SVAR Model Issues

[Nils Holstein]

Hey,

I am trying to estimate a VAR-Model which plots an IRF of the EPU Index of Baker et al (2016) on macroeconomic
variables. The EPU Index is a proxy for economic policy uncertainty and my aim is to single out the effect of an uncertainty shock. A similar model was implemented in the Baker et al paper, only with monthly instead of quarterly data.

I start out with a VAR(3) with the following time series variables:

1. The EPU index
2. LN(S&P500)
3. Federal Funds ratio
4. log(Unemployment)
5. log(industrial_production)

My problem is the model itself, I can't get it to become significant. After the first output of the VAR(3), which is the first appended output, I move to a SVAR model in which I constraint all the non-significant lags of variables to be 0. However, in the SVAR model I still have three output variables which are not significant and I would also like to exclude them from the model(/a_5_1, /a_3_2, /a_4_2, /a_5_3).

Another problem I encountered is the rejected null hypothesis of the Jarque-Bera normality test on the log(Unemployment) and the log(industrial_production) variable...is the output statistically relevant if those variables are not normally distributed in the first place?

I hope you can help me, this is on my mind for some time now.

Best
Nils

Vector autoregression

Sample: 1985q4 - 2017q2 No. of obs = 127
Log likelihood = 760.9783 AIC = -10.72407
FPE = 1.52e-11 HQIC = -9.996156
Det(Sigma_ml) = 4.30e-12 SBIC = -8.932453

Equation Parms RMSE R-sq chi2 P>chi2
----------------------------------------------------------------
sd_EPU 16 .738514 0.5297 143.0122 0.0000
ln_SP 16 .069865 0.9905 13185.38 0.0000
FFR 16 .394922 0.9816 6768.14 0.0000
ln_UNEM 16 .027652 0.9891 11550.52 0.0000
ln_IND_PROD 16 .00758 0.9987 100447.4 0.0000
----------------------------------------------------------------

