Dr Łukasz Goczek - coin.wne.uw.edu.plcoin.wne.uw.edu.pl/lgoczek/pdf/Makroekonometria9.pdf · var...
Transcript of Dr Łukasz Goczek - coin.wne.uw.edu.plcoin.wne.uw.edu.pl/lgoczek/pdf/Makroekonometria9.pdf · var...
use C:\Users\as\Desktop\Money.dta, clear
format t %tm (oznaczamy
tsset t
tsline M3
0
2000
4000
6000
8000
1000
0
M3
1960m1 1970m1 1980m1 1990m1 2000m1 2010m1t
dfuller M3
Dickey-Fuller test for unit root Number of obs = 565
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) 21.745 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
Przypomnienie: H0 – pierwiastek jednostkowy, proces niestacjonarny
g dm3=d.M3
dfuller dm3
Dickey-Fuller test for unit root Number of obs = 564
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -9.759 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000
dfuller FFR
dfuller FFR
Dickey-Fuller test for unit root Number of obs = 565
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -2.168 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.2180
g dFFR=d.FFR
dfuller dFFR
Dickey-Fuller test for unit root Number of obs = 564
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -15.872 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000
Rozwiązanie heteroskedastyczności:
g lnM3=ln(M3)
dfuller lnM3
Daje wynik na „granicy”, zatem:
pperron lnM3
Phillips-Perron test for unit root Number of obs = 565
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) -0.329 -20.700 -14.100 -11.300
Z(t) -2.107 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.2417
Generujemy różnice
g dlnM3=d.lnM3
Generujemy różnice
g dlnM3=d.lnM3
Phillips-Perron test for unit root Number of obs = 564
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) -183.113 -20.700 -14.100 -11.300
Z(t) -10.465 -3.430 -2.860 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000
Podobne wyniki pozostałych zmiennych.
Niestacjonarne szeregi, w pierwszych różnicach
stacjonarne – zatem wszystko to procesy I(1)
Rozważmy model autoregresyjny bez ograniczeń
(VAR) z poprzedniego wykładu.
Zmienne zerojedynkowe (patrz dodatkowy tutorial ze Staty u
mnie na stronie):
generate m=month(dofm(t))
tab m, g(y)
drop y12
varsoc dlnM3 dFFR dPPI dCPI, maxlag(24) exog(y*)
Selection-order criteria
Sample: 1961m2 - 2006m2 Number of obs = 541
+---------------------------------------------------------------------------+
|lag | LL LR df p FPE AIC HQIC SBIC |
|----+----------------------------------------------------------------------|
| 0 | 1209.4 1.6e-07 -4.29352 -4.14455 -3.91258 |
| 1 | 1511.89 604.99 16 0.000 5.6e-08 -5.35264 -5.15402 -4.84473* |
| 2 | 1546.15 68.521 16 0.000 5.2e-08 -5.42015 -5.17187 -4.78526 |
| 3 | 1588.74 85.185 16 0.000 4.7e-08 -5.51846 -5.22052* -4.7566 |
| 4 | 1611.36 45.224 16 0.000 4.6e-08 -5.5429 -5.19531 -4.65406 |
| 5 | 1645.76 68.814 16 0.000 4.3e-08 -5.61095 -5.2137 -4.59513 |
| 6 | 1664.92 38.313 16 0.001 4.3e-08 -5.62262 -5.17571 -4.47982 |
| 7 | 1690.4 50.969 16 0.000 4.1e-08 -5.65768 -5.16112 -4.38791 |
| 8 | 1713.63 46.447 16 0.000 4.0e-08 -5.68439 -5.13817 -4.28764 |
| 9 | 1734.7 42.148 16 0.000 3.9e-08 -5.70315 -5.10727 -4.17942 |
| 10 | 1762.08 54.751 16 0.000 3.8e-08 -5.7452 -5.09967 -4.0945 |
| 11 | 1789.2 54.256 16 0.000 3.6e-08 -5.78634 -5.09115 -4.00866 |
| 12 | 1809.08 39.748 16 0.001 3.6e-08 -5.80066 -5.05581 -3.896 |
| 13 | 1828.64 39.128 16 0.001 3.5e-08 -5.81384 -5.01933 -3.7822 |
| 14 | 1843.11 28.941 16 0.024 3.5e-08 -5.80818 -4.96402 -3.64957 |
| 15 | 1865.32 44.41 16 0.000 3.5e-08* -5.83112* -4.9373 -3.54553 |
| 16 | 1874.48 18.324 16 0.305 3.6e-08 -5.80584 -4.86237 -3.39327 |
