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Prediction Intervals for Macroeconomic Variables Based on Uncertainty Measures

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Prediction Intervals for Macroeconomic Variables Based on Uncertainty Measures Prediction Intervals for Macroeconomic Variables Based on Uncertainty Measures Pei-Hua (Peggy) Hsieh ANR: 591577 Academic supervisor: Prof. Dr. Bertrand Melenberg Second reader: Prof. Dr. Pavel Ciˇzekˇ Internship supervisor: Dr. Adam Elbourne A thesis submitted in partial fulfillment of the requirements for the degree: Master of Science in Econometrics and Mathematical Economics Tilburg School of Economics and Management Tilburg University The Netherlands Date: September 26, 2016 Prediction Intervals for Macroeconomic Variables Based on Uncertainty Measures Pei-Hua (Peggy) Hsieh ∗ October 7, 2016 Abstract This paper develops a method for incorporating uncertainty measures into the formation of confidence intervals around predictions of macroeconomic variables. These intervals are used for plotting fan charts, a graphical rep- resentation of forecasts pioneered by the Bank of England, which is commonly employed by central banks. I demonstrate and evaluate the proposed method by using it to plot fan charts for real GDP growth rate in the Netherlands. This paper aims to provide concrete recommendations for the Centraal Planbureau (CPB). ∗I am indebted to Prof. Dr. Bertrand Melenberg for his inspiring guidance and support. I would also like to thank my supervisor from the CPB Dr. Adam Elbourne for providing me with data and helpful comments. Finally, I thank my family, instructors at Tilburg university and colleagues from the CPB. 1 Contents 1 Introduction6 2 Methodology 10 2.1 Step 1................................... 11 2.2 Step 2................................... 12 2.3 Step 3................................... 15 3 Data description 16 4 Summary Statistics 19 4.1 Dependent Variable............................ 19 4.2 Explanatory Variables.......................... 23 5 Empirical results 24 5.1 Short dataset: using data from Consensus Economics......... 24 5.2 Specification 1............................... 26 5.2.1 Step 1 - The effect of uncertainty on forecasting errors.... 26 5.2.2 Step 2 - Uncertainty measures prediction intervals....... 29 5.2.3 Step 3 - Real GDP growth rate prediction intervals...... 42 5.3 Specification 2............................... 44 5.4 Comparison with CPB fan chart..................... 48 6 Conclusion 49 Appendix 51 2 List of Tables 1 Summary statistics of explanatory variables.............. 23 2 Correlogram of explanatory variables.................. 23 3 Regression results: short data (MAE).................. 25 4 Regression results: short data (RMSE)................. 25 5 Explanatory variables correlogram (short data)............ 26 6 Dependent variable: forecast error (Mean absolute error)....... 27 7 Dependent variable: forecast error (RMSE)............... 27 8 Results from Dickey-Fuller tests..................... 32 9 Results from KPSS tests......................... 33 10 Model selection.............................. 36 11 Prediction summary........................... 36 12 Dependent variable: forecast error (Mean absolute error)....... 45 13 Dependent variable: forecast error (RMSE)............... 45 14 Prediction summary (specification 2).................. 46 List of Figures 1 Standard deviation of within-country forecast error: before and after 2008....................................7 2 Bank of England Fan Chart for CPI Inflation.............8 3 Forecast performance score by country (1975-2014).......... 20 4 Forecast performance score by country (2004-2014).......... 21 5 Aggregate measures of forecast error.................. 22 6 Summary statistics of forecast error................... 22 7 CPB predictions and fitted aggregate forecast errors (spring, RMSE) 29 8 Raw time series: oil............................ 30 9 Raw time series: esi............................ 30 10 Raw time series: news.......................... 31 11 Raw time series: vox........................... 31 12 ACF and PACF for oil.......................... 34 13 ACF and PACF for news......................... 34 14 ACF and PACF for esi.......................... 35 15 ACF and PACF for vox......................... 35 3 16 Selected model: oil............................ 37 17 Selected model: news........................... 37 18 Selected model: esi............................ 38 19 Selected model: vox............................ 38 20 Residuals: oil............................... 39 21 Residuals: esi............................... 40 22 Residuals: news.............................. 40 23 Residuals: vox............................... 41 24 Tests for autocorrelation in the residuals................ 42 25 Fan chart using MAE, December forecasts............... 43 26 Fan chart using RMSE, December forecasts.............. 