Monetary Business cycles –
Lesson 6
The benchmark Neo-Keynesian model
Introduction
Previous lessons
Nominal rigidities in a static model (Blanchard-Kiyotaki)
Price staggering + NK Phillips curve
This lesson
Incorporate this in a standard dynamic model
Consumption vs. Savings
Money vs. Bond
Work vs. leisure
Modern IS/LM model
Full-fledged dynamic model
Response to monetary shocks? To other shocks?
Introduction
Outline:
The Neo-Keynesian model
The log-linear model
The household’s block (neoclassical)
The firm’s block (imperfect competition and
Calvo price staggering)
New IS-LM
New Phillips curve
Taylor rules
Simulations
Sources:
Olivier Blanchard, course materials for 14.452
Macroeconomic Theory II, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/),
Massachusetts Institute of Technology
Wickens, Chapter 9
Walsh, Chapter 5
King: « The New IS-LM Model »
Neo-Keynesian model
Extension of the MIU model seen previously
New « ingredients »:
Imperfect competition + Price staggering à la
Calvo
Monetary policy represented by a rule for setting
the nominal interest rate (Taylor rule)
Capital stock is fixed
Simple linear macroeconomic model useful
for policy analysis but derived from agents’
optimal behavior
Neo-Keynesian model
2 agents:
Representative household:
owns all the firms
Supplies labor in a competitive labor market
Has a demand for differenciated goods
Firms:
Distribute profits to households
Hire labor in the competitive labor market
Set prices
Neo-Keynesian model – Households
Households’ objective:
Subject to:
Neo-Keynesian model – Households
FOC:
Neo-Keynesian model – Firms
Firms produce differentiated goods with the linear production
function:
They take the wage as given
Set prices à la Calvo (probability δ to change price each period)
Firms mimimize:
where p*t+s is the optimal price at date t+s
Neo-Keynesian model – Firms
Date t+s profits:
With
Optimal price P* :
Mark-up
Then:
=Calvo price setting
in logs:
Nominal
marginal
cost
Neo-Keynesian model – Firms
Aggregate price level:
In recursive form:
Neo-Keynesian model – Closing the
model
Budget constraint of the government:
Zero-supply of bonds by the government:
Aggregate budget constraint of the economy:
Labor demand:
Neo-Keynesian model – New IS/LM
We use Ct=Yt
IS (Euler equation):
LM (Demand for money):
Neo-Keynesian model – Functional forms
Then the system is log-linearized around the zero-inflation
steady state
xt=log(Xt)-log(X) where X is the steady state value
Log-linearized NK model – New IS-LM
Log-linearize around steady-state inflation:
Euler
+
Fisher
IS
LM
Modern
IS/LM
Exercise: compare monetary transmission
mechanism in this dynamic model and:
in the neoclassical model
in the static model of Blanchard-Kiyotaki
Log-linearized NK model
Log-linearize the rest of the system:
Labor supply
Production function
Price setting
Price index
Useful case: u(c)=log(c) Φ=1
Log-linearized NK model –Phillips curve
Price determination:
More generally:
How is the marginal cost related to the output gap?
Real marginal cost
Log-linearized NK model –Phillips curve
Flexible-price/second-best/capacity output
Given by qt=pt=wt-zt
Replace pt in labor supply equation (log case)
Replace nt in production function
Output gap= yt-zt :
(deviation from capacity)
?
Log-linearized NK model –Phillips curve
Using the price-setting equation:
Along with the labor supply and production equations:
=New Keynesian Phillips curve
Log-linearized NK model –Phillips curve
Why does inflation depend on output gap?
Compare with Calvo pricing (lesson 5)
Log-linearized NK model – Interest rate
rule
LM equation links M and i:
+ price stickiness
For the government, it is equivalent to set the money supply
M and the nominal interest rate i
Monetary policy can be represented either by a monetary rule
or an interest rate rule
Examples:
Simple monetary rule
Interest rate rule
(Taylor rule)
Log-linearized NK model – Bare bones
Demand block
Monetary
policy block
Price setting
block
IS
LM+
monetary or
rule
Interest rate rule
Phillips
curve
Simulations
First, compare with neoclassical model: What is the
effect of an shock in money growth?
