One simple New Keynesian model would be http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf but I do not restrict my question to this model only.
Let us for now ignore the problem of linearizing around zero-growth-rate, and assume that there is no problem in modelling constant natural growth rate.
Let us suppose that monetary shock occurred, due to stochastic or forecast errors or intentional deviation. Can this shock result in technology shock also? (ex. change in $A_t$ in production function?)
I am sure that there exists a model that does this, but in most models, and especially Gali's model as linked above, is this true?