Exogenous Regime Switching Models


I'm new to the site, so bear with me!

I currently have a model that measures inflation expectations as follows:

y(t) = a*x(t) + (1-a)*y(t-1)

I'm looking to create a regime switching models that change the values of "a" based upon a shock to an exogenous variable (let's say "z(t)"). Are there any methods which estimate the threshold of z(t) that would merit an switch in the regime of this particular model?? As far as I'm aware, threshold models are purely endogenous, rather than exogenous...