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EC3115 :: L.13 : Monetary policy under uncertainty Almaty, KZ :: 22 January 2016

EC3115 Monetary EconomicsLecture 13: Monetary policy under uncertainty

Anuar D. Ushbayev

International School of EconomicsKazakh-British Technical University

https://anuarushbayev.wordpress.com/teaching/ec3115-2015/

Tengri Partners | Merchant Banking & Private [email protected] – www.tengripartners.com

Almaty, Kazakhstan, 22 January 2016

ISE – KBTU A.D. Ushbayev (2016)

https://anuarushbayev.wordpress.com/teaching/ec3115-2015/

EC3115 :: L.13 : Monetary policy under uncertainty - 2 / 52 -

Relevant reading

Must-read articles

W. Brainard. (1967). “Uncertainty and the effectiveness of policy”, Amer-ican Economic Review, Vol. 57, No. 2, pp. 411-425.

W. Poole. (1970). “Optimal choice of monetary policy instrument in asimple stochastic macro model”, Quarterly Journal of Economics, Vol. 84,No. 2, pp. 197-216.

N. Batini, B. Martin and C. Salmon. (1999). “Monetary policy and uncer-tainty”, Bank of England Quarterly Bulletin, Quarter 2.

B. Sack. (2000). “Does the Fed act gradually? A VAR analysis”, Journalof Monetary Economics, No. 46, pp.229-256.

R. Dennis. (2005). “Uncertainty and monetary policy”, FRBSF EconomicLetter, No. 33.

B. Aruoba. (2008). “Data revisions are not well-behaved”, Journal ofMoney, Credit and Banking, Vol. 40 No. 2-3, pp. 319-340.


http://www.bbk.ac.uk/ems/faculty/aksoy/teaching/gradmoney/Brainard%20(1967).pdf

http://adam.vwl.uni-mannheim.de/fileadmin/user_upload/adam/Makro_B/Poole_1969_Monetary_Instrument_.pdf

http://adam.vwl.uni-mannheim.de/fileadmin/user_upload/adam/Makro_B/Poole_1969_Monetary_Instrument_.pdf

http://www.bankofengland.co.uk/archive/Documents/historicpubs/qb/1999/qb990205.pdf

http://www.bankofengland.co.uk/archive/Documents/historicpubs/qb/1999/qb990205.pdf

http://www.federalreserve.gov/pubs/feds/1998/199817/199817pap.pdf

http://www.frbsf.org/economic-research/files/el2005-33.pdf

http://www.eabcn.org/sites/all/files/papers/21.pdf

EC3115 :: L.13 : Monetary policy under uncertainty - 3 / 52 - Introduction to policy under uncertainty

Section 1

Introduction to policy under uncertainty



Up to now we have implicitly assumed that the central bank:

knows the “true” structural model1 of the economy,knows the values of the model parameters with certainty,makes timely observes and accurate measures all relevant variables,knows sources and statistical properties of economic disturbances.

In practice, conducting monetary policy is a lot more difficult.

There is tremendous uncertainty about the true structure of the economy,the impact policy actions have on the economy, and even about the stateof the economy itself.

1Uncertainty over the structure of the economic model, or reduced-form model instability,which manifests itself through the Lucas critique – which we’ve already studied – is one formof model uncertainty that the monetary authorities must consider when deciding on policy.

We will now examine other forms of uncertainty that will determine which monetary variablethe authorities should target and how aggressively the policy should be used in order to reachthe policy goals.



“Unfortunately, actually to use such a strategy in practice, you haveto use forecasts, knowing that they may be wrong. You have to baseyour thinking on some kind of a monetary theory, even though thattheory might be wrong. And you have to attach numbers to the theory,knowing that your numbers might be wrong, and that all you’ve got isa statistical average anyway. We at the Fed have all these fallible tools,and no choice but to use them. It’s a tough world, but that’s the way itis.”

– Alan S. Blinder1, (1995), “The Strategy of Monetary Policy”, The Region,Federal Reserve Bank of Minneapolis, No. 9.

