Econometria: exercício crescimento municipal em Mato Grosso entre 2001 e 2010 - seleção de variáveis

Abstract

This is an undergrad student level exercise for class use. We analyse 139 municipal cross-section data for the Brazilian State of Mato Grosso on a static growth model.

Licença

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

License: CC BY-SA 4.0

Citação

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Econometria: exercício crescimento municipal em Mato Grosso entre 2001 e 2010 - seleção. Campo Grande-MS,Brasil: RStudio/Rpubs, 2021. Disponível em http://rpubs.com/amrofi/growth_mt2001_2010_selecao.

1 Introdução

Neste exercício, farei uso dos dados do post https://rpubs.com/amrofi/growth_mt2001_2010, (e video em https://youtu.be/JvBRjFeERoE) e adaptarei para a seleção de modelos ao estilo (farei adaptação) do exercício https://rpubs.com/amrofi/Faraway_backward_selection e video (https://youtu.be/eyc2zs__7jo). Ou seja, aplicarei os métodos backward selection e stepwise sobre os dados de crescimento.

Portanto, seja o enunciado como no post inicial (https://rpubs.com/amrofi/growth_mt2001_2010).

Exemplo sobre crescimento municipal adaptado da dissertacao de William Marquezin (2014) na UFMT. Dados de 139 municipios de MT, em que 2001 é o ano base e o crescimento refere-se até 2010. A variável dependente do modelo é a taxa de crescimento da renda per capita municipal (barro) conforme Barro e Sala-i-Martin (1992)=“BARRO”. Outras variáveis são:
# “ordem” = ordenacao dos municipios
# “KEY” = ordem
# “MUNICIPIO” = nome do municipio
# “BARRO” = variavel dependente (acima descrita)
# “DASSOW” = alternativa para a variavel dependente (nao utilizada)
# Variáveis explicativas:
# 1) Renda per capita no ano inicial “LNYI_T_1”
# 2) Composição industrial (Sind): “SIND”
# 3) Composição da agropecuária (Sagro): “SAGRO”
# 4) Composição do setor de serviços (Sserv): “SSERV”
# 5) Composição da administração pública (Spub): “SPUB”
# 6) Capital humano (h): “H”
# 7) Densidade demográfica (dd): “DD”
# 8) Despesas orçamentárias (dorc): “DORC”
# 9) Operações de crédito (cred): “CRED”
# 10) Exportações Municipais (expor): “EXPOR”
# 11) Importações Municipais (impor): “IMPOR”
# 12) Mercado Regional (mreg): “MREG”
# 13) Carga tributária total municipal (t): “T”
# 14) Transferências Intergovernamentais do ICMS (ticms): “TICMS”
# 15) Transferências Intergovernamentais do FPM (tfpm): “TFPM”
# 16) O índice de GINI (gini): “GINI”
# 17) índice de THEIL (theil): “THEIL”
# variavel auxiliar não utilizada: “TMREG”
# variavel auxiliar não utilizada: “CCOM” corrente de comercio

Um data.frame com 139 observations para 24 variáveis.

Para reprodução, pode-se fazer o download prévio dos dados a partir de https://github.com/amrofi/crescimento_mt/blob/master/crescimento.rds, e armazenar no diretório do projeto, ou olhar os dados embeded no code .Rmd.

library(dynlm)
library(car)
library(lmtest)
library(sandwich)
library(tseries)
library(kableExtra)
# o arquivo dados está em formato dput embeded no script, em um chunk oculto
# que o leitor tem acesso ao baixar o Rmd, clicando em code

summary(dados)

     ordem            KEY         MUNICIPIO             BARRO         
 Min.   :  1.0   Min.   :  1.0   Length:139         Min.   :-0.07986  
 1st Qu.: 35.5   1st Qu.: 35.5   Class :character   1st Qu.: 0.03466  
 Median : 70.0   Median : 70.0   Mode  :character   Median : 0.04971  
 Mean   : 70.0   Mean   : 70.0                      Mean   : 0.05413  
     DASSOW            LNYI_T_1           SIND              SAGRO         
 Min.   :-0.05696   Min.   : 8.219   Min.   :-0.14688   Min.   :-0.37391  
 1st Qu.: 0.04068   1st Qu.: 8.840   1st Qu.: 0.02745   1st Qu.: 0.09529  
 Median : 0.06269   Median : 9.077   Median : 0.05442   Median : 0.22181  
 Mean   : 0.08061   Mean   : 9.222   Mean   : 0.06737   Mean   : 0.22179  
     SSERV               SPUB                H                DD          
 Min.   :-0.56295   Min.   :0.006014   Min.   : 2.662   Min.   :  0.2792  
 1st Qu.: 0.07236   1st Qu.:0.077798   1st Qu.:12.590   1st Qu.:  1.1508  
 Median : 0.12822   Median :0.108222   Median :15.828   Median :  2.2449  
 Mean   : 0.14414   Mean   :0.127134   Mean   :17.684   Mean   :  7.2235  
      DORC             CRED            EXPOR              IMPOR         
 Min.   : 532.4   Min.   :   0.0   Min.   :    0.00   Min.   :    0.00  
 1st Qu.:1348.8   1st Qu.:   0.0   1st Qu.:    0.00   1st Qu.:    0.00  
 Median :1606.9   Median : 757.6   Median :   39.21   Median :    0.00  
 Mean   :1800.4   Mean   :1589.0   Mean   : 2128.94   Mean   :  205.89  
      CCOM               MREG             T                TFPM         
 Min.   :    0.00   Min.   : 5863   Min.   :0.03508   Min.   :   60.68  
 1st Qu.:    0.00   1st Qu.:11363   1st Qu.:0.04787   1st Qu.:  300.37  
 Median :   92.58   Median :13452   Median :0.05877   Median :  535.94  
 Mean   : 2334.82   Mean   :16629   Mean   :0.06865   Mean   :  973.11  
     TICMS             TMREG              GINI            THEIL       
 Min.   :  87.68   Min.   :0.00849   Min.   :0.3600   Min.   :0.1900  
 1st Qu.: 243.31   1st Qu.:0.03445   1st Qu.:0.5300   1st Qu.:0.4750  
 Median : 382.59   Median :0.04830   Median :0.5800   Median :0.5500  
 Mean   : 445.03   Mean   :0.04925   Mean   :0.5755   Mean   :0.5809  
 [ reached getOption("max.print") -- omitted 2 rows ]

attach(dados)
class(dados)

[1] "tbl_df"     "tbl"        "data.frame"

# algumas variaveis vou dividir por 1000000 para nivelar expor_6 impor_6 mreg_6
# tfpm_6 ticms_6 cred_6

Estimando o modelo linear de regressão múltipla fazendo conforme a expressão do enunciado.

