Sign-restrictions

[msh855]

I get an error when I try to use sign restrictions.

irf(run, opt_irf)
Error in sign_restr(sigma_chol = sigma_chol, sign_restr = sign_restr,  : 
  No matrix fitting the sign restrictions found.

Below MWE to reproduce:

data = na.omit(data_raw)
data[, names(data[1])] <- as.Date(data[, names(data[1])])  
data = xts(data[, 2:length(colnames(data))], data[, names(data[1])])

keep <- c("X10Y_GER_daily_change", "EUR_Stocks_daily_log_dif","US_Stocks_daily_log_dif","EURUSD_daily_log_dif",  "Spread_yields_daily_change")
data_var = data[,keep]

mn <- bv_minnesota(lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5), alpha = bv_alpha(mode = 2), var = 1e07)
priors <- bv_priors(mn = bv_mn(b = 0))
mh <- bv_metropolis(scale_hess = 0.05, adjust_acc = TRUE, acc_lower = 0.25, acc_upper = 0.45)
run <- bvar(data_var, lags = 5, priors = priors, 
            mh = mh, 
            n_draw = 50000, 
            n_burn = 25000, 
            n_thin = 1,
            verbose = TRUE)

sr <- matrix(c(1, -1, NA, 1, 1, 
               1, 1, NA, 1,1, 
               1,NA,-1,-1,-1,
               1,NA,1,-1,-1,
               1,1,1,1,-1), ncol = 5)


opt_irf <- bv_irf(horizon = 10, identification = TRUE,  sign_restr = sr)
irf_model <-irf(run, opt_irf, conf_bands = c(0.05, 0.16))

Attached the raw data
bvar_data_raw.csv

[nk027]

Hey Moustafa,
This is not an issue with the code, but rather the restrictions in light of the data (and arguably the algorithm to find suitable matrices). If you think the signs ought to work and this is an issue, you can increase the number of draw attempts (from 1000):

opt_irf <- bv_irf(horizon = 10, identification = TRUE,  sign_restr = sr, sign_lim = 10000)

[msh855]

Thank you,

Still does not work

I literary followed and imposed the sign restrictions as in this paper:

https://www.ecb.europa.eu/pub/pdf/scpwps/ecb.wp2560~f98f3c7d78.en.pdf

Though the paper does not follow the HBVAR method, but I expect not be an issue this difference.

[nk027]

That's interesting - if it doesn't stop early on (no shocks found at all) you can increase the allowed draws further. Otherwise I'll try to have a look.

[msh855]

I tried already with a very large number of draws.

I would appreciate if you can test it. I send before the input data and the relevant code.

[nk027]

Could it be that the ordering of the variables in Table 1 is off? They list

• restrictive EA MP & EA LTY versus 10Y GER
• fav EA macro & EA equity versus EUR Stocks
• restrictive US MP & US equity versus US Stocks
• fav US macro & EUR-USD versus EUR-USD
• fav global risk & LTY spread versus Spreads

Seems like restrictive US MP doesn't fit?

[msh855]

Not sure I fully understand what you mean.

Can you please suggest how the table with the sign restrictions should be ?

[msh855]

Update
-------

The identification strategy worked with the BEAR toolbox by ECB.

So, it might be the case that Hierarchical BVARs need other configurations or not stable for this problem.

[nk027]

They name a restrictive EA MP shock as based on German bonds, and a favourable EA macro shock as based on European stocks. However, for the US they base a restrictive MP shock o US stocks. That seems inconsistent?

Interesting, that shouldn't be the case – but gives me something to work with.

[msh855]

The way you should read from the economics point of view is that a restrictive US MP shock should simultaneously a) increase EURO's area yields, b) depress asset prices in the US, c) narrow the bond spreads and d) appreciate USD vs EUR.

Their identification strategy makes a lot of sense and I don't see some inconsistency (working in trading floor myself what they say is also very true and accurate).

In their identification strategy, they also take into account the global position of US. i.e. if the US "sneezes the rest of the world catches a cold". This is why in their paper discuss about spillovers.

I recommend to try the BEAR toolbox (i can help sending the file with the data in the format BEAR wants it as this part is a bit of a pain) and see why BEAR can do it and not your library.

I think your package has a lot of potentials if you keep working on it - you only need some extra functionalities (e.g. Historical decomposition, ) and make it as robust and flexible as possible.

Please keep me updated and thanks for the help.

[luisgruber]

Update -------

The identification strategy worked with the BEAR toolbox by ECB.

So, it might be the case that Hierarchical BVARs need other configurations or not stable for this problem.

I don't think that Hierarchical BVARs are not stable for this problem. It seems to me that negative/restrictive shocks are not allowed in the current implementation:

bvar/R/62_sign_restr.R

Line 88 in 14cfbb8

Q <- Q %*% diag((diag(Q) > 0) - (diag(Q) < 0)) # Positive

So, with the sign matrix under consideration,

> sr <- matrix(c(1, -1, NA, 1, 1, 
+                1, 1, NA, 1,1, 
+                1,NA,-1,-1,-1,
+                1,NA,1,-1,-1,
+                1,1,1,1,-1), ncol = 5)
> sr
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    1    1    1    1
[2,]   -1    1   NA   NA    1
[3,]   NA   NA   -1    1    1
[4,]    1    1   -1   -1    1
[5,]    1    1   -1   -1   -1

it will not be possible finding a matrix fitting the sign restrictons.

Would it be valid to change the signs in the columns with a negative diagonal element, then compute the IRFs and eventually change the signs of the IRFs where one is interested in a restrictive shock? E.g.

set.seed(123)
mn <- bv_minnesota(lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5), alpha = bv_alpha(mode = 2), var = 1e07)
priors <- bv_priors(mn = bv_mn(b = 0))
mh <- bv_metropolis(scale_hess = 0.05, adjust_acc = TRUE, acc_lower = 0.25, acc_upper = 0.45)
run <- bvar(data_var, lags = 5, priors = priors, 
            mh = mh, 
            n_draw = 100, 
            n_burn = 90, 
            n_thin = 1,
            verbose = TRUE)
sr_star <- t(t(sr)*c(1,1,-1,-1,-1))
opt_irf <- bv_irf(horizon = 10, identification = TRUE,  sign_restr = sr_star, sign_lim = 50000)
irf_model <-irf(run, opt_irf, conf_bands = c(0.05, 0.16))
irf_model$quants <- aperm(aperm(irf_model$quants,c(4,1,2,3))*c(1,1,-1,-1,-1),c(2,3,4,1))
plot(irf_model)

[nk027]

Hey, I haven't had time to retrace everything, but figured I'd mention that Lukas updated the sign-restriction algorithm in a branch:
https://github.com/nk027/bvar/tree/dev_signs
These restrictions seem to work there, but if there's a bug I'm happy for more details or a PR.

Also, note to self – we really need to test and release these fixed and the HDecomp features.

[nk027]

Had the time to revisit this –
@luisgruber, your approach makes a lot of sense to me.
@msh855, e647054 merges the improvement to how sign restrictions are computed into the main branch – your code runs now – provided you increase sign_lim = 100000 or somewhere around that. I'm leaving the lower default to avoid users getting stuck waiting, but the error message once it fails due to the limit is now more verbose (also irf() now has a verbose argument, which can be used to track the progress).