44 27 CPB predictions and fitted aggregate forecast errors (spring, RMSE) - Specification 2.............................. 46 28 Fan chart using MAE, December forecasts (Specification 2)...... 47 29 Fan chart using RMSE, December forecasts (Specification 2)..... 48 30 CPB fan chart (September 20, 2016).................. 49 31 CPB predictions and fitted aggregate forecast errors, (spring, MAE). 51 32 CPB predictions and fitted aggregate forecast errors, (June, MAE).. 52 33 CPB predictions and fitted aggregate forecast errors, (September, MAE) 52 34 CPB predictions and fitted aggregate forecast errors, (December,MAE) 53 35 CPB predictions and fitted aggregate forecast errors, (June, RMSE). 53 36 CPB predictions and fitted aggregate forecast errors, (September, RMSE)................................... 54 37 CPB predictions and fitted aggregate forecast errors, (December, RMSE) 54 38 CPB predictions and fitted aggregate forecast errors, (June,MAE) (Specification 2).............................. 55 39 CPB predictions and fitted aggregate forecast errors, (September, MAE) (Specification 2).......................... 55 40 CPB predictions and fitted aggregate forecast errors, (December, MAE) (Specification 2).......................... 56 41 CPB predictions and fitted aggregate forecast errors, (spring, RMSE) (Specification 2).............................. 56 42 CPB predictions and fitted aggregate forecast errors, (June, RMSE) (Specification 2).............................. 57 4 43 CPB predictions and fitted aggregate forecast errors, (September, RMSE) (Specification 2)......................... 57 44 CPB predictions and fitted aggregate forecast errors, (December, RMSE) (Specification 2)......................... 58 45 Fan chart using MAE, Spring forecasts................. 58 46 Fan chart using RMSE, Spring forecasts................ 59 47 Fan chart using MAE, June forecasts.................. 59 48 Fan chart using RMSE, June forecasts................. 60 49 Fan chart using MAE, September forecasts............... 60 50 Fan chart using RMSE, September forecasts.............. 61 51 CPB predictions and fitted aggregate forecast errors, (June, MAE) (Specification 2).............................. 61 52 CPB predictions and fitted aggregate forecast errors, (September, MAE) (Specification 2).......................... 62 53 CPB predictions and fitted aggregate forecast errors, (December, MAE) (Specification 2).......................... 62 54 CPB predictions and fitted aggregate forecast errors, (spring, RMSE) (Specification 2).............................. 63 55 CPB predictions and fitted aggregate forecast errors, (June, RMSE) (Specification 2).............................. 63 56 CPB predictions and fitted aggregate forecast errors, (September, RMSE) (Specification 2)......................... 64 57 CPB predictions and fitted aggregate forecast errors, (December, RMSE) (Specification 2)......................... 64 58 Fan chart using MAE, Spring forecasts (specification 2)........ 65 59 Fan chart using RMSE, Spring forecasts (specification 2)....... 65 60 Fan chart using MAE, June forecasts (specification 2)......... 66 61 Fan chart using RMSE, June forecasts (specification 2)........ 66 62 Fan chart using MAE, September forecasts (specification 2)...... 67 63 Fan chart using RMSE, September forecasts (specification 2)..... 67 5 ; 1 Introduction Economic forecasting occupies a distinguished position in econometrics, as it pro- vides important information for policy analysis. Policy decisions that take economic forecasts as inputs can have long lasting significant impacts on members of the econ- omy. Therefore, forecasting accuracy is a key target for econometricians. Examples of macroeconomic variables which are commonly forecasted include unemployment rates, price indexes, interest rates, exchange rates, and commodity prices. This pa- per focuses on improving the current methodology which the Centraal Planbureau (CPB) uses for predicting future real GDP growth rate. In particular, I use measures of uncertainty to construct confidence intervals around the central projections. Following the 2008 financial crisis, prediction accuracy has improved in the Netherlands, both compared to past performance and to other countries' perfor- mance. This can be seen in figure1, where, for each country, the left bar is the standard deviation of forecast errors before 2008 and the right bar is using the years following 2008.1 The forecast accuracy in most of countries has became worse since 2008, the year of the global financial crisis (Greece, Finland, Germany, United King- dom and Denmark), while the forecast accuracy in the Netherlands and Belgium had improved after the crisis. In some countries (Ireland, Luxembourg and Swe- den), while forecasting performance had improved, the forecast errors still remained relatively high. It is important for the CPB to determine whether this improvement is due the
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