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The Residual Error in the Canadian National Accounts*
Published online by Cambridge University Press: 07 November 2014
Extract
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.
- Type
- Articles
- Information
- Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 30 , Issue 4 , November 1964 , pp. 559 - 569
- Copyright
- Copyright © Canadian Political Science Association 1964
Footnotes
*
I am indebted to Mrs. B. Tatlow for assistance with the computations.
References
1 A description of the residual error may be found in National Accounts, Income and Expenditure, 1928–56, secs. 522–4. Briefer descriptions are given in other issues of the National Accounts.
2 Ibid, sec. 524.
3 This is the procedure adopted in a forthcoming paper by D. J. Smyth and R. Lévesque.
4 For an analysis of the residual error in the United States national accounts see Gartaganis, A. J. and Goldberger, A. S., “A Note on the Statistical Discrepancy in the National Accounts,” Econometrica, 04 1955, 166–73Google Scholar; and de Janosi, P. E., “The Statistical Discrepancy in the National Accounts Revisited,” Econometrica, 07 1961, 427–9.Google Scholar The residual errors in the Australian and United Kingdom national accounts are analysed in D. J. Smyth, “The Statistical Discrepancy in the Australian National Accounts” and “Saving and the Residual Error,” nos. 40 (Oct. 1963) and 43 (Nov. 1963) respectively of the Faculty of Commerce and Social Science, University of Birmingham, Discussion Papers, Series A. These two papers are to appear in Australian Economic Papers and the Bulletin of the Oxford Institute of Economics and Statistics respectively.
5 Only one percentage series is considered, that of current prices, as deflators for the residual error and gross national product move together.
6 The values appearing on the product side are equal in magnitude (except for an occasional unit difference due to rounding) but opposite in sign.
7 For a discussion of the advantages and disadvantages of non-parametric tests compared with parametric tests see Siegel, S., Non-parametric Statistics for the Behavioral Sciences (New York, 1956), 30–4.Google Scholar
8 On the χ2 test see any standard statistics textbook. Yates's correction has been applied in all cases when the χ2 test has been used.
9 On this test see Massey, F. J. Jr., “The Kolmogorov-Smirnov Test for Goodness of Fit,” Journal of the American Statistical Association, 03 1951, 68–78.CrossRefGoogle Scholar
10 On this test see Wallis, W. A. and Moore, G. H., “A Significance Test for Time Series Analysis,” Journal of the American Statistical Association, 09 1941, 401–9CrossRefGoogle Scholar, and “A Significance Test for Time Series,” Technical Paper 1 (National Bureau of Economic Research, 1941).Google Scholar A description of the test may be found in Tintner, G., Econometrics (New York, 1952), 234–8.Google Scholar
11 On the Mann-Kendall test see Mann, H. B., “Non-parametric Tests against Trends,” Econometrica, 04 1945, 245–59Google Scholar; and Kendall, M. G., Rank Correlation Methods (London, 1948).Google Scholar Tintner, , Econometrics, 211–15Google Scholar, gives a description of the test.
12 Durbin, J. and Watson, G. S., “Testing for Serial Correlation in Least Squares Regression, II, Biometrika, 38 (1951), 159–78.CrossRefGoogle ScholarPubMed
13 Griliches, Z., Maddala, G. S., Lucas, R. and Wallace, N., “Notes on Estimated Aggregate Quarterly Consumption Functions,” Econometrica, 07 1962, 497.Google Scholar
14 As an illustration the contingency table obtained for the annual percentage series indicating positive serial correlation (χ2 = 18.733) is
15 Making use of the binomial expansion.
16 National Accounts, Income and Expenditure, 1926–56, sec. 524.
17 There are too few observations to consider the pre-war and post-war periods separately.
18 The values for the whole period and the pre-war series are so low as surely to be significant at the 0.1 per cent level if tables of such a significance level were available.