2 Resultados

2.1 Estimação

Fazendo as regressoes. Algumas variáveis foram construídas com uso de logaritmos e portanto, deve-se olhar a especificação destas.

# regressao multipla de BARRO~LNYI_T_1+SIND+SAGRO+SSERV+SPUB+H+DD+DORC
# +I(CRED*10^-6)+I(EXPOR*10^-6)+I(IMPOR*10^-6)+I(MREG*10^-6)+I(TFPM*10^-6)
# +I(TICMS*10^-6)+GINI variaveis transformadas
attach(dados)
Exporta <- I(EXPOR * 10^-6)
Importa <- I(IMPOR * 10^-6)
Mregio <- (MREG * 10^-6)
FPM <- I(TFPM * 10^-6)
TICMSm <- I(TICMS * 10^-6)
credito <- I(CRED * 10^-6)
mod1 <- lm(BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DD + DORC + T + Exporta +
    Importa + Mregio + FPM + TICMSm + credito, data = dados)

Vamos utilizar o pacote stargazer posteriormente para organizar as saídas de resultados. Se a saída fosse apenas pelo comando summary, sairia da forma:

summary(mod1)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DD + DORC + T + Exporta + Importa + Mregio + FPM + TICMSm + 
    credito, data = dados)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039810 -0.008103  0.000716  0.006618  0.031697 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.663e-01  3.869e-02  12.050  < 2e-16 ***
LNYI_T_1    -5.058e-02  4.582e-03 -11.037  < 2e-16 ***
SIND         1.284e-01  1.911e-02   6.721 6.00e-10 ***
SAGRO        1.075e-01  8.151e-03  13.187  < 2e-16 ***
SSERV        5.461e-02  1.970e-02   2.772  0.00644 ** 
SPUB        -1.438e-01  2.029e-02  -7.090 9.22e-11 ***
H            2.522e-04  2.098e-04   1.202  0.23177    
DD           4.799e-05  5.502e-05   0.872  0.38478    
DORC         4.773e-06  2.981e-06   1.601  0.11195    
T            2.015e-02  9.462e-02   0.213  0.83172    
Exporta     -2.968e-01  3.898e-01  -0.761  0.44784    
Importa      4.759e+00  1.377e+00   3.457  0.00075 ***
Mregio      -1.942e-01  1.898e-01  -1.023  0.30838    
FPM         -1.464e+00  8.606e-01  -1.701  0.09155 .  
TICMSm       4.507e+01  9.618e+00   4.686 7.27e-06 ***
credito      1.029e+00  9.060e-01   1.135  0.25843    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01302 on 123 degrees of freedom
Multiple R-squared:  0.8901,    Adjusted R-squared:  0.8767 
F-statistic: 66.39 on 15 and 123 DF,  p-value: < 2.2e-16

Agora, com a geração de AIC e BIC:

(mod1$AIC <- AIC(mod1))

[1] -795.4259

(mod1$BIC <- BIC(mod1))

[1] -745.5398

2.2 Correlação

library(corrplot)
corel <- cor(dados[, 6:24])  # somente var. explicativas
corrplot(corel, method = "number", type = "lower", number.digits = 2)

2.3 Seleção de modelos

2.3.1 Backward Selection

Vou separar o dataset com apenas as variáveis utilizadas em Mod1.

dados2 <- cbind(dados[, c(4, 6:13, 19)], Exporta, Importa, Mregio, FPM, TICMSm, credito)
# MODELO COMPLETO
mod2 <- lm(BARRO ~ ., dados2)
summary(mod2)

Call:
lm(formula = BARRO ~ ., data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039810 -0.008103  0.000716  0.006618  0.031697 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.663e-01  3.869e-02  12.050  < 2e-16 ***
LNYI_T_1    -5.058e-02  4.582e-03 -11.037  < 2e-16 ***
SIND         1.284e-01  1.911e-02   6.721 6.00e-10 ***
SAGRO        1.075e-01  8.151e-03  13.187  < 2e-16 ***
SSERV        5.461e-02  1.970e-02   2.772  0.00644 ** 
SPUB        -1.438e-01  2.029e-02  -7.090 9.22e-11 ***
H            2.522e-04  2.098e-04   1.202  0.23177    
DD           4.799e-05  5.502e-05   0.872  0.38478    
DORC         4.773e-06  2.981e-06   1.601  0.11195    
T            2.015e-02  9.462e-02   0.213  0.83172    
Exporta     -2.968e-01  3.898e-01  -0.761  0.44784    
Importa      4.759e+00  1.377e+00   3.457  0.00075 ***
Mregio      -1.942e-01  1.898e-01  -1.023  0.30838    
FPM         -1.464e+00  8.606e-01  -1.701  0.09155 .  
TICMSm       4.507e+01  9.618e+00   4.686 7.27e-06 ***
credito      1.029e+00  9.060e-01   1.135  0.25843    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01302 on 123 degrees of freedom
Multiple R-squared:  0.8901,    Adjusted R-squared:  0.8767 
F-statistic: 66.39 on 15 and 123 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -795.4259

BIC(mod2)

[1] -745.5398

Vou retirar as variáveis uma a uma.