| 17 | 1887.57 26.175 16 0.052 3.6e-08 -5.79507 -4.80194 -3.25553 |
var dlnM3 dFFR dPPI dCPI, lags(1/15) lutstats exog(y*)
Vector autoregression
Sample: 1960m5 - 2006m2 No. of obs = 550
Log likelihood = 1907.55 (lutstats) AIC = -17.41533
FPE = 3.27e-08 HQIC = -16.68038
Det(Sigma_ml) = 1.14e-08 SBIC = -15.53464
Equation Parms RMSE R-sq chi2 P>chi2
----------------------------------------------------------------
dlnM3 72 .002495 0.5919 797.8297 0.0000
dFFR 72 .501866 0.3540 301.4258 0.0000
dPPI 72 .650932 0.3356 277.8 0.0000
dCPI 72 .216822 0.5503 673.0012 0.0000
----------------------------------------------------------------
vargranger
Granger causality Wald tests
+------------------------------------------------------------------+
| Equation Excluded | chi2 df Prob > chi2 |
|--------------------------------------+---------------------------|
| dlnM3 dFFR | 24.868 15 0.052 |
| dlnM3 dPPI | 29.091 15 0.016 |
| dlnM3 dCPI | 29.262 15 0.015 |
| dlnM3 ALL | 87.222 45 0.000 |
|--------------------------------------+---------------------------|
| dFFR dlnM3 | 25.544 15 0.043 |
| dFFR dPPI | 24.012 15 0.065 |
| dFFR dCPI | 19.049 15 0.212 |
| dFFR ALL | 64.809 45 0.028 |
|--------------------------------------+---------------------------|
| dPPI dlnM3 | 15.622 15 0.408 |
| dPPI dFFR | 19.315 15 0.200 |
| dPPI dCPI | 63.206 15 0.000 |
| dPPI ALL | 101.81 45 0.000 |
|--------------------------------------+---------------------------|
| dCPI dlnM3 | 24.294 15 0.060 |
| dCPI dFFR | 36.037 15 0.002 |
| dCPI dPPI | 30.251 15 0.011 |
| dCPI ALL | 101.7 45 0.000 |
+------------------------------------------------------------------+
varnorm, jbera skewness kurtosis
Jarque-Bera test
+--------------------------------------------------------+
| Equation | chi2 df Prob > chi2 |
|--------------------+-----------------------------------|
| dlnM3 | 36.884 2 0.00000 |
| dFFR | 3.0e+04 2 0.00000 |
| dPPI | 1493.881 2 0.00000 |
| dCPI | 822.912 2 0.00000 |
| ALL | 3.2e+04 8 0.00000 |
+--------------------------------------------------------+
Skewness test
+--------------------------------------------------------+
| Equation | Skewness chi2 df Prob > chi2 |
|--------------------+-----------------------------------|
| dlnM3 | .10562 1.023 1 0.31190 |
| dFFR | -2.488 567.447 1 0.00000 |
| dPPI | -.33108 10.048 1 0.00153 |
| dCPI | .16487 2.492 1 0.11445 |
| ALL | 581.009 4 0.00000 |
+--------------------------------------------------------+
varnorm, jbera skewness kurtosis
Kurtosis test
+--------------------------------------------------------+
| Equation | Kurtosis chi2 df Prob > chi2 |
|--------------------+-----------------------------------|
| dlnM3 | 4.2509 35.861 1 0.00000 |
| dFFR | 38.815 2.9e+04 1 0.00000 |
| dPPI | 11.047 1483.833 1 0.00000 |
| dCPI | 8.9833 820.420 1 0.00000 |
| ALL | 3.2e+04 4 0.00000 |
+--------------------------------------------------------+
.
varlmar, mlag(12)
Lagrange-multiplier test
+--------------------------------------+
| lag | chi2 df Prob > chi2 |
|------+-------------------------------|
| 1 | 15.0588 16 0.52033 |
| 2 | 16.4301 16 0.42337 |
| 3 | 9.0864 16 0.90981 |
| 4 | 25.9794 16 0.05432 |
| 5 | 23.6558 16 0.09730 |
| 6 | 9.2176 16 0.90418 |
| 7 | 18.1382 16 0.31586 |
| 8 | 18.5490 16 0.29274 |
| 9 | 23.9841 16 0.08985 |
| 10 | 30.2229 16 0.01688 |
| 11 | 27.2626 16 0.03865 |
| 12 | 12.3244 16 0.72136 |
+--------------------------------------+
H0: no autocorrelation at lag order
.
varstable, graph
All the eigenvalues lie inside the unit circle.
