Two Country Model- Technology shocks are too persistent

Hello everybody! I am currently trying to solve a two country model by using the algorithm of devereux and sutherland 2007. To determine the steady state portfolio, one needs to rewrite the model in a specific way, take the steady state portofolio component as given and determine the policy and transition functions (I am particularly interested in dynamics of consumption in period t+1). I am trying to achieve this with dynare. Unfortunately I am not really happy with my output. Firstly, dynare reports nonzero coefficients on some of the state variables for excess return which is iid. All coeffcients are small in magnitude though. Can I interpret this as approximation error? Secondly the technology shock has a particularly persistent effect among others on capital (stst is reached after 1000 periods…). I am wondering what is the cause for this persistence. Maybe it is one of the eigenvalues which is equal to 0.995. …