2º Avaliação - Macroeconometria

1. Utilizando a base de dados QUARTERLY, estime o VAR com 3 defasagens de que trata o exercício 9 do livro do Enders na página 339 com o ordenamento ∆lip, ∆unemp e s (spread de juros).

summary(var_model)

VAR Estimation Results:
========================= 
Endogenous variables: dlip, dunemp, s 
Deterministic variables: const 
Sample size: 208 
Log Likelihood: 554.153 
Roots of the characteristic polynomial:
0.8005 0.7518 0.7518 0.5129 0.5129 0.4941 0.4941 0.3861 0.3861
Call:
VAR(y = data, p = 3, type = "const")


Estimation results for equation dlip: 
===================================== 
dlip = dlip.l1 + dunemp.l1 + s.l1 + dlip.l2 + dunemp.l2 + s.l2 + dlip.l3 + dunemp.l3 + s.l3 + const 

            Estimate Std. Error t value Pr(>|t|)    
dlip.l1    5.610e-01  1.013e-01   5.536 9.74e-08 ***
dunemp.l1 -6.289e-03  5.259e-03  -1.196    0.233    
s.l1      -1.071e-03  1.663e-03  -0.644    0.520    
dlip.l2   -8.249e-02  1.065e-01  -0.775    0.439    
dunemp.l2  7.212e-03  5.398e-03   1.336    0.183    
s.l2      -9.415e-04  2.391e-03  -0.394    0.694    
dlip.l3    1.919e-01  1.011e-01   1.899    0.059 .  
dunemp.l3  4.679e-03  4.790e-03   0.977    0.330    
s.l3       8.134e-05  1.699e-03   0.048    0.962    
const     -5.530e-04  1.897e-03  -0.292    0.771    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Residual standard error: 0.01242 on 198 degrees of freedom
Multiple R-Squared: 0.4046, Adjusted R-squared: 0.3776 
F-statistic: 14.95 on 9 and 198 DF,  p-value: < 2.2e-16 


Estimation results for equation dunemp: 
======================================= 
dunemp = dlip.l1 + dunemp.l1 + s.l1 + dlip.l2 + dunemp.l2 + s.l2 + dlip.l3 + dunemp.l3 + s.l3 + const 

           Estimate Std. Error t value Pr(>|t|)    
dlip.l1   -7.372118   1.938976  -3.802 0.000191 ***
dunemp.l1  0.329196   0.100643   3.271 0.001264 ** 
s.l1       0.011522   0.031831   0.362 0.717763    
dlip.l2    0.295902   2.037186   0.145 0.884661    
dunemp.l2 -0.073243   0.103304  -0.709 0.479156    
s.l2       0.001648   0.045750   0.036 0.971300    
dlip.l3   -2.737375   1.934281  -1.415 0.158584    
dunemp.l3 -0.038370   0.091671  -0.419 0.675987    
s.l3       0.050335   0.032512   1.548 0.123167    
const      0.168639   0.036292   4.647 6.14e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Residual standard error: 0.2377 on 198 degrees of freedom
Multiple R-Squared: 0.5219, Adjusted R-squared: 0.5002 
F-statistic: 24.02 on 9 and 198 DF,  p-value: < 2.2e-16 


Estimation results for equation s: 
================================== 
s = dlip.l1 + dunemp.l1 + s.l1 + dlip.l2 + dunemp.l2 + s.l2 + dlip.l3 + dunemp.l3 + s.l3 + const 

          Estimate Std. Error t value Pr(>|t|)    
dlip.l1    3.06994    4.29574   0.715  0.47567    
dunemp.l1 -0.37053    0.22297  -1.662  0.09814 .  
s.l1       1.06119    0.07052  15.048  < 2e-16 ***
dlip.l2    0.45851    4.51333   0.102  0.91918    
dunemp.l2  0.39479    0.22887   1.725  0.08609 .  
s.l2      -0.31763    0.10136  -3.134  0.00199 ** 
dlip.l3    3.28676    4.28534   0.767  0.44401    
dunemp.l3 -0.27995    0.20309  -1.378  0.16963    
s.l3       0.14334    0.07203   1.990  0.04797 *  
const     -0.21507    0.08040  -2.675  0.00810 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Residual standard error: 0.5267 on 198 degrees of freedom
Multiple R-Squared: 0.8254, Adjusted R-squared: 0.8175 
F-statistic:   104 on 9 and 198 DF,  p-value: < 2.2e-16 



Covariance matrix of residuals:
             dlip    dunemp         s
dlip    0.0001543 -0.002119  0.001198
dunemp -0.0021188  0.056517 -0.022737
s       0.0011976 -0.022737  0.277405

Correlation matrix of residuals:
          dlip  dunemp       s
dlip    1.0000 -0.7174  0.1830
dunemp -0.7174  1.0000 -0.1816
s       0.1830 -0.1816  1.0000

a)Verifique se s (spread de juros) Granger causa ∆lip.

causality(var_model, cause = "s")

$Granger

    Granger causality H0: s do not Granger-cause dlip dunemp

data:  VAR object var_model
F-Test = 3.6948, df1 = 6, df2 = 594, p-value = 0.001295


$Instant

    H0: No instantaneous causality between: s and dlip dunemp

data:  VAR object var_model
Chi-squared = 7.7517, df = 2, p-value = 0.02074

b)Verifique se s (spread de juros) Granger causa ∆unemp. c)Analise a decomposição da variância desse VAR.

d)Analise as funções de impulso resposta.