The AR(1) model - that is, y(t) = a*y(t-1) + other terms + an error term - occurs in models of technology transfer between and within countries. It is also widely used in other areas of economics such as growth theory and pensions.
In technology transfer, it is known as the Gompertz model. The coefficient a measures diffusion speed, since the equation can be rewritten
y(t)-y(t-1) = (a-1)*y(t-1) + other terms + error,
so that the increase in y will be larger when a is larger.
As with growth theory, using a lagged term presents some problems and it would be a good idea to work towards finding more precise determinants which reduce its significance.
Given the ubiquity of the AR(1), I think I will write up my earlier work on its estimation with GMM. Some of it has been put on this blog.