JEM 027 Monetary Economics Monetary policy under uncertainty

JEM 027 Monetary Economics Monetary policy under uncertainty Tomáš Holub Tomas. Holub@cnb. cz December 7, 2015 Based on presentation of Kateřina Šmídková from 2013 Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague

Central bankers‘ dream ▪ Driving in your own car (i. e. with well known model and MP transmission) on a straight road (i. e. without shocks and unknowns). ▪ The reality is far from this dream. JEM 027 – Monetary Economics 1

Monetary policy in reality “ One thing is certain about monetary policy. There is uncertainty. ” ▪ Monetary policy is similar to driving a borrowed car through a blind corner ▪ We know exactly neither the transmission (how the car reacts), nor the forthcoming shocks (what is behind the hill) JEM 027 – Monetary Economics 2

What can monetary policy do? ▪ The purpose of this lecture is to discuss how monetary policy can approach uncertainty ▪ One example is to follow the Brainard principle and be more cautious when changing interest rates ▪ But there are other cases and options as well JEM 027 – Monetary Economics 3

Time axis of the literature 1920 ▪ Pioneering work 1 (Knight speaks of complex uncertainty) 1960 s ▪ Pioneering work 2 (Brainard states his principle) 1990 s ▪ Revival of uncertainty literature (uncertainty classification, Brainard extended) 2000 s ▪ Policy-makers criticized research for ignoring Knight ▪ Research responds by improving methodology (robust control) …i. e. it is not from simple to complex forms of uncertainty; but we will go like that in the lecture due to didactic reasons. JEM 027 – Monetary Economics 4

Overview of the lecture Analytical framework – basics ▪ ▪ Certainty benchmark Introducing linear uncertainty Classification of uncertainty ▪ ▪ Simple uncertainty Complex (and very complex) cases Researchers versus policy-makers ▪ ▪ ▪ Researchers return to uncertainty Policy makers complain Researchers respond JEM 027 – Monetary Economics 5

Certainty benchmark The model No Noshocks The loss function (pure IT) Optimization problem for year t JEM 027 – Monetary Economics 6

Certainty benchmark: optimization Substitution (1) Substitution (2) Minimizing loss function wrt. Rt JEM 027 – Monetary Economics 7

Certainty benchmark: outcome Optimal reaction function Plug into (2) to get F. O. C. Actual inflation in time t+2 JEM 027 – Monetary Economics 8

Recall the Lecture on Inflation Targeting (i) ▪ Under strict IT and with no shocks, inflation would always be at the target on the MP horizon. JEM 027 – Monetary Economics 9

Certainty benchmark: two questions ▪ Would the optimal rule be the same if our central bank faced some shocks? ▪ Would inflation be the same in this case? ▪ Why we want to know it – If no difference in rule then central bankers could ignore uncertainty when setting interest rates – If no difference in inflation then central bankers could ignore uncertainty when explaining policy JEM 027 – Monetary Economics 10

Monetary policy under simple uncertainty ▪ Under simple uncertainty, central bankers have more difficult life ▪ They still have their car (transmission certain) ▪ They do not know exactly what is behind the hill, but can guess reasonably well with small errors (shocks) ▪ Such situation is called the simple uncertainty case ▪ Shocks are additive, normally distributed and not correlated JEM 027 – Monetary Economics 11

Simple uncertainty The model No shocks Example of shock … where εt+1 and ηt+1 are white noise random shocks The loss function (pure IT) Optimization problem for year t JEM 027 – Monetary Economics 12

Simple uncertainty: optimization Substitution (1) Substitution (2) Minimizing expected loss function wrt. Rt JEM 027 – Monetary Economics 13

Simple uncertainty: optimal reaction Covariances are zero Optimal reaction function JEM 027 – Monetary Economics 14

Simple uncertainty: outcome Optimal reaction: same as in the certainty benchmark F. O. C. Actual inflation in time t+2 (optimal reaction function substituted into (2)) Deviation of actual inflation from the forecast (and target) JEM 027 – Monetary Economics 15

