The New IS-LM

• Microfoundations allow to– Address the Lucas critique– Perform welfare analysis– Integrate intertemporal budget constraints and

expectations.

• The new microfoundations include– Sticky (but endogenous) prices, usually staggered– A motive for holding money– Monopolistic competition by firms selling differentiated

products

The Krugman model

• Endowmen economy

• A representative consumer maximizes PDV of utility

• One must hold enough cash to purchase consumption

• All variables are constant from t=2 on = the long run

• Prices are flexible from t=2 on

• Prices may be rigid at t=1

• The model may be used to analyze the role of a liquidity trap

Preferences

Timing

a b

t t+1

a b

Trade bonds for cashGet Mt, Bt

TradeConsumePay taxes

The second sub-period:

• At t-b, I have an endowment yt that I must trade to consume

• I can’t consume more than my money holdings: PtCt <= Mt

• The government issues money and bonds, levies taxes, and rebates seignorage:

• Net tax Tt = TAXt – (Mt+1 – Mt).

The first subperiod

• People exchange money for bonds

• Bonds pay a nominal interest rate it between date t-a and date t+1-a

The budget constraint

The optimization problem

The Euler equation

• Substituting the value of μ into the FOC for consumption and dividing between two consecutive periods we get the Euler equation

The long run

• For t >= 1, Mt = M*, Yt = Y*

• Prices are fully flexible Ct = C* = Yt = Y*

• Assume prices are constant: Pt = P*

• Then it = i* = 1/δ – 1 from Euler

• CIA must then be binding

• This condition determines the price level: P* = M*/Y*

The short run: IS

• At t=0, variables differ from their long-run values.• The Euler equation gives us a relationship

between C, i and P• It is similar to the IS curve• Expectations about future activity play a role• Inflationary expectations also play a role

C

i

IS

The short run: LM

• If the CIA constraint is binding, then i > 0 and C = M/P.

• If the CIA constraint is not binding, then i = 0 and C < M/P

• This defines an L-shaped LM curve

i

C

LM

M/P

The flexible price case

• The IS and LM curve can be rewritten in the (p,i) plane

Regime 1: CIA binding

IS

LM

M/Y

p

i

Regime I is like a purely « real » model

• Price is proportional to money, P = M/Y

• Real interest rate is determined by intertemporal MRS: 1+r = (Y/Y*)-ρ/δ

• Nominal interest rate determined by Fisher equation 1+i = (1+r)P*/P =(1+r)(1+π)

• This regime holds if M < (Y/Y*)-ρ/δ.P*Y

Regime 2: CIA not binding

IS

LM

M/Y

p

i

Regime II is a Liquidity trap

• Nominal interest rate is zero money is useless at the margin

• The price level is determined by expectations and activity, does not respond to money: P = (Y/Y*)-ρP*/δ

• This regime takes place if M >(Y/Y*)-ρ/δ.P*Y

Determination of P

• Unresponsive to current money

• Higher if future prices are higher

• Higher if future activity is higher

• Higher if current activity is lower

What’s going on?

• Given the future, the real interest rate must be such that C = Y

• To understand the adjustment, assume future activity Y* goes up

• Regime I: I want to consume more, need more money, sell bonds for cash, the nominal rate goes up, so does the real rate, I prefer to postpone consumption.

• Regime II: I don’t need more money, excess demand for goods, price level goes up, increases the real rate, I prefer to postpone consumption.

Another interpretation

• There exists an equilibrium rate of return r• This defines the maximum rate of

deflation; higher rates would imply i<0• The larger M, the larger the rate of

deflation at which people are willing to hold it (ROR on money = -deflation)

• When this required rate is more than the maximum, the economy is in a liquidity trap

LT is more likely when

• Current consumption is too low relative to real money, i.e. when

• M is large

• P* is low

• Y* is low

Rigid prices

• P is fixed, and the standard IS-LM diagram is used

• One is in that regime provided it yields C < Y

Rigid prices: regime I

• CIA is binding: C = M/P (AD)

• An increase in M raises C and lowers i

• An increase in Y* raises C and i

• An increase in P* raises C and i

Rigid prices: regime II

• C determined by Euler with i=0

• Monetary policy is ineffective

• One may get rid of the LT by reducing the money stock to move the economy to regime I, but it is contractionary

• Otherwise, one must increase expectations of future activity and/or inflation

Ricardian equivalence

• In standard IS-LM, budget deficits shift the IS curve and increase output

• Here, as long as PDV(taxes)=PDV(expenditure), consumption does not react to the timing of debt

• Debt accumulation is useless to get you out of the liquidity trap

• If taxes are distortionary, it can actually be harmful