Uk Business Investment: Long-run Elasticities and Short-run Dynamics

Theory tells us that output, the capital stock and the user cost of capital are cointegrated. From the capital accumulation identity, it also follows that the capital stock and investment have a long-run proportional relationship. This has been used to justify the estimation of investment equations embodying a long-run relation between investment and output, rather than between the capital stock and output. But the theory implies two cointegrating relationships exist, of which the investment-output relationship is a reduced form (and therefore itself cointegrating). The dynamic structure thus implies a multicointegrating framework, in which separate cointegrating relationships are identifiable. In this paper, a new investment equation is estimated in this framework, exploiting an internally constructed measure of the capital stock, and a long series for the weighted cost of capital. A CES production function is assumed, and a well-determined estimate of the elasticity of substitution is obtained by a variety of measures. The robust result is that the elasticity of substitution is significantly different from unity (the Cobb-Douglas case), at about 0.5. Over-identifying restrictions on the long-run relationship are all accepted. Although the key long-run parameter (the elasticity of substitution) is highly robust to alternative specifications, single-equation investment relationships may obscure the dynamics. There is evidence that the Johansen method is over-sized, but given this a test for excluding the capital accumulation identity from the investment equation is much better than using a single equation ECM.