1Vice Chairman of the Board of Governors of the Federal Reserve System (1994-1996).


https://www.minneapolisfed.org/publications/the-region/the-strategy-of-monetary-policy


“What can you do to try to guard against failure? There are two principlesthat monetary policy makers need to keep in mind. First of all, becautious. Don’t oversteer the ship. If you yank the steering wheel reallyhard, a year later you may find yourself on the rocks.

Second, you must have a long-run strategy in mind. The Federal OpenMarket Committee meets eight times a year. You can’t be thinking onlyabout what’s going to happen in the next six or seven weeks; that’sbasically irrelevant to the monetary policy decision. You must thinkabout a long-term strategy, execute the first step of that strategy, andthen watch. You must be flexible and prepared to modify or evenabandon your strategy if things look to be going wrong.”

– Alan S. Blinder, (1995), “The Strategy of Monetary Policy”, The Region,Federal Reserve Bank of Minneapolis, No. 9.




“People often misunderstand and think that we can’t have a long-runstrategy because of all these uncertainties and because the world isconstantly changing. That is quite wrong. You must have a long-runstrategy, but you must be willing to modify it as new information be-comes available. Can this stitch-in-time strategy lead you into erroranyway? You bet it can! But the other strategy – the Bunker Hill strategy– is sure to lead you into error. And that makes it, to me, a very easychoice.”

– Alan S. Blinder, (1995), “The Strategy of Monetary Policy”, The Region,Federal Reserve Bank of Minneapolis, No. 9.

This advice for caution in monetary policy-making translates into a smoothadjustment of interest rates.

The reasons for smooth adjustment of interest rates can be due to:data uncertainty (additive),

parameter uncertainty (multiplicative).



EC3115 :: L.13 : Monetary policy under uncertainty - 8 / 52 - Poole’s model of (data) additive uncertainty

Section 2

Poole’s model of (data) additive uncertainty



Economic agents (policy makers, financial agents, firms, households)possess information and form their forecast in real time. As it turns out,most macroeconomic data is subject to continuous revisions. We candefine data revisions in the following way.

X ft = X p

t + r ft

where:X f

t – is the final or true value of the same variable,

X pt – is the statistical agency’s initial announcement of a variable that

was realised at time t ,

r ft – is the final revision which may potentially be never observed.

The data revisions, r ft , can be due to:

short run revisions based on additional source data or

benchmark revisions based on structural changes or updating baseyear.



If those above revisions are done because of new data arrivals that arenot forecastable at the time of the forecast (news), we can refer to“well behaved” revisions since there is nothing economic agents cando about these.

If, however, future data revisions are forecastable at the time of theforecast these are not well behaved revisions (noise).

By not making use of the forecastablity of future revisions, economicagents would violate one of the main assumption of modernmacroeconomics, that is rationality.

Well behaved revisions have three properties:Revisions should have a mean zero. i.e. initial announcement of thestatistical agency should be an unbiased estimate of the final value ofthe data,Final revision should be unpredictable given the information set at thetime of the initial announcement, andThe variance of the final revision should be small compared to thevariance of the final value of the data.



Aruoba (2008) shows vast empirical evidence that none ofabove-mentioned properties of well behaved revisions are full-filledin the US data.

The measurement problem is more important for output series than itis for inflation or employment/unemployment series.

We will now look at a case where we assume that the structure of theeconomy is known with certainty, but the economy may be subject toadditive shocks and this creates data uncertainty.



Poole (1970) analysed the implication of adding such news shocks toboth the IS and LM schedules.

Such shocks could come about from for instance changes in consumertastes or government expenditures shocks on the IS side and stockmarket crashes and financial crises such as the collapse of LTCM in1998 or a change in the central bank behaviour on the LM side.

Poole’s model assumes that the parameters and structure of themodel are known with certainty, which is an unrealistic assumption,but allows the IS and LM schedules to be subject to zero-meanrandom errors, again the so called news shocks.



