All the variables that are known or determined before period t should be subscripted as time t variable. A typical example is the capital k in basic RBC model. The resource constraint is:
k(t+1) = A*k(t) - c(t)
In dynare, we should express k as predetermined variable. So the model part equation should be expressed as:
k = A*k(-1) - c
My question is, what if the capital stock k(t+1) undergoes an exogenous shock at the beginning of period t+1, as if:
k(t+1) = s(t+1)(Ak(t)-c(t))
(1) Under this condition, at the begining of peiod t+1, k seems determined at period t, so the dynare equation should be
k(+1) = s(+1)(Ak - c)Under this condition, at the beginning of period t+1, k seems determined at period t, so the dynare equation should be
k(+1) = s(+1)(Ak - c)a
(2) or we just express k as the end of period variable as before as
k = s(+1)(Ak(-1)-c)
Which one should be right, (1) or (2)? Anybody can help me figure it out?
According to my understanding, your example consider k as non predetermined variable for this case. Am I right?
Let’s write down the formula. At the beginning of period t+1, capital undergoes an exogenous shock. So
k(t+1) = exp(-eps_cap(t+1))*(invest(t) + (1-delta)*k(t))
What you are doing is to just consider k as non-predetermined because the value of capital is the outcome of both the exogenous shock of t+1 and the time t variables i(t) and k(t).
In dynare, what you are doing is just move the time backward by one period that
k = exp(-eps_cap)*(invest(-1) + (1-delta)*k(-1))
But, I am still confused about this. You see in the model k(t+1)/exp(-eps_cap(t+1)) is still determined in period t but has subscrpit t+1 so this whole formula should be predetermined at period t
k(t+1)/exp(-eps_cap(t+1)) = invest(t) + (1-delta)*k(t)
Would you please point out my reasoning mistake here?
In my original question, I consider k as predetermined. So express kt as k(t-1) in dynare but keep the shock still at t+1. So my version of your setup is:
k = exp(-eps_cap(+1))*(invest + (1-delta)*k(-1))
According to my understanding, your example consider k as non predetermined variable for this case. Am I right?
Let’s write down the formula. At the beginning of period t+1, capital undergoes an exogenous shock. So
k(t+1) = exp(-eps_cap(t+1))*(invest(t) + (1-delta)*k(t))
What you are doing is to just consider k as non-predetermined because the value of capital is the outcome of both the exogenous shock of t+1 and the time t variables i(t) and k(t).
In dynare, what you are doing is just move the time backward by one period that
k = exp(-eps_cap)*(invest(-1) + (1-delta)*k(-1))
But, I am still confused about this. You see in the model k(t+1)/exp(-eps_cap(t+1)) is still determined in period t but has subscrpit t+1 so this whole formula should be predetermined at period t
k(t+1)/exp(-eps_cap(t+1)) = invest(t) + (1-delta)*k(t)
Would you please point out my reasoning mistake here?
k(t+1)/exp(-eps_cap(t+1)) is not determined at time t as you write. If it were, you would know the value of the capital quality shock eps_cap when decisions like consumption are made.