Cargando los datos

load("C:/Users/hp/Desktop/Andrea Esmeralda Cortéz Herrera - smoke.RData")

Modelo Estimado

options(scipen = 9999999)
library(foreign)
modelo_estimado<-lm(cigs~cigpric+lcigpric+income+lincome+age+agesq+educ+white+restaurn,data = data)
print(modelo_estimado)
## 
## Call:
## lm(formula = cigs ~ cigpric + lcigpric + income + lincome + age + 
##     agesq + educ + white + restaurn, data = data)
## 
## Coefficients:
##   (Intercept)        cigpric       lcigpric         income        lincome  
##  340.80437460     2.00226767  -115.27346445    -0.00004619     1.40406118  
##           age          agesq           educ          white       restaurn  
##    0.77835901    -0.00915035    -0.49478062    -0.53105164    -2.64424135

Resumen del modelo con Stargazer

options(scipen = 999999)
library(stargazer)
modelo_hac<-lm(cigs~cigpric+lcigpric+income+lincome+age+agesq+educ+white+restaurn,data = data)
stargazer(modelo_estimado,type = "text",title = "Modelo para estimadores HAC")
## 
## Modelo para estimadores HAC
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                cigs            
## -----------------------------------------------
## cigpric                        2.002           
##                               (1.493)          
##                                                
## lcigpric                     -115.273          
##                              (85.424)          
##                                                
## income                       -0.00005          
##                              (0.0001)          
##                                                
## lincome                        1.404           
##                               (1.708)          
##                                                
## age                          0.778***          
##                               (0.161)          
##                                                
## agesq                        -0.009***         
##                               (0.002)          
##                                                
## educ                         -0.495***         
##                               (0.168)          
##                                                
## white                         -0.531           
##                               (1.461)          
##                                                
## restaurn                     -2.644**          
##                               (1.130)          
##                                                
## Constant                      340.804          
##                              (260.016)         
##                                                
## -----------------------------------------------
## Observations                    807            
## R2                             0.055           
## Adjusted R2                    0.044           
## Residual Std. Error      13.413 (df = 797)     
## F Statistic           5.169*** (df = 9; 797)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

Pruebas de Heterocedasticidad y Autocorrelación

Prueba de White (prueba de Breusch Pagan)

library(lmtest)
white_test<-bptest(modelo_estimado,~I(cigpric^2)+I(lcigpric^2)+I(income^2)+I(lincome^2)+I(age^2)+I(agesq^2)+I(educ^2)+I(white^2)+I(restaurn^2)+(cigpric*lcigpric)+(cigpric*income)+(cigpric*lincome)+(cigpric*age)+(cigpric*agesq)+(cigpric*educ)+(cigpric*white),data = data)
print(white_test)
## 
##  studentized Breusch-Pagan test
## 
## data:  modelo_estimado
## BP = 42.143, df = 21, p-value = 0.004037

Hay evidencia de heterocedasticidad ya que pvalue<0.05

Prueba del Multiplicador de Lagrange (Breusch Godfrey)

Autocorrelación de 2º Orden:

library(lmtest)
prueba_LM<-bgtest(modelo_estimado,order = 2)
print(prueba_LM)
## 
##  Breusch-Godfrey test for serial correlation of order up to 2
## 
## data:  modelo_estimado
## LM test = 0.26889, df = 2, p-value = 0.8742

No hay evidencia de Autocorrelación de 2º orden ya que pvalue>0.05

Autocorrelación de 1º orden (prueba de Durbin Watson)

library(car)
durbinWatsonTest(model = modelo_estimado)
##  lag Autocorrelation D-W Statistic p-value
##    1    -0.009243664      2.017442   0.858
##  Alternative hypothesis: rho != 0

No hay evidencia de Autocorrelación de 1º orden ya que pvalue>0.05

Estimación Robusta (uso del estimador HAC)

