Near Singular Matrix Error for Impulse response fonctions

[sivakizildag]

Hello,

In order to analyse the interactions between the following data, I made an SVAR:

- tourist arrivals in France --> A_TOT_SA
- accomodation capacity in number of rooms in hotels (in first difference) --> D(OFF_SA)
- a consumer confidence index for OECD countries --> D(E_OECD)

There is one last dummy variable for the Paris terror attacks (EVENT_ATT_NOV_15).

With these variables, I make the SVAR (SVAR):

1. I estimate the VAR with 4 lags (results in TABLE01)
2. Using matrixes ZA and ZB, I make the VAR and SVAR (results in TABLE02)

When I ask Eviews for the IRF, I get an Error Message: "Near singular matrix".
I aso installed the sirf add-in for scaled IRFs, I also get the same message.

Why is that?

One last things that might help: on the IRF menu, when I switch the Analytic (asymptotic) to None in the Response Standard Errors section, I get the IRFs but without the confidence intervals. Could you please tell me why this is happening?

Thank you very much,

Best regards,

[EViews Matt]

Hello,

Let me address your questions in reverse order. First, regarding the missing confidence intervals when you select the "None" option under "Response Standard Errors". The confidence interval presentation make use of the standard errors, so if you choose to omit the standard errors then the confidence intervals are omitted too.

Second, regarding the near singular matrix error when you select the "Analytic (asymptotic)" option under "Response Standard Errors". One of the intermediate calculations performed behind the scenes is the second moment matrix of the VAR regressors, which is then inverted. Unfortunately, for your data that moment matrix is ill-conditioned (the estimated condition number is on the order of 10^18). EViews detects that the moment matrix is near singular and cannot be safely inverted, producing the error you experienced. From a numerical perspective, the problem seems to arise from the large magnitude of your first endogenous variable (a_tot_sa).

[sivakizildag]

Thanks you so much!

Indeed, it works now that I took the first difference with logarithms!

[sivakizildag]

I have another question, about the LR restrictions:

In the SVAR, what are the coefficients estimated in the long-run pattern matrix?

I mean, there is the formula on top: Model: Ae = Bu where E[uu']=I

Down below we have the estimated A and B matrixes.

So what are the coefficients C(1) to C(5)

[EViews Matt]

Hello,

It would probably help to review the relevant section of the SVAR documentation, but the short answer is the following relation:

C = Ψ * A^-1 * B

where C is the long-term factorization matrix (the one you specify the pattern for and contains the coefficients), Ψ is the vector moving average matrix, and A and B are the two factorization matrices you're already familiar with. In order to solve this equation EViews assumes that A = I, so the solution will come in the form of B = Ψ^-1 * C.