I need to check if the impact of a specific variable (z) is growing over time. More specifically, I need to estimate a model like this:

x(t) = a + b*y(t) + c(t)*z(t) + e(t)

The parameters "a" and "b" don't vary, but "c" does. I think this is possible via the Kalman filter, but I'm not sure about that (unfortunately, I don't master this filter).