Variables instrumentales
2024-03-03
Paquetes o librerías
library(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerlibrary(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(AER)## Loading required package: car## Loading required package: carData## Loading required package: sandwich## Loading required package: survivallibrary(markdown)library(haven)Datos
library(wooldridge)datos <- fertil1
head(datos)## year educ meduc feduc age kids black east northcen west farm othrural town
## 1 72 12 8 8 48 4 0 0 1 0 0 0 0
## 2 72 17 8 18 46 3 0 0 0 0 0 1 0
## 3 72 12 7 8 53 2 0 0 1 0 0 1 0
## 4 72 12 12 10 42 2 0 0 1 0 0 0 1
## 5 72 12 3 8 51 2 0 0 0 0 1 0 0
## 6 72 8 8 8 50 4 0 0 1 0 1 0 0
## smcity y74 y76 y78 y80 y82 y84 agesq y74educ y76educ y78educ y80educ y82educ
## 1 0 0 0 0 0 0 0 2304 0 0 0 0 0
## 2 0 0 0 0 0 0 0 2116 0 0 0 0 0
## 3 0 0 0 0 0 0 0 2809 0 0 0 0 0
## 4 0 0 0 0 0 0 0 1764 0 0 0 0 0
## 5 0 0 0 0 0 0 0 2601 0 0 0 0 0
## 6 0 0 0 0 0 0 0 2500 0 0 0 0 0
## y84educ
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0# Estructura del dataframe
#------------------------------
str(datos)## 'data.frame': 1129 obs. of 27 variables:
## $ year : int 72 72 72 72 72 72 72 72 72 72 ...
## $ educ : int 12 17 12 12 12 8 12 10 12 12 ...
## $ meduc : int 8 8 7 12 3 8 12 12 8 6 ...
## $ feduc : int 8 18 8 10 8 8 10 5 8 13 ...
## $ age : int 48 46 53 42 51 50 47 46 41 36 ...
## $ kids : int 4 3 2 2 2 4 0 1 2 4 ...
## $ black : int 0 0 0 0 0 0 0 0 0 0 ...
## $ east : int 0 0 0 0 0 0 0 0 0 0 ...
## $ northcen: int 1 0 1 1 0 1 1 1 1 1 ...
## $ west : int 0 0 0 0 0 0 0 0 0 0 ...
## $ farm : int 0 0 0 0 1 1 0 0 0 1 ...
## $ othrural: int 0 1 1 0 0 0 0 0 0 0 ...
## $ town : int 0 0 0 1 0 0 1 0 0 0 ...
## $ smcity : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y74 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y76 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y78 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y80 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y82 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y84 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ agesq : int 2304 2116 2809 1764 2601 2500 2209 2116 1681 1296 ...
## $ y74educ : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y76educ : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y78educ : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y80educ : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y82educ : int 0 0 0 0 0 0 0 0 0 0 ...
## $ y84educ : int 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "time.stamp")= chr "25 Jun 2011 23:03"summary(datos)## year educ meduc feduc
## Min. :72.00 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.:74.00 1st Qu.:12.00 1st Qu.: 7.000 1st Qu.: 8.000
## Median :78.00 Median :12.00 Median : 8.000 Median :10.000
## Mean :78.14 Mean :12.69 Mean : 9.132 Mean : 9.716
## 3rd Qu.:82.00 3rd Qu.:14.00 3rd Qu.:12.000 3rd Qu.:12.000
## Max. :84.00 Max. :20.00 Max. :20.000 Max. :20.000
## age kids black east
## Min. :35.00 Min. :0.000 Min. :0.00000 Min. :0.0000
## 1st Qu.:38.00 1st Qu.:2.000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :43.00 Median :3.000 Median :0.00000 Median :0.0000
## Mean :43.48 Mean :2.743 Mean :0.08503 Mean :0.2489
## 3rd Qu.:48.00 3rd Qu.:4.000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :54.00 Max. :7.000 Max. :1.00000 Max. :1.0000
## northcen west farm othrural
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.3198 Mean :0.1081 Mean :0.1984 Mean :0.1019
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## town smcity y74 y76
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.3171 Mean :0.1258 Mean :0.1532 Mean :0.1346
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## y78 y80 y82 y84
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1267 Mean :0.1258 Mean :0.1647 Mean :0.1568
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## agesq y74educ y76educ y78educ
