<p>I have a question regarding the NKPC. I would like to know if it is possible to derive the NKPC from a sticky prices model, without making assumptions regarding the production function firms face. I am trying to estimate an open economy NKPC. As far as I am concerned, much of the extensions of the NKPC for the open economy involve substituting the commonly used Cobb-Douglas function for  another one which explicitly incorporates imported goods. Some examples of this approach are  <a href="https://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/01/Fic/dt0109e.pdf" rel="nofollow noreferrer">Galí and López-Salido</a>, <a href="https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness" rel="nofollow noreferrer">Balakrishnan and López-Salido</a>,  and <a href="https://link.springer.com/article/10.1007/s11079-007-9028-6" rel="nofollow noreferrer">Rumler</a>. However, almost all of the the derivations of the NKPC assume that firms face a Cobb-Douglass production function, as you can see in <a href="https://www.sciencedirect.com/science/article/abs/pii/S0304393299000239" rel="nofollow noreferrer">Gali and Gertler</a>, <a href="https://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/01/Fic/dt0109e.pdf" rel="nofollow noreferrer">Galí and López-Salido</a>, <a href="https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness" rel="nofollow noreferrer">Balakrishnan and López-Salido</a>, <a href="https://b-ok.lat/book/5329009/5a8c0b" rel="nofollow noreferrer">Romer</a>, and <a href="https://b-ok.lat/book/873271/6033fc" rel="nofollow noreferrer">Galí</a>. Wouldn´t there be a contradicction if (this is the approach followed by <a href="https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness" rel="nofollow noreferrer">Balakrishnan and López-Salido</a>), one assumes that firms face a Cobb-Douglas function but at the aggregate level one assumes a different production function, such as a CES production function that incorporates imported inputs? I am having trouble with reconciling the assumption of different production functions. Because of this apparent contradiction, I thought that, if it is posibble to derive the NKPC from a sticky prices model without assuming a Cobb-Douglass production function (or any other production function for that matter), I could easily bypass the problem.  Hope I made my case clear. Thank you in advance!</p>
<p>P.S. I know that <a href="https://link.springer.com/article/10.1007/s11079-007-9028-6" rel="nofollow noreferrer">Rumler</a> derives a NKPC assuming just a CES  production function. However, I havent been able to understand exactly how he estimated the coefficients of his model nor what variables he actually used. For an undergradute such as me, estimating such a model seems to be out of reach. However, if someone is willing to give me a hand, I would really appreciate it. Thank you!</p>

CC BY-SA 4.0
2021-04-13T20:43:19.590Z
Hi. Welcome to Econ Stack Exchange. Try not to use abbreviations unless you first define them. This helps with discoverability with search engines, not to mention the average reader.
jmbejara
CC BY-SA 4.0
2021-04-15T01:48:30.087Z
Hi, I am sorry, I didn't notice I hadn't. I have fixed it. Thanks!
Daniel José Aguilar
<macroeconomics><inflation><new-keynesian-economics><dsge>
Deriving the New Keynesian Phillips Curve (NKPC)
Daniel José Aguilar
# Deriving the New Keynesian Phillips Curve (NKPC)

(Asked by: username_0 on 2021-04-13)

I have a question regarding the NKPC. I would like to know if it is possible to derive the NKPC from a sticky prices model, without making assumptions regarding the production function firms face. I am trying to estimate an open economy NKPC. As far as I am concerned, much of the extensions of the NKPC for the open economy involve substituting the commonly used Cobb-Douglas function for another one which explicitly incorporates imported goods. Some examples of this approach are [Galí and López-Salido](https://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/01/Fic/dt0109e.pdf), [Balakrishnan and López-Salido](https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness), and [Rumler](https://link.springer.com/article/10.1007/s11079-007-9028-6). However, almost all of the the derivations of the NKPC assume that firms face a Cobb-Douglass production function, as you can see in [Gali and Gertler](https://www.sciencedirect.com/science/article/abs/pii/S0304393299000239), [Galí and López-Salido](https://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/01/Fic/dt0109e.pdf), [Balakrishnan and López-Salido](https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness), [Romer](https://b-ok.lat/book/5329009/5a8c0b), and [Galí](https://b-ok.lat/book/873271/6033fc). Wouldn´t there be a contradicction if (this is the approach followed by [Balakrishnan and López-Salido](https://www.bankofengland.co.uk/working-paper/2002/understanding-uk-inflation-the-role-of-openness)), one assumes that firms face a Cobb-Douglas function but at the aggregate level one assumes a different production function, such as a CES production function that incorporates imported inputs? I am having trouble with reconciling the assumption of different production functions. Because of this apparent contradiction, I thought that, if it is posibble to derive the NKPC from a sticky prices model without assuming a Cobb-Douglass production function (or any other production function for that matter), I could easily bypass the problem. Hope I made my case clear. Thank you in advance!

P.S. I know that [Rumler](https://link.springer.com/article/10.1007/s11079-007-9028-6) derives a NKPC assuming just a CES production function. However, I havent been able to understand exactly how he estimated the coefficients of his model nor what variables he actually used. For an undergradute such as me, estimating such a model seems to be out of reach. However, if someone is willing to give me a hand, I would really appreciate it. Thank you!

**Tags:** macroeconomics, inflation, new-keynesian-economics, dsge
> **Comments:**
> **username_1**: Hi. Welcome to Econ Stack Exchange. Try not to use abbreviations unless you first define them. This helps with discoverability with search engines, not to mention the average reader.  
> **username_0**: Hi, I am sorry, I didn't notice I hadn't. I have fixed it. Thanks!  

---

## 0 answers

