I’m having some trouble with the volatilities and the IRF of a working capital model, The IRF of a variable is discontinuous, and standard deviation of investment is too low while capital is too high.

What is your version of Dynare? I do not observe anything wrong, except for the IRF of rn with respect to e_lambda which is noisy (but of the order 10^{-7} so I am not sure it is significant). You can reduce the noise by increasing the value of the replic option of stoch_simul (see the reference manual).

I’m using Dynare 4.5.3. I think it’s solved the IRF of rn. But the std of Inv is quite low, and k is quite high. I think dynare is interpreting inv as control and k as state.

You are currently looking at absolute deviations from steady state, not percentage deviations. As the steady state level of capital is much higher than the one of capital, the fluctuations in absolute terms are also bigger.