The energy-capital complementarity debate: An example of a bootstrapped sensitivity analysis

The aggregate production function approach is one way to forecast future energy demand (a step in forecasting carbon dioxide emissions, for example) and to analyse the aggregate economic effects of measures such as the increase of taxes on energy use. The results of such an approach tend to hinge on whether energy and capital are substitutes, implying that increases in energy prices will increase the demand for capital stock; or are complements, implying that increases in energy prices will reduce the demand for capital stock. In a famous but controversial paper, Berndt and Wood find energy and capital are complements using aggregate time series manufacturing data for the United States, 1947-1971. In a later paper, Ilmakunnas shows that much of the analysis is sensitive to the imposition of theoretical economic restrictions and provides a range of point estimates in a sensitivity analysis. The current paper discusses these issues further and, taking the Berndt-Wood study as an empirical example, shows that the estimation sensitivity is due to one particular set of restrictions known as symmetry restrictions and provides a bootstrap analysis which suggests that estimation sensitivity is almost entirely in the means of the sampling distributions and not in their shapes or degrees of dispersion.