Abstract

In the specification of linear regression models it is common to indicate a list of candidate variables from which a subset enters the model with nonzero coefficients. In some cases any combination of variables may enter, but in others certain necessary conditions must be satisfied: e.g., in time series applications it is common to allow a lagged variable only if all shorter lags for the same variable also enter. This paper interprets this specification as a mixed continuous-discrete prior distribution for coefficient values. It then utilizes a Gibbs sampler to construct posterior moments. It is shown how this method can incorporate sign constraints and provide posterior probabilities for all possible subsets of regressors. The methods are illustrated using some standard data sets.

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