01610cam a22002297 4500001000600000003000500006005001700011008004100028100002300069245009200092260006600184490005100250500001700301520070200318530006101020538007201081538003601153710004201189830008601231856003701317856002601354t0025NBER20140711080757.0140711s1982 mau||||fs|||| 000 0 eng d1 aShiller, Robert J.10aSmoothness Priors and Nonlinear Regressionh[electronic resource] /cRobert J. Shiller. aCambridge, Mass.bNational Bureau of Economic Researchc1982.1 aNBER technical working paper seriesvno. t0025 aAugust 1982.3 aIn 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0025.4 uhttp://www.nber.org/papers/t0025 uurn:doi:10.3386/t0025