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• Thread: 62 Goods vs 13 No Goods

1. Economist
   69a0
   

   Continuous time can sometimes give you closed form solutions for stuff, which is nice. Moving to the computer is a little harder, though. Besides that, they're pretty similar. Maybe get comfortable with Hamilton Jacobi Bellman equations and viscosity solutions?

   That's the problem with continuous-time stuff, it's a big investment. Getting comfortable with HJB and viscosity solutions will take time if you don't have a good background in stochastic calculus...

   What? You can solve HJBs and find viscosity solutions without any stochastic calculus. Conversely, you can do stochastic calculus without touching HJBs or viscosity solutions. (Of course, if you’re doing stochastic calculus in economics, you will probably need an HJB, or even a viscosity solution, but my point stands.)

   This post conflates two different things that are separate.

   3 years ago # QUOTE 0 Volod 0 Vlad !

2. Economist
   69a0
   

   To be clear, my point is that HJBs and viscosity solutions are understood when studying PDEs and optimal control problems, and you need little to no stochastic calculus to do this.

   3 years ago # QUOTE 0 Volod 0 Vlad !

3. Economist
   e468
   

   Ps. This means that you should do discrete. Langrangians are easier than Hamiltonians and more computer friendly.

   You can do discrete-time Hamiltonians and Lagrangians aren’t easier just more familiar

   3 years ago # QUOTE 0 Volod 0 Vlad !

4. Economist
   e555
   

   Continuous time can sometimes give you closed form solutions for stuff, which is nice. Moving to the computer is a little harder, though. Besides that, they're pretty similar. Maybe get comfortable with Hamilton Jacobi Bellman equations and viscosity solutions?

   That's the problem with continuous-time stuff, it's a big investment. Getting comfortable with HJB and viscosity solutions will take time if you don't have a good background in stochastic calculus...

   What? You can solve HJBs and find viscosity solutions without any stochastic calculus. Conversely, you can do stochastic calculus without touching HJBs or viscosity solutions. (Of course, if you’re doing stochastic calculus in economics, you will probably need an HJB, or even a viscosity solution, but my point stands.)
   This post conflates two different things that are separate.

   Yes of course but who cares, this is an economics forum... I mentioned HJB because above poster did so, but uf you insist, I should have said "learning optimal control in continuous-time take time". And if OP comes from econ undergrad, I don't think it's worth it now, unless there is a special idea in mind.

   3 years ago # QUOTE 0 Volod 0 Vlad !

5. Economist
   5af8
   

   Continuous time can sometimes give you closed form solutions for stuff, which is nice. Moving to the computer is a little harder, though. Besides that, they're pretty similar. Maybe get comfortable with Hamilton Jacobi Bellman equations and viscosity solutions?

   That's the problem with continuous-time stuff, it's a big investment. Getting comfortable with HJB and viscosity solutions will take time if you don't have a good background in stochastic calculus...

   What? You can solve HJBs and find viscosity solutions without any stochastic calculus. Conversely, you can do stochastic calculus without touching HJBs or viscosity solutions. (Of course, if you’re doing stochastic calculus in economics, you will probably need an HJB, or even a viscosity solution, but my point stands.)
   This post conflates two different things that are separate.

   Yes of course but who cares, this is an economics forum... I mentioned HJB because above poster did so, but uf you insist, I should have said "learning optimal control in continuous-time take time". And if OP comes from econ undergrad, I don't think it's worth it now, unless there is a special idea in mind.

   My research agenda (OP here) is heterogeneous agents models (I am interested in the incorporation of a richer description of firms' portfolio choice and financial sector (especially maturity transformation) to these models). Because I know, that these models are computationally very challenging, If you want to build something bigger & more realistic, and hence I get interested in continuous time, because (according to people like JFV, Judd, Moll,...) it allows to solve these models much more efficiently than what you can achieve in discrete-time settings.

   3 years ago # QUOTE 0 Volod 0 Vlad !

6. Economist
   2edd
   

   does Ken Juddd really favor continuous time?

   3 years ago # QUOTE 0 Volod 0 Vlad !

7. Economist
   5af8
   

   does Ken Juddd really favor continuous time?

   http://ice.uchicago.edu/2008_presentations/Judd/Curse_in_Dallas.pdf From this and also his work on integrated assessment models I would guess, that definitely yes.

   3 years ago # QUOTE 0 Volod 0 Vlad !

8. Economist
   9e35
   

   I prefer a continuous-discrete hybrid approach.

   3 years ago # QUOTE 0 Volod 0 Vlad !

9. Economist
   99e3
   

   The sequence-space business of ABRS is discrete time and wildly outperforms any existing method (https://github.com/shade-econ/sequence-jacobian)

   3 years ago # QUOTE 0 Volod 0 Vlad !

