Unit Root Test with Structural Breaks

[Zankawa]

Hi,
I am estimating a VAR model and I have tested the series for a unit with structural breaks using the Lee and Stracizich unit root test. I tested a break model and crash model for both series and the results are pasted below. Both series are non stationary in the crash model but in the break model, they are both stationary. There are also structural breaks in both models which occurred at different dates. I have considered including appropriate dummies in the VAR based on the structural breaks and I am wondering whether to use the break dates in the crash models or the dates for the break models. Any advice will be very much appreciated.
Thank you

@LSUNIT(LAGS=5,MODEL=BREAK,BREAKS=2,METHOD=GTOS) LEXR
Lee-Strazicich Unit Root Test, Series LEXR
Regression Run From 1977:01 to 2014:01
Observations 38
Trend Break Model with 2 breaks
With 5 lags chosen from 5

Variable Coefficient T-Stat
S{1} -0.5120 -6.5169
Constant -1.9657 -5.3196
D(1981:01) -1.8034 -4.9641
DT(1981:01) 2.7711 6.5693
D(1994:01) 0.2610 0.9331
DT(1994:01) -0.5369 -4.6529

@LSUNIT(LAGS=5,MODEL=CRASH,BREAKS=2,METHOD=GTOS) LEXR
Lee-Strazicich Unit Root Test, Series LEXR
Regression Run From 1977:01 to 2014:01
Observations 38
Crash Model with 2 breaks
With 5 lags chosen from 5

Variable Coefficient T-Stat
S{1} -0.0814 -3.3305
Constant 0.1057 0.9037
D(1980:01) -0.8097 -1.8844
D(1999:01) 0.5208 1.3295

@LSUNIT(LAGS=5,MODEL=BREAK,BREAKS=2,METHOD=GTOS) LIR
Lee-Strazicich Unit Root Test, Series LIR
Regression Run From 1977:01 to 2014:01
Observations 38
Trend Break Model with 2 breaks
With 0 lags chosen from 5

Variable Coefficient T-Stat
S{1} -1.0072 -5.9266
Constant 0.0069 0.1875
D(1997:01) -0.0260 -0.1554
DT(1997:01) -0.1767 -2.7961
D(2007:01) 0.3271 1.9048
DT(2007:01) 0.0732 0.8752

@LSUNIT(LAGS=5,MODEL=CRASH,BREAKS=2,METHOD=GTOS) LIR
Lee-Strazicich Unit Root Test, Series LIR
Regression Run From 1977:01 to 2014:01
Observations 38
Crash Model with 2 breaks
With 5 lags chosen from 5

Variable Coefficient T-Stat
S{1} -0.1173 -2.2844
Constant 0.1379 2.8245
D(1981:01) -0.7704 -3.8060
D(1990:01) -0.5903 -3.2804

[TomDoan]

First of all, it's not clear that any of these actually make sense. The LS test is for trending data, and your data don't appear to have a trend. However, it's very clear that the CRASH model doesn't work at all, which I suspect would be obvious by looking at the data. (CRASH means a sudden change in level without change in trend rate) so why would the CRASH choice of break dates be relevant?

However, the main problem is that these are tests for unit roots. They are not tests for structural breaks. The break points are chosen not to best explain the data, but to be least supportive of the unit root hypothesis. If you're looking at analyzing breaks in a VAR, see Bai, Lumsdaine and Stock.