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TRABAJO PRÁCTICO DE ECONOMETRÍA
VAR (p) con dos variables
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Vector Autoregression Estimates Date: 10/09/16 Time: 16:47 Sample (adjusted): 1972 2014 Included observations: 43 after adjustments Standard errors in ( ) & t-statistics in [ ]
GASTO INGRESO
GASTO(-1) 0.446895 -1.268034 (0.38032) (0.57486)[ 1.17505] [-2.20580]
GASTO(-2) 0.248667 1.057439 (0.32010) (0.48384)[ 0.77684] [ 2.18552]
INGRESO(-1) 0.620654 2.147987 (0.23873) (0.36085)[ 2.59981] [ 5.95261]
INGRESO(-2) -0.343716 -0.944695 (0.21668) (0.32752)[-1.58627] [-2.88438]
C 4.91E+10 1.18E+11 (4.2E+10) (6.3E+10)[ 1.17854] [ 1.86975]
R-squared 0.999414 0.999036 Adj. R-squared 0.999352 0.998934 Sum sq. resids 4.41E+23 1.01E+24 S.E. equation 1.08E+11 1.63E+11 F-statistic 16200.29 9843.137 Log likelihood -1150.696 -1168.460 Akaike AIC 53.75329 54.57953 Schwarz SC 53.95808 54.78432 Mean dependent 6.45E+12 7.90E+12 S.D. dependent 4.23E+12 4.99E+12
Determinant resid covariance (dof adj.) 4.68E+43 Determinant resid covariance 3.65E+43 Log likelihood -2278.613 Akaike information criterion 106.4471 Schwarz criterion 106.8567
El cuadro que se observa, es el modelo VAR que se debe corregir ya que este es un modelo no estacionario.
Aplicando el test de Dickey - Fuller Aumentado vemos si la variable tiene o no tiene raíz unitaria
GASTO
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Null Hypothesis: GASTO has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 2.398525 1.0000
Test critical values: 1% level -3.592462
5% level -2.931404
10% level -2.603944
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GASTO)
Method: Least Squares
Date: 10/09/16 Time: 16:56
Sample (adjusted): 1972 2014
Included observations: 43 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
GASTO(-1) 0.013868 0.005782 2.398525 0.0212
D(GASTO(-1)) 0.431743 0.145698 2.963283 0.0051
C 9.79E+10 3.80E+10 2.573433 0.0139
R-squared 0.516821 Mean dependent var 3.14E+11
Adjusted R-squared 0.492662 S.D. dependent var 1.63E+11
S.E. of regression 1.16E+11 Akaike info criterion 53.85477
Sum squared resid 5.36E+23 Schwarz criterion 53.97764
Log likelihood -1154.878 Hannan-Quinn criter. 53.90008
F-statistic 21.39249 Durbin-Watson stat 1.931941
Prob(F-statistic) 0.000000
Con el 100 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(GASTO) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.921157 0.0512Test critical values: 1% level -3.592462
5% level -2.93140410% level -2.603944
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(GASTO,2)Method: Least SquaresDate: 10/09/16 Time: 17:15Sample (adjusted): 1972 2014Included observations: 43 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GASTO(-1)) -0.336469 0.115183 -2.921157 0.0056C 1.12E+11 3.97E+10 2.835147 0.0071
R-squared 0.172272 Mean dependent var 1.02E+10Adjusted R-squared 0.152083 S.D. dependent var 1.33E+11S.E. of regression 1.22E+11 Akaike info criterion 53.94263Sum squared resid 6.13E+23 Schwarz criterion 54.02455Log likelihood -1157.767 Hannan-Quinn criter. 53.97284F-statistic 8.533159 Durbin-Watson stat 2.089776Prob(F-statistic) 0.005648
Aplicando un diferencial se puede observar que tenemos un 5% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el GASTO.
CONSUMO
Null Hypothesis: INGRESO has a unit rootExogenous: Constant
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Lag Length: 1 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 2.222055 0.9999Test critical values: 1% level -3.592462
5% level -2.93140410% level -2.603944
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(INGRESO)Method: Least SquaresDate: 10/09/16 Time: 17:22Sample (adjusted): 1972 2014Included observations: 43 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INGRESO(-1) 0.014482 0.006517 2.222055 0.0320D(INGRESO(-1)) 0.390338 0.149320 2.614104 0.0125
C 1.26E+11 5.45E+10 2.309906 0.0261
R-squared 0.405385 Mean dependent var 3.76E+11Adjusted R-squared 0.375654 S.D. dependent var 2.14E+11S.E. of regression 1.69E+11 Akaike info criterion 54.61029Sum squared resid 1.14E+24 Schwarz criterion 54.73317Log likelihood -1171.121 Hannan-Quinn criter. 54.65560F-statistic 13.63521 Durbin-Watson stat 1.836458Prob(F-statistic) 0.000031
Con el 99,99 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(INGRESO) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.274152 0.0224Test critical values: 1% level -3.592462
5% level -2.93140410% level -2.603944
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(INGRESO,2)Method: Least SquaresDate: 10/09/16 Time: 17:23Sample (adjusted): 1972 2014
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Included observations: 43 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INGRESO(-1)) -0.420403 0.128400 -3.274152 0.0022C 1.66E+11 5.38E+10 3.089407 0.0036
R-squared 0.207271 Mean dependent var 1.38E+10Adjusted R-squared 0.187936 S.D. dependent var 1.96E+11S.E. of regression 1.77E+11 Akaike info criterion 54.68017Sum squared resid 1.28E+24 Schwarz criterion 54.76209Log likelihood -1173.624 Hannan-Quinn criter. 54.71038F-statistic 10.72007 Durbin-Watson stat 1.915621Prob(F-statistic) 0.002158
Aplicando un diferencial se puede observar que tenemos un 2% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el GASTO.
Aplicamos el test de Granger
VAR Granger Causality/Block Exogeneity Wald TestsDate: 10/09/16 Time: 17:34Sample: 1970 2014Included observations: 42
Dependent variable: DGASTO
Excluded Chi-sq df Prob.
DINGRESO 8.463362 2 0.0145
All 8.463362 2 0.0145
Dependent variable: DINGRESO
Excluded Chi-sq df Prob.
DGASTO 6.516912 2 0.0384
All 6.516912 2 0.0384
Aplicando el test podemos observar los resultados y decir que el gasto se ve influenciado por el ingreso y el ingreso se ve influenciado por el gasto.
VAR Lag Order Selection CriteriaEndogenous variables: DGASTO DINGRESO Exogenous variables: C Date: 10/09/16 Time: 17:38
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Sample: 1970 2014Included observations: 40
Lag LogL LR FPE AIC SC HQ
0 -2149.096 NA 1.76e+44 107.5548 107.6392 107.58531 -2130.591 34.23351 8.53e+43 106.8296 107.0829 106.92122 -2127.056 6.186913 8.75e+43 106.8528 107.2750 107.00553 -2116.332 17.69502 6.28e+43 106.5166 107.1077 106.73034 -2105.332 17.05025* 4.46e+43* 106.1666* 106.9266* 106.4414*
* indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion
En este caso tanto Akaike, Schawrtz y Hannan Quinn indican que se debe utilizar cuatro rezagos lo cual se demostrara en el siguiente cuadro.
