A Parametric Approach to Flexible Nonlinear Inference
This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt = Âµ(xt) + et where the functional form of Âµ(.) is unknown. We propose viewing Âµ(.) itself as the outcome of a random process. The paper introduces a new stationary random random field m(.) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for Âµ(.). We view the parameters that characterize the relation between a given realization of m(.) and the particular value of Âµ(.) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions Âµ(.). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment tradeoff may explain the previously reported uneven empirical success of the Phillips Curve.
|Date of creation:||01 Jan 1999|
|Date of revision:|
|Contact details of provider:|| Postal: 9500 Gilman Drive, La Jolla, CA 92093-0508|
Phone: (858) 534-3383
Fax: (858) 534-7040
Web page: http://www.escholarship.org/repec/ucsdecon/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:cdl:ucsdec:qt68s8157x. 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: (Lisa Schiff)
If references are entirely missing, you can add them using this form.