## Min. :1225 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.:1444 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median :1849 Median : 0.000 Median : 0.000 Median : 0.000
## Mean :1925 Mean : 1.885 Mean : 1.647 Mean : 1.601
## 3rd Qu.:2304 3rd Qu.: 0.000 3rd Qu.: 0.000 3rd Qu.: 0.000
## Max. :2916 Max. :20.000 Max. :20.000 Max. :20.000
## y80educ y82educ y84educ
## Min. : 0.00 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 0.00 Median : 0.000 Median : 0.00
## Mean : 1.62 Mean : 2.179 Mean : 2.08
## 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.00
## Max. :20.00 Max. :20.000 Max. :20.00Estimación MCO
MCO <- lm(year ~ educ + age + kids + black + east + northcen + west, data = datos)
summary(MCO)##
## Call:
## lm(formula = year ~ educ + age + kids + black + east + northcen +
## west, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.512 -3.498 0.115 3.387 8.340
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 80.10866 1.13533 70.560 < 2e-16 ***
## educ 0.18535 0.04636 3.998 6.80e-05 ***
## age -0.07507 0.02037 -3.685 0.000239 ***
## kids -0.38683 0.07444 -5.196 2.41e-07 ***
## black 1.33238 0.43879 3.036 0.002449 **
## east -0.49146 0.32171 -1.528 0.126877
## northcen 0.16603 0.30197 0.550 0.582558
## west -0.36449 0.41901 -0.870 0.384553
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.953 on 1121 degrees of freedom
## Multiple R-squared: 0.07271, Adjusted R-squared: 0.06692
## F-statistic: 12.56 on 7 and 1121 DF, p-value: 1.431e-15stargazer(MCO, type = 'text', title = "Regresión OLS", df = F, digits = 4)##
## Regresión OLS
## ===============================================
## Dependent variable:
## ---------------------------
## year
## -----------------------------------------------
## educ 0.1853***
## (0.0464)
##
## age -0.0751***
## (0.0204)
##
## kids -0.3868***
## (0.0744)
##
## black 1.3324***
## (0.4388)
##
## east -0.4915
## (0.3217)
##
## northcen 0.1660
## (0.3020)
##
## west -0.3645
## (0.4190)
##
## Constant 80.1087***
## (1.1353)
##
## -----------------------------------------------
## Observations 1,129
## R2 0.0727
## Adjusted R2 0.0669
## Residual Std. Error 3.9525
## F Statistic 12.5576***
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Interpretación.
Educ = 0.18. Se estima que aumentar en un año la educación del individuo, con el resto constante, provocaría que la esperanza de years aumentase en 0.18 unidades. El p valor = 0.000 < 0.05. Tenemos evidencia empírica para rechazar H0 al 5%. Por tanto, la educación es significativa.
Age = -0.07. Se estima que aumentar en un año la edad del individuo, con el resto constante, provocaría que la esperanza de years disminuyese en 0.07 unidades. EL pvalor = 0.0002 < 0.05. Tenemos evidencia empírica suficiente para rechazar H0 al 5%. Por tanto, la edad es estadísticamente significativa.
Kids = -0,38 Se estima que un individuo que aumente en hijo, con el resto constante, se estima que la esperanza de years disminuya en 0.38 unidades. El p valor = 0.000 < 0.05. Tenemos evidencia empírica suficiente para rechazar H0 al nivel del 5%. El número de hijos es relevante.
Black = 1.33 Se estima que un individuo negro tendrá un 1.33 unidades más de years, con el resto de factores independientes. El p-valor = 0.002 < 0.05. Tenemos evidencia empírica suficiente para rechaar H0 al 5%. Por tanto, el efecto diferenciador por ser negro es relevante al 95% de confianza.
Northcen = 0.16 Se estima que un individuo que vive en el norte tendrá 0.16 unidades adicionales que el mismo individuo que vive en el sur, respecto a years. El p valor es 0.58 > 0.05. Se acepta la hipótesis nula de que el coeficiente es irrelevante al 5%.
East = -0.49 Se estima que un individuo que vive en el norte tendrá 0.49 unidades menos que el mismo individuo que vive en el sur, respecto a years. El p valor es 0.12 > 0.05. Tenemos evidencia empírica suficiente para aceptar la hipótesis nula de que el efecto diferenciador es irrelevante al 5%.
West = 0.38. Se estima que un individuo que vive en el norte tendrá 0.36 unidades menos que el mismo individuo que vive en el sur, respecto a years. El p valor es 0.38 > 0.05. Tenemos evidencia empírica suficiente para aceptar la hipótesis nula de que el efecto diferenciador es irrelevante al 5%.
Constante = 80.10 Se estima que la media de years de los individuos que van en el sur es de 80.10 años, independientemente del resto de variables. El p-valor = 0.000 < 0.05. Por tanto, el valor medio de los ciudadanos del sur es diferente de cero.