Vector Autoregression Estimates Date: 10/09/16 Time: 17:42 Sample (adjusted): 1975 2014 Included observations: 40 after adjustments Standard errors in ( ) & t-statistics in [ ]
DGASTO DINGRESO
DGASTO(-1) -0.983006 -1.989568 (0.47032) (0.68280)[-2.09007] [-2.91384]
DGASTO(-2) 0.562521 0.757941 (0.46824) (0.67978)[ 1.20134] [ 1.11498]
DGASTO(-3) 0.306475 0.147211 (0.56314) (0.81754)[ 0.54423] [ 0.18007]
DGASTO(-4) 0.391590 1.383386 (0.52400) (0.76073)[ 0.74731] [ 1.81850]
DINGRESO(-1) 1.019281 1.669798 (0.32249) (0.46818)[ 3.16069] [ 3.56661]
DINGRESO(-2) -0.300133 -0.384630 (0.30969) (0.44960)[-0.96914] [-0.85550]
DINGRESO(-3) -0.229071 -0.233129 (0.40459) (0.58737)[-0.56618] [-0.39690]
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DINGRESO(-4) 0.010661 -0.635723 (0.34753) (0.50453)[ 0.03068] [-1.26002]
C 5.98E+10 1.49E+11 (4.8E+10) (7.0E+10)[ 1.23660] [ 2.12662]
R-squared 0.607393 0.539944 Adj. R-squared 0.506075 0.421220 Sum sq. resids 3.75E+23 7.90E+23 S.E. equation 1.10E+11 1.60E+11 F-statistic 5.994924 4.547891 Log likelihood -1068.607 -1083.518 Akaike AIC 53.88035 54.62591 Schwarz SC 54.26034 55.00591 Mean dependent 3.31E+11 3.95E+11 S.D. dependent 1.57E+11 2.10E+11
Determinant resid covariance (dof adj.) 2.97E+43 Determinant resid covariance 1.79E+43 Log likelihood -2105.332 Akaike information criterion 106.1666 Schwarz criterion 106.9266
Observando en las estimaciones de auto regresión podemos decir que solo en un periodo el ingreso en función del gasto y en función el gasto, el gasto en función del ingreso, el ingreso en función del gasto y el ingreso en función del ingreso son significativos, pero la pendiente debe ser teóricamente mayor a 0 y menor a 1 y aquí demuestra lo contrario lo cual en teoría económica este modelo está mal.
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Según las gráficas:
En la primera Gráfica podemos decir que el gasto respecto al gasto después del primer periodo se vuelve cero.
En la segunda Gráfica podemos decir que el gasto respecto al ingreso después del primer periodo se vuelve cero.
En la tercera Gráfica podemos decir que el ingreso respecto al gasto después del primer periodo se vuelve cero.
En la cuarta Gráfica podemos decir que el ingreso respecto al ingreso después del primer periodo se vuelve cero.
Esto significa que este modelo VAR es inefectivo.
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Con las gráfica diferenciada del ingreso y del gasto se comportan de una forma muy aleatoria.
Conclusión
En teoría económica este modelo está mal porque no explica lo que se necesita, por lo tanto se utilizará un modelo VEC .
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Aplicamos modelo VEC
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Date: 10/09/16 Time: 18:46Sample: 1970 2014Included observations: 43Series: GASTO INGRESO Lags interval: 1 to 1
Selected (0.05 level*) Number of
Cointegrating Relations by
Model
Data Trend: None None Linear Linear QuadraticTest Type No Intercept Intercept Intercept Intercept Intercept
No Trend No Trend No Trend Trend TrendTrace 1 1 2 2 1
Max-Eig 1 1 0 0 0
*Critical values based on MacKinnon-Haug-Michelis (1999)
Information Criteria by Rank and
Model
Data Trend: None None Linear Linear QuadraticRank or No Intercept Intercept Intercept Intercept Intercept
No. of CEs No Trend No Trend No Trend Trend Trend
Log Likelihood by Rank (rows)
and Model (columns)
0 -2292.919 -2292.919 -2288.350 -2288.350 -2282.1951 -2282.981 -2282.455 -2281.340 -2279.563 -2273.9952 -2281.491 -2278.613 -2278.613 -2272.555 -2272.555
Akaike Information Criteria by
Rank (rows) and Model (columns)
0 106.8334 106.8334 106.7140 106.7140 106.52071 106.5573 106.5793 106.5739 106.5378 106.3253*2 106.6740 106.6331 106.6331 106.4444 106.4444
Schwarz Criteria by
Rank (rows) and Model (columns)
0 106.9973 106.9973 106.9597 106.9597 106.84841 106.8849 106.9479 106.9835 106.9884 106.8168*2 107.1655 107.2066 107.2066 107.0997 107.0997
Observando el test de Trace y Max – Eig, puede notarse que con Trace los 5 modelos superan 0, Akaike y Schawrtz nos indican que se utilice el modelo 5 y un rezago, por tanto se puede validar que si tenemos un modelo de cointegración.
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Vector Error Correction Estimates Date: 10/09/16 Time: 18:55 Sample (adjusted): 1972 2014 Included observations: 43 after adjustments Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
GASTO(-1) 1.000000
INGRESO(-1) -0.962486 (0.02647)[-36.3596]
@TREND(70) 4.52E+10
C 6.80E+10
Error Correction: D(GASTO) D(INGRESO)
CointEq1 -0.134253 0.230296 (0.19284) (0.27761)[-0.69620] [ 0.82958]
D(GASTO(-1)) -0.225606 -1.016737 (0.32444) (0.46705)[-0.69538] [-2.17692]
D(INGRESO(-1)) 0.390689 1.063134 (0.22199) (0.31957)[ 1.75997] [ 3.32680]
C 7.75E+10 9.93E+10 (3.9E+10) (5.6E+10)[ 1.97524] [ 1.75755]
@TREND(70) 7.12E+09 8.73E+09 (2.1E+09) (3.1E+09)[ 3.34818] [ 2.85260]
R-squared 0.590967 0.509953 Adj. R-squared 0.547911 0.458369 Sum sq. resids 4.54E+23 9.40E+23 S.E. equation 1.09E+11 1.57E+11 F-statistic 13.72551 9.885881 Log likelihood -1151.296 -1166.963 Akaike AIC 53.78120 54.50990 Schwarz SC 53.98599 54.71469 Mean dependent 3.14E+11 3.76E+11 S.D. dependent 1.63E+11 2.14E+11
Determinant resid covariance (dof adj.) 3.77E+43 Determinant resid covariance 2.95E+43 Log likelihood -2273.995 Akaike information criterion 106.3253 Schwarz criterion 106.8168
Vector Error Correction Estimates Date: 10/09/16 Time: 19:11 Sample (adjusted): 1972 2014 Included observations: 43 after adjustments Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
GASTO(-1) 1.000000
INGRESO(-1) -0.909164 (0.01512)[-60.1414]
C -1.58E+11 (1.1E+11)[-1.39656]
Error Correction: D(GASTO) D(INGRESO)
CointEq1 -0.307234 -0.426310 (0.06136) (0.09416)[-5.00745] [-4.52767]
D(GASTO(-1)) -0.248524 -1.046387 (0.30837) (0.47323)[-0.80592] [-2.21116]
D(INGRESO(-1)) 0.342968 0.886979 (0.20567) (0.31562)
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[ 1.66759] [ 2.81028]
R-squared 0.602220 0.458438 Adj. R-squared 0.582331 0.431360 Sum sq. resids 4.41E+23 1.04E+24 S.E. equation 1.05E+11 1.61E+11 F-statistic 30.27900 16.93024 Log likelihood -1150.696 -1169.112 Akaike AIC 53.66028 54.51683 Schwarz SC 53.78316 54.63971 Mean dependent 3.14E+11 3.76E+11 S.D. dependent 1.63E+11 2.14E+11
Determinant resid covariance (dof adj.) 5.05E+43 Determinant resid covariance 4.37E+43 Log likelihood -2282.455 Akaike information criterion 106.5793 Schwarz criterion 106.9479
Esta modelo cumple con teoría económica porque la pendiente es menor a 1 quiere decir que el 90 % del ingreso está destinado al gasto de bienes y servicios.
