# Economic accounts: Frequently asked questions

## Input-output accounts

### How often are supply and use tables and input-output tables published?

Supply and use tables (industry by product) and symmetric input-output tables (industry by industry) are published annually. The following information is available:

### Does Statistics Canada have an input-output model to calculate the impact of spending or investment in the Canadian economy?

Statistics Canada offers input-output modelling services on a cost recovery basis. Two models are available, a national model (service 36-23-0001) and an interprovincial model (service 36-23-0002). Both models provide estimates of the direct, indirect and induced effects on numerous economic variables including output, GDP, jobs and taxes on production and products.

### Does Statistics Canada calculate multipliers by industry?

Statistics Canada calculates national, provincial and territorial input-output multipliers for the industries found in the input-output industry classification. The information is available in tables 36-10-0013-01, 36-10-0113-01, 36-10-0594-01 and 36-10-0595-01.

### Does Statistics Canada have a publication or documentation on the input-output tables and models?

Users interested in learning more about the supply and use tables and the input-output model can consult the following references:

## Productivity accounts

### How is productivity defined?

Productivity measures the economic efficiency with which resources such as labour or capital are employed in the production process. There are two widely used productivity statistics; labour productivity and multifactor productivity.

### What is the difference between labour and multifactor productivity?

Labour productivity is measured as real output per hour worked. It is the most commonly used productivity measure. Multifactor productivity, a broader measure of efficiency, is measured as real output per unit of combined inputs, which consist of labour and capital, and in some cases, intermediate inputs such as energy, materials and purchased services.

### Why is a productivity measure important?

Progress in productivity constitutes a significant source of increased standard of living. In the long run, increases in real hourly earnings are tied to productivity gains. The Canadian economy has been able to produce more goods and services over time, not by requiring a proportional increase of resources such as labour, but by making production more efficient.

### Why does productivity change?

Productivity increases when more output is produced without increasing the input, or when the same output is produced with less input.

Productivity decreases when less output is produced without decreasing the input, or when the same output is produced with more input.

### How is productivity measured by Statistics Canada?

Indexes of labour productivity, multifactor productivity, and related measures for the business sector, broad economic sectors and industries are published by Statistics Canada. Productivity is measured by comparing the quantity of goods and services produced with the inputs which were used in production. Labour productivity is calculated by divided real output by hours worked. Multifactor productivity is calculated by divided real output by a combination of inputs (which may include labour, capital, energy, materials, and purchased services). Quarterly and annual measures of output per hour worked, together with comparable measures of compensation per hour and unit labour costs, are maintained for the business sector and its constituent sectors and industries. Quarterly labour productivity for the business sector is measured as real gross domestic product (deliveries in chained dollars of final goods and services by the business sector to the final demand categories, such as households, investments, governments and the foreign sector) per hour worked. It is the productivity statistic most often cited by the press. For major sectors and industries, labour productivity is measured as real value added per hour worked .

The multifactor productivity indexes for the business sector measure gross domestic product per combined unit of labour and capital inputs. Multifactor productivity indexes at the industry level, based on a variety of output measures (gross output, value added and sector output) are also maintained, to serve a variety of analytical needs. The growth of capital input in the business sector is an aggregate of the different classes of capital stocks (information technology, other machinery and equipment and structures) weighted by their respective rental prices. Similarly, the growth of labour input is an aggregate of the growth of hours worked by different classes of workers, weighted by the hourly wages of each class.

### Are annual data on productivity measures available for the provinces and the territories?

Yes. Annual data on labour productivity and related measures are not only available at national level, but also at the provincial and territorial level.

### Why does Statistics Canada revise its productivity measures?

Productivity estimates are produced using different data sources. They are often revised when additional data sources and more accurate information become available. Accordingly, productivity measures are periodically revised to include more up-to-date information from censuses, annual surveys, tax statistics, etc.

Occasionally, historical revisions take place following changes in concepts or methodology.

Merchandise import data are based on customs documentation collected by the Customs Border Services Agency (CBSA). Customs records are also used for the compilation of merchandise export statistics, from sources like the United States Census Bureau (USCB) for exports to the United States, and from CBSA for exports to other countries.