Define IS and LM schdules as:

Y = a− bR+ εM = c − dR+ eY +η

where ε and η are zero-mean additive IS and LM shocks whosevariances are σ2

ε and σ2η, respectively, and for simplicity we ignore the

price level in the LM curve.

Alternatively, assume the monetary authorities can control realmoney balances, denoted by M . The authorities can either set themoney supply, M , or the interest rate, R, but not both.

With a downward-sloping money demand schedule, either R or Mcan be set and the other variable will have to change to allow themarkets to clear.



If the authorities set the interest rate, then from the IS schedule, theexpected value of output, Y , given R, denoted E [Y |R] will be:

E [Y |R] = a− bR

Assume that the goal of the policy makers is to minimise the varianceof output. From the above we deduce that:

Y −E [Y |R] = ε

and so the variance of output given that the authorities set theinterest rate will be

Var [Y |R] = E�

(Y −E [Y |R])2�

= E�

ε2�

= σ2ε

(Alternatively, the monetary authorities could set the money supply,M . In order to calculate the variance of output in this scenario, weneed to calculate Y as a function of M only.)



From the LM schedule, we can calculate R as a function of M , Y and ηand then substitute this into the IS curve.

M = c − dR+ eY +η

⇒ R = −M − c − eY −η

dSubstituting this into the IS curve and solving for Y gives:

Y = a− b�

−M − c − eY −η

d

�

+ ε

Y +beY

d= a+ b

�M − c −ηd

�

+ ε

Y (d + be) = ad + b�

M − c −η�

+ dε

Y =ad + b

�

M − c −η�

+ dε

d + be

Y =ad − bc

d + be+

b

d + be+

dε − bη

d + beISE – KBTU A.D. Ushbayev (2016)


We can now of course also find E [Y |M] and (Y −E [Y |M]):

E [Y |M] =ad − bc

d + be+

b

d + be

Y −E [Y |M] =1

d + be

�

dε − bη�

and the variance of output given that the authorities could directlycontrol the money stock in this model:

Var [Y |M] = E�

(Y −E [Y |M])2�

= E

�

� 1

d + be

�

dε − bη�

�2�

=� 1

d + be

�2

d2E�

ε2�

− d b E [ε]E�

η�

︸︷︷︸

=0

+b2E�

η2�

=� 1

d + be

�2�

d2σ2ε + b2σ2

η

�



We can now examine which policy instrument, when set by theauthorities, will result in a lower output variance.

�

Only LM shocks,σ2ε = 0

�

Var [Y |R] = 0< Var [Y |M] =�

bd+be

�2σ2η

�

Only IS shocks,σ2η = 0

�

Var [Y |R] = σ2ε > Var [Y |M] =

�

dd+be

�2σ2ε

Consider the case where there are no IS shocks, i.e. σ2ε = 0:

Output variance under both interest rate and money targeting regimes isgiven in the top line of the table above.

It is clear that setting the interest rate and allowing money to change toclear the market is the optimal strategy.

However, if there are no LM shocks, i.e. σ2η = 0, then:

Output variance is smaller under a policy of fixed money supply, asshown see the bottom line of the table.



Therefore, in this model:If an economy is prone to IS shocks, the authorities should keep themoney supply constant.

If the economy is prone to money market, LM, shocks, the interest rateshould be the instrument of choice.

This can also be seen from the graphs below:



The left panel shows the case with IS shocks only.

The output variation when the interest rate is fixed at R∗ is shown by |R , in which casethe money supply has to change to clear the money markets causing the LM curve toshift so that equilibrium is at points A or B.

If the money supply was kept fixed then output deviations are shown by |M .

Therefore, with IS shocks, in order to keep output variance at a minimum, it is best tokeep the money supply fixed.



The right panel shows the case with LM shocks only.

By keeping the interest rate fixed after LM shocks, equilibrium will be unchanged atpoint E and output variance will therefore be zero.

