Aula 1 de econometria com o R
Anderson Moreira Aristides dos Santos
Introdução
Apresentaremos alguns gráficos e estimações baseadas na primeira parte da disciplina de econometria.
Gráfico de Dispersão
Exemplo da relação entre pobreza e renda utilizando dados dos municípios de Alagoas do ano 2010:
aula<-url("https://sites.google.com/site/andersonmoreiraadossantos/base-de-dados/aula.RData")
load(aula)
library("scatterD3")
library(ggplot2)
ggplot(pobreza, aes(x= renda, y= pobreza ))+
geom_point() 
ggplot(pobreza, aes(x= renda, y= pobreza, label=mun))+
geom_point() +
geom_text(aes(label=ifelse(pobreza==47.02,as.character(mun),'')),hjust=0,vjust=0)
ggplot(pobreza, aes(x= renda, y= pobreza, label=mun, colour=meso))+
geom_point() +
geom_text(aes(label=ifelse(pobreza==47.02,as.character(mun),'')),hjust=0,vjust=0)
Histogramas e dispersão com o comando plot
Exemplos de histogramas das variáveis renda, pobreza e índice de Gini.
hist(pobreza$pobreza, col="green")
hist (pobreza$gini, col="blue")
hist(pobreza$renda, col="yellow")
summary(pobreza)## mun gini renda pobreza
## Length:102 Min. :0.4200 Min. :151.6 Min. :15.57
## Class :character 1st Qu.:0.4900 1st Qu.:204.6 1st Qu.:40.60
## Mode :character Median :0.5300 Median :233.4 Median :46.94
## Mean :0.5344 Mean :251.2 Mean :45.94
## 3rd Qu.:0.5675 3rd Qu.:269.0 3rd Qu.:51.48
## Max. :0.6700 Max. :792.5 Max. :67.57
## micro meso
## Length:102 Length:102
## Class :character Class :character
## Mode :character Mode :character
##
##
## ggplot(pobreza, aes(x= renda, y= pobreza ))+
geom_point() +
stat_smooth(method = "lm", col = "blue")
ggplot(pobreza, aes(x= gini, y= pobreza ))+
geom_point() +
stat_smooth(method = "lm", col = "green")
Modelo de regressão- MQO: lin-lin e log-log
Estimações baseadas nos dados dos gráficos que já foram observados.
## Modelo lin-lin
reg_pob<-lm(pobreza~gini+renda, data=pobreza)
summary(reg_pob)##
## Call:
## lm(formula = pobreza ~ gini + renda, data = pobreza)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5786 -1.7780 -0.4004 1.8718 18.8251
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.288127 3.574381 6.515 3.05e-09 ***
## gini 92.797415 6.535587 14.199 < 2e-16 ***
## renda -0.107257 0.004177 -25.677 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.309 on 99 degrees of freedom
## Multiple R-squared: 0.8904, Adjusted R-squared: 0.8882
## F-statistic: 402 on 2 and 99 DF, p-value: < 2.2e-16## Modelo log-log
reg_lnpob<-lm(log(pobreza)~log(gini)+log(renda), data=pobreza)
summary(reg_lnpob)##
## Call:
## lm(formula = log(pobreza) ~ log(gini) + log(renda), data = pobreza)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.153560 -0.039385 0.003969 0.033929 0.117157
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.24945 0.13559 68.22 <2e-16 ***
## log(gini) 0.77194 0.06272 12.31 <2e-16 ***
## log(renda) -0.90347 0.02357 -38.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05867 on 99 degrees of freedom
## Multiple R-squared: 0.9423, Adjusted R-squared: 0.9412
## F-statistic: 809 on 2 and 99 DF, p-value: < 2.2e-16## Modelo log-log gerando o ln das variáveis
pobreza$lnpobreza<-log(pobreza$pobreza)
pobreza$lngini<-log(pobreza$gini)
pobreza$lnrenda<-log(pobreza$renda)
reg_logpobreza2<-lm(lnpobreza~lngini+lnrenda, data=pobreza)
summary(reg_logpobreza2)##
## Call:
## lm(formula = lnpobreza ~ lngini + lnrenda, data = pobreza)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.153560 -0.039385 0.003969 0.033929 0.117157
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.24945 0.13559 68.22 <2e-16 ***
## lngini 0.77194 0.06272 12.31 <2e-16 ***
## lnrenda -0.90347 0.02357 -38.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05867 on 99 degrees of freedom
## Multiple R-squared: 0.9423, Adjusted R-squared: 0.9412
## F-statistic: 809 on 2 and 99 DF, p-value: < 2.2e-16## Organizando os resultados em tabelas
library(stargazer)##