### Are merchandise trade statistics published on a customs or a balance of payment basis?

Both, Statistics Canada publishes merchandise trade statistics on a customs basis and on a balance of payment basis. The customs-based statistics provide a measure of the change in the stock of material resources within a country that result from the physical movement of goods across the border. Balance of payments adjustments are made to the customs-based data in order to conceptually align them with other macroeconomic account statistics, such as gross domestic product, based on international standards. These data provide a measure of economic transactions in goods between Canadian residents and non-residents that result from a change in ownership.

### What are the classifications used to publish these statistics?

There are two main classification systems for merchandise trade data. First, the North American Product Classification System (NAPCS) classifies merchandise trade to different product categories. Customs basis and balance of payment basis data are available under the NAPCS classification. To consult the classification structure, please visit Variant of NAPCS Canada 2017 Version 1.0 - Merchandise import and export accounts.

Second, customs basis data are published under the Harmonized System Classification, which is an international commodity classification system that assigns 6 digit (HS-06) to categorize all traded goods. For more information on this commodity classification, please visit Commodity classification.

Finally, merchandise trade data are also available by industry (North American Industry Classification System - NAICS), by exporter and importer characteristics, and by Broad Economic Categories (BEC).

### When are data on merchandise trade statistics available?

Canadian International merchandise trade is a major economic indicator and the publication of trade data is deemed mission critical by Statistics Canada. It is published on a monthly basis, around 35 days after the end of the reference period.

## Stock program

### What method of evaluation of capital stock is used in the stock program?

The stock program uses the perpetual inventory method (PIM) to obtain estimates of capital stock by industry for a given year.

### Why choose the PIM over another method?

The PIM is the method most frequently used by international statistical organizations. It is generally the preferred method, as it represents a flexible way of producing time series for capital stock. Basically, it involves adding, every year, gross investment (gross fixed capital formation) to the capital stock from the previous year.

### What are the input data for the PIM?

The PIM requires information on investment value, price indexes of capital goods, service lives and depreciation methods. Statistics Canada gathers most of the annual data required to apply the PIM via the Capital and Repair Expenditures Survey (CRES) from the Investment, Science and Technology Division (ISTD), specifically:

• capital expenditures, that is, spending for the acquisition of new assets and the renovation, retrofit, refurbishing, overhauling and restauration of existing assets;
• the useful service life of acquired assets;
• the original cost and age of assets that are being retired or destroyed;
• sales and purchases of used assets;
• the value of work in progress at year-end.

### How does the PIM work, practically speaking?

The first step consists of transforming gross fixed capital formation (GFCF) at current prices into constant prices by using the most detailed price indexes for assets that exist. The PIM then involves using data in constant prices to obtain fixed capital consumption and net and gross stocks at constant prices. The price indexes are only applied to reconvert the data into current prices during the final step.

### When is a new capacity added to the stock?

An investment (GFCF) declared for year t is presumed to be implemented, on average, in the middle of year t. Hence, its depreciation over the course of the second semester of year t is included in the depreciation calculated for year t.

### What is meant by gross capital stock?

Gross stock is equal to the accumulation of past gross investments from which the value of assets that cease to exist that same year (decommissioned) are deducted annually. Therefore, this measure of capital stock is based on the hypothesis that the asset's efficiency remains constant throughout its entire service life.

The concept of gross stocks aims to reflect the replacement cost of tangible assets.

### What is meant by the replacement cost of an asset?

The replacement cost is the amount that would be needed, for a particular year, to replace all the existing assets with comparable new assets.

### What is meant by a retired, discarded or decommissioned asset?

An asset is retired, discarded or decommissioned when it is removed from capital stock at the end of its useful service life.

It should be noted that the retirement of assets from the same generation can be staggered over a certain number of years instead of being done all at once.

### How are discards carried out within the stock program?

Within the stock program, the discard function follows a truncated (normal) bell curve distribution, with lower and upper limits corresponding, respectively, to 50% (L/2) and 150% (3L/2) of the average service life L, to account for variation in the moment when identical assets are removed from stock.

### What is meant by net capital stock?

The concept of net stock aims to evaluate the production capacity of capital stock.

The value of net stock for a given year is meant to reflect the market value or economic value of the assets that make up the capital stock.

### What is meant by an asset's market value?

The market value is the amount for which assets could be sold, given that stock includes assets that are no longer new, have been subjected to some wear and are slightly outdated compared to new assets of an equivalent type.

