The New NormativeMacroeconomics

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

Policy Rule

Constant Real Interest Rate

Interest rate

Inflation rateTarget

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 = gt + ht-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 = ht

 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 = -gt (aggregate demand/inflation eq.)

-- Substitute (2) into (1) to get 1AR in , from which thevariance of inflation can be found.-- Variance of y then comes from (2).-- As policy parameter g changes, the variance of y movesinversely to .-- Shape and position of curve depends on modelparameters.

Varianceofoutput

Variance of inflation

Inflation Rate

Real Output (Deviation)

AD

PA

0

target

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 = gt + 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 gy

Rule I 1.5 0.5 0.0 Rule II 1.5 1.0 0.0 Rule III 3.0 0.8 1.0 Rule IV 1.2 1.0 1.0 Rule V 1.2 .06 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 Inflation Output rank rank Ball 1.85 1.62 1 2 Batini-Haldane 1.38 1.05 1 2 McCallum-Nelson 1.96 1.12 2 2 Rudebusch-Svensson 3.46 2.25 1 2 Rotemberg-Woodford 2.71 1.97 2 2 Fuhrer-Moore 2.63 2.68 1 2 MSR 0.70 0.99 1 2 FRB 1.86 2.92 1 2 TMCM 2.58 2.89 2 2 Rank sum -- -- 12 18 Rule I Ball 2.01 1.36 2 1 Batini-Haldane 1.46 0.92 2 1 McCallum-Nelson 1.93 1.10 1 1 Rudebusch-Svensson 3.52 1.98 2 1 Rotemberg-Woodford 2.60 1.34 1 1 Fuhrer-Moore 2.84 2.32 2 1 MSR 0.73 0.87 2 1 FRB/US 2.02 2.21 2 1 TMCM 2.36 2.55 1 1 Rank sum -- -- 15 9 Rule II

Standard Deviation Inflation Output Inflation Output rank rank

Ball 2.27 23.06 1 2 Haldane-Batini 0.94 1.84 1 2 McCallum-Nelson 1.09 1.03 1 1 Rudebusch-Svensson 1 1 Rotemberg-Woodford 0.81 2.69 2 2 Fuhrer-Moore 1.60 5.15 1 2 MSR 0.29 1.07 1 2 FRB/US 1.37 2.77 1 2 TMCM 1.68 2.70 1 2

Rank sum -- -- 10 16 Rule III Ball 2.56 2.10 2 1 Batini-Haldane 1.56 0.86 2 1 McCallum/Nelson 1.19 1.08 2 2 Rudebusch-Svensson 1 1 Rotemberg-Woodford 1.35 1.65 3 1 Fuhrer-Moore 2.17 2.85 2 1 MSR 0.44 0.64 3 1 FRB/US 1.56 1.62 3 1 TMCM 1.79 1.95 2 1

Rank sum -- -- 20 10 Rule IV Ball 3 3 Batini-Haldane 3 3 McCallum-Nelson 1.31 1.12 3 3 Rudebusch-Svensson 1 1 Rotemberg-Woodford 0.62 3.67 1 3 Fuhrer-Moore 7.13 21.2 3 3 MSR 0.41 1.95 2 3 FRB 1.55 6.32 2 3 TMCM 2.06 4.31 3 3

Rank sum -- -- 21 25 Rule V

Historical confirmation: in the U.S. the federal funds rate has been close to monetary policy rule I

0

2

4

6

8

10

12

89 90 91 92 93 94 95 96 97 98

Percent

Federal Funds Rate

0%

3%

0

2

4

6

8

10

12

60 65 70 75 80 85 90

Smothoed inflation rate

(4 quarter average)

1968.1: Funds

rate was 4.8%

1989.2: Funds

rate was 9.7%

-6

-4

-2

0

2

4

60 65 70 75 80 85 90 95

percent

GDP gap with HP trend for potential GDP

-10

-5

0

5

10

15

20

60 65 70 75 80 85 90 95

percent

Real GDP growth rate (Quarterly)

Output Stability Comparisons

Period gapgrowth

1959.2-1999.3 1.6 3.6

1959.2- 1982.4 1.8 4.3

1982.4-1999.3 1.1 2.3

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))

Policy Rule

Constant Real Interest Rate

Interest rate

Inflation rate0Target

Inflation Rate

Real Output (Deviation)

AD

PA

0

The role of the exchange rate

Extended policy rule 

it = gt + gyyt + ge0et + ge1et-1 + it-1

 whereit 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

ge0 ge1

_________ Ball -.37 .17 slight improvement Svensson -.45 .45 can’t rank Taylor -.25 .15 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.