1. A Leading index for the Colombian economic activity Colombian economic activity Luis Fernando Melo Fabio Nieto Mario Ramos Luis Fernando Melo Fabio Nieto Mario Ramos

2. It permits to lead the turning points of the economy or, in a global manner, the dynamics of the economic activity. This information is very useful for economic policy and decision making. The problem: Design of a leading index In previous solutions: Usually, the design is accomplished by means of a weighted average of a group of variables. The weights are selected in a heuristic way In Colombia: Melo et al. (1988), Ripoll et al. (1995), Maurer and Uribe (1996) and Maurer et al. (1996)]

3. The statistical problem (Stock and Watsons approach): Find a stochastic process that leads, in some sense, the turning points of the so-called state of the economy. Basic step: find an optimal estimate of the state of the economy which is called a coincident index. Nieto and Melo (2001) have proposed an appropriate methodology for computing a coincident index for the economic activity, which is based on a modification to Stock and Watsons (1989, 1991, 1992) procedures.

4. Coincident Index Model : state of the economy (not observable ). : coincident variables, which are integrated of order 1. 1) 2) 3)

5. In matrix form: 1) 2) 3)

6. Model estimation Maximum likelihood approach via state space models (Kalman filter). State Space representation of the Coincident Index Model: Observation equation: (eq. 1) System equation: (eq. 2, 3) t : state vector

7. Stock and Watson coincident index CtCt C t (1) = C t / 199.79 C t (2) = C t (1) + 0.88 t / N C t (3) = exp(C t (2) ) C t (4) = 100C t (3) / C 3 (3)

8. Simulations of the Stock and Watson coincident index model MSE of C t|t Then, the state space model used by S-W does not exhibit the steady-state property.

9. Likelihood surface for simulated models

10. Our modifications Coincident equation. (eq. 1) Identifiability of the model. Restriction over some parameters of the model. State space model representation - Our model has the steady-state property. - We include seasonal effects (do not use adjusted variables). - A strategy for providing the initial values is proposed. - Coincident index:

11. Leading Index Model 1) 2) 4) 3) In matrix form: : state of the economy (not observable ). : C oincident variables. : Leading variables. Where:

12. Model estimation Maximum likelihood approach via state space models (Kalman filter). State Space representation of the Leading Index Model: Observation equation: (eq. 1) System equation: (eq. 2, 3, 4) t *: state vector

13. Leading index (L t ) where,, denotes the prediction of given given the information up to time t. Note that the information used in the context of the leading index is given by both the coincident and leading variables. where denotes the coincident index for. Stock and Watsons idea was: leads if and are very close,

14. The leading index model includes two kind of observed variables. Coincident ( X t ): Melo et al. (2002) Leading ( Y t ): We consider 83 series (Appendix B) based on the following criteria: Monthly periodicity Opportunity (lag information less than 2 ½ months) Availability (since January of 1980) An empirical application of the leading index methodology

15. Unit root test Co-movement statistics w.r.t. IPR and C t Cross-Correlation function with double prewhitening Selection of the leading series Seasonal unit root test Spectral Analysis: Coherence Canovas statistics

16. Predictive Content Predictive power w.r.t. IPR and C t for k=1,6,12 Marginal predictive content for k=6,12 where R t is the reference series and W t is a candidate for a leading variable.

17. The optimum group was select according to : Selection of the leading index model Coincident series: Melo et al. (2002) Leading series: different sub-groups of the selected leading variables Economic criteria AIC Residual diagnostics Model stability Leading performance of the resulting index

18. Leading performance Cross-correlation between L t and M t where L t is the resulting leading index: and with the super-index C denoting the estimations from N-M. Then, if L t and M t are very close L t can be considered as a leading index for { C t }.

19. The final leading index model includes the following leading series: Approved building area (areacon) Real money supply M1 (m1r) Real Interest rate of 90-day certificate of deposit for banks and corporations (cdttr) Consumption good imports in real terms (impr_bco) Business conditions (clineg) Confidence indicator (incon)

20. L t vs. M t

21. L t vs. reference series

22. September 1997 November 1997 January 1998 March 1998 Recession exercise for L t

23. Coincident Index (up to May 2003)

24. Leading Indicator (up to May 2003)