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Smoothness Priors and Nonlinear Regression

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  • Robert J. Shiller

Abstract

In applications, the linear multiple regression model is often modified to allow for nonlinearity in an independent variable. It is argued here that in practice it may often be desirable to specify a Bayesian prior that the unknown functional form is "simple" or "uncomplicated" rather than to parametize the nonlinearity. "Discrete smoothness priors" and "continuous smoothness priors" are defined and it is shown how posterior mean estimates can easily be derived using ordinary multiple linear regression modified with dummy variables and dummy observations. Relationships with spline and polynomial interpolation are pointed out. Illustrative examples of cost function estimation are provided.

Suggested Citation

  • Robert J. Shiller, 1982. "Smoothness Priors and Nonlinear Regression," NBER Technical Working Papers 0025, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0025
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    References listed on IDEAS

    as
    1. Mark Gersovitz & James G. MacKinnon, 1977. "Seasonality in Regression: An Application of Smoothness Priors," Working Paper 257, Economics Department, Queen's University.
    2. Fomby, Thomas B, 1979. "MSE Evaluation of Shiller's Smoothness Priors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 203-215, February.
    3. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
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    Cited by:

    1. Peter C.B. Phillips & Binbin Guo & Zhijie Xiao, 2002. "Efficient Regression in Time Series Partial Linear Models," Cowles Foundation Discussion Papers 1363, Cowles Foundation for Research in Economics, Yale University.

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