In a DSGE model, monetary policy shock (Taylor rule style) increases interest rate. So output and inflation falls, which feedback contemporaneously to the interest rate. Thus, interest rate ($i_t$) rises after the shock, output ($y_t$) and inflation ($\pi_t$) falls contemporaneously, which feedback at period $t$ to interest rate via the Taylor rule ($i_t = f(y_t,\pi_t, ...)$). So the final change in $i_t$ is ambiguous depending how strong the feedback is. Thus, $i_t$ can even fall.
But we can not study such a contemporaneous feedback relationship using an empirical-reduced-form model, right? In a VAR, there is only lagged feedback. In SVAR, you have to place zero contemporaneous restrictions on a trivariate model of $i_t$, $y_t$ and $\pi_t$ otherwise you will have unidentified SVAR model, right?
So I guess in SVAR, you have to choose which variables affects others contemporaneously. And there is no way to make all variables affect each other contemporaneously, right? Or perhaps there is a model to study such contemporaneous relationships?
Oy maybe one can use single equation models like distributed lags? But that makes strong exogeneity assumptions that may not hold, right...although I see people using it.
The only alternative is DSGE?
I have a similar problem like that, but with different variables. Domestic commodity production affects world prices since economy is second largest producer, but world prices also affects domestic production since individual firms are price takers. I can model that maybe in a two-country DSGE model...but I guess it is not possible in a reduced form model. Or may be it is?