Base Shifting

For a variety of reasons, it frequently becomes necessary to change the reference base of an index number series from one time to another without returning to the original raw data and recomputing the entire series. This change of reference base period is usually referred to as “shifting the base”. There are two important reasons for shifting the base:

1.    The previous base has become too old and is almost useless for purposes of comparison. By shifting the base it is possible to state the series in terms of a more recent time period.

2.    It may be desired to compare several index number series which have been compared on different base period; particularly if the several series are to be shown on the same graph, it different base periods; particularly if the several series are to be shown graph, it may be desirable for them to have the same base period. This may necessitate a shift in the base period.

When base period is to be changed, one possibility is to recompute all index numbers using the new base period. A simpler approximate method is to divide all index numbers for the various years corresponding to the old base period by the index number corresponding to the new base period, expressing the results as percentage. These results represent the new index numbers, the index number for the new base period beings 100%.

Mathematically speaking, this method is strictly applicable only if the index numbers satisfy the circular test. However, for many types of index numbers the method, fortunately, yields results which in practice are close enough to those which would be obtained theoretically.

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