Flash Estimation and Variable Selection Techniques

1. Flash Estimation and Variable Selection Techniques “Raiders of the Lost Arch Model”

2. Foreword: The Flash Estimation Network • In 2006, Eurostat launched a call for proposal for the production of reliable flash estimates for IPI (t+30), GDP (t+30) and LCI (t+45). • Joint answer from 4 NSI’s accepted by Eurostat: France, Germany, Italy and United-Kingdom • Objectives: Check the feasibility and propose methodolog(ies)y for Eurostat and Member States • A 2-year project: • First year, preparatory work: survey to check for existing experiences, databases, bibliography, methodologies; • Second year, run simulations, propose methods and estimates, prepare programs and transfer of knowledge • Here, we focus on the methodology

3. Foreword • Lots of papers on the same subject. • What is really different? The methodology used • No formula in this presentation but quite technical: lots of statistical techniques are mixed in this strategy to look for a model « Any sufficiently advanced technology is undistinguishable from magic » Arthur C. Clarke, Profiles to the Future, 1961

4. Outline • What is a “flash estimate”? • What is a “good” model? • The variable selection problem • Variable selection techniques • Where should I dig? A method based on HCA • An example: nowcasting the Eurozone GDP • Data and process • Comparing “usual” and HCA results • Conclusions

5. What is a “flash estimate”? • Very difficult and sensitive question • Lots of discussions (not to say arguments) • Why? Soft and hard data • An agreement • Pure AR models (no new information) can be used as benchmarks but are not accepted for FE • Still a disagreement • Can a model be based on soft data (BCS) only? • A compromise • FE models must incorporate hard data (as much as possible). Much easier for quarterly data.

6. What is a “good” model? • Reminder: the model will be used in production! • Main characteristics • Simple (few variables) • Interpretable • Good “statistical properties” including robustness • And last (and least) good nowcasts • Other considerations • Stay close to the user database as much as possible in order to minimize “interactions” during the production process. • Provide the user with a “built-in” but flexible methodology (and program) based on his/her tools.

7. The variable selection problem • Example: nowcasting the EA GDP • Potential explanatory variables: • IPI, New orders, Energy prices, HICP, Unemployment, Business surveys (Industry, Retail trade, Construction, Services) etc. Easy to find at least 20 variables (monthly and/or quarterly) • 13 countries + EA, 2 lags? • It comes to 20*(13+1)*3=840 potential variables • More than 20 billions possible models with 4 explanatory variables!!!!

8. Variable selection methods • You must (Do you?) reduce the set of explanatory variables • Trial and Error approach DOES NOT work • NIESR approach (J. Mitchell) • Drastically restrict the set (Expert knowledge) and then evaluate all possible models • GETS (General to specific) approach • Start from an overparametrized model and use statistical tests to reduce it • Dynamic Factor Analysis approach • Summarize the set of variables with uncorrelated factors and use some of them in the model • Cluster Analysis approach

9. Step 0: Selecting a batch of explanatory variables • Here, we take all the information present in the Euro-Indicator database. • But with some a priori selection • If the Y-variable is SA, we will use SA indicators • You may (or not) exclude some variables (small countries, not reliable series etc.) • Or better, flag them using some a priori knowledge, example: • 0 : I would exclude it • 1 : I do not know, • 2 : could be interesting, • 3 : I would appreciate to see it in a model

10. Step 1: The dependant variable • Checking the main characteristics of the dependant variable • seasonality, trading-day effect, outliers etc. • Size of the irregular, revision analysis • what can we really expect in terms of precision?

11. The Y-variable : Euro-area GDP • Quarterly growth rate of the SA series (EA CLV) • Irregular SD: 0.142

12. Step 2: Preparing the data • Y-variable • Checking for log-transformation • Removing outliers: they will be “re-incorporated” at the end of the flash-estimate process • Removing seasonality if present (annual growth rate) or modeling it • X-variables • Checking for log-transformation and differencing (with Tramo) • Removing seasonality, outliers and TD effects: Seasonal and TD dynamics may be different between variables • Forecasting missing months when nowcasting a quarterly Y-variable

13. Looking for X-variables • Example • We want to flash-estimate 2007Q4 at 30 days. • Checking date 30/01/2008 • Variables from Euro-Indicators • Monthly and Quarterly variables; • 668 Monthly; 162 Quarterly (B1GM_UK) • For monthly variables, we know at least 1 or 2 months of the quarter to “nowcast” • Cleaning and “forecasting” of X-variables

14. Step 3: First selection with Cluster analysis • Variable selection • Cluster analysis: clusters of “similar X-variables” (various clustering criteria available) • Selecting a few variables (Medoids and/or Dynamic factors) in each cluster using Hsiao-Granger causality test, coherence between growth-rates, correlation • Example: 6 clusters, 2 variables per cluster, 2 lags  36 potential variables 60,000 models with 4 explanatory variables

15. Step 4: First selection of models • Looking for the n “best models” using usual OLS regression analysis • Several possible criteria: • R-square, Mallow’s Cp, Adjusted R-square etc. • First statistical evaluation of the models but still “no dynamics” • Possible second selection of the model using “economic” criteria or expert knowledge (which models are “relevant”?)

16. Step 5: Statistical evaluation of the models • In-depth statistical evaluation of the model using PROC AUTOREG (autoregressive error) • Statistical criteria: • R-square, AIC, BIC, Reset tests, Chow tests, Durbin-Watson tests, Arch tests, Stationarity tests, Godfrey tests etc. • Coherence between growth rate signs • One-step and 2-step ahead forecasting error • Dynamic evaluation of the models using the real-time database

17. Step 6: Choosing the model(s) • The choice is now based on statistical criteria and “expert knowledge”: • Does the model have good statistical properties? • Is the model simple and robust enough? • Is the model “relevant” from the Economic point of view? USUALLY NOT !!! • But …… could be improved changing a variable for another one, more “relevant” (“flagged” variables) from the same cluster.

18. First results

19. Improving the models • Third model: IO_PL, IP_EA13, UE_NL • IO_PL belongs to the same cluster than T_EXP_EA13 • UE_NL close to UN_FR or UN_EA13 • And we have a new model • T_EXP_EA13, IP_EA13, UN_EA13 • RMSE=0.15543

20. Comparing with « traditional » approach • We estimate 9 different models • Model1: IP, CPI, RET, CARS • Model2: GDP-1, SentInd • Model3: qsind, qsserv • Model4: qsind, qsret, qsconst • Model5: share-1, compe12-2, spread • Model6: GDP-1, cli • Model7: IP, CPI, RET • Model8: GDP-1, cli, CARS • Model9: qsind, qsret, qsserv, qsconst

21. Results

22. Examples