Simple uncertainty compared to certainty benchmark Actual inflation rates in time t+2 compared Optimal reaction functions compared JEM 027 – Monetary Economics 16

Recall the Lecture on Inflation Targeting (ii) ▪ With shocks, inflation can in the end deviate from the target (and forecast). ▪ Challenge for communication. JEM 027 – Monetary Economics 17

Simple uncertainty: two answers ▪ Is the optimal rule the same if our central bank faces shocks? – Yes ▪ Central bankers can neglect this type of uncertainty during policy decisions under simple uncertainty (with a quadratic loss function) ▪ Is inflation the same with shocks? – No ▪ Shocks deviate inflation from the target ▪ Even under simple uncertainty, central bankers cannot neglect shocks completely – they must communicate differently Do they need to communicate less or more in the case of shocks? Raise your hands who thinks that less JEM 027 – Monetary Economics 18

Overview of the lecture Analytical framework – basics ▪ ▪ Certainty benchmark Introducing linear uncertainty Classification of uncertainty ▪ ▪ Simple uncertainty Complex (and very complex) cases Researchers versus policy-makers ▪ ▪ ▪ Researchers return to uncertainty Policy makers complain Researchers respond JEM 027 – Monetary Economics 19

Uncertainty is not always simple “ Uncertainty accompanies every step of the process that links instruments of monetary policy with the variables of interest ▪ Unfortunately, there are more types of uncertainty than ” the simple one ▪ Complex ones have implications not only for communication, but also for actual decision-making ▪ We need to have more detailed classification – not just certainty versus (linear) uncertainty JEM 027 – Monetary Economics 20

Simple and complex uncertainty Simple uncertainty ▪ Own car, not fully known road ▪ Can be neglected during decisions ▪ Policy rule the same ▪ Cannot be neglected in communication ▪ Inflation not at the target Complex uncertainty ▪ Unknown car, not fully known road ▪ Cannot be neglected during decisions ▪ Policy rule different ▪ Cannot be neglected in communication ▪ Inflation not at the target JEM 027 – Monetary Economics 21

Non-linear uncertainty ▪ Complex uncertainty is non-linear ▪ Examples: multiplicative shocks in linear model equations (uncertain parameters), uncertain functional form of one equation (e. g. Phillips curve) ▪ Model of the economy: known only to some extent ▪ Model uncertainty: shock distribution known and easily approximated ▪ Policy reaction: different from the certainty benchmark ▪ Communication: more difficult than in the certainty benchmark (inflation differs from target) JEM 027 – Monetary Economics 22

Very complex uncertainty (off-model) ▪ The worst case of uncertainty is the one that cannot be approximated inside the model ▪ Examples: model uncertainty (several parallel models), noise in data (significant data revisions) ▪ Model of the economy: not known ▪ Uncertainty: shock distribution not known, approximation difficult („Knightian“ uncertainty) ▪ Policy reaction: different from the certainty benchmark ▪ Communication: more difficult than in the certainty benchmark (inflation differs from target) JEM 027 – Monetary Economics 23

Brainard's principle (revived version) ▪ We use the same set-up as in the simple (linear) uncertainty case ▪ We add parameter uncertainty The extended model … where Ct+1 is random variable (c, χ2) JEM 027 – Monetary Economics 24

Non-linear uncertainty: optimization Substitution (1) Substitution (2) Minimizing expected loss function wrt. Rt JEM 027 – Monetary Economics 25

Non-linear uncertainty: optimal policy Covariances are zero Optimal reaction function JEM 027 – Monetary Economics 26

Non-linear uncertainty: outcome F. O. C. ▪ Note χ2/c 2 is the measure of relative uncertainty ▪ If χ=0 then we have the case of linear uncertainty ▪ For very large χ2: policy rate does not change at all, it is always neutral Rt =πt (we assume that equilibrium real rate is zero) JEM 027 – Monetary Economics 27