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sd_EPU |
sd_EPU |
L1. | .3773742 .0903324 4.18 0.000 .2003259 .5544226
L2. | -.1772667 .1039996 -1.70 0.088 -.3811021 .0265688
L3. | .416248 .1016437 4.10 0.000 .2170299 .615466
|
ln_SP |
L1. | -1.186835 .982723 -1.21 0.227 -3.112936 .7392672
L2. | 3.310793 1.230366 2.69 0.007 .89932 5.722267
L3. | -.4331015 .946114 -0.46 0.647 -2.287451 1.421248
|
FFR |
L1. | -.0345656 .1774159 -0.19 0.846 -.3822944 .3131632
L2. | .0890542 .2655623 0.34 0.737 -.4314383 .6095467
L3. | .0669558 .1717884 0.39 0.697 -.2697432 .4036548
|
ln_UNEM |
L1. | 5.099615 2.577913 1.98 0.048 .0469978 10.15223
L2. | -7.141286 4.236745 -1.69 0.092 -15.44515 1.162583
L3. | 3.477543 2.627267 1.32 0.186 -1.671806 8.626892
|
ln_IND_PROD |
L1. | -18.6611 10.21339 -1.83 0.068 -38.67896 1.356771
L2. | 32.02366 17.8281 1.80 0.072 -2.91878 66.9661
L3. | -17.66039 10.20754 -1.73 0.084 -37.6668 2.346015
|
_cons | -4.416305 6.422103 -0.69 0.492 -17.00339 8.170785
-------------+----------------------------------------------------------------
ln_SP |
sd_EPU |
L1. | -.0468072 .0085456 -5.48 0.000 -.0635563 -.0300581
L2. | .0463005 .0098386 4.71 0.000 .0270172 .0655837
L3. | -.003597 .0096157 -0.37 0.708 -.0224434 .0152495
|
ln_SP |
L1. | .9291611 .0929675 9.99 0.000 .7469481 1.111374
L2. | -.0253709 .1163951 -0.22 0.827 -.253501 .2027593
L3. | .0733856 .0895043 0.82 0.412 -.1020395 .2488107
|
FFR |
L1. | -.0182258 .0167839 -1.09 0.278 -.0511216 .01467
L2. | .0428365 .0251227 1.71 0.088 -.0064032 .0920761
L3. | -.018867 .0162515 -1.16 0.246 -.0507194 .0129854
|
ln_UNEM |
L1. | -.5846862 .2438757 -2.40 0.017 -1.062674 -.1066987
L2. | .8114733 .4008045 2.02 0.043 .025911 1.597036
L3. | -.1701399 .2485446 -0.68 0.494 -.6572785 .3169986
|
ln_IND_PROD |
L1. | .2147505 .9662064 0.22 0.824 -1.678979 2.10848
L2. | .0804122 1.686574 0.05 0.962 -3.225211 3.386036
L3. | -.2155195 .9656533 -0.22 0.823 -2.108165 1.677126
|
_cons | -.6983134 .6075436 -1.15 0.250 -1.889077 .4924501
-------------+----------------------------------------------------------------
FFR |
sd_EPU |
L1. | -.0721569 .0483055 -1.49 0.135 -.1668339 .0225201
L2. | .0992088 .055614 1.78 0.074 -.0097927 .2082103
L3. | -.1221723 .0543542 -2.25 0.025 -.2287047 -.01564
|
ln_SP |
L1. | -.4321243 .5255135 -0.82 0.411 -1.462112 .5978633
L2. | -.5843136 .6579413 -0.89 0.374 -1.873855 .7052277
L3. | .4717173 .5059368 0.93 0.351 -.5199005 1.463335
|
FFR |
L1. | 1.172084 .0948736 12.35 0.000 .9861351 1.358033
L2. | -.2126476 .1420101 -1.50 0.134 -.4909823 .065687
L3. | -.1217567 .0918642 -1.33 0.185 -.3018073 .0582939
|
ln_UNEM |
L1. | -1.315887 1.378545 -0.95 0.340 -4.017786 1.386013
L2. | -.4763776 2.26561 -0.21 0.833 -4.916892 3.964136
L3. | 1.032038 1.404937 0.73 0.463 -1.721589 3.785665
|
ln_IND_PROD |
L1. | 8.822979 5.461633 1.62 0.106 -1.881624 19.52758
L2. | -13.2313 9.533621 -1.39 0.165 -31.91685 5.454254
L3. | 4.94653 5.458506 0.91 0.365 -5.751945 15.64501
|
_cons | 8.985027 3.434235 2.62 0.009 2.25405 15.716
-------------+----------------------------------------------------------------
ln_UNEM |
sd_EPU |
L1. | .0070317 .0033823 2.08 0.038 .0004026 .0136608
L2. | -.0138668 .003894 -3.56 0.000 -.0214989 -.0062347
L3. | .0047118 .0038058 1.24 0.216 -.0027474 .012171
|
ln_SP |
L1. | -.0518036 .0367955 -1.41 0.159 -.1239215 .0203142
L2. | -.0213394 .0460678 -0.46 0.643 -.1116307 .0689519
L3. | .0528226 .0354248 1.49 0.136 -.0166086 .1222539
|
FFR |
L1. | -.0060717 .0066429 -0.91 0.361 -.0190915 .0069481
L2. | -.0033878 .0099433 -0.34 0.733 -.0228762 .0161007
L3. | .01491 .0064322 2.32 0.020 .0023031 .0275168
|
ln_UNEM |
L1. | 1.119787 .0965232 11.60 0.000 .9306051 1.308969
L2. | .1852991 .1586339 1.17 0.243 -.1256175 .4962158
L3. | -.2996606 .0983712 -3.05 0.002 -.4924645 -.1068566
|
ln_IND_PROD |
L1. | -1.18347 .3824135 -3.09 0.002 -1.932987 -.4339536
L2. | 1.787074 .6675267 2.68 0.007 .4787454 3.095402
L3. | -.4884549 .3821946 -1.28 0.201 -1.237543 .2606327
|
_cons | -.4333058 .2404589 -1.80 0.072 -.9045965 .0379849
-------------+----------------------------------------------------------------
ln_IND_PROD |
sd_EPU |
L1. | -.0027899 .0009272 -3.01 0.003 -.0046071 -.0009727
L2. | .0042434 .0010674 3.98 0.000 .0021513 .0063355
L3. | -.002446 .0010433 -2.34 0.019 -.0044908 -.0004013
|
ln_SP |
L1. | .0254236 .0100865 2.52 0.012 .0056545 .0451927
L2. | -.0162531 .0126282 -1.29 0.198 -.0410039 .0084978
L3. | -.0015133 .0097107 -0.16 0.876 -.020546 .0175193
|
FFR |
L1. | .0027261 .001821 1.50 0.134 -.0008429 .0062951
L2. | -.0023844 .0027257 -0.87 0.382 -.0077266 .0029578
L3. | -.0010598 .0017632 -0.60 0.548 -.0045156 .002396
|
ln_UNEM |
L1. | .0360306 .0264592 1.36 0.173 -.0158284 .0878896
L2. | -.0463621 .0434851 -1.07 0.286 -.1315913 .0388671
L3. | .0123904 .0269657 0.46 0.646 -.0404615 .0652422
|
ln_IND_PROD |
L1. | 1.783078 .1048281 17.01 0.000 1.577618 1.988537
L2. | -1.036379 .182984 -5.66 0.000 -1.395021 -.6777368
L3. | .2155163 .1047681 2.06 0.040 .0101747 .420858
|
_cons | .1052368 .0659151 1.60 0.110 -.0239545 .2344281
------------------------------------------------------------------------------

matrix A = (1, 0, 0, 0, 0 \ ., 1, 0, 0, 0 \ ., ., 1, 0, 0 \ ., ., ., 1, 0\ ., ., ., ., 1)
matrix B = (., 0, 0, 0, 0 \ 0, ., 0, 0, 0 \ 0, 0, ., 0, 0\ 0, 0, 0, ., 0\ 0, 0, 0, 0, .)

svar sd_EPU ln_SP FFR ln_UNEM ln_IND_PROD, aeq(A) beq(B) la(1/3) varconst(1/48) noislog