Retirando T

Retiro o T e o modelo melhora.

mod2 <- update(mod2, . ~ . - T)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DD + DORC + Exporta + Importa + Mregio + FPM + TICMSm + 
    credito, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039609 -0.008059  0.000518  0.006724  0.031386 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.639e-01  3.686e-02  12.586  < 2e-16 ***
LNYI_T_1    -5.019e-02  4.201e-03 -11.947  < 2e-16 ***
SIND         1.280e-01  1.893e-02   6.761 4.79e-10 ***
SAGRO        1.070e-01  7.856e-03  13.627  < 2e-16 ***
SSERV        5.703e-02  1.602e-02   3.561 0.000525 ***
SPUB        -1.437e-01  2.020e-02  -7.114 7.92e-11 ***
H            2.668e-04  1.976e-04   1.350 0.179464    
DD           5.156e-05  5.219e-05   0.988 0.325081    
DORC         4.618e-06  2.880e-06   1.603 0.111395    
Exporta     -3.028e-01  3.873e-01  -0.782 0.435739    
Importa      4.723e+00  1.361e+00   3.471 0.000715 ***
Mregio      -1.983e-01  1.881e-01  -1.054 0.293842    
FPM         -1.446e+00  8.533e-01  -1.694 0.092688 .  
TICMSm       4.521e+01  9.558e+00   4.730 6.00e-06 ***
credito      1.052e+00  8.957e-01   1.175 0.242322    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01297 on 124 degrees of freedom
Multiple R-squared:   0.89, Adjusted R-squared:  0.8776 
F-statistic: 71.68 on 14 and 124 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -797.3746

BIC(mod2)

[1] -750.423

Retirarei Exporta.

Veja que atualizo sobre o último mod2. Melhora mais um pouco.

mod2 <- update(mod2, . ~ . - Exporta)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DD + DORC + Importa + Mregio + FPM + TICMSm + credito, 
    data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039812 -0.007997  0.001034  0.006485  0.030941 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.715e-01  3.549e-02  13.286  < 2e-16 ***
LNYI_T_1    -5.101e-02  4.065e-03 -12.549  < 2e-16 ***
SIND         1.261e-01  1.875e-02   6.727 5.57e-10 ***
SAGRO        1.080e-01  7.748e-03  13.941  < 2e-16 ***
SSERV        5.448e-02  1.566e-02   3.480 0.000691 ***
SPUB        -1.434e-01  2.016e-02  -7.113 7.74e-11 ***
H            2.677e-04  1.973e-04   1.357 0.177242    
DD           5.371e-05  5.203e-05   1.032 0.303974    
DORC         4.904e-06  2.853e-06   1.719 0.088075 .  
Importa      4.284e+00  1.238e+00   3.461 0.000737 ***
Mregio      -1.980e-01  1.878e-01  -1.054 0.293695    
FPM         -1.419e+00  8.513e-01  -1.667 0.098024 .  
TICMSm       4.284e+01  9.051e+00   4.733 5.88e-06 ***
credito      1.074e+00  8.939e-01   1.201 0.231969    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01295 on 125 degrees of freedom
Multiple R-squared:  0.8895,    Adjusted R-squared:  0.878 
F-statistic: 77.39 on 13 and 125 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -798.6909

BIC(mod2)

[1] -754.6738

Retirarei DD

Veja que atualizo sobre o último mod2. Melhora mais um pouco.

mod2 <- update(mod2, . ~ . - DD)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + Mregio + FPM + TICMSm + credito, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039352 -0.008188  0.000604  0.006660  0.031126 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.719e-01  3.549e-02  13.297  < 2e-16 ***
LNYI_T_1    -5.109e-02  4.065e-03 -12.568  < 2e-16 ***
SIND         1.248e-01  1.871e-02   6.672 7.17e-10 ***
SAGRO        1.072e-01  7.711e-03  13.903  < 2e-16 ***
SSERV        5.712e-02  1.545e-02   3.697 0.000324 ***
SPUB        -1.433e-01  2.017e-02  -7.104 7.93e-11 ***
H            3.152e-04  1.919e-04   1.643 0.102951    
DORC         4.534e-06  2.831e-06   1.602 0.111732    
Importa      4.147e+00  1.231e+00   3.369 0.001003 ** 
Mregio      -1.742e-01  1.864e-01  -0.934 0.352012    
FPM         -9.286e-01  7.065e-01  -1.314 0.191118    
TICMSm       4.249e+01  9.047e+00   4.696 6.81e-06 ***
credito      8.804e-01  8.743e-01   1.007 0.315849    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01295 on 126 degrees of freedom
Multiple R-squared:  0.8885,    Adjusted R-squared:  0.8779 
F-statistic:  83.7 on 12 and 126 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -799.5112

BIC(mod2)

[1] -758.4285

Retirarei Mregio

Veja que atualizo sobre o último mod2. Melhora mais um pouco.

mod2 <- update(mod2, . ~ . - Mregio)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + FPM + TICMSm + credito, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038785 -0.008216  0.000828  0.006975  0.031357 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.762e-01  3.518e-02  13.536  < 2e-16 ***
LNYI_T_1    -5.183e-02  3.984e-03 -13.010  < 2e-16 ***
SIND         1.248e-01  1.870e-02   6.674 6.95e-10 ***
SAGRO        1.082e-01  7.636e-03  14.168  < 2e-16 ***
SSERV        5.482e-02  1.524e-02   3.596 0.000461 ***
SPUB        -1.429e-01  2.015e-02  -7.090 8.29e-11 ***
H            3.135e-04  1.918e-04   1.635 0.104588    
DORC         4.675e-06  2.825e-06   1.655 0.100441    
Importa      3.961e+00  1.214e+00   3.262 0.001419 ** 
FPM         -9.323e-01  7.062e-01  -1.320 0.189128    
TICMSm       4.162e+01  8.995e+00   4.627 9.01e-06 ***
credito      8.604e-01  8.736e-01   0.985 0.326550    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01295 on 127 degrees of freedom
Multiple R-squared:  0.8878,    Adjusted R-squared:  0.878 
F-statistic: 91.32 on 11 and 127 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -800.5518

BIC(mod2)

[1] -762.4037

Retirarei credito

Veja que atualizo sobre o último mod2. Melhora mais um pouco.

mod2 <- update(mod2, . ~ . - credito)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + FPM + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039267 -0.007461  0.000338  0.007006  0.031563 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.667e-01  3.381e-02  13.802  < 2e-16 ***
LNYI_T_1    -5.069e-02  3.811e-03 -13.300  < 2e-16 ***
SIND         1.240e-01  1.868e-02   6.637 8.19e-10 ***
SAGRO        1.066e-01  7.453e-03  14.297  < 2e-16 ***
SSERV        6.198e-02  1.339e-02   4.627 8.95e-06 ***
SPUB        -1.427e-01  2.015e-02  -7.082 8.42e-11 ***
H            3.643e-04  1.847e-04   1.972  0.05072 .  
DORC         4.414e-06  2.812e-06   1.569  0.11903    
Importa      3.866e+00  1.210e+00   3.194  0.00177 ** 
FPM         -8.200e-01  6.968e-01  -1.177  0.24149    
TICMSm       3.994e+01  8.830e+00   4.523 1.37e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01294 on 128 degrees of freedom
Multiple R-squared:  0.8869,    Adjusted R-squared:  0.8781 
F-statistic: 100.4 on 10 and 128 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -801.4942