By keeping the money supply fixed, however, LM shocks will cause equilibrium to movebetween points A and B and output variance will be positive, equal to∆Y |M .

So, the main source of economic shocks (goods or money markets) will determinewhich monetary instrument the authorities should target.


EC3115 :: L.13 : Monetary policy under uncertainty - 21 / 52 - Brainard’s model of (parameter) multiplicative uncertainty

Section 3

Brainard’s model of (parameter) multiplicative uncertainty



Whereas Poole considered the case where shocks were additive innature, Brainard (1967) examined the case where the values of theparameters in the model were not known with certainty.

This is, arguably, more realistic since any model must be estimatedfrom data.

An estimated model will not only give point estimates of theparameters but will also give standard errors since there will always bemeasurement error, model mis-specification and other problems thatcause us not to know the exact structure of the economic model.



Suppose output, y , depends on a policy mix, X , a vector containingfiscal and monetary instruments that the government can control.

The relationship between y and X is given by2:

y = gX

For simplicity, assume X is a single policy instrument so that g is ascalar parameter estimate with mean g and variance σ2

g .

The aim of the authorities is to minimize the variance of y aroundsome target level, y∗, full employment level of output for example,subject to the constraint:

minX

E�

�

y − y∗�2�

s.t. y = gX

We can deduce from above that:

y = E�

y�

= E�

gX�

= gX2You could alternatively formulate this for any choice of other target variable and policy

instrument, e.g. π= gi, where π is inflation, and i is the policy interest rate.ISE – KBTU A.D. Ushbayev (2016)


The above problem can then be rewritten as:

minX

E�

�

y − y∗�2�

s.t. y = gX

⇒ minX

E�

��

y − y�

−�

y∗ − y��2�

⇒ minX

E�

��

g − g�

X −�

y∗ − gX��2�

⇒ minX

E�

�

g − g�2

X 2 − 2�

g − g�

X�

y∗ − gX�

+�

y∗ − gX�2�

Noting that E�

�

g − g�2�

= σ2g and E

�

g − g�

= g − g = 0, theproblem becomes:

minX

�

X 2σ2g +�

y∗ − gX�2�



Differentiating�

X 2σ2g +�

y∗ − gX�2�

with respect to X , the choicevariable, and setting equal to zero:

∂�

X 2σ2g +�

y∗ − gX�2�

∂ X= 2Xσ2

g − 2 g�

y∗ − gX�

= 0

Solving for X , this gives:

2Xσ2g − 2 g

�

y∗ − gX�

= 0

2X�

σ2g + g2

�

= 2 g y∗

X =g y∗

σ2g + g2

which implies:

y = gX =

�

g2

σ2g + g2

�

y∗ < y∗



“Brainard uncertainty principle”

Policy thus faces a trade-off between reaching the target output andminimizing its variability.

The implication of the model is that because of the presence ofuncertainty (σ2

g > 0), the authorities will never push aggressivelyenough to make average output equal to the target level, y∗.

To do so will simply cause output variation to increase to anintolerable level. The policy maker would rather have a stable level ofoutput below the full employment level than very volatile outputwhose average was y∗.

The Brainard principle states that policy should exhibitcaution/conservatism in the face of uncertainty.

There are exceptions to this principle in the literature and one occurswhen the uncertainty involves the degree of persistence of inflation.In such models, an aggressive response rather than a conservativeresponse is optimal.



“Brainard uncertainty principle” illustrated

y = gX and y = gX imply that σ2y = σ

2g X 2, which means X =

σy

σg.

Substituting this into y = gX = gσy

σgproduces the linear policy constraint on

the above graph.



“Brainard uncertainty principle” illustrated

The authorities try to reach the indifference curve closest to y∗, the targetlevel, subject to the policy constraint and as can be seen in the above graph.

The presence of uncertainty, σ2g , causes the authorities to opt for a less

aggressive policy stance, causing equilibrium output to be below y∗.


