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I have the following model that I would like to rebuild:

$Y_{i,t}=a+bx_{i,t}+cx_{i,t-1}+e_{i,t}$

I' am wondering now whether this is the same as the model above:

$Y_{i,t}=a+ d\Delta x_{i,t}+e_{i,t}$, where $\Delta x_{i,t}=x_{i,t} - x_{i,t-1}$?

I believe this is true but i just need to be 100% sure.

Thank you

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  • $\begingroup$ I replaced "delta" with "\Delta". Hopefully that's what you intended. If not, you can edit. You should include an edit or additional discussion to clarify your question (see Alexis' answer). $\endgroup$
    – Glen_b
    Aug 9, 2014 at 2:09
  • $\begingroup$ this is indeed the notation I had in mind. thank you for clarification $\endgroup$
    – Gritti
    Aug 9, 2014 at 6:30
  • $\begingroup$ Now that you ask a clear question, it's easy to answer: The two models are not the same, but the second model is a special case of the first, with $b=1$ and $c=-1$. $\endgroup$
    – Glen_b
    Aug 9, 2014 at 7:32

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I would say a few things.

First, I wonder if your notation is off? In the second model, do you mean: $Y_{i,t}=a+ d\Delta x_{i,t}+e_{i,t}$, where $\Delta x_{i,t}=x_{i,t} - x_{i,t-1}$?

If that is so, then I would say that these models are not equivalent, because there are at least two kinds of short term effects $x$ can have on $Y$ (1) effects of change in $x$ (i.e. $\Delta x$), and (2) level effects (i.e. effects of $x$ itself).

Your second model includes only the effects of change in $x$.

You first model includes the effect of the level of $x$, plus an adjustment for the effect of the level of $x$ from last time, which indirectly gives an effect of change in $x$.

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  • $\begingroup$ thank you for your detailed answer! The problem with my data/model is that it puts too much emphasis on the these two variables although in the overall model they "should" only play a tangential role. I was hoping to circumvent this problem by including only the change but as you mentioned I'll loose the level effects. Are there any possibilities to "control" a certain emphasis on model variables? $\endgroup$
    – Gritti
    Aug 9, 2014 at 6:28
  • $\begingroup$ Not sure what you mean... do mean the effect sizes for your $x$ variables are larger than for some other variables that you care about? $\endgroup$
    – Alexis
    Aug 9, 2014 at 7:29
  • $\begingroup$ I was referring to the coefficients. From an economical point of view the coefficients should take on certain levels that "make sense". I fear that my model somehow overestimates the effect of xi,t−xi,t−1 (bookvalues) these values and thus the coefficients are way off values you would expect. $\endgroup$
    – Gritti
    Aug 9, 2014 at 7:57
  • $\begingroup$ So it sounds like your expectations may need updating? :) $\endgroup$
    – Alexis
    Aug 9, 2014 at 8:22

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