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• Thread: 62 Goods vs 13 No Goods

1. Economist
   5af8
   

   Hi,

   first-year Ph.D. student here. I would like to ask you guys about your opinion about continuous vs discrete-time methods in macro. In my macro-classes, we are covering standard discrete-time methods ala SLP, LS,... I saw a few continuous time models during my undergrad, but just deterministic ones (class followed Romer's Advanced macroeconomics, so, there was Ramsey & some Endogenous growth models). Intuitively, I prefer discrete-time models, because of their intuitive nature (today/tomorrow distinction, contraction mapping arguments,...), however from reading literature, I get an impression, that frontier is moving back towards continuous-time methods.
   Many people, that I respect a lot (JFV, Ken Judd, Ben Moll,...) are highlighting spectacular computational advantages of continuous compared to discrete-time settings. As wanna-be macroeconomist (my interest are heterogeneous agents macro models), I am very interested in this trend (because I am not HRM, I don't have access to some spectacular computer cluster), and since I am at the beginning of grad school I had some time and possibility to jump into this stuff (my uni had cool Math department). However, I read (mainly here on EJRM) some criticisms of the continuous-time macro. Can somebody please elaborate a bit on this issue (relative advantages and disadvantages of continuous vs discrete-time in macro), especially with respect to (if there are any) economic implications of used time framework.I would like to

   Any guidance/suggestions would be welcomed.

   Best
   MacroBro

   3 years ago # QUOTE 2 Volod 2 Vlad !

2. Economist
   e69c
   

   It’s the same s**t. You’ll always get the same result.

   3 years ago # QUOTE 2 Volod 1 Vlad !

3. Economist
   e69c
   

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

   3 years ago # QUOTE 2 Volod 2 Vlad !

4. Economist
   b0f1
   

   For computational purpose, it may be tricky to evaluate an infinite sum, but you can use the change of variable method to get from an indefinite integral to a definite one, then use gauss curvature or monte-carlo simulations to approximate the integral.

   3 years ago # QUOTE 0 Volod 1 Vlad !

5. Economist
   2abf
   

   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.

   3 years ago # QUOTE 15 Volod 1 Vlad !

6. Economist
   5af8
   

   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.

   Just trying to get some opinions. On EJRM one can often wind many interesting, and from time-to-time helpfull pieces of information

   3 years ago # QUOTE 6 Volod 0 Vlad !

7. Economist
   1517
   

   People have been moving to continuousv time for computational reasons

   3 years ago # QUOTE 3 Volod 0 Vlad !

8. Economist
   1aac
   

   ‘People have been moving to x’ is a very superficial statement that cannot be taken seriously. Ben Moll (and coauthors) is just a small group who recently started working on continuous time models which is still a small sized area relative to the rest of macro. I don’t think one can justify continuous time in many other questions that involve data. As a macroeconomist I don’t think the profession is moving to a certain direction. Continuous timers gonna continuous time and discrete timers gonna discrete time.

   3 years ago # QUOTE 3 Volod 0 Vlad !

9. Economist
   2abf
   

   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.

   Just trying to get some opinions. On EJRM one can often wind many interesting, and from time-to-time helpfull pieces of information

   I agree (though I would change often for occasionally), and its cool to look for opinions. My point is that you said in your original post that you starting having doubts about CT macro because of opinions in here, which most of the times comes from ugrads/1st year grad students who basically repeat what they hear (exhibit A: "macro no good"). Moreover, I insist, your advisor would know better (unless you are extremely UVLRM in which case you are probably going in for a teaching job and it doesn't matter much whether you use CT or DT).

   3 years ago # QUOTE 1 Volod 0 Vlad !

10. Economist
    c1fe
    

    Both are methods you should have in your toolbox. Learn both. Use when needed.

    3 years ago # QUOTE 3 Volod 0 Vlad !

11. Economist
    8e9d
    

    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?

    3 years ago # QUOTE 2 Volod 0 Vlad !

12. Economist
    2989
    

    A good book that uses continuous time throughout is Végh's Open Economy Macroeconomics in Developing Countries

    3 years ago # QUOTE 0 Volod 0 Vlad !

13. Economist
    8b81
    

    The best theory is not rejected by the data. Continuous time models are the hardest to test with data therefore they are harder reject. Therefore, they are better.

    3 years ago # QUOTE 0 Volod 0 Vlad !

14. Economist
    504d
    

    Hahaha. You are going to be roadkill when the feminist train rolls over you. The only good macro is women’s macro.

    3 years ago # QUOTE 0 Volod 0 Vlad !

15. 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...

    3 years ago # QUOTE 1 Volod 0 Vlad !

16. CZeconomist
    Rep: 0

    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...

    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.

    3 years ago # QUOTE 0 Volod 0 Vlad !

17. Economist
    ebce
    

    Numerical methods for CT macro models are less developed. Sometimes you get nice features that bear some computational advantage, but on the other hand the pde may get extremely complicated and difficult to understand, compared to a difference equation in discrete time. Having said that, I agree that the profession is now interested more in continuous time, especially macro-finance. I would recommend for PhD student to learn these tools.

    3 years ago # QUOTE 2 Volod 0 Vlad !

18. Economist
    5f6c
    

    How on earth would u use cont. time in macro when data are in quarterly and yearly?

    3 years ago # QUOTE 4 Volod 5 Vlad !

19. Economist
    3c03
    

    I would recommend against learning period. But if you insist on learning, learn only what is strictly necessary.

    3 years ago # QUOTE 1 Volod 0 Vlad !

20. Economist
    90aa
    

    I have better advice for you.

    Starting thinking about QUESTIONS. If you spend your PhD learning tools, your JMP will start with the sentence “I build a model to understand X”. And it will suck. This is a particularly high danger if you are not at a top 10 school.

    The profession rightly places a massive premium on novelty. Learn tools when you need to. Don’t start there.

    3 years ago # QUOTE 2 Volod 0 Vlad !

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