# Replication of Bilbiie, Melitz 2007 with actual prices

**URL:** <https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698>\
**Category:** Replication Attempts\
**Created:** [6 November 2024 19:27 UTC](https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698 "2024-11-06T19:27:44Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Oscarernst](https://forum.dynare.org/letter_avatar_proxy/v4/letter/o/87869e/32.png) [@Oscarernst](https://forum.dynare.org/u/Oscarernst)\
**Post date:** [6 November 2024 19:27 UTC](https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698/1 "2024-11-06T19:27:45Z")

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Hi everyone.

I am trying to replicate their paper from 2007, using actual producer prices and consumer prices rather than the relative price. I run into some trouble, as I get a price of approximately 0 for both, but a realistic relative price. Since the actual prices are non-stationary, shocks etc, results in prices never returning to SS.

Is there a method, to fix this problem and model both the relative price, and the actual price?

Best regards  
[Model\_actual\_price.mod](https://forum.dynare.org/uploads/short-url/hc5j42qLtMbRVJYfeXYR8yB7jlY.mod) (3.4 KB)  
[19893231.pdf](https://forum.dynare.org/uploads/short-url/ig4HQn5vcVmHvm1NthCRdYodjfX.pdf) (37.1 KB)

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**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 November 2024 13:29 UTC](https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698/2 "2024-11-07T13:29:23Z")

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If the model has a unit root in prices, then only the relative price is uniquely determined. That means there are infinitely many steady states for the price levels. Numerically searching for one will then pick an arbitrary one. This is a case where you need to provide an analytical steady state.

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**Author:** ![Oscarernst](https://forum.dynare.org/letter_avatar_proxy/v4/letter/o/87869e/32.png) [@Oscarernst](https://forum.dynare.org/u/Oscarernst)\
**Post date:** [7 November 2024 14:01 UTC](https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698/3 "2024-11-07T14:01:07Z")

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Thanks a lot. I intent to open up the model and implement it in a SOE. But in this case, I would need the actual domestic prices, the find the aggregate price level. Would I just be able to choose some arbitrary prices that satisfy the relative prices then?

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**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 November 2024 14:28 UTC](https://forum.dynare.org/t/replication-of-bilbiie-melitz-2007-with-actual-prices/26698/4 "2024-11-07T14:28:04Z")

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Part of my reply was swallowed. I restored it above.