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...
| Publicado en: | Econometrica Vol. 69; no. 3; pp. 537 - 574 |
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| Formato: | Artículo |
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Wiley-Blackwell
May 2001
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| Acceso en línea: | Ver este registro en EBSCOhost |
| Sumario: | 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. |
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