The Residual Error in the Canadian National Accounts

Abstract

Gross national product is estimated in the Canadian National Accounts in two substantially independent ways: by adding the various components of production (mainly incomes); and by adding the various components of final expenditure. As both aggregates measure the value of goods and services produced by Canadians in a given period they should be equal. However, all measurements are subject to some error so that there is a statistical discrepancy between the two totals. In this way the residual error item arises.The procedure adopted in the tables in the National Accounts is to present one half the difference between the independently calculated aggregates as an addition to the smaller aggregate or as a deduction from the larger aggregate. This averaging procedure is regarded as preferable to showing the entire amount of the discrepancy on one side of the Accounts (as is the practice in most countries) for two reasons. First, rough appraisals of the relative accuracy of the product and expenditure sides of the Accounts suggest that they have approximately equal reliability and so should be given equal weight on the average. Secondly, the aggregate which generates the residual error is considerably larger than gross national product itself. This is so because the error-generating aggregate is obtained by summing the components of gross national product and gross national expenditure without regard to sign and then deducting certain items common to both totals (such as the imputed items) and this is considerably larger than gross national product or expenditure as both gross national product and expenditure contain very large negative quantities (such as imports and farm operating expenses). Consequently, comparing one half the basic discrepancy with gross national product gives roughly the same result as comparing the whole discrepancy with the larger aggregate.Clearly there will be some tendency for errors to cancel out so that a small residual error does not mean that components are free of error.