Según las gráficas:
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En la primera Gráfica podemos decir que el gasto respecto al gasto se mantiene estática lo cual es correcto.
En la segunda Gráfica podemos decir que el gasto respecto al ingreso es creciente, lo cual es correcto ya que a mayor ingreso mayor es el gasto.
En la tercera Gráfica podemos decir que el ingreso respecto al gasto se mantiene estática lo cual es correcto.
En la cuarta Gráfica podemos decir que el ingreso respecto al ingreso es creciente aunque esto no se toma en cuenta.
Conclusión
Aplicando el modelo VEC se pudo afirmar que el gasto está en función del ingreso, a mayor el ingreso mayor es el gasto se puede observar en la segunda gráfica.
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VAR (p) con tres variables Vector Autoregression Estimates Date: 10/09/16 Time: 19:40 Sample (adjusted): 1992 2014 Included observations: 23 after adjustments Standard errors in ( ) & t-statistics in [ ]
PIB FORMBRUCAP PEA
PIB(-1) 0.669383 -0.030815 1.95E-06 (1.32932) (1.01200) (3.1E-06)[ 0.50355] [-0.03045] [ 0.63773]
PIB(-2) 0.247500 0.011742 -1.86E-06 (1.27935) (0.97396) (2.9E-06)[ 0.19346] [ 0.01206] [-0.63108]
FORMBRUCAP(-1) 1.109412 1.239811 -2.01E-07 (1.85590) (1.41288) (4.3E-06)[ 0.59778] [ 0.87751] [-0.04692]
FORMBRUCAP(-2) -1.061301 -0.604371 6.11E-07 (1.30405) (0.99276) (3.0E-06)[-0.81385] [-0.60878] [ 0.20347]
PEA(-1) -122792.7 -60567.23 0.882779 (88000.5) (66993.8) (0.20280)[-1.39536] [-0.90407] [ 4.35302]
PEA(-2) 147434.1 85671.90 -0.002639 (80078.6) (60962.9) (0.18454)[ 1.84112] [ 1.40531] [-0.01430]
C -2.10E+12 -2.45E+12 16244412 (3.4E+12) (2.6E+12) (7747648)[-0.62428] [-0.95895] [ 2.09669]
R-squared 0.997317 0.957307 0.998108 Adj. R-squared 0.996311 0.941297 0.997399 Sum sq. resids 6.85E+23 3.97E+23 3.64E+12 S.E. equation 2.07E+11 1.58E+11 476812.9 F-statistic 991.2743 59.79506 1406.858 Log likelihood -627.7393 -621.4663 -329.1844 Akaike AIC 55.19472 54.64924 29.23343 Schwarz SC 55.54031 54.99482 29.57901 Mean dependent 1.18E+13 2.47E+12 1.49E+08
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S.D. dependent 3.41E+12 6.50E+11 9348642.
Determinant resid covariance (dof adj.) 4.62E+54 Determinant resid covariance 1.55E+54 Log likelihood -1532.888 Akaike information criterion 135.1207 Schwarz criterion 136.1574
El cuadro que se observa, es el modelo VAR que se debe corregir ya que este es un modelo no estacionario.
Aplicando el test de Dickey - Fuller Aumentado vemos si la variable tiene o no tiene raíz unitaria
PIB
Null Hypothesis: PIB has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=5)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 0.903425 0.9937Test critical values: 1% level -3.737853
5% level -2.99187810% level -2.635542
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(PIB)Method: Least SquaresDate: 10/09/16 Time: 19:47Sample (adjusted): 1991 2014Included observations: 24 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PIB(-1) 0.012653 0.014005 0.903425 0.3761C 3.34E+11 1.62E+11 2.058634 0.0516
R-squared 0.035772 Mean dependent var 4.74E+11Adjusted R-squared -0.008057 S.D. dependent var 2.32E+11S.E. of regression 2.33E+11 Akaike info criterion 55.26719Sum squared resid 1.20E+24 Schwarz criterion 55.36537Log likelihood -661.2063 Hannan-Quinn criter. 55.29324F-statistic 0.816178 Durbin-Watson stat 1.239786Prob(F-statistic) 0.376086
Con el 99 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
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Null Hypothesis: D(PIB) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=5)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.144548 0.0371Test critical values: 1% level -3.752946
5% level -2.99806410% level -2.638752
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(PIB,2)Method: Least SquaresDate: 10/09/16 Time: 19:49Sample (adjusted): 1992 2014Included observations: 23 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(PIB(-1)) -0.625326 0.198860 -3.144548 0.0049C 3.12E+11 1.03E+11 3.030608 0.0064
R-squared 0.320128 Mean dependent var 2.13E+10Adjusted R-squared 0.287754 S.D. dependent var 2.57E+11S.E. of regression 2.17E+11 Akaike info criterion 55.12938Sum squared resid 9.91E+23 Schwarz criterion 55.22812Log likelihood -631.9878 Hannan-Quinn criter. 55.15421F-statistic 9.888184 Durbin-Watson stat 1.803975Prob(F-statistic) 0.004893
Aplicando un diferencial se puede observar que tenemos un 3% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el PIB.
FORMACIÓN BRUTA DE CAPITAL
Null Hypothesis: FORMBRUCAP has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=5)
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t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.617273 0.8490Test critical values: 1% level -3.737853
5% level -2.99187810% level -2.635542
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(FORMBRUCAP)Method: Least SquaresDate: 10/09/16 Time: 19:52Sample (adjusted): 1991 2014Included observations: 24 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
FORMBRUCAP(-1) -0.032981 0.053430 -0.617273 0.5434C 1.67E+11 1.30E+11 1.291945 0.2098
R-squared 0.017025 Mean dependent var 9.05E+10Adjusted R-squared -0.027656 S.D. dependent var 1.73E+11S.E. of regression 1.75E+11 Akaike info criterion 54.69834Sum squared resid 6.77E+23 Schwarz criterion 54.79651Log likelihood -654.3801 Hannan-Quinn criter. 54.72439F-statistic 0.381026 Durbin-Watson stat 1.380376Prob(F-statistic) 0.543391
Con el 84 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(FORMBRUCAP) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=5)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.441262 0.0198Test critical values: 1% level -3.752946
5% level -2.99806410% level -2.638752
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(FORMBRUCAP,2)Method: Least SquaresDate: 10/09/16 Time: 19:53Sample (adjusted): 1992 2014Included observations: 23 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
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D(FORMBRUCAP(-1)) -0.715893 0.208032 -3.441262 0.0024C 7.20E+10 3.99E+10 1.805676 0.0853
R-squared 0.360580 Mean dependent var 1.06E+10Adjusted R-squared 0.330132 S.D. dependent var 2.09E+11S.E. of regression 1.71E+11 Akaike info criterion 54.65185Sum squared resid 6.15E+23 Schwarz criterion 54.75059Log likelihood -626.4963 Hannan-Quinn criter. 54.67668F-statistic 11.84229 Durbin-Watson stat 1.928309Prob(F-statistic) 0.002449
Aplicando un diferencial se puede observar que tenemos un 1,9% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es la Formación Bruta de Capital.
