The pure expectations theory occurs when there are no k terms, so that [R.
Implication for permanent changes in interest rates: Notably, the pure expectations theory predicts that if interest rates increase at date tin a manner which agents expect to be permanent, then there is a one-for-one effect of such a permanent increase on the level of the long rate because the weights sum to one, i.
Implications for temporary changes in interest rates: Temporary changes in interest rates have a smaller effect under the pure expectations theory, with the extent of this effect depending on how sustained the temporary changes are assumed to be.
Further, while the pure expectations theory is a useful expository device, it is simply rejected: one of the stylized facts is that long rates are generally higher than short rates (there is a positive average value to the term spread).
The starting point is Campbell and Shiller's (1987) observation that present value models have cointegration implications, if the underlying series are nonstationary in levels, and that these implications survive the introduction of stationary deviations from the pure expectations theory such as time-varying term premia.