BIC(mod2)

[1] -766.2805

Retirarei FPM

Veja que atualizo sobre o último mod2. Melhora mais um pouco.

mod2 <- update(mod2, . ~ . - FPM)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038940 -0.007222  0.000099  0.006958  0.032152 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.639e-01  3.378e-02  13.733  < 2e-16 ***
LNYI_T_1    -5.038e-02  3.808e-03 -13.230  < 2e-16 ***
SIND         1.223e-01  1.865e-02   6.557 1.20e-09 ***
SAGRO        1.079e-01  7.377e-03  14.627  < 2e-16 ***
SSERV        5.937e-02  1.323e-02   4.488 1.58e-05 ***
SPUB        -1.423e-01  2.018e-02  -7.054 9.51e-11 ***
H            3.158e-04  1.803e-04   1.752  0.08223 .  
DORC         4.341e-06  2.816e-06   1.542  0.12564    
Importa      4.014e+00  1.206e+00   3.329  0.00114 ** 
TICMSm       4.038e+01  8.835e+00   4.570 1.13e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01296 on 129 degrees of freedom
Multiple R-squared:  0.8857,    Adjusted R-squared:  0.8777 
F-statistic: 111.1 on 9 and 129 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -801.9986

BIC(mod2)

[1] -769.7194

Retirarei DORC

Veja que atualizo sobre o último mod2. Melhora mais um pouco pelo BIC mas não pelo AIC nem pelo \(R^2\) ajustado. Vou optar por manter o DORC no modelo.

mod2 <- update(mod2, . ~ . - DORC)
summary(mod2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + Importa + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038231 -0.007231 -0.000428  0.006942  0.036033 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.4758882  0.0330407  14.403  < 2e-16 ***
LNYI_T_1    -0.0515334  0.0037531 -13.731  < 2e-16 ***
SIND         0.1257862  0.0186154   6.757 4.27e-10 ***
SAGRO        0.1093928  0.0073513  14.881  < 2e-16 ***
SSERV        0.0496722  0.0116988   4.246 4.11e-05 ***
SPUB        -0.1362400  0.0198922  -6.849 2.67e-10 ***
H            0.0004369  0.0001632   2.677  0.00839 ** 
Importa      3.8473462  1.2070479   3.187  0.00180 ** 
TICMSm      50.2771919  6.0990409   8.243 1.58e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01303 on 130 degrees of freedom
Multiple R-squared:  0.8836,    Adjusted R-squared:  0.8764 
F-statistic: 123.3 on 8 and 130 DF,  p-value: < 2.2e-16

AIC(mod2)

[1] -801.4614

BIC(mod2)

[1] -772.1167

Portanto, a estimação final foi:

final <- lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC +
    Importa + TICMSm, data = dados2)
summary(final)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038940 -0.007222  0.000099  0.006958  0.032152 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.639e-01  3.378e-02  13.733  < 2e-16 ***
LNYI_T_1    -5.038e-02  3.808e-03 -13.230  < 2e-16 ***
SIND         1.223e-01  1.865e-02   6.557 1.20e-09 ***
SAGRO        1.079e-01  7.377e-03  14.627  < 2e-16 ***
SSERV        5.937e-02  1.323e-02   4.488 1.58e-05 ***
SPUB        -1.423e-01  2.018e-02  -7.054 9.51e-11 ***
H            3.158e-04  1.803e-04   1.752  0.08223 .  
DORC         4.341e-06  2.816e-06   1.542  0.12564    
Importa      4.014e+00  1.206e+00   3.329  0.00114 ** 
TICMSm       4.038e+01  8.835e+00   4.570 1.13e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01296 on 129 degrees of freedom
Multiple R-squared:  0.8857,    Adjusted R-squared:  0.8777 
F-statistic: 111.1 on 9 and 129 DF,  p-value: < 2.2e-16

final$AIC <- AIC(final)
final$BIC <- BIC(final)

2.3.2 Escolha de Modelos baseados em critérios

A função leaps::regsubsets faz a seleção dos modelos por busca exaustiva para frente e para trás, stepwise, ou reposição sequencial. Observe que nos plots de AIC para cada modelo, deseja-se um modelo de menor AIC. O slot com as informações de quais variáveis estão em cada modelo tem nome which dentro do summary do objeto de regsubsets, neste caso chamado de “b” (o objeto resultante do summary foi chamado de rs e dentro dele estará também o resultado do BIC de cada modelo).

require(leaps)
b <- regsubsets(BARRO ~ ., data = dados2, method = c("exhaustive"))
rs <- summary(b)
rs$which

  (Intercept) LNYI_T_1  SIND SAGRO SSERV  SPUB     H    DD  DORC     T Exporta
1        TRUE    FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE   FALSE
2        TRUE    FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE   FALSE
3        TRUE     TRUE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE   FALSE
4        TRUE     TRUE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE   FALSE
5        TRUE     TRUE  TRUE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE   FALSE
6        TRUE     TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE   FALSE
  Importa Mregio   FPM TICMSm credito
1   FALSE  FALSE FALSE  FALSE   FALSE
2   FALSE  FALSE FALSE  FALSE   FALSE
3   FALSE  FALSE FALSE  FALSE   FALSE
4    TRUE  FALSE FALSE  FALSE   FALSE
5   FALSE  FALSE FALSE   TRUE   FALSE
6   FALSE  FALSE FALSE   TRUE   FALSE
 [ reached getOption("max.print") -- omitted 2 rows ]

# a escolha é com o BIC

rs$bic

[1]  -89.91415 -126.76529 -175.14756 -198.33254 -226.75252 -243.01860 -251.99235
[8] -254.51611

# plot do BIC
NA

[1] NA

NA

[1] NA

which.max(rs$adjr2)

