Download Model of debt crisis, Romer 4th edition section 12.10

Issues on fiscal policy
Tax-Smoothing (Barro 1979) Romer (2012) section 12.4
Distortion costs from raising Tt:
 Tt
Ct  Yt f 
 Yt

,

f (0)  0,
f '()  0,
f ''()  0,
The government chooses the path that minimizes this
distortion:

1
min 
Yf
t t
T0 ,T1 ,...
t  0 (1  r )

 Tt 
 
 Yt 

1
1
s.t : 
T  B0  
Gt
t t
t
t  0 (1  r )
t  0 (1  r )
Costs are minimized when:
Tt Tt 1

Yt Yt 1
This result is very interesting under uncertainty:
Tt
Tt 1
 Et
Yt
Yt 1
Tt
Tt 1
 Et
Yt
Yt 1
Discussion: T/Y follows a random walk (no predictable changes in
T/Y.
1) Important role for debt financing: War
2) Recessions
Model of debt crisis, Romer 4th edition
section 12.10
• One period model
• D debt has to be rolled over (issue D of new debt to pay off
the debt coming due)
• T tax revenues the following period,
• Government want investors to hold the debt for one period
• T is random with cumulative function F()
• R is the interest factor (1+r) and R-1 is the interest rate r
• If T is less than RD full default
• Default is all-or-nothing
• Investors are risk neutral
• The riskless interest factor RMIN is independent of R and D.
• π is the expected probability of default
Arbitrage between risky and riskless assets implies
• (1-π)R = RMIN
• Or π = (R-RMIN)/R (12.42)
• Example European debt crisis
• 12.42 is plotted in the following graph
Condition for investors to be willing to hold government debt
From 12.42
1
π
RMIN
R
Second equilibrium condition:
government defaults if T < RD
•
•
•
•
•
•
T distribution function is F()
π = F(RD) (12.43)
The maximum value of T is TMAX
The minimum value of T is TMIN
Density function is bell-shaped
The cumulative distribution function is Sshaped
The probability of default as a function of the interest factor
1
𝜋 = 1 𝑖𝑓 𝑅 ≥ 𝑇𝑀𝐴𝑋/𝐷
π
𝜋 = 0 𝑖𝑓
𝑅 ≤ 𝑇𝑀𝐼𝑁/𝐷
TMIN/D
TMAX/D
R
The determination of the interest factor and the probability of default
1
B
π
πA
TMIN/D
B is unstable (p. 636)
Two stable equilibria, A
And π=1
A
RMIN
TMAX/D
R
Analysis
• So there are two equilibria, one when the interest factor
and the probability of default are low, one where no
investor want to hold the debt
• For a sufficiently large riskless rate RMIN (Figure 12.6
next) the red curve is on the right of the blue curve and
the only equilibrium is π=1. You don’t need large
change in fundamental to have π moving from a low πA
to π=1
• For RMIN below this point, and increase in RMIN
increase the low πA
• Read page 637-638 (the conclusion on expectation,
beliefs about beliefs about fundamentals is Keynesian).