PEA
Null Hypothesis: PEA has a unit rootExogenous: ConstantLag Length: 5 (Automatic - based on SIC, maxlag=5)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.223459 0.0044Test critical values: 1% level -3.831511
5% level -3.02997010% level -2.655194
*MacKinnon (1996) one-sided p-values.Warning: Probabilities and critical values calculated for 20 observations and may not be accurate for a sample size of 19
Augmented Dickey-Fuller Test EquationDependent Variable: D(PEA)Method: Least SquaresDate: 10/09/16 Time: 19:57Sample (adjusted): 1996 2014Included observations: 19 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PEA(-1) -0.107690 0.025498 -4.223459 0.0012D(PEA(-1)) 0.307267 0.202217 1.519488 0.1545D(PEA(-2)) -0.448428 0.227480 -1.971285 0.0722D(PEA(-3)) 0.230122 0.223038 1.031764 0.3225D(PEA(-4)) -0.504102 0.204308 -2.467363 0.0296D(PEA(-5)) -0.334014 0.191693 -1.742439 0.1070
C 18708497 4249370. 4.402652 0.0009
R-squared 0.766030 Mean dependent var 1272422.Adjusted R-squared 0.649045 S.D. dependent var 769738.5S.E. of regression 456004.3 Akaike info criterion 29.17570
19
Sum squared resid 2.50E+12 Schwarz criterion 29.52365Log likelihood -270.1692 Hannan-Quinn criter. 29.23459F-statistic 6.548103 Durbin-Watson stat 2.529782Prob(F-statistic) 0.002940
En este caso no se aplicará ningún diferencial ya que al observar que tenemos un 0,04% de probabilidad de tener raíz unitaria, con una nivel de confianza del 99%de la variable PEA.
Aplicamos el test de Granger
VAR Granger Causality/Block Exogeneity Wald TestsDate: 10/09/16 Time: 20:51Sample: 1990 2014Included observations: 22
Dependent variable: DPIB
Excluded Chi-sq df Prob.
DFORMBRUCAP 5.733646 2 0.0569
PEA 7.264363 2 0.0265
All 11.47948 4 0.0217
Dependent variable: DFORMBRUCAP
Excluded Chi-sq df Prob.
DPIB 7.560896 2 0.0228PEA 7.379443 2 0.0250
All 20.87878 4 0.0003
Dependent variable: PEA
Excluded Chi-sq df Prob.
DPIB 0.874525 2 0.6458DFORMBRUC
AP 1.999097 2 0.3680
All 20.27376 4 0.0004
Aplicando el test podemos observar los resultados y decir que el PIB si se ve influenciado por la Formación Bruta de capital y por la PEA.
20
Aplicando el test podemos observar los resultados y decir que la Formación Bruta de Capital se ve influenciado por las dos variables.
Aplicando el test podemos observar los resultados y decir que la PEA se ve influenciado por las dos variables.
VAR Lag Order Selection CriteriaEndogenous variables: DPIB DFORMBRUCAP PEA Exogenous variables: C Date: 10/09/16 Time: 20:56Sample: 1990 2014Included observations: 23
Lag LogL LR FPE AIC SC HQ
0 -1637.619 NA 1.82e+58 142.6625 142.8106 142.69971 -1549.582 145.4518* 1.91e+55* 135.7897* 136.3822* 135.9387*
* indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion
En este caso tanto Akaike, Schawrtz y Hannan Quinn indican que se debe utilizar un rezago lo cual se demostrara en el siguiente cuadro.
Vector Autoregression Estimates Date: 10/09/16 Time: 21:01 Sample (adjusted): 1992 2014 Included observations: 23 after adjustments Standard errors in ( ) & t-statistics in [ ]
DPIBDFORMBRUCA
P PEA
DPIB(-1) -0.553807 -0.929119 2.47E-06 (0.58030) (0.43885) (1.2E-06)[-0.95435] [-2.11715] [ 2.02245]
DFORMBRUCAP(-1) 1.273697 1.415857 -1.09E-06 (0.75731) (0.57272) (1.6E-06)[ 1.68187] [ 2.47216] [-0.68138]
PEA(-1) 7308.911 3970.691 0.934089 (5878.56) (4445.70) (0.01238)[ 1.24332] [ 0.89315] [ 75.4312]
21
C -4.44E+11 -1.79E+11 10072058 (7.6E+11) (5.7E+11) (1598820)[-0.58551] [-0.31226] [ 6.29968]
R-squared 0.258302 0.265776 0.998017 Adj. R-squared 0.141192 0.149846 0.997704 Sum sq. resids 8.59E+23 4.91E+23 3.81E+12 S.E. equation 2.13E+11 1.61E+11 447994.0 F-statistic 2.205634 2.292559 3187.072 Log likelihood -630.3476 -623.9220 -329.7268 Akaike AIC 55.16066 54.60191 29.01972 Schwarz SC 55.35814 54.79939 29.21720 Mean dependent 4.86E+11 9.64E+10 1.49E+08 S.D. dependent 2.29E+11 1.74E+11 9348642.
Determinant resid covariance (dof adj.) 1.18E+55 Determinant resid covariance 6.64E+54 Log likelihood -1549.582 Akaike information criterion 135.7897 Schwarz criterion 136.3822
Observando en las estimaciones de auto regresión podemos decir que la PEA en función de la PIB es significativa y la Formación Bruta de Capital en función de si misma es significativa, pero la pendiente debe ser teóricamente mayor a 0 y menor a 1 y aquí demuestra lo contrario lo cual en teoría económica este modelo está mal.
22
Según las gráficas:
Observando las gráficas podemos decir que a excepción de las últimos tres cuadros los otros cuadros después de un determinado periodo se vuelven cero.
Con las gráfica diferenciada el PIB y la Formación Bruta de Capital gasto se comportan de una forma muy aleatoria, en el caso de la PEA se comporta de una manera estática.
Conclusión
En teoría económica este modelo está mal porque no explica lo que se necesita, por lo tanto se utilizará un modelo VEC .
23
Aplicamos modelo VEC
Date: 10/09/16 Time: 21:31Sample: 1990 2014Included observations: 23Series: PIB FORMBRUCAP PEA Lags interval: 1 to 1
Selected (0.05 level*) Number of
Cointegrating Relations by
Model
Data Trend: None None Linear Linear QuadraticTest Type No Intercept Intercept Intercept Intercept Intercept
No Trend No Trend No Trend Trend TrendTrace 2 3 2 2 1
Max-Eig 2 3 2 2 1
*Critical values based on MacKinnon-Haug-Michelis (1999)
Information Criteria by Rank and
Model
Data Trend: None None Linear Linear QuadraticRank or No Intercept Intercept Intercept Intercept Intercept
No. of CEs No Trend No Trend No Trend Trend Trend
Log Likelihood by Rank (rows) and Model (columns)
0 -1564.306 -1564.306 -1556.306 -1556.306 -1549.8421 -1551.587 -1547.667 -1543.358 -1535.033 -1528.5932 -1542.633 -1537.734 -1533.696 -1525.006 -1523.0763 -1541.289 -1532.888 -1532.888 -1519.494 -1519.494
Akaike Information Criteria by
24
Rank (rows) and Model (columns)
0 136.8092 136.8092 136.3744 136.3744 136.07321 136.2249 135.9710 135.7702 135.1333 134.7472*2 135.9681 135.7160 135.4519 134.8701 134.78933 136.3729 135.9033 135.9033 134.9995 134.9995
Schwarz Criteria by
Rank (rows) and Model (columns)
0 137.2535 137.2535 136.9668 136.9668 136.81371 136.9655 136.7609 136.6589 136.0713 135.7839*2 137.0049 136.8515 136.6367 136.1537 136.12223 137.7059 137.3843 137.3843 136.6287 136.6287
Observando el test de Trace y Max – Eig, puede notarse que con ambos los 5 modelos superan 0, Akaike y Schawrtz nos indican que se utilice el modelo 5 y un rezago, por tanto se puede validar que si tenemos un modelo de cointegración.
