Modeling monetary policy in real time: does discreteness matter?

1. Modeling monetary policy in real time:does discreteness matter? Andrei Sirchenko European University Institute, Florence, Italy This research was supported financially by the Global Development Network’s grant # R05-1861, distributed by the Economics Education and Research Consortium. The author is also grateful to: Michael Beenstock, Wojciech Charemza and Victor Polterovich - for valuable comments and support; Patrick Graham, Beata Idzikowska, Jarosław Jakubik, Jakub Jaworowski, Marynia Kruk, Tomasz Łyziak, Barbara Sladkowska, Piotr Szpunar, Mark Wynne and Reuters-Warsaw for help with getting statistical data; Joao Santos Silva for useful suggestions and explanations; TechnoNICOL for providing a computer; Timo Mitze, Alexis Belianin, Michał Brzoza-Brzezina, Dariusz Filar, Andrzej Sławiński and other participants at XIIIth Spring Meeting of Young Economists and Research Seminars at Higher School of Economics and National Bank of Poland for useful comments.

2. How do the policy interest rates respond to the state of the economy?Do discreteness of policy rates and real-time data matter?

3. “The central bank must have a highly regular and predictable policy rule or response pattern that links policy actions to the state of the economy.”- William Poole, then-President of the Federal Reserve Bank of St. Louis

4. “It is not possible to make use of a simple policy rule, which could be known ex ante to market participants.”- National Bank of Poland, Monetary Policy Council

5. “If practitioners in financial markets gain a better understanding of how policy is likely to respond to incoming information, asset prices and bond yields will tend to respond to economic data in ways that further the central bank's policy objectives.”- Ben Bernanke, President of the Federal Reserve System

6. Discrete-choice approach • Real-time data • MPC’s meetings as a unit of observation

7. Frequency distribution of historical NBP reference rate changes

8. The paper compiles a novel Polish real-time data set incorporating historical values of about 140 economic and financial indicators, truly available to policymakers and public at each monthly policy meeting during the period 1998 – 2007

9. The decision-making meetings of monetary authority as a unit of observation

10. This sample design carefully simulates the actual policy-action-generating process

11. Brief summary of results

12. Policy regime change in 2002 • The systematic policy responses demonstrate remarkable structural differences prior to and after April 2002

13. Sup-LR test for structural change with unknown change pointIndependent variables: GVARna_Y and ExInf_T_MSample: 1999/02 - 2006/10 40 LR LR chi-square 1% CV 5% CV 35 30 25 20 15 10 Nov-01 Feb-02 May-02 Aug-02 Nov-02 Feb-03 May-03 Aug-03 Nov-03

14. Sup-LR test for structural change with unknown change pointIndependent variables: EReu and CPIxac_T_YMSample: 1999/02 - 2006/10 30 LR LR chi-square 1% CV 5% CV 25 20 15 10 5 0 Nov-01 Feb-02 May-02 Aug-02 Nov-02 Feb-03 May-03 Aug-03 Nov-03

15. Switch from backward- to forward-looking behavior • In its reaction to the deviation of inflation from the target the central bank has shifted from the backward-looking to forward-looking behavior

16. Switch from exchange rate to real activity • Prior to 2002 the central bank reacted to the real activity measures far less, but to the exchange rate far more regular than later on

17. Switch from backward- to forward-looking behavior

18. Focus on inflation and exchange rate before 2002

19. Asymmetric responses to inflationary expectations • The central bank reacts highly asymmetrically to the changes in inflationary expectations, depending on whether the expected inflation is above or below the inflation target

20. Policy rule in 2002/04 - 2006/10

21. No evidence for policyinertia • The policy rate appears to be driven by the key economic indicators without evidence for deliberate interest-smoothing by the central bank

22. Monetary policy inertia in 1999/02 - 2002/03 • The very existence of partial adjustment in the context of policy rule in differences does not seem to be an issue in the first sub-period at all.

23. Tests for monetary policy inertia in 2002/04 - 2006/10 P-Value 0.28 0.44

24. In-sample fit • The estimated simple models explain correctly about 95 percent of observed policy adjustments. • The reference rate appears to be changed in response to month-to-month change in the spread between the expected rate of inflation over the next 12 months from Ipsos survey and the inflation target,the annual growth rate ofindex of gross domestic product (or, alternatively, gross value added)and the positive change since the last MPC’s meeting in the 12-month WIBOR.

