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Money in the Competitive Equilibrium Model Part 2PowerPoint Presentation

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

Money and Real Ecomomic Variables

- 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: money is neutral and superneutral.
(exact)

or r = R – p (approx)

where R = nominal rate

r = real rate

inflation rate =

Explicit Money Demand money is neutral and superneutral.

- 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 money is neutral and superneutral.:
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) or r = R – p (approx)

where

- Timeline money is neutral and superneutral.
- Budget Constraint (nominal terms)
(BC)

Total Sources of Income = Total Uses

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

- State Variables: money is neutral and superneutral.
Control Variables:

- Bellman Equation:
subject to

(transition equation)

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

Cash-in-Advance Model money is neutral and superneutral.

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

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

- State Variables: money is neutral and superneutral.
Control Variables:

- Bellman Equation:
CIA Constraint

subject to

- FOC & Envelope money is neutral and superneutral.
(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 {c money is neutral and superneutral.t, 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 M money is neutral and superneutral.s 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.

Figure 15.4 money is neutral and superneutral.Scatter Plot of the Inflation Rate vs. the Growth Rate in M0 for the United States, 1960–2003

CIA Model with Production money is neutral and superneutral.

- 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 money is neutral and superneutral.
(FOC1)

(FOC2)

- Firm FOC: money is neutral and superneutral.
(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 money is neutral and superneutral.steady state equilibrium occurs where N, c, y, (M/P) are constants (to be determined, NOT exogenous):

- Steady State CE Values money is neutral and superneutral.:
(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 money is neutral and superneutral.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.

Inflation & Employment: Cross Country Study [Cooley & Hansen (1989)]

Xass 1976-1985

Austria, Belgium

Demark, Finland

France, Germany

Greece, Ireland, Italy

Netherlands, Norway

Portgual, Spain

Switzerland, UK

Canada, US, Australia New Zealand, Japan

Chile, Venezuela

Vertical Axis =

employment

Costs of Inflation and Optimal Monetary Policy Hansen (1989)]

- 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 transactions with currency (“shoe-leather” costs).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 “ transactions with currency (“shoe-leather” costs).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 = 0 m* = 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 transactions with currency (“shoe-leather” costs).
* 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.

M1 Money Supply, 2000-2010 transactions with currency (“shoe-leather” costs).Levels

M1 Money Supply, 2000-2010 transactions with currency (“shoe-leather” costs).Growth Rate

- Current monetary policy and the Friedman rule: transactions with currency (“shoe-leather” costs).
- 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

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