Vector Error Correction Estimates Date: 10/09/16 Time: 21:35 Sample (adjusted): 1993 2014 Included observations: 22 after adjustments Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
PIB(-1) 1.000000
FORMBRUCAP(-1) 2.736811 (0.52032)[ 5.25985]
PEA(-1) 103943.7 (19856.8)[ 5.23467]
@TREND(90) -8.87E+11
C -2.16E+13
Error Correction: D(PIB)D(FORMBRUC
AP) D(PEA)
CointEq1 0.227503 0.009939 -3.73E-07 (0.29794) (0.21371) (7.0E-07)[ 0.76358] [ 0.04651] [-0.53452]
D(PIB(-1)) -1.098670 -0.150485 4.45E-06 (2.29065) (1.64307) (5.4E-06)[-0.47963] [-0.09159] [ 0.83046]
25
D(PIB(-2)) -2.337271 -1.246066 -9.05E-07 (1.68775) (1.21061) (3.9E-06)[-1.38485] [-1.02929] [-0.22929]
D(FORMBRUCAP(-1)) 1.278908 0.250758 -2.90E-06 (2.21731) (1.59047) (5.2E-06)[ 0.57678] [ 0.15766] [-0.55820]
D(FORMBRUCAP(-2)) 3.120473 1.749168 1.99E-06 (1.99259) (1.42927) (4.7E-06)[ 1.56604] [ 1.22382] [ 0.42660]
D(PEA(-1)) -228334.6 -128552.6 0.012188 (127194.) (91235.9) (0.29757)[-1.79516] [-1.40901] [ 0.04096]
D(PEA(-2)) -5174.531 6175.975 0.287195 (109593.) (78610.7) (0.25639)[-0.04722] [ 0.07856] [ 1.12015]
C 1.85E+12 7.42E+11 286375.2 (1.3E+12) (9.5E+11) (3112190)[ 1.38722] [ 0.77781] [ 0.09202]
@TREND(90) 1.49E+10 4.90E+08 -70301.21 (2.1E+10) (1.5E+10) (50102.7)[ 0.69721] [ 0.03191] [-1.40314]
R-squared 0.566984 0.619043 0.780843 Adj. R-squared 0.300513 0.384608 0.645978 Sum sq. resids 4.95E+23 2.55E+23 2.71E+12 S.E. equation 1.95E+11 1.40E+11 456559.9 F-statistic 2.127752 2.640575 5.789789 Log likelihood -597.3650 -590.0552 -312.1221 Akaike AIC 55.12410 54.45956 29.19292 Schwarz SC 55.57043 54.90589 29.63925 Mean dependent 4.91E+11 9.76E+10 1364867. S.D. dependent 2.33E+11 1.78E+11 767330.7
Determinant resid covariance (dof adj.) 1.50E+54 Determinant resid covariance 3.09E+53 Log likelihood -1448.483 Akaike information criterion 134.4076 Schwarz criterion 135.8954
Vector Error Correction Estimates Date: 10/09/16 Time: 21:39 Sample (adjusted): 1993 2014 Included observations: 22 after adjustments Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
PIB(-1) 1.000000
26
FORMBRUCAP(-1) -10.89533 (1.30361)[-8.35782]
PEA(-1) 228256.7 (72922.8)[ 3.13012]
C -2.96E+13 (8.7E+12)[-3.39477]
Error Correction: D(PIB)D(FORMBRUC
AP) D(PEA)
CointEq1 -0.273118 -0.162909 1.04E-08 (0.10250) (0.08186) (2.5E-07)[-2.66446] [-1.99000] [ 0.04143]
D(PIB(-1)) -1.572860 -1.034030 4.60E-06 (1.58969) (1.26958) (3.9E-06)[-0.98941] [-0.81446] [ 1.17925]
D(PIB(-2)) -4.208227 -2.940629 -4.04E-06 (1.56247) (1.24785) (3.8E-06)[-2.69332] [-2.35656] [-1.05255]
D(FORMBRUCAP(-1)) 0.470596 0.258327 -3.57E-06 (1.47311) (1.17648) (3.6E-06)[ 0.31946] [ 0.21958] [-0.98729]
D(FORMBRUCAP(-2)) 4.218470 2.990075 4.26E-06 (1.64634) (1.31483) (4.0E-06)[ 2.56234] [ 2.27412] [ 1.05311]
D(PEA(-1)) -68983.54 -33376.38 0.334258 (79555.8) (63536.3) (0.19525)[-0.86711] [-0.52531] [ 1.71195]
D(PEA(-2)) -24835.24 -17568.32 0.432818 (95414.2) (76201.4) (0.23417)[-0.26029] [-0.23055] [ 1.84831]
R-squared 0.390033 0.334754 0.660249 Adj. R-squared 0.146046 0.068655 0.524348 Sum sq. resids 6.97E+23 4.45E+23 4.20E+12 S.E. equation 2.16E+11 1.72E+11 529208.7 F-statistic 1.598584 1.258008 4.858328 Log likelihood -601.1340 -596.1873 -316.9448 Akaike AIC 55.28491 54.83521 29.44952 Schwarz SC 55.63206 55.18236 29.79667 Mean dependent 4.91E+11 9.76E+10 1364867. S.D. dependent 2.33E+11 1.78E+11 767330.7
Determinant resid covariance (dof adj.) 4.06E+54 Determinant resid covariance 1.29E+54
27
Log likelihood -1464.163 Akaike information criterion 135.3784 Schwarz criterion 136.6183
Esta modelo no cumple con teoría económica porque la pendiente es mayor a 1 incluso habiendo utilizando el modelo VEC.
Según las gráficas:
De los nueve cuadros el primero el segundo cuarto quinto séptimo y octavo si muestran una dependencia respecto a la otra variable, pero en el caso de la PEA no influye en las demás variables.
Conclusión
28
Aplicando el modelo VEC se pudo observar que el modelo económico que se utilizó no explica lo que realmente se necesita, por lo cual el modelo esta mal esto se debe a que no se aplicó log a la base de datos del modelo económico Cobb Douglas.
