TY - JOUR
AU - Shiller,Robert J.
TI - Alternative Prior Representations of Smoothness for Distributed Lag Estimation
JF - National Bureau of Economic Research Working Paper Series
VL - No. 89
PY - 1975
Y2 - June 1975
DO - 10.3386/w0089
UR - http://www.nber.org/papers/w0089
L1 - http://www.nber.org/papers/w0089.pdf
N1 - Author contact info:
Robert J. Shiller
Yale University, Cowles Foundation
Box 208281
30 Hillhouse Avenue
New Haven, CT 06520-8281
Tel: 203/432-3708
Fax: 203/432-6167
E-Mail: robert.shiller@yale.edu
AB - In some applications of the distributed lag model, theory requires that all lag coefficients have a positive sign. A distributed lag estimator which provides estimated coefficients with positive sign is developed here which is analogous to an earlier distributed lag estimator derived from "smoothness priors" which did not assure that all estimated coefficients be positive. The earlier estimator with unconstrained signs was a posterior mode of the coefficients based on a spherically normal "smoothness prior" in the d+l order differences of the coefficients. The newer estimator with constrained sign is a posterior mode of the logs of the coefficients based on spherically normal "smoothness prior" on the d+l order differences of the logs of the coefficients. The meaning of both categories of prior is discussed in this paper and they are compared to prior parameterizations of the lag curve. Both varieties of "smoothness prior", in contrast to the parameterizations, allow the coefficients to assume any "smooth" shape subject to the sign constraint. The sign-constrained estimator has the additional advantage that it easily forms asymptotes. Moreover, the sign con-strained estimator is easily implemented. The estimate can be obtained by an iterative procedure involving regressions with dummy observations similar to those used to find the unconstrained sign estimator. An illustrative example of the application of both estimators is given at the end of the paper.
ER -