Canadian Quarterly Labour Productivity Accounts — Technical Notes: a revised version - 2021
By Mustapha Kaci and Marc Tanguay
Quarterly estimates of labour productivity growth and related variables were published for the first time on December 20, 2000 for the aggregate business sector and on December 12, 2003 for its major industrial sectors.Footnote 1
The seasonally adjusted statistical series at the aggregate level (total economy, business sector and non-business sector) begins at the first quarter of 1981, while those at the industry level are available only back to the first quarter of 1997. These quarterly estimates are meant to help those who are focused on analysis of the short-term relationship between real output, employment, hours worked and compensation.
Quarterly estimates of labour productivity and related series are published in index form (using a base year consistent with National Accounts) at the aggregate and industry levels.
Hours worked for all jobs
Hours worked represents the total number of hours that a person devotes to work, whether paid or unpaid. Generally, this includes regular and overtime hours, coffee breaks, on-the-job training, as well as time lost due to momentary interruptions in production when the persons involved remain on the job. However, time lost due to strikes or lockouts, to statutory holidays, vacations, as well as illness, maternity or other personal leave are all excluded from the total number of hours worked.
Quarterly estimates of labour input make the distinction between two main categories of jobs:
- Paid workers jobs, which comprise employee jobs as well as jobs held by owners of an incorporated enterprise.
- Jobs occupied by self-employed workers which comprise employers of an unincorporated business, unincorporated own-account jobs and unpaid family-related jobs.
The number of hours worked is calculated as the product of the number of jobs times the average hours worked that is collected by the Labour Force Survey (LFS).
The number of jobs in the business sector is obtained residually by subtracting all jobs occupied in non-commercial activities from the number of jobs in the total economy. An estimate of the number of jobs for the overall economy is first produced from LFS estimates for all ten Canadian provincesFootnote 2, to which are added secondary jobs of workers with more than one job. Employees who hold a job but were not at work during the LFS reference week, and have no right to compensation during their absence, are removed from the estimates. Finally, all workers in self-employed jobs who were not at work during the reference week are also excluded.
In the System of National Accounts (SNA), non-commercial activities comprise two main components: the government sector and non-profit institutions servicing households. The number of jobs estimates for the government sector come mainly from the Survey of Employment, Payroll and Hours (SEPH). Estimates for non-profit institutions servicing households mainly encompass social and community services including religious groups, philanthropic foundations, civic, professional and other similar organizations. Employment for non-profit institutions is built from a linkage between the edited PD7Footnote 3 files and SNA's T4 allocation system developed from Business Register information.
Once the number of jobs for the business sector has been derived, the number of hours worked is calculated by multiplying each component of jobs by their respective average hours worked.
At the industry level, all data on average hours worked by industry and by category of worker are taken from LFS. However, the industrial breakdown for the employee jobs are mainly from SEPH. Only data from LFS are used to estimate the employee jobs in agriculture, agricultural services, and fishing and hunting. In the case of the categories of jobs occupied by self-employed workers, the industrial detail is obtained by integrating information from the five-year censuses and the LFS.
Jobs and hours worked estimates by industry are then adjusted to their respective business sector total of jobs and hours worked, obtained residually from the total economy and the non-commercial sector.
Finally, to ensure consistency with the annual data from the labour productivity database, the quarterly indices of labour input are adjusted to their respective annual benchmarks when they become available. A new yearly benchmark becomes available at the business sector level upon the release of the first quarter indices for the business sector, and upon the release of the third quarter indices at the industry level.
Real gross domestic product (GDP) as the measure of output
Quarterly estimates of real value added (or real GDP) used to calculate the productivity in the business sector and its component two-digit industries are built-up using a chained Fisher volume index method.
For the business sector, quarterly estimates of output are derived from chained Fisher volume indexes of GDP at market prices (expenditure-based), sourced from Quarterly Income and Expenditure Accounts. These quarterly estimates of real GDP in the business sector are constructed after removing the value added of the government sector, non-profit institutions, and the rental value of owner-occupied dwellings. Value added related to paid employees of private household employees is also removed. This approach is similar to that used for the quarterly measures of productivity in the United States.
Corresponding exclusions are also made for labour compensation and hours worked, in order to make output and the labour statistics consistent with one another. In 2019, nominal GDP in the business sector accounted for roughly 73.5% of the Canadian economy.
