Theory and Application of Benchmarking in Business Surveys - PowerPoint PPT Presentation

kyrie
theory and application of benchmarking in business surveys l.
Skip this Video
Loading SlideShow in 5 Seconds..
Theory and Application of Benchmarking in Business Surveys PowerPoint Presentation
Download Presentation
Theory and Application of Benchmarking in Business Surveys

play fullscreen
1 / 66
Download Presentation
Presentation Description
133 Views
Download Presentation

Theory and Application of Benchmarking in Business Surveys

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Theory and Application of Benchmarking in Business Surveys Susie Fortier and Benoit Quenneville Statistics Canada -TSRAC ICES – June 2007

  2. Content • Introduction • Notation • Benchmarking methods • Timeliness issue • Implied forecasts and annual growth rates • Other uses: • Seasonally adjusted data • Linking problem • Conclusions

  3. Introduction Main references • Dagum, E.B. and Cholette, P. (2006) Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series, New York: Springer-Verlag, Lecture Notes in Statistics 186. • Bloem, A. M., R. J. Dippelsman, and N. Ø. Mæhel (2001): Quarterly National Accounts Manual, Concepts, Data Sources and Compilation. International Monetary Fund, Washington DC.

  4. Introduction Benchmarking : • Combining a series of high-frequency data with a series of less frequent data into a consistent time series.

  5. Introduction Issues in Benchmarking : • Preserve period to period movement of the indicator (monthly/quarterly) series while simultaneously attaining the level of the benchmarks (annual). • Consider the timeliness of the benchmarks.


  6. Introduction Example of a quarterly series

  7. Introduction A quarterly series with its auxiliary source

  8. Timeliness issue Introduction

  9. Introduction Benchmarked series

  10. Notation Methodological details :

  11. Notation Methodological details : • With binding benchmarking, the benchmarked series is such that

  12. Notation • A bias parameter can be estimated and used to pre-adjust the indicator series: • A bias corrected series is obtained as:

  13. Notation • Alternatively, the bias can be expressed in terms of a ratio: • The bias corrected series is then:

  14. Notation • Bias correction is a preliminary adjustment to reduce, on average, the discrepancies between the two sources of data. • Useful for periods not covered by benchmarks.

  15. Notation Effect of the Bias Correction (ratio)

  16. Methods : Pro-rating • A simple way to respect the constraints is to use This is the well-known formula for pro-rating.

  17. Methods : Pro-rating Benchmarked series with pro-rating

  18. Methods : Pro-rating BI ratio with pro-rating

  19. Methods : Pro-rating Growth rates with pro-rating

  20. Methods : Pro-rating Growth rates with pro-rating

  21. Methods : Proportional Denton Benchmarked series with Prop. Denton

  22. Methods : Proportional Denton BI ratio with Prop. Denton

  23. Methods : Proportional Denton Growth rates with Prop. Denton

  24. Methods : Proportional Denton Growth rates with Prop. Denton

  25. Main method • Based on Dagum and Cholette (2006). • Generalization of many well-known methods: • Pro-rating • Denton (and proportional Denton) • Implemented at Statistics Canada with a user-defined SAS procedure: PROC BENCHMARKING • Project Forillon • Software Demo

  26. Main method : Formula • The benchmarked series can be obtained as the solution of a minimization problem. • For given parameters and find the values that minimize the following function of : subject to

  27. Main method : Formula • Solution when : Solution: “Regression-based” model from Dagum & Cholette

  28. Main method : Formula • Solution when : Solution: where W is the T x M upper-right corner matrix from :

  29. Main method : Formula • We can obtain pro-rating with the general formula with and : minimise under gives

  30. Main method : Effect of • Consider the case where and . The function to be minimized under the constraints which aims at preserving the period-to-period change in the original series. Modified Dentonmethod

  31. Main method : Effect of • Consider the case where and . The function to be minimized under the constraints which seeks to minimize the change in the ratios (not to preserve the growth rates but a fairly close approx). Variant of Proportional Dentonmethod with positive data!

  32. Main method : Effect of • 3 parameters at play: • : model adjustment parameter • : “smoothing” parameter • bias (implied with ) subject to

  33. Main method : Effect of

  34. Main method : Effect of bias Benchmarking without bias ( )

  35. Main method : Effect of bias Benchmarking with bias ( )

  36. Main method : Effect of bias Benchmarking without bias ( )

  37. Main method : Effect of bias Benchmarking with bias ( )

  38. Timeliness issues • Adjustments for periods without benchmarks: • Benchmarked series give an implicit forecast for the unknown annual values. • The better the forecast, the lesser the revision! Proportional Denton (ρ=1, λ=1) Benchmarking with bias (ρ=0.93, λ=1)

  39. Timeliness issues • 2 implicit forecasts for 2006: • Enhanced benchmarking method with explicitforecasts

  40. Timeliness issues • One possibility for explicit forecast: • Use the annual growth rate from the indicator series on the last known benchmark.

  41. Timeliness issues With explicit forecast ( )

  42. Timeliness issues With explicit forecast ( )

  43. Timeliness issues With ″recent″ bias( , bias=0.94)

  44. Timeliness issues With ″recent″ bias( , bias=0.94)

  45. Timeliness issues Minimize revision?

  46. Methods : Summary so far! • Summary of methods presented: • Pro-rating • Denton (and proportional Denton) • Regression-based (Dagum and Cholette) • with or without bias correction • Denton with explicit forecast • Results from all of the above can be obtained by PROC BENCHMARKING.

  47. Methods • Other methods • Other numerical methods revolve around different minimisation functions. • Statistical model-based approaches • See annex 6.1 in Bloem, Dippelsman, and Mæhel (2001) for variants and references • See also Chen and Wu (2006) for link between numerical, regression based and signal extraction methods. • Future version of PROC benchmarking?

  48. Syntax : PROC Benchmarking PLEASE SEE SOFTWARE DEMO !! PROCBENCHMARKING BENCHMARKS=myBenchmarks SERIES=mySeries OUTBENCHMARKS=outBenchmarks OUTSERIES=outSeries OUTGRAPHTABLE=outGraph RHO=0.729 LAMBDA=1 BIASOPTION=3; RUN;

  49. In SAS Enterprise Guide®(Demo)

  50. Other uses : Seasonal adjustment • Seasonally adjusted series can be required to ″match″ given annual totals : • System of National Accounts (typical cases) • X-12-ARIMA version 0.3+ • FORCE spec (table D11 A) • With argument Type=regress : same methodology as PROC BENCHMARKING