3 Data sets

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Because trend gross domestic product (GDP) and the real stock of public capital appear similar, it will be difficult to ascertain the elasticity of public capital when multifactor productivity (MFP) and public capital are placed in the same model. In an effort to improve parameter estimates, panel datasets that potentially provide more variation are employed. A provincial panel is used to estimate a production function so as to provide more degrees of freedom and more variability between the growth in GDP and the growth in public capital than can be derived from estimates for the economy as a whole. Subsequently, an industry panel is employed to estimate the cost savings associated with an additional unit of public capital.

Provincial panel data

The provincial panel spans 1981 to 2005. This covers the period over which trend GDP growth is approximately linear. The panel comprises business sector real GDP, capital stock, hours worked and public capital stock by province. The real GDP estimates are formed by removing the estimates of government expenditure and the value added from owner-occupied dwellings from provincial real GDP estimates.

The hours worked estimates are taken from the Canadian Productivity Accounts (CPA) estimates of provincial hours worked. The estimates are consistent with the hours worked estimate for Canada currently produced for the CPA. Estimates of public and private capital stocks are taken from the Investment and Capital Stock Division of Statistics Canada.

Industry panel data

The industry panel data variables are taken from the Input–Output tables developed by the Industry Division of Statistics Canada and from the Capital, Labour, Energy, Materials and Services (KLEMS) dataset produced by the Micro-economic Analysis Division of Statistics Canada as part of the Productivity Accounts. Estimates of business sector nominal and real GDP, the GDP deflator and labour cost are taken from the KLEMS dataset (for more information, see Baldwin and Gu 2007; Gellatly, Tanguay and Yan 2003; Harchaoui and Tarkhani 2003; and, Gu et al. 2003).

Description

The user cost of capital is estimated as where q_i,k,t-1 is the past price of the capital good, r_t is the nominal rate of return paid for the asset, δ_k,t is the asset specific depreciation rate, π_i,k,t is the asset price change from t −1 to t, τ_i,k,t is the effective tax on capital income and φ_k,t captures property taxes.

While estimates of the user cost of capital are available in the KLEMS dataset, they are derived using an endogenous rate of return estimate. This may not be an appropriate measure for estimating a cost function because the internal rate of return adjusts to exhaust the economic surplus making the user cost of capital volatile. The internal rates of return respond quickly and, in some cases, strongly when industries experience demand and supply shocks. In these instances the change in the cost of capital is due to short-run extraordinary gains or losses that can be quickly unwound. The cost of capital estimates can become excessively volatile and lead to problems with econometric routines.

The short-term volatility induced in the endogenous rate of return can create an errors–in- variables problem if the true cost of capital does not adjust as quickly. One solution for errors-in- variables problems is the use of instrumental variables that are uncorrelated with the short-run shock but highly correlated with the true rate of return. In this paper, the five-year moving average of the long-term government bond rate is used (See Baldwin and Gu 2007 for a discussion of these issues).

Estimates of nominal transportation costs for the North American Industry Classification System (NAICS) industry classification are taken from the L-level input–output tables. As will be explained later, these estimates are used to capture the cost of using public infrastructure, and ultimately define an upper bound for the impact of public capital.

The KLEMS dataset provides estimates of economic aggregates for a range of NAICS industries at the L-level aggregation. Not all of the industries are employed here. Education, Health and Public Administration are removed from the dataset because they are not private-sector industries.