Since October 1st, 2012, the output series reflect the capitalization of research and development activities and military weapons systems introduced by the Canadian System of National Economic Accounts. This change brought Canada in line with the United States, thereby improving the comparability of the quarterly measures of productivity with those published by the U.S. Bureau of Labor Statistics.
At the industry level, quarterly estimates of output are obtained from the estimates of value added at basic prices, published by the Industry Accounts Division. The chained Fisher volume index is used in years for which final supply and use tables are available. For the most current years without these annual benchmarks, real value added is based on a fixed-weight Laspeyres volume index. It should be noted that quarterly estimates of the value added used to calculate the productivity in the service-producing businesses as well as its component — the real estate, rental and leasing sector — exclude the rental value of owner occupied dwellings as there are no data on the number of hours that homeowners spend on dwelling maintenance services. Private households are also excluded from other business services — the industry grouping to which they would normally be associated.
All quarterly estimates by industry are available for two-digit NAICS industries, the goods-producing business sector, and the service-producing business sector.
It should be noted again that the GDP in the business sector is at market prices but the GDP by industry series is at basic pricesFootnote 4. As the valuation of output in the business sector differs from that used at the industry level, these measures are not directly comparable.
Labour productivity: a measure of real GDP per hour worked
Quarterly estimates of productivity for the total economy, business sector and by industry are based on a Fisher-chained volume index of GDP.
The labour productivity measures relate real output (real GDP) to labour input (hours worked). They estimate the change in the output per hour worked from one period to another. In other words, the growth of labour productivity is meant to estimate the efficiency with which the number of hours worked in all jobs involved in one sector is used in production. Economic performance, as measured by labour productivity, must be interpreted carefully, since these estimates reflect changes in other inputs, in particular the capital, in addition to the efficiency growth of production processes.
As a consequence of the use of different index numbers and of the different valuation of output measures — market prices for the aggregate of the business sector and basic pricesof the major industrial sectors— the aggregation framework of productivity accounts for the business sector as a whole is not entirely consistent with those that are detailed by industrial sector.
Total labour compensation and unit labour cost
Labour compensation measures the value of labour services entering in the production process. This compensation consists of all payments in cash or in kind made by domestic producers to workers for services rendered – in other words, total payroll. It includes the compensation of employees consisting of wages and salaries (including bonuses, gratuities, taxable allowances and retroactive wage payments) and supplementary labour income of paid workers (various contributions to employees), plus an imputed labour income for self-employed workers.
As was the case for estimating jobs, the labour compensation estimates in the business sector are obtained residually by subtracting the wages, salaries and supplementary labour income for the non-business sector from labour compensation for the total economy.
The data on income for all paid jobs in the total economy and at the industry level are taken directly from the estimates of compensation of employees in the quarterly income and expenditure accounts. Compensation of employees for self-employed workers is established by imputation. This imputation is based on relative distance modelling (as observed in 5-year censuses) between compensation rates for self-employed workers and paid employees, and varies from one industry to another.
No compensation of employees is imputed to unpaid family workers since by definition, they get no compensation for their work.
In all sectors, labour compensation is comprised not only of wages and salaries, but also of employer's contributions to indirect benefits (such as the pension and insurances plans). These initial estimates are also obtained from the quarterly income and expenditure accounts, but for productivity measures, an additional industry distribution is carried out.
Compensation per hour worked (or hourly compensation) is the ratio of the total compensation for all jobs to the number of hours worked.
Unit labour cost is the labour cost per unit of output. It is calculated as labour compensation divided by real value added. It is also equal to the ratio of labour compensation per hour worked (hourly compensation) and labour productivity. In other words, it is the joint result of changes in hourly compensation and productivity: unit labour cost increases when labour compensation per hour worked increases more rapidly than labour productivity. It is widely used to measure inflation pressures arising from wage growth.
The unit labour cost in U.S. dollars is equivalent to the ratio of the Canadian unit labour cost to the exchange rate. The latter corresponds to the U.S. dollar value, expressed in Canadian dollars. The exchange rate used is the monthly average exchange rate in Canadian dollars, published by the Bank of Canada.
Relative unit cost is an often-used concept for determining Canadian businesses' competitiveness compared to a foreign competitor. The relative unit cost is defined as the difference between the rate of growth of Canada's unit labour cost and that of a foreign country, with these costs expressed in a common currency for purposes of comparison.
