Relationship between stock/state and flow variable

I have a general modeling doubt.
Suppose I is the investment and X is stock.

Now there are two ways to represent the relationship between the two (assuming no depreciation):

First case:

X(+1) = I + X


Second case:

X = I + X(-1)

Are these equivalent? How to choose between the two? I think in first case X is pre-determined, while in the second case it is not. Am I right?

No, the two are not equivalent. In the first case, the investment in this period only adds to the capital stock next period, while in the second case, it adds to the capital stock right now.
Two additional remarks:

  1. The economic meaning would still depend on how capital is used in the rest of the model
  2. In Dynare, the first case would have a different interpretation, because the X(+1) actually means E_t(X_{t+1}).
  3. The two timing conventions are equivalent if you use the predetermined_variables-command. See the manual

Ok, Thank you, just a follow up:

I am attaching my .mod file. It runs when K_g is not pre-determined. But when I make it pre-determined Blanchard conditions are not satisfied.

Can you suggest what is wrong!!?

MSP_more_refined.mod (13.3 KB)

Now I have simplified my model greatly, but now my equations are lesser than variables.I have checked but not able to find why!!

easy_MSP.mod (4.2 KB)

Sorry, but this is a problem you need to solve on your own. You are the only person who knows what the 40 variables are and which equations are involved in the model.