Knowledge that Transforms

Considering first the case of a known autocorrelation coefficient $, Klein observes that (4) may be viewed as a structural linear relation between the latent variables yt' -et, xI and yt'-l -et-,. Even knowing $, two of those variables are not observable. But the y' and yt' may be computed; et and et-, may be considered as errors of observation of the corresponding latent variables. In comparison with the classical models containing errors in variables, (4) is somewhat particular. Indeed, the value of the third variable (yt'_l) in observation t is identical to the value of the first variable (yt) in observation t -1. If we write qt and Qt for the latent variables corresponding respectively to yt and yI-1, we should take into account that tt 1tsince both are equal to yt'-l -et -. Now, Klein's method for the estimation of cx and A amounts to applying the maximum likelihood procedure as if Qt were not necessarily equal to qt-l