Carga de Datos

library(wooldridge)
data("hprice1")
head(hprice1,n=5)

##   price assess bdrms lotsize sqrft colonial   lprice  lassess llotsize   lsqrft
## 1   300  349.1     4    6126  2438        1 5.703783 5.855359 8.720297 7.798934
## 2   370  351.5     3    9903  2076        1 5.913503 5.862210 9.200593 7.638198
## 3   191  217.7     3    5200  1374        0 5.252274 5.383118 8.556414 7.225482
## 4   195  231.8     3    4600  1448        1 5.273000 5.445875 8.433811 7.277938
## 5   373  319.1     4    6095  2514        1 5.921578 5.765504 8.715224 7.829630

1. Estimación del Modelo

Modelo_Estimado <- lm(formula = price~lotsize+sqrft+bdrms, data = hprice1)
stargazer::stargazer(Modelo_Estimado,type = "text")

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                price           
## -----------------------------------------------
## lotsize                      0.002***          
##                               (0.001)          
##                                                
## sqrft                        0.123***          
##                               (0.013)          
##                                                
## bdrms                         13.853           
##                               (9.010)          
##                                                
## Constant                      -21.770          
##                              (29.475)          
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                             0.672           
## Adjusted R2                    0.661           
## Residual Std. Error      59.833 (df = 84)      
## F Statistic           57.460*** (df = 3; 84)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

2. Verificación de Colinealidad

a. Indice de condición

options(scipen = 999999)
Matriz.X <- model.matrix(Modelo_Estimado)
Matriz.XX <- t(Matriz.X)%*%Matriz.X
stargazer::stargazer(Matriz.XX,type = "text")

## 
## ==============================================================
##             (Intercept)    lotsize         sqrft       bdrms  
## --------------------------------------------------------------
## (Intercept)     88         793,748        177,205       314   
## lotsize       793,748   16,165,159,010 1,692,290,257 2,933,767
## sqrft         177,205   1,692,290,257   385,820,561   654,755 
## bdrms           314       2,933,767       654,755      1,182  
## --------------------------------------------------------------

Sn <- solve(diag(sqrt(diag(Matriz.XX))))
stargazer::stargazer(Sn,type = "text")

## 
## ==========================
## 0.107    0      0      0  
## 0     0.00001   0      0  
## 0        0    0.0001   0  
## 0        0      0    0.029
## --------------------------

XX.Normal <- (Sn%*%Matriz.XX)%*%Sn
stargazer::stargazer(XX.Normal, type = "text", digits = 4)

## 
## ===========================
## 1      0.6655 0.9617 0.9736
## 0.6655   1    0.6776 0.6712
## 0.9617 0.6776   1    0.9696
## 0.9736 0.6712 0.9696   1   
## ---------------------------

Lambdas <- eigen(XX.Normal,symmetric = T)
stargazer::stargazer(Lambdas$values, type = "text")

## 
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------

k <- sqrt(max(Lambdas$values)/min(Lambdas$values))
print(k)

## [1] 11.86778

El indice de condición K es menor a 20 por lo que hay evidencia de que los regresores carecen o tienen leve colinealidad.

b. Prueba de Farrar-Glaubar

Zn<-scale(Matriz.X[,-1])
stargazer::stargazer(head(Zn,n=5),type = "text")

## 
## =======================
##   lotsize sqrft  bdrms 
## -----------------------
## 1 -0.284  0.735  0.513 
## 2  0.087  0.108  -0.675
## 3 -0.375  -1.108 -0.675
## 4 -0.434  -0.980 -0.675
## 5 -0.287  0.867  0.513 
## -----------------------

## Calculo de R

n<-nrow(Zn)
R<-(t(Zn)%*%Zn)*(1/(n-1))
stargazer::stargazer(R,type = "text")

## 
## ===========================
##         lotsize sqrft bdrms
## ---------------------------
## lotsize    1    0.184 0.136
## sqrft    0.184    1   0.531
## bdrms    0.136  0.531   1  
## ---------------------------

## Determinante de R

determinante_R<-det(R)
print(determinante_R)

## [1] 0.6917931

## Estadistico de FG

m<-ncol(Matriz.X[,-1])
n<-nrow(Matriz.X[,-1])
FG <--(n-1-(2*m+5)/6)*log(determinante_R)
print(FG)

## [1] 31.38122

## Valor critico

gl<-m*(m-1)/2
VC<-qchisq(p = 0.95,df = gl)
print(VC)

## [1] 7.814728

como \(FG\) > \(VC\) hay evidencia de colinealidad en los regresores, por lo tanto, se rechaza la hipotesis Nula

Graficar FG con fastGraph

options(scipen = 99999)
library(fastGraph)
shadeDist(xshade = FG, ddist = "dchisq",parm1 = gl,lower.tail = F,sub=paste("VC:", VC, "FG",FG), col = c("red","turquoise"))

c. Factores Inflacionarios de la Varianza

inversa.R<-solve(R)
VIF <- diag(inversa.R)
print(VIF)

##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663

#Gráfica

library(mctest)
mc.plot(mod = Modelo_Estimado, vif = 2)

Los VIF estan por debajo de 2, por lo tanto los regresores presenta colinealidad leve.

Multicolinealidad

Asignatura: Econometría

Grupo Teórico: 3

Osvaldo Enrique Roche Romero