10. Economist
    a2b9
    

    That is why I am asking whether it is a good investment (my interest is heterogeneous agents macro, and because of having econ undergrad, I had next-to-no experience with stochastic calculus) to learn these techniques, or simply save time, and focus on other things.

    holy s**t it's that troll from around a year or two ago that used to always ask about continuous time macro. Did you get into PSU or what?

    3 years ago # QUOTE 0 Volod 0 Vlad !

11. Economist
    8691
    

    People have been moving to continuousv time for computational reasons

    Example?

    2 years ago # QUOTE 0 Volod 0 Vlad !

12. Economist
    26e1
    

    When you have sample size of ten or less that's a very important question indeed

    2 years ago # QUOTE 0 Volod 0 Vlad !

13. Economist
    d669
    

    I have papers in both. In each case, the model I used was the more tractable one. There's no meaningful difference beyond tractability, unless you're an a$$hat who wants to take your models very literally.

    2 years ago # QUOTE 0 Volod 0 Vlad !

14. Economist
    75f2
    

    I don't know much about what you are asking (not my field), but I can give you a piece of advice: don't ever take decisions based on what is written in EJMR. Talk to your advisor or profs working on that area in your dept.

    This post saved OP's career.

    1 year ago # QUOTE 0 Volod 0 Vlad !

15. Economist
    c8f2
    

    So is cts-time worth the effort? Moll et al still seem to champion it, but I just saw this: https://www.sciencedirect.com/science/article/pii/S0165188922002263
    and it seems to imply the computational benefits are illusory?

    2 months ago # QUOTE 0 Volod 0 Vlad !

16. Economist
    3aca
    

    So is cts-time worth the effort? Moll et al still seem to champion it, but I just saw this: https://www.sciencedirect.com/science/article/pii/S0165188922002263
    and it seems to imply the computational benefits are illusory?

    All continuous-time models need to be discretized before being brought in contact with data. Is this new?

    2 months ago # QUOTE 1 Volod 0 Vlad !

17. Economist
    c8f2
    

    So is cts-time worth the effort? Moll et al still seem to champion it, but I just saw this: https://www.sciencedirect.com/science/article/pii/S0165188922002263
    and it seems to imply the computational benefits are illusory?

    All continuous-time models need to be discretized before being brought in contact with data. Is this new?

    I was under the impression that cts-time was much faster (based on Moll et al pushing it) but I never invested the time to understand it. The above paper claims that it isn't faster it seems? Just exploit sparseness in the discrete-time setting and you get all the benefits of cts-time without the technical stuff?

    2 months ago # QUOTE 0 Volod 0 Vlad !

18. Economist
    3aca
    

    So is cts-time worth the effort? Moll et al still seem to champion it, but I just saw this: https://www.sciencedirect.com/science/article/pii/S0165188922002263
    and it seems to imply the computational benefits are illusory?

    All continuous-time models need to be discretized before being brought in contact with data. Is this new?

    I was under the impression that cts-time was much faster (based on Moll et al pushing it) but I never invested the time to understand it. The above paper claims that it isn't faster it seems? Just exploit sparseness in the discrete-time setting and you get all the benefits of cts-time without the technical stuff?

    Intuitively why would it make a difference whether you discretize a continuous model or model it in discrete time from the start? "Continuous time claims to be faster" sounds like a strawman to me.

    2 months ago # QUOTE 1 Volod 0 Vlad !

19. Economist
    c8f2
    

    So is cts-time worth the effort? Moll et al still seem to champion it, but I just saw this: https://www.sciencedirect.com/science/article/pii/S0165188922002263
    and it seems to imply the computational benefits are illusory?

    All continuous-time models need to be discretized before being brought in contact with data. Is this new?

    I was under the impression that cts-time was much faster (based on Moll et al pushing it) but I never invested the time to understand it. The above paper claims that it isn't faster it seems? Just exploit sparseness in the discrete-time setting and you get all the benefits of cts-time without the technical stuff?

    Intuitively why would it make a difference whether you discretize a continuous model or model it in discrete time from the start? "Continuous time claims to be faster" sounds like a strawman to me.

    Ok well perhaps I'm missing something basic, but wasn't the whole point of Moll et al's recent lectures and ReStud paper that one could avoid all sorts of bottlenecks by utilizing methods from PDE theory instead of the "usual" discrete-time DP we all know (e.g. SLP)? The above paper seems to claim that if one just exploits sparseness in the discrete-time formulation then all of this new PDE math doesn't speed things up? At least that's how I interpret the intro and abstract.

    2 months ago # QUOTE 0 Volod 0 Vlad !

20. Economist
    7f29
    

    I think one computational advantage in continuous time is that you lose the today/tomorrow distinction, and thus you roughly speaking remove one variable and achieve sparsity.

    What is less clear to me is how stochastic shocks, which are necessarily discrete are integrated in the framework. One can use jump processes I suppose but then some of the elegance seems to be lost.

    2 months ago # QUOTE 0 Volod 0 Vlad !

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