EC3115 :: L.13 : Monetary policy under uncertainty - 29 / 52 - Parameter uncertainty in a New Keynesian model

Section 4

Parameter uncertainty in a New Keynesian model



In this section we will apply Brainard’s ideas to a simple model in theNew Keynesian spirit.

We will show that if there is no parameter uncertainty, and theeconomy is subject to additive shocks with zero mean and constantvariance, the policy maker should behave in a certainty equivalentmanner, that is as if the economic shocks did not occur.

If, however, the economy is subject to structural changes asexemplified in parameter uncertainty, then Brainard conservatismapplies.



Data (additive) uncertainty

Suppose that the economy is characterised by:¨

πt = yt + aπt−1

yt = −bit + εt

where:πt is inflation,

y is the business cycle component of real output (or income),

i is the short term rate that the policy maker can control,

ε is the stochastic demand shocks hitting the economy with zero meanand constant variance, i.e. ε ∼

�

0,σ2ε

�

, known to the central bank, and

a and b are constants.



Combining the above gives an expression for current inflation:

πt = aπt−1 − bit + εt

as a function of past inflation, the policy rate and the shocks hittingthe economy.

The central bank cares about inflation stabilisation, with the followingsimple quadratic loss function:

L =�

πt −π∗�2

where π∗ is target inflation.

In other words, whenever the current inflation deviates form thetarget inflation, the policy maker has an incentive to bring back theinflation to its target level by manipulating the policy rate, i.



The only source of uncertainty is the presence of stochastic shocks.

Given that the policy maker knows the nature of the shocks isε ∼

�

0,σ2ε

�

, it will form an expectation about these.

Substitute the perceived structure of the economy into the objectivefunction of the central bank:

Le = Et

�

�

aπt−1 − bit + εt −π∗�2�

= a2π2t−1 + b2i2

t +Et

�

ε2t

�

︸︷︷︸

=σ2ε

+π∗2 − 2aπt−1 bit + 2aπt−1 Et

�

εt

�

︸︷︷︸

=0

−2aπt−1π∗ − 2bit Et

�

εt

�

︸︷︷︸

=0

+2bitπ∗ − 2 Et

�

εt

�

︸︷︷︸

=0

π∗

The job of the central bank now is to minimize this expected lossfunction with respect to the policy variable, the short term interestrate it.



Differentiating with respect to the interest rate and setting to zerogives:

∂ Le

∂ it= 2b2it + 2bπ∗ − 2aπt−1 b = 0

which is solved by:

2b2it = −2b�

π∗ − aπt−1

�

it =aπt−1 −π∗

b

It is important to notice that the policy rate set by the policy maker isthe same as the one that it would set if there were no shocks hittingthe economy, since σ2

ε does not figure in the expression for it .

This is the certainty equivalence result. The above means that additiveshocks do not affect the way monetary policy is conducted. The bestthe policy maker can do is simply to ignore them.



Parameter (multiplicative) uncertainty

Now suppose we complicate the above model slightly by allowingparameter b in the equation for real output to vary over time suchthat we now have:

¨

πt = yt + aπt−1

yt = −bt it + εt

where:ε is the stochastic demand shocks with ε ∼

�

0,σ2ε

�

, as before, but

bt is no longer a constant, and instead is distributed as bt ∼�

b,σ2b

�

,where once again we assume that the first two moments of b’sdistribution are known to the central bank.

Combining the above similarly gives an expression for currentinflation:

πt = aπt−1 − bt it + εt



The problem of the central bank now becomes:

Le = Et

�

�

aπt−1 − bt it + εt −π∗�2�

= a2π2t−1+Et

�

b2t

�

i2t+Et

�

ε2t

�

︸︷︷︸

=σ2ε

+π∗2−2aπt−1 Et

�

bt

�

︸︷︷︸

b

it+2aπt−1 Et

�

εt

�

︸︷︷︸

=0

−2aπt−1π∗ − 2 Et

�

bt

�

︸︷︷︸

b

it Et

�

εt

�

︸︷︷︸

=0

+2 Et

�

bt

�

︸︷︷︸

b

itπ∗ − 2 Et

�

εt

�

︸︷︷︸

=0

π∗

= a2π2t−1+Et

�

b2t

�

i2t +σ

2ε +π

∗2−2aπt−1 bit −2aπt−1π∗+2bitπ

∗

Using the definition of variance, we can replace the Et

�

b2t

�

termabove as:

