Executive summary

Quarterly productivity estimates are produced by Statistics Canada to provide timely information on technological change and potential output trends. At one time, Statistics Canada only produced annual estimates of the growth in labour productivity data and these were produced with a considerable lag — about six months after the end of the year. The introduction in 2001 of the quarterly program has led to more timely data being made available to the analyst community.

Statistics Canada's role is not only to provide timely data but also to provide users with a full understanding of the quality of the data so that they may judge its appropriate uses. To this end, this paper focuses on the nature of the quarterly data and the nature of the revision process. It asks two questions.

1) How stable are quarterly productivity growth rates?

The paper describes various products associated with the quarterly labour productivity program. It outlines the nature of the volatility in the very short-run estimates (quarter-on-quarter growth rates) and emphasizes that the short-run estimates are much more volatile (have a higher variance) than alternates that make use of quarterly information averaged with recent values using a moving average — or other suitable prediction tools. The quarter-on-quarter growth rate is used to create annualized growth rates, its variance is twice as large as the variance of these alternatives.

Using information from a quarter in conjunction with that from adjacent recent quarters (the annual growth rates from the same quarter in the previous year, for example) provides data series that are less volatile, have quite a different profile and provide a clearer-cut picture of longer-run trends.

2) How large are the revisions that are made to the quarterly growth rate?

Users of the quarterly series need information on the nature and size of the revision process that arises because more comprehensive and more accurate data on both gross domestic product (GDP) and hours worked (the two components of labour productivity growth) are gradually incorporated into the estimates. This is a process that occurs in many of the macroeconomic aggregates that the System of National Accounts produces.

The study therefore examines properties of the revisions made to the estimates of Canadian labour productivity and its components (GDP and hours worked) since the inception of the program in 2001. The analysis examines revisions between the initial estimate and the estimate two years (nine quarters) later. The paper also compares Canadian revisions with U.S. ones.

The analysis of revisions focused on the following questions:

1. Are revisions of the preliminary estimates of Canadian quarterly labour productivity growth over the two years subsequent to first release significant?

   The study examined several indicators that describe the size of revisions made to the quarterly labour productivity estimates. The study found that the mean revision for Canadian labour productivity growth is quite small and not significantly different from zero at all revision horizons. The Canadian Productivity Accounts produce unbiased preliminary estimates of quarterly labour productivity. Thus, the data do not have a significant tendency to be revised in a particular direction (i.e., up or down). The paper also examined the extent to which the estimates from different vintages of quarterly labour productivity track one another. The correlation coefficient between the first release and the release one or two years later is 0.5. Comparison of the size of the mean absolute revision over successive vintages of a release suggests that the size of the revisions is about the same in the first and second years of the revision cycle. Moreover, the absolute difference between the first estimate and the estimate two years later has no discernible trend over the time period studied.

2. Since the quarterly estimates of the growth rates provide information on the changes in the direction (expansion or contraction) of the longer-run average productivity growth rates in Canada, are the preliminary estimates a good proxy for the final estimates in terms of size and trend prediction?

   Several tests were conducted to see whether information contained in the 'final' estimates is accurately reflected in the first estimates. First, the sign of the final growth rate was compared with the sign of the first estimate. In most cases (in 59% to 73% of revisions), the sign of the 'final' estimate of the growth rate is consistent with the sign of the earlier estimate. Second, incremental information provided by new quarterly productivity estimates was compared with the forecast 'trend' value. To do so, the sign of the difference in the estimate of the average of the quarter-on-quarter growth rates over the last year and the average of past rates over four years was calculated. This compares information on recent trends with longer-run trends — to see whether the productivity series is 'breaking' below or above the long-run trend. The sign of this difference was the same in over 73% of the cases for the final estimate as it was for the first estimate. Third, the time patterns of the differences between the actual and forecast estimates derived form the first and final estimates were examined. They were found to track one another closely. Fourth, time paths of the first estimates were analyzed to see whether they generally fell within the bounds of the subsequent revised estimates, including the final estimate (second quarter, first year and second year). Generally, this was the case.

3. How do the revisions in the Canadian Productivity Accounts compare with those of the United States?

   Comparison of Canadian and U.S. revisions indicate that the size, significance and signal properties of the revisions in the two countries are very similar. The size of the mean revision for the United States between the first and 'final' estimate two years later is slightly larger than the size of Canada's mean revision. Both are not significantly different from zero. On the other hand, the U.S. mean absolute revision was smaller than the mean absolute revision for Canada. The latter difference stemmed not from differences in the mean absolute revision to GDP but from the mean absolute revision to hours worked. The mean absolute revision to GDP in Canada is smaller than the mean absolute revision to GDP in the United States but the opposite is the case for hours worked. The Canadian labour data are subject to greater mean absolute revisions than those of the United States because Canada has a greater tendency to revise its hours worked by incorporating Census of Population benchmarks. Maynard (2007) points out that the U.S. labour estimates, when derived from the Current Population Survey, do not make backward revisions when they benchmark to the U.S. population census to the same extent that the Canadian estimates do. This accounts for part of the difference in the size of the absolute revision for hours worked in Canada. The Canadian data are therefore subject to greater revisions, for the sake of accuracy. This finding points to the need to not forget that revisions are made to make estimates more accurate.

View the publication Revisions to the Quarterly Labour Productivity Estimates in PDF format.