COINTEGRACION

El objetivo es encontrar relaciones escondidas de LP que puedan hacer que todo el sistema sea estable.

Si el VAR es estable , calculamos la función impulso respuesta, descomposición de la varianza, etc.

Si no es estable tratamos de hacer integración

Tenemos un conjunto de variables y nuestro trabajo es buscar relaciones posibles (validas económicamente ) que puedan hacer que haya relaciones escondidas de cointegracion .

En un VAR en la matriz ᶲ tiene las filas son linealmente independientes, el nro de filas indep nos indican el nro de vectores de cointegracion

Alfa es la velocidad de ajuste que hace que la variable regrese a su velocidad de ajuste

si el rango es cero hay inestabilidad

Existe posiblemente quiebre estructural

Date: 11/02/13 Time: 12:42Sample (adjusted): 1976Q2 1987Q3Included observations: 46 after adjustmentsTrend assumption: No deterministic trend (restricted constant)Series: LRM LRY IB IDExogenous series: D2C D3C D4CWarning: Critical values assume no exogenous seriesLags interval (in first differences): 1 to 8

Hypothesized Trace 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None **  0.891011  191.1292  53.12  60.16At most 1 **  0.604425  89.16967  34.91  41.07At most 2 **  0.490326  46.50856  19.96  24.60At most 3 **  0.286143  15.50531   9.24  12.97

 Trace test indicates 4 cointegrating equation(s) at both 5% and 1% levels *(**) denotes rejection of the hypothesis at the 5%(1%) level

Hypothesized Max-Eigen 5 Percent 1 PercentNo. of CE(s) Eigenvalue Statistic Critical Value Critical Value

None **  0.891011  101.9595  28.14  33.24At most 1 **  0.604425  42.66112  22.00  26.81At most 2 **  0.490326  31.00325  15.67  20.20

At most 3 **  0.286143  15.50531   9.24  12.97

 Max-eigenvalue test indicates 4 cointegrating equation(s) at both 5% and 1% levels *(**) denotes rejection of the hypothesis at the 5%(1%) level

 Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

LRM LRY IB ID C-343.6973  300.1023 -1457.627  834.6860  2409.670 195.2821 -151.4541  679.3830 -203.7246 -1483.757 126.5132 -188.9086  206.4878  120.9135 -404.9735 46.40270 -85.66164  135.5111 -306.6267 -27.46787

 Unrestricted Adjustment Coefficients (alpha):

D(LRM) -0.003374 -0.004448  0.000851  0.000380D(LRY) -0.007166 -0.001357  0.000160  0.004504D(IB)  0.002658  0.000380 -0.000543  0.001346D(ID)  0.000817  0.000474 -0.001625 -0.000474

1 Cointegrating Equation(s): Log likelihood  777.3373

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000 -0.873159  4.241021 -2.428550 -7.011023 (0.02984)  (0.11683)  (0.16867)  (0.18681)

Adjustment coefficients (standard error in parentheses)D(LRM)  1.159701

 (0.65306)D(LRY)  2.463008

 (0.97380)D(IB) -0.913489

 (0.30800)D(ID) -0.280692

 (0.27975)

2 Cointegrating Equation(s): Log likelihood  798.6678

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000  0.000000 -2.576890  9.965803 -12.26284 (2.79466)  (5.78986)  (0.22906)

 0.000000  1.000000 -7.808330  14.19485 -6.014731 (3.22002)  (6.67112)  (0.26393)

Adjustment coefficients (standard error in parentheses)D(LRM)  0.291126 -0.338966

 (0.50502)  (0.42945)D(LRY)  2.198064 -1.945116

 (1.10710)  (0.94145)D(IB) -0.839365  0.740133

 (0.35105)  (0.29853)D(ID) -0.188099  0.173277

 (0.31624)  (0.26892)

3 Cointegrating Equation(s): Log likelihood  814.1694

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000  0.000000  0.000000  5.751092 -12.29073 (1.75044)  (0.17137)

 0.000000  1.000000  0.000000  1.423694 -6.099251 (1.05705)  (0.10349)

 0.000000  0.000000  1.000000 -1.635580 -0.010824 (0.23406)  (0.02292)

Adjustment coefficients (standard error in parentheses)D(LRM)  0.398816 -0.499769  2.072325

 (0.51835)  (0.48156)  (2.02490)D(LRY)  2.218357 -1.975416  9.557055

 (1.16223)  (1.07975)  (4.54017)D(IB) -0.908051  0.842695 -3.728355

 (0.36164)  (0.33598)  (1.41273)D(ID) -0.393673  0.480238 -1.203818

 (0.25449)  (0.23643)  (0.99416)