Estimating short-run parameters

Iteration 0: log likelihood = -878.68538
Iteration 1: log likelihood = -515.30772
Iteration 2: log likelihood = -292.78888
Iteration 3: log likelihood = 2.4346955
Iteration 4: log likelihood = 262.41784
Iteration 5: log likelihood = 425.27928
Iteration 6: log likelihood = 540.132
Iteration 7: log likelihood = 640.54338
Iteration 8: log likelihood = 699.62344
Iteration 9: log likelihood = 704.38365
Iteration 10: log likelihood = 704.48143
Iteration 11: log likelihood = 704.48148

Structural vector autoregression

( 1) [a_1_1]_cons = 1
( 2) [a_1_2]_cons = 0
( 3) [a_1_3]_cons = 0
( 4) [a_1_4]_cons = 0
( 5) [a_1_5]_cons = 0
( 6) [a_2_2]_cons = 1
( 7) [a_2_3]_cons = 0
( 8) [a_2_4]_cons = 0
( 9) [a_2_5]_cons = 0
(10) [a_3_3]_cons = 1
(11) [a_3_4]_cons = 0
(12) [a_3_5]_cons = 0
(13) [a_4_4]_cons = 1
(14) [a_4_5]_cons = 0
(15) [a_5_5]_cons = 1
(16) [b_1_2]_cons = 0
(17) [b_1_3]_cons = 0
(18) [b_1_4]_cons = 0
(19) [b_1_5]_cons = 0
(20) [b_2_1]_cons = 0
(21) [b_2_3]_cons = 0
(22) [b_2_4]_cons = 0
(23) [b_2_5]_cons = 0
(24) [b_3_1]_cons = 0
(25) [b_3_2]_cons = 0
(26) [b_3_4]_cons = 0
(27) [b_3_5]_cons = 0
(28) [b_4_1]_cons = 0
(29) [b_4_2]_cons = 0
(30) [b_4_3]_cons = 0
(31) [b_4_5]_cons = 0
(32) [b_5_1]_cons = 0
(33) [b_5_2]_cons = 0
(34) [b_5_3]_cons = 0
(35) [b_5_4]_cons = 0

Sample: 1985q4 - 2017q2 No. of obs = 127
Exactly identified model Log likelihood = 704.4815

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/a_1_1 | 1 (constrained)
/a_2_1 | .0109458 .0079675 1.37 0.170 -.0046703 .0265619
/a_3_1 | .263686 .0525308 5.02 0.000 .1607275 .3666446
/a_4_1 | -.0079894 .0033366 -2.39 0.017 -.014529 -.0014497
/a_5_1 | -.000119 .0008069 -0.15 0.883 -.0017004 .0014625
/a_1_2 | 0 (constrained)
/a_2_2 | 1 (constrained)
/a_3_2 | .3830203 .5807449 0.66 0.510 -.7552187 1.521259
/a_4_2 | .0447213 .0337533 1.32 0.185 -.0214341 .1108766
/a_5_2 | -.0220152 .0080393 -2.74 0.006 -.0377719 -.0062585
/a_1_3 | 0 (constrained)
/a_2_3 | 0 (constrained)
/a_3_3 | 1 (constrained)
/a_4_3 | .0142345 .0051486 2.76 0.006 .0041434 .0243255
/a_5_3 | -.0020404 .001254 -1.63 0.104 -.0044982 .0004174
/a_1_4 | 0 (constrained)
/a_2_4 | 0 (constrained)
/a_3_4 | 0 (constrained)
/a_4_4 | 1 (constrained)
/a_5_4 | .136399 .0209902 6.50 0.000 .0952589 .177539
/a_1_5 | 0 (constrained)
/a_2_5 | 0 (constrained)
/a_3_5 | 0 (constrained)
/a_4_5 | 0 (constrained)
/a_5_5 | 1 (constrained)
-------------+----------------------------------------------------------------
/b_1_1 | .7406548 .0464728 15.94 0.000 .6495698 .8317399
/b_2_1 | 0 (constrained)
/b_3_1 | 0 (constrained)
/b_4_1 | 0 (constrained)
/b_5_1 | 0 (constrained)
/b_1_2 | 0 (constrained)
/b_2_2 | .066503 .0041728 15.94 0.000 .0583246 .0746815
/b_3_2 | 0 (constrained)
/b_4_2 | 0 (constrained)
/b_5_2 | 0 (constrained)
/b_1_3 | 0 (constrained)
/b_2_3 | 0 (constrained)
/b_3_3 | .43524 .0273094 15.94 0.000 .3817146 .4887654
/b_4_3 | 0 (constrained)
/b_5_3 | 0 (constrained)
/b_1_4 | 0 (constrained)
/b_2_4 | 0 (constrained)
/b_3_4 | 0 (constrained)
/b_4_4 | .0252533 .0015845 15.94 0.000 .0221476 .0283589
/b_5_4 | 0 (constrained)
/b_1_5 | 0 (constrained)
/b_2_5 | 0 (constrained)
/b_3_5 | 0 (constrained)
/b_4_5 | 0 (constrained)
/b_5_5 | .0059736 .0003748 15.94 0.000 .005239 .0067082
------------------------------------------------------------------------------