Estimation procedures

[ThomasKronhol]

Hi @donotdespair

I have some questions regarding the estimation procedure.

1. Can I simply use the code provided in lecture 15 including the functions, where a cholesky decomposition is applied to make a structural model, as my "baseline" model? Or should I use the code provided in lecture 12?

2. If I want to extend my model using dummy priors, how do I get artifficial data, which seems to be required?

Kind regards Thomas

[donotdespair]

Hi @ThomasKronhol

BINGO on both points!

1. I'm not sure. What restrictions do you want to use? I would entirely suggest exclusion restrictions on the long-run effects since you're working with nonstationary variables. In such a case, you'd need to code the algorithm by Rubio-Ramirez, Waggoner & Zha (2010), as we discussed in the last meeting.
2. Yes, Section 6 of my paper Bayesian Vector Autoregressions mentions two papers by Chris Sims that provide such methods. They discuss non-stationarity and cointegration-coherent priors there :) (Indeed, you might not have a DSGE model to simulate the data from in line with the other paper.)

Please, remember to tag me below whenever you want a reply from me

Cheers,

@donotdespair

[ThomasKronhol]

Hi again, @donotdespair

I think that I might want to start out by just having a identified model using choleksy (not taking long run restrictions into account) per se - or is this indeed required?

If I want to do something else then dummy priors, what kind of suggestions would you have in terms of the hyper parameters or similar, which I could investigate?

// Thomas

[donotdespair]

Hi @ThomasKronhol

Happy to help one point at a time!

OK, you can begin by coding the model with Cholesky decomposition as a simple model. But I would insist that you later on code the RRWZ2010 algorithm. One of the requirements for this assignment was to work with Uhlig's algorithm for sign restrictions or Waggoner & Zha (2003) for the model with exclusion restrictions. I would be happy to replace WZ2003 by RRWZ2010 algorithm, but just a triangular system estimated by applying Cholesky decomposition is too little for this assignment.

So, please develop the RRWZ2010 algo subsequently and apply at least one long-term restriction to implement it in your empirical example.

[donotdespair]

Hey @ThomasKronhol

If it's about the dummy observation prior...

1. The first go-to resource would be the article Woźniak (2016) Bayesian Vector Autoregressions provided in the lecture materials. Section 6 explicitly discusses the setup and the estimation. Having studied this part you will know how to implement the prior and estimate a model with it.
2. Now, you need a research paper that would tell you how to generate artificial data to generate the prior. Section 6, which I mentioned above, mentions two papers by Chris Sims that scrutinise such priors. These two papers include nonstationarity and cointegration coherent dummy observations prior. Another option is a recent article Domenico Giannone, Michele Lenza & Giorgio E. Primiceri (2019) Priors for the Long Run, Journal of the American Statistical Association, 114:526, 565-580, DOI: 10.1080/01621459.2018.1483826 but it seems to require a DSGE model that you might not have for your example.

Please let me know, when you would need more input from me. Please, remember to tag me in such a post. Thanks, @donotdespair

[ThomasKronhol]

@donotdespair

Would I also need to implement long run restrictions if I do not want to work with dummy priors?

• I apologise for the confusion, but I do not quite understand whether this is in relation to a possible introduction of dummy priors are a general restriction required for SBVAR's with non-stationary data.

additionally, are we allowed to use your package?

// Thomas

[donotdespair]

@ThomasKronhol Cool! No worries! These are two separate things.

1. The type of estimation algorithm, like RRWZ2010, must be aligned with the way you chose to identify the model/shocks. This will be implemented in both your models, the basic one and the extended one.
2. Dummy observation prior is one of the options by which you can extend your basic model.

Does this make sense? T

[ThomasKronhol]

@donotdespair Can I drop by your office tomorrow? // Thomas

[donotdespair]

@donotdespair Can I drop by your office tomorrow? // Thomas

Hi @ThomasKronhol Can we keep arrangements regarding meetings to emails? This gets published online in the end. Folks can even search this content :) Thanks. I have sent you the email.

