Here, epsilon is the shock and I computed the variable log(Yj) in dynare. I’m wondering if this expression is equal to logYj_esp_i(1) (first value of my IRF after simulation)

Thanks professor, but I’m not sure I get what you want to explain. In a system linearized at first order with a Taylor expansion (such as in Dynare if the option order=1 is put in the stoch_simul command), isn’t the first value of the IRF vector of a variable the same thing as the derivative evaluated at the steady state ?

Yes, it is the derivative w.r.t the current shock. But due to linearity it does not matter under which initial condition you evaluate the partial derivative. In other words, the partial effect of a shock is always the same in a linear model.