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Evaluating generalised calibration / Fay-Herriot model in CAPEX

Evaluating generalised calibration / Fay-Herriot model in CAPEX. Tracy Jones, Angharad Walters, Ria Sanderson and Salah Merad (Office for National Statistics). Overview. Introduction Generalised calibration estimation Fay-Herriot model Conclusions and further work. Introduction.

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Evaluating generalised calibration / Fay-Herriot model in CAPEX

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  1. Evaluating generalised calibration / Fay-Herriot model in CAPEX Tracy Jones, Angharad Walters, Ria Sanderson and Salah Merad (Office for National Statistics)

  2. Overview • Introduction • Generalised calibration estimation • Fay-Herriot model • Conclusions and further work

  3. Introduction • Quarterly survey of capital expenditure (Capex) • Sample size – 28,000 • Stratified by industry and size • Main user is National Accounts • Many zeros and some very large values • Aim to reduce costs and respondent burden • Reduce the sample size whilst maintaining quality • Investigated two strategies • Calibration estimation in cut-off sampling • Fay-Herriot model

  4. Sampled (20-299) Fully enumerated (300+) Not sampled (<20) Current cut-off sampling • Not sample businesses with < 20 employees • G-weights adjusted to account for this

  5. Sampled (50-299) Fully enumerated (300+) Not sampled (<50) Extension of cut-off sampling • Extend to a cut-off of < 50 employees • Sample size reduced by about 9,000 • Reduce bias introduced through cut-off sampling

  6. Relationship between acquisitions and employment

  7. Direct calibration • Find set of weights wi such that: distance (d,w) is minimised while • Solution

  8. Generalised calibration (Deville 2002) The set of calibration equations Can be generalised to yield the set of equations

  9. Generalised calibration • In context of cut-off sampling, Haziza et al (2010) assumed a linear function F of the form • And obtained weights

  10. Applying generalised calibration • Cut-off set deterministically based on employment • Consider two auxiliary variables: • x well correlated with variable of interest • employment from the business register • z well correlated with probability of being above the cut-off • turnover from the business register

  11. Generalised calibration estimation • 2008 sample data – Bands 2 to 4 • 3 Estimates • Ratio estimate using full sample data • Ratio estimate with extended g-weight adjustment • Generalised calibration estimate • Relative difference compared to ratio estimate using full sample data

  12. Results

  13. Industries with largest contribution to total acquisitions in size-bands 2-4

  14. Summary – Extension of cut-off sampling • Adjusted g-weights method performs better overall • Generalised calibration estimation does not consistently improve on simple method in any industry • Residual relationship between x and p

  15. Fay-Herriot model • Combine direct estimate with synthetic estimate • Fay-Herriot aggregate level model fitted to obtain synthetic estimator i=1, 2, …,m

  16. Fay-Herriot model - BLUP

  17. Fay-Herriot model • 2008 sample data • Two variables - total acquisitions and total disposals • Auxiliary variables for Fay-Herriot model • VAT turnover and expenditure • Scaled estimates and auxiliary variables using the total number of employees • Fitted mixed model

  18. Plot of Residuals against Predicted (mixed model with no transformation)

  19. Transformation • Transformation needed • Implementation of BLUP becomes complicated • noted by Chandra and Chambers, 2006

  20. Plot of Residuals against Predicted(mixed model)

  21. Plot of Residuals against Predicted(linear model without random effects)

  22. Back transformation • Used back transformation to obtain synthetic estimate (Chambers and Dorfman, 2003) • Calculation of gamma - variance of random effects required back transformation

  23. Evaluating use of Fay-Herriot model • Gamma very high • Gamma using back transformation may not be suitable • Investigated combined estimate using a fixed value for gamma • Evaluation is via re-sampling • Reduced the sample size by 25% (about 6,000 units) • Repeated sub-sampling • Set gamma to 0.7 • Calculated a combined estimate

  24. Evaluating use of Fay-Herriot model • Estimated Bias and MSE of combined estimate

  25. Results • Average of the direct estimates very similar to the direct estimate from the full sample • Variance of the synthetic estimate is small • Variance of combined estimate lower than variance of direct estimate from full sample • Bias is high in most industries • Relative bias also large • High bias ratio resulted in higher Mean Square Error in most divisions

  26. Results – Acquisitions Q2 2008

  27. Conclusions and further work • Cut-off sampling with g-weight adjustment performed best • Know this has bias • More work to be done • Impact on growth • Modelling at unit level • Additional covariates • Alternative estimation methods • Model-based direct approach (Chandra and Chambers, 2006)

  28. Questions

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