Download Monetary and financial macroeconomics

Monetary and financial macroeconomics
Money and expectations
April, 2014
What did we learn so far?
• Increase in money supply (Mt ) reduce prices of money in
terms of goods
• Increase in the growth rate of money (µ(t)) reduce the
return on money
• The effect on seignoriage is ambigous (it depends on
which side of the Bailey curve we are)
• So far, no impact on GDP because we worked in
endowment economy
What does data say?
Figure: Champ, Freeman and Hastag (2010)
• Data USA (1948 - 1969). Phillips Curve
What does data say?
Figure: Champ, Freeman and Hastag (2010)
• Data USA (1970 - 2010). Phillips Curve
What does data say?
• Phillips Curve (Phillips 1958): significant statistical
relationship between inflation and unemployment
• How did people understood this relationship initially? The
government can exploit it: the government can generate
inflation to reduce unemployment and increase GDP
• Governments tried to exploit this relationship
• After 70, the relationship changed
• Is there a link between inflation and growth?
What does data say?
Figure: Champ, Freeman and Hastag (2010), Lucas (1973)
• International comparison
How do we reconcile this information?
• Short run relationship between GDP and inflation
• It disappears when the government tries to exploit it
• Negative long run relationship
• “Expectations and the Neutrality of Money” Lucas (1972)
• Champ, Freeman and Haslag (2010) Ch 5
The islands model?
• Lucas model had a large impact on how to do macro
• It’s one of the first mayor applications of Rational
Expectations
• Lucas Critique
• Key for the rational expectations revolution
Today
• Study a simplified model of Lucas’ Island
• Extending OLG model
• Use the model to study expected and unexpected
monetary policy (monetary surprises)
• We want to answer
• What is the effect of monetary policy on output?
• What type of monetary policy affects output?
• Can we use monetary policy systematically to affect
output?
Islands’ Model
Setup
• OLG
• The economy is an archipelago
• Population is distributed among 2 islands
• Nt = N
Islands’ Model
Setup
• Young are asymmetrically distributed
• 1/3 in one island, and 2/3 in the other
• Each island has the same probability of having a large or
small number of young agents
• Old are symmetrically distributed
Islands’ Model
Setup - Example
• Young h is born in island A
• When young works in A
• The following period he is old
• With probability p, he remains in A, with prob 1 − p he
travels to B, and consumes
Islands’ Model
Setup
• Assume
M(t) = µM(t − 1)
1
M(t) − M(t − 1) = 1 −
M(t)
µ
• µ denotes the growth rate of money
• Money is transfer to old agents
• Transfers to the old: At = 1 − µ1 pm (t)M(t)
• Transfers to each old in period t, at = ANt
Islands’ Model
Setup: Information
• Period t, young cannot observe the number of young
• Cannot observe transfers to the old
• Do not observe money in t, instead observe M(t − 1)
• Observe their own prices only
• No communication between islands
Islands’ Model
Setup: Information
• Incomplete information
• Rational choices
• Know the true model of the economy
• Know all probabilities
• Max U subject to constraints and informational frictions
• Rational expectations
Islands’ Model
Setup
• young receive time endowment y
• When young, they can consume a share of the endowment
(leisure) or work
• If they work, they generate output that is sold to old
agents in their island
• Each unit of labor produces one of good
• Denote lit = l(pi )t labor supply of a young born in i in
period t that observes p
Islands’ Model
Setup
• BC agent h in island i at period t, is
i,h i
i,h
i,h i
i,m
ci,h
t (t) + lt (p ) = ct (t) + p (t)mt (p ) = y
• Money demand equals labor supply!
• BC when old
i,j,h
i
ct (t + 1) = pj,m (t + 1)mi,h
t ( p ) + at + 1
i,j,h
ct (t + 1) =
pj,m (t + 1) i,h i
l (p ) + at+1
pi,m (t) t
Islands’ Model
Setup
• Note consumption when old depends on whether he
travels or not (random)
• Young max U taking into account that t + 1 he might be in
any of the 2 islands
• When choosing labor supply, they only observe pi,m (t)
pj,m (t+1)
• Note i,m
is the return to work. The young works in
p (t)
island i, wage is pi,m (t) which is used to consume in t + 1,
pj,m (t + 1)
Islands’ Model
Setup
• Income and substitution effect
• Labor supply depends on real wage
• Assume substitution effect dominates
Islands’ Model
Case 1: Deterministic monetary policy
• Assume M(t) = µM(t − 1)
• Rational agents infer the stock of money
• Consider island i with population of Ni young
• Money demand per young is
i
pi,m (t)mi,h
t (p ) =
i
mi,h
i
t (p )
= li,h
t (p (t))
pi ( t )
Islands’ Model
Case 1: Deterministic monetary policy
i
• Aggregate money demand in island i is Ni li,h
t (p (t))
• Money supply M(t), and old guys distributed equally
• Money supply island i is pi,m (t) M2(t)
• Equilibrium?
