Money in the competitive equilibrium model part 2
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Money in the Competitive Equilibrium Model Part 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).

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Money in the Competitive Equilibrium Model Part 2

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Money in the competitive equilibrium model part 2

Money in the Competitive Equilibrium ModelPart 2

Explicit Money Demand

Cash-in-Advance Model

Optimal Monetary Policy


Money and real ecomomic variables

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.


Money in the competitive equilibrium model part 2

  • 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.


Money in the competitive equilibrium model part 2

  • Reminder: Nominal versus Real Interest Rates:

    (exact)

    orr = R – p (approx)

    whereR = nominal rate

    r = real rate

    inflation rate =


Explicit money demand

Explicit Money Demand

  • 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 in the competitive equilibrium model part 2

  • 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


Money in the competitive equilibrium model part 2

  • Timeline

  • Budget Constraint (nominal terms)

    (BC)

    Total Sources of Income = Total Uses

  • Optimization: Choose {ct, Mt, Bt} to

    subject to (BC)


Money in the competitive equilibrium model part 2

  • State Variables:

    Control Variables:

  • Bellman Equation:

    subject to

    (transition equation)


Money in the competitive equilibrium model part 2

  • 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.


Cash in advance model

Cash-in-Advance Model

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

  • New Timeline

  • Cash-In-Advance Constraint

    (CIA)


Money in the competitive equilibrium model part 2

  • State Variables:

    Control Variables:

  • Bellman Equation:

    CIA Constraint

    subject to


Money in the competitive equilibrium model part 2

  • 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)


Money in the competitive equilibrium model part 2

  • 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)


Money in the competitive equilibrium model part 2

  • 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.


Money in the competitive equilibrium model part 2

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


Cia model with production

CIA Model with Production

  • 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


Money in the competitive equilibrium model part 2

  • Household FOCs

    (FOC1)

    (FOC2)


Money in the competitive equilibrium model part 2

  • 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)


Money in the competitive equilibrium model part 2

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


Money in the competitive equilibrium model part 2

  • 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.


Money in the competitive equilibrium model part 2

  • 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.


Inflation employment cross country study cooley hansen 1989

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

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


Costs of inflation and optimal monetary policy

Costs of Inflation and Optimal Monetary Policy

  • Recall relation between nominal and real interest rates:

    (approx)

    (actual)

  • CEM (in steady state)  r* = r constant.

  • increase mincreases p  increases R


Money in the competitive equilibrium model part 2

  • 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?


Money in the competitive equilibrium model part 2

  • 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.


Money in the competitive equilibrium model part 2

  • 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 = 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)


Money in the competitive equilibrium model part 2

  • 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.


M1 money supply 2000 2010 levels

M1 Money Supply, 2000-2010Levels


M1 money supply 2000 2010 growth rate

M1 Money Supply, 2000-2010Growth Rate


Money in the competitive equilibrium model part 2

  • 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


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