[1] 8

NA

[1] NA

# abline(0,1)

O melhor resultado inclui: LNYI_T_1,SIND,SAGRO,SSERV,SPUB,H,Importa,TICMSm. Ou seja,

final2 <- lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + Importa +
    TICMSm, data = dados2)
summary(final2)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + Importa + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038231 -0.007231 -0.000428  0.006942  0.036033 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.4758882  0.0330407  14.403  < 2e-16 ***
LNYI_T_1    -0.0515334  0.0037531 -13.731  < 2e-16 ***
SIND         0.1257862  0.0186154   6.757 4.27e-10 ***
SAGRO        0.1093928  0.0073513  14.881  < 2e-16 ***
SSERV        0.0496722  0.0116988   4.246 4.11e-05 ***
SPUB        -0.1362400  0.0198922  -6.849 2.67e-10 ***
H            0.0004369  0.0001632   2.677  0.00839 ** 
Importa      3.8473462  1.2070479   3.187  0.00180 ** 
TICMSm      50.2771919  6.0990409   8.243 1.58e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01303 on 130 degrees of freedom
Multiple R-squared:  0.8836,    Adjusted R-squared:  0.8764 
F-statistic: 123.3 on 8 and 130 DF,  p-value: < 2.2e-16

final2$AIC <- AIC(final2)
final2$BIC <- BIC(final2)

2.3.3 Stepwise

O Stepwise Regression é uma combinação de eliminação backward (para trás) e seleção forward (para frente - inclusão). É a situação em que variáveis são adicionadas e removidas no processo e a cada estágio existem variações diversas de como proceder. O usual é minimizar AIC ou BIC. A função será step de um modelo de regressão, dentro do pacote stats que já vem no R básico. A função step retornará os vários modelos estimados e respectivos AIC até otimizar.

lmod <- lm(BARRO ~ ., data = dados2)
step(lmod)

Start:  AIC=-1191.89
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DD + DORC + 
    T + Exporta + Importa + Mregio + FPM + TICMSm + credito

           Df Sum of Sq      RSS     AIC
- T         1 0.0000077 0.020856 -1193.8
- Exporta   1 0.0000983 0.020946 -1193.2
- DD        1 0.0001290 0.020977 -1193.0
- Mregio    1 0.0001773 0.021025 -1192.7
- credito   1 0.0002185 0.021067 -1192.4
- H         1 0.0002448 0.021093 -1192.3
<none>                  0.020848 -1191.9
- DORC      1 0.0004344 0.021282 -1191.0
- FPM       1 0.0004902 0.021338 -1190.7
- SSERV     1 0.0013021 0.022150 -1185.5
- Importa   1 0.0020261 0.022874 -1181.0
- TICMSm    1 0.0037216 0.024570 -1171.1
- SIND      1 0.0076562 0.028504 -1150.4
- SPUB      1 0.0085203 0.029368 -1146.3
- LNYI_T_1  1 0.0206475 0.041496 -1098.2
- SAGRO     1 0.0294758 0.050324 -1071.4

Step:  AIC=-1193.84
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DD + DORC + 
    Exporta + Importa + Mregio + FPM + TICMSm + credito

           Df Sum of Sq      RSS     AIC
- Exporta   1 0.0001028 0.020959 -1195.2
- DD        1 0.0001642 0.021020 -1194.8
- Mregio    1 0.0001869 0.021043 -1194.6
- credito   1 0.0002321 0.021088 -1194.3
<none>                  0.020856 -1193.8
- H         1 0.0003065 0.021162 -1193.8
- DORC      1 0.0004324 0.021288 -1193.0
- FPM       1 0.0004829 0.021339 -1192.7
- Importa   1 0.0020259 0.022882 -1183.0
- SSERV     1 0.0021327 0.022988 -1182.3
- TICMSm    1 0.0037631 0.024619 -1172.8
- SIND      1 0.0076883 0.028544 -1152.2
- SPUB      1 0.0085127 0.029368 -1148.3
- LNYI_T_1  1 0.0240074 0.044863 -1089.4
- SAGRO     1 0.0312306 0.052086 -1068.6

Step:  AIC=-1195.16
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DD + DORC + 
    Importa + Mregio + FPM + TICMSm + credito

           Df Sum of Sq      RSS     AIC
- DD        1  0.000179 0.021137 -1196.0
- Mregio    1  0.000186 0.021145 -1195.9
- credito   1  0.000242 0.021200 -1195.6
<none>                  0.020959 -1195.2
- H         1  0.000309 0.021267 -1195.1
- FPM       1  0.000466 0.021424 -1194.1
- DORC      1  0.000495 0.021454 -1193.9
- Importa   1  0.002009 0.022967 -1184.4
- SSERV     1  0.002030 0.022989 -1184.3
- TICMSm    1  0.003757 0.024715 -1174.2
- SIND      1  0.007587 0.028545 -1154.2
- SPUB      1  0.008484 0.029443 -1149.9
- LNYI_T_1  1  0.026403 0.047362 -1083.8
- SAGRO     1  0.032585 0.053544 -1066.8

Step:  AIC=-1195.98
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa + 
    Mregio + FPM + TICMSm + credito

           Df Sum of Sq      RSS     AIC
- Mregio    1  0.000146 0.021284 -1197.0
- credito   1  0.000170 0.021307 -1196.9
- FPM       1  0.000290 0.021427 -1196.1
<none>                  0.021137 -1196.0
- DORC      1  0.000430 0.021568 -1195.2
- H         1  0.000453 0.021590 -1195.0
- Importa   1  0.001904 0.023041 -1186.0
- SSERV     1  0.002293 0.023430 -1183.7
- TICMSm    1  0.003700 0.024837 -1175.5
- SIND      1  0.007468 0.028605 -1155.9
- SPUB      1  0.008465 0.029602 -1151.2
- LNYI_T_1  1  0.026498 0.047636 -1085.0
- SAGRO     1  0.032428 0.053565 -1068.7

Step:  AIC=-1197.02
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa + 
    FPM + TICMSm + credito

           Df Sum of Sq      RSS     AIC
- credito   1  0.000163 0.021446 -1198.0
- FPM       1  0.000292 0.021576 -1197.1
<none>                  0.021284 -1197.0
- H         1  0.000448 0.021731 -1196.1
- DORC      1  0.000459 0.021742 -1196.0
- Importa   1  0.001784 0.023067 -1187.8
- SSERV     1  0.002167 0.023450 -1185.5
- TICMSm    1  0.003589 0.024872 -1177.4
- SIND      1  0.007465 0.028748 -1157.2
- SPUB      1  0.008424 0.029707 -1152.7
- LNYI_T_1  1  0.028365 0.049648 -1081.3
- SAGRO     1  0.033641 0.054924 -1067.2

