Willi, thank you for this amazing video. I teach these topics and always find myself looking for handouts/materials with clear explanations like yours. This channel is a great public resource. That said, I have a small question. The expressions you obtain for the auxiliary variables for the pricing problem (s_{1,t}, s_{2,t}) are different from the ones you use at the end. In the algebra steps you get: (A) s_{1,t} = y_t + \theta\beta E_t [ (\lambda_{t+1}/\lambda_t) \Pi_{t+1}^{\epsilon-1} s_{1,t+1} ]; and s_{2,t} = y_t mc_t + \theta\beta E_t [ (\lambda_{t+1}/\lambda_t) \Pi_{t+1}^{\epsilon} s_{2,t+1} ]. However, in the final system you use (B): s_{1,t} = y_t \lambda_t + \theta\beta E_t [ \Pi_{t+1}^{\epsilon-1} s_{1,t+1} ]; and s_{2,t} = y_t mc_t \lambda_t + \theta\beta E_t [ \Pi_{t+1}^{\epsilon} s_{2,t+1} ] ... are both type of expressions in (A) and (B) equivalent? or maybe I am missing some intermediate step you explained for getting from (A) to (B)? ... Thanks a lot.
Yes, in the written notes I forgot to carry over some terms. The expressions on the slides are correct though. I updated the description of the video to point this out.
@@wmutschl Hi Willi, thanks for replying. I’m still not sure the typo is fixed (I’m omitting the E[.] operator below for simplicity) In the handwritten notes you get: s_2t = y_t*mc_t + \theta\beta s_2t+1 In the corrected slides you have: s_2t = y_t*mc_t*\lambda_t + \theta\beta \Pi_t+1^\eps*s_2t+1 But by the algebra it should be: s_2t = y_t*mc_t + \theta\beta*\lambda_t+1/(\lambda_t)*\Pi_t+1^\eps*s_2t+1 That is, the only errors/differences are not the inclusion of the inflation and E[.] operator on the second RHS term, the term is also missing the ratio of marginal utilities (unless that beta is already the Stochastic Discount Factor). Furthermore, the first term on the RHS is y_t*mc_t, but in your slides' final expression, it’s being multiplied by the marginal utility of consumption. Maybe I’m missing some additional steps, but I still don’t get how the first term now has the marginal utility multiplying and by the second no longer has the ratio of utilities. Thanks for any further clarification! Great video again! (and amazing work with the GitHub) (Note: For your expressions, I'm looking at 49:55 and 49:58, for the algebra I redid the steps)
@@jocagraca You are correct, but the expressions on the slides are actually also correct (sounds paradox I know). What I did is to multiply the expression by lambda_t, such that the auxiliary sum equations have S_{1,t}*lambda_{t} and S_{2,t}*lambda_t on the left-hand side. Now on the right-hand side you have the same expression at t+1, i.e. S_{1,t+1}*lambda_{t+1} and S_{2,t+1}*lambda_{t+1}. So if you set s_{1,t} = S_{1,t}*lambda_{t} and s_{2,t} = S_{2,t}*lambda_{t} (note the lower-case and upper-case letters), you see that the equations on the slides are correct. But of course, you are right. It was not good from my side to omit this step, thanks for pointing this out! I will let people know in the description below.
I have also a pdf on GitHub which should be correct: github.com/wmutschl/Computational-Macroeconomics/blob/main/booklet/ex3.pdf If not, please open an issue so I can correct it.
@@wmutschl Thank you, Willi! It's clear now with the change of variable (lower case s_2). I guess you could use one or the other (s or S) in the final system to solve. Also thanks for pointing me to the file in github.
Thanks a lot for this video! It's really helpful and clean! Question. How can I derive a standard Calvo New Keynesian Phillips Curve out of this? In this setup optimal pricing is defined by those equations for S1t, etc... Is it possible to get a Phillips Curve out of it?
Sir, if possible, can u please make a video on dynamic programming for infinite time horizon? Euler eqn. , Bellman eqn. , Hamiltonian...It would be very helpful Sir.
