One of the most important features of estimating a production function is the presence of an I(2) capital stock series. Given the empirical regularity that the first difference of capital stock -i.e. investment- is an I(1) series, capital stock tends to have a double unit root. Using Ethiopian data from 1960/61 to 2001/02, we showed that the existence of cointegrating relationship is rejected under the I(1) analysis while the I(2) analysis fail to reject the existence of cointegrating relationship. This indicates the possibility of polynomial cointegration. We also argued that the polynomial cointegration can be motivated theoretical apart from being an empirical issue alone.