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 |
| Variable | Type | Rho | Pr < Rho | Tau | Pr < Tau |
| GDP_BG | Zero Mean | -8.62 | 0.0402 | -1.95 | 0.0495 |
| | Single Mean | -15.03 | 0.0348 | -2.64 | 0.0885 |
| | Trend | -17.17 | 0.108 | -2.93 | 0.1564 |
| GDP_EA | Zero Mean | -42.7 | <.0001 | -4.44 | <.0001 |
| | Single Mean | -48.69 | 0.0011 | -4.75 | 0.0002 |
| | Trend | -48.02 | 0.0004 | -4.73 | 0.001 |
| Unemp_BG | Zero Mean | -0.18 | 0.6399 | -0.22 | 0.6043 |
| | Single Mean | -5.76 | 0.36 | -1.77 | 0.3947 |
| | Trend | -7.8 | 0.5888 | -2.33 | 0.4161 |
| HICP_BG | Zero Mean | -1.13 | 0.4495 | -0.48 | 0.5071 |
| | Single Mean | -3.39 | 0.6051 | -1.18 | 0.6833 |
| | Trend | -12.61 | 0.2665 | -2.51 | 0.3215 |
| HP_BG | Zero Mean | -13.83 | 0.0087 | -2.61 | 0.0093 |
| | Single Mean | -14 | 0.0458 | -2.61 | 0.0929 |
| | Trend | -14.24 | 0.1953 | -2.74 | 0.2225 |
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 |
| Lag | Variable | GDP_BG | GDP_EA | Unemp_BG | HICP_BG | HP_BG |
| 1 | GDP_BG | 1.51695 | -0.32323 | -0.07316 | 0.0208 | 0.04657 |
| | GDP_EA | 0.04184 | 1.54188 | -0.0317 | -0.00889 | 0.02111 |
| | Unemp_BG | 0.0585 | -0.13691 | 1.01772 | 0.02646 | -0.01353 |
| | HICP_BG | -0.09687 | -0.17317 | 0.45338 | 0.26286 | 0.05087 |
| | HP_BG | 0.40168 | -0.6717 | -0.16238 | 0.07366 | 1.52713 |
| 2 | GDP_BG | -1.24578 | 0.57102 | 0.24424 | -0.007 | -0.01004 |
| | GDP_EA | -0.01199 | -1.08216 | 0.046 | -0.00174 | -0.01859 |
| | Unemp_BG | -0.03327 | 0.1483 | -0.32875 | -0.02099 | 0.01321 |
| | HICP_BG | 0.02011 | 1.41164 | -0.48313 | -0.00346 | -0.11958 |
| | HP_BG | -0.27895 | 2.18608 | -0.45604 | 0.22938 | -1.32891 |
| 3 | GDP_BG | 0.4411 | -0.33352 | -0.25461 | -0.04826 | 0.01708 |
| | GDP_EA | 0.02513 | 0.38162 | -0.01667 | -0.01701 | 0.01481 |
| | Unemp_BG | -0.02864 | 0.10291 | -0.01005 | -0.03522 | 0.00014 |
| | HICP_BG | 0.31382 | -1.4971 | -0.1214 | 0.14482 | 0.10065 |
| | HP_BG | 0.35618 | -2.09016 | 0.63977 | 0.11498 | 0.54739 |
| | | | | | | |
| Schematic Representation of Parameter Estimates | | | |
| Variable/Lag | AR1 | AR2 | AR3 | | | |
| 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?
