Money and Banking

Lecture IV: The Macroeconomic E↵ects of Monetary Policy: IS-LMModel

Guoxiong ZHANG, Ph.D.

Shanghai Jiao Tong University, Antai

November 1st, 2016

Keynesian Matters

Source: http://letterstomycountry.tumblr.com

Road Map

IS-LM ModelKeynesian Cross

commodity market: IS curve

money market: LM curve

IS-LM and monetary policy

Aggregate Demand and Aggregate Supplyliquidity preference and aggregate demand

long run and short run aggregate supply

AD-AS and monetary policy

Dynamic Aggregate Demand and Aggregate Supplydynamic IS curve

Philips curve

adaptive expectation

Taylor rule and Taylor principal

Keyesian Cross

Planned expenditure:consumption

planned investment

government spending

net export

Actual expenditure:consumption

investment = planned investment + unexpected inventory investment

government spending

net export

The economy is at equilibrium when planned expenditure equals actualexpenditure.

Consumption function

In Keynes’s view, consumption is determined by dispensable income:

C = C0

+mpc ⇤ Yd,

where C0

is autonomous consumption, mpc is marginal propensity toconsume, and Yd = Y � T is dispensable income.

Keynes believed that mpc must be between 0 and 1.Is it still true today?

What will happen if mpc is heterogeneous?

Multipliers

Taking the interest rates as given, multipliers that measure output’sresponse to exogenous shocks can be calculated from the Keynesian cross:

Y = C0

+mpc ⇤ (Y � T ) + I +G+NX.

private spending multiplier (C0

and I): 1

1�mpc

government spending multiplier (G): 1

1�mpc

government tax multiplier (T): � mpc1�mpc

net export multiplier (NX): 1

1�mpc

Commodity Market: IS Curve

IS curve originates from the notion that planned investment is negativelyrelated to the interest rate:

Y = C0

+mpc ⇤ (Y � T ) + I(r) +G+NX.

interest rate shifts the planned expenditure in the Keynesian cross andin turn a↵ects the aggregate output;

interest rate here is the real interest rate;

therefore we have a downward sloping IS curve

Money Market: LM Curve

LM curve originates from Keynes’ liquidity theory of money:

(MP

)d = L(Y, i).

money demand is negatively related totextcolor[rgb]1.00,0.00,0.00nominal interest rate and positively relatedto aggregate income;

therefore for a given money supply, aggregate income and nominalinterest rate are positively related;

Fisher equation:

i = r + ⇡e,

which gives a one-to-one relationship between nominal and real interestrates given economic agents’ expectation on future inflation to beconstant;

therefore we have a upward sloping LM curve

Exogenous Shocks that A↵ect IS-LM Equilibrium

Exogenous shocks that right-shift the IS curve:increase in autonomous consumption (wealth e↵ect)

increase in investment that not driven by lower interest rate (animal

spirit, technology progress)

expansionary fiscal policy shock

increase in net export (technology progress; preference shock; trade

policy shock)

Exogenous shocks that right-shift the LM curvemonetary policy shock

liquidity preference shock

Fiscal Policy vs Monetary Policy in IS-LM

When money demand is not elastic with respect to interest rate(vertical LM curve), monetary policy is e↵ective while fiscal policy isine↵ective;

When money demand is extremely elastic with respect to interest rate(liquidity trap), fiscal policy is e↵ective while monetary policy isine↵ective;

Generally the more sensitive money demand is with respect to interestrate, the more e↵ective fiscal policy is compared to monetary policy.

IS-LM and Aggregate Demand

Rising price level lowers real money supply (nominal money supply isgiven) and hence shifts the LM curve to the left;

Left-moving LM curve cause a lower equilibrium aggregate income inthe IS-LM curve;

Therefore we have an aggregate demand curve that describe a negativerelationship between price level and aggregate income;

Factors that shift the aggregate demand curve:factors that shift the IS curve shift the aggregate demand curve at the

same direction;

factors that shift the LM curve shift the aggregate demand curve

(except for the price level) shift the aggregate demand curve at the same

direction.

Aggregate Supply

Long-run aggregate supply curve is vertical (it’s determined by factorendowments and technology);

Short-run aggregate supply curve is upward sloping (wage and pricestickiness);

Factors that shift the short run aggregate supply curve:labor market friction;

financial market friction;

other production cost shocks (oil price, etc.)

Dynamic IS Curve

Similar as the IS curve, a dynamic IS curve also portraits a negativerelationship between the real interest rate and aggregate income:

Yt = Yt � ↵(rt � ⇢) + ✏t

Yt: natural output

rt: real interest rate

⇢: natural interest rate

✏t: demand shock

Fisher Equation

Fisher equation relates nominal interest rate and real interest rate:

rt = it � Et⇡t+1

rt: ex ante real interest rate

it � ⇡t+1

: ex post real interest rate

Philips Curve

Philips curve relates inflation and aggregate income:

⇡t = Et�1

⇡t + �(Yt � Yt) + ⌫t

Firms form their expectation on future inflation when setting prices;

When actual output exceeds natural output, labor market is tightened,production cost is raised, and therefore price becomes higher;

⌫t: supply shock

Adaptive Expectation

Adaptive expectation is the simplest form of expectation formation:

Et⇡t+1

= ⇡t

just simply a short-cut: in real macro we use rational expectationequilibrium (REE).

Taylor Rule and Taylor Principal

A common way to characterize monetary policy response is to use a form ofTaylor rule:

it = ⇡t + ⇢+ ✓t(⇡t � ⇡⇤t ) + ✓Y (Yt � Yt) + ut

⇡⇤t : inflation target (not exactly inflation targeting)

ut: monetary policy shock

✓t > 0, ✓Y > 0

Taylor Principle: 1 + ✓t > 1

Taylor rule: US Experience

⇢ = 2.0, ✓t = 0.5, ✓Y = 0.5, ⇡⇤t = 2.0

Dynamic AD-AS

A dynamic aggregate demand and aggregate supply model:

Yt = Yt � ↵(rt � ⇢) + ✏t

rt = it � Et⇡t+1

⇡t = Et�1

⇡t + �(Yt � Yt) + ⌫t

Et⇡t+1

= ⇡t

it = ⇡t + ⇢+ ✓t(⇡t � ⇡⇤t ) + ✓Y (Yt � Yt) + ut

After some algebra we can eliminate the expectation and solve the modelinto two equations:

dynamic aggregate supply

⇡t = ⇡t�1

+ �(Yt � Yt) + ⌫t

ut: dynamic aggregate demand

Yt = Yt �↵✓⇡

1 + ↵✓⇡(⇡t � ⇡⇤

t ) +1

1 + ↵✓⇡✏t +

↵✓⇡1 + ↵✓⇡

ut.

Long Run Economic Growth

Supply Shock

Demand Shock

Growth vs Inflation

Taylor Principal