Estimaciones econométricas
Alejandro Uribe Jiménez
11/4/2021
ITAEE - Delincuencia, en logaritmos
Causalidades de Granger
Causalidad de Granger de la incidencia delictiva al ITAEE de uno a 4 rezagos. En ningún caso la incidencia delictiva ‘causa’ al ITAEE.
Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1) + Lags(Dbase1$d_delitos, 1:1)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1)
Res.Df Df F Pr(>F)
1 87
2 88 -1 1.199 0.2765Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2) + Lags(Dbase1$d_delitos, 1:2)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2)
Res.Df Df F Pr(>F)
1 84
2 86 -2 1.1477 0.3223Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3) + Lags(Dbase1$d_delitos, 1:3)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3)
Res.Df Df F Pr(>F)
1 81
2 84 -3 0.76 0.5198Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4) + Lags(Dbase1$d_delitos, 1:4)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4)
Res.Df Df F Pr(>F)
1 78
2 82 -4 0.8821 0.4787Causalidad de Granger del ITAEE a la incidencia delictiva de uno a 4 rezagos. En ningún caso el ITAEE ‘causa’ a la incidencia delictiva.
Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1) + Lags(Dbase1$d_itaee, 1:1)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1)
Res.Df Df F Pr(>F)
1 87
2 88 -1 0.0139 0.9064Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2) + Lags(Dbase1$d_itaee, 1:2)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2)
Res.Df Df F Pr(>F)
1 84
2 86 -2 0.0901 0.9139Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3) + Lags(Dbase1$d_itaee, 1:3)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3)
Res.Df Df F Pr(>F)
1 81
2 84 -3 0.4029 0.7513Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4) + Lags(Dbase1$d_itaee, 1:4)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4)
Res.Df Df F Pr(>F)
1 78
2 82 -4 0.4203 0.7935RAÍCES UNITARIAS
Raíces unitarias del logaritmo del ITAEE.
Augmented Dickey-Fuller Test
data: base1$l_itaee
Dickey-Fuller = -1.728, Lag order = 4, p-value = 0.6884
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: base1$l_itaee
Dickey-Fuller Z(alpha) = -14.174, Truncation lag parameter = 3, p-value
= 0.2877
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: base1$l_itaee
KPSS Level = 2.3282, Truncation lag parameter = 3, p-value = 0.01Raíces unitarias de sus diferencias logarítmicas.
Augmented Dickey-Fuller Test
data: Dbase1$d_itaee
Dickey-Fuller = -4.3733, Lag order = 4, p-value = 0.01
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: Dbase1$d_itaee
Dickey-Fuller Z(alpha) = -71.495, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: Dbase1$d_itaee
KPSS Level = 0.060353, Truncation lag parameter = 3, p-value = 0.1Raíces unitarias del logaritmo de la incidencia delictiva.
Augmented Dickey-Fuller Test
data: base1$l_delitos
Dickey-Fuller = -2.9259, Lag order = 4, p-value = 0.1946
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: base1$l_delitos
Dickey-Fuller Z(alpha) = -4.7177, Truncation lag parameter = 3, p-value
= 0.8423
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: base1$l_delitos
KPSS Level = 0.39426, Truncation lag parameter = 3, p-value = 0.07963Raíces unitarias de sus diferencias logarítmicas.
Augmented Dickey-Fuller Test
data: Dbase1$d_delitos
Dickey-Fuller = -3.0141, Lag order = 4, p-value = 0.1584
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: Dbase1$d_delitos
Dickey-Fuller Z(alpha) = -101.17, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: Dbase1$d_delitos
KPSS Level = 0.38029, Truncation lag parameter = 3, p-value = 0.08565Modelo VAR
Modelo VAR con los logaritmos de las series
$selection
AIC(n) HQ(n) SC(n) FPE(n)
5 1 1 5
$criteria
1 2 3 4 5
AIC(n) -1.473538e+01 -1.466269e+01 -1.470099e+01 -1.468155e+01 -1.480928e+01
HQ(n) -1.466558e+01 -1.454636e+01 -1.453813e+01 -1.447216e+01 -1.455335e+01
SC(n) -1.456175e+01 -1.437330e+01 -1.429586e+01 -1.416066e+01 -1.417264e+01
FPE(n) 3.985944e-07 4.287439e-07 4.128353e-07 4.213097e-07 3.713005e-07
6 7 8
AIC(n) -1.479130e+01 -1.474351e+01 -1.466425e+01
HQ(n) -1.448885e+01 -1.439452e+01 -1.426873e+01
SC(n) -1.403891e+01 -1.387536e+01 -1.368035e+01
FPE(n) 3.787878e-07 3.984152e-07 4.328324e-07Modelo VEC
######################
# Johansen-Procedure #
######################
Test type: trace statistic , without linear trend and constant in cointegration
Eigenvalues (lambda):
[1] 1.747980e-01 5.927394e-02 -1.732962e-16
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 1 | 5.44 7.52 9.24 12.97
r = 0 | 22.54 17.85 19.96 24.60
Eigenvectors, normalised to first column:
(These are the cointegration relations)
l_itaee.l3 l_delitos.l3 constant
l_itaee.l3 1.000000 1.0000000 1.000000
l_delitos.l3 0.479358 -0.7473619 1.265335
constant -6.478676 0.1246630 -12.416460
Weights W:
(This is the loading matrix)
l_itaee.l3 l_delitos.l3 constant
l_itaee.d 0.006859010 -0.004092407 1.973407e-15
l_delitos.d 0.001229403 0.066690097 -1.503669e-15Matriz Beta
l_itaee.l3 l_delitos.l3 constant
l_itaee.l3 1.0000 1.0000 1.0000
l_delitos.l3 0.4794 -0.7474 1.2653
constant -6.4787 0.1247 -12.4165Pruebas de estacionariedad a los residuales
Los residuales son estacionarios 
Augmented Dickey-Fuller Test
data: resids[, 1]
Dickey-Fuller = -4.0303, Lag order = 4, p-value = 0.01169
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: resids[, 1]
Dickey-Fuller Z(alpha) = -88.061, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: resids[, 1]
KPSS Level = 0.050886, Truncation lag parameter = 3, p-value = 0.1ITAEE-Desocupación-Delincuencia, en logaritmos
Causalidades de Granger
Excepto por la causalidad al 90% del ITAEE a la desocupación en el 1er y 2do rezago, ninguna variable ‘causa’ a cualquier otra.
Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:1) + Lags(Dbase1$d_delitos, 1:1)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 0.0035 0.9529Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:2) + Lags(Dbase1$d_delitos, 1:2)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 0.6994 0.5015Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:3) + Lags(Dbase1$d_delitos, 1:3)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 1.0084 0.397Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:4) + Lags(Dbase1$d_delitos, 1:4)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 0.9215 0.4596Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1) + Lags(Dbase1$d_desocupada, 1:1)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 0.4368 0.5114Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2) + Lags(Dbase1$d_desocupada, 1:2)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 0.2694 0.7649Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3) + Lags(Dbase1$d_desocupada, 1:3)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 1.0402 0.3831Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4) + Lags(Dbase1$d_desocupada, 1:4)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 1.4311 0.2388Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1) + Lags(Dbase1$d_delitos, 1:1)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 0.9178 0.3422Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2) + Lags(Dbase1$d_delitos, 1:2)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 1.0132 0.3701Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3) + Lags(Dbase1$d_delitos, 1:3)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 0.8089 0.4951Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4) + Lags(Dbase1$d_delitos, 1:4)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 0.9953 0.4197Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1) + Lags(Dbase1$d_desocupada, 1:1)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 0.9379 0.3371Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2) + Lags(Dbase1$d_desocupada, 1:2)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 2.1831 0.1229Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3) + Lags(Dbase1$d_desocupada, 1:3)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 1.9457 0.1345Granger causality test
Model 1: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4) + Lags(Dbase1$d_desocupada, 1:4)
Model 2: Dbase1$d_itaee ~ Lags(Dbase1$d_itaee, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 1.741 0.1572Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:1) + Lags(Dbase1$d_itaee, 1:1)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 3.8805 0.05389 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:2) + Lags(Dbase1$d_itaee, 1:2)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 2.4372 0.09733 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:3) + Lags(Dbase1$d_itaee, 1:3)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 1.8068 0.1582Granger causality test
Model 1: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:4) + Lags(Dbase1$d_itaee, 1:4)
Model 2: Dbase1$d_desocupada ~ Lags(Dbase1$d_desocupada, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 1.4924 0.22Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1) + Lags(Dbase1$d_itaee, 1:1)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:1)
Res.Df Df F Pr(>F)
1 55
2 56 -1 0.6967 0.4075Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2) + Lags(Dbase1$d_itaee, 1:2)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:2)
Res.Df Df F Pr(>F)
1 52
2 54 -2 0.3189 0.7284Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3) + Lags(Dbase1$d_itaee, 1:3)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:3)
Res.Df Df F Pr(>F)
1 49
2 52 -3 0.3224 0.8091Granger causality test
Model 1: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4) + Lags(Dbase1$d_itaee, 1:4)
Model 2: Dbase1$d_delitos ~ Lags(Dbase1$d_delitos, 1:4)
Res.Df Df F Pr(>F)
1 46
2 50 -4 0.4548 0.7684RAÍCES UNITARIAS
Raíces unitarias del logaritmo y la diferencia logarítmica de la tasa de desocupación, respectivamente
Augmented Dickey-Fuller Test
data: base1$l_desocupada
Dickey-Fuller = -2.1514, Lag order = 3, p-value = 0.5136
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: base1$l_desocupada
Dickey-Fuller Z(alpha) = -14.771, Truncation lag parameter = 3, p-value
= 0.2305