R2 = 0.0727. La variación de las variables explicativas permite explicar el 7.27% de las variaciones de years, alrededor de su media.
Explicar por qué la variable educ es potencialmente endógena. ¿Qué propiedades tiene nuestro estimador?
Educación = beta x Educ_padre + gamma x Educ_madre + error
Educación es endógena, dado que tiene un término de error que la hace aleatoria. Al incluir variables endógenas como explicativas, nuestro modelo tiene un problema de endogeneidad y las estimaciones son sesgadas e inconsistentes.
Obtenga la forma reducida de educación con los instrumentos Educ_padre y educ_madre. Determine la condición de relevancia
EDUC <- lm(educ ~ feduc + meduc + age+ kids + black + east + northcen + west, data = datos)
summary(EDUC)##
## Call:
## lm(formula = educ ~ feduc + meduc + age + kids + black + east +
## northcen + west, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.3254 -1.3364 -0.2025 1.1446 9.7554
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.217806 0.587505 15.690 < 2e-16 ***
## feduc 0.210965 0.024967 8.450 < 2e-16 ***
## meduc 0.176246 0.021643 8.143 1.02e-15 ***
## age 0.005647 0.011609 0.486 0.62673
## kids -0.255560 0.041145 -6.211 7.40e-10 ***
## black 0.759109 0.246524 3.079 0.00213 **
## east 0.399549 0.181100 2.206 0.02757 *
## northcen 0.257073 0.171061 1.503 0.13317
## west 0.214743 0.236443 0.908 0.36395
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.221 on 1120 degrees of freedom
## Multiple R-squared: 0.2976, Adjusted R-squared: 0.2925
## F-statistic: 59.3 on 8 and 1120 DF, p-value: < 2.2e-16feduc tiene un p valor = 0.000 < 0.05. Sería estadísticamente significativa meduc tiene un p valor = 0.000 < 0.05. Sería estadísticamente significativa
No obstante, hay que hacer un contraste de significación conjunta para hacer de las dos variables a la vez.
stargazer(EDUC, type = "text", digits =4)##
## ===============================================
## Dependent variable:
## ---------------------------
## educ
## -----------------------------------------------
## feduc 0.2110***
## (0.0250)
##
## meduc 0.1762***
## (0.0216)
##
## age 0.0056
## (0.0116)
##
## kids -0.2556***
## (0.0411)
##
## black 0.7591***
## (0.2465)
##
## east 0.3995**
## (0.1811)
##
## northcen 0.2571
## (0.1711)
##
## west 0.2147
## (0.2364)
##
## Constant 9.2178***
## (0.5875)
##
## -----------------------------------------------
## Observations 1,129
## R2 0.2976
## Adjusted R2 0.2925
## Residual Std. Error 2.2207 (df = 1120)
## F Statistic 59.3049*** (df = 8; 1120)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01library(lmtest)EDUC2 <- lm(educ ~ age+ kids + black + east + northcen + west, data = datos)
summary(EDUC2)##
## Call:
## lm(formula = educ ~ age + kids + black + east + northcen + west,
## data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.2557 -1.2665 -0.3936 1.3132 7.9686
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.60036 0.58697 24.874 < 2e-16 ***
## age -0.03448 0.01308 -2.636 0.0085 **
## kids -0.36215 0.04670 -7.754 1.99e-14 ***
## black 0.51343 0.28215 1.820 0.0691 .
## east 0.82621 0.20570 4.017 6.29e-05 ***
## northcen 0.82109 0.19291 4.256 2.25e-05 ***
## west 0.65962 0.26911 2.451 0.0144 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.545 on 1122 degrees of freedom
## Multiple R-squared: 0.07558, Adjusted R-squared: 0.07063
## F-statistic: 15.29 on 6 and 1122 DF, p-value: < 2.2e-16R2 no restringido = 0.2976 R2 sí restringido = 0.07558
F = [(R2 no - R2 si)/q]/[(1-R2 no)/(n-k*)]
stargazer(EDUC2, type = "text", digits =4)##
## ===============================================
## Dependent variable:
## ---------------------------
## educ
## -----------------------------------------------
## age -0.0345***
## (0.0131)
##
## kids -0.3621***
## (0.0467)
##
## black 0.5134*
## (0.2822)
##
## east 0.8262***
## (0.2057)
##
## northcen 0.8211***
## (0.1929)
##
## west 0.6596**
## (0.2691)
##
## Constant 14.6004***
## (0.5870)
##
## -----------------------------------------------
## Observations 1,129
## R2 0.0756
## Adjusted R2 0.0706
## Residual Std. Error 2.5453 (df = 1122)
## F Statistic 15.2881*** (df = 6; 1122)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01R2no <- 0.2976
R2si <- 0.07558
q = 2
df = 1129 - 8
F = ((R2no - R2si)/q)/((1-R2no)/df)
F## [1] 177.1672# P valor
#------------------------------
pf(F, df1 = q, df2 = df, lower.tail = FALSE)## [1] 1.383097e-67El p valor es 0.000 < 0.05. Tenemos evidencia empírica suficiente para rechazar H0 al 5%. Por tanto, educ del padre y educ de la madre son conjuntamente significativas. Como la variable dependiente de la primera etapa = EDUC, quiere decir que explican la educación del individuo. Si los instrumentos se encuentran correlacionados con el regresor estocástico que pretenden sustituir, son relevantes.
