I am interested whether there is a name for the below process / models, so I can read up on more of the statistical literature on this. Consider the following situation where I want to estimate the effect of X(t) on Y(t): Y(t)=b1*X(t)+error1(t) However, I am interested in the case where X(t)=b2*Y(t-1)+error2(t) such that Y(t) indirectly depends on Y(t-1). The equation Y(t)=b1*X(t)+error1(t) is NOT an autoregressive model, but it does share some properties with AR processes, such as that the variance in (Y) tends to increase with sample size, which may cause the estimate of b1 to be biased at low sample size when using simple linear regression. Is there a name for this type of model, or does anyone have any hints where I can find more on which type of models are best suited to analyse such data?
Any hints are much appreciated, Martijn