### How is net stock at time t calculated?

Net stock at time t is obtained by subtracting the depreciation incurred over the course of year t from the sum of the net stock from the previous period t–1 and the investment at time t. The depreciation incurred during year t consists of the depreciation of both the net stock from the previous period and the current investment.

### What is the consumption of fixed capital (CFC)?

The consumption of fixed capital can be defined in general terms as the decrease, over the course of the accounting period, in the current value of the stock of fixed assets that are held and used by a producer, following their physical deterioration (or wear), normal obsolescence or normal accidental damages. It excludes the value of fixed assets that have been destroyed by acts of war or exceptional events such as very rare major natural disasters.

### Is the consumption of fixed capital observable?

The consumption of fixed capital is not usually observable. It is generally calculated based on the hypothesis that the prices of assets decrease in an orderly fashion over the course of an asset's useful service life.

It must be noted that the consumption of fixed capital must nearly always be estimated in this way, so that the capital stock results from the PIM or from another method or survey.

### Is there a difference between depreciation in year t and consumption of fixed capital for the same period?

No. The terms 'depreciation', 'amortization', 'consumption of fixed capital' and 'capital consumption allowance' are synonyms.

### How is depreciation during year t calculated?

The most natural method of calculating depreciation during year t is to multiply by the depreciation rate δ the sum of the stock from year t–1 and half of the investment from year t. Practically speaking, depreciation is obtained by using other approaches.

${\text{Dep}}_{t}=\delta \left({\text{Stock}}_{t-1}+\frac{1}{2}{\text{Inv}}_{t}$

### How is the depreciation rate δ determined?

The depreciation rate δ depends on hypotheses created for the ageing and loss of efficiency curve for assets. Three types of depreciation are often used in the calculation of net capital stock: linear depreciation, geometric or regressive depreciation and hyperbolic or deferred depreciation.

As such, δ =1/L for a linear depreciation and δ =R/L where R represents the 'declining balance rate' (DBR) for a geometric depreciation. However, the formula for a hyperbolic depreciation is complicated.

### How can different types of depreciation be distinguished from one another?

The most well-known model of depreciation is undoubtedly the linear model, according to which equal amounts are deducted from the stock each year. It is mostly considered for its accounting interest.

Hyperbolic depreciation is, in turn, the type that permits the most accurate measurement possible of the economic value of assets. Economic value is defined here as the services that can be withdrawn from these assets.

The geometric type, however, is the depreciation model that measures the market value of assets. Here, market value means the resale value of assets on the second-hand market.

### How is depreciation/capital consumption allowance determined in the stock program?

In the case of linear depreciation, depreciation is obtained by dividing the sum of investments up until time t by the service life (number of years over which the asset amortized).

In the case of hyperbolic depreciation, depreciation is given by the weighted sum of the investments (weighted according to their beta obsolescence factors) up until time t.

In the case of geometric depreciation, however, depreciation is calculated residually using the net stocks from t–1 and t as well as gross investment during year t.

### How is net capital stock according to the geometric depreciation model calculated practically speaking?

The calculation of net stock according to a geometric depreciation is based on the notion of contribution to the net capital stock at the end of given year t of the investment carried out during a given previous year x. Net capital stock at the end of year t is then obtained by summing the contributions on all the generations of investment flows for this element.

### How are the average service lives of assets determined?

Average service lives were estimated using information, collected via the CRES, on the service lives and age‑price profiles of retired assets. These service lives based on survey data, introduced starting in the reference year 1987, are generally shorter than the hypothetical service lives that were used to calculate estimates of capital stock before the survey data were available. The periodic evaluation of service lives based on survey data has shown that they are stable at current levels. A geometric interpolation permitted their introduction for the years prior to 1987.

### How is the average age of capital stock calculated?

The average age reflects the age of the assets in place in the capital stock. It is obtained via a sum of the age of each generation of assets that is weighted by the investments that still exist. Since age is a function of an asset's service life, the investments in place influence the age of this stock of assets according to their respective service lives as well as their relative importance within this stock.

### How are declining balance rates (DBRs) defined?

Using a regressive method (geometric depreciation), it is hypothesized that the market value in constant prices decreases at a constant rate during every period. The depreciation factor can be written as R/T where T is the total useful service life and R is the DBR. Depreciation for the period t is obtained by multiplying the residual value of the asset in the period t-1 by the depreciation factor R/T. There are several ways of calculating the DBR.

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