25. Policy rule in 2002/04 - 2006/10 P-Value 0.28 0.44

26. Out-of-sample forecasting • In forecasting the next twenty policy decisions the model correctly predicts seventeen ‘no changes’ and three ‘hikes’, erroneously forecasting only the timing of one hike with a monthly lag and outperforming the market anticipation, made one day prior to each policy meeting.

27. Out-of-sample forecasting of next policy decision

28. Out-of-sample forecasting of next policy decision

29. Summary of results • The reported in- and out-of-sample forecasting performance, exceeding the typical one in the literature, is shown to be partially due to the employed methodology, combining the use of discrete regression approach, real-time data and decision-making meetings of monetary authority as a unit of observation.

30. This methodological framework carefully mimics the actual policy-action-generating process since • most major central banks alter interest rates by discrete adjustments; • policy decisions are naturally made using information available in the real-time setting; • they are typically made 8-12 times per year at special policy meetings

31. However, the empirical studies routinely estimate the monetary policy rules by • applying the regression methods for a continuous dependent variable; • using currently available series of economic data; • analyzing the systematic responses of policy rate’s averages to economic data averages for a given month or quarter

32. Obviously, such practice distorts the actual data-generating process because • regression methods for a continuous dependent variable are shown to be inadequate when it is discrete; • the latest versions of statistical data may differ from the real-time ones due to revisions; • time aggregation misaligns the timing of policy decisions and availability of statistical data as well as raises the problem of simultaneity

33. The discrete-choice approach vs. Conventional OLS regression

34. Monthly averages of ex post revised datavs. the real-time non-aggregated data

35. Does real-time ‘policy-meeting’ data matter? • Yes, the use of real-time data set with the policy-making meetings as a unit of observation does matter in the econometric identification of Polish monetary policy

36. Comparison of policy rules, based on revised and real-time data

37. Does discreteness matter? • Can we address the above problems by the conventional simpler linear regression model?

38. Does discreteness matter? • Virtually all measures of fit, constructed for the LRM (linear regression model) estimated by OLS, cannot be applied for the OPM (ordered probit model), and vice versa.

39. Does discreteness matter? • The likelihood functions of GLM (generalized linear model) and OPM, have different nature and cannot be compared either.

40. Does discreteness matter? • It seems impossible to construct a formal test based on the likelihood to compare the LRM and OPM. Are there any other appropriate ways to compare them?

41. Does discreteness matter? • One possible approach is to define the expected value of dependent variable for the OPM and compare it with the LRM counterpart.

42. Does discreteness matter? • For the LRM: E(Y|X) = X*b • For the OPM: E(Y|X) = Pr(Y=-0.5|X)*(-0.5) + Pr(Y=-0.25|X)*(-0.25) + Pr(Y=0|X)*(0) + Pr(Y>0|X)*(0.5+0.5+0.25)/3

43. Does discreteness matter? • An alternative approach is to compute the conditional distribution of rate changes by defining the probabilities of discrete events for the LRM and compare them with the OPM counterparts.

44. Does discreteness matter? Let us ignore for a moment the discreteness of policy rate and evaluate the following simple LRM using OLS: ΔRRt = Xtβ + εt, where ΔRRt – the reference rate change, Xt- vector of explanatory variables, and εt – disturbance term, assumed to be normal iid (0, σ²).

45. Does discreteness matter? We can define the probabilities of discrete outcomes of ΔRRt as follows: Pr (ΔRRt = -0.50) = Pr (-∞< Xtβ + εt < c1) Pr (ΔRRt = -0.25) = Pr (c1 ≤ Xtβ + εt < c2) Pr (ΔRRt = 0.00) = Pr (c2 ≤ Xtβ + εt < c3) Pr (ΔRRt >= 0.25) = Pr (c3 ≤ Xtβ + εt < ∞), where -∞< c1< c2< c3< ∞ are some knownfixed cut-points.

46. Does discreteness matter? • Let us refer to such a LRM, extended to estimate the probabilities of discrete events, as to a ‘rounded linear regression’ model (RLRM). To compute the probabilities we just have to choose the values of cut-points.

47. Does discreteness matter? • The probabilities of discrete outcomes for the RLRM can be now contrasted to the corresponding probabilities for the OPM

48. Does discreteness matter? • These measures of fit are useful in comparing competing models, but can provide only a rough guidance in selecting the preferred model. Without doing a formal test, however, it is unclear which model is the best one.

49. Does discreteness matter? • Formal comparison of RLRM and OPM can be done by noting that the RLRM is a actually a special case of interval regression model (IRM), while the IRM itself is nested in the OPM. • Consequently, all three models can be estimated by ML and, hence, may be compared using, for example, the LR chi-square test.

50. Does discreteness matter?