<p>The mathematical theory behind DSGE models can be found in any textbook on stochastic dynamic optimisation.</p>

<p>One common reference that economists use for this is <a href="http://www.hup.harvard.edu/catalog.php?isbn=9780674750968" rel="noreferrer">Stokey, Lucas and Prescott</a>. Of course, they focus exclusively on recursive methods, but (perhaps) the lion’s share of dynamic problems in economics are solved in this way.</p>

<p>There is also a treatment of dynamic optimisation (including non-recursive and/or continuous-time methods) in <a href="https://press.princeton.edu/titles/8764.html" rel="noreferrer">Acemoglu</a>.</p>

CC BY-SA 4.0
2019-11-01T01:12:53.473Z
I agree that Stokey, Lucas & Prescott has the most rigorous approach I've seen, to the point of being extremely dense. They even include a chapter on Measure Theory to justify swapping limits in and out of an integral.
one_teach_wonder
CC BY-SA 3.0
2017-12-04T15:23:11.077Z
2017-12-04T15:23:11.077Z
Theoretical Economist
<p>One I can introduce is &quot; <a href="https://rads.stackoverflow.com/amzn/click/com/0674028147" rel="nofollow noreferrer" rel="nofollow noreferrer"><strong>ABC of RBC</strong></a> &quot;
It was so helpful to me.</p>

CC BY-SA 4.0
2021-03-25T09:45:48.407Z
Hi: Another one is "structural macro-econometrics" by dejong et al but I can't compare it to the other ones because I'm not famiiar with them. It seems pretty good on an absolute level but I haven't gone through all of it either.
mark leeds
CC BY-SA 4.0
2021-03-23T12:24:20.310Z
2021-03-23T12:24:20.310Z
Ali Mehdizadeh
<p>I'm reading David Romer's Macroeconomics. However, what I don't like is that he doesn't go at all into detail about the mathematical underpinnings of RBC/DSGE models. When it comes to the central mathematical parts of these models, such as how to derive and solve an expectational recurrence equation in a mathematically rigorous way, Romer instead treats it very hand-wavy and skips over steps. </p>

<p>Perhaps that is fine for some people, but I would like more mathematical rigour.</p>

<p>However, the problem is that every textbook I've found so far that is about mathematical economics only treats deterministic dynamic models.</p>

<p><strong>So my question is: Is there a good textbook that treats stochastic dynamic models in a mathematically rigorous way?</strong> Note I am NOT talking about the econometric estimation of these models, but merely the purely theoretical treatment of dynamic stochastic models. </p>

<macroeconomics><reference-request><dynamic-optimization><dsge><rbc>
Textbook on the mathematics of RBC/DSGE models?
user56834
# Textbook on the mathematics of RBC/DSGE models?

(Asked by: username_0 on 2017-12-04)

I'm reading David Romer's Macroeconomics. However, what I don't like is that he doesn't go at all into detail about the mathematical underpinnings of RBC/DSGE models. When it comes to the central mathematical parts of these models, such as how to derive and solve an expectational recurrence equation in a mathematically rigorous way, Romer instead treats it very hand-wavy and skips over steps.

Perhaps that is fine for some people, but I would like more mathematical rigour.

However, the problem is that every textbook I've found so far that is about mathematical economics only treats deterministic dynamic models.

**So my question is: Is there a good textbook that treats stochastic dynamic models in a mathematically rigorous way?** Note I am NOT talking about the econometric estimation of these models, but merely the purely theoretical treatment of dynamic stochastic models.

**Tags:** macroeconomics, reference-request, dynamic-optimization, dsge, rbc

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## 2 answers

### Answer by username_1 on 2017-12-04. Score: 7

The mathematical theory behind DSGE models can be found in any textbook on stochastic dynamic optimisation.

One common reference that economists use for this is [Stokey, Lucas and Prescott](http://www.hup.harvard.edu/catalog.php?isbn=9780674750968). Of course, they focus exclusively on recursive methods, but (perhaps) the lion’s share of dynamic problems in economics are solved in this way.

There is also a treatment of dynamic optimisation (including non-recursive and/or continuous-time methods) in [Acemoglu](https://press.princeton.edu/titles/8764.html).

> **Comments:**
> **username_2**: I agree that Stokey, Lucas & Prescott has the most rigorous approach I've seen, to the point of being extremely dense. They even include a chapter on Measure Theory to justify swapping limits in and out of an integral.  

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### Answer by username_3 on 2021-03-23. Score: 1

One I can introduce is " [**ABC of RBC**](https://rads.stackoverflow.com/amzn/click/com/0674028147) "
It was so helpful to me.

> **Comments:**
> **username_4**: Hi: Another one is "structural macro-econometrics" by dejong et al but I can't compare it to the other ones because I'm not famiiar with them. It seems pretty good on an absolute level but I haven't gone through all of it either.  

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