¹ DBS 62-518, The Consumer Price Index for Canada (1949 = 100) (Revision Based on 1957 Expenditures) (Ottawa, 03, 1961)Google Scholar, hereafter referred to as Consumer.

² DBS, The Consumer Price Index–January 1949–August 1952 (Ottawa, 1952).Google Scholar

³ It should be noted that complaints made here about lack of information concern published information. The officials in the Prices Division are very co-operative in supplying information in response to specific requests.

⁴ US Congress, Joint Economic Committee, Government Price Statistics, Hearings, Part 1, January 24, 1961 (Washington, 1961), hereafter referred to as Hearings, Part 1.Google Scholar

⁵ Consumer, 7.

⁶ Hearings, Part 1, 51–56.

⁷ US Congress, Joint Economic Committee, Government Price Statistics, Hearings, Part 2, May, 1961 (U.S. Government Printing Office, Washington, 1961) (hereafter referred to as Hearings, Part 2), 579.Google Scholar

⁸ A COL, since it is a welfare index for a group, is only concerned with net purchases by the group from other groups in the society, and the weight for used items would be much smaller than for the CPI. See Hearings, Part 1, 47.

⁹ Hurwitz, A., “Constants and Compromise in the Consumer Price Index,” Journal of the American Statistical Association, LVII, 12, 1962, 825.Google Scholar

¹⁰ Consumer, 7. In a similar vein, the Commissioner of Labor Statistics, US Department of Labor, Ewan Clague has stated: “The Consumer Price Index measures that part of the change in the cost of living which is the result of change in market prices.” Hearings, Part 2, 578.

¹¹ Consumer, 15 (emphasis supplied).

¹² Ibid., 13 (emphasis supplied).

¹³ Ibid., 15.

¹⁴ Hearings, Part 2, 598.

¹⁵ DBS 62-517, City Family Expenditure–1957 (Ottawa, 01, 1961), 22.Google Scholar

¹⁶ This practice is only mentioned in a footnote. “These changes are additional to continual changes in varieties which have taken place quite independently of the current revision of the index for items already in the index. Examples of such changes are shifts from wringer to automatic washers, and the addition of compact and European cars to standard North American cars.” Consumer, 10, n. 5.

¹⁷ Ibid., 18.

¹⁸ Hoover, Ethel D., “The CPI and Problems of Quality Change,” Monthly Labor Review, 11, 1961, p. 1178.Google Scholar Hurwitz, , “Constants and Compromise,” 820.Google Scholar

¹⁹ Assume, for the sake of illustration, that the upward bias in the automobile index is 30 per cent from 1949 to 1961, then the bias in the total index is less than 0.5 per cent (equal to the weight of the automobile price component in the 1947–48 weighted index (0.015) multiplied by 30 per cent).

²⁰ Hurwitz, , “Constants and Compromise,” 821 Google Scholar, mentions only the latter condition.

²¹ DBS 62-515, Industry Selling Price Indexes 1956–59 (Ottawa, 01, 1961), 11.Google Scholar

²² The weights for the 1947–48 weight-based index were 0.56 for independent stores and 0.44 for chain stores, while for the 1957 weight-based index they were 0.45 and 0.55 for independent and chain stores respectively.

²³ Hurwitz has stated, for the United States CPI, “For the period during which supermarket and discount merchandising became prevalent, the level of the Consumer Price Index was probably higher than a true consumer price index would have been.” “Constants and Compromise,” 823, n. 5.

²⁴ Assume that the average price paid by consumers for a typical food item was $0.80; the present price of this item in independent and chain stores is $1.05 and $1.00, respectively; base period weights are 0.56 and 0.44 for independent and chain stores, respectively, while the present relative importance of these outlets has changed to 0.45 and 0.55. The index number for this item would be [(0.56) (1.05) + (0.44) (1.00)]/0.80 = 128.5. If the weights appropriate for the present were used, the index number would be [(0.45) (1.05) + (0.55) (1.00)//0.80 = 127.8. If the quality of associated services in these outlets is the same, then the upward bias due to using fixed weights is 0.7 index points. Assuming this is the average bias for all food items, and thus for the food index, the bias in the total index would be approximately 30 per cent of this or 0.2 index points.