Et

�

b2t

�

= σ2b +�

Et

�

bt

��2= σ2

b + b2



The above expression for Le then becomes:

Le = a2π2t−1+

�

σ2b + b2

�

i2t+σ

2ε+π

∗2−2aπt−1 bit−2aπt−1π∗+2bitπ

∗

Differentiating with respect to the interest rate and setting to zerogives:

∂ Le

∂ it= 2

�

σ2b + b2

�

it − 2aπt−1 b+ 2bπ∗ = 0

which is solved by:

2�

σ2b + b2

�

it = −2b�

π∗ − aπt−1

�

it =b�

aπt−1 −π∗�

σ2b + b2


b+�

σ2b

�

b�



Compare the cases without and with the uncertainty in parameter b:


bit =

aπt−1 −π∗

b+�

σ2b

�

b�

You should recognise the expression�

σ2b

�

b�

from your statisticsclasses as the coefficient of variation (CV), measuring the dispersion ofb’s probability distribution.It represents the trade-off between returning inflation to target, andthe increasing uncertainty about inflation depends on the variance ofparameter b relative to its mean.A large CV means that for a small reduction in the inflation bias thecentral bank induces a large variance into future inflation.Once parameter uncertainty is taken into account inflation variancedepends on the interest rate reactions.

The central bank’s decisions affect uncertainty of future inflation.Hence, a gradual policy reaction is preferable to an aggressive one.



Graphical exposition (no uncertainty)

Suppose that there is a negative relationship between real output(horizontal axis) and policy rates (vertical axis), which characterises theIS curve.

Above graph shows the case of no uncertainty.

As is clear whenever the actual output deviates from desired output,the policy maker can adjust policy rates to reach the desired level.



Graphical exposition (data uncertainty)

Above graph shows the case with additive uncertainty (only newsshocks are considered here).

Here, the policy maker is not sure about the quality of the data itreceives (as shown by parallel dashed lines).

Nevertheless, it acts as if it knows the data with certainty, as there isnothing it can do about the shocks (certainty equivalence).



Graphical exposition (parameter uncertainty)

Above graph shows the case with parameter uncertainty.

Since, the nature of the relationship between output and policy rate istime-varying, the slope is changing over time.

If the policy makers acts with aggression, that is, trying to reach thedesired output by increasing the policy rate a lot, the economy mayfind itself at an equilibrium that is even less desirable than before.



What can the policy maker do?

Sack (2000) demonstrates that a possible alternative to an aggressivepolicy that can potentially result in an undesired negative outcome isthat of gradualism in interest rate-setting:

The policy maker moves in small steps in the same direction forconsecutive periods (interest rate smoothing):

First, the central bank adjusts the policy rates in the right direction.

Later, when the (relatively benign) state of the economy is revealed, itmoves again in the same direction.

The policy maker thereby exploits arrival of new information and canreduce the size of potential errors it can commit.



Interest rate smoothing



Is Brainard uncertainty empirically relevant?

Sack (2000) has studied the Fed’s behaviour and found that it hashistorically adjusted policy rates in a smooth fashion, in large part dueto parameter uncertainty, as well as the uncertainty about the state ofthe economy.

This deliberate pace of movements in policy interest rates has beenconsidered as evidence of an interest-rate smoothing incentive on thepart of central banks.

Under this interpretation, the central bank is reluctant to change thepolicy rate aggressively, choosing instead to move the interest ratetentatively towards its new level.

Sack (2000) models the structure of the economy using a fivedimensional vector autoregression in the industrial production growthrate, the unemployment rate, consumer price inflation, commodityprice inflation (to control for price puzzles) and the federal funds rate.



