1. Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague JEM027 Monetary Economics Monetary policy under uncertainty Tomáš Holub Tomas.Holub@cnb.cz December 7, 2015 Based on presentation of Kateřina Šmídková from 2013

2. JEM027 – Monetary Economics 1 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.

3. JEM027 – Monetary Economics 2 ▪ 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) One thing is certain about monetary policy. There is uncertainty. ” “ Monetary policy in reality

4. JEM027 – Monetary Economics 3 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

5. JEM027 – Monetary Economics 4 Time axis of the literature ▪ Pioneering work 1 (Knight speaks of complex uncertainty) ▪ Pioneering work 2 (Brainard states his principle) ▪ Revival of uncertainty literature (uncertainty classification, Brainard extended) ▪ Policy-makers criticized research for ignoring Knight ▪ Research responds by improving methodology (robust control) 1920 1990s 1960s 2000s …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.

6. JEM027 – Monetary Economics 5 Overview of the lecture ▪ Certainty benchmark ▪ Introducing linear uncertainty Analytical framework – basics ▪ Simple uncertainty ▪ Complex (and very complex) cases Classification of uncertainty ▪ Researchers return to uncertainty ▪ Policy makers complain ▪ Researchers respond Researchers versus policy-makers

7. JEM027 – Monetary Economics 6 Certainty benchmark The model No shocks The loss function (pure IT) Optimization problem for year t

8. JEM027 – Monetary Economics 7 Certainty benchmark: optimization Substitution (1) Substitution (2) Minimizing loss function wrt. R t

9. JEM027 – Monetary Economics 8 Certainty benchmark: outcome Optimal reaction function Plug into (2) to get F.O.C. Actual inflation in time t+2

10. JEM027 – Monetary Economics 9 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.

11. JEM027 – Monetary Economics 10 JEM027 – Monetary Economics 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

12. JEM027 – Monetary Economics 11 JEM027 – Monetary Economics 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

13. JEM027 – Monetary Economics 12 JEM027 – Monetary Economics Simple uncertainty The loss function (pure IT) Optimization problem for year t The model No shocks Example of shock … where ε t+1 and η t+1 are white noise random shocks

14. JEM027 – Monetary Economics 13 JEM027 – Monetary Economics Simple uncertainty: optimization Substitution (1) Substitution (2) Minimizing expected loss function wrt. R t

15. JEM027 – Monetary Economics 14 JEM027 – Monetary Economics Simple uncertainty: optimal reaction Optimal reaction function Covariances are zero

16. JEM027 – Monetary Economics 15 JEM027 – Monetary Economics Simple uncertainty: outcome Deviation of actual inflation from the forecast (and target) Optimal reaction: same as in the certainty benchmark F.O.C. Actual inflation in time t+2 (optimal reaction function substituted into (2))

17. JEM027 – Monetary Economics 16 JEM027 – Monetary Economics Simple uncertainty compared to certainty benchmark Actual inflation rates in time t+2 compared Optimal reaction functions compared

18. JEM027 – Monetary Economics 17 JEM027 – Monetary Economics Recall the Lecture on Inflation Targeting (ii) ▪ With shocks, inflation can in the end deviate from the target (and forecast). ▪ Challenge for communication.

19. JEM027 – Monetary Economics 18 JEM027 – Monetary Economics 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

20. JEM027 – Monetary Economics 19 JEM027 – Monetary Economics Overview of the lecture ▪ Certainty benchmark ▪ Introducing linear uncertainty Analytical framework – basics ▪ Simple uncertainty ▪ Complex (and very complex) cases Classification of uncertainty ▪ Researchers return to uncertainty ▪ Policy makers complain ▪ Researchers respond Researchers versus policy-makers

21. JEM027 – Monetary Economics 20 JEM027 – Monetary Economics 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

22. JEM027 – Monetary Economics 21 JEM027 – Monetary Economics 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

23. JEM027 – Monetary Economics 22 JEM027 – Monetary Economics 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)

24. JEM027 – Monetary Economics 23 JEM027 – Monetary Economics 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)

25. JEM027 – Monetary Economics 24 JEM027 – Monetary Economics Brainard's principle (revived version) ▪ We use the same set-up as in the simple (linear) uncertainty case ▪ We add parameter uncertainty … where C t+1 is random variable (c, χ 2 ) The extended model

26. JEM027 – Monetary Economics 25 JEM027 – Monetary Economics Non-linear uncertainty: optimization Substitution (1) Substitution (2) Minimizing expected loss function wrt. R t

27. JEM027 – Monetary Economics 26 JEM027 – Monetary Economics Non-linear uncertainty: optimal policy Optimal reaction function Covariances are zero

