f (k )
A1 (c1 , c2 , k )  A2 (c1 , c2 , k ) 
2
This is the worst possible S.P.E.
Trigger strategy equilibrium
If we define vi (k ) as the utility in the fast consumption strategy, we
use it in order to construct an agreed consumption path that
represent an equilibium outcome of this problem.
The allocation plan must satisfy the INDIVIDUAL
RATIONALITY CONSTRAINT at every point in time:
(c , c t ) :   U (c t )  vi (k )
1
t
2
t
t
i
Deviation
Take a sequence (c1t , c 2 t ) , for any shock of capital and
equilibirum consumption of the other player, the value of
deviating is


vi  max w (k , c), vi (k )
D
D
where

1
'
w (k , c)  max
u
(
c
)


u
f
f
(
k
)

c

c
2
0 c '  f ( k )  c

k1  f (k )  c  Ai (k , c, c ' )
and
kt 1  f (kt )  Ai (c1 (kt ), c2 (kt ), kt )
D
   f (0) 
  1   u 2 




IMPORTANT
For an allocation path to be an equilibrium outcome it will have to
be the case that
vi (c , c t , k )  v i (k , c)
1
t
2
D
i
This inequality could be satisfied for certain k levels but not for
others
(different from fast consumption)
Wealth dependent growth
Now growth depends on the capital level. Thus there may be
values of k s.t.
vi (c1t , c 2t , k )  v Di (k , c)
and thus there would be maximum growth (First Best Solution).
Besides, there may be values of k s.t.
vi (c , c t , k )  v i (k , c)
1
t
2
D
where v(k) is the value of an equilibrium with growth.
Example: Growth Trap
Two key assumptions
1. Low (high) marginal utility at high (low) wealth level
2. marginal product of capital not too high for low level of wealth
k 1
 AK
f (k )  
k 1
 A  B( K  1)
with
B  2, A  5 / 2   1 / 2
c
U (c )  
1  b(c  1)
c 1
c 1
There are three regions for
k  k1  negative growth

k  (k1 , k 2 )  sec ond best sol
k  k  first best sol
2
