Dear Forum,
In my model I am using t-1 as the timing convention for the capital input in the production function i.e. Y_t = A_t K_{t-1}^{\alpha}N_{t}^{1-\alpha} and the capital accumulation equation is K_t = (1-\delta)K_{t-1}+ S_tK_{t-1} where S_t = S \biggl(\frac{I_t}{K_{t-1}}\biggr) is the capital adjustment cost. Now if I write my model like this in dynare i.e. writing the capital accumulation equation as mentioned above, I get an error ‘BK Condition not satisfied’ and my model doesn’t run. On the other hand, if I just shift the capital accumulation equation one period ahead, like this K_{t+1}= (1-\delta)K_t+ S_{t+1}K_t, the model runs. I have not changed any other equations. Can some one explain why this is the case and also is it legit to do?
There is one unique timing. If the correct initial timing results in a violation of the Blanchard Kahn conditions, then there must be a mistake somewhere else. You cannot fix it by simply altering the correct timing of the law of motion for capital. That will correct the number of unstable eigenvalues, but will result in wrong model dynamics.