A Bootstrap for Theil's Best Linear Index Numbers

By Blankmeyer, Eric | Atlantic Economic Journal, December 2009 | Go to article overview

A Bootstrap for Theil's Best Linear Index Numbers


Blankmeyer, Eric, Atlantic Economic Journal


If the prices and the corresponding quantities of K commodities are observed in a cross section of R regions, the data may be arrayed in two matrices, P and Q respectively, each having R rows and K columns. Theil [Econometrica, 1960] defines the cross-value matrix C = PQ' as a positive-valued array whose typical element [c.sub.rt] measures the aggregate monetary value of the quantities in region t at the prices in region r. While the rank of C is usually the smaller of R and K, Theil proposes to approximate C by a matrix of rank one in the orthogonal regression model

C = pq' + E, (1)

where the R-element column vectors p and q are respectively the regional price and quantity indexes, and E is a matrix of independently distributed random errors. By minimizing the trace of E'E, Theil shows that the orthogonal least-squares estimate of the price index is the eigenvector corresponding to [lambda], the largest eigenvalue of CC'. Likewise, the quantity index is estimated by the eigenvector for the largest eigenvalue of C'C , which is also [lambda]. The algebraic properties of these best linear index numbers are examined in detail by Theft and by Kloek and DeWit [Econometrica, 1961].

However, these authors do not discuss the problem of inference, an understandable omission since the sampling properties of the eigenvectors may be intractable unless CC' and C'C are covariance matrices [Bat et al., Annals of Probability, 2007]. This is problematic because all the elements of C are positive. In any case, only large-sample results could be obtained analytically. On the other hand, resampling methods are a practical way to compute standard errors and test hypotheses for Theil's price and quantity indexes. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

A Bootstrap for Theil's Best Linear Index Numbers
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.