Second, effect of other shocks (productivity, demand)
with a Taylor rule (more realistic)
Simulations – Baseline calibration
% deviation from SS
Responses to a shock in money supply
0.4
inflation
0.2
0
-0.2
-0.4
-2
nominal rate
0
2
4
Years after shock
% deviation from SS
% deviation from SS
Shock in the growth rate of money,
γ=0 (no autocorrelation)
6
8
Responses to a shock in money supply
0
-0.2
-0.4
real rate
-0.6
-0.8
-2
0
2
4
Years after shock
Responses to a shock in money supply
1.5
output
1
0.5
0
-2
0
2
4
Years after shock
6
8
6
8
Shock in the growth rate of money
Comparison with neoclassical:
Effect of money on output, even if the shock is not
anticipated
Liquidity effect
Positive effect on output
Responses to a shock in interest rate
nominal rate
% deviation from SS
1
0.5
0
-0.5
-2
inflation
0
2
4
Years after shock
6
8
Responses to a shock in interest rate
1
real rate
0.5
0
-2
0
2
4
Years after shock
Responses to a shock in interest rate
% deviation from SS
% deviation from SS
Interest rule – Shock in the interest rate
γ=0 (no autocorrelation)
0
-0.5
-1
-2
output
0
2
4
Years after shock
6
8
6
8
Interest rule – Shock in the interest rate
Negative shock to interest rate has the same
effect as a positive shock on money growth
Indeed, the central bank controls the interest
rate by setting money supply
Taylor rules
Effects of other shocks: productivity shocks, demand
shocks?
The effects of these shocks depend also on how
monetary policy reacts to them.
We must be careful in specifying monetary policy
We take a more realistic interest rate rule to represent
monetary policy: the Taylor rule:
How to calibrate the parameters of the Taylor rule?
Empirical issue
Taylor rules in practice
In deviation from steady state:
In levels:
δп and δx can be estimated
Issue: how to measure x?
Complicated
OK
Actual
output
Potential
output
Taylor rules in practice
Typically,
is measured by the trend of real
GDP
xt is detrended GDP
Taylor (1993): US (1987-1991)
Fed funds rate
Inflation rate
over previous 4
quarters
Percent deviation
of real GDP
from the linear
trend
Taylor (1993)
Taylor (1993)
Taylor rules in practice
Clarida, Gali and Gertler (2000): US (19601996)
Compare pre-Volcker (before 1979) and postVolcker era (after 1979)
Use several measures for output gap
From the Congressional budget office (CBO)
Percent deviation of real GDP from the quadratic trend
Percent deviation of unemployment from the quadratic
trend
Clarida, Gali and Gertler (2000) – With
CBO output gap
Clarida, Gali and Gertler (2000) – With
alternative output gap measures
Taylor rules in practice
Since Volcker: stronger emphasis on
controling inflation
Post-Volcker:
δп =1.5-2.5
δx =0.2-1.3
OECD: similar estimates
Taylor rules – The Taylor principle
Notice that δп is usually >1
δп >1 is the Taylor principle: ensures that
monetary policy is not destabilizing
Intuition
Baseline calibration: δп =2 and δx =0.6
% deviation from SS
Responses to a shock in technology
0
inflation
-0.05
nominal rate
-0.1
-2
1
0
2
4
Years after shock
6
8
Responses to a shock in technology
output
0.5
0
-2
0
2
4
Years after shock
6
Responses to a shock in technology
0
-0.02
-0.04
real rate
-0.06
-2
% deviation from SS
% deviation from SS
% deviation from SS
Taylor rule – Shock in technology
8
0
2
4
Years after shock
6
8
Responses to a shock in technology
0
-0.01
-0.02
output gap
-0.03
-2
0
2
4
6
Years after shock
8
Taylor rule – Demand shock
Responses to a shock in demand
% deviation from SS
0.8
nominal rate
0.6
0.4
0.2
inflation
0
-2
0
2
4
Years after shock
6
8
0.8
real rate
0.6
0.4
0.2
0
-2
0
2
4
Years after shock
Responses to a shock in demand
% deviation from SS
% deviation from SS
Responses to a shock in demand
1
output
0.5
0
-2
0
2
4
Years after shock
6
8
6
8
Taylor rule
Technology shock
Demand shock
Output increases, but less than capacity due to nominal
rigidities
Negative output gap
The Central bank decreases the interest rate as a response
to low inflation and negative output gap
Output (output gap) and inflation increase, interest rate
increases as a response.
