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In a RBC context, what I mean by growth shock is a total factor productivity shock that follows a stochastic trend $ln(a_t) = ln(a_{t−1}) + \gamma + \epsilon^a_t$.

I.e. the technology $a_t$, has a unit root and grows at an average rate $\gamma$

My question is: is this considered as endogenous growth ? If I want to get rid of this method should I replace the growth shock by a productivity shock ? Under what form should this productivity shock be and would it be considered as exogenous growth?

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