28. JEM027 – Monetary Economics 27 JEM027 – Monetary Economics Non-linear uncertainty: outcome F.O.C. ▪ Note χ 2 /c 2 is the measure of relative uncertainty ▪ If χ=0 then we have the case of linear uncertainty ▪ For very large χ 2 : policy rate does not change at all, it is always neutral R t =π t (we assume that equilibrium real rate is zero)

29. JEM027 – Monetary Economics 28 JEM027 – Monetary Economics Linear and non-linear uncertainty compared Optimal reaction functions compared Summary comparison … where

30. JEM027 – Monetary Economics 29 JEM027 – Monetary Economics Non-linear uncertainty: two answers ▪ Central bankers cannot neglect uncertainty when they communicate in both cases (linear and non-linear uncertainty) We know already that inflation is not the same as in the case of certainty benchmark ▪ Central bankers cannot neglect this type of uncertainty during policy decisions In addition, with non-linear uncertainty, optimal rule is not the same as in the case of certainty benchmark

31. JEM027 – Monetary Economics 30 JEM027 – Monetary Economics 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

32. JEM027 – Monetary Economics 31 JEM027 – Monetary Economics Brainard’s principle and gradualism ▪ Moving in two smaller steps reduces the range of possible outcomes. Instrument Target variable

33. JEM027 – Monetary Economics 32 JEM027 – Monetary Economics 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?

34. JEM027 – Monetary Economics 33 JEM027 – Monetary Economics 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

35. JEM027 – Monetary Economics 34 JEM027 – Monetary Economics Example with expectations ▪ 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 ▪ 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

36. JEM027 – Monetary Economics 35 JEM027 – Monetary Economics Knightian uncertainty Two types of uncertainty ▪ For policy makers the second type of uncertainty is more difficult, but unfortunately quite frequent 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

37. JEM027 – Monetary Economics 36 JEM027 – Monetary Economics Driving again Stochastic uncertaintyKnightian uncertainty

38. JEM027 – Monetary Economics 37 JEM027 – Monetary Economics Stochastic versus Knightian uncertainty Stochastic uncertaintyKnightian uncertainty Crash

39. JEM027 – Monetary Economics 38 JEM027 – Monetary Economics Overview of the lecture ▪ Certainty benchmark ▪ Introducing linear uncertainty Analytical framework – basics ▪ Simple uncertainty ▪ Complex (and very complex) cases Classification of uncertainty ▪ Researchers return to uncertainty ▪ Policy makers complain ▪ Researchers respond Researchers versus policy-makers

40. JEM027 – Monetary Economics 39 JEM027 – Monetary Economics Return of uncertainty: 1990s ▪ In 1990s, 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)

41. JEM027 – Monetary Economics 40 JEM027 – Monetary Economics 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

42. JEM027 – Monetary Economics 41 JEM027 – Monetary Economics 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

43. JEM027 – Monetary Economics 42 JEM027 – Monetary Economics Central bankers’ observation Researchers see our decisions so simplified! Preferences Policy maker Forecast Stochastic core model R Shocks normally distributed

44. JEM027 – Monetary Economics 43 JEM027 – Monetary Economics Central bankers’ complaints Our decisions are much more complex! Core model Off-model info Sub-models Forecast Info set 1 Info set 2 Info set 3 Shocks not normally distributed Expert 2 Expert 1 Expert 3 Preferences 2 Policy maker 2 Preferences 3 Policy maker 3 Preferences 1 Policy maker 1 R

45. JEM027 – Monetary Economics 44 JEM027 – Monetary Economics Response by researchers: 2000s ▪ 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

46. JEM027 – Monetary Economics 45 JEM027 – Monetary Economics Response by researchers: robust control We propose to tackle the model uncertainty Preferences Policy maker Forecast Model 1 (core model) R Shocks normally distributed Model 2 (robust control)

47. JEM027 – Monetary Economics 46 JEM027 – Monetary Economics Working with several models Optimization problem for year t The loss function Two models

48. JEM027 – Monetary Economics 47 JEM027 – Monetary Economics 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?

49. JEM027 – Monetary Economics 48 JEM027 – Monetary Economics Uncertainty: summary Uncertainty Complexity increase Additive Linear Multiplicative Non-linear Model/ Knightian Example ▪ Equation error in linear model ▪ Uncertain time lag in linear model ▪ Uncertain coefficient(s) ▪ Uncertain functional form of Phillips curve ▪ Model uncertainty ▪ Equation uncertain (fixed exchange rate) ▪ Noise in data Implication for policy relative to certainty case ▪ None ▪ More aggressive or cautious (depends on study) ▪ More cautios ▪ More aggressive or cautious (depends on study) ▪ More aggressive or cautious (depends on model) ▪ More cautious

50. JEM027 – Monetary Economics 49 JEM027 – Monetary Economics 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?