Transcript The New Normative Macroeconomics John B. Taylor Stanford University XXI Encontro Brasileiro de Econometria 9 December 1999

The New Normative
Macroeconomics
John B. Taylor
Stanford University
XXI Encontro
Brasileiro de
Econometria
9 December 1999
Some Historical Background
• Rational expectations assumption was introduced to
macroeconomics nearly 30 years ago
– now most common expectations assumption in macro
– work on improving it ( e.g. learning) continues
• The “rational expectations revolution” led to
–
–
–
–
–
new classical school
new Keynesian school
real business cycle school
new neoclassical synthesis
new political macroeconomic school
• Now as old as the Keynesian revolution was in early 70s
But this raises a question
• We know that many interesting schools have
evolved from the rational expectations revolution,
but has policy research really changed?
• The answer: Yes. It took a while, but if you look
you will see a whole new normative
macroeconomics which has emerged in the 1990s
– Interesting, challenging theory and econometrics
– Already doing some good
• Policy guidelines for decisions at central banks
• Helping to implement inflation targeting
• Constructive rather than destructive
• Look at
– policy models, policy rules, and policy tradeoffs
Policy Models: Systems of stochastic
expectational difference equations:
fi (yt, yt-1,...,yt-p, Etyt+1,...,Etyt+q,ai, xt) = uit
i = 1,...,n,
yt = vector of endogenous variables at time t,
xt = vector of exogenous variables at time t,
uit = vector of stochastic shocks at time t,
ai = parameter vector.
Characteristics of the Policy Models
• Similarities
– price and wage rigidities
• combines forward-looking and backward-looking
• frequently through staggered price or wage setting
– monetary transmission mechanism through interest
rates and/or exchanges rates
– all viewed as “structural” by the model builders
• Differences
– size (3 equations to nearly 100 equations)
– degree of openness
– degree of formal optimization
• all hybrids: some with representative agents (RBC style), other
based directly on decision rules
Examples of Policy Models
• Taylor (Ed.) Monetary Policy Rules has 9 models
• Taylor multicountry model (www.stanford.edu/~johntayl)
• Rotemberg-Woodford
• McCallum-Nelson
• But there are many many more in this class
– Svensson
– This conference: Hillbrecht, Madalozzo, and Portugal
– Central Bank Research (not much different)
•
•
•
•
•
•
Fed: FRB/US
Bank of Canada (QPM)
Riksbank (similar to QPM)
Central Bank of Brazil (Freitas, Muinhos)
Reserve Bank of New Zealand (Hunt, Drew)
Bank of England (Batini, Haldane)
Solving the Models
• Solution is a stochastic process for yt
• In linear fi case
– Blanchard-Kahn, eigenvalues, eigenvectors
• In non-linear fi case
– Iterative methods
• Fair-Taylor
– simple, user friendly (can do within Eviews), slow
• Ken Judd
Policy Rules
• Most noticeable characteristic of the new normative
macroeconomics
– interest in policy rules has exploded in the 1990s
• Normative analysis of policy rules before RE
– A.W. Phillips, W. Baumol, P. Howrey
– motivated by control engineering concerns (stability)
• But extra motivation from RE
– need for a policy rule to specify future policy actions in order
to estimate the effect of policy
• Dealing constructively with the Lucas critique
– time inconsistency less important
Interest rate
Constant Real
Interest Rate
Policy
Rule
Inflation rate
Target
Example of a Monetary Policy Rule
The Timeless Method for
Evaluating Monetary Policy Rules
• Stick a policy rule into model fi (.)
• Solve the model
• Look at the properties of the stochastic steady
state distribution of the variables (inflation, real
output, unemployment)
• Choose the rule that gives the most satisfactory
performance (optimal)
– a loss function derived from consumer utility might be
useful
• Check for robustness using other models
Simple model illustrating expectations effects of policy rule:
(1)
yt = -(rt + Etrt+1) + t
Policy Rule:
(2)
rt = gt + ht-1
Plug in rule (2) into model (1) and find var(y) and var(r).
Find policy rule parameters (g and h) to minimize
var(yt) + var(rt)
Observe that Etrt+1 = ht
If h = 0, then by raising h and lowering g
one can and get the same variance of yt and
a lower variance of rt.
Policy Tradeoffs
• Original Phillips curve was viewed as a
policy tradeoff: could get lower
unemployment with higher inflation
– but theory (Phelps-Friedman) and data (1970s)
proved that there is no permanent trade off
• But there is a short run policy tradeoff
– at least in models with price/wage rigidities
– even in models with rational expectations
• New normative macroeconomics
characterizes the tradeoff in terms of the
variability of inflation and unemployment
A simple illustration of an
output-inflation variability tradeoff
(1) t = t-1 + byt-1 + t (price adjustment eq.)
(2) yt = -gt
(aggregate demand/inflation eq.)
-- Substitute (2) into (1) to get 1AR in , from which the
variance of inflation can be found.
-- Variance of y then comes from (2).
-- As policy parameter g changes, the variance of y moves
inversely to .
-- Shape and position of curve depends on model
parameters.
Variance
of
output
Variance of inflation
Inflation Rate
AD
PA
target
0
Real Output
(Deviation)
Inflation targeting
• Keep inflation rate “close” to target inflation rate
• In mathematical terms: minimize, over an
“infinite” horizon, the expectation of the sum of
the following period loss function, t = 1,2,3…
w1(t - *)2 + w2 (yt – yt*)2
Or minimize this period loss function in the steady
state
Try to have y* equal to the “natural” rate of
output
Evaluating Simple Rules
Looked at five monetary policy rules of the form
it = gt + gyyt + it-1
where i is the nominal interest rate,
 is the inflation rate
y is the deviation of real GDP from potential GDP.
g
Rule I
Rule II
Rule III
Rule IV
Rule V
1.5
1.5
3.0
1.2
1.2
gy

