Executive summary

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Public capital provides the foundation for the Canadian economy. The roads, water and sewer systems that make up the majority of public capital allow for lower transportation costs and greater concentrations of people and firms, promote agglomeration economies and provide access to broader, deeper markets.

Despite the contribution that public capital makes to the economy, it has proven difficult to generate a robust estimate of the rate of return that investment in public capital produces. In Canada, public capital provision is primarily funded through taxation. It does not have a private sector equivalent that could be used as a proxy for its rate of return, nor does it have commercial markets for its output. As a result, it is necessary to econometrically estimate the rate of return.

Econometric techniques, however, have not led to a consensus about what a reasonable rate of return may be. Depending on the method used, estimates as high as 50% and as low as 0% have been generated.

The uncertainty around the estimates has proven sufficiently large that no economic rate of return is attached to public capital when public sector gross domestic product (GDP) is estimated. Only the depreciation of public capital enters the calculation for GDP in the public sector.

This paper investigates issues surrounding the uncertainty arising from rate of return estimates. It uses a variety of econometric techniques, and it pays special attention to time series issues in estimation. Through the course of the paper, a number of questions surrounding the uncertainty are addressed.

• Why is it so difficult to estimate the rate of return?

The growth in public capital and multifactor productivity (MFP) are very similar. As a result, including MFP and public capital in a regression leads to multi-colinearity. This is a data problem that hinders accurate estimation of the rate of return. Estimates of public capital's impact are either captured by MFP leading to no impact, or capture elements of MFP inflating public capital's impact. This is especially true of aggregate production functions.

• Which approach is preferable: a cost or a production function?

Cost function estimates tend to suggest that the impact of public capital is positive and lower in magnitude than production function estimates. They are generally viewed as more credible. This paper assumes that both approaches contain some useful information. It uses cost and production function estimates to 'triangulate' on what a reasonable impact from public capital could be. The 'triangulation' suggests that an elasticity between 0.10 and 0.15 and a rate of return centered on 17% is appropriate.

• Which estimation approach is preferable?

A variety of estimation techniques are employed to verify the robustness of the estimates. Time series analysis, for elements such as unit roots, is employed in order to avoid spurious results. As well, because the analysis uses panel data sets the estimation procedure controls for unit specific fixed effects. Outside of these considerations, the analysis is robust to changes in estimation strategy.

• What is a reasonable rate of return for public capital?

The paper shows that, while it is difficult to place an exact number on the rate of return from public capital, it is larger than zero. Moreover, it also shows that high rates of return presented in the literature likely result from the elasticity estimate capturing elements of MFP growth. More precision requires data sets that allow for more variation in the underlying series. This paper does so by moving to provincial cost data. The 'triangulated' range supports both of these arguments. Rates of return are produced with a mean 17%, but they continue to cover a relatively wide range, from near 5% to 29%, Nevertheless, they support the contention that the average long-term government bond rate can be used as a conservative estimate for public capital's rate of return.