IDEAS home Printed from https://ideas.repec.org/a/anr/reveco/v6y2014p21-51.html
   My bibliography  Save this article

Ill-Posed Inverse Problems in Economics

Author

Listed:
  • Joel L. Horowitz

    () (Department of Economics, Northwestern University, Evanston, Illinois 60208)

Abstract

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an ill-posed inverse problem. Such problems arise in many settings in economics and other fields in which the parameter of interest is a function. This article explains how ill-posedness arises and why it causes problems for estimation. The need to modify or regularize the identifying mapping is explained, and methods for regularization and estimation are discussed. Methods for forming confidence intervals and testing hypotheses are summarized. It is shown that a hypothesis test can be more precise in a certain sense than an estimator. An empirical example illustrates estimation in an ill-posed setting in economics.

Suggested Citation

  • Joel L. Horowitz, 2014. "Ill-Posed Inverse Problems in Economics," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 21-51, August.
  • Handle: RePEc:anr:reveco:v:6:y:2014:p:21-51
    as

    Download full text from publisher

    File URL: http://www.annualreviews.org/doi/abs/10.1146/annurev-economics-080213-041213
    Download Restriction: Full text downloads are only available to subscribers. Visit the abstract page for more information.

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    regularization; nonparametric estimation; density estimation; deconvolution; nonparametric instrumental variables; Fredholm equation;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:anr:reveco:v:6:y:2014:p:21-51. 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: (http://www.annualreviews.org). General contact details of provider: http://www.annualreviews.org .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.