How to model this problem?


I have the following problem:

y= intercept + y(-1)+ x1 factors + x2 factors which the literature models using dynamic panel models (since y depends on its lagged value)
y(-1) is the lagged y variable
x1 factors are firm specific
x2 factors are macroeconomic factor

I want to investigate the effects of y falling below a certain value on x1 variables. In other words assume that a benchmark=100 when y<100 I want to see how the firm reacts and changes its x1s.

How can i model this problem? which regression or series of regressions should I use?
You seem to imply that there is a reflexive relationship between Y on the one hand and {X1, X2} on the other hand. If that is the case, one framework for studying the mechanism of impacts is Structural Vector Autoregression (SVAR). It can be rephrased in an equivalent VAR form.