Uncertainty and Monetary Policy:

Theory and Practice

Central Bank of Argentina, 2007

Money and Banking Conference

Joseph Tracy, Federal Reserve Bank of NY

Monetary Policy under Uncertainty

� Alan Greenspan, Jackson Hole WY, 29 Aug 2003

� “Uncertainty is not just an important feature of the monetary policy landscape; it is the defining characteristic of that landscape. As a consequence, the conduct of monetary policy in the United Statesat its core involves crucial elements of risk management, a process that requires an understanding of the many sources of risk and uncertainty that policymakers face and the quantifying of those risks when possible. It also entails devising, in light of those risks, a strategy for policy directed a maximizing the probabilities of achieving over time our goal of price stability and maximum sustainable growth that we associate with it.”

Risk management approach to monetary

policy

� Objective is not to maximize the benefits

based the expected evolution of the economy

� Rather, to maximize the probability of

achieving the goals of the Central Bank

� Essential elements

� Understanding of risks to the forecast

� Consequences associated with each risk

� Focus on the distribution of possible outcomes for inflation and growth

Examples illustrating this approach

� Russia Default, Fall 1998� FOMC eased policy despite view that economy

was expanding at a satisfactory pace and would likely continue to do so even without easing

� Insurance against any “contagion”

� Deflation scare, Spring 2003� FOMC eased policy even though deflation was

not viewed as the most probable outcome given the existing policy stance

� Insurance against the downside risk

� Monetary policymakers must make decisions under uncertainty� Where has the economy been (interpretation,

measurement)

� Where is it now (interpretation, measurement)

� Where will it be in the future (interpretation, expectations, transmission mechanism, future shocks)

� Quantifying uncertainty and monetary policy is controversial, difficult and an area of active research

� Presentation will describe current methods used to quantify future uncertainty at FRBNY

Decisionmaking under Uncertainty

� Central Banks can ignore uncertainty if certainty equivalence (CE) holds

� Strong assumptions required: Policymaker has a quadratic loss function, linear economy with all aspects known except future value of Gaussian shocks

� Many Central Banks act and communicate as if certainty equivalence does not hold

� Policy actions implemented in non-CE environments require dealing with uncertainty

� Bayesian approach quantify uncertainty through forecast distributions

� Robust Control approach does not quantify uncertainty

When Uncertainty Matters

� Use structural economic models

� Use reduced form time series models

� Using quantified judgment, present a forecast

distribution that uses a wide range of formal and

informal information.

� Elements from all 3 approaches can (and should) be

combined

Before explaining our judgmental approach need to agree on

some terminology

Methods for Constructing Forecast Distributions

� No consensus method of describing balance of risks or uncertainty around the judgmental forecast

� Central Bank point forecasts often interpreted as the mode: most likely outcome

� Other measures of “central tendency” are the mean

(expected value) and median (50% above, 50% below)

� When the median is not equal to mean, information

content in stating "balance of risks“

� For now focus on mean versus mode/judgmental

forecast

– upside risk to judgmental forecast: mean > mode

– downside risk to judgmental forecast: mean < mode

Balance of Risks

� Quantify uncertainty and balance of risks with forecast origin T (eg 2007Q1) and horizon h (eg 4 quarters)

with 3 numbers:

� µT+h is BoE central forecast, mode of forecast distribution

� σT+h is a measure of outcome dispersion around forecast

� λ percent of the time values lower than mode value are expected to occur

� If λ = 0.5 ⇒ mean=mode: risks are balanced

� If λ > 0.5 ⇒ mean less than mode: downside risk

� If λ < 0.5 ⇒ mean greater than mode: upside risk

Bank of England Fan Charts

� Choose central forecast, dispersion and amount of

downside risk.

� If risks are balanced then generate realizations from

a distribution centered at central point forecast with

given dispersion

� µiT+h = µT+h + εi , where εi ~ N(0,σt+h)

� If risks are unbalanced

� λ percent of realizations given byµi

T+h = µT+h − | εi |

� (1− λ) percent of realizations given by

µiT+h = µT+h + εi

Implementing Bank of England Approach

� Allow for dynamically varying balance of risks

� Interpret the upside and downside risks as scenarios

� Place positive probability on a scenario associated with

judgmental forecast

� Now three scenarios: central bank forecast, downside scenario, upside scenario

� Uncertainty now varies, consider two extreme cases:

� 50% weight on upside scenario, 50% weight on downside scenario – maximum uncertainty

� 100% weight on central scenario – minimum uncertainty

� Same implications for mean but very different implications

for uncertainty and changes in central forecast

First Generalization of BoE Approach

� Choose central forecast, dispersion and dynamic weights

on central scenario ( λ0,T+h ) and downside ( λ1,T+h )

� At each horizon h

� λ0,T+h percent of realizations generated by

µiT+h = µT+h + εi, where εi ~ N(0,σt+h)

� λ1,T+h percent of realizations generated by

µiT+h = µT+h − | εi |

� ( 1 − λ0,T+h − λ1,T+h ) percent of realizations generated by

µiT+h = µT+h + | εi |

Implementing Generalization

� Usually risks are balanced at forecast origin

� Eventually probability on central scenario goes to 1

� Central scenario at longer horizons constrained

� mean=mode=median ( long-run balanced risks )

� expected inflation at implicit target ( CB expects to

achieve inflation objective )

