money in the competitive equilibrium model part 1
DESCRIPTION
Money in the Competitive Equilibrium Model Part 1. Ad-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? - PowerPoint PPT PresentationTRANSCRIPT
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