## Please cite as:## Hlavac, Marek (2015). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2. http://CRAN.R-project.org/package=stargazerstargazer(reg_pob, reg_lnpob, type="text")##
## ==========================================================
## Dependent variable:
## ----------------------------
## pobreza log(pobreza)
## (1) (2)
## ----------------------------------------------------------
## gini 92.797***
## (6.536)
##
## renda -0.107***
## (0.004)
##
## log(gini) 0.772***
## (0.063)
##
## log(renda) -0.903***
## (0.024)
##
## Constant 23.288*** 9.249***
## (3.574) (0.136)
##
## ----------------------------------------------------------
## Observations 102 102
## R2 0.890 0.942
## Adjusted R2 0.888 0.941
## Residual Std. Error (df = 99) 3.309 0.059
## F Statistic (df = 2; 99) 402.031*** 809.036***
## ==========================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Problema de Heterocedasticidade
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric# Teste de Breusch-Pagan
reg_lnpob##
## Call:
## lm(formula = log(pobreza) ~ log(gini) + log(renda), data = pobreza)
##
## Coefficients:
## (Intercept) log(gini) log(renda)
## 9.2495 0.7719 -0.9035bptest(reg_lnpob)##
## studentized Breusch-Pagan test
##
## data: reg_lnpob
## BP = 14.067, df = 2, p-value = 0.0008819#Regressão robusta
library(car)
coeftest(reg_lnpob, vcov=hccm)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.249452 0.228803 40.425 < 2.2e-16 ***
## log(gini) 0.771944 0.074498 10.362 < 2.2e-16 ***
## log(renda) -0.903467 0.042561 -21.227 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# MQG Considerando que Var(u)=sigma2 * lnrenda
mqg_lnpob<-lm(log(pobreza)~log(gini)+log(renda), data=pobreza, weight=1/log(renda))
summary(mqg_lnpob)##
## Call:
## lm(formula = log(pobreza) ~ log(gini) + log(renda), data = pobreza,
## weights = 1/log(renda))
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -0.065061 -0.016610 0.002243 0.015028 0.048804
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.19400 0.13640 67.40 <2e-16 ***
## log(gini) 0.76488 0.06193 12.35 <2e-16 ***
## log(renda) -0.89418 0.02401 -37.25 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02483 on 99 degrees of freedom
## Multiple R-squared: 0.9405, Adjusted R-squared: 0.9393
## F-statistic: 782.5 on 2 and 99 DF, p-value: < 2.2e-16Modelos de Equação salarial, exemplo do Wooldridge
library(car)
#Interceptos diferentes
reg_lnw<-lm(log(w)~educ+ exper + I(exper^2) + mulher, data=salario)
summary(reg_lnw)##
## Call:
## lm(formula = log(w) ~ educ + exper + I(exper^2) + mulher, data = salario)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.80836 -0.27728 -0.01813 0.25637 1.23896
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3904831 0.1022096 3.820 0.000149 ***
## educ 0.0841361 0.0069568 12.094 < 2e-16 ***
## exper 0.0389100 0.0048235 8.067 5.00e-15 ***
## I(exper^2) -0.0006860 0.0001074 -6.389 3.71e-10 ***
## mulher -0.3371868 0.0363214 -9.283 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4134 on 521 degrees of freedom
## Multiple R-squared: 0.3996, Adjusted R-squared: 0.395
## F-statistic: 86.69 on 4 and 521 DF, p-value: < 2.2e-16# Teste F beta_educ*mulher=0 e beta_mulher=0
library(car)
myH0<-c("mulher=0", "educ=0")
linearHypothesis(reg_lnw, myH0)## Linear hypothesis test
##
## Hypothesis:
## mulher = 0
## educ = 0
##
## Model 1: restricted model
## Model 2: log(w) ~ educ + exper + I(exper^2) + mulher
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 523 132.903
## 2 521 89.059 2 43.845 128.25 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo com Interceptos e inclinações diferentes
reg_lnw2<-lm(log(w)~educ+ exper + I(exper^2) + mulher + I(mulher*educ), data=salario)
summary(reg_lnw2)##
## Call:
## lm(formula = log(w) ~ educ + exper + I(exper^2) + mulher + I(mulher *
## educ), data = salario)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.80847 -0.27707 -0.01697 0.25645 1.24113
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3873644 0.1227335 3.156 0.00169 **
## educ 0.0843801 0.0087540 9.639 < 2e-16 ***
## exper 0.0389047 0.0048295 8.056 5.44e-15 ***
## I(exper^2) -0.0006858 0.0001076 -6.377 4.00e-10 ***
## mulher -0.3294333 0.1724333 -1.910 0.05662 .
## I(mulher * educ) -0.0006201 0.0134809 -0.046 0.96333
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4138 on 520 degrees of freedom
## Multiple R-squared: 0.3996, Adjusted R-squared: 0.3938
## F-statistic: 69.22 on 5 and 520 DF, p-value: < 2.2e-16