EVALUATING CORE INFLATION INDICATORS Carlos Robalo Marques Pedro Duarte Neves

1. EVALUATING CORE INFLATION INDICATORS Carlos Robalo Marques Pedro Duarte Neves Luís Morais Sarmento

2. WHY SHOULD CENTRAL BANKS AVOID THE USE OF THE UNDERLYING INFLATION INDICATOR Carlos Robalo Marques Pedro Duarte Neves Afonso Gonçalves da Silva

3. MOTIVATION • PURPOSE OF THE FIRST PAPER: To propose a set of testable conditions to evaluate alternative core inflation indicators. • PURPOSE OF THE SECOND PAPER: To test the “excluding food and energy” indicators for several countries using the criteria suggested in the first paper.

4. CORE (OR TREND) INFLATION DEFINITION • We assume that, for any given period t, we have by definition = + Where • = Inflation; • = Core or trend inflation; • = Temporary component, with . • Note that we cannot have , because in this case will include a permanent component (the expected value of ), which, by definition, must be included in

5. COMMENTS ON SOME COMMONLYSUGGESTED EVALUATION CRITERIA: HABILITY TO FORECAST FUTURE HEADLINE INFLATION • Laflèche (1997), Bryan and Cecchetti(1994), Freeman(1998) Vega and Wynne (2001); • First comment: Evaluation is made in relative rather than absolute terms, and so no conclusion can be drawn on the properties of the selected indicator(s).

6. Second comment: the forecast ability is not a sensible requirement for a core inflation indicator. In fact, we should not expect a core inflation measure to be a good predictor of future headline inflation because is the long run component of and the long run component has no information about the short run. By definition = - and so in the model = ƒ( ) we have in fact + = ƒ( ). Can we expect to be able to forecast ( + ), as has no information about ? Of course, not. Statistical argument: A smooth series ( ) cannot (by definition) be able to accurately forecast a volatile series ( ).

7. THE “REFERENCE MEASURE” APPROACH • Ex: Bryan and Cecchetti (1994), Bryan, Cecchetti and Wiggins II (1997), Bakhshi and Yates (1999), Coimbra and Neves (1997),Vega and Wynne (2001); • The selected indicator is the one that best approximates the “reference measure” (minimises the MSE): usually a centred moving average of the inflation rate.

8. Comment: • The properties of the reference measure are unknown; • If the reference measure is not the best proxy for the unknown “true trend” of inflation, this approach does not guarantee that the best indicator is selected, as the core inflation that best approximates the “reference measure” is not necessarily the one that best approximates the “true” trend of inflation

9. NECESSARY CONDITIONSIMPORTANT ASSUMPTIONS • . We assume that, for any given period t, we have by definition • . The temporary disturbances in the inflation rate, , are caused by developments such as changes in weather conditions, disturbances in the supply of goods, etc. • 3. By definition is expected to have zero mean and finite variance, and therefore, non-stationary is excluded on theoretical grounds. • 4. In what follows it is assumed that , the inflation rate, is I(1). • 5. The candidates to be a core inflation measure are timely and not subject to revisions.

10. NECESSARY CONDITIONS (CONT.) I) is I(1) and and are cointegrated with unitary coefficient, i.e., - is a stationary variable with zero mean; • When inflation, , is I(1), we say that is a core inflation measure if: • Condition i) follows directly from the definition of core or trend inflation and implies that inflation and the core inflation measure cannot exhibit a systematically diverging trend, in which case the latter will give false signals to the monetary authority. • This condition was first proposed in Freeman (1998).

11. NECESSARY CONDITIONS (CONT.) • If does not have zero mean, then is not capturing the whole systematic component of . • Also, if is stationary, but , does not account for the whole permanent component of . The net result shall correspond to either a faster (if ) or slower (if ) systematic growth of vis-à-vis and therefore the two variables tend to drift apart.

12. NECESSARY CONDITIONS (CONT.) ii) There is an error correction mechanism given by for , i.e., may be written as • Condition ii) implies that if is a trend measure of then must be an “attractor” for , in the sense that in the long run, must converge to . So, we must have in the ECM model.

13. NECESSARY CONDITIONS (CONT.) • If this is not the case the use of as a core inflation measure is not useful at all. If there is no reason to expect that will converge to , there is no point in knowing whether in a given period is above or below . However, if condition ii) holds, we can ensure that if in a given period is above (below) , there is a reason to expect that, sooner or later, will start to decrease (increase) and converge to . • Condition ii) is a special case of Granger causality. In particular, this condition requires that Granger causes through the error correction term. In this sense, is a leading indicator of .

14. NECESSARY CONDITIONS (CONT.) iii) is strongly exogenous for the parameters of the previous equation. • Condition iii) aims at preventing that condition ii) does occur the other way around, i.e. that is not an attractor for and also that is not sensitive to observed outliers in . Otherwise it will be very difficult, if not impossible, to anticipate the future path of inflation by looking at . The fact, for instance that in a given period is above , allows us to anticipate the future path of only if is not a function of .

15. NECESSARY CONDITIONS (CONT.) Strong exogeneity of implies simultaneously that the error correction term does not appear in the equation for (i.e., that is weakly exogenous for the parameters of the cointegrating vector) and also that does not Granger cause . In other words, condition iii) implies that in the error correction model for we must have

16. HYPOTHESIS TESTING • Condition i): use unit root tests on the series , in order to assess if is a zero mean stationary variable. Alternative: Johansen approach to test for cointegration between and and see whether (1, -1) is a cointegrating vector. • Condition ii): test the hypothesis using the conventional t-ratio of in following ECM: Alternative: use the Johansen approach to show that is not weakly exogenous for the parameters of the cointegrating vector.

17. HYPOTHESIS TESTING (CONT.) • Condition iii): test the hypothesis in the following ECM model The test of this condition is carried out in two steps: i) week exogeneity is tested ( = 0) using the t-ratio of or the Johansen approach (weak exogeneity of ) ii) Test (1 = 2 = … = s = 0) only for the weakly exogenous indicators, i.e. meet the first step.

18. EVALUATING THE CORE INFLATION INDICATORS FOR THE UNITED STATES • (1) The ”Excluding food and energy indicator” (EFE); • (2) The ”8% (symmetric) trimmed mean” (TM8); • (3) The “median of price changes distribution” (MED); • MAIN CONCLUSIONS: • TM8 and MED meet the three conditions and so can be used as useful core inflation indicators. • TM8 is slightly less volatile than MED. • The EFE indicator does not meet conditions ii) and iii).

19. EVALUATING THE “EXCLUDING FOOD AND ENERGY” INDICATOR FOR 6 COUNTRIES (1) USA; (2) Germany; (3) France; (4) Italy; (5) Spain; (6) Portugal; MAIN CONCLUSION: For none of the six countries does the EFE indicator meet the 3 conditions. For USA, Germany and France the EFE indicator fails conditions ii) and iii);For Italy and Portugal fails condition i); For Spain fails condition ii)

20. Comment on the results: The conclusion that the EFE indicator does not meet conditions ii) and iii) was to be expected.In fact, in order to compute the EFE indicator we exclude from the CPI, the prices of energy and unprocessed food, which are goods that enter as intermediate inputs into the production process. Therefore, changes in the energy or in the unprocessed food directly and contemporaneously affect the CPI inflation, but affect the prices of the other CPI items, i.e. the EFE indicator, only with a lag. This being so, the prices of energy and unprocessed food are a leading indicator of the EFE indicator, and as they affect prices contemporaneously, the inflation rate itself also appears as a leading indicator of the EFE indicator.