Dario Rukelj Ministry of Finance of the Republic of Croatia Barbara Ulloa Central Bank of Chile

1. Incorporating Uncertainties into Economic Forecasts: an Application to Forecasting Economic Activity in Croatia Dario Rukelj Ministry of Finance of the Republic of Croatia Barbara Ulloa Central Bank of Chile Young Economists’ Seminar (YES) Dubrovnik Economic Conference June 23, 2010

2. Uncertainty is the only certainty there is, and knowing how tolive with insecurity is the only security... John Allen Paulos

3. 1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

4. MOTIVATION FORECASTS OF THE EUROZONE REAL GDP GROWTH

5. DEALING WITH UNCERTAINTY • Point forecasts • Mode of distribution • Interval forecasts • Consists of an upper and a lower limit • Density forecasts • The whole probability distribution of the forecasts

6. 1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

7. STOCHASTIC SIMULATION APPROACH* • Data generating process assumed to be VAR model, estimated in the finite sample: • Forecasts incorporating future uncertainties: • Forecasts incorporating future and parameter uncertainties: • Simulate s in sample values of y • For each of these estimated models, r replications of the forecasts are calculated *Garrat, Pessaran and Shin (2003 and 2006)

8. SIMULATED SHOCKS • Parametric approach : • Unbalanced risks: • Non-parametric approach: • random draws with replacements from the in sample residuals

9. CALCULATION • Future uncertainty • Obtain the set of simulated shocks • Generate the forecasts using the simulated shocks • Sort the forecasted values of the variable of interest • Determine probability bands by the deciles • Future and parameter uncertainty • Using initial values for the number of lags determined by the order of the VAR, calculate forecasts ahead using estimated parameters of the initial model, as well as applying a shock to each observation in each period • Re estimate the models with each set of time series obtained in this way • Based on these models forecasts are made like under only future uncertainty

10. 50% 60% 70% Probability density 80% 90% PRESENTATION Probability Distribution Fanchart

11. EVALUATION In Sample Fancharts Probability Integral Transform

12. KOLMOGOROV – SMIRNOV TEST • Kolmogorov – Smirnov test can be used for comparing two distributions • Comparing Probability Integral Transform of outturns with uniform distribution • Let F(a) be the cumulative distribution function of uniform distribution • Cumulative distribution function of empirical distribution is given by: where t is the number of observations of variable b such that • If variable b comes from uniform distribution then D should be small

13. 1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

14. BENCHMARK MODEL Reduced form VECM from Rukelj (2010) considered: where xt is vector of endogenous variables (m, g and y). Rewritten in a VAR form:

15. FUTURE UNCERTAINTY Fanchart – Parametric Approach PIT – Parametric Approach

16. FUTURE UNCERTAINTY Fanchart – Non Parametric Approach PIT – Non Parametric Approach

17. FUTURE UNCERTAINTY Fanchart – Skewed Distribution PIT – Skewed Distribution

18. FUTURE AND PARAMETER UNCERTAINTY Fanchart – Parametric Approach PIT – Parametric Approach

19. FUTURE AND PARAMETER UNCERTAINTY Fanchart – Non Parametric Approach PIT – Non Parametric Approach

20. KOLMOGOROV – SMIRNOV TEST RESULTS

21. 1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

22. FORECASTING WITH UNCERTAINTY Probability Forecasts for the Real GDP Growth

23. CONCLUSION • In this paper we have shown how to calculate, present and evaluate density forecasts by stochastic simulation approach • An application of this methodological framework to the chosen benchmark model showed that: • parametric and non-parametric approach yielded similar results • incorporating parameter uncertainty results in a much wider probability bands of the forecasts • evaluation of the density forecasts indicate a better performance when only future, without parameter uncertainties are considered • Future research in this topic should incorporate model uncertainty and additional goodness of fit tests

24. Thank you for your attention!