Islands’ Model
Case 1: Deterministic monetary policy
i
i,m
Ni li,h
t (p (t)) = p (t)
• Price level
pi ( t ) =
M(t)
2
M(t)
2
i,h i
i
N lt (p (t))
• Number of young guys in the island affect prices!
• Prices contain information (you don’t have to know in
which island you are, the price already contains that info!)
Islands’ Model
Case 1: Deterministic monetary policy
• Suponse NA < NB
pA (t) =
M(t)
2
A,h A
A
N lt (p (t))
pB (t) =
M(t)
2
NB lB,h
(
pB (t))
t
• Then
• NA = N/3 y NB = 2N/3
• It can be shown that pA (t) > pB (t)
Islands’ Model
Case 1: Deterministic monetary policy
• Return on money
j,h
pj,m (t + 1)
M(t) Nj lt (pj (t))
=
i
M(t + 1) Ni li,h
pi,m (t)
t (p (t))
• An increase in the stock of money
• Does not affect relative prices
• Does not affect labor supply
• Money is neutral
Islands’ Model
Case 1: Deterministic monetary policy
• Permanent increase in µ
j,h
pj,m (t + 1)
1 Nj lt (pj (t))
=
i
µ Ni li,h
pi,m (t)
t (p (t))
• Reduce the return on labor
• “Inflationary tax” to labor, then substitute labor by leisure
• Output falls
Islands’ Model
Case 1: Deterministic monetary policy
Figure: Champ, Freeman and Hastag (2010)
• High and low growth rate of money
Islands’ Model
Case 2: Random Monetary Policy
• Now assume M(t) = M(t − 1) with prob θ
• M(t) = 2M(t − 1) with prob 1 − θ
• That is, µ(t) = {1, 2}
• µ(t) is know only at t + 1
Islands’ Model
Case 2: Random Monetary Policy
• Price
i
p (t) =
z(t)M(t−1)
2
i
Ni li,h
(
t p (t))
• Signal extraction problem: the young observe a price, but
he does not observe why it is high (low)
• Why would someone want to distinguish the source of
price variations?
Islands’ Model
Case 2: Random Monetary Policy
• Suppose you observe a high price
• If it is high because there are few young, then you know
real wage is high
• If it is high because of high money growth, real wage is not
high
Islands’ Model
Case 2: Random Monetary Policy
Figure: Champ, Freeman and Hastag (2010)
• pa (t) < pb (t) = pc (t) < pd (t)
Islands’ Model
Case 2: Random Monetary Policy
• If you observe pd (t) you know: few young + high money
growth
• If you observe pa (t) you know: many young + low money
growth
• If pb (t) = pc (t), no idea
Islands’ Model
Case 2: Random Monetary Policy
Figure: Champ, Freeman and Hastag (2010)
• Supply an intermediate level of labor
Islands’ Model
Case 2: Random Monetary Policy
• This policy does not generate higher labor supply in any
circunstance
• If you observe pc (t) young are in an island with many
young guys and with high money growht, they work more
than with pa (t)
• If you observe pb (t) young are in island with few young
and low growth rate of money, and they work less than in
pd (t)
Islands’ Model
Case 2: Random Monetary Policy
Figure: Champ, Freeman and Hastag (2010)
Islands’ Model
Case 2: Random Monetary Policy
• If µ = 1, labor supply is between cases a y b
• If µ = 2, labor supply is between cases c y d
Islands’ Model
Lucas critique
• Assume estimate a Phillips curve with negative slope
• Strategy: induce higher inflation to stimulate the economy
• This strategy only works if the policy is not anticipated by
the young
• The “Stimulus” only work when you are uncertain
between cases “c” and “b”
• If you anticipate you are in “c” (or attach a high
probability to this event) labor supply is not high
Islands’ Model
Lucas critique
• Employment and inflation relationship depends on
government policies
• If agents anticipate inflation, there will be no response of
employment