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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

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What you are describing is an autoregressive distributed lag (ADL) model that is often used in economics. A good introductory text by Keele and Kelly is available here.

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  • $\begingroup$ Thanks! That was a very useful resource you directed me to. Including Yt-1 as a lagged dependent variable (LDV: Y(t)=b1*X(t)+b2*Y(t-1)+error1(t) ) seems to reduce the bias in b1-estimate quite a lot at low sample size (short time series), although not completely in my simulated datasets. One limitation though of LDV models is that they cannot be combined with random effects, which I also aim to include. Any ideas on this, or isn't there a good solution to this yet? $\endgroup$ – Martijn Jun 28 '17 at 15:10

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