[donotdespair]

Hi @ThomasKronhol

You asked whether you can use my bsvars package. My answer is a conditional YES. I mean by that, that yes, you can use the package, but you also need to submit a pull request to the package repo with your proposal of a new utility function. Your assignment will be accepted, provided that the function's quality is sufficient to include it in the package. This includes writing up the help file for the function, which is not that difficult. So, yes, you can use my package, but you still have to write original code. Your contribution will be acknowledged in the section contributors of the package. If you want to pursue this option, please, let me know and we'll talk about what this function can be.

[ThomasKronhol]

Hi @donotdespair

Having simulated the artificial data, I get the following error when running it through the code of WG2003:

The code used to simulate the data is as follows:

n <- 1000

initial values for the random walk

x0 <- c(0, 0)

cov matrix

cov_mat <- diag(2)

RW process

x <- matrix(1, n, 2) x[1,] <- x0

for (i in 2:n) { x[i,] <- mvrnorm(1, x[i-1,], cov_mat) }

Y=x[2:1000,] y = Y Y = ts(y) p = 1 X = matrix(1,nrow(Y),1) for (i in 1:p){ X = cbind(X,y[2:1000-i,]) } X = ts(X)

Running the lines found in the code WZ2003:

run the posterior simulations and save their output

burn-in run: sampling B0 from the posterior distribution using Gibbs

t0 = proc.time() B0.posterior = rgn(n=S.burnin, S=S.post, nu=nu.post, V=FF.V, B0.initial=B0.initial)

Gives the following error (the error is from computing the orthogonal matrix using the function found in L16 codes.R: out = as.matrix(tmp[,(N[2]+1):N[1]])): Error in tmp[, (N[2] + 1):N[1]] : subscript out of bounds

Any suggestions on what might cause and resolve this?

Kind regards T

[donotdespair]

OK, @ThomasKronhol

These lines:

Y=x[2:1000,]

X = cbind(X,y[2:1000-i,])

should be:

Y=x[(1+p):1000,]

X = cbind(X,y[(1+p):1000-i,])

Let me know if this work :)

[ThomasKronhol]

Hi @donotdespair

It gives the same error message unfortunately :(

[donotdespair]

OK @ThomasKronhol

Use n consequently:

n= 300

x0 <- c(0, 0)
x <- matrix(1, n, 2)
x[1,] <- x0

cov_mat <- diag(2)

for (i in 2:n) {
  x[i,] <- mvtnorm::rmvnorm(1, x[i-1,], cov_mat)
}

p = 1
Y=x[(1+p):n,]
Y = ts(Y)
X = matrix(1,nrow(Y),1)
for (i in 1:p){
  X = cbind(X,y[(p+1):n-i,])
}
X = ts(X)

[ThomasKronhol]

Hi @donotdespair

Do we need to impose our restrictions in this assignment or do we only need to show, that the estimation runs using artificial data?

Kind regards T

[donotdespair]

@ThomasKronhol, the latter, please. But you need to use some restrictions to estimate your target model :)

[ThomasKronhol]

Hi @donotdespair

Does it make sense, that the estimation would take longer, in case the number of artificial data points increases from fx 500 to 1000? In my mind it would make sense if it did not affect the speed, as it is simply matrix multiplications?

Kind regards T

[donotdespair]

Hi @ThomasKronhol

Yes, it might take longer, especially when you recompute these matrices in each Gibbs step. I would still think ti shouldn't take that much longer, but apparently, it does. Cheers, T

[ThomasKronhol]

Hi @donotdespair

I have problems running my estimation with large numbers of draws. I get the following error:

Lowering the number of draws, the code runs perfectly fine, although slow. Any idea why this might be the case or what might resolve it?

