money in the competitive equilibrium model part 1 ad-hoc money demand in ce model hyperinflation...
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Money in the Competitive Equilibrium Model
Part 1Ad-Hoc Money Demand in CE Model
Hyperinflation Dynamics
• How can we incorporate money demand into the competitive equilibrium model?
• How will the quantity of money affect real variables, prices, and inflation?
• What are the implications for monetary policy?
• Two Approaches for adding money in CE model:
(i) Ad-Hoc (exogenous) money demand.
(ii) Explicit Money Demand as a choice variable for households.
(Search Model / Shortcuts)
Ad-Hoc Money Demand
• Money Demand Function:
where Ly > 0, LR < 0 and R = r + e
• Money Market Equilibrium: y = y* and r = r* from CE model
or
MD L y R ( , )
M
PL y r
se ( * , * ) M PL y rs e ( * , * )
• The ad-hoc money demand function can be “added” onto the CE model. Money market only determines prices:
CE Model y*, r*, c*, N*, *
Money Market P*
(arrows flow one way only!)
• A competitive equilibrium in a two-period model with production is and
for t = 1,2 solving:
(1 eq)
(2 eq)
(2 eq)
(4 eq)
(1 eq)
*}*,*,{ ttt yNc *}*,*,{ Pr t
*)1(/ 21 rUU cc
tctlt UU /
)(' tt Nf)( ttt Nfyc
)**,(/* es ryLMP
• Equilibrium Prices:
dP/dy* < 0 and dP/dr* > 0
• Productivity Shocks (z)
Temp: dy*/dz > 0, dr*/dz < 0 dP/dz < 0
Perm: dy*/dz > 0, dr*/dz = 0 dP/dz < 0
• Neutrality of Money:
dP/P = dM/M
inflation rate () = money growth ()
• Classical Dichotomy: Real variables are independent from nominal variables (P,M)
y*, r*, c*, N*, *
Money Market P*
(arrows flow one way only!)
Inflation Dynamics
• Historically many countries around the world have experienced hyperinflaiton.
(1) Hyperinflation in 1980sIsrael – 370%Argentina – 1,100%Bolivia – 8000%
(2) German Hyperinflation (1/22 – 12/23, 4000%)Daily Newspaper Price$0.30 (1/21)$1,000,000 (10/23)$7,000,000 (11/23)
• Cagan (1956) asks:
(i) Is there a systematic process by which inflation expectations are formed?
(ii) How did inflation expectations contribute to hyperinflations?
• Note from money market clearing: dP/de > 0• Cagan (log) Money Demand Function:
L y R te( , )
• Where is constant (related to y*, r*) and > 0 measures the sensitivity (elasticity) of MD to e.
• Money Market-Clearing
or (1)
• Adaptive Expectation
(2)
0 < < 1 represents the speed of adjustment.
MDPM tt )/log(
ett
et 11 )1(
ettt pm
• Estimation
- Solve for te from (1), lag it to get t-1
e
- Substitute into (2) and then plug (2) into (1)
(3)
Country Germany 322 5.46 0.20
Russia 57 3.06 0.35
))(1( 111 ttttt pmpm
• Stability
Substitute t-1 = pt – pt-1 into (3) and re-arrange:
If mt – mt-1 =m constant, then
])1()[1
1()
11( 11
tttt mmpp
1
)()
11( 1
mpp tt
• pt is stable (non-explosive) if
or • A sufficient condition for hyperinflation: • Germany:
Russia:
11
1
• Intuition:
• Expected inflation adapts faster to actual inflation (high ) and the more sensitive MD is to expected inflation (high ) hyperinflation more likely.
and PMDet
Rational Expectations
• Cagan Model with rational expectations:
• Money Market Equilibrium:
• Fed Money Supply Rule:
where are constants and is a random money demand shock created by the Fed.
tttttttet ppEppEE 11t )()info(
)( 1 ttttt ppEpm
ttt mm 110
M1 Nominal Money Supply, 2002-2006
Monetary Policy: 2004 - 2008
• Implications
(i) Current pt depends upon current and future money supplies mt.(ii) The impact of a shock to the money supply
() depends upon whether it’s temporary or permanent.
* small temp small effect on pt
* close to 1 perm large effect on pt
• Nominal versus Real
Quantities: Real = Nominal/P
Interest Rates:
(exact)
or r = R – (approx)
where R = nominal rate
r = real rate
inflation rate =
t
tt
Rr
1
1)1(
111
t
t
t
ttt P
P
P
PP