7 Concluding remarks

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Estimates of the rate of return to public capital that are found in the literature vary considerably. In order to evaluate what the rate of return for Canada might be, this paper builds on previous research at Statistics Canada (Harchaoui and Tarkhani 2003). It examines the extent to which different approaches and methodologies might provide a method of triangulating upon a central estimate of public capital's rate of return that may be used to inform the present discussions in the National Accounts community about how to account for the return that should be incorporated into estimates of value added in the public sector.

To do so, the paper uses a special data set derived from Statistic Canada's productivity accounts, a provincial and an industry panel data set, two different approaches (production function and cost function) and a number of different econometric techniques. Nevertheless, a need for additional research exists. Assumptions about the relationship between public capital and transportation costs, possible endogeneity problems in production and cost function estimation, the role of differing depreciation rates and methods for addressing parameter uncertainty all warrant further investigation.

The production function approach yields estimates for the elasticity of private capital and labour that accord well with their respective income shares. However, the elasticity of public capital and multifactor productivity (MFP) growth are difficult to disentangle. As a result, the range within which the rate of return likely lies is quite large.

The cost function approach presents an additional set of challenges. The time series properties of the data suggest that, in order to avoid spurious estimation results, the data should be first- differenced. In this framework there is less of a problem in separating out the impact of public capital from MFP; and, the resulting estimate of the elasticity of public capital (and the corresponding rate of return) falls within the confidence interval provided by the production function approach.

The estimated elasticity of cost savings from public capital is, on average, around 0.11. In both cases, the cost savings correspond to elasticity values that fall within the 95% confidence interval from production function estimates for the elasticity of public capital. They are also similar to the elasticity of cost savings from public capital of 0.06 reported in Harchaoui and Tarkhani (2003), who use a cost function, but estimate it in level, not first-difference, form. Moreover, after accounting for time series issues and unit heterogeneity, the results are robust across estimation methods.

Despite the 'triangulating' between the cost and production function approaches, there is still a range of plausible elasticity values. The weighted average from our preferred estimator suggests a 17% return. Nevertheless, the confidence interval around these estimates is plus or minus 12 percentage points, which leaves room for further refinement with improved databases.