1 / 12

Reinsdorf-Balk Transformation and Additive Decomposition of Indexes

Reinsdorf-Balk Transformation and Additive Decomposition of Indexes. I. Introduction II. Reinsdorf-Balk Transformation III. Additive Decompositions of Fisher Index IV. Additive Decomposition of Chain Indexes V. Numerical Illustrations (skip) VI. Concluding Remarks.

garrett-duke
Download Presentation

Reinsdorf-Balk Transformation and Additive Decomposition of Indexes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Reinsdorf-Balk Transformationand Additive Decomposition of Indexes I. Introduction II. Reinsdorf-Balk Transformation III. Additive Decompositions of Fisher Index IV. Additive Decomposition of Chain Indexes V. Numerical Illustrations (skip) VI. Concluding Remarks Ki-Hong Choi(NPRI) and Hak K. Pyo(SNU)

  2. I. Introduction • Arithmetic mean index and decomposition of growth rate arithmetic mean index decomposition in %-change • Geometric mean index and decomposition of growth rate geometric mean index decomposition in log-change

  3. II. Reinsdorf-Balk Transformation • Literature Reinsdorf(1997, 2002), Balk(1999, 2004) Kohli(2007), “Truly remarkable” • Some need for improvements • Reinsdorf’s proof is hard to follow. • Though Balk’s proof is easy and clear, there is a better alternative.

  4. Balk’s Identity: from A index to G index Reinsdorf’s Identity: from G index to A index

  5. III. Additive Decompositions of Fisher Index • Conventional Decompositions • Decomposition in % changes van IJzeren(1952)=Dumagan(2002)=Ehemann et al(2002)

  6. Decomposition in log-changes Reinsdorf(1997), Reinsdorf et al(2002), Balk(2004)  Less satisfactory decomposition by Vartia(1976)

  7. New Decompositions Decomposition in % changes Reinsdorf et al.(2002), applying Reinsdorf identity to the geometric mean version of Fisher index.

  8. Reinsdorf et al(2002), “numerically identical”

  9. Decomposition in log-changes • Applying Balk’s identity to the van IJzeren form of Fisher index

  10. IV. Additive Decomposition of Chain Indexes • Difficulty with additive decomposition of cumulative (compound) growth rates of chain indexes • Cumulative growth rates is decomposable in log-changes • But decomposition in log-change is not good since it deviates from %-changes

  11. R-B transformation gives solution to this dilemma

  12. VI. Concluding remarks • R-B transformation is interesting since it makes arithmetic mean and geometric mean indexes interchangeable. • R-B transformation is useful since it can provide an additive decomposition of cumulative growth rates by chain indexes.  Thank you! 

More Related