VAR (p) con cuatro variables
Vector Autoregression Estimates Date: 10/09/16 Time: 22:08 Sample (adjusted): 1962 2014 Included observations: 53 after adjustments Standard errors in ( ) & t-statistics in [ ]
PIB_PERCAPITA
AHORRO_INTERNO
IMPORTACIONES
EXPORTACIONES
PIB_PERCAPITA(-1) 1.401560 19409712 -1.12E+08 -81613024 (0.35490) (5.1E+07) (8.9E+07) (5.0E+07)[ 3.94912] [ 0.37785] [-1.26076] [-1.62947]
PIB_PERCAPITA(-2) -0.212846 10406673 1.50E+08 1.08E+08 (0.35470) (5.1E+07) (8.8E+07) (5.0E+07)[-0.60007] [ 0.20271] [ 1.69062] [ 2.16738]
AHORRO_INTERNO(-1) 2.23E-09 1.310628 1.267177 0.833085 (2.0E-09) (0.28774) (0.49577) (0.28056)[ 1.12362] [ 4.55482] [ 2.55595] [ 2.96938]
AHORRO_INTERNO(-2) -4.54E-09 -0.807445 -1.629188 -1.106469 (1.7E-09) (0.25137) (0.43311) (0.24510)[-2.61501] [-3.21212] [-3.76161] [-4.51442]
IMPORTACIONES(-1) 1.81E-09 0.261929 1.362590 -0.049684 (1.6E-09) (0.23089) (0.39782) (0.22513)[ 1.13193] [ 1.13442] [ 3.42513] [-0.22069]
IMPORTACIONES(-2) -2.47E-09 -0.451095 -0.220866 0.222398 (1.5E-09) (0.22139) (0.38145) (0.21586)[-1.61473] [-2.03757] [-0.57902] [ 1.03029]
EXPORTACIONES(-1) -7.57E-09 -0.860095 -1.302192 0.817765 (2.3E-09) (0.33705) (0.58073) (0.32863)
29
[-3.25083] [-2.55181] [-2.24234] [ 2.48837]
EXPORTACIONES(-2) 7.14E-09 1.042843 0.726143 -0.308366 (2.4E-09) (0.34388) (0.59250) (0.33530)[ 3.00553] [ 3.03254] [ 1.22556] [-0.91968]
C -63.82136 -1.93E+10 -5.43E+10 -2.97E+10 (156.194) (2.3E+10) (3.9E+10) (2.2E+10)[-0.40860] [-0.85534] [-1.39468] [-1.34872]
R-squared 0.999498 0.996053 0.989561 0.994069 Adj. R-squared 0.999407 0.995335 0.987663 0.992991 Sum sq. resids 7096473. 1.49E+23 4.41E+23 1.41E+23 S.E. equation 401.6011 5.81E+10 1.00E+11 5.67E+10 F-statistic 10957.86 1387.884 521.3713 921.8832 Log likelihood -388.0314 -1383.925 -1412.759 -1382.584 Akaike AIC 14.98232 52.56320 53.65130 52.51262 Schwarz SC 15.31689 52.89778 53.98588 52.84720 Mean dependent 23725.09 1.22E+12 8.84E+11 6.93E+11 S.D. dependent 16493.39 8.51E+11 9.02E+11 6.77E+11
Determinant resid covariance (dof adj.) 1.80E+68 Determinant resid covariance 8.56E+67 Log likelihood -4445.939 Akaike information criterion 169.1298 Schwarz criterion 170.4681
El cuadro que se observa, es el modelo VAR que se debe corregir ya que este es un modelo no estacionario.
Aplicando el test de Dickey - Fuller Aumentado vemos si la variable tiene o no tiene raíz unitaria
PIB - PERCÁPITA
Null Hypothesis: PIB_PERCAPITA has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 1.986188 0.9998Test critical values: 1% level -3.560019
5% level -2.91765010% level -2.596689
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(PIB_PERCAPITA)Method: Least Squares
30
Date: 10/09/16 Time: 22:11Sample (adjusted): 1962 2014Included observations: 53 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PIB_PERCAPITA(-1) 0.010487 0.005280 1.986188 0.0525D(PIB_PERCAPITA(-1)) 0.446820 0.128778 3.469690 0.0011
C 311.2671 138.9706 2.239806 0.0296
R-squared 0.385833 Mean dependent var 968.5264Adjusted R-squared 0.361267 S.D. dependent var 660.0130S.E. of regression 527.4876 Akaike info criterion 15.42907Sum squared resid 13912156 Schwarz criterion 15.54059Log likelihood -405.8703 Hannan-Quinn criter. 15.47195F-statistic 15.70557 Durbin-Watson stat 1.859090Prob(F-statistic) 0.000005
Con el 99 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(PIB_PERCAPITA) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.712276 0.0066Test critical values: 1% level -3.560019
5% level -2.91765010% level -2.596689
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(PIB_PERCAPITA,2)Method: Least SquaresDate: 10/09/16 Time: 22:13Sample (adjusted): 1962 2014Included observations: 53 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(PIB_PERCAPITA(-1)) -0.421465 0.113533 -3.712276 0.0005C 426.5242 129.8699 3.284243 0.0019
R-squared 0.212732 Mean dependent var 31.67407Adjusted R-squared 0.197295 S.D. dependent var 605.5146S.E. of regression 542.5035 Akaike info criterion 15.46727Sum squared resid 15009810 Schwarz criterion 15.54162Log likelihood -407.8827 Hannan-Quinn criter. 15.49586F-statistic 13.78100 Durbin-Watson stat 1.928150Prob(F-statistic) 0.000509
31
Aplicando un diferencial se puede observar que tenemos un 0,06% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el PIB PERCAPITA.
AHORRO INTERNO BRUTO
Null Hypothesis: AHORRO_INTERNO has a unit rootExogenous: ConstantLag Length: 4 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 1.815009 0.9997Test critical values: 1% level -3.568308
5% level -2.92117510% level -2.598551
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(AHORRO_INTERNO)Method: Least SquaresDate: 10/09/16 Time: 22:18Sample (adjusted): 1965 2014Included observations: 50 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
AHORRO_INTERNO(-1) 0.022701 0.012508 1.815009 0.0763D(AHORRO_INTERNO(-1)) 0.290096 0.142527 2.035376 0.0479D(AHORRO_INTERNO(-2)) -0.086778 0.146709 -0.591500 0.5572D(AHORRO_INTERNO(-3)) -0.214387 0.155738 -1.376594 0.1756D(AHORRO_INTERNO(-4)) -0.430492 0.154018 -2.795068 0.0077
C 4.40E+10 1.81E+10 2.439480 0.0188
R-squared 0.428424 Mean dependent var 5.52E+10Adjusted R-squared 0.363473 S.D. dependent var 8.30E+10S.E. of regression 6.62E+10 Akaike info criterion 52.78297Sum squared resid 1.93E+23 Schwarz criterion 53.01241Log likelihood -1313.574 Hannan-Quinn criter. 52.87034F-statistic 6.596036 Durbin-Watson stat 1.987149Prob(F-statistic) 0.000117
32
Con el 99,97 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(AHORRO_INTERNO) has a unit rootExogenous: ConstantLag Length: 3 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.484920 0.0000Test critical values: 1% level -3.568308
5% level -2.92117510% level -2.598551
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(AHORRO_INTERNO,2)Method: Least SquaresDate: 10/09/16 Time: 22:19Sample (adjusted): 1965 2014Included observations: 50 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(AHORRO_INTERNO(-1)) -1.283830 0.234065 -5.484920 0.0000D(AHORRO_INTERNO(-1),2) 0.637017 0.188793 3.374145 0.0015D(AHORRO_INTERNO(-2),2) 0.579481 0.173829 3.333626 0.0017D(AHORRO_INTERNO(-3),2) 0.375612 0.154823 2.426069 0.0193
C 6.44E+10 1.45E+10 4.432314 0.0001
R-squared 0.433601 Mean dependent var 3.29E+09Adjusted R-squared 0.383254 S.D. dependent var 8.65E+10S.E. of regression 6.79E+10 Akaike info criterion 52.81517Sum squared resid 2.07E+23 Schwarz criterion 53.00637Log likelihood -1315.379 Hannan-Quinn criter. 52.88798F-statistic 8.612310 Durbin-Watson stat 1.933825Prob(F-statistic) 0.000030
Aplicando un diferencial se puede observar que tenemos un 0% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el Ahorro Interno Bruto
IMPORTACIONES
Null Hypothesis: IMPORTACIONES has a unit root
33
Exogenous: ConstantLag Length: 10 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.373562 0.9047Test critical values: 1% level -3.588509
5% level -2.92973410% level -2.603064
