IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Enhancing the Convergence Properties of the BLP (1995) Contraction Mapping

Listed author(s):
  • Jo Reynaerts
  • Ravi Varadhan
  • John C. Nash

In the wake of Dub´e, Fox and Su (2012), this paper (i) analyzes the consequences for the BLP Contraction Mapping (Berry, Levinsohn and Pakes, 1995) of setting the inner-loop convergence tolerance at the required level of in D 10 14 to avoid propagation of approximation error from inner to outer loop, and (ii) proposes acceleration as a viable alternative within the confines of the Nested-Fixed Point paradigm (Rust, 1987) to enhance the convergence properties of the inner-loop BLP Contraction Mapping. Drawing upon the equivalence between nonlinear rootfinding and fixed-point iter- ation, we introduce and compare two alternative methods specifically designed for handling large-scale nonlinear problems, in particular the derivative-free spectral al- gorithm for nonlinear equations (La Cruz et al., 2006, DF-SANE), and the squared polynomial extrapolation method for fixed-point acceleration (Varadhan and Roland, 2008, SQUAREM). Running a Monte Carlo study with specific scenarios and with Newton-Raphson as a benchmark, we study the characteristics of these algorithms in terms of (i) speed, (ii) robustness, and (iii) quality of approximation. Under the worst of circumstances we find that (i) SQUAREM is faster (up to more than five times as fast) and more robust (up to 14 percentage points better suc- cess rate) than BLP while attaining a comparable quality of approximation, and (ii) also outperforms DF-SANE in nearly all scenarios. Eliminating averaging bias against more robust algorithms, a performance profile subsequently shows that (iii) SQUAREM is both faster, delivers the best quality approximation, and is more robust than BLP, DF-SANE and Newton-Raphson.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by KU Leuven, Faculty of Economics and Business, VIVES Research Centre for Regional Economics in its series Working Papers VIVES Research Centre for Regional Economics with number 35.

in new window

Date of creation: 2012
Handle: RePEc:ete:vivwps:35
Contact details of provider: Web page:

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ete:vivwps:35. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (library EBIB)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.