Step:  AIC=-1197.96
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa + 
    FPM + TICMSm

           Df Sum of Sq      RSS     AIC
- FPM       1  0.000232 0.021678 -1198.5
<none>                  0.021446 -1198.0
- DORC      1  0.000413 0.021859 -1197.3
- H         1  0.000652 0.022098 -1195.8
- Importa   1  0.001710 0.023156 -1189.3
- TICMSm    1  0.003428 0.024874 -1179.3
- SSERV     1  0.003588 0.025034 -1178.5
- SIND      1  0.007381 0.028827 -1158.8
- SPUB      1  0.008403 0.029849 -1154.0
- LNYI_T_1  1  0.029637 0.051083 -1079.3
- SAGRO     1  0.034246 0.055692 -1067.3

Step:  AIC=-1198.46
BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa + 
    TICMSm

           Df Sum of Sq      RSS     AIC
<none>                  0.021678 -1198.5
- DORC      1  0.000399 0.022077 -1197.9
- H         1  0.000516 0.022194 -1197.2
- Importa   1  0.001863 0.023541 -1189.0
- SSERV     1  0.003385 0.025063 -1180.3
- TICMSm    1  0.003510 0.025188 -1179.6
- SIND      1  0.007225 0.028903 -1160.5
- SPUB      1  0.008361 0.030039 -1155.1
- LNYI_T_1  1  0.029415 0.051093 -1081.3
- SAGRO     1  0.035952 0.057631 -1064.6

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + TICMSm, data = dados2)

Coefficients:
(Intercept)     LNYI_T_1         SIND        SAGRO        SSERV         SPUB  
  4.639e-01   -5.038e-02    1.223e-01    1.079e-01    5.937e-02   -1.423e-01  
          H         DORC      Importa       TICMSm  
  3.158e-04    4.341e-06    4.014e+00    4.038e+01  

O melhor modelo foi

final3 <- lm(BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa +
    TICMSm, data = dados2)
summary(final3)

Call:
lm(formula = BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + 
    H + DORC + Importa + TICMSm, data = dados2)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.038940 -0.007222  0.000099  0.006958  0.032152 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.639e-01  3.378e-02  13.733  < 2e-16 ***
LNYI_T_1    -5.038e-02  3.808e-03 -13.230  < 2e-16 ***
SIND         1.223e-01  1.865e-02   6.557 1.20e-09 ***
SAGRO        1.079e-01  7.377e-03  14.627  < 2e-16 ***
SSERV        5.937e-02  1.323e-02   4.488 1.58e-05 ***
SPUB        -1.423e-01  2.018e-02  -7.054 9.51e-11 ***
H            3.158e-04  1.803e-04   1.752  0.08223 .  
DORC         4.341e-06  2.816e-06   1.542  0.12564    
Importa      4.014e+00  1.206e+00   3.329  0.00114 ** 
TICMSm       4.038e+01  8.835e+00   4.570 1.13e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01296 on 129 degrees of freedom
Multiple R-squared:  0.8857,    Adjusted R-squared:  0.8777 
F-statistic: 111.1 on 9 and 129 DF,  p-value: < 2.2e-16

final3$AIC <- AIC(final3)
final3$BIC <- BIC(final3)

Pelo AIC, este foi melhor, mas não pelo BIC.

Colocarei todos lado a lado com o stargazer.

library(stargazer)
stargazer(final, final2, final3, title = "Título: Resultados da Seleção", align = TRUE,
    type = "text", style = "all", keep.stat = c("AIC", "BIC", "rsq", "adj.rsq", "n"))

Título: Resultados da Seleção
=======================================================
                            Dependent variable:        
                    -----------------------------------
                                   BARRO               
                        (1)         (2)         (3)    
-------------------------------------------------------
LNYI_T_1             -0.050***   -0.052***   -0.050*** 
                      (0.004)     (0.004)     (0.004)  
                    t = -13.230 t = -13.731 t = -13.230
                     p = 0.000   p = 0.000   p = 0.000 
SIND                 0.122***    0.126***    0.122***  
                      (0.019)     (0.019)     (0.019)  
                     t = 6.557   t = 6.757   t = 6.557 
                     p = 0.000   p = 0.000   p = 0.000 
SAGRO                0.108***    0.109***    0.108***  
                      (0.007)     (0.007)     (0.007)  
                    t = 14.627  t = 14.881  t = 14.627 
                     p = 0.000   p = 0.000   p = 0.000 
SSERV                0.059***    0.050***    0.059***  
                      (0.013)     (0.012)     (0.013)  
                     t = 4.488   t = 4.246   t = 4.488 
                    p = 0.00002 p = 0.00005 p = 0.00002
SPUB                 -0.142***   -0.136***   -0.142*** 
                      (0.020)     (0.020)     (0.020)  
                    t = -7.054  t = -6.849  t = -7.054 
                     p = 0.000   p = 0.000   p = 0.000 
H                     0.0003*    0.0004***    0.0003*  
                     (0.0002)    (0.0002)    (0.0002)  
                     t = 1.752   t = 2.677   t = 1.752 
                     p = 0.083   p = 0.009   p = 0.083 
DORC                  0.00000                 0.00000  
                     (0.00000)               (0.00000) 
                     t = 1.542               t = 1.542 
                     p = 0.126               p = 0.126 
Importa              4.014***    3.847***    4.014***  
                      (1.206)     (1.207)     (1.206)  
                     t = 3.329   t = 3.187   t = 3.329 
                     p = 0.002   p = 0.002   p = 0.002 
TICMSm               40.377***   50.277***   40.377*** 
                      (8.835)     (6.099)     (8.835)  
                     t = 4.570   t = 8.243   t = 4.570 
                    p = 0.00002  p = 0.000  p = 0.00002
Constant             0.464***    0.476***    0.464***  
                      (0.034)     (0.033)     (0.034)  
                    t = 13.733  t = 14.403  t = 13.733 
                     p = 0.000   p = 0.000   p = 0.000 
-------------------------------------------------------
Observations            139         139         139    
R2                     0.886       0.884       0.886   
Adjusted R2            0.878       0.876       0.878   
Akaike Inf. Crit.    -801.999    -801.461    -801.999  
Bayesian Inf. Crit.  -769.719    -772.117    -769.719  
=======================================================
Note:                       *p<0.1; **p<0.05; ***p<0.01

Olhando a tabela, o resultado do AIC indica pelos modelos final e final3. Pelo BIC, seria o final2, mas que teve R2 menor que os demais.

