Advanced Macroeconomics: Lecture 8 - MP 1 IS-PC-MR Flashcards
What the raasclaat does IS-PC-MR stand for?
New Keynesian Model of the Macroeconomy.
IS: IS curve
PC: Phillips curve
MR: Monetary rule (interest-rate-based monetary policy rule)
Brief intro: New Consensus Macroeconomics (NCM)
Debates since the 1970s between classical schools of thought and different strands ofKeynesian economics have shaped a New Macroeconomic Consensus (NCM) to conduct monetary policy.
Basis/assumptions of the Consensus
Business cycle is demand driven in the short-run.
MP affects output in the short-run. (i.e. stimulative environment allows short-term “overheating,” increased output of which inflation is the byproduct.)
In the long-run, MP cannot affect output (only supply-side policies like investment in capital and better education can do this).
Phillips curve must account for expectations, either forward or backward looking
Central bank sets interest rates with the aim of controlling inflation. There is a lag so the CB must be forward looking.
Fiscal policy is subject to crowding-out effects and/or interferes with the CB aims of controlling inflation, and so the target should be balanced books (no major contractionary/expansionary fiscal policy)
THE 3-EQUATIONS or IS-PC-MR MODEL ILLUSTRATES THE ABOVE ASSUMPTIONS
Building blocks: 3 ASSUMPTIONS of the IS-curve
ASSUMPTION 1.
Negative relationship between real output (y) and real interest rates (r), but there is a time lag, so R0 (rates today) impacts Y1 (output tomorrow).
Y1 = A - ar0
Where:
Y1 = output in the next period
A = exogenous demand of public and private sectors
r0 = interest rates in current period
a > 0 = sensitivity of y1 to r0
By plugging Ye (equilibrium output) into the equation above we get the below equation and can determine the level of interest rate that would deliver Ye:
Ye = A - ars
Where:
Ye = equilibrium output
A = exogenous demand of public and private sectors
rs = stabilizing interest rate
a > 0 = sensitivity of y1 to r0
ASSUMPTION 2.
“A” accounts for fiscal policy (FP), but FP does not play a role in the model due to the crowding-out assumption and risk of interfering with MP.
ASSUMPTION 3.
The economy has an equilibrum output (Ye). This is the level at which both wage-setters and price-setters make no attempt to change the prevailing real wage.
Building blocks: IS-curve cont.
A useful formulation of the IS-curve is the IS-output gap form:
y1 - ye = -a(r0 - rs)
Where:
y1 - ye = output gap in period 1
r0 - rs = difference between actual interest rates (in current period) and stabilizing interest rates. i.e. the necessary change in interest rates to stabilize the economy.
When y1 ≠ ye, r0 ≠ rs, that is: when there is an output gap in period 1, real rates are not at stabilizing level.
-a is because the relationship is NEGATIVE. i.e. if rates are above stabilizing level, output gap will be negative, and vice versa.
In the current period (t = 0) the CB will choose interest rates that allow them to close the output gap in the next period (t = 1). There is a time-lag, because changes in interest rates in the current period (r0) do not affect output until the next period (y1).
Building blocks: 2 ASSUMPTIONS of the Phillips Curve (PC)
- Phillips curve suggests a positive relationship between output and inflation:
π1 = πE + a(y1 - ye)
Where:
π1 = inflation in period 1
πE = inflation expectation for the following period
y1 - ye = output gap in period 1
a = sensitivity of inflation in period 1 to output gap in same period
- Inflation expectations for next period are equal to inflation in current period. πE = π0 = πt-1. So, if inflation is 3% this year, we expected inflation to be 3% next year.
Hence, plugging πE = π0 into our initial Phillips curve, we get an inertial Phillips curve:
π1 = π0 + a(y1 - ye)
Two reasons to use this inertial PC:
1. Adaptive inflation expectations
2. Prices and wages are sticky
Graphically, we get a cluster of PCs depending on what past or inertial inflation is (π1)
When there is a positive output gap (y1 > ye), inflation rises (delta π > 0) & unemployment < NAIRU
When there is a negative output gap (y1 < ye), inflation falls (delta π < 0) & unemployment > NAIRU
Building blocks: ASSUMPTIONS of Monetary Policy Rule (MR)
- There is policy lag.
y0 –> π0 (output in current period impacts inflation in current period)
π0 –> π1 (inflation in current period sets expectations for inflation - and thus price setting - in next period)
r0 –> y1 (real interest rates in current period impact output in next period)
y1 –> π1 (Actual output in current period drives inflation in current period)
CONSEQUENTLY, the CB setting r0 cannot affect inflation in the current period, but it can affect output in the next period (y1) which affects inflation in the next period
- Central Bank is assumed to set nominal rates in t = 0 (i0), but since the inflation rate in t = 0 is predetermined, by setting nominal interest rates the bank is choosing the real interest rates at which it wants the economy to operate: r0 = i0 - π0 (Fisher equation).
In short: real interest rates = inflation + nominal interest rates
- It is assumed the CB has two interests: inflation (π) & output (y) and that it wishes to minimize fluctuations away from its target inflation rate (πT) and equilibrium/potential output (ye)
- This behaviour can be formulated in the below loss-minimizing function:
L = (y1 - ye)^2 + β(π1 - πT)^2
Where:
(y1 - ye)^2 = absolute value of output gap (hence squared)
(π1 - πT)^2 = absolute value of inflation variance from target inflation
β = weighting of preferences… whether the CB care more about inflation or output
β = 1, CB care equally about inflation and output
β < 1, CB care more about output (unemployment averse)
β > 1, CB care more about inflation (inflation averse)
Building Blocks: Monetary Policy Rule (MR) cont.
Assume β = 1 for simplicity, they care equally about inflation and output. In this case, we get concentric rings that act as indifference curves for the CB. The dot at the middle of the concentric rings is point (Ye, πT).
Building Blocks: Monetary Policy Rule (MR) mathematically
Subject to constraint of the PC because CB can only control inflation indirectly by the relationship between output and inflation outlined by the PC.
Building Blocks: Monetary Policy Rule (MR) graphically
MR denotes a negative relationship between output and inflation.
MR line shows the optimal combinations of π and Y in period 1 that minimize the CBs loss function in period 0.
Slope of the MR curve depends on both alpha and beta.
Full 3 equations model: (IS-PC-MR)
We can now put together the 3 building blocks to get the IS-PC-MR model.
IS output gap form:
y1 - ye = -a(r0 - rs)
PC (inertial):
π1 = π0 + a(y1 - ye)
MR (monetary rule):
(y1 - ye) = -αβ(π1 - πT)
There is policy lag, so the CB is constantly forward-looking to see if its current r0 can deliver πT and Ye.
If it can –> no intervention.
If it can’t –> must change rates.
Interest Rate Rule (“Taylor Rule”)
The “Taylor Rule” is a combination of the 3 equations.
It tells us by how much the CB must change interest rates given current inflation ≠ target inflation.
Summary of New Consensus in Macroeconomics (NCM)
- CB sets interest rates to control inflation
- Phillips Curve (PC) is a short run concept. There is only a trade off between inflation and unemployment in the short-term. In the long-run, we operate at long-run supply equilibrium
- Fiscal policy not really considered as it can cause crowding out and interfere with CBs monetary policy
