Testing for the Existence of a Lagged Relationship within Almon's Method

Abstract

RESEARCHERS using the Almon lag method (Almon, 1965) are generally familiar with the work by Schmidt and Waud (1973), wherein several of the pitfalls of Almon's method are considered. Among other things, Schmidt and Waud (SW however, they select different models with contradictory findings.2 The primary purpose of this study is to demonstrate that existing specification error tests allow a researcher to empirically determine if an incorrect length of lag and/or degree of polynomial has been chosen in Almon's method. In other words, the existence of a lagged relationship is a testable proposition within Almon's method, and at the same time it is generally possible to detect the use of an incorrect degree polynomial. As the result of this finding, there is an inferentially sound method of selecting parameters within the Almon lag technique. Empirical research based upon this parameter selection criterion demonstrates that specification error tests form a viable method of obtaining consistent and theoretically pleasing results within Almon's method (see Harper, 1975 and Harper and Fry, 1976). At least this is the finding within the single equation approach to the monetary versus fiscal policy debate. This promising viable parameter selection criterion stands in contradiction to and provides an alternative to the generally accepted belief that there is no inferentially sound method for selecting parameters within Almon's method.3 A close examination reveals that it is not always meaningful to search for both the length of lag and the degree of polynomial. It may well be the situation that the lag length is in fact a policy parameter and is, consequently, known to the researcher. If this is the situation, the parameter selection technique should be utilized only to select the degree of polynomial to be inserted with the known length of lag. In this manner, the researcher can determine the effects upon the dependent variable of a given lag length or of altering the lag length. It is necessary to rely upon theory to determine whether the length of lag is a known policy parameter or an endogenous variable that must be estimated. Received for publication December 31, 1975. Revision accepted for publication August 2, 1976. *The author is indebted to Thomas R. Saving, Michael J. McDonough, Oral B. Crawford and two anonymous referees for many helpful comments on an earlier draft of this paper. 'Some of the participants in this debate are Andersen and Jordan (1968, 1969), Andersen (1969), De Leeuw and Kalchbrenner (1969), Corrigan (1970), Silber (1971), and Schmidt and Waud (1973). 2Actually, Schmidt and Waud minimize the standard error of the regression, but this is identical to maximizing R 2. Note that such model selection criteria are precarious at best, since each of these criteria is biased in an unknown direction and reliance on such criteria is inferentially unsound. See Barten (1962), Frost (1975), Gilbert (1969), and Goldberger (1964) for verification of this claim. 3This is not meant to imply that Almon's method is the best distributed lag technique under all circumstances. The more general Shiller lag procedure is probably superior to Almon's method in many cases, because Shiller's method lessens the multicollinearity problem and characteristically imposes a smooth pattern of weights. However, there is at least one severe limitation of Shiller's method in that units of measurement affect empirical results. Unless one is working with differences in logs, or the like, it is recommended to use Almon's over Shiller's method.