UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA DEPARTAMENTO DE ECONOMIA

SOLUCIÓN DE LA SEXTA PRÁCTICA CALIFICADA DE ECONOMETRIA II

1º Construya un modelo de vectores autoregresivos para el periodo 1993:01 - 2010:12 para el IGB y el IPBI. Considere el máximo

retardos = 12, criterio Akaike. (13 puntos)

No existe quiebre estructural.

Existe quiebre estructural.

100

200

300

400

500

600

700

800

25 50 75 100 125 150 175 200 225

F FT FM

-5

-4

-3

-2

-1

0

1

50 75 100 125 150 175

ZIVOTM VCRITM

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

50 75 100 125 150 175

ZIVOTT VCRITT

-6

-5

-4

-3

-2

-1

0

1

2

50 75 100 125 150 175

ZIVOT VCRIT

400

800

1,200

1,600

2,000

2,400

2,800

25 50 75 100 125 150 175 200 225

F FT FM

-5

-4

-3

-2

-1

0

50 75 100 125 150 175

ZIVOTM VCRITM

-6

-5

-4

-3

-2

-1

50 75 100 125 150 175

ZIVOTT VCRITT

-6

-5

-4

-3

-2

-1

50 75 100 125 150 175

ZIVOT VCRIT

2

Dependent Variable: IPBI

Method: LeastSquares

Sample: 1 233 Variable Coefficient Std. Error t-Statistic Prob. C 88.47843 1.354062 65.34297 0.0000

DUM139 -8.758006 2.149015 -4.075358 0.0001

@TREND 0.349552 0.016964 20.60519 0.0000

DUT139 0.672870 0.034905 19.27706 0.0000 R-squared 0.957077 Mean dependentvar 138.3874

Adjusted R-squared 0.956514 S.D. dependentvar 38.48423

S.E. of regression 8.025185 Akaikeinfocriterion 7.020065

Sum squaredresid 14748.42 Schwarzcriterion 7.079310

Log likelihood -813.8376 Hannan-Quinncriter. 7.043955

Dependent Variable: IPBI

Method: LeastSquares

Sample: 1 233 Variable Coefficient Std. Error t-Statistic Prob. C 88.75007 1.238903 71.63603 0.0000

@TREND 0.343522 0.012728 26.99031 0.0000

DUT153 0.703947 0.036407 19.33550 0.0000 R-squared 0.956742 Mean dependentvar 138.3874

Adjusted R-squared 0.956366 S.D. dependentvar 38.48423

S.E. of regression 8.038871 Akaikeinfocriterion 7.019246

Sum squaredresid 14863.39 Schwarzcriterion 7.063680

Log likelihood -814.7422 Hannan-Quinncriter. 7.037164

Se corrige quiebre estructural en tendencia.

Modified: 1 233 // ipbic=ipbi-c(3)*dut153

1 85,01944 80,40388 84,65303 83,42716 87,17331

6 87,91812 84,17403 81,68151 80,97782 85,71912

11 84,79590 89,30589 79,58114 83,49815 89,28040

16 88,37837 90,70414 94,19493 89,46444 90,09849

21 87,39613 87,83669 88,86591 94,32695 91,93066

26 90,34324 99,25388 99,97141 106,0702 103,4961

Niveles.-

60

80

100

120

140

160

180

200

94 96 98 00 02 04 06 08 10

IPBIC

@MEAN(IPBIC,"1993m01 2010m12")

0

4,000

8,000

12,000

16,000

20,000

24,000

94 96 98 00 02 04 06 08 10

IGB @MEAN(IGB,"1993m01 2010m12")

3

IGB

Sample: 1993M01 2010M12

Includedobservations: 216 Autocorrelation PartialCorrelation AC PAC Q-Stat Prob .|******* .|******* 1 0.969 0.969 205.59 0.000