0.5
1.0
0.8
1.0
.06
0.0 
0.0
1.0
1.0
1.3
Robustness Testing Grounds
-- Ball Model
-- Batini and Haldane Model
-- McCallum and Nelson Model
-- Rudebusch and Svensson Model
-- Rotemberg and Woodford Model
-- Fuhrer and Moore Model
-- MSR Model (small model used at the Fed)
-- FRB/US Model (large model used at the Fed)
-- TMCM (multicountry model of Taylor)
Standard Deviation of:
Inflation
Output
Ball
1.85
1.62
Batini-Haldane
1.38
1.05
McCallum-Nelson
1.96
1.12
Rudebusch-Svensson 3.46
2.25
Rotemberg-Woodford 2.71
1.97
Fuhrer-Moore
2.63
2.68
MSR
0.70
0.99
FRB
1.86
2.92
TMCM
2.58
2.89
Rank sum
--Ball
2.01
1.36
Batini-Haldane
1.46
0.92
McCallum-Nelson
1.93
1.10
Rudebusch-Svensson 3.52
1.98
Rotemberg-Woodford 2.60
1.34
Fuhrer-Moore
2.84
2.32
MSR
0.73
0.87
FRB/US
2.02
2.21
TMCM
2.36
2.55
Rank sum
---
Inflation Output
rank
rank
1
2
1
2
2
2
1
2
2
2
1
2
1
2
1
2
2
2
12
18
 Rule I
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
15
9  Rule II
Standard Deviation
Inflation Output
Inflation Output
rank
rank
Ball
Haldane-Batini
McCallum-Nelson
Rudebusch-Svensson
Rotemberg-Woodford
Fuhrer-Moore
MSR
FRB/US
TMCM
2.27
0.94
1.09

0.81
1.60
0.29
1.37
1.68
23.06
1.84
1.03

2.69
5.15
1.07
2.77
2.70
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
2
2
Rank sum
-2.56
1.56
1.19

1.35
2.17
0.44
1.56
1.79
-2.10
0.86
1.08

1.65
2.85
0.64
1.62
1.95
10
16
2
2
2
1
3
2
3
3
2
1
1
2
1
1
1
1
1
1
-

1.12

3.67
21.2
1.95
6.32
4.31
20
10
Ball
Batini-Haldane
McCallum-Nelson
Rudebusch-Svensson
Rotemberg-Woodford
Fuhrer-Moore
MSR
FRB
TMCM
-

1.31

0.62
7.13
0.41
1.55
2.06
3
3
3
1
1
3
2
2
3
3
3
3
1
3
3
3
3
3
Rank sum
--
--
21
25
Ball
Batini-Haldane
McCallum/Nelson
Rudebusch-Svensson
Rotemberg-Woodford
Fuhrer-Moore
MSR
FRB/US
TMCM
Rank sum
Rule III
Rule IV
Rule V
Historical confirmation: in the U.S.
the federal funds rate has been
close to monetary policy rule I
Percent
12
10
8
6
0%
4
3%
Federal Funds Rate
2
0
89
90
91
92
93
94
95
96
97
98
12
10
Smothoed inflation rate
(4 quarter average)
8
6
1968.1: Funds
rate was 4.8%
1989.2: Funds
rate was 9.7%
4
2
0
60
65
70
75
80
85
90
percent
4
2
0
-2
GDP gap with HP trend
for potential GDP
-4
-6
60
65
70
75
80
85
90
95
percent
20
Real GDP growth rate (Quarterly)
15
10
5
0
-5
-10
60
65
70
75
80
85
90
95
Output Stability Comparisons
Period
gap growth
1959.2-1999.3
1.6
3.6
1959.2- 1982.4 1.8
4.3
1982.4-1999.3
2.3
1.1
Interest rate hitting zero problem
• To estimate likelihood of hitting zero and
getting stuck, put simple policy rule in
policy model and see what happens:
– pretty safe for inflation targets of 1 to 2 percent
• Modify simple rule:
– Interest rate stays near zero after the expected
crises (Reifschneider and Williams (1999))
Interest rate
Constant Real
Interest Rate
Policy
Rule
Inflation rate
0
Target
Inflation Rate
AD
PA
0
Real Output
(Deviation)
The role of the exchange rate
Extended policy rule
it = gt + gyyt + ge0et + ge1et-1 + it-1
where
it is the nominal interest rate,
t is the inflation rate (smoothed over four quarters),
yt is the deviation of real GDP from potential GDP,
et is the exchange rate (higher e is an appreciation).
Effect on inflation and output variability from adding
exchange rate terms to benchmark rule. (No exchange rate
term in loss fucntion)
Set g = 1.5, gy = 0.5,  = 0, and
Ball
Svensson
Taylor
ge0
ge1
_________
-.37 .17
-.45 .45
-.25 .15
slight improvement
can’t rank
can’t rank
In conclusion
• The “new normative macroeconomics” is
currently a huge and exciting research effort
– it demonstrates how policy research has changed since
the rational expectations revolution
– it has probably improved policy decisions already in
some countries
• With a great amount of macro instability still
existing in the world there is still much to do.