KKLS
July 16, 2017, 4:16pm
7
This post is edited!
You say :
It is really a matter of timing. In equations 8 and 9, q_t, K_{t+1}^i, and L_t+1^i and omega_{t+1}^{i,a} are contained in the information set at time t, i.e. known at time t. The latter three are actually predetermined variables (loan stock, capital stock, ex-ante return). The only difference is the return to capital.
In equation 8, you have E_t(R_{t+1}^k). This expected values is known at time t as well, making the whole right-hand side known at time t. Thus, R_{t+1}^L on the left should actually get the timing R_t^L in Dynare, because it is contained in this information set.
Let me assume that I do not use the predetermined_variables command (hence K_t = (1-delta) K_(t-1) + INV_t )… then all the terms in equation (8) will be written with subscript (t), except for ‘’ Rk_t+1 ‘’ which will take the subscript ‘‘t+1’’ in Dynare ? Correct ??
RL_t = Rk_t+1 * omega_t * q_t *K_t *L_t (eq. 8 )
Question: Then in the last paragraph:
In contrast, equation (you meant 9) contains an R_{t+1}^k, implying the R_{t+1}^L is only contained in the information set at time t+1. But we are not trying to define an expected lending rate at time t, but the actual lending rate at time t (remember, we are defining a recursive equilibrium system to pin down variables at time t, not t+1). To make this equation state-contingent, i.e. hold for every single state realization, you have to shift the whole equation by one period to the past. You will then have an equation defining R_t^L and linking it to R_t^k and a bunch of predetermined variables.[/quote]
The way I understand this is (assuming I do not use predetermined_variables command), I should write in Dynare :
RL_t = Rk_t * omega_t * q_t-1 *K_t-1 *L_t-1 (eq. 9)
Is this reading correct ?
If it is then I will not be able to derive equation (12) in the working paper (in page 8 in print, or page 18 in electronic numbering)
Question 3.
[quote] where expectations are taken with respect to the random variable Rk_t+1, and ω^i_t+1 is a function of realization of Rk_t+1 (and therefore, function of the states).
Is he trying to say exactly this: that ''omega_{t+1}^{i,a} ‘’ is predetermined ? Unlike in BGG original paper who take expectations w.r.t both, ''omega_{t+1}^{i,a} ‘’ and ‘‘Rk_t+1’’.
Am I reading it right ?
Regards