2.4 Teste de Multicolinearidade (vif)

Farei o teste no modelo final3, saído do stepwise. Não temos multicolinearidade preocupante.

library(car)
reg1.vif <- vif(final3)
reg1.vif

LNYI_T_1     SIND    SAGRO    SSERV     SPUB        H     DORC  Importa 
4.650939 1.691263 1.544229 2.164569 2.627808 2.034318 3.631505 1.527390 
  TICMSm 
5.964815 

2.5 Heterocedasticidade

2.5.1 Teste de White no modelo 1

# final3: BARRO ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa +
# TICMSm, data=dados2) teste de White para heterocedasticidade, sem termos
# cruzados por causa do grau de liberdade do modelo (n=78obs)

m <- final3
data <- dados
# rotina do teste com base em m e data
u2 <- m$residuals^2

reg.auxiliar <- lm(u2 ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa +
    TICMSm + I(LNYI_T_1^2) + I(SIND^2) + I(SAGRO^2) + I(SSERV^2) + I(SPUB^2) + I(H^2) +
    I(DORC^2) + Importa^2 + TICMSm^2, data = dados2)
summary(reg.auxiliar)

Call:
lm(formula = u2 ~ LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + 
    DORC + Importa + TICMSm + I(LNYI_T_1^2) + I(SIND^2) + I(SAGRO^2) + 
    I(SSERV^2) + I(SPUB^2) + I(H^2) + I(DORC^2) + Importa^2 + 
    TICMSm^2, data = dados2)

Residuals:
       Min         1Q     Median         3Q        Max 
-4.288e-04 -1.232e-04 -4.039e-05  4.828e-05  1.341e-03 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)   -3.736e-03  4.402e-03  -0.849   0.3977  
LNYI_T_1       6.510e-04  9.113e-04   0.714   0.4764  
SIND          -1.852e-04  5.467e-04  -0.339   0.7354  
SAGRO         -2.422e-04  2.397e-04  -1.010   0.3144  
SSERV         -2.362e-04  4.144e-04  -0.570   0.5698  
SPUB           1.023e-03  9.575e-04   1.069   0.2873  
H              3.689e-06  9.408e-06   0.392   0.6956  
DORC           2.619e-07  1.552e-07   1.687   0.0941 .
Importa        2.260e-03  2.909e-02   0.078   0.9382  
TICMSm         1.189e-01  1.906e-01   0.624   0.5338  
I(LNYI_T_1^2) -3.009e-05  4.729e-05  -0.636   0.5258  
I(SIND^2)      7.275e-04  2.001e-03   0.364   0.7168  
I(SAGRO^2)     5.888e-04  4.193e-04   1.404   0.1628  
I(SSERV^2)    -9.168e-05  8.229e-04  -0.111   0.9115  
I(SPUB^2)     -1.788e-04  1.450e-03  -0.123   0.9021  
I(H^2)        -7.436e-08  1.785e-07  -0.417   0.6777  
I(DORC^2)     -4.778e-11  3.158e-11  -1.513   0.1328  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.0002493 on 122 degrees of freedom
Multiple R-squared:  0.1718,    Adjusted R-squared:  0.06318 
F-statistic: 1.582 on 16 and 122 DF,  p-value: 0.08358

Ru2 <- summary(reg.auxiliar)$r.squared
LM <- nrow(data) * Ru2
# obtendo o numero de regressores menos o intercepto
k <- length(coefficients(reg.auxiliar)) - 1
k

[1] 16

p.value <- 1 - pchisq(LM, k)  # O TESTE TEM k TERMOS REGRESSORES EM reg.auxiliar
# c('LM','p.value')
#'Resultado do teste de White sem termos cruzados
c(LM = LM, p.value = p.value)

         LM     p.value 
23.87930247  0.09217401 

Ou pelo bptest:

bptest(final3, ~LNYI_T_1 + SIND + SAGRO + SSERV + SPUB + H + DORC + Importa + TICMSm +
    I(LNYI_T_1^2) + I(SIND^2) + I(SAGRO^2) + I(SSERV^2) + I(SPUB^2) + I(H^2) + I(DORC^2) +
    Importa^2 + TICMSm^2, data = dados2)

    studentized Breusch-Pagan test

data:  final3
BP = 23.879, df = 16, p-value = 0.09217

Precisa corrigir para presenca de heteroscedasticidade.

2.5.2 Correção de Var-cov conforme White

# library(car) possibilidades:
# hccm(regressao1,type=c('hc0','hc1','hc2','hc3','hc4'))
vcov.white0 <- hccm(final3, type = c("hc1"))
#
coeftest(final3, vcov.white0)

t test of coefficients:

               Estimate  Std. Error  t value  Pr(>|t|)    
(Intercept)  4.6387e-01  3.2707e-02  14.1826 < 2.2e-16 ***
LNYI_T_1    -5.0378e-02  3.8373e-03 -13.1285 < 2.2e-16 ***
SIND         1.2231e-01  1.8662e-02   6.5542 1.219e-09 ***
SAGRO        1.0790e-01  9.1380e-03  11.8075 < 2.2e-16 ***
SSERV        5.9370e-02  1.1784e-02   5.0383 1.550e-06 ***
SPUB        -1.4232e-01  2.8151e-02  -5.0556 1.437e-06 ***
H            3.1584e-04  1.8541e-04   1.7035 0.0908908 .  
DORC         4.3408e-06  3.2549e-06   1.3336 0.1846715    
Importa      4.0136e+00  1.2014e+00   3.3406 0.0010935 ** 
TICMSm       4.0377e+01  1.0138e+01   3.9826 0.0001132 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.6 Resultado do stargazer (com e sem correção de White)

cov <- vcov.white0
robust.se <- sqrt(diag(cov))

stargazer(final3, final3, se = list(NULL, robust.se), column.labels = c("MQO-final3",
    "robusto"), title = "Título: Resultado da Regressão", align = TRUE, type = "text",
    style = "all", keep.stat = c("aic", "bic", "rsq", "adj.rsq", "n"))