.|******* .|. | 2 0.940 0.013 399.82 0.000

.|******* .|. | 3 0.908 -0.053 582.00 0.000

.|******| .|. | 4 0.875 -0.042 751.91 0.000

.|******| .|. | 5 0.846 0.054 911.59 0.000

.|******| .|. | 6 0.820 0.039 1062.4 0.000

.|******| .|. | 7 0.795 -0.009 1204.7 0.000

.|******| .|. | 8 0.771 0.002 1339.2 0.000

.|***** | .|. | 9 0.744 -0.061 1465.0 0.000

.|***** | .|. | 10 0.719 0.024 1583.2 0.000

.|***** | .|. | 11 0.696 0.015 1694.3 0.000

.|***** | .|. | 12 0.669 -0.056 1797.7 0.000

IPBIC

Sample: 1993M01 2010M12

Includedobservations: 216 Autocorrelation PartialCorrelation AC PAC Q-Stat Prob .|******* .|******* 1 0.914 0.914 183.08 0.000

.|******| .|* | 2 0.849 0.081 341.76 0.000

.|******| .|* | 3 0.801 0.084 483.69 0.000

.|******| .|** | 4 0.796 0.261 624.31 0.000

.|******| .|** | 5 0.825 0.320 776.36 0.000

.|******| *|. | 6 0.812 -0.099 924.35 0.000

.|******| .|. | 7 0.792 0.035 1065.7 0.000

.|***** | **|. | 8 0.727 -0.231 1185.4 0.000

.|***** | .|. | 9 0.697 0.070 1295.9 0.000

.|***** | .|* | 10 0.706 0.146 1409.9 0.000

.|***** | .|** | 11 0.742 0.228 1536.4 0.000

.|******| .|* | 12 0.782 0.178 1677.4 0.000

H0: IGB TIENE R. U. PRUEBA ESTADISTICO VALOR CRÍTICO TIENE R. U.

1 % 5 % 1 % 5 % ADF -1.854481 -4.001311 -3.430864 SI SI PP -1.562663 -4.001108 -3.430766 SI SI GLS -1.776032 -3.461500 -2.927000 SI SI ERS 5.135598 4.042800 5.656800 SI NO N MZa -23.7891 -23.8000 -17.3000 SI NO

G MZT -3.28533 -3.42000 -2.91000 SI NO

- MSB 0.13810 0.14300 0.16800 NO NO

P MSB 4.81205 4.03000 5.48000 SI NO H0: IGB NO TIENE RAÍZ UNITARIA

4

KPSS 0.299252 0.216000 0.146000 NO NO

H0: IPBIC TIENE R. U. PRUEBA ESTADISTICO VALOR CRÍTICO TIENE R. U.

1 % 5 % 1 % 5 % ADF -3.109170 -4.001311 -3.430864 SI SI PP -7.636557 -4.001108 -3.430766 NO NO GLS -2.057370 -3.461500 -2.927000 SI SI ERS 22.54121 4.042800 5.656800 SI SI N MZa -1.69860 -23.8000 -17.3000 SI SI

G MZT -0.83054 -3.42000 -2.91000 SI SI

- MSB 0.48896 0.14300 0.16800 SI SI

P MSB 46.2825 4.03000 5.48000 SI SI H0: IPBIC NO TIENE RAÍZ UNITARIA KPSS 0.160586 0.216000 0.146000 SI NO

Primera diferencia.-

-5,000

-4,000

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

4,000

94 96 98 00 02 04 06 08 10

D(IGB)

@MEAN(D(IGB),"1993m01 2010m12")

-30

-20

-10

0

10

20

94 96 98 00 02 04 06 08 10

D(IPBIC)

@MEAN(D(IPBIC),"1993m01 2010m12")

D(IGB)

Sample: 1993M01 2010M12

Included observations: 216 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|* | .|* | 1 0.207 0.207 9.3931 0.002

.|** | .|** | 2 0.331 0.301 33.437 0.000

.|** | .|* | 3 0.240 0.149 46.123 0.000

.|* | *|. | 4 0.087 -0.070 47.820 0.000

.|. | **|. | 5 -0.061 -0.211 48.645 0.000

.|. | .|. | 6 0.004 -0.015 48.649 0.000

*|. | *|. | 7 -0.151 -0.084 53.771 0.000

.|. | .|* | 8 -0.010 0.101 53.792 0.000

.|. | .|. | 9 -0.042 0.051 54.198 0.000

.|. | .|* | 10 0.055 0.093 54.882 0.000

.|* | .|* | 11 0.094 0.082 56.927 0.000

.|. | *|. | 12 -0.030 -0.170 57.134 0.000

5

D(IPBIC)