Sin corregir

options(scipen = 99999)
library(lmtest)
#Sin corregir:
coeftest(modelo_estimado)
## 
## t test of coefficients:
## 
##                   Estimate     Std. Error t value     Pr(>|t|)    
## (Intercept)  340.804374604  260.015587269  1.3107     0.190334    
## cigpric        2.002267667    1.492831189  1.3413     0.180220    
## lcigpric    -115.273464445   85.424315195 -1.3494     0.177585    
## income        -0.000046194    0.000133491 -0.3460     0.729402    
## lincome        1.404061178    1.708165841  0.8220     0.411340    
## age            0.778359013    0.160555612  4.8479 0.0000015001 ***
## agesq         -0.009150353    0.001749292 -5.2309 0.0000002158 ***
## educ          -0.494780616    0.168180198 -2.9420     0.003356 ** 
## white         -0.531051635    1.460721806 -0.3636     0.716287    
## restaurn      -2.644241351    1.129998690 -2.3400     0.019528 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Corregido (usando un estimador HAC)

options(scipen = 99999)
library(lmtest)
library(sandwich)
#Corregido
#HC0 Corrige Sólo Heterocedasticidad, use HC1 para corregir también Autocorrelación de Primer Orden
vcov_HAC<-vcovHC(modelo_estimado,type = "HC0") 

coeftest(modelo_estimado,vcov. =  vcov_HAC)
## 
## t test of coefficients:
## 
##                   Estimate     Std. Error t value        Pr(>|t|)    
## (Intercept)  340.804374604  278.565072885  1.2234        0.221530    
## cigpric        2.002267667    1.602727983  1.2493        0.211927    
## lcigpric    -115.273464445   91.344424879 -1.2620        0.207331    
## income        -0.000046194    0.000115593 -0.3996        0.689540    
## lincome        1.404061178    1.228970726  1.1425        0.253602    
## age            0.778359013    0.136944678  5.6837 0.0000000184838 ***
## agesq         -0.009150353    0.001451548 -6.3039 0.0000000004804 ***
## educ          -0.494780616    0.162968371 -3.0361        0.002475 ** 
## white         -0.531051635    1.361907703 -0.3899        0.696691    
## restaurn      -2.644241351    1.038254938 -2.5468        0.011058 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Modelo original y modelo corregido

library(stargazer)
library(sandwich)

vcov_HAC<-vcovHC(modelo_estimado,type="HC0")
robust.se<-sqrt(diag(vcov_HAC))

stargazer(modelo_estimado,modelo_hac, 
          se=list(NULL, robust.se),
          column.labels=c("Modelo Original","Modelo Corregido"), 
          align=TRUE,
          type = "text",title = "Comparativa")
## 
## Comparativa
## ===============================================================
##                                      Dependent variable:       
##                                --------------------------------
##                                              cigs              
##                                Modelo Original Modelo Corregido
##                                      (1)             (2)       
## ---------------------------------------------------------------
## cigpric                             2.002           2.002      
##                                    (1.493)         (1.603)     
##                                                                
## lcigpric                          -115.273         -115.273    
##                                   (85.424)         (91.344)    
##                                                                
## income                            -0.00005         -0.00005    
##                                   (0.0001)         (0.0001)    
##                                                                
## lincome                             1.404           1.404      
##                                    (1.708)         (1.229)     
##                                                                
## age                               0.778***         0.778***    
##                                    (0.161)         (0.137)     
##                                                                
## agesq                             -0.009***       -0.009***    
##                                    (0.002)         (0.001)     
##                                                                
## educ                              -0.495***       -0.495***    
##                                    (0.168)         (0.163)     
##                                                                
## white                              -0.531           -0.531     
##                                    (1.461)         (1.362)     
##                                                                
## restaurn                          -2.644**         -2.644**    
##                                    (1.130)         (1.038)     
##                                                                
## Constant                           340.804         340.804     
##                                   (260.016)       (278.565)    
##                                                                
## ---------------------------------------------------------------
## Observations                         807             807       
## R2                                  0.055           0.055      
## Adjusted R2                         0.044           0.044      
## Residual Std. Error (df = 797)     13.413           13.413     
## F Statistic (df = 9; 797)         5.169***         5.169***    
## ===============================================================
## Note:                               *p<0.1; **p<0.05; ***p<0.01