money in the competitive equilibrium model part 1

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