Smoothness Priors and Nonlinear Regression

Robert Shiller

No 25, NBER Technical Working Papers from National Bureau of Economic Research, Inc

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.

Date: 1982-08
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Published as Shiller, Robert J. "Smoothness Priors and Nonlinear Regression." Journal of the American Statistical Association, Vol. 79, No. 387, (September 1984) .

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