I am estimating an error correction model of the following form, using panel data where $i$ are countries and $t$ are years:
$\Delta y_{it} = \alpha + \phi_1 y_{it-1} + \phi_2 y_{it-2} + \gamma x_{it-1} + \mu_i + \epsilon_{it}$
(Note that I do not estimate the immediate impact of $x_{it}$ on $\Delta y_{it}$, only the effect of the lagged value.)
Alternatively, one can express the model in the ADL form:
$y_{it} = \alpha + (\phi_1+1) y_{it-1} + \phi_2 y_{it-2} + \gamma x_{it-1} + \mu_i + \epsilon_{it}$
Under either specification, $\gamma$ is the short run effect of $x$ on $\Delta y_{it}$.
My first question: is the long run effect as follows?
$\frac{-\gamma}{\phi_1 + \phi_2}$
And my second question: how would I calculate the yearly impact of (a) a temporary 1-unit increase in $x$ and (b) a permanent 1-unit increase in $x$? I am ultimately interested in plotting these effects over a period of time (e.g. 25 years), so I need the effects in year 1, 2, 3, and so on.
