How to introduce search and matching in NK (or RBC)

I’m looking for introductory bibliography regarding DSGE (RBC or NK baseline) models with search and matching dynamics in the labor market that allows for employment/unemployment explicit modelling.

In the other hand, to my best knowledge Lagrange method for optimization is no longer valid in this kind of problems, and one is forced to use Bellman equation and related theorems for optimality conditions, therefore I’d be thankful if you could provide me some introductory literature, I’ve already checked very superficially Ljungqvist and Sargent’s (2012) “Recursive Macroeconomic Theory”, nevertheless I’m not aware if this book is suitable for self-taught introduction, so I’d like to know if it’s worth to do that with this book.

Last but not least, will equilibrium and optimality conditions resulting from such kind of models be supported by Dynare simulation functions (particularly stoch_simul)?

Many thanks!
PD: I’m aware I’ve asked three questions, I think they can be covered in one topic, yet let me know if I should open different topics for each one of them.

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Have a look at Shimer’s book “Labor Markets and Business Cycles”. Most of it can be done in Dynare.

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Thanks for the reference!

Hi Professor Pfeifer. I checked some of the contents of the book you recommended and the “Nash bargaining” approach took my attention, given that I found this paper of Blanchard and Galí (2010) where they introduce a “cost of hiring” labor market rigidity, which as they say in a footnote (in the published version p.5) is equivalent (to certain degree) to a matching function, but has the advantage of being more tratable mathematically through the Nash bargaining process (this conclusion is from my best understanding). Following that, is this kind of implementation (hiring cost instead of matching function) able to run in Dynare? and if so also I’d be very thankful if you may refer me (if exist) to some examples of this kind of set-up implemented in Dynare. Many many thanks.

Is that the same setup as DSGE_mod/Gali_2010.mod at master · JohannesPfeifer/DSGE_mod · GitHub ?

Indeed looks like fundamentally the same framework! Yet I’m unable to run the code, don’t know if I’m doing something wrong, would appreciate your help, I’m using 4.5.7. I’m sending the logs and exact code (didn’t change anything from the original repository).
Gali_2010_calib_target.mod (12.6 KB)
Gali_2010_calib_target_steadystate.m (4.1 KB)
Gali_2010_steadystate.m (3.5 KB)
Gali_2010.mod (12.0 KB)
Gali_2010_calib_target_log.txt (1.4 KB)
Gali_2010_log.txt (1.4 KB)

Please use Dynare 4.6

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It works flawlessly in 4.6.4, thanks!

Greetings Professor Pfeifer. I’m studying Galí (2010), from where the mentioned code comes. And I’m thinking in two things: i) Whether it is possible to implement the non-log-linear version of the model in Dynare? (to my best knowledge there shouldn’t be any problem for that, so I ask just for checking) ii) If so, the equivalent equation for equations (16) and (17) (in the .mod), corresponding to:

Evolution of real wage (16)
\hat\omega_t = \hat\omega_{t-1}+\hat\pi_{t}^w-\pi_{t}^p

Wage philips curve (17)

One of their equivalent in levels model would be optimal wage FOC (eq. 32 in the book chapter):

E_t\left\{ \sum_{k=0}^{\infty}((1-\delta)\theta_w)^k\Lambda_{t,t+k}\left(\frac{W_{t}^\ast}{P_{t+k}}-\Omega_{t+k|t}^{tar} \right)\right\}=0 (A)

What would be the oher equivalent equation in levels?

My try is that, as in Calvo wages, the general wage will be a weighted sum of both sticky and optimally chosen wages, then assuming that the sticky wage is just the previous period wage:

W_t = \int_{0}^{\theta_w}W_{t-1}dj+\int_{\theta_w}^{1}W_{t}^\ast dj

\implies W_t \equiv\theta_wW_{t-1}+(1-\theta_w)W_{t}^\ast (B)

And therefore I should code (A) and (B) instead of (16) and (17) in the levels version of the model in Dynare (A in a recursive form, of course. And B may should be arranged for expressing real term, but hope I transmit the main idea correctly).

Is that right?

Yes, that seems all correct. DSGE_mod/Derivation_Recursive_Pricing_Equation.pdf at master · JohannesPfeifer/DSGE_mod · GitHub may be helpful in the endeavor

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I would stay away from Gali in this case. I believe a better reference for you would be chapter 8 in Carl Walsh’s monetary theory text. The latest version has a very good introduction to search and matching frictions in a New Keynesian model that also has Calvo price stickiness. That section of the chapter is based on his AEJ paper with Ravenna which is also definitely worth a read.

Thanks for the reference! I’m curious why should not Galí be a good source in this case? What I’m looking for is a way of modelling the labor market explicitly without losing parsimony in the model, actually have found the mentioned Galí (2010, chapter 10) which is similar to the mentioned Blanchard and Galí (2010) a very solid and tratable alternative for this. But maybe here’s a thing “I don’t know that I don’t know”, please share your knowledge.

Nevertheless, I’ll be checking that Walsh chapter.



(cool name, by the way). I think for a first go-through, it is easier to wrap ones mind around the approach Walsh (and others, such as Tristani, Monacelli, etc.) takes. I’ve seen and studied both, but they are not the same.
4edch8.pdf (719.1 KB)

I’ve attached a very early pre-print of the chapter. See section 5.2.

It depends on what you are trying to do. The Galí approach is very tractable, but it’s not truly a search and matching framework as the mentioned other papers.

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@ChrisL, thanks in lack of creativity I chose this name haha. I get it, following that you’d say it’s better to take Walsh as a first approach, but for building a model what would you say are the main pros and cons of one or other compared to Galí? And contrasted with empirical moments do they perform similar or is there one that is superior to the other? (I know is a little bit broad this question, but I hope you know what I mean) Besides, do you know if there’s a Dynare replication of that model of Walsh or similar? Also, thanks for the pre-print.

@jpfeifer Well at the end my final aim is to model labor markets in NK framework with unemployment and informality, actually there’s two main papers (to my best knowledge) with explicit modelling of labor market dynamics that include this aspect, where one uses Blanchard and Galí approach, and the other uses directly search and matching.

The first one is a 2013 working paper, and the latter was published in the Journal of Development Economics, nevertheless this is not the main component of my work, and actually I find more important to be able to replicate empirical second moments.

If you want to meaningfully talk about labor market objects like vacancies, then you obviously need a full search and matching model. The Gali approach is more of a shortcut if you want to talk about involuntary unemployment. If that is all you care about, it may be sufficient.

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May you have any dynare replication of a pure labor market search and matching model that helps understanding basic dynamics? Thanks.

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No, but there must be example in the forum.