I would like to set an initial value for one of my endogenous model variables at the beginning of the Kalman smoother. Therefore, I use the “filter_initial_state”-Block of Dynare. For instance, my endogenous variable is named k. If I were to set k(0) = 5 within the “filter_initial_state”-Block, does that mean, that I specified the mean of the initial state to 5? If yes, is it also possible to set the variance of the initial state? Or does this imply that when I look at the smoothedVariables output of Dynare that k starts at value 5?

By default, the Kalman filter is initialized at the steady state with the unconditional variance of the states. With the filter_initial_state you can alter the mean of this initialization. We do not have a interface for altering the variance.

But that does not fix the smoother mean for the first period to a particular value. First of all, we are talking about the initial value before the first observation. Second, the smoother does a forward and a backward pass. The latter will also alter out best estimate of the initial condition.