VAR satisfies stability condition.
.
-1-.
50
.51
Imag
inary
-1 -.5 0 .5 1Real
Roots of the companion matrix
varwle
Equation: dlnM3
+------------------------------------+
| lag | chi2 df Prob > chi2 |
|-----+------------------------------|
| 1 | 122.6979 4 0.000 |
| 2 | 12.07769 4 0.017 |
| 3 | 14.81815 4 0.005 |
| 4 | 1.105539 4 0.893 |
| 5 | 9.81928 4 0.044 |
| 6 | 2.545643 4 0.636 |
| 7 | 7.480774 4 0.113 |
| 8 | 13.22252 4 0.010 |
| 9 | 2.737011 4 0.603 |
| 10 | 6.656334 4 0.155 |
| 11 | 14.30326 4 0.006 |
| 12 | 4.559196 4 0.336 |
| 13 | 7.040044 4 0.134 |
| 14 | 12.24436 4 0.016 |
| 15 | 10.28816 4 0.036 |
+------------------------------------+
varwle
cd.
Equation: dFFR
+------------------------------------+
| lag | chi2 df Prob > chi2 |
|-----+------------------------------|
| 1 | 100.658 4 0.000 |
| 2 | 11.92328 4 0.018 |
| 3 | 7.11665 4 0.130 |
| 4 | 6.672551 4 0.154 |
| 5 | 2.617613 4 0.624 |
| 6 | 14.26101 4 0.007 |
| 7 | 25.09046 4 0.000 |
| 8 | 8.87384 4 0.064 |
| 9 | 4.80737 4 0.308 |
| 10 | 2.497883 4 0.645 |
| 11 | 5.015153 4 0.286 |
| 12 | 6.703731 4 0.152 |
| 13 | 15.54222 4 0.004 |
| 14 | 1.063314 4 0.900 |
| 15 | 3.162494 4 0.531 |
+------------------------------------+
Equation: dPPI
+------------------------------------+
irf set "_varbasic.irf„
irf create nazwa, step(30)
irf cgraph (VAR dPPI dCPI irf, noci) (VAR dPPI dlnM3 irf,
noci) (VAR dPPI dFFR irf, noci)
-.05
0
.05
0 10 20 30step
irf
VAR: dPPI -> dCPI
0
.0005
.001
0 10 20 30step
irf
VAR: dPPI -> dlnM3
-.1
0
.1
.2
0 10 20 30step
irf
VAR: dPPI -> dFFR
irf set "_varbasic.irf„
irf create nazwa, step(30)
irf cgraph (VAR dPPI dCPI fevd, noci) (VAR dPPI dlnM3
fevd, noci) (VAR dPPI dFFR fevd, noci)
0
.2
.4
0 10 20 30step
fevd
VAR: dPPI -> dCPI
0
.02
.04
.06
0 10 20 30step
fevd
VAR: dPPI -> dlnM3
0
.02
.04
.06
0 10 20 30step
fevd
VAR: dPPI -> dFFR
irf set "_varbasic.irf„
irf create nazwa, step(30)
irf cgraph (VAR dPPI dCPI irf, noci) (VAR dPPI dlnM3 irf,
noci) (VAR dPPI dFFR irf, noci)
vecrank dm3 dPPI dCPI dFFR, trend(constant) lags(15) sindicators(y*)
max ic level99
Johansen tests for cointegration
Trend: constant Number of obs = 550
Sample: 1960m5 - 2006m2 Lags = 15
-------------------------------------------------------------------------------
1%
maximum trace critical
rank parms LL eigenvalue statistic value
0 272 -2816.4821 . 93.9064 54.46
1 279 -2788.2315 0.09763 37.4052 35.65
2 284 -2773.2145 0.05314 7.3713* 20.04
3 287 -2769.5762 0.01314 0.0947 6.65
4 288 -2769.5289 0.00017
vec dlnM3 dPPI dCPI dFFR, trend(constant) rank(2) lags(12)
sindicators(y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11) alpha dforce
Vector error-correction model
Sample: 1960m2 - 2006m2 No. of obs = 553
AIC = -5.853304
Log likelihood = 1854.439 HQIC = -5.133795
Det(Sigma_ml) = 1.44e-08 SBIC = -4.011668
Equation Parms RMSE R-sq chi2 P>chi2
----------------------------------------------------------------
D_dlnM3 58 .002561 0.3348 248.6172 0.0000
D_dPPI 58 .665292 0.5262 548.6824 0.0000
D_dCPI 58 .220155 0.5185 531.8789 0.0000
D_dFFR 58 .504407 0.4539 410.5917 0.0000
----------------------------------------------------------------
cd.
