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I want to estimate a VAR model based on the Dufour and Engle paper "Time and the Price Impact of a Trade" (2000).

There, the parameter $ b_{i} $ of the endogenous variable $ x_{i} $ is dependent on the strictly exogenous variable $ T_{t-i} $ :

$$ b_{i}x_{t-i}=[ \gamma_{i} +\delta_{i} T_{t-i} ] x_{t-i} \ \ (1) $$

The authors state, that they estimated this system by OLS, but I am not quite sure how the estimator looks like in this case. I thought of multiplying out the equation and defining a new variable, say $ z_{t-i} $

$$ \gamma_{i} x_{t-i} +\delta_{i} [ T_{t-i} x_{t-i}] = \gamma_{i} x_{t-i} +\delta_{i} z_{t-i} $$

which would consist of an exogenous and endogenous part though, which I think makes this procedure methodically incorrect. Can anybody give an explanation how such a system as in (1) is estimated using OLS? I plan to use the vars-Package in R btw.

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  • $\begingroup$ The link is broken, can you fix that? I found another version of this paper and glanced through it. I did not find the problem you mention, could you be more precise where exactly this statement was stated in the paper? $\endgroup$
    – mpiktas
    Dec 2, 2013 at 14:41
  • $\begingroup$ Thanks for your answer. Here's another link to the paper You find the equation on page 14 (2480) as part of a longer equation. My idea was to multiply it out and regress on z as an exogeneous variable (which hasn't an own equation in the VAR). $\endgroup$
    – Ahlerich
    Dec 5, 2013 at 2:24

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