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(IMPORTACIONES)Method: Least SquaresDate: 10/09/16 Time: 22:22Sample (adjusted): 1971 2014Included observations: 44 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
IMPORTACIONES(-1) -0.065475 0.175271 -0.373562 0.7112D(IMPORTACIONES(-1)) 0.349728 0.282799 1.236667 0.2252D(IMPORTACIONES(-2)) -0.185722 0.244266 -0.760326 0.4526D(IMPORTACIONES(-3)) 0.222771 0.327429 0.680364 0.5012D(IMPORTACIONES(-4)) -0.034895 0.345314 -0.101052 0.9201D(IMPORTACIONES(-5)) 0.123141 0.354101 0.347758 0.7303D(IMPORTACIONES(-6)) 0.633997 0.569928 1.112416 0.2742D(IMPORTACIONES(-7)) -0.064861 0.544036 -0.119222 0.9058D(IMPORTACIONES(-8)) 1.780575 0.578755 3.076562 0.0043D(IMPORTACIONES(-9)) -2.182781 0.507543 -4.300683 0.0001
D(IMPORTACIONES(-10)) 1.330677 0.643239 2.068714 0.0467C 2.46E+10 2.56E+10 0.963667 0.3424
R-squared 0.715794 Mean dependent var 6.40E+10Adjusted R-squared 0.618098 S.D. dependent var 1.36E+11S.E. of regression 8.38E+10 Akaike info criterion 53.36818Sum squared resid 2.25E+23 Schwarz criterion 53.85477Log likelihood -1162.100 Hannan-Quinn criter. 53.54863F-statistic 7.326757 Durbin-Watson stat 2.140929Prob(F-statistic) 0.000005
Con el 90,47 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(IMPORTACIONES,2) has a unit rootExogenous: ConstantLag Length: 8 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
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Augmented Dickey-Fuller test statistic -2.712769 0.0799Test critical values: 1% level -3.588509
5% level -2.92973410% level -2.603064
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(IMPORTACIONES,3)Method: Least SquaresDate: 10/09/16 Time: 22:24Sample (adjusted): 1971 2014Included observations: 44 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(IMPORTACIONES(-1),2) -7.002182 2.581194 -2.712769 0.0104D(IMPORTACIONES(-1),3) 5.318333 2.545988 2.088908 0.0443D(IMPORTACIONES(-2),3) 4.362407 2.400670 1.817162 0.0780D(IMPORTACIONES(-3),3) 3.526944 2.163791 1.629984 0.1123D(IMPORTACIONES(-4),3) 2.557321 1.869666 1.367796 0.1803D(IMPORTACIONES(-5),3) 1.651810 1.593666 1.036484 0.3073D(IMPORTACIONES(-6),3) 1.174709 1.216762 0.965439 0.3411D(IMPORTACIONES(-7),3) 0.464363 0.799764 0.580625 0.5653D(IMPORTACIONES(-8),3) 1.398399 0.447520 3.124772 0.0036
C 1.29E+10 1.45E+10 0.887857 0.3809
R-squared 0.955218 Mean dependent var 2.07E+09Adjusted R-squared 0.943364 S.D. dependent var 3.49E+11S.E. of regression 8.30E+10 Akaike info criterion 53.31894Sum squared resid 2.34E+23 Schwarz criterion 53.72444Log likelihood -1163.017 Hannan-Quinn criter. 53.46932F-statistic 80.58160 Durbin-Watson stat 2.200952Prob(F-statistic) 0.000000
Aplicando dos diferenciales se puede observar que tenemos un 7,99% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el Ahorro Interno Bruto
EXPORTACIONES
. Null Hypothesis: EXPORTACIONES has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 3.145772 1.0000
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Test critical values: 1% level -3.5574725% level -2.916566
10% level -2.596116
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(EXPORTACIONES)Method: Least SquaresDate: 10/09/16 Time: 22:27Sample (adjusted): 1961 2014Included observations: 54 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
EXPORTACIONES(-1) 0.048407 0.015388 3.145772 0.0027C 1.20E+10 1.39E+10 0.867248 0.3898
R-squared 0.159880 Mean dependent var 4.29E+10Adjusted R-squared 0.143723 S.D. dependent var 7.77E+10S.E. of regression 7.19E+10 Akaike info criterion 52.87125Sum squared resid 2.69E+23 Schwarz criterion 52.94492Log likelihood -1425.524 Hannan-Quinn criter. 52.89966F-statistic 9.895883 Durbin-Watson stat 2.187087Prob(F-statistic) 0.002739
Con el 100 % de probabilidad de incertidumbre la variable tiene raíz unitaria, por lo tanto se debe diferenciar para corregir la variable y mejorar el modelo.
Null Hypothesis: D(EXPORTACIONES) has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -6.332231 0.0000Test critical values: 1% level -3.560019
5% level -2.91765010% level -2.596689
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test EquationDependent Variable: D(EXPORTACIONES,2)Method: Least SquaresDate: 10/09/16 Time: 22:28Sample (adjusted): 1962 2014Included observations: 53 after adjustments
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Variable Coefficient Std. Error t-Statistic Prob.
D(EXPORTACIONES(-1)) -0.879506 0.138893 -6.332231 0.0000C 3.86E+10 1.23E+10 3.146717 0.0028
R-squared 0.440158 Mean dependent var 1.47E+09Adjusted R-squared 0.429181 S.D. dependent var 1.04E+11S.E. of regression 7.84E+10 Akaike info criterion 53.04520Sum squared resid 3.14E+23 Schwarz criterion 53.11955Log likelihood -1403.698 Hannan-Quinn criter. 53.07379F-statistic 40.09715 Durbin-Watson stat 1.993055Prob(F-statistic) 0.000000
Aplicando un diferencial se puede observar que tenemos un 0% de probabilidad de tener raíz unitaria, es manejable entonces se determina que diferenciando una vez es suficiente para esta variable que es el Ahorro Interno Bruto
Aplicamos el test de Granger
VAR Granger Causality/Block Exogeneity Wald TestsDate: 10/09/16 Time: 22:36Sample: 1960 2014Included observations: 51
Dependent variable: DPIBPER
Excluded Chi-sq df Prob.
DAHORRO 2.362628 2 0.3069DIMPORTACIONES 2.798171 2 0.2468DEXPORTACIONES 6.778491 2 0.0337
All 17.87970 6 0.0065
Dependent variable: DAHORRO
Excluded Chi-sq df Prob.
DPIBPER 0.411344 2 0.8141DIMPORTACIONES 7.101665 2 0.0287DEXPORTACIONES 1.684417 2 0.4308
All 15.27694 6 0.0182
Dependent variable: DIMPORTACIONES
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Excluded Chi-sq df Prob.
DPIBPER 0.624770 2 0.7317DAHORRO 1.052440 2 0.5908
DEXPORTACIONES 13.10071 2 0.0014
All 38.36184 6 0.0000
Dependent variable: DEXPORTACIONES
Excluded Chi-sq df Prob.
DPIBPER 1.111343 2 0.5737DAHORRO 2.319585 2 0.3136
DIMPORTACIONES 7.063288 2 0.0293
All 23.37268 6 0.0007
Aplicando el test podemos observar los resultados y decir que el pib percapita se ve influenciado por las exportaciones, el ahorro interno bruto se ve influenciado por las importaciones, las importaciones se ven influenciadas por las exportaciones y las exportaciones se ven influenciadas por las importaciones.
VAR Lag Order Selection CriteriaEndogenous variables: DPIBPER DAHORRO DIMPORTACIONES DEXPORTACIONES Exogenous variables: C Date: 10/09/16 Time: 22:43Sample: 1960 2014Included observations: 49
Lag LogL LR FPE AIC SC HQ
0 -4278.616 NA 9.66e+70 174.8006 174.9551 174.85921 -4157.272 217.9229 1.32e+69 170.5009 171.2731* 170.79392 -4128.771 46.53282 8.01e+68 169.9906 171.3806 170.51803 -4106.716 32.40662 6.48e+68 169.7435 171.7512 170.50524 -4065.658 53.62737* 2.49e+68* 168.7207* 171.3461 169.7168*
* indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion
En este caso tanto Akaike y Hannan Quinn indican que se debe utilizar cuatro rezagos y Schawrtz un rezago, lo cual se demostrara en el siguiente cuadro.