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: base1$l_desocupada
KPSS Level = 0.6688, Truncation lag parameter = 3, p-value = 0.01638
Augmented Dickey-Fuller Test
data: Dbase1$d_desocupada
Dickey-Fuller = -5.1796, Lag order = 3, p-value = 0.01
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: Dbase1$d_desocupada
Dickey-Fuller Z(alpha) = -66.012, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: Dbase1$d_desocupada
KPSS Level = 0.071187, Truncation lag parameter = 3, p-value = 0.1Raíces unitarias del logaritmo y la diferencia logarítmica de la incidencia delictiva, respectivamente
Augmented Dickey-Fuller Test
data: base1$l_incidencia
Dickey-Fuller = -1.2579, Lag order = 3, p-value = 0.8747
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: base1$l_incidencia
Dickey-Fuller Z(alpha) = -5.8621, Truncation lag parameter = 3, p-value
= 0.77
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: base1$l_incidencia
KPSS Level = 0.93733, Truncation lag parameter = 3, p-value = 0.01
Augmented Dickey-Fuller Test
data: Dbase1$d_delitos
Dickey-Fuller = -2.15, Lag order = 3, p-value = 0.5142
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: Dbase1$d_delitos
Dickey-Fuller Z(alpha) = -63.916, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: Dbase1$d_delitos
KPSS Level = 0.11284, Truncation lag parameter = 3, p-value = 0.1Raíces unitarias del logaritmo y la diferencia logarítmica del ITAEE, respectivamente
Augmented Dickey-Fuller Test
data: base1$l_itaee
Dickey-Fuller = -1.6411, Lag order = 3, p-value = 0.7198
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: base1$l_itaee
Dickey-Fuller Z(alpha) = -11.844, Truncation lag parameter = 3, p-value
= 0.4078
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: base1$l_itaee
KPSS Level = 1.5674, Truncation lag parameter = 3, p-value = 0.01
Augmented Dickey-Fuller Test
data: Dbase1$d_itaee
Dickey-Fuller = -5.5768, Lag order = 3, p-value = 0.01
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: Dbase1$d_itaee
Dickey-Fuller Z(alpha) = -44.188, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: Dbase1$d_itaee
KPSS Level = 0.10974, Truncation lag parameter = 3, p-value = 0.1VAR
$selection
AIC(n) HQ(n) SC(n) FPE(n)
8 1 1 1
$criteria
1 2 3 4 5
AIC(n) -1.931726e+01 -1.91956e+01 -1.926033e+01 -1.915025e+01 -1.926149e+01
HQ(n) -1.914463e+01 -1.88935e+01 -1.882875e+01 -1.858921e+01 -1.857097e+01
SC(n) -1.886697e+01 -1.84076e+01 -1.813461e+01 -1.768682e+01 -1.746034e+01
FPE(n) 4.083349e-09 4.63018e-09 4.381920e-09 4.980290e-09 4.588650e-09
6 7 8
AIC(n) -1.932363e+01 -1.914878e+01 -1.933833e+01
HQ(n) -1.850364e+01 -1.819932e+01 -1.825940e+01
SC(n) -1.718477e+01 -1.667220e+01 -1.652404e+01
FPE(n) 4.507950e-09 5.723753e-09 5.176998e-09VEC
######################
# Johansen-Procedure #
######################
Test type: trace statistic , without linear trend and constant in cointegration
Eigenvalues (lambda):
[1] 4.953326e-01 2.657178e-01 1.490660e-01 -8.244273e-16
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 2 | 8.39 7.52 9.24 12.97
r <= 1 | 24.45 17.85 19.96 24.60
r = 0 | 60.02 32.00 34.91 41.07
Eigenvectors, normalised to first column:
(These are the cointegration relations)
l_desocupada.l8 l_itaee.l8 l_incidencia.l8 constant
l_desocupada.l8 1.0000000 1.0000000 1.000000 1.0000000
l_itaee.l8 0.8487840 -0.8581494 2.155272 -3.0533791
l_incidencia.l8 -0.4039901 3.0464468 -1.140982 0.4425072
constant -3.2917005 -16.6137774 -4.232242 9.3553829
Weights W:
(This is the loading matrix)
l_desocupada.l8 l_itaee.l8 l_incidencia.l8 constant
l_desocupada.d -0.918348457 0.08785921 -0.02609780 -5.881163e-14
l_itaee.d -0.004827088 0.00563764 0.02998199 2.123563e-14
l_incidencia.d -0.291016127 -0.06434670 0.01321903 -2.458187e-13Matriz Beta
l_desocupada.l8 l_itaee.l8 l_incidencia.l8 constant
l_desocupada.l8 1.0000 1.0000 1.0000 1.0000
l_itaee.l8 0.8488 -0.8581 2.1553 -3.0534
l_incidencia.l8 -0.4040 3.0464 -1.1410 0.4425
constant -3.2917 -16.6138 -4.2322 9.3554Pruebas de estacionariedad a los residuales
Los residuales son estacionarios 
Augmented Dickey-Fuller Test
data: resids[, 1]
Dickey-Fuller = -3.4898, Lag order = 3, p-value = 0.05143
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: resids[, 1]
Dickey-Fuller Z(alpha) = -44.77, Truncation lag parameter = 3, p-value
= 0.01
alternative hypothesis: stationary
KPSS Test for Level Stationarity
data: resids[, 1]
KPSS Level = 0.091864, Truncation lag parameter = 3, p-value = 0.1