Statistical adjustments
Seasonal Adjustment
Economic time series observed monthly or quarterly often show seasonal patterns that repeat every year during the same month or quarter. Seasonal patterns are changes that occur regularly during a given period of time. They relate to the seasons, sociological patterns and the pace of human activity.
All necessary basic variables for productivity analyses (such as hours worked, jobs, output and compensation) are seasonally adjusted using Statistics Canada's X-12-ARIMA program. Seasonal adjustment consists in removing the combined seasonal and calendar effects from the series, and it therefore helps to highlight the most relevant fluctuations (from an economic point of view). A series that is affected by seasonal fluctuations presents little interest or benefit for economic interpretation since these fluctuations substantially mask cyclical trends.
For information on seasonal adjustment, see Seasonally adjusted data – Frequently asked questions.
Seasonal adjustment is generally made by two main categories of workers (paid workers and unincorporated self-employed workers) at the industry level, and the seasonally-adjusted aggregates of jobs and hours worked are obtained by summation. In the hours worked series for the total economy, the class of paid workers is split between employees and incorporated self-employed, which facilitates the reconciliation with the data published by LFS.
Regression models to adjust for reference week effects and holiday effects on hours worked
The definition of the LFS reference week (usually the week with the 15th day of the month) implies that the actual dates of the week vary from year to year. This variability may impact the month-to-month change in hours worked estimates. In addition, hours worked are affected by variability in the dates of the reference week, combined with the presence of fixed (Thanksgiving, Remembrance Day) or moving (Easter Friday and Easter Monday) holidays. Specifically, in some years, holidays may occur during the reference week, reducing work hours during that week. This variability could introduce significant fluctuations in estimates of hours worked, and it is therefore removed from the series prior to seasonal adjustment.
In order to remove reference week effects and holiday effects, hours worked series are the subject of prior adjustments. These corrections remove the effects attributable to the situations where the 15th of the month falls relatively early or late for reference week and the situations where some holidays fall outside the reference week.
These effects are estimated by the seasonal adjustment method X-12-ARIMA using appropriate regression specifications with ARIMA residuals.
Benchmark adjustment
As a result of using different data sources and methodologies, the annual values (jobs, hours worked, GDP, compensation) and the yearly totals of the independently produced quarterly estimates are not identical. For instance, some components of labour statistics are processed only on an annual basis such as the employment in the three Canadian territories, the employment on Indian reserves, the international flows of workers, etc. However, this difference between the two sets of estimates is eliminated by integrating the annual benchmark values into the quarterly estimates. This integration process, called benchmarking, generates a series which moves as much as possible with the original quarterly series and sums to the annual benchmarks. In other words, this procedure restores coherence between time series data of the same target variable measured at different frequencies (e.g. quarterly and annually).Starting in June 2011, Statistics Canada's in-house SAS Proc Benchmarking program has been used for this purpose. This procedure is available in G-Series production versions v1.04 and v2.0.Footnote 5
Raking procedure used in seasonal adjustment
Seasonally adjusted estimates of overall jobs and hours worked for the business sector are derived by subtracting adjusted estimates for the non-business sector from those of the total economy. The resulting overall estimate is used as a quarterly benchmark for other seasonally adjusted series by industry. For example, hours worked estimates by industry are adjusted independently and then adjusted so that their total sums to the overall quarterly benchmark, while maintaining consistency with the annual detail. This procedure is known as raking. Starting in June 2011, Statistics Canada's in-house SAS Proc TSRaking program has been used for this purpose. This procedure is available in G-Series production versions v1.04 and v2.0.
Revisions to the quarterly series
Statistical revisions are carried out to incorporate the most recent information from quarterly and annual surveys, taxation statistics, public accounts, censuses, etc., as well as from the annual benchmarking process to the supply and use tables.
Quarterly labour productivity estimates and related measures are released four times per year. As shown above, the estimates are produced from various data sources, and they are often revised as a result of the updates to benchmark data, methodologies, and seasonal adjustment.
Data are released within 63-67 days after the reference period. Estimates for each quarter are revised when those for subsequent quarters of the same year are published. At the time of the third quarter of each year, revisions are generally undertaken back three years in conjunction with the National Economic Accounts Quarterly GDP revision process. Benchmarked estimates are not normally revised again except when periodic comprehensive revisions are carried out to incorporate the latest international concepts, classifications, and estimation methods.
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