Seasonal Variation in Interest Rates: Another Perspective

Abstract

The presence or absence of seasonal influences on interest rates is an important issue both for policy (Gibson, 1970) and for estimation of monetary relationships (Lombra and Kaufman, 1975). Thus conflict between recent research findings of Barth and Bennett (1975) (hereafter B-B) in this REVIEW and previous work is unsettling.' B-B examined two sets of data: (a) monthly observations on several interest rate series over period 1947-1970, and (b) daily observations on 90-day Treasury bill rate from May 1961 to December 1965. Using monthly dummy variables they concluded that seasonal effects do not appear to be present in interest rates examined. However, daily observations do yield significant seasonal effects for short term Treasury rate. B-B resolve this conflict by suggesting that the process of averaging daily data into monthly arithmetic means reduces variation in interest rate enough that one cannot detect (1975, p. 82). In what follows we reformulate their model in a framework consistent with problems noted by Bagshaw and Phaup (1977) and Bolch and Huang (1977).2 Our results using monthly data from April 1951 to March 1973 indicate statistically significant seasonal influences. Moreover, we demonstrate that averaging a data series will not eliminate seasonal pattern underlying B-B model. Thus B-B explanation of conflict of their results with daily and monthly data is not appropriate.3 The method selected for estimating seasonal components of an economic time series will depend on definition selected for seasonality.4 B-B's findings are relevant to only one such definition and implicitly assume one can model seasonal influences on interest rates independently from modeling of process of change in rates themselves.5 Accordingly discrepancy with past evidence supporting seasonality may be result of these factors. To illustrate this point we have selected an amended model consistent with Barth and Bennett's own suggestions (1975, p. 80, fn. 2) and following Nelson's (1970) analysis of term structure of interest rates. Equation (1) defines our model: