Abstract
In this paper, the polynomial approximation of distributed lags is investigated within the framework of linear restrictions in linear regression models.
In the first part, the polynomial approximation is analysed assuming well known the truncation point and the degree of the polynomial. The polynomial approximation is shown to involve linear restrictions on regression coefficients; two equivalent representations of these restrictions are used to clarify relationships between previous works byAlmon and byShiller. The difficulties related to the treatment of exact restrictions in a Bayesian framework are then tackled in the present context and alternative procedures are presented.
In the second part, the analysis is extended to the case of unknown truncation point and/or unknown degree of the polynomial. This leads to consider mixed prior distributions as for the problem of choosing among different models. The paper ends by investigating the sensitivity of a particular set of data w.r.t. changes in the truncation point, in the degreee of the polynomial and in the prior tightness of the polynomial approximation.
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Mouchart, M., Orsi, R. Polynomial approximation of distributed lags and linear restrictions: A Bayesian approach. Empirical Economics 1, 129–152 (1976). https://doi.org/10.1007/BF01764613
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DOI: https://doi.org/10.1007/BF01764613