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# st: IRF and Cholesky Order: Inconsistent Results

 From Maximilian Rodel To Subject st: IRF and Cholesky Order: Inconsistent Results Date Mon, 6 Sep 2010 17:52:15 +0200

```Hi,

I am estimating a VAR that is based on several financial performance series
and macroeconomic variables. Goal is to understand the reactions to a shock
using an IRF.

In its simplest form the VAR includes eight time series (all endogenously)
and one lag (VAR(1)). When specifying the Cholesky order I recognized some
seemingly inconsistent results.

1. ONE specific Cholesky order returns MULTIPLE results if the variables in
the VAR change order (while the coefficient matrix of the VAR is 100%
identical).

2. Specifying an EXPLICIT Cholesky order returns DIFFERENT results than SAME
DEFAULT Cholesky order. The VAR coefficients are estimated 100% identically.

[see below for code examples. I have the same issue in stata version 9.2 and
11]

Both observations are somehow interlinked. What is going wrong here? Any
experience with this Cholesky "randomness"?

Thanks so much,

Max

Code Examples, ad 1:
====================

*** Alternative 1 ***
local tEndoVars = "`tCountry'infcpi `tCountry'bndbil `tCountry'bndlde
`tCountry'comcid `tCountry'reslis `tCountry'eqtcou `tCountry'othtsp
`tCountry'othdiv"

var `tEndoVars' if tPeriod > 0 , lags(1)

local tEndoCholOrder = "`tCountry'infcpi `tCountry'comcid `tCountry'eqtcou
`tCountry'reslis `tCountry'bndlde `tCountry'bndbil `tCountry'othtsp
`tCountry'othdiv"

irf create order1, step(100) order(`tEndoCholOrder') set(myirf1, replace)

*** End Alternative 1 ***

vs.

*** Alternative 2 ***
local tEndoVars = "`tCountry'bndbil `tCountry'bndlde `tCountry'comcid
`tCountry'reslis `tCountry'eqtcou `tCountry'othtsp `tCountry'othdiv
`tCountry'infcpi"

*** Rest as above; End Alternative 2 ***

==> Estimate VAR Coefficients 100% identical
==> Resulting IRF significantly different (e.g. often only series swapped;
sometimes completely different shapes/ values)

Code Examples, ad 2:
====================

*** Alternative 1 ***
As above

*** Alternative 2 with VAR ordered as in Cholesky order and Default ordering
in IRF ***
local tEndoVars = "`tCountry'infcpi `tCountry'comcid `tCountry'eqtcou
`tCountry'reslis `tCountry'bndlde `tCountry'bndbil `tCountry'othtsp
`tCountry'othdiv"

var `tEndoVars' if tPeriod > 0 , lags(1)

irf create order1, step(100) set(myirf1, replace)
*** End Alternative 2 ***

==> Estimate VAR Coefficients 100% identical
==> Resulting IRF significantly different (e.g. often only series swapped;
sometimes completely different shapes/ values)

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