@@tusharmisra8401 No it is not complete yet. I am still in the process of creating (and actually doing it). The course is not video only, but based on exercises which I have available on my github account.
Hi Professor, The coding way of DSGE model on matlab (without dynare) remains an important topic. Please, can you explain it with example ? Have a nice day
Hi Professor，thank you for your video, I have learned a lot. In the past few weeks, I have been studying the open macro model. At present, I don't think I have a clear understanding of the framework of the open macro model. If possible, could you please recommend some relevant learning materials to me? Thanks a lot!
you should look into the work by Gali and Monacelli; Gali's textbook also has a chapter on this. Moreover, Schmitt-Grohe and Uribe have a textbook, available online, called open economy macroeconomics.
dear professor, tack yun distortion p* in your notes should be greater than one, because p* appear with the aggregate final ouput (RHS), not in the aggregate intermeidate goods (LHS)
Sir, I have a very important question. Please answer it. I want to write excellent research papers involving open economy DSGE models. Is your course in this channel sufficient to gain the skills or do I have to learn even more and what?
No. This course might be sufficient to get a hold on the methods required but an excellent research paper involving open economy DSGE models needs a very good research question and a model that is suitable to answer you research question. This course is NOT about the art of DSGE modeling, but on the methods useful for processing, solving and simulating any DSGE model with both Dynare and MATLAB. It is a methodological course.
Basic undergraduate knowledge of macroeconomics as well as econometrics are required. Programming skills in a scripting language are advantageous, but not necessary.
This is what I needed for my preparation for Advanced Macroeconomics exam preparation!
YOU ARE A HERO❤(nice video)
Amazing thank you so much for simplifying things
Willi, thank you for this amazing video. I teach these topics and always find myself looking for handouts/materials with clear explanations like yours. This channel is a great public resource. That said, I have a small question. The expressions you obtain for the auxiliary variables for the pricing problem (s_{1,t}, s_{2,t}) are different from the ones you use at the end. In the algebra steps you get: (A) s_{1,t} = y_t + \theta\beta E_t [ (\lambda_{t+1}/\lambda_t) \Pi_{t+1}^{\epsilon-1} s_{1,t+1} ]; and s_{2,t} = y_t mc_t + \theta\beta E_t [ (\lambda_{t+1}/\lambda_t) \Pi_{t+1}^{\epsilon} s_{2,t+1} ]. However, in the final system you use (B): s_{1,t} = y_t \lambda_t + \theta\beta E_t [ \Pi_{t+1}^{\epsilon-1} s_{1,t+1} ]; and s_{2,t} = y_t mc_t \lambda_t + \theta\beta E_t [ \Pi_{t+1}^{\epsilon} s_{2,t+1} ] ... are both type of expressions in (A) and (B) equivalent? or maybe I am missing some intermediate step you explained for getting from (A) to (B)? ... Thanks a lot.
Yes, in the written notes I forgot to carry over some terms. The expressions on the slides are correct though. I updated the description of the video to point this out.
@@wmutschl Hi Willi, thanks for replying.
I’m still not sure the typo is fixed (I’m omitting the E[.] operator below for simplicity)
In the handwritten notes you get: s_2t = y_t*mc_t + \theta\beta s_2t+1
In the corrected slides you have: s_2t = y_t*mc_t*\lambda_t + \theta\beta \Pi_t+1^\eps*s_2t+1
But by the algebra it should be: s_2t = y_t*mc_t + \theta\beta*\lambda_t+1/(\lambda_t)*\Pi_t+1^\eps*s_2t+1
That is, the only errors/differences are not the inclusion of the inflation and E[.] operator on the second RHS term, the term is also missing the ratio of marginal utilities (unless that beta is already the Stochastic Discount Factor).
Furthermore, the first term on the RHS is y_t*mc_t, but in your slides' final expression, it’s being multiplied by the marginal utility of consumption.
