Working Paper no. 196
Colin Ellis and Simon Price
Theory tells us that output, the capital stock and the user cost of capital are related. From the capital accumulation identity, it also follows that the capital stock and investment have a long-run proportional relationship. The dynamic structure thus implies a multi-cointegrating framework, in which separate cointegrating relationships are identifiable. This has been used to justify the estimation of investment equations embodying a reduced-form long-run relationship between investment and output (rather than between the capital stock and output). In this paper, a new investment equation is estimated in the full structural framework, exploiting a measure of the capital stock constructed by the Bank, and a long series for the 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 0.45. Overidentifying 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 oversized, but given this, a test for excluding the capital accumulation identity from the investment equation is much better than using a single-equation ECM.