� expected output gap at zero ( CB expects to achieve

growth objective )

� uncertainty around these values close to historical averages

Constraints on Forecast Distributions

� Replace upside and downside risk scenarios with general scenarios about inflation and output

� Integrate scenarios with the assessment of uncertainty

� No fixed number of scenarios – keep to most important

� Examples:

� Productivity Boom: draw values of output > mode, inflation < mode

� Productivity Slump: draw values of output < mode, inflation > mode

� Overheating: draw inflation >> mode; initial output > mode, then output < mode

� Over-Tightening: output << mode, inflation << mode

Further Generalization of BoE Approach

1.0

1.5

2.0

2.5

3.0

2006 2007 2008 2009

1.0

1.5

2.0

2.5

3.0

Alternative Scenarios of Core PCE Inflation

% Change – Year to Year

Source: MMS Function (FRBNY)

Productivity Boom

Overheating

Productivity Slump

Central Scenario

Over-Tightening

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

2006 2007 2008 2009

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Alternative Scenarios of Real GDP Growth

Source: MMS Function (FRBNY)

Productivity Boom

Productivity Slump

Overheating

Central Scenario

Over-Tightening

% Change – Year to Year

� Retain the same restrictions on dynamic evolution:

� Risks are balanced, usually at forecast origin, with initial weight 1 on central scenario

� Choose an initial probability weight for each scenario

� Choose how long each scenario will last if it occurs

� As forecast horizon increases, probability weight on central scenario goes to 1

� Generalize over earlier method by allowing for uncertainty over probabilities and duration of scenario

Probability Weights on Scenarios

Scenario Probabilities

Source: MMS Function (FRBNY)

0

10

20

30

40

50

Productivity Boom

Productivity Slump

Effects ofOverheating

Over-Tightening

0

10

20

30

40

50Percent

Prob. of being in the scenario in 2007Q4

Prob. of being in the scenario in 2008Q4

Prob. of being in the scenario in 2009Q4

Prob. of remaining in scenario through 2009Q4

� Plausibility of results based on introspection

� Does "continuing expansion" probability look sensible?

� Do inflation risks look sensible?

� Comparison with other measures

� Time series models� No forward judgment but allows for structural change in

past

Reliability Checks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

2006 2007 2008 2009

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Core PCE Inflation Forecast Distribution

% Change – Year to Year

Note: The probability interval shows the 50, 75, and 90 percent chance that the four quarter change in core PCE inflation will be within the respective range. The yellow line represents the expected value of the forecast, while the red line represents the actual FRBNY forecast.

Source: MMS Function (FRBNY)

-1

0

1

2

3

4

5

2006 2007 2008 2009

-1

0

1

2

3

4

5

Real GDP Growth Forecast Distribution

% Change – Year to Year

Note: The probability interval shows the 50, 75, and 90 percent chance that the four quarter change in real GDP growth will be within the respective range. The yellow line represents the expected value of the forecast, while the red line represents the actual FRBNY forecast.

Source: MMS Function (FRBNY)

Forecast

� Assume central bank uses a Taylor-type rule to determine FFR

from inflation and output gaps

� In the short run, adjust to discreteness of FOMC moves

� Choice of a particular rule and forecast distribution for inflation

and output produces a forecast distribution for FFR

� Examine variants on baseline policy rule

� Opportunistic Disinflation: slower rate cuts than baseline rule if inflation above 2%

� Dove: faster rate cuts than baseline if negative output gap

Distributions for Fed Funds Rate (FFR)

� Use futures and options prices to generate a forecast

distribution for the FFR

� Market distribution affected by

• Compensation for risk

• Market misunderstanding FOMC communication on objectives,

reaction function or outlook

• Markets view of the outlook and risks on real activity and inflation

� FRBNY distribution has been close to markets

� Sensitive to weight on productivity scenarios

� Another reliability check

� Do changes in market distribution and in our distribution line up?

Comparison to Market Forecast Distribution

3.0

3.5

4.0

4.5

5.0

5.5

2006 2007 2008 2009

3.0

3.5

4.0

4.5

5.0

5.5

Nominal FFR under Different Policy Rules

Percent

Source: MMS Function (FRBNY)

Baseline

Opportunistic Disinflation

Dove

Market-Implied

Comparison with BoE and BoG� Bank central forecast

� FRBNY judgment but at further horizons converges to assumed inflation target and zero output gap

� BoG judgment, FRBUS, etc.� BoE produced by numerous economists, MPC members and a

large number of models

� Dispersion

� FRBNY forecast error behavior, implied volatility and introspection

� BoG given by last 18-20 years of forecast errors for GB or residuals from FRBUS

� BoE exponential smoother of last 10 years of observed forecast errors

� Balance of Risks around forecast� FRBNY as described above� BoG does not allow explicitly for unbalanced risks� BoE produced by the MPC

Comparison with BoE and BoG

� Scenarios

� FRBNY scenarios produce forecast distribution

� BoG scenarios unrelated to forecast distribution

� BoE no explicit scenario analysis

� Option price information

� FRBNY forecast distribution converted to FFR using policy rule, dispersion calibrated to be similar to markets

� BoG forecast distribution of FFR from estimated policy rule in FRBUS compared to implied volatility

� BoE present implied volatility on short-term interest rate only

Role of scenarios and information from option prices