# Expectations vs realized

**URL:** <https://forum.dynare.org/t/expectations-vs-realized/6356>\
**Category:** Dynare help (legacy posts)\
**Created:** [15 July 2017 07:53 UTC](https://forum.dynare.org/t/expectations-vs-realized/6356 "2017-07-15T07:53:19Z")\
**Posts on this page:** 1\
**Showing post:** 7

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**Author:** ![KKLS](https://forum.dynare.org/letter_avatar_proxy/v4/letter/k/ecd19e/32.png) [@KKLS](https://forum.dynare.org/u/KKLS)\
**Post date:** [16 July 2017 16:16 UTC](https://forum.dynare.org/t/expectations-vs-realized/6356/7 "2017-07-16T16:16:47Z")

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This post is edited!

1. 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 )

1. 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.  
> A final confirmation. You say ''omega\_{t+1}^{i,a} ‘’ is predetermined. the author of the working paper says in page 5 (printed page 5, electronic page15):
> 
> [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

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