²⁵ An error was discovered in the Unking of the 1926 based index to the 1935–39 based index, when the series was being prepared for the forthcoming publication Historical Statistics for Canada. The published figures for the total category for 1913–1934, on the 1935–1939 base (and by linking on the 1949 base), were obtained by combining the linked index numbers for the five major components of the CPI using the 1935–39 group weights. This result is different from, and less appropriate than, the one obtained if the total category is linked in the usual manner. The consumption pattern in the early part of this period is better represented by the 1913 and 1926 group weights than by the 1935-39 group weights. The importance of food and clothing, in particular, is underestimated from 1913 to 1925 by this procedure. These two groups showed the greatest price increases after the First World War, and thus the total index published by DBS is lower than a correctly linked index for the immediate post-World War I period. The difference between the two indexes is over 3 per cent for 1920. The corrected index was available well before the release of the publication under review. It is a pity that it did not carry the historical series beyond 1935 so that the corrected index would be available to interested students two to three years before the publication of Historical Statistics for Canada.

²⁶ The difference between the link ratio for a particular month and the average of the ratios for several months, may not be large, but this does not affect the principle discussed in the text.

²⁷ See Steiner, P. O., “Consumer Durables in an Index of Consumer Prices,” Staff paper no. 6, in Hearings, Part 1, 305–36Google Scholar, for the view that the latter interpretation should be followed.

²⁸ Consumer, 15.

²⁹ Ibid.

³⁰ Canadian Non-Farm Family Expenditures—1947–1948, DBS Reference Paper no. 42 (Ottawa, 06, 1953).Google Scholar

³¹ The survey group was larger than the target population group for the CPI and some difference between the percentage reported and the weight for automobiles can be expected for this reason.

³² Consumer, 15. The U.S. Bureau of Labor Statistics imputes the weight of such an item “to the movement of other priced items in the same group for which prices can be obtained.” Hearings, Part 2, 608.

³³ The Consumer Price Index, January 1949—August 1952, 15.

³⁴

.

.

³⁵ This index formula is criticised in Rothwell, Doris P., “Use of Varying Seasonal Weights in Price Index Construction,” Journal of the American Statistical Association, III, 03, 1958, 66–77 CrossRefGoogle Scholar, and in Zarnowitz, V., “Index Numbers and the Seasonality of Quantities and Prices,” Staff Paper no. 5, in Hearings, Part 1, 233–304.Google Scholar

³⁶ Consumer, 14.

³⁷

.

³⁸

³⁹ Consumer, 14.

⁴⁰ From the equation in note 37 we can deduce that

.

for all j, and therefore, in particular,

.

⁴¹ A similar approach to the problem of seasonal weights, which uses a quantity index to adjust for differences in monthly baskets, is advocated by Rothwell, “Use of Varying Seasonal Weights.” Her formula is

and the month-to-month change would equal

the ratio of costs of the baskets in the two months divided by a measure of change in the quantity in the two months. This formula has the advantage of not requiring adjustment of the quantity consumed, but it also depends critically on the acceptability of the quantity index used in this manner.

⁴² Consumer, 13. Zarnowitz, , “Index Numbers and Seasonality,” 279–80Google Scholar, recommends that seasonal items be combined into groups which “would give the ‘average consumer’ approximately equal utility or satisfaction in each month of the year.” He notes that “this approach requires some departure from the strict concept of a price index in the direction of a cost of living index.”

⁴³ The use of different seasonal food baskets for the 1947–48 and 1957 based indexes has resulted in different seasonal movements in the food and total categories of the CPI. The Bank of Canada Statistical Summary very properly notes, in the table presenting the CPI figures, that the revised system of seasonal weights has affected the seasonal pattern beginning in 1961. The DBS monthly, Prices and Price Indexes, does not include any such caution in its presentation of pre- and post-January, 1961, CPI monthly indexes.