Linear and non-linear uncertainty compared Optimal reaction functions compared Summary comparison … where JEM 027 – Monetary Economics 28

Non-linear uncertainty: two answers We know already that inflation is not the same as in the case of certainty benchmark ▪ Central bankers cannot neglect uncertainty when they communicate in both cases (linear and non-linear uncertainty) In addition, with non-linear uncertainty, optimal rule is not the same as in the case of certainty benchmark ▪ Central bankers cannot neglect this type of uncertainty during policy decisions JEM 027 – Monetary Economics 29

Brainard’s principle ▪ If there is an uncertainty about transmission between R and p, central banker should react with policy interest rates less than in the case of certainty ▪ The bigger the uncertainty (delta), the less she/he should react Recall: if uncertain about car, drive slowly JEM 027 – Monetary Economics 30

Target variable Brainard’s principle and gradualism ▪ Moving in two smaller steps reduces the range of possible outcomes. Instrument JEM 027 – Monetary Economics 31

Can research say what to do? ▪ When research knows that central bank cannot neglect uncertainty, can it give some rule of thumb on how to decide under uncertainty? ▪ Can we extend the Brainard’s principle (that says that in the case of uncertainty about the impact of policy rates on output gap, the interest rate should change less) to all types of uncertainty? JEM 027 – Monetary Economics 32

Should we always drive slowly? ▪ Unfortunately, this simple rule of thumb will not always help us ▪ Imagine that suddenly a racing car appears behind you; despite driving a borrowed car through a blind corner, you may want to speed up to avoid a crash JEM 027 – Monetary Economics 33

Example with expectations ▪ If another parameter is uncertain, the policy conclusion can be just the opposite ▪ For example, if the coefficient on current inflation is uncertain … where e has the mean equal to one ▪ It can be shown that policy rate should be changed more ▪ Sometimes this is called the Leiderman’s principle ▪ If uncertain about expectations, be more aggressive to gain credibility JEM 027 – Monetary Economics 34

Knightian uncertainty Two types of uncertainty 1 One can be approximated by mathematical functions (e. g. normally distributed shock) 2 One cannot be approximated by math because it has too “irregular” shape ▪ For policy makers the second type of uncertainty is more difficult, but unfortunately quite frequent JEM 027 – Monetary Economics 35

Driving again Stochastic uncertainty Knightian uncertainty JEM 027 – Monetary Economics 36

Stochastic versus Knightian uncertainty Stochastic uncertainty Knightian uncertainty Crash JEM 027 – Monetary Economics 37

Overview of the lecture Analytical framework – basics ▪ ▪ Certainty benchmark Introducing linear uncertainty Classification of uncertainty ▪ ▪ Simple uncertainty Complex (and very complex) cases Researchers versus policy-makers ▪ ▪ ▪ Researchers return to uncertainty Policy makers complain Researchers respond JEM 027 – Monetary Economics 38

Return of uncertainty: 1990 s ▪ In 1990 s, researchers added various contributions to the first two building stones (by Knight and by Brainard) ▪ Classification of types of uncertainty and suggestions on what to do with policy interest rates in the case of specific uncertainties ▪ Development of methods that improve forecasts by considering a combination of some uncertainties inside the forecasting framework (stochastic simulations) JEM 027 – Monetary Economics 39

Linear and non-linear uncertainty combined ▪ In pioneering papers, one uncertainty at time analysed ▪ In more advanced papers, various types of uncertainty combined ▪ Various linear and non-linear uncertainties represented with normally distributed stochastic shocks inside a simple model ▪ Hall, Salmon, Yates, Batini (1999) Uncertainty and simple monetary policy rules – An illustration for the United Kingdom JEM 027 – Monetary Economics 40

Policy-makers react ▪ Policy-makers reacted to research outcomes critically ▪ Practice is different from models because forecast based on such a simplified model can only be one input to decisions ▪ Policy makers face Knightian uncertainty, not the stochastic one ▪ No rules of thumb possible ▪ Issing (1999) The Monetary Policy of the ECB in a World of Uncertainty JEM 027 – Monetary Economics 41