Sample: 1993M01 2010M12

Included observations: 216 Autocorrelation Partial Correlation AC PAC Q-Stat Prob *|. | *|. | 1 -0.095 -0.095 1.9940 0.158

*|. | *|. | 2 -0.121 -0.131 5.2087 0.074

**|. | ***|. | 3 -0.329 -0.364 29.126 0.000

**|. | ***|. | 4 -0.276 -0.453 46.067 0.000

.|** | .|* | 5 0.337 0.107 71.477 0.000

.|. | *|. | 6 0.006 -0.199 71.485 0.000

.|** | .|* | 7 0.329 0.200 95.801 0.000

**|. | *|. | 8 -0.246 -0.168 109.45 0.000

**|. | **|. | 9 -0.293 -0.230 129.01 0.000

*|. | ***|. | 10 -0.147 -0.383 133.95 0.000

.|. | **|. | 11 -0.028 -0.317 134.14 0.000

.|******| .|**** | 12 0.799 0.567 281.66 0.000

Hypothesis Testing for D(IGB)

Sample: 1993M01 2010M12

Included observations: 216

Test of Hypothesis: Mean = 0.000000 Sample Mean = 106.4890

Sample Std. Dev. = 815.7792

Method Value Probability

t-statistic 1.918487 0.0564

H0: D(IGB) TIENE R. U. PRUEBA ESTADISTICO VALOR CRÍTICO TIENE R. U.

1 % 5 % 1 % 5 % ADF -3.566659 -2.575813 -1.942317 NO NO PP -12.27709 -2.575712 -1.942303 NO NO GLS -3.811275 -2.575813 -1.942317 NO NO ERS 0.008831 1.916400 3.177200 NO NO N MZa -12855.8 -13.8000 -8.10000 NO NO

G MZT -80.1611 -2.58000 -1.98000 NO NO

- MSB 0.00624 0.17400 0.23300 NO NO

P MSB 0.00416 1.78000 3.17000 NO NO H0: D(IGB) NO TIENE RAÍZ UNITARIA KPSS 0.206401 0.739000 0.463000 NO NO

H0: D(IPBIC) TIENE R. U. PRUEBA ESTADISTICO VALOR CRÍTICO TIENE R. U.

1 % 5 % 1 % 5 % ADF -2.384092 -2.575813 -1.942317 SI NO

6

PP -22.27023 -2.575712 -1.942303 NO NO GLS -0.103277 -2.575813 -1.942317 SI SI ERS 60.84888 1.916400 3.177200 SI SI N MZa 0.90492 -13.8000 -8.10000 SI SI

G MZT 2.62789 -2.58000 -1.98000 SI SI

- MSB 2.90401 0.17400 0.23300 SI SI

P MSB 526.543 1.78000 3.17000 SI SI H0: D(IPBIC) NO TIENE RAÍZ UNITARIA KPSS 0.086566 0.739000 0.463000 NO NO

IGB es integrada de orden 1.

Segunda diferencia.-

D(IPBIC,2)

Sample: 1993M01 2010M12

Included observations: 216 Autocorrelation Partial Correlation AC PAC Q-Stat Prob ****|. | ****|. | 1 -0.485 -0.485 51.448 0.000

.|* | *|. | 2 0.081 -0.201 52.884 0.000

*|. | **|. | 3 -0.117 -0.228 55.886 0.000

**|. | ****|. | 4 -0.254 -0.589 70.169 0.000

.|*** | *|. | 5 0.435 -0.126 112.42 0.000

**|. | ***|. | 6 -0.298 -0.384 132.39 0.000

.|*** | .|. | 7 0.399 0.060 168.23 0.000

**|. | .|. | 8 -0.240 0.053 181.22 0.000

*|. | .|* | 9 -0.093 0.074 183.18 0.000

.|. | *|. | 10 0.022 -0.136 183.29 0.000

**|. | *****|. | 11 -0.313 -0.637 205.82 0.000

.|***** | .|* | 12 0.752 0.101 336.40 0.000

H0: D2IPBIC TIENE R. U. PRUEBA ESTADISTICO VALOR CRÍTICO TIENE R. U.

