The role of approximate prior restrictions in distributed lag estimation

In distributed lag models we often parameterize the lag distribution’s form so that only small finite numbers of parameters are required even when it is likely that the model so written involves some specification error. The effects of such error depend on the autocorrelation properties of the independent variable; quasi-difference transforms of the data will have effects, possibly undesirable, on the nature of error due to approximation. Certain hypotheses, e.g., those concerning the sum of coefficients or the mean lag of the distribution, may be untestable in time series regressions in the presence of approximation error of this type.