Using lagged income to proxy for a single accumulating factor

This post is a small extension to last Thursday's "Lagged income and the omitted accumulating factors" post. In studies of technology's effect on growth, the change in lagged income is sometimes used as a proxy for the change in technology. If we look at the formulas presented in the previous post, it follows that the lagged term is capturing the accumulation of all variables, including capital and education which are usually already present in the empirical specification. Thus, collinearity of variables will be increased and interpreting coefficients will be more difficult. Moreover, technology is identified with all excluded accumulating variables, so must be defined in a broad sense for the approximation to work.