Best T

[donotdespair]

OK @ThomasKronhol

My guess is that there is a bug somewhere in the code! It might be the one in the rgn sampler that prevents us from reproducing the results, but it also might be something else. I will have some time to check function rgn on Friday. In the meantime, you check if you save and compute everything else correctly.

This is this part of polishing the code that is the most difficult. Everything seems to work and be as it should, but it isn't. And we have to figure out what that is. It's an unavoidable part of code development.

Good luck!

T

[ThomasKronhol]

Hi @donotdespair

I'm trying to plot my impulse responses, and it's going well, when using the basic model.

However, when running the extended model (outside of my quarto file, where it works perfectly), I get the following error. It's inside the RGN, and I have not changed anything compared to the quarto file. Any suggestions on why the following is occuring?

Best, T

[donotdespair]

Hi @ThomasKronhol

I get your point and thanks for the reminder! I'm not sure at all! I'd need more access to your code...

Shall we meet on Monday in my office?

[ThomasKronhol]

Hi @donotdespair

Before submitting the empirical analysis, are we then allowed to "delete" the estimation done on the artificial data, thus improving the speed of the computations, or should we keep it, and try and use "cache"?

Best

T

[donotdespair]

Hey @ThomasKronhol I'd day that cache would be the most suitable here! Thanks

[ThomasKronhol]

Hi @donotdespair

I've included Federal funds into my model, and it gives the following IRF's.

1. I dont understand why the confidence bands on FF is so wide?
2. I gues the response from FF make sense in some way, as lower GDP and inflation will trigger Fed. to stimulate the economy. However, I dont think it is co nsistent with a positive shock of NFCI, where the treasury rate is included - nevertheless it might be the case that financial conditions tightn while Fed. stimulates the real economy. Could that be the story?

Best T

[donotdespair]

Hi @ThomasKronhol

There are a few things to say about your setup.

1. The main point is that your shock to financial conditions is the last in a lower-triangular identification system. This lower triangularity implies the same for IRFs at horizon 0. So, all of your variables have responses constrained to zero at horizon 0. This is not an optimal setup to investigate these relationships. Maybe redefining your shock and putting the NFCI first would be somehow justified.
2. The direction and precision of the estimation of the FF response could be related to the point above. But I agree the shape of FF response is somehow surprising. It's a bit difficult to understand and conceptualise, but one way of approaching this problem would be to understand the financial conditions shock in a setup where you control for the interest rates as one that captures the effects beyond the monetary policy. In these circumstances, the Fed is monitoring the situation and provides help to the market by making the availability of credit easier. So in NFCI terms, the monetary policy is counter-cyclical: it provides help when the market is tight and constrains the access when the financial market is too lose.

What do you think?

Cheers, T

[ThomasKronhol]

Hi @donotdespair

Thanks for the suggestions. I have tried changing the order, which yielded in slightly less interpretable responses (see attached).

I think the argument of fci conditions affecting the real economy with a lag is somewhat more justified compared to contemporaneous effects, so I might keep the order as before. Nevertheless, regarding the FF I think the suggested cause is good, and "makes sense" in an economic sense!

Thanks a lot!

Best T

[donotdespair]

Hi @ThomasKronhol

Thanks for sending these outputs! Actually, I love them! Most of them are quite interpretable. Well, except for the initial responses at horizon zero, that usually have the opposite sign compared to those at longer horizons. But also, they are, in the end, not that different from your original ones if you look at the mid- and long-term implications.

How about presenting the results with the NFCI as the last variable as your benchmark results and those with this variable as the first as a robustness check (which works at all but the initial horizon)?

Cheers,

@donotdespair

[ThomasKronhol]

@donotdespair

It's a deal!

[donotdespair]

Hi @ThomasKronhol

The materials for the Student t error terms are not numerous. One is the appendix to a textbook by Bauwens, Lubrano, Richards (1999). Another is the article by Geweke (1993).

And the Paper Nathan found instructive to him was by Bobeica and Hartwig