Determinar la condición de exogeneidad con Hausman
# Estimar e error de la forma reducida
#-------------------------------------------
error <- EDUC$residuals
plot(error)
HT <- lm (educ ~feduc + meduc + error + age + kids + black + east + northcen + west, data = datos)
summary(HT)## Warning in summary.lm(HT): essentially perfect fit: summary may be unreliable##
## Call:
## lm(formula = educ ~ feduc + meduc + error + age + kids + black +
## east + northcen + west, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.864e-14 -1.160e-16 1.120e-16 3.130e-16 2.242e-14
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.218e+00 8.526e-16 1.081e+16 <2e-16 ***
## feduc 2.110e-01 3.623e-17 5.822e+15 <2e-16 ***
## meduc 1.762e-01 3.141e-17 5.611e+15 <2e-16 ***
## error 1.000e+00 4.337e-17 2.306e+16 <2e-16 ***
## age 5.647e-03 1.685e-17 3.352e+14 <2e-16 ***
## kids -2.556e-01 5.971e-17 -4.280e+15 <2e-16 ***
## black 7.591e-01 3.578e-16 2.122e+15 <2e-16 ***
## east 3.995e-01 2.628e-16 1.520e+15 <2e-16 ***
## northcen 2.571e-01 2.483e-16 1.035e+15 <2e-16 ***
## west 2.147e-01 3.432e-16 6.258e+14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.223e-15 on 1119 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 8.411e+31 on 9 and 1119 DF, p-value: < 2.2e-16El error tiene un p valor de 0.057 > 0.057 es irrelevante. Por tanto, educm y educp son instrumentos exógenos.
stargazer(HT, type = "text", digits =4)##
## =====================================================================================
## Dependent variable:
## -----------------------------------------------------------------
## educ
## -------------------------------------------------------------------------------------
## feduc 0.2110***
## (0.0000)
##
## meduc 0.1762***
## (0.0000)
##
## error 1.0000***
## (0.0000)
##
## age 0.0056***
## (0.0000)
##
## kids -0.2556***
## (0.0000)
##
## black 0.7591***
## (0.0000)
##
## east 0.3995***
## (0.0000)
##
## northcen 0.2571***
## (0.0000)
##
## west 0.2147***
## (0.0000)
##
## Constant 9.2178***
## (0.0000)
##
## -------------------------------------------------------------------------------------
## Observations 1,129
## R2 1.0000
## Adjusted R2 1.0000
## Residual Std. Error 0.0000 (df = 1119)
## F Statistic 84,111,264,516,509,786,296,204,860,604,420.0000*** (df = 9; 1119)
## =====================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01MCVI <- ivreg(year ~educ + age + kids + black + east + northcen + west
|feduc + meduc+ age + kids + black + east + northcen + west, data = datos)
summary(MCVI)##
## Call:
## ivreg(formula = year ~ educ + age + kids + black + east + northcen +
## west | feduc + meduc + age + kids + black + east + northcen +
## west, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.07728 -3.47482 -0.02366 3.27812 9.61069
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 76.20655 1.67927 45.381 < 2e-16 ***
## educ 0.45261 0.09600 4.715 2.72e-06 ***
## age -0.06586 0.02087 -3.155 0.001645 **
## kids -0.29004 0.08139 -3.564 0.000381 ***
## black 1.19516 0.44732 2.672 0.007653 **
## east -0.71228 0.33368 -2.135 0.033010 *
## northcen -0.05342 0.31403 -0.170 0.864963
## west -0.54078 0.42874 -1.261 0.207458
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.011 on 1121 degrees of freedom
