Transcript WELFARE STATE: GENERAL TRANSFER

The political economy of government debt
Advanced Political Economics
Fall 2011
Riccardo Puglisi
Main Questions
Why do we observe such large differences in
public debt policies across countries and
within one country across time?
Optimal taxation and Ricardian equivalence
provide no valid intution
Idea (guess what)
We need to link debt policy to
political environment
Political
Environment
Debt
Policy
Different solutions:
•Debt issue changes the incentives for future policy
makers
•
•
PERSSON-SVENSON (QJE 1989): different expenditure
levels
• TABELLINI-ALESINA (AER 1990): different
expenditure composition
Debt redistributes across generations-TABELLINI (JPE
1991)
• Weak Government do not control the expenditure:
common pool problem -VELASCO 1992
• Budget institutions matter -ALESINA-PEROTTI (1996)
TABELLINI-ALESINA (AER 1990)
“Voting on the budget deficit”
Different majorities may differ in their desired composition
of government consumption.
If the current majority can be replaced by a different
majority in the future, the current one can have the incentive
to favor budget deficit in order to influence future
decisions.
Deficit as a state variable which affects future policy
decisions
PREDICTION: Political instability induces larger deficits
The model:
1. Heterogenous agents decide on two public goods (f, g)
2. Two-period economy
3. The economy is endowed with one unit of output each
period
4. Small-open economy
borrowing/lending takes
place at a given interest rate, equal in the two periods
HP: The debt has to
be fully repaid at the
end of the second
period
•Budget constraints:
g1  f1  1  b
g2  f 2  1  b
with f>0 and g>0, in any period, and
b  (1,1)
•Preferences for agent i
2


w  E (  i u ( gt )  (1   i )u ( f t ) )
i
t 1
with u () concave, strictly increasing and
i
distributed [0,1]
Notice that these are intermediate-preferences over (f,g). We can
apply Median voter theorem.
Voting behavior
1. At the beginning of each period, voters choose
(g,f)
2. No pre-commitment device
Bidimensional voting in period 1
Unidimensional voting in period 2
To determine the political equilibrium we
use backward induction
LAST PERIOD:  2 is the median voter in period 2
m
The problem is


max2 u( g2 )  (1  2 )u( f 2 )
under the constraint
m
g2  f 2  1  b
m
FOC:
2 u' ( g2 )  (1  2 )u' (1  b  g2 )  0
m
m
That defines implicitly:
 g 2*  G ( 2 m , b)



 *
*
m
 f 2  1  b  g 2  F ( 2 , b )


Notice that,
 2  1  g2  1 b  f2  0
m
*
*
 2  0  g2  0  f2  1 b
m
*
*
We move back to the first period...
The problem here is:

 E

max 1 u( g1 )  (1  1 )u(1  b  g1 ) 
m
m
g1 ,b
1
m

u(G( 2 , b))  (1  1 )u( F ( 2 , b))
m
m
m
Notice that the decision over b has both a direct impact
and a strategic one. The higher b today, the lower will
be the income at disposal tomorrow.
FOC
•With respect to g1
 u' ( g1 )  (1   )u' (1  b  g1 )  0
m
1
m
1
that defines
g  g (1 , b)
*
1
m


f1  f (1 , b)
*
m


such that
f (1, b)  g (0, b)  0
*
1
*
1
f1 (0, b)  g1 (1, b)  1  b
*
*
•With respect to b


1mu ' ( g1 (1m , b)  E 1mu ' (G ( 2 m , b)) Gb  (1  1m )u ' ( F ( 2 m , b)) Fb  0
Marginal
Gain of b
Marginal Cost of b
INTUITION: An increase on debt today, increases your
consumption today but decreases it tomorrow.
The higher is the distance on preferences between today and
tomorrow majority, the higher will be the incentive for today
majority to issue debt.
Solution
To solve the game, we have to impose some restrictions on the
distribution of α
CASE I
  2  
m
1
m
m
In case we have always the same median voter we can rewrite the
FOC in the first period as:
 u' ( g ( , b))  E u' (G( , b))
m
m
m
m
Because of the last period FOC and because of the budget
constraint:
f 2 g 2
f2  g2  1  b 

 1
b b
This situation implies b=0
INTUITION: If median voter today and tomorrow have identical
preferences, there is no incentive to debt issue
CASE II
  2
m
1
m
with positive probability
m
m


1


2 0
(A) Consider the case that either 2
In this case, we know that in the second period
 2m  0  f2  1  b
 2m  1  f2  1  b
PROP. 1: (i) If either 2 m  1 2 m  0, then b*>0 (ii) b* is greater
m

the larger is the difference between 1 and the expected value
of  2 m
INTUITION: Again an increase in today’s debt increases utility
today but decreases tomorrow spending. However, with positive
probability, this reduction will only affect the good the median
voter cares little ( no fully internalization of costs)
(B) Consider that
c.d.f. H( )
 2  (0,1) and it is distributed according to the
m
Then, the FOC for the first period becomes:
1
1


1 u ( g )   v( 2 )dH ( 2 )    u ( g )  v( 2 ) dH ( 2 )
m '
Where
*
1
m
m
0
0

m '
1
*
1
m
m
u ' ( g 2 )u ' ( f 2 ) 1  ( f 2 )  (1  1 ) ( g 2 )
m
v( 2 ) 
*
*
*
*
u ' ( g 2 )  ( g 2 )  u ' ( f 2 ) ( f 2 )
*
*
m
*
and λ is a concavity index on the utility, such that:
u ' ' ()
 ()  
u' ()2
m
*

HP: The concavity index of u(x), λ(x) is decreasing in x, for any
x  (0,1)
An example of function that satisfies this condition is
u ( x) 
x

m

PROP. 2: Given 2  (0,1) , then b*>0 if the above
assumption is satisfied
Idea of the proof (sketchy): At b=0, the FOC is still positive,
meaning
 u ( g )  v( 2 )  0
m '
1
*
1
m
then, the optimal level of debt must be positive.
DEF (Polarization): The probability distribution H(α) is more
polarized relative to α than K(α), if for any continous increasing
function f( ), the following condition is true:
1

0
1
f ( |  2  1 |) dH ( 2 )   f ( |  2  1 |) dK( 2 )
m
m
m
m
m
m
0
The idea is that a more polarized distribution assigns more weight
to values of  2 m that are more further away from 1m
PROP. 3: If the hypothesis is satisfied, b* is larger the more
polarized is the probability distribution of  2 m relative to 1m over
the interval (0,1)
NOTICE: The opposite of proposition 2 and 3 is true for λ
increasing
•The downward sloping line
is the budget constraint if
b=0
•A and B are the point
m
chosen by 1 and  2 m at
b=0
•u1 and u2 are the
indifference curves of one
individual in the two periods
•EP1 and EP2 are the income
expansion paths of the two
types
EP2
u2
B
u1
A EP1
Intuition
Then, in general, at b=0, there are two opposing effects of a
change in b:
1. If b<0 (surplus), less income in the first period and more
income in the second. Then, u1 moves to the left and u2 to the
right; equivalent to buy an insurance
2. If b>0 (deficit), more income in the first and less in the
second. u1 moves to the right and u2 to the left. Add more
consumption today, when the median voter decides the
composition of spending, and decrease consumption
tomorrow.
If the condition on the concavity index is satisfied (2)>(1)
DEFICIT
Positive implications
1. The greater the instability, the larger the deficit
2. The greater polarization, the larger the deficit