Next lesson: optimal policy
What are the effect of the parameters of monetary
policy on the response of the economy to shocks
Taylor rule –Shock in technology –
Sensitivity to policy
0
-0.01 0
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.09
Responses to a shock in technology
0
4
8
12
16
20
24
% deviation from SS
% deviation from SS
Responses to a shock in technology
28
-0.005 0
4
8
Nominal rate
-0.02
Inflation
-0.03
Quarters after shock
Responses to a shock in technology
Responses to a shock in technology
20
24
28
0
% deviation from SS
16
% deviation from SS
% deviation from SS
12
28
-0.01
1.2
8
24
-0.035
0
4
20
-0.025
Responses to a shock in technology
1
-0.005
0.8
-0.02
-0.03
16
-0.015
Quarters after shock
-0.01 0
12
0.6
Real rate
-0.04
Output
0.4
0
0
-0.06
Quarters after shock
δп =2 and δx =0.6 (baseline)
δп =5 and δx =0.6
δп =5 and δx =1.5
4
8
12
16
20
Quarters after shock
24
28
4
8
12
16
20
-0.01
-0.015
0.2
-0.05
0
Output gap
-0.02
-0.025
Quarters after shock
24
28
Taylor rule –Demand shock – Sensitivity
to policy
Responses to a demand shock
Responses to a demand shock
% deviation from SS
% deviation from SS
0.14
0.12
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.08
0.06
0.04
Nominal rate
Inflation
0.02
0
0
4
8
12
16
20
24
28
0
4
8
Quarters after shock
% deviation from SS
% deviation from SS
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Real rate
0
4
8
12
16
20
24
Quarters after shock
δп =2 and δx =0.6 (baseline)
δп =5 and δx =0.6
δп =5 and δx =1.5
16
20
24
28
Responses to a demand shock
Responses to a demand shock
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
12
Quarters after shock
28
Output
0
4
8
12
16
20
Quarters after shock
24
28
Taylor rule – Sensitivity to policy
Stronger policy responses to inflation and output
gap:
Closes the output gap following a technology shock:
Limits deflation
Output below its potential because firms cannot decrease
prices as much as they would like
Fall in interest rate compensates for that by making demand
increase
Increase in marginal cost limits the needs for price adjustment
Closes the output gap and reduces inflation following a
demand shock
Conclusion
Benchmark NK model
Improvement on Neoclassical Model: fits the data better
Improvement on traditional IS/LM: incorporates optimal individual
behavior and rational expectations
Very successful: benchmark model for policy analysis, widely
used by Central Banks, with various extensions
Nominal rigidities also affect the way the economy
responds to a technology shock
Nominal rigidities changes radically the response of the
economy to a monetary shock
In particular, output increases less than capacity
Should monetary policy correct for that?
How? See next lesson
Conclusion
Possible extensions
Nominal wage rigidities
Capital
Open economy
Financial imperfections (idiosyncratic risk, credit
constraints)
Labor market imperfections: no unemployment here!
Role of the banking system
Medium and large size NK models
Calibration/estimation issue