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Vector Autoregression Estimates Date: 10/09/16 Time: 22:48 Sample (adjusted): 1963 2014 Included observations: 52 after adjustments Standard errors in ( ) & t-statistics in [ ]
DPIBPER DAHORRODIMPORTACIO
NESDEXPORTACIO
NES
DPIBPER(-1) 0.777286 -17945815 -15832307 6292859. (0.20197) (2.9E+07) (5.4E+07) (3.1E+07)[ 3.84843] [-0.61552] [-0.29456] [ 0.20239]
DAHORRO(-1) 1.12E-09 0.676111 0.608328 0.303241 (1.4E-09) (0.20323) (0.37466) (0.21674)[ 0.79480] [ 3.32680] [ 1.62368] [ 1.39911]
DIMPORTACIONES(-1) 3.16E-11 -0.066301 -0.117689 -0.024299 (4.8E-10) (0.06969) (0.12847) (0.07432)[ 0.06545] [-0.95141] [-0.91608] [-0.32696]
DEXPORTACIONES(-1) -3.98E-09 -0.107860 -1.665603 -0.035043 (1.4E-09) (0.20544) (0.37874) (0.21910)[-2.79698] [-0.52501] [-4.39780] [-0.15994]
C 357.2384 4.12E+10 5.80E+10 2.47E+10 (144.156) (2.1E+10) (3.8E+10) (2.2E+10)[ 2.47813] [ 1.98155] [ 1.51167] [ 1.11399]
R-squared 0.456591 0.270066 0.519986 0.103766 Adj. R-squared 0.410344 0.207943 0.479133 0.027491 Sum sq. resids 11962588 2.49E+23 8.47E+23 2.84E+23 S.E. equation 504.5029 7.28E+10 1.34E+11 7.77E+10 F-statistic 9.872767 4.347336 12.72843 1.360412 Log likelihood -394.7821 -1371.746 -1403.553 -1375.092 Akaike AIC 15.37624 52.95178 54.17512 53.08046 Schwarz SC 15.56386 53.13940 54.36274 53.26808 Mean dependent 983.7426 5.35E+10 1.88E+09 4.45E+10 S.D. dependent 656.9982 8.18E+10 1.86E+11 7.88E+10
Determinant resid covariance (dof adj.) 7.13E+68 Determinant resid covariance 4.76E+68 Log likelihood -4406.654 Akaike information criterion 170.2559 Schwarz criterion 171.0064
Observando en las estimaciones de auto regresión podemos decir que ninguna de los variables no son significativos, pero la pendiente debe ser teóricamente mayor a 0 y menor a 1 y aquí demuestra lo contrario lo cual en teoría económica este modelo está mal.
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Según las gráficas:
En este caso no se pudo aplicar las gráficas esto debido a los datos que botó el resultado del cuadro anterior. Esto significa que este modelo VAR es inefectivo.
Con las gráfica diferenciada del ingreso y del gasto se comportan de una forma muy aleatoria, excepto el pib percapita .
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Conclusión
En teoría económica este modelo está mal porque no explica lo que se necesita, por lo tanto se utilizará un modelo VEC .
Aplicamos modelo VEC
Vector Error Correction Estimates Date: 10/09/16 Time: 23:23 Sample (adjusted): 1962 2014 Included observations: 53 after adjustments Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
PIB_PERCAPITA(-1) 1.000000
AHORRO_INTERNO(-1) -1.30E-08 (3.7E-09)[-3.51814]
IMPORTACIONES(-1) 2.06E-08 (4.8E-09)[ 4.26418]
EXPORTACIONES(-1) -3.93E-08 (7.8E-09)[-5.01003]
@TREND(60) 107.4640
C -2264.749
Error Correction:D(PIB_PERCA
PITA)D(AHORRO_IN
TERNO)D(IMPORTACI
ONES)D(EXPORTACI
ONES)
CointEq1 0.051885 4715443. 17950010 14842666 (0.02324) (3681286) (5713783) (3210459)[ 2.23265] [ 1.28092] [ 3.14153] [ 4.62322]
D(PIB_PERCAPITA(-1)) -0.223846 -1.36E+08 -1.67E+08 -1.30E+08 (0.29472) (4.7E+07) (7.2E+07) (4.1E+07)[-0.75952] [-2.91923] [-2.30711] [-3.20388]
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D(AHORRO_INTERNO(-1)) 5.97E-09 1.199522 1.671839 1.172346
(1.7E-09) (0.26834) (0.41649) (0.23402)[ 3.52153] [ 4.47018] [ 4.01409] [ 5.00962]
D(IMPORTACIONES(-1)) 2.80E-09 0.482428 0.241033 -0.196381 (1.6E-09) (0.25227) (0.39156) (0.22001)[ 1.76099] [ 1.91232] [ 0.61557] [-0.89260]
D(EXPORTACIONES(-1)) -7.26E-09 -0.807387 -0.829357 0.274666 (2.2E-09) (0.35032) (0.54374) (0.30551)[-3.28262] [-2.30471] [-1.52529] [ 0.89903]
C 201.9682 2.63E+10 -5.68E+09 3.52E+09 (136.566) (2.2E+10) (3.4E+10) (1.9E+10)[ 1.47890] [ 1.21654] [-0.16915] [ 0.18680]
@TREND(60) 30.07027 3.71E+09 5.57E+09 3.68E+09 (6.19721) (9.8E+08) (1.5E+09) (8.6E+08)[ 4.85223] [ 3.77573] [ 3.65263] [ 4.29432]
R-squared 0.657890 0.433354 0.427189 0.535122 Adj. R-squared 0.613267 0.359443 0.352475 0.474486 Sum sq. resids 7749498. 1.94E+23 4.68E+23 1.48E+23 S.E. equation 410.4477 6.50E+10 1.01E+11 5.67E+10 F-statistic 14.74330 5.863230 5.717623 8.825108 Log likelihood -390.3642 -1391.040 -1414.340 -1383.787 Akaike AIC 14.99487 52.75624 53.63548 52.48254 Schwarz SC 15.25510 53.01647 53.89571 52.74277 Mean dependent 968.5264 5.27E+10 5.38E+10 4.37E+10 S.D. dependent 660.0130 8.12E+10 1.25E+11 7.82E+10
Determinant resid covariance (dof adj.) 2.29E+68 Determinant resid covariance 1.30E+68 Log likelihood -4457.039 Akaike information criterion 169.3977 Schwarz criterion 170.5873
Esta modelo no cumple con teoría económica porque la pendiente es mayor a 1 incluso habiendo utilizando el modelo VEC.
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Según las gráficas:
El pib percapita respecto de si misma y del ahorro interno bruto se ve influenciado por cada periodo de tiempo que transcurre.
El ahorro interno bruto, respecto de si mismo, del pib percapita y las importaciones si se ve influenciado cada periodo de tiempo que transcurre.
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Las importaciones respecto del pib percapita y de si mismas si se ve influenciado cada periodo de tiempo que transcurre.
Las exportaciones respecto del pib percapita y las importaciones si se ve influenciado cada periodo de tiempo que transcurre.
Conclusión
Aplicando el modelo VEC se pudo observar que el modelo económico que se utilizó explica bastantes cosas pero no lo que realmente se necesita, por lo cual el modelo está mal esto se debe a que no se aplicó una teoría económica contando cuatro variables correspondientes al modelo.
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