Ho: es el numero de cointegracion

Tabla uno:Fila 1 Ho:

noexiste ningún vector de

cointegracionFila2: existe a lo mas un vector de

cointegracion

Diferencia con la opción: freeze(tabla_coint2) var1.coint(cvsize=0.05, b, 8)

Date: 11/02/13 Time: 13:06Sample (adjusted): 1976Q2 1987Q3Included observations: 46 after adjustmentsTrend assumption: No deterministic trend (restricted constant)Series: LRM LRY IB IDExogenous series: D2C D3C D4CWarning: Critical values assume no exogenous seriesLags interval (in first differences): 1 to 8

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None *  0.891011  191.1292  54.07904  0.0000At most 1 *  0.604425  89.16967  35.19275  0.0000At most 2 *  0.490326  46.50856  20.26184  0.0000At most 3 *  0.286143  15.50531  9.164546  0.0028

 Trace test indicates 4 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None *  0.891011  101.9595  28.58808  0.0000At most 1 *  0.604425  42.66112  22.29962  0.0000At most 2 *  0.490326  31.00325  15.89210  0.0001At most 3 *  0.286143  15.50531  9.164546  0.0028

 Max-eigenvalue test indicates 4 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

 Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

LRM LRY IB ID C-343.6973  300.1023 -1457.627  834.6860  2409.670 195.2821 -151.4541  679.3830 -203.7246 -1483.757 126.5132 -188.9086  206.4878  120.9135 -404.9735 46.40270 -85.66164  135.5111 -306.6267 -27.46787

 Unrestricted Adjustment Coefficients (alpha):

D(LRM) -0.003374 -0.004448  0.000851  0.000380D(LRY) -0.007166 -0.001357  0.000160  0.004504D(IB)  0.002658  0.000380 -0.000543  0.001346D(ID)  0.000817  0.000474 -0.001625 -0.000474

1 Cointegrating Equation(s): Log likelihood  777.3373

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000 -0.873159  4.241021 -2.428550 -7.011023 (0.02984)  (0.11683)  (0.16867)  (0.18681)

Adjustment coefficients (standard error in parentheses)D(LRM)  1.159701

 (0.65306)D(LRY)  2.463008

 (0.97380)D(IB) -0.913489

 (0.30800)D(ID) -0.280692

 (0.27975)

2 Cointegrating Equation(s): Log likelihood  798.6678

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000  0.000000 -2.576890  9.965803 -12.26284 (2.79466)  (5.78986)  (0.22906)

 0.000000  1.000000 -7.808330  14.19485 -6.014731 (3.22002)  (6.67112)  (0.26393)

Adjustment coefficients (standard error in parentheses)D(LRM)  0.291126 -0.338966

 (0.50502)  (0.42945)D(LRY)  2.198064 -1.945116

 (1.10710)  (0.94145)D(IB) -0.839365  0.740133

 (0.35105)  (0.29853)D(ID) -0.188099  0.173277

 (0.31624)  (0.26892)

3 Cointegrating Equation(s): Log likelihood  814.1694

Normalized cointegrating coefficients (standard error in parentheses)LRM LRY IB ID C

 1.000000  0.000000  0.000000  5.751092 -12.29073 (1.75044)  (0.17137)

 0.000000  1.000000  0.000000  1.423694 -6.099251 (1.05705)  (0.10349)

 0.000000  0.000000  1.000000 -1.635580 -0.010824 (0.23406)  (0.02292)

Adjustment coefficients (standard error in parentheses)D(LRM)  0.398816 -0.499769  2.072325

 (0.51835)  (0.48156)  (2.02490)D(LRY)  2.218357 -1.975416  9.557055

 (1.16223)  (1.07975)  (4.54017)D(IB) -0.908051  0.842695 -3.728355

 (0.36164)  (0.33598)  (1.41273)D(ID) -0.393673  0.480238 -1.203818

 (0.25449)  (0.23643)  (0.99416)

tabla 2 de coint1

corresponde a las B relaciones de LP

Lo segundo es el alfa

Se normaliza para tener ecuaciones independientes

Si las relaciones de cointegacion normalizadas son validas aplico un t etadistico que seria :

-0.873159/0.02984

NOSOTROS MISMOS PONEMOS RESTRICCIONES

=0 significa que pasamos las que no

aha sido normalizadas al lado derecho

Es acorde con la teoría economica