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Money in the Competitive Equilibrium Model Part 2

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Money in the Competitive Equilibrium ModelPart 2

Explicit Money Demand

Cash-in-Advance Model

Optimal Monetary Policy

- Neutrality of Money a one-time change in the level of the nominal money supply has no effect on real economic variables (only nominal).
- Superneutrality of Money a change in the growth rate of the money supply has no effect on real economic variables.
- Sometimes “superneutrality” definition exclued the real money supply as a “real” economic variable.

- CE model with Ad-Hoc money demand (e.g. Cagan model) money is neutral and superneutral.
- An increase in the money growth rate
- Classical dichotomy No change in CE values of y*,N*,c*, and r*.
- This result may not be true in CE model with explicit money demand.

- Reminder: Nominal versus Real Interest Rates:
(exact)

orr = R – p (approx)

whereR = nominal rate

r = real rate

inflation rate =

- Incorporate use of money as a decision of the representative household.
- Assumptions:
(A1)Income yt is exogenous

(A2)Households make an asset allocation decision between nominal money (M) and bonds (B).

(A3)TO BE ADDED

(A4)Government directly sets nominal Ms

(A6)No uncertainty

- Money Supply:
where Xt = transfer of money to public (“helicopter drop”) and m = money growth rate

- Reminder: Real vs Nominal Interest Rates:
(1+r) = (1+R)/(1+p)orr = R – p (approx)

where

- Timeline
- Budget Constraint (nominal terms)
(BC)

Total Sources of Income = Total Uses

- Optimization: Choose {ct, Mt, Bt} to
subject to (BC)

- State Variables:
Control Variables:

- Bellman Equation:
subject to

(transition equation)

- FOC and Envelope conditions contradict unless R = 0.
- If R > 0 then M = 0. Money is an inferior asset to bonds and valueless.
- Need another constraint to give money value.

(A3): Consumption must be purchased with cash carried in advance from previous period.

- New Timeline
- Cash-In-Advance Constraint
(CIA)

- State Variables:
Control Variables:

- Bellman Equation:
CIA Constraint

subject to

- FOC & Envelope
(1)

- Market-Clearing (MC):
Goods:ct = yt = y*

Money:Mt = Mts

Bonds:Bt = 0

(Note from BC if two of the three markets clear, the third one will also clear)

- The CE are values for {ct, yt, Bt, rt, m=(M/P), R, p} solving (1), (2) and (MC) conditions.
- CE Values:
c* = y*(exogenous)

p* = m

r* = (1/b – 1) = r

(M/P)* = c*(Neutrality)

(1+R) = (1+r*)(1+p*)(Fisher Effect)

- One time changes in the level of Ms are neutral.
- Increases in the growth rate of money (m) leads to an increase in p* and R* while leaving c*, y*, r* unchanged. (Superneutrality)
- This result comes from exogenous income and is not general when model is modified.
- Consider adding labor market and firms to the model.

- Cooley and Hansen (1989 – AER)
- Modify to Include Labor and Production
(1)yt = f(Nt)

(2)Utility in each period: U(ct,lt) = u(ct) + u(lt)

(3)Firms demand labor to max P = f(N) - wN

(4)Modify (BC)

(BC)

(5)(CIA) is the same

- Household FOCs
(FOC1)

(FOC2)

- Firm FOC:
(FOC3)

- Market-Clearing (MC):
Goods:ct = yt

Money:Mt = Mts

Bonds:Bt = 0

Labor:Nts = Ntd = Nt

- Utility: Assume u(c,l) = ln(c) + ln(l)

- A steady state equilibrium occurs where N, c, y, (M/P) are constants (to be determined, NOT exogenous):

- Steady State CE Values:
(s1)p* = m

(s2)r* = (1/b – 1) = r

(s3)(1+R) = (1+r*)(1+p*)(Fisher Effect)

(s4)

(s5)c* = y* = f(N*) = (M/P)=m*

- Notice (s4) N* and there will be an inverse relationship between N* and m.

- In CIA model with production money is neutral but not superneutral.
- Money growth and inflation negatively affects employment, consumption, output, real balances.
- Inverse Phillips Curve - relation between inflation and “unemployment” is upward sloping.
- Inflation “taxes” work and households substitute towards leisure.

Xass1976-1985

Austria, Belgium

Demark, Finland

France, Germany

Greece, Ireland, Italy

Netherlands, Norway

Portgual, Spain

Switzerland, UK

Canada, US, AustraliaNew Zealand, Japan

Chile, Venezuela

Vertical Axis =

employment

- Recall relation between nominal and real interest rates:
(approx)

(actual)

- CEM (in steady state) r* = r constant.
- increase mincreases p increases R

- High inflation leads to higher costs of conducting transactions with currency (“shoe-leather” costs).
- Welfare costs of inflation: Lucas (2000, Econometrica) estimates that reducing US steady inflation from 10% to 0% is equivalent to 1% gain in real GDP.
- What is the optimal money growth rate m* in the CE/CIA model with production?
- What’s the “optimal” inflation rate in the long-run?

- What value of m maximizes utility of the representative household?
- The best (welfare maximizing) allocation is the Pareto Optimal allocation:
MRSl,c = w

MRSct,ct+1 = (1+r*)

- Money distorts the optimal decisions of individuals away from social planner.

- The “Friedman Rule” says that the optimal monetary policy is to deflate the money supply and prices at a rate which drives R = 0:
(i)If R = r* + p , R = 0 m* = p = -r* < 0

(ii)If (1+R) = (1+r)(1+p) = (1+p)/b

R = 0m* = p = b - 1 < 0

- The Friedman Rule requires deflation at the real interest rate or rate of time preference.
(M. Friedman – The Optimum Quantity of Money, 1969)

- Practical Considerations
*Drive the nominal rate on riskless assets (government bonds) to zero.

*Nominal variables (wages) are downward rigid.

*There are always temptations to inflate the money supply (funding G, business cycles).

*Assumes certainty about money/prices.

*Most economists agree that low inflation (rather than deflation) is more practical.

- Current monetary policy and the Friedman rule:
- High money growth rate
- Historically Low Nominal Interest Rates
- Moderate/Low Inflation

- Model provides good description of long-runor steady inflation but lacks “liquidity effects” important for business cycle analysis.
- Solution? Modify Model or abandon market-clearing (stick prices, IS-LM?)
- Readings:
Williamson, Ch 10, p 363-368, 377-388, 395-399

Williamson, Ch 15, p 559-575