Maybe I’m missing some additional steps, but I still don’t get how the first term now has the marginal utility multiplying and by the second no longer has the ratio of utilities.
Thanks for any further clarification! Great video again! (and amazing work with the GitHub)
(Note: For your expressions, I'm looking at 49:55 and 49:58, for the algebra I redid the steps)
@@jocagraca You are correct, but the expressions on the slides are actually also correct (sounds paradox I know). What I did is to multiply the expression by lambda_t, such that the auxiliary sum equations have S_{1,t}*lambda_{t} and S_{2,t}*lambda_t on the left-hand side. Now on the right-hand side you have the same expression at t+1, i.e. S_{1,t+1}*lambda_{t+1} and S_{2,t+1}*lambda_{t+1}. So if you set s_{1,t} = S_{1,t}*lambda_{t} and s_{2,t} = S_{2,t}*lambda_{t} (note the lower-case and upper-case letters), you see that the equations on the slides are correct. But of course, you are right. It was not good from my side to omit this step, thanks for pointing this out! I will let people know in the description below.
I have also a pdf on GitHub which should be correct: github.com/wmutschl/Computational-Macroeconomics/blob/main/booklet/ex3.pdf If not, please open an issue so I can correct it.
@@wmutschl Thank you, Willi! It's clear now with the change of variable (lower case s_2). I guess you could use one or the other (s or S) in the final system to solve. Also thanks for pointing me to the file in github.
Thanks a lot for this video! It's really helpful and clean!
Question. How can I derive a standard Calvo New Keynesian Phillips Curve out of this? In this setup optimal pricing is defined by those equations for S1t, etc... Is it possible to get a Phillips Curve out of it?
Sir, if possible, can u please make a video on dynamic programming for infinite time horizon? Euler eqn. , Bellman eqn. , Hamiltonian...It would be very helpful Sir.
You might find the following book interesting: Miao, J. 2014. Economic Dynamics in Discrete Time. MIT Press. ISBN: 978-0262325608
@@wmutschl Is your course on macroeconomics complete? Or u are planning to upload something more in this channel?
@@tusharmisra8401 No it is not complete yet. I am still in the process of creating (and actually doing it). The course is not video only, but based on exercises which I have available on my github account.
Hi Professor,
The coding way of DSGE model on matlab (without dynare) remains an important topic. Please, can you explain it with example ?
Have a nice day
Yes, I will post a video on preprocessing models with MATLAB (not Dynare) shortly.
Hi Professor，thank you for your video, I have learned a lot. In the past few weeks, I have been studying the open macro model. At present, I don't think I have a clear understanding of the framework of the open macro model. If possible, could you please recommend some relevant learning materials to me? Thanks a lot!
you should look into the work by Gali and Monacelli; Gali's textbook also has a chapter on this. Moreover, Schmitt-Grohe and Uribe have a textbook, available online, called open economy macroeconomics.
God work!
Thx!
Very interesting video, I'd like to ask you if there is a mistake in the stochastic discount factor: should z have t instead of T as subscript?
Yes
dear professor, tack yun distortion p* in your notes should be greater than one, because p* appear with the aggregate final ouput (RHS), not in the aggregate intermeidate goods (LHS)
Thanks for spotting this, it depends how you define it.
Sir, I have a very important question. Please answer it. I want to write excellent research papers involving open economy DSGE models. Is your course in this channel sufficient to gain the skills or do I have to learn even more and what?
No. This course might be sufficient to get a hold on the methods required but an excellent research paper involving open economy DSGE models needs a very good research question and a model that is suitable to answer you research question. This course is NOT about the art of DSGE modeling, but on the methods useful for processing, solving and simulating any DSGE model with both Dynare and MATLAB. It is a methodological course.
@@wmutschl Sir, any prerequisites before starting this course? That's really important
Basic undergraduate knowledge of macroeconomics as well as econometrics are required.
Programming skills in a scripting language are advantageous, but not necessary.
@@wmutschl Thank you Sir
nice one.
Thank you!