1 % 5 % 1 % 5 % ADF -12.80892 -2.575864 -1.942324 NO NO PP -114.3145 -2.575712 -1.942303 NO NO GLS -0.117329 -2.575864 -1.942324 SI SI ERS 38331.29 1.916400 3.177200 SI SI N MZa 1.18607 -13.8000 -8.10000 SI SI

G MZT 4.63512 -2.58000 -1.98000 SI SI

- MSB 3.90797 0.17400 0.23300 SI SI

P MSB 1007.73 1.78000 3.17000 SI SI H0: D2IPBIC NO TIENE RAÍZ UNITARIA KPSS 0.270935 0.739000 0.463000 NO NO

7

IPBIC es integrada de orden 2.

Determinación de retardo óptimo.-

VAR Lag Order Selection Criteria

Endogenous variables: D(IGB) D(IPBIC,2)

Exogenous variables: C

Sample: 1993M01 2010M12

Included observations: 214 Lag LogL LR FPE AIC SC HQ 0 -2562.965 NA 88267082 23.97163 24.00309 23.98434

1 -2528.648 67.67143 66488985 23.68830 23.78267 23.72643

2 -2511.993 32.53154 59073327 23.57003 23.72732 23.63359

3 -2500.335 22.55224 54995112 23.49846 23.71867 23.58744

4 -2450.584 95.31907 35863104 23.07087 23.35399 23.18528

5 -2438.423 23.07189 33232212 22.99460 23.34064 23.13443

6 -2412.404 48.87629 27054555 22.78882 23.19777 22.95407

7 -2409.636 5.146733 27372437 22.80034 23.27221 22.99102

8 -2405.287 8.008423 27288852 22.79707 23.33185 23.01317

9 -2402.735 4.651204 27667979 22.81060 23.40830 23.05213

10 -2396.688 10.90668 27152723 22.79147 23.45209 23.05842

11 -2266.970 231.5531 8389157. 21.61654 22.34007 21.90891

12 -2241.045 45.79200* 6838128.* 21.41164* 22.19808* 21.72943*

Evaluación.-

Roots of Characteristic Polynomial

Endogenous variables: D(IGB) D(IPBIC,2)

Exogenous variables: C

Lag specification: 1 12 Root Modulus 0.498877 - 0.870467i 1.003290

0.498877 + 0.870467i 1.003290

-0.002406 - 0.995304i 0.995306

-0.002406 + 0.995304i 0.995306

0.858824 + 0.495940i 0.991734

0.858824 - 0.495940i 0.991734

-0.858606 - 0.494786i 0.990968

-0.858606 + 0.494786i 0.990968

-0.511867 + 0.841439i 0.984900

-0.511867 - 0.841439i 0.984900

-0.635145 + 0.673154i 0.925497

-0.635145 - 0.673154i 0.925497

0.239454 - 0.877136i 0.909233

0.239454 + 0.877136i 0.909233

-0.266799 - 0.868582i 0.908635

-0.266799 + 0.868582i 0.908635

0.774112 - 0.474300i 0.907860

0.774112 + 0.474300i 0.907860

-0.896517 0.896517

-0.876494 + 0.165642i 0.892008

-0.876494 - 0.165642i 0.892008

0.833060 + 0.152003i 0.846814

0.833060 - 0.152003i 0.846814

-0.504129 0.504129

8

VAR Lag Exclusion Wald Tests

Sample: 1993M01 2010M12

Included observations: 214 Chi-squared test statistics for lag exclusion:

Numbers in [ ] are p-values D(IGB) D(IPBIC,2) Joint Lag 1 5.602929 466.9226 473.6316

[ 0.060721] [ 0.000000] [ 0.000000]

Lag 2 23.90320 304.9389 330.6234

[ 6.45e-06] [ 0.000000] [ 0.000000]

Lag 3 21.63908 262.8184 285.4953

[ 2.00e-05] [ 0.000000] [ 0.000000]

Lag 4 2.191779 233.5798 236.7059

[ 0.334242] [ 0.000000] [ 0.000000]

Lag 5 10.19507 178.4518 189.7137

[ 0.006112] [ 0.000000] [ 0.000000]

Lag 6 3.485490 158.8073 163.1615

[ 0.175039] [ 0.000000] [ 0.000000]

Lag 7 14.12949 152.2079 167.1863

[ 0.000855] [ 0.000000] [ 0.000000]

Lag 8 5.930337 154.2182 161.3452

[ 0.051552] [ 0.000000] [ 0.000000]

