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B/VAR - Insignificance of non-diagonal AR parameters

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B/VAR - Insignificance of non-diagonal AR parameters

 

I am trying to estimate a Macroeconomic VAR/BVAR for the purpose of forecasting/impulse response simulations.

 

I have a total of 5 macro variables that are 4 country specific and 1 for the Euro Area :

GDP_BG - GDP ; HICP_BG - Inflation; HP_BG - House prices ; Unemp_BG - Unemployment ; GDP_EA - GDP euro area

 

I have colelcted quarterly and monthly data for the period 2006 - 2016. After cubic interpolation of the quarterly data all series are in monthly year on year grwoth format.

 

1. DF tests indicate non-stationarity of the series:

Dickey-Fuller Unit Root Tests
VariableTypeRhoPr < RhoTauPr < Tau
GDP_BGZero Mean-8.620.0402-1.950.0495
 Single Mean-15.030.0348-2.640.0885
 Trend-17.170.108-2.930.1564
GDP_EAZero Mean-42.7<.0001-4.44<.0001
 Single Mean-48.690.0011-4.750.0002
 Trend-48.020.0004-4.730.001
Unemp_BGZero Mean-0.180.6399-0.220.6043
 Single Mean-5.760.36-1.770.3947
 Trend-7.80.5888-2.330.4161
HICP_BGZero Mean-1.130.4495-0.480.5071
 Single Mean-3.390.6051-1.180.6833
 Trend-12.610.2665-2.510.3215
HP_BGZero Mean-13.830.0087-2.610.0093
 Single Mean-140.0458-2.610.0929
 Trend-14.240.1953-2.740.2225

2. Taking this into account I run the VAR(3) - suggested by the minimum information criteria

 

/* VAR with 1st Difference*/
proc varmax data=DATA_ALL.MACRO_CLEAN_ALL;
   model GDP_BG GDP_EA Unemp_BG HICP_BG HP_BG / p=3 noint dftest dify=(1)  
                 print=(estimates);
run;

 

3. The DF test now indicates stationarity, however, there is no significant relationship apart from the diagonal elements of the AR parameters, except for higher order lags:

 

AR Coefficient Estimates
LagVariableGDP_BGGDP_EAUnemp_BGHICP_BGHP_BG
1GDP_BG1.51695-0.32323-0.073160.02080.04657
 GDP_EA0.041841.54188-0.0317-0.008890.02111
 Unemp_BG0.0585-0.136911.017720.02646-0.01353
 HICP_BG-0.09687-0.173170.453380.262860.05087
 HP_BG0.40168-0.6717-0.162380.073661.52713
2GDP_BG-1.245780.571020.24424-0.007-0.01004
 GDP_EA-0.01199-1.082160.046-0.00174-0.01859
 Unemp_BG-0.033270.1483-0.32875-0.020990.01321
 HICP_BG0.020111.41164-0.48313-0.00346-0.11958
 HP_BG-0.278952.18608-0.456040.22938-1.32891
3GDP_BG0.4411-0.33352-0.25461-0.048260.01708
 GDP_EA0.025130.38162-0.01667-0.017010.01481
 Unemp_BG-0.028640.10291-0.01005-0.035220.00014
 HICP_BG0.31382-1.4971-0.12140.144820.10065
 HP_BG0.35618-2.090160.639770.114980.54739
       
Schematic Representation of Parameter Estimates   
Variable/LagAR1AR2AR3   
GDP_BG+....-....+....   
GDP_EA.+....-....+...   
Unemp_BG..+....-.......   
HICP_BG...+.......-...   
HP_BG....+...+-.-..+   
+ is > 2*std error,  - is < -2*std error,  . is between,  * is N/A   

 

If I proceed with imposing a BVAR prior the  higher order lags are eliminated by the prior and the resulting model has significant parameters at low order diagonal parameters.

 

I don't understand the reason for these results. How is it possible that stationary macro variables do not have any dependence between each other? Any suggestions for what am I making wrong and what could I try?

 

Could the monthly frequency be the reason for these results? If so should I test much higher lag orders (p=12) and then restrict the insgignificant parameters?

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