On Biases of the Price-Deflator

With the increasing role that price-deflators play in econometric analysis, the delicate numerical effects caused by using deflator-series must be closely scrutinized. In some cases another model-setting of analysis might be preferred at seeing some unexpected results of one model due to the biases of deflator. The ipiases of price-deflatorsl can be classified into three types : the model bias, the formula bias and the data bias. By the model bias is meant the sort of biasing effect caused by a model in which the deflator and the deflatand2 are related in some function. In ordinary uses the deflator-series are taken as denominators for the deflatand series under the assumption that the factor of pricelevel is included in the deflatand money value as a product-factor. This assumption, however, is not due where, for instance, the price-level acts as one of the regressors explaining the money value of the regressand. If we apply the denominator form of the dailator to this regression analysis, a sort of model bias is found in this misapplication. Sceondly, the formula type of bias has a connection to the formula used for the construction of the price-deflator. The Laspeyres formula is well-known to have a limitation in its power of expressing the change of the price-1evel, to the effect that its use as deflator includes this second type of bias. We can, how-ever, neglect these first two types of bias when possible. But the third type of bias can we never neglect in any case. That is the data-bias which stems inevitably from the discrepancies on the nature of data between the deflatand and the deflator. As a matter of course we try to select appropriate deflator-series so as to fit well to the nature of the deflatand-series. Nevertheless there are apt to remain some discrepancies between the two series-e.g. the total expenditure of a family as the deflatant and the Consumers' Price Indices as deflator, m the pomt of therr "coverage", This sort of discrepancies will be ever deepened so long as the Laspeyres formula will hold without any revision of the weightsystem. Among these three the third type, the data bias type, will be treated in this paper, the other two beinb" Put aside for the time being.