An Examination of Public Capital's Role in Production

This paper examines whether or not the long-term government bond rate could reasonably be employed as the rate of return on public capital when calculating public sector gross domestic product. It finds that the rate of return on public capital is lower than often reported and is roughly consistent with the rate of return on private capital. Given that there is a range of estimates that are plausible, the paper concludes that the long-run government bond rate could be used as a conservative estimate for the rate of return for public infrastructure. Previous studies have shown that production function estimates tend to find rates of return that are implausibly large, while cost function estimates appear more reasonable. This paper shows that public capital and total factor productivity (TFP) growth behave similarly, and argues that production function estimates for the impact of public capital overstate its impact as a result, catching part of what belongs in estimates of TFP. It also shows that the similarity between the growth in public capital and TFP leads to a large confidence interval around public capital elasticity estimates derived from the production function framework. The paper then proceeds by generating a confidence interval from the production function estimated first with and then without TFP growth. It then uses a cost function to pinpoint more precisely estimates for the marginal cost savings from public capital. Importantly, the estimate derived from the cost function is found in the lower part of the confidence interval derived from the production function. The rate of return associated with the overlapping estimates is then shown to cover a range that extends from the average long-run government bond rate to the rate of return on private capital.