A family of theory-based parametric lag shapes for distributed-lag linear regression

Distributed-lag linear regression is a widely used tool in economic analysiswhen several explanatory variables are supposed to influence an outcome over severalperiods. In distributed-lag linear regression, the lag shape of an explanatory variableis the set of the coefficients associated to its temporally delayed (lagged) instances. Un-fortunately, distributed-lag linear regression with no constraints on the lag shapes mayentail problems of inference, due to potential multicollinearity and large number of freeparameters, and of interpretation, since the lag shapes may have an irregular form andmay not meet theoretical requirements. In this paper, we present type II constrained lagshapes, a new family of parametric lag shapes designed to represent theory-based lagstructures through a small number of parameters. The proposed family improves theAlmon’s polynomial lag shape in terms of interpretability, and includes the well knownendpoint-constrained quadratic and Gamma lag shapes. The applicability of the proposedfamily is illustrated through an economic impact assessment problem.