Structure is imposed by a recursive Choleski factorization in which thefederal funds rate is ordered last.

Assuming the model is correctly identified, the first four equations inthe model describe the structural form of the economy whilst the lastequation is the estimated policy function of the Fed3.

The following objective function is assumed for the Fed:

L = −1

2Et

� ∞∑

i=1

β i�

�

πt+i −π∗�2+λu

�

ut+i − u∗�2+λy

�

yt+i − y∗�2��

where the weights 1, λu and λy determine the relative importance ofthe deviation of inflation, unemployment and production growthfrom their respective targets.

3Because this is not a true structural model based on microfoundations it may besubjected to the Lucas critique problems.



Notice that the objective function does not contain any explicit reasonto smooth interest rates, since the purpose was to investigate whethergradual funds rate movements can be explained without simplyassuming that the Fed prefers to act gradually.

After estimating the model with OLS, Sack (2000) calculates a“certainty equivalent” policy rule by assuming that the point estimatesfrom the VAR are the true values known with certainty.

This rule will be linear in the past values of the variables in the systemsince it is a standard linear-quadratic control problem.

The coefficients depend on preferences λu and λy , and the pointestimates of the VAR coefficients.



This rule is then compared to a “Brainard” policy rule which takes intoaccount that the point estimates of the VAR are uncertain.

The standard OLS errors of the parameter estimates are used as anindicator of the uncertainty surrounding each parameter.

The new optimal rule is still a linear function of past values of variablesin the system but now the coefficients of the rule depend on both thepoint estimates of the VAR and the variance-covariance matrix of thecoefficient estimates.

Sack (2000) then calculates the impulse response functions impliedby the optimal rules with and without allowance for parameteruncertainty and compares these to those estimated purely from thedata.



He finds, as the graph clearly shows, that the optimal policy ruletaking parameter uncertainty into account (rather than disregarding)tracks the federal funds rate better, suggesting that caution inducedby Brainard uncertainty is quantitatively important.Both of the optimal policy rules exhibit considerable persistence ininterest rates which is a suggestion for gradualism.


EC3115 :: L.13 : Monetary policy under uncertainty - 49 / 52 - Model uncertainty

Section 5

Model uncertainty



The analysis above still assumes that the policy-makers knowprecisely how uncertain they are – to devise optimal policy rules,central banks must know

the variance of the uncertain structural parameters and additive shocks,and

the nature of measurement errors.

A more realistic assumption may be that uncertainty is morepervasive than this.

In particular, and fundamentally, policy-makers are uncertain aboutthe basic form of the “true” model of the economy. This would be thecase, for example, if it was unclear which variables to omit or includein the model.

Theorists have considered how policy should be set, given such“model uncertainty”.



Model averaging and robustness

One idea is that policy rules could be designed that perform wellacross a range of plausible fully specified models of the economy.

Such “robust” policy rules would not, by definition, perform as well asan optimal rule designed for a particular model.

But they would be designed to perform quite well both with thismodel and a range of similar models, whereas the optimal rule mightperform poorly with other models.

Sargent (1999)4 takes a simple macro-policy model similar to aboveand calculates a policy rule robust to small mis-specifications aroundthis model.

4T. Sargent. (1999). “Comment: Policy Rules for Open Economies”, in Monetary Policy Rules,J. Taylor (ed.). Chicago: University of Chicago Press.


http://www.tomsargent.com/research/ball1.ps


Unlike the Brainard conservatism result for parameter uncertainty,Sargent finds that the robust rule respond more aggressively toshocks than the certainty-equivalent optimal rule in the model.

The intuition for this result in Sargent (1999) is that, by pursuing amore aggressive policy,the central bank can prevent the economyfrom encountering situations where model mis-specification might beespecially damaging.

For the simple model presented above, it is possible to show that a“Sargent robust rule” coincides with the certainty-equivalent optimalrule.


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