Central bankers’ observation Researchers see our decisions so simplified! Stochastic core model Forecast Preferences Policy maker Shocks normally distributed R JEM 027 – Monetary Economics 42

Central bankers’ complaints Off-model info Expert 1 Core model Expert 2 Sub-models Expert 3 Shocks not normally distributed Forecast Our decisions are much more complex! Preferences 1 Policy maker 1 Info set 1 Preferences 2 Policy maker 2 Info set 2 Preferences 3 Policy maker 3 Info set 3 R JEM 027 – Monetary Economics 43

Response by researchers: 2000 s ▪ Robust control (model uncertainty) – Tetlow, von zur Muehlen (2000) Robust monetary policy with Misspecified models: Does model uncertainty always call for attenuated policy? ▪ Improved representation of uncertainty (Bayesian approach) – Cogley, Morozov, Sargent (2003) Bayesian Fan Charts for U. K. Inflation ▪ Experimental analysis (how groups decide) – Lombardelli, Proudman, Talbot (2002) Committees versus individuals: an experimental analysis of monetary policy decision-making JEM 027 – Monetary Economics 44

Response by researchers: robust control We propose to tackle the model uncertainty Model 1 (core model) Forecast Preferences Policy maker Model 2 (robust control) Shocks normally distributed R JEM 027 – Monetary Economics 45

Working with several models Two models The loss function Optimization problem for year t JEM 027 – Monetary Economics 46

Robust control: conclusions ▪ Optimal rules are different than in the certainty benchmark and/or cases of complex (but in-model) uncertainty ▪ Interest rates are set according to the minimax decision rule ▪ What does it mean for monetary policy? ▪ On the one hand, researchers have made a significant step towards producing a forecast that is robust to the model uncertainty ▪ On the other hand, central bankers still not happy ▪ They implement the “best expected value” decision rule that would produce other outcomes than the minimax – Goodhart (2003) What is the Monetary Policy Committee attempting to achieve? JEM 027 – Monetary Economics 47

Uncertainty: summary Uncertainty Additive Linear Multiplicative Non-linear Model/ Knightian Example ▪ Complexity increase Implication for policy relative to certainty case Equation error in linear model Uncertain time lag in linear model ▪ None ▪ Uncertain coefficient(s) ▪ ▪ Uncertain functional form of Phillips curve ▪ More aggressive or cautious (depends on study) More cautios ▪ Model uncertainty ▪ ▪ Equation uncertain (fixed exchange rate) Noise in data ▪ ▪ More aggressive or cautious (depends on study) More aggressive or cautious (depends on model) More cautious JEM 027 – Monetary Economics 48

References ▪ Blinder (1998) Central Banking in Theory and Practice ▪ ▪ Brainard (1967) Uncertainty and the effectiveness of policy Classics! Cogley, Morozov, Sargent (2003) Bayesian Fan Charts for U. K. Inflation Goodhart (2003) What is the Monetary Policy Committee attempting to achieve? Hall, Salmon, Yates, Batini (1999) Uncertainty and simple monetary policy rules – An illustration for the United Kingdom ▪ ▪ Issing (1999) The Monetary Policy of the ECB in a World of Uncertainty Knight (1921) Risk, Uncertainty and Profit Classics! Leiderman L. (1999) Some Lessons from Israel, in Monetary Policy-Making under Uncertainty Lombardelli, Proudman, Talbot (2002) Committees versus individuals: an experimental analysis of monetary policy decision-making ▪ ▪ Srour G. (1999) Inflation Targeting Under Uncertainty Šmídková (2005) How Inflation Targeters (Can) Deal with Uncertainty Šmídková et al. (2008) Evaluation of the Fulfilment of the CNB's Inflation Targets 1998 -2007 Tetlow, von zur Muehlen (2000) Robust monetary policy with Misspecified models: Does model uncertainty always call for attenuated policy? JEM 027 – Monetary Economics 49