3 Canadian-U.S. comparisons of capital intensity

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The construction of comparable estimates of capital stock for Canada and the United States permits us to evaluate the relative importance of investment in the two countries. We do so in two ways. In the first case, we ask how much of gross domestic product (GDP) is devoted to investment of different types over the recent past by examining the investment-to-GDP ratio. Also, since investment when accumulated just equals capital stock, we also examine the capitalto- GDP ratio.

To some, these ratios depict whether there is a 'capital' gap. While we provide these ratios for the interested reader, we offer the following caution in interpreting them. Investment involves foregone consumption. Countries with high investment-to-GDP ratios are in that stage of development where sacrifices may simply reflect the need for large up-front expenditures to provide the infrastructure needed for future production. Therefore, high investment-to-GDP ratios need to be interpreted within context. For example, expenditures on oil exploration are investments for future production and there may be a very long hiatus between the exploration and finding of reserves and their production—as Newfoundland and Labrador has discovered.

The same caveats apply to capital-to-GDP ratios. It should be recognized that the inverse of this ratio is simply a partial capital-to-productivity ratio—telling us how much output an economy obtains per unit of capital. The higher this ratio is, the more efficient an economy is in terms of transforming capital into output. But the inverse of this ratio is also used to assess the importance of capital in an economy—since the higher the capital-to-GDP ratio is, the higher is the share going to capital; and the share going to capital depends on the type of production function, the factor price ratio in the country and the type of technical change taking place.

Finally, it should be noted that the cross-country ratio of capital to GDP can also depend on industry composition if production functions vary across industries. Some industries may require much larger capital inputs than others. For example, utilities, communications and transportation systems are heavy consumers of capital. And these infrastructure industries may be more important in countries with large resource bases or that are geographically spread out with a low population density. Mineral and oil exploration require large amounts of capital. Differences in industry composition, therefore, may be the cause of differences in capital intensity across countries.

For this reason, we also examine the extent to which differences in capital intensity come from differences in industrial structure in the two countries.

3.1 Decomposition method

This section presents the methodology used in decomposing industry and asset sources of the capital intensity difference between Canada and the United States.

3.1.1 Industry contributions to the Canadian-U.S. capital intensity difference

In order to decompose differences in capital intensity between the two countries into components, we make use of logarithmic transformations.¹⁶

The log difference in capital–output ratio between Canada and the United States is defined as

This equation indicates that the log difference in capital–output ratios in Canada and the United States is equal to the log difference in capital stock minus the log difference in output in the two countries. The method for measuring the difference in capital or output between two countries is similar to the one for measuring the changes in capital or output over time within a country. The difference between logarithms of capital for Canada and the United States is calculated as

where

Description

Kⁱ denotes capital in country i ; i indexes country and equals C for Canada and U for the United States; Kⁱ_j is capital stock of industry j in country i; Pⁱ_{k, j} is acquisition price of capital for industry j in country i .

Similarly, the difference between logarithms of output for Canada and the United States is calculated as

where,

Description

Substituting Equations (9) and (10) in Equation (8), we have the decomposition of the aggregate capital-output difference into the contributions of individual industries.

Equation (11) shows that the aggregate capital intensity level difference can be decomposed into two components: the intensity component and the structure component. The first term captures industry capital intensity level differences between Canada and the United States. The second term reflects differences in industry output composition between Canada and the United States. This term is presented as a sum across all industries in order to show industry structure effects.

While the logarithmic transformations have the desirable property that they can be decomposed exactly and allow the relative importance of each component to be estimated, they have to be reestimated to provide estimates of the percentage gap between Canada and the United States by taking antilogs. When this is done, the direct decomposition presented above is no longer exact. There is a residual that we choose not to allocate to any particular category—and which we denote in the attached tables as the residual contribution. When the percentage gap in capital intensity is small, so too is this residual.

3.1.2 Asset contributions to the Canadian-U.S. capital intensity difference

We can also decompose the overall difference in capital–output ratios in Canada and the United States into contributions stemming from individual assets. The decomposition formula is

where a denotes asset type. The equation decomposes the overall capital intensity gap into the contributions of individual assets.¹⁷

 

^16. These logarithmic transformations allow us to create categories that are additive and exhaustive.

^17. The sum of the contribution of individual assets is approximately equal to the overall capital intensity gap if the capital intensity gap is small.