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 = |Gm(|WbX[|WB]t) + |Get where...
| Published in: | Econometrica Vol. 69; no. 3; pp. 537 - 574 |
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| Format: | Article |
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Wiley-Blackwell
May 2001
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=513098115&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 513098115 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00129682 ECN jtl: Econometrica issn: 00129682 maglogo: N pubinfo: dt: May 2001 vid: 69 iid: 3 pid: 480 pub: Wiley-Blackwell artinfo: ui: 513098115 10.1111/1468-0262.00205 ppf: 537 ppct: 37 formats: tig: atl: A parametric approach to flexible nonlinear inference. aug: au: Hamilton, James D. su: Probability theory Phillips curve Nonlinear theories sug: subj: Probability theory Phillips curve Nonlinear theories ab: 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 = |Gm(|WbX[|WB]t) + |Get where the functional form of |Gm(∙) is unknown. We propose viewing |Gm(∙) itself as an outcome of a random process. The paper introduces a new stationary 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 |Gm(∙). We view the parameters that characterize the relation between a given realization of m(∙) and the particular value of |Gm(∙) 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 |Gm(∙). 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 trade-off may explain the previously reported uneven empirical success of the Phillips Curve. Reprinted by permission of the Econometric Society. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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