Cointegrating equations
Equation Parms chi2 P>chi2
-------------------------------------------
_ce1 2 66.97018 0.0000
_ce2 2 76.4827 0.0000
-------------------------------------------
cd.
Identification: beta is exactly identified
Johansen normalization restrictions imposed
------------------------------------------------------------------------------
beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_ce1 |
dlnM3 | 1 . . . . .
dPPI | 3.47e-18 . . . . .
dCPI | .0026112 .0119567 0.22 0.827 -.0208235 .0260459
dFFR | -.1062535 .013092 -8.12 0.000 -.1319134 -.0805937
_cons | -.0167214 . . . . .
-------------+----------------------------------------------------------------
_ce2 |
dlnM3 | (omitted)
dPPI | 1 . . . . .
dCPI | -.777459 .2198926 -3.54 0.000 -1.208441 -.3464774
dFFR | -1.771007 .2407715 -7.36 0.000 -2.242911 -1.299104
_cons | .2052105 . . . . .
------------------------------------------------------------------------------
cd.
Identification: beta is exactly identified
Johansen normalization restrictions imposed
------------------------------------------------------------------------------
beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_ce1 |
dlnM3 | 1 . . . . .
dPPI | 3.47e-18 . . . . .
dCPI | .0026112 .0119567 0.22 0.827 -.0208235 .0260459
dFFR | -.1062535 .013092 -8.12 0.000 -.1319134 -.0805937
_cons | -.0167214 . . . . .
-------------+----------------------------------------------------------------
_ce2 |
dlnM3 | (omitted)
dPPI | 1 . . . . .
dCPI | -.777459 .2198926 -3.54 0.000 -1.208441 -.3464774
dFFR | -1.771007 .2407715 -7.36 0.000 -2.242911 -1.299104
_cons | .2052105 . . . . .
------------------------------------------------------------------------------
cd.
------------------------------------------------------------------------------
alpha | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
D_dlnM3 |
_ce1 |
L1. | -.0144611 .008811 -1.64 0.101 -.0317303 .0028081
|
_ce2 |
L1. | .0009488 .000561 1.69 0.091 -.0001507 .0020483
-------------+----------------------------------------------------------------
D_dPPI |
_ce1 |
L1. | 9.327865 2.288678 4.08 0.000 4.842139 13.81359
|
_ce2 |
L1. | -.6173326 .1457166 -4.24 0.000 -.9029318 -.3317333
-------------+----------------------------------------------------------------
D_dCPI |
_ce1 |
L1. | -.6319104 .7573556 -0.83 0.404 -2.1163 .8524793
|
_ce2 |
L1. | -.0699541 .0482197 -1.45 0.147 -.1644629 .0245547
-------------+----------------------------------------------------------------
D_dFFR |
-1-.
50
.51
Imag
inary
-1-.50.51Real
The VECM specification imposes 2 unit moduli
Roots of the companion matrix
1. Badanie stacjonarności
2. Sprowadzamy do tego samego poziomu integracji
(pamiętajmy o sensie, czy jest sens?) różnicując
3. Wybór liczby opóźnień
4. Diagnostyka – stabilność, normalność, wyłączenia
opóźnień, egzogeniczność, autokorelacja.
5. Wyniki przy pomocy funkcji reakcji i
dekompozycji wariancji
6. Test kointegracji.
7. Oszacowanie VEC
8. Diagnostyka jak w przypadku VAR.