Título: Resultado da Regressão
================================================
                        Dependent variable:     
                    ----------------------------
                               BARRO            
                      MQO-final3      robusto   
                         (1)            (2)     
------------------------------------------------
LNYI_T_1              -0.050***      -0.050***  
                       (0.004)        (0.004)   
                     t = -13.230    t = -13.129 
                      p = 0.000      p = 0.000  
SIND                   0.122***      0.122***   
                       (0.019)        (0.019)   
                      t = 6.557      t = 6.554  
                      p = 0.000      p = 0.000  
SAGRO                  0.108***      0.108***   
                       (0.007)        (0.009)   
                      t = 14.627    t = 11.808  
                      p = 0.000      p = 0.000  
SSERV                  0.059***      0.059***   
                       (0.013)        (0.012)   
                      t = 4.488      t = 5.038  
                     p = 0.00002    p = 0.00000 
SPUB                  -0.142***      -0.142***  
                       (0.020)        (0.028)   
                      t = -7.054    t = -5.056  
                      p = 0.000     p = 0.00000 
H                      0.0003*        0.0003*   
                       (0.0002)      (0.0002)   
                      t = 1.752      t = 1.703  
                      p = 0.083      p = 0.089  
DORC                   0.00000        0.00000   
                      (0.00000)      (0.00000)  
                      t = 1.542      t = 1.334  
                      p = 0.126      p = 0.183  
Importa                4.014***      4.014***   
                       (1.206)        (1.201)   
                      t = 3.329      t = 3.341  
                      p = 0.002      p = 0.001  
TICMSm                40.377***      40.377***  
                       (8.835)       (10.138)   
                      t = 4.570      t = 3.983  
                     p = 0.00002    p = 0.0001  
Constant               0.464***      0.464***   
                       (0.034)        (0.033)   
                      t = 13.733    t = 14.183  
                      p = 0.000      p = 0.000  
------------------------------------------------
Observations             139            139     
R2                      0.886          0.886    
Adjusted R2             0.878          0.878    
Akaike Inf. Crit.      -801.999      -801.999   
Bayesian Inf. Crit.    -769.719      -769.719   
================================================
Note:                *p<0.1; **p<0.05; ***p<0.01

2.7 Autocorrelação dos resíduos

library(car)
library(lmtest)
library(sandwich)

dw.mod2 <- dwtest(final3)
dw.mod2

    Durbin-Watson test

data:  final3
DW = 2.0866, p-value = 0.709
alternative hypothesis: true autocorrelation is greater than 0

Fiz uma rotina para rodar vários BGtest até ordem 12.

# padrao do teste de BG, com distribuição qui-quadrado
bgorder = 1:12  # definindo até a máxima ordem do bgtest
d = NULL
for (p in bgorder) {
    bgtest.chi <- bgtest(final3, order = p, type = c("Chisq"), data = dados)
    print(bgtest.chi)
    d = rbind(d, data.frame(bgtest.chi$statistic, bgtest.chi$p.value))
}

    Breusch-Godfrey test for serial correlation of order up to 1

data:  final3
LM test = 0.28808, df = 1, p-value = 0.5915


    Breusch-Godfrey test for serial correlation of order up to 2

data:  final3
LM test = 1.4421, df = 2, p-value = 0.4862


    Breusch-Godfrey test for serial correlation of order up to 3

data:  final3
LM test = 1.4646, df = 3, p-value = 0.6905


    Breusch-Godfrey test for serial correlation of order up to 4

data:  final3
LM test = 2.4191, df = 4, p-value = 0.6592


    Breusch-Godfrey test for serial correlation of order up to 5

data:  final3
LM test = 4.57, df = 5, p-value = 0.4706


    Breusch-Godfrey test for serial correlation of order up to 6

data:  final3
LM test = 4.6906, df = 6, p-value = 0.5841


    Breusch-Godfrey test for serial correlation of order up to 7

data:  final3
LM test = 5.1586, df = 7, p-value = 0.6406


    Breusch-Godfrey test for serial correlation of order up to 8

data:  final3
LM test = 6.7512, df = 8, p-value = 0.5637


    Breusch-Godfrey test for serial correlation of order up to 9

data:  final3
LM test = 8.7766, df = 9, p-value = 0.4581


    Breusch-Godfrey test for serial correlation of order up to 10

data:  final3
LM test = 12.956, df = 10, p-value = 0.2262


    Breusch-Godfrey test for serial correlation of order up to 11

data:  final3
LM test = 13.226, df = 11, p-value = 0.2788


    Breusch-Godfrey test for serial correlation of order up to 12

data:  final3
LM test = 13.29, df = 12, p-value = 0.3483

d

Não concluiu por autocorrelação residual!

2.8 Teste de Jarque-Bera para normalidade

u.hat <- resid(final3)
library(tseries)
JB.mod2 <- jarque.bera.test(u.hat)
JB.mod2

    Jarque Bera Test

data:  u.hat
X-squared = 2.9947, df = 2, p-value = 0.2237

2.9 Teste RESET de Ramsey com potencias de 2 e 3

TesteRESET.power <- lmtest::resettest(final3, power = 2:3)
TesteRESET.power

    RESET test

data:  final3
RESET = 6.4532, df1 = 2, df2 = 127, p-value = 0.002142

2.10 Investigação de outliers - teste de Bonferroni para outlier (modelo 2)

outlierTest(final3)

No Studentized residuals with Bonferroni p < 0.05
Largest |rstudent|:
    rstudent unadjusted p-value Bonferroni p
58 -3.209014          0.0016835      0.23401

qqPlot(final3)

[1]  58 121

vif(final3)

LNYI_T_1     SIND    SAGRO    SSERV     SPUB        H     DORC  Importa 
4.650939 1.691263 1.544229 2.164569 2.627808 2.034318 3.631505 1.527390 
  TICMSm 
5.964815 

O outlier 58 é o município de Juruena.

Referências

MARQUEZIN, William Ricardo. O Fundo de Participação dos Municípios e sua contribuição para a redução da desigualdade econômica em Mato Grosso. Universidade Federal de Mato Grosso, Faculdade de Economia, Programa de Pós-Graduação em Agronegócio e Desenvolvimento Regional. UFMT: Cuiabá-MT, 2014. Dissertação (Mestrado). Disponível em: https://www.ufmt.br/adr/arquivos/6b93f9815cfad275fb05f3502deffda6.pdf.