Key concepts

Public infrastructure

For the purpose of this paper, we define public infrastructure as consisting of the following five assets: roads including highways^2. bridges including overpasses, water supply systems³, wastewater treatment facilities⁴ and sewer systems⁵. Investments in these infrastructure assets are financed for the most part by federal, provincial, and local governments but may also include private sources. Investment represents spending on assets for repairing, upgrading and expanding existing stocks. Such assets generally have a service life of more than one year and include new fixed capital formation and investment in replacement assets. The value of an asset is discarded from the value of the gross stock at the end of its service life.

Data in this paper are presented for Canada and for each province separately. Unless otherwise indicated, data for the Yukon Territory, the Northwest Territories and the Nunavut are included in the Canada total but are not presented separately because of confidentiality.

Useful life and mortality function⁶

The useful life of an asset is its estimated productive life, that is, the length of its useful life at the time of its acquisition. For example, an asphalt roadway-whether it is a road or highway-has a mean service life of about 28 years. The service life is an average based on data from the Capital and Repair Expenditure Survey and has been confirmed by empirical studies that link the value of gross stock with asset useful life and other engineering information. The survey also provides data on the age-price profiles of discarded assets.

The mortality function determines the retirement (decommissioning) of assets from capital stock when the assets reach the end of their useful life. The function used for asset retirement is represented by a normal distribution truncated at the tails.7 The distribution reflects service life variation due to asset quality and maintenance.

Average age of capital stock

For analytical purposes, economists use a complex formula to estimate the age of public assets such as roads and bridges. The key factor is the amount of investment in public infrastructure. Without sufficient investment, the stock of infrastructure declines and its age increases.

More precisely, the variables used to compute the average age of capital stock are the investment, the survival function, the year in which the investment was made, and year-end gross capital stock. In practice, there can be several different types of distributions for a given average age. For example, there can be structures whose ages are clustered around the average age, or a combination of young structures with much older structures. Hence, short-term investments required to extend the useful life of different sets of assets with similar average ages can vary greatly depending on the age distribution of the various asset components.

Average age as a percent of useful life

The ratio of the average age per year of useful life provides a relative measure of the amount of useful life expended for a given set of asset. This ratio is useful for comparing the oldness of assets with different lengths of useful life.