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Public capital provides a vital input for private sector production. It consists primarily of roads, bridges, sewer systems and water treatment facilities. Public capital enables geographic concentrations of economic resources and provides wider and deeper markets for output and employment.

Despite public capital's importance, its impact on business sector productivity growth or total economy GDP has not been widely analyzed. The omission largely results from a dearth of comprehensive data on infrastructure and the lack of a consensus about how best to estimate the impact of public capital. Public capital in North America tends to be publicly owned and financed through taxation so no markets exist for its output. Additionally, public capital in North America lacks close substitutes in the private sector making it infeasible to use private sector information as a proxy for the public sector. As a result, estimates of public capital's impact are not easily obtained.

Consequently, the role of public capital in business sector productivity growth has not been thoroughly investigated. This paper asks how much of labour productivity and multifactor productivity (MFP) growth can be attributed to investments in infrastructure.

The growth accounting framework currently employed for productivity analysis focuses on private sector inputs and outputs. MFP is calculated as the difference between the rate of growth of business sector output and a weighted sum of the growth in labour and capital that are applied by the business sector to the production process. The impact public capital at present is subsumed in MFP.

This paper makes use of a growth accounting framework and an estimate of the elasticity of business sector output with respect to public capital to examine the impact of public capital on productivity growth in the Canadian business sector. It does so by extending the inputs considered in the standard framework that estimates multifactor productivity to include both private sector inputs (labour and capital) but to also include public sector capital.

The paper examines several questions:

1. How much of labour productivity growth came from public capital deepening?

Public capital's contribution to labour productivity averaged 0.2 percentage points per year from 1962 to 2006. Although modest when compared with the average contribution of 1.3 percentage points from private capital deepening, public capital nonetheless accounted for an average of 9 percent of labour productivity growth during the sample period.

2. How much of the conventional MFP growth estimate is due to public capital?

The conventional MFP growth estimate is measured as a residual after accounting for changes in private sector inputs. It, therefore, includes the contribution that public capital makes to private sector production. The conventional MFP growth estimate averages 0.4 percent per year.

The experimental MFP estimate calculated in this paper comes from analysis that explicitly includes a contribution to private sector value added from public capital. It, therefore, excludes the contribution of public capital from MFP growth. The experimental estimate averages 0.2 percent per year, half of the conventional estimate. Thus, 50% of the conventional estimate was due to the growth in public infrastructure.

3. Is public capital's contribution to productivity growth constant over time?

No. It was considerably larger in the earlier post-war period when investments in public infrastructure were largest. The largest contributions to labour productivity growth from public capital occurred in the 1962-1966 and 1967-1973 periods. During these years, public capital contributed 0.4 and 0.3 percentage points respectively to labour productivity growth. After 1980, public capital's contribution to labour productivity averaged only 0.1 percentage points per year.

Analysts using conventional multifactor productivity estimates have long been faced with the conundrum that productivity growth was much higher before 1980 than afterwards. The new measures that take into account the impact of public infrastructure substantially reduce the difference between the two periods, thereby demonstrating that part of the higher growth in the earlier period came from the very substantial growth in public infrastructure before 1980.

4. Did a reduction in government capital investment cause the productivity slowdown?

While the slowdown in productivity growth experienced in Canada coincided with slower growth in the stock of public capital, it is not possible to infer causality based on the analysis reported here. The slowdown in public capital investment occurred as decades of cross-country highway expansion came to an end and scheduled projects came to a conclusion. The investment opportunities for the public sector were lessened as a result, leading to a natural decline in public sector investment.

5. How robust are the rate of return estimates used to gauge the impact of public capital on output?

The impact of public infrastructure is derived from the rate of return estimates of public infrastructure in Macdonald (2008). Because this rate of return estimate is derived from econometric techniques, it is subject to statistical error. The true rate of return lies within a range around the estimate derived from the econometric technique. To address the uncertainty surrounding the true rate of return, a sensitivity analysis is performed which uses several approaches to gauge the robustness of results to alternate estimates of the rate of return:

1. Rate of return estimates of plus/minus 10 percentage points around the 17% value used in the main calculations are used to assess the sensitivity of results to alternate values of the rate of return. The magnitude of the average contribution of public capital to labour productivity growth varies from 0.1 to 0.3 percentage points as the rate of return changes; however, the conclusion that public capital makes an important contribution to productivity growth remains unchanged.
2. The base method used in the paper assumes that public capital's impact is constant over time. Analyses are performed to assess the sensitivity of the results to the use of a rate of return that varies over time. The time varying rate of return leads to results that generally agree with the results from the fixed rate of return. Public capital continues to be an important input into the private production process, and continues to be subsumed in traditional MFP estimates.
3. Finally, a more comprehensive view of the impact of public infrastructure has a second benefit. It also allows for a more accurate depiction of the manner in which output in the public sector is derived from labour as opposed to capital inputs. Estimates of the labour share of income for the public sector are re-calculated assuming a 17% return on public capital, and are compared with their business sector counterparts. When the 17% return is included in public sector GDP, labour share of income in the public sector becomes similar to business sector calculations, declining from 0.8 before inclusion of the impact of public infrastructure to between 0.5 and 0.6 afterwards, depending on the year chosen for the calculation. The labour share of income in the business sector averages 0.6 from 1961 to 2006.