## Multiple R-Squared: 0.04522, Adjusted R-squared: 0.03926
## Wald test: 13.15 on 7 and 1121 DF, p-value: 2.301e-16stargazer(MCVI, type = "text", digits =4)##
## ===============================================
## Dependent variable:
## ---------------------------
## year
## -----------------------------------------------
## educ 0.4526***
## (0.0960)
##
## age -0.0659***
## (0.0209)
##
## kids -0.2900***
## (0.0814)
##
## black 1.1952***
## (0.4473)
##
## east -0.7123**
## (0.3337)
##
## northcen -0.0534
## (0.3140)
##
## west -0.5408
## (0.4287)
##
## Constant 76.2066***
## (1.6793)
##
## -----------------------------------------------
## Observations 1,129
## R2 0.0452
## Adjusted R2 0.0393
## Residual Std. Error 4.0107 (df = 1121)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01stargazer(MCO, MCVI, type = 'text', digits = 4)##
## ======================================================================
## Dependent variable:
## --------------------------------------
## year
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## educ 0.1853*** 0.4526***
## (0.0464) (0.0960)
##
## age -0.0751*** -0.0659***
## (0.0204) (0.0209)
##
## kids -0.3868*** -0.2900***
## (0.0744) (0.0814)
##
## black 1.3324*** 1.1952***
## (0.4388) (0.4473)
##
## east -0.4915 -0.7123**
## (0.3217) (0.3337)
##
## northcen 0.1660 -0.0534
## (0.3020) (0.3140)
##
## west -0.3645 -0.5408
## (0.4190) (0.4287)
##
## Constant 80.1087*** 76.2066***
## (1.1353) (1.6793)
##
## ----------------------------------------------------------------------
## Observations 1,129 1,129
## R2 0.0727 0.0452
## Adjusted R2 0.0669 0.0393
## Residual Std. Error (df = 1121) 3.9525 4.0107
## F Statistic 12.5576*** (df = 7; 1121)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Cuando los regresores son endógenos y aplicamos MCVI (Mínimos Cuadrados de Variables Instrumentales) con instrumentos exógenos y relevantes, obtenemos coeficientes consistentes. Por tanto, los resultados adecuados son los de la segunda columna.
MCVI$rcontrasts## NULLsargan <- 1129*0.0452
sargan## [1] 51.0308# F = 12.55 < 10. Los instrumentos son conjuntamente relevanteserrorVI <- MCVI$residuals
plot(errorVI)
SarganM <- lm(errorVI ~ meduc + feduc+ age+ kids + black + east + northcen + west, data = datos)
summary(SarganM)##
## Call:
## lm(formula = errorVI ~ meduc + feduc + age + kids + black + east +
## northcen + west, data = datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.8366 -3.4398 -0.0021 3.2867 9.6110
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0558095 1.0610851 -0.053 0.958
## meduc -0.0338641 0.0390894 -0.866 0.386
## feduc 0.0387177 0.0450924 0.859 0.391
## age -0.0002644 0.0209665 -0.013 0.990
## kids 0.0010548 0.0743117 0.014 0.989
## black -0.0026279 0.4452435 -0.006 0.995
## east 0.0150314 0.3270821 0.046 0.963
## northcen -0.0101727 0.3089508 -0.033 0.974
## west -0.0256616 0.4270357 -0.060 0.952
##
## Residual standard error: 4.011 on 1120 degrees of freedom
## Multiple R-squared: 0.0008239, Adjusted R-squared: -0.006313
## F-statistic: 0.1154 on 8 and 1120 DF, p-value: 0.9987stargazer(SarganM, type = "text", digits =4)##
## ===============================================
## Dependent variable:
## ---------------------------
## errorVI
## -----------------------------------------------
## meduc -0.0339
## (0.0391)
##
## feduc 0.0387
## (0.0451)
##
## age -0.0003
## (0.0210)
##
## kids 0.0011
## (0.0743)
##
## black -0.0026
## (0.4452)
##
## east 0.0150
## (0.3271)
##
## northcen -0.0102
## (0.3090)
##
## west -0.0257
## (0.4270)
##
## Constant -0.0558
## (1.0611)
##
## -----------------------------------------------
## Observations 1,129
## R2 0.0008
## Adjusted R2 -0.0063
## Residual Std. Error 4.0108 (df = 1120)
## F Statistic 0.1154 (df = 8; 1120)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Sargan = 1129*0.0008
Sargan## [1] 0.9032pchisq(Sargan, df = 2, lower.tail = FALSE)## [1] 0.6366088P valor = 0.63 > 0.05. Tenemos evidencia empírica suficiente para aceptar (H0). Los instrumentos son conjuntamente relevantes.