Lag 9 4.952181 180.9569 186.9616

[ 0.084071] [ 0.000000] [ 0.000000]

Lag 10 14.22851 237.3064 253.0321

[ 0.000813] [ 0.000000] [ 0.000000]

Lag 11 5.249888 238.8671 245.1956

[ 0.072444] [ 0.000000] [ 0.000000]

Lag 12 16.32392 32.65710 49.30116

[ 0.000285] [ 8.10e-08] [ 5.05e-10] df 2 2 4

VAR Residual Portmanteau Tests for Autocorrelations

Null Hypothesis: no residual autocorrelations up to lag h

Sample: 1993M01 2010M12

Included observations: 214 Lags Q-Stat Prob. Adj Q-Stat Prob. df 13 36.84151 0.0000 38.06789 0.0000 4

VAR Residual Serial Correlation LM Tests Null Hypothesis: no serial correlation at lag order h

Sample: 1993M01 2010M12

Included observations: 214 Lags LM-Stat Prob 1 15.31777 0.0041

2 10.30763 0.0356

Probs from chi-square with 4 df.

VAR Residual Normality Tests

9

Orthogonalization: Cholesky (Lutkepohl)

Null Hypothesis: residuals are multivariate normal

Sample: 1993M01 2010M12

Included observations: 214 Component Jarque-Bera df Prob.

1 237.1675 2 0.0000

2 2.683827 2 0.2613 Joint 239.8514 4 0.0000

VAR Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares)

Sample: 1993M01 2010M12

Included observations: 214 Joint test:

Chi-sq df Prob. 282.7112 147 0.0000 Individual components:

Dependent R-squared F(49,164) Prob. Chi-sq(49) Prob. res1*res1 0.690723 7.474887 0.0000 147.8148 0.0000

res2*res2 0.199091 0.831989 0.7709 42.60558 0.7285

res2*res1 0.505723 3.424446 0.0000 108.2248 0.0000

Simulación.-

-400

-200

0

200

400

600

800

1 2 3 4 5 6 7 8 9 10

Response of D(IGB) to D(IGB)

-400

-200

0

200

400

600

800

1 2 3 4 5 6 7 8 9 10

Response of D(IGB) to D(IPBIC,2)

-6

-4

-2

0

2

4

1 2 3 4 5 6 7 8 9 10

Response of D(IPBIC,2) to D(IGB)

-6

-4

-2

0

2

4

1 2 3 4 5 6 7 8 9 10

Response of D(IPBIC,2) to D(IPBIC,2)

Response to Cholesky One S.D. Innovations ± 2 S.E.

Variance Decomposition of D(IGB):

Period S.E. D(IGB) D(IPBIC,2) 1 683.5248 100.0000 0.000000

2 692.9115 99.38669 0.613308

10

3 731.0669 99.24999 0.750015

4 785.6009 99.27575 0.724248

5 804.2682 99.28586 0.714141

6 805.4334 99.25329 0.746708

7 813.6119 98.81433 1.185668

8 824.4987 98.79872 1.201276

9 828.3241 98.19847 1.801535

10 833.7169 97.33605 2.663952 Variance Decomposition of D(IPBIC,2):

Period S.E. D(IGB) D(IPBIC,2) 1 3.426218 0.039029 99.96097

2 6.004817 0.052123 99.94788

3 6.396251 0.784848 99.21515

4 6.459307 0.906000 99.09400

5 6.464223 1.053376 98.94662

6 6.527608 1.836969 98.16303

7 6.634751 3.191360 96.80864

8 6.679353 3.377293 96.62271

9 6.711506 3.705065 96.29494

10 6.739225 4.242519 95.75748

obs IGB IGB_1 IPBI IPBI_1

2011M01 22887.41 24903,95 210.9839 213,1065

2011M02 22842.96 26288,63 205.8776 213,3378

2011M03 21957.49 26973,18 222.3688 231,3443

2011M04 19636.22 27076,96 232.3530 242,6853

2011M05 21566.07 27052,27 245.4241 257,2509

2º Comente y fundamente su respuesta: (7 puntos) 2.1. El modelo de vectores autoregresivos se estima por mínimos cuadrados generalizados. 2.2. El modelo de vectores autoregresivos se identifica igual que un modelo multiecuacional.