# End of period convention and decision lag

**URL:** <https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014>\
**Category:** Replication Attempts\
**Created:** [4 February 2017 19:56 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014 "2017-02-04T19:56:25Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![miked](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/ed655f/32.png) [@miked](https://forum.dynare.org/u/miked)\
**Post date:** [4 February 2017 19:56 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/1 "2017-02-04T19:56:25Z")

</div>

I am trying to replicate the model Trigari (2009) “Equilibirum Unemployment, Job Flows, and Inflation Dynamics”. The code is running and the impulse responses look quite similar, but now I am actually wondering whether I have made a mistake with respect to the timing convention of state variables.

Trigaris model features the following law of motion for employment:

```auto
n_t =(1-rho_{t-1})n_{t-1}+m_{t-1}
```

The number of employed workers at the beginning of period n\_t are those employed workers n\_{t-1} who are not separated endogenously with prob rho\_{t-1}, in addition to new matches formed m\_{t-1}.  
I have typed this equation and all the others where n features into dynare without changing the timing, and the code runs.  
But in staying true with the end of period convention of dynare, shouldn’t the law of motion for employment in the code look like this:

```auto
n_{t-1} =(1-rho_{t-1})n_{t-2}+m_{t-1}
```

since the level of employment at the beginning of date t is actually decided at date t-1 right?  
However, using this line in dynare, in addition to lagging n in all the other equations, results in the Blanchard Kahn conditions not being satisfied.  
What am I not seeing here?

Another thing:  
Trigari makes a limited information assumption following Rotemberg and Woodford (1997) that households make their choices about consumption,pricing,separation, vacancy posting at date t with the information available at time t-2.  
This is done ino order to better compare the impulse responses to VAR estimates of a monetary policy shock, where a similar identifying restriction was made.  
First does this change anything besides delaying all the impulse responses in response to the shock by 2 periods? To my eyes, apart from that delay my impulse responses look very similar.  
If it does, can I implement it in dynare somehow?

Thanks for your help!

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [5 February 2017 17:14 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/2 "2017-02-05T17:14:44Z")

</div>

Actually, from what you describe, I think the law of motion for n should be

```auto
n_t =(1-rho_{t})n_{t-1}+m_{t}
```

You inherit employment n\_{t-1} from the previous period, some matches dissolve based on rho\_t and you get new matches m\_t. This is similar to the law of motion for capital. Alternatively, you could shift the whole equation by 1 period:

```auto
n_{t+1} =(1-rho_{t})n_{t}+m_{t}
```

and use

```auto
predetermined_variables n
```

Regarding the limited information assumption, you need to change the information set of the expectations operator in Dynare. You can use the `EXPECTATION(-2)` operator for that (see the manual). You can see the change in timing in the working paper version at  
[ecb.europa.eu/pub/pdf/scpwps/ecbwp304.pdf?0ea454554115cfcd977fa9cc2bd4b493](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp304.pdf?0ea454554115cfcd977fa9cc2bd4b493)

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<div class="post-metadata">

**Author:** ![miked](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/ed655f/32.png) [@miked](https://forum.dynare.org/u/miked)\
**Post date:** [7 February 2017 15:51 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/3 "2017-02-07T15:51:08Z")

</div>

Thanks for your help, I had no idea the limited information assumption would be so easy to implement.  
I will also play around a bit more with the law of motion and see what happens, thanks for the tips!

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [7 February 2017 17:56 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/4 "2017-02-07T17:56:07Z")

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If you manage to replicate the paper, could you please provide me with the mod-file

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<div class="post-metadata">

**Author:** ![miked](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/ed655f/32.png) [@miked](https://forum.dynare.org/u/miked)\
**Post date:** [25 February 2017 19:08 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/5 "2017-02-25T19:08:32Z")

</div>

Here is the replication so far:  
Several warnings:

1. The information given in the paper( targeted steady state values and chosen parameters) yields negative unemployment benefits from the steady state relationships (b=-0.02), as opposed to a value of around 0.08 consistent with the replacement rate b/(w\*h)=0.1 given in the paper.
2. At first I typed in the loglinearized system of equations as it is given in the working paper, but the impulse responses for vacancy creation and destruction looked very different. So I did the loglinearizations myself which yielded slightly different equations for vacancy posting and job destruction. Now, surprisingly the impulse responses are a lot closer.  
The author unfortunately hasn’t answered so far.

Also I’m still not sure that I have wrapped my head around the timing thing:  
So again the model features this equation:

```auto
n_t =(1-rho_{t-1})n_{t-1}+m_{t-1}
```

The number of employed workers at the beginning of period n\_t are those employed workers n\_{t-1} who are not separated endogenously with prob rho\_{t-1}, in addition to new matches formed m\_{t-1}.  
To implement it in dynare I have used your first suggestion

```auto
n_t =(1-rho_{t})n_{t-1}+m_{t}
```

Now I have to think of the stock of employment n\_t as the end of period stock in the code equivalent to the beginning of period stock in the model, and this is why the impulse response of n in dynare now shows an immediate jump, correct?

The model also features an equation for the amount of searching workers u\_t

```auto
u_t =1- (1-rho_{t})n_{t}
```

In words: the amount of searching workers at the beginning of period t, u\_t includes those that separate from from firms at the beginning of period t and start searching for work in the same period.

In the code I did this through

```auto
u_t =1- (1-rho_{t})n_{t-1}
```

And I changed the timing of n in all other equations as well…  
I don’t understand why doing this had no effect in the model except shifting the impulse response of n by one period.  
[trigarit09.mod](https://forum.dynare.org/uploads/default/original/2X/d/dc9a04f58eb0ce78a39d2f4e714ebce841f645cd.mod) (5 KB)

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [9 March 2017 07:26 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/6 "2017-03-09T07:26:24Z")

</div>

Hi,  
I sent you the Appendix to the paper via PM.

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<div class="post-metadata">

**Author:** ![binwang4](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/85f322/32.png) [@binwang4](https://forum.dynare.org/u/binwang4)\
**Post date:** [15 September 2018 13:26 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/7 "2018-09-15T13:26:06Z")

</div>

Have you ever figured out this issue? I am also confused about the timing of search and matching model. Should n and u be predetermined?

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [16 September 2018 08:04 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/8 "2018-09-16T08:04:15Z")

</div>

There is no general answer as papers differ with respect to the timing structure they embed, i.e. when jobs come online and separations occur.

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<div class="post-metadata">

**Author:** ![binwang4](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/85f322/32.png) [@binwang4](https://forum.dynare.org/u/binwang4)\
**Post date:** [16 September 2018 08:29 UTC](https://forum.dynare.org/t/end-of-period-convention-and-decision-lag/6014/9 "2018-09-16T08:29:07Z")

</div>

Yes, I just ask a similar question but use the basic rbc model as an example. Would you please take a look?

> [@About the predetermined and non predetermined variable](https://forum.dynare.org/t/about-the-predetermined-and-non-predetermined-variable/12417):
>
> 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 thi…