Análise de Eficiência no Mercado Bancário
Resultados do Modelo RDD
Prof. Pedro Ivo
11/10/2019
Introdução
A análise em RDD implica no cômputo de uma running variable que a partir de limites bem definidos pode dar validade a hipótese de suporte comum.
Análise em R
Estatística Descritivas
##
## Please cite as:## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.2. https://CRAN.R-project.org/package=stargazerA análise completa dos dados se encontra no link Clique Aqui
Começando pela análise descritiva do Ativo Total para depois passar para a análise da running variabel \(\frac{AtivoTotal_t}{PIB_t}_i\)
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## Attaching package: 'gplots'## The following object is masked from 'package:stats':
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## lowess## [1] 136
## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.
Aqui cabe uma discussão do porquê os 6 bancos mais relevantes, quais são, e como a hipótese de suporte comum sobre o RDD se sustenta.
Estimação do RDD
A única variável com um desenho correto é a Receita de serviços e Margem Financeira. As demais não apresentaram um desenho que motive a hipótese de suporte comum. Excelentes resultados sobre as duas últimas.
Principal Components and RDD design
A análise do ambiente regulatório promovido para o cômputo do impacto da Resolução 4.193, obedeceu a metodologia de RDD (Boyle et al. 2009; de Blasio et al. 2018). A hipótese por trás da metodologia é a de suporte comum, com base na premissa de que existe variabilidade próximo ao cutoff ou seja, que existe observações comparáveis e que passam a ser um bom contrafactual, através da distância do corte.
No nosso modelo, a running variabel é o Ativo Total dos bancos no tempo, em comparação ao PIB. Assim, se esse valor atingir 10% o tratamento passa a estar ativo, com base na resolução do BACEN.1
(Thistlethwaite and Campbell 1960) foi o primeiro artigo a utilizar essa metodologia para verificar o efeito de prêmios por mérito com base em uma determinada nota, ou running-variable. O suporte comum, também pode ser entendido como controle não preciso, indica que há variabilidade ao redor do cutoff, e com isso é possível utilizar essa proximidade como um tipo de instrumento.
(Asadullah 2005) utiliza a metodologia para avaliar o efeito do tamanho das salas. e o instrumento é dado por \(Y-Csize_j=E_{j10}/((E_{j10}-1)/c^{max}]+1\), onde \(Y\) é a variável de impacto, que pode ser afetada pelo tamanho da classe, e o tamanho da classe, em comparação com a maior turma, gera a descontinuidade que será a variável instrumental para \(Csize_j\).2.
Modelo:
\(Ef_{it}=F(R, X|\theta)\)
queremos medir o efeito da regulação na eficiência bancária. Tomando as derivadas e linearizando, teremos:
\(\frac{\partial EF_{it}}{\left(\partial\left(R\right|\theta\right)}=F_{R_{it}}+F_X.\ \left(\frac{dX}{\left(d\left(R\right|\theta\right)}\right)\)
onde \(F_X.\ \left(\frac{dX}{\left(d\left(R\right|\theta\right)}\right)\) poderia ser o viés da linearização e \(\theta são os controles\).
Com RDD leva em consideração apenas o efeito no cutoff, nossa premissa é que o instrumento é não correlacionado com o termo que geraria o viés.
Resultados
##
## Call:
## RDestimate(formula = roa ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.02506 58 -0.0003730 0.001126 -0.3311
## Half-BW 0.01253 36 0.0007552 0.001610 0.4691
## Double-BW 0.05012 92 0.0013420 0.001543 0.8699
## Pr(>|z|)
## LATE 0.7406
## Half-BW 0.6390
## Double-BW 0.3844
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 7.493 7 50 7.448e-06
## Half-BW 5.801 7 28 6.360e-04
## Double-BW 12.582 7 84 1.255e-10## [,1] [,2]
## LATE -0.0003729508 0.7405887
## [1] "X" "bancos" "data" "aliq" "ata"
## [6] "car" "cov" "dummy_be" "dummy_dae" "dummy_de"
## [11] "dummy_de2" "dummy_de3" "ihh_at" "ihh_cred" "iie"
## [16] "il" "indicador" "le" "lev" "marfi"
## [21] "npl" "opc" "pib" "pib_value" "pla"
## [26] "prov" "rec_s" "roa" "roe" "selic"
## [31] "spread" "varcred" "pca"## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
##
## Call:
## RDestimate(formula = roa ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.02506 58 -0.0003730 0.001126 -0.3311
## Half-BW 0.01253 36 0.0007552 0.001610 0.4691
## Double-BW 0.05012 92 0.0013420 0.001543 0.8699
## Pr(>|z|)
## LATE 0.7406
## Half-BW 0.6390
## Double-BW 0.3844
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 7.493 7 50 7.448e-06
## Half-BW 5.801 7 28 6.360e-04
## Double-BW 12.582 7 84 1.255e-10##
## Call:
## RDestimate(formula = roe ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.03942 76 0.026927 0.02455 1.097
## Half-BW 0.01971 53 0.007729 0.02215 0.349
## Double-BW 0.07884 206 0.055972 0.02154 2.599
## Pr(>|z|)
## LATE 0.272741
## Half-BW 0.727100
## Double-BW 0.009352 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 23.77 7 68 1.110e-15
## Half-BW 15.52 7 45 7.643e-10
## Double-BW 49.76 7 198 0.000e+00##
## Call:
## RDestimate(formula = spread ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.0324 67 0.003695 0.007461 0.4952
## Half-BW 0.0162 45 0.010701 0.006540 1.6363
## Double-BW 0.0648 119 0.008673 0.007457 1.1630
## Pr(>|z|)
## LATE 0.6205
## Half-BW 0.1018
## Double-BW 0.2448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 20.89 7 59 1.550e-13
## Half-BW 19.78 7 37 1.989e-10
## Double-BW 17.64 7 111 3.109e-15##
## Call:
## RDestimate(formula = rec_s ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.17575 4091 0.03872 0.01298 2.984
## Half-BW 0.08788 316 0.01453 0.01103 1.317
## Double-BW 0.35151 4091 0.03960 0.01259 3.145
## Pr(>|z|)
## LATE 0.002842 **
## Half-BW 0.187927
## Double-BW 0.001660 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 12.32 7 4083 2.220e-15
## Half-BW 45.07 7 308 0.000e+00
## Double-BW 11.26 7 4083 6.573e-14##
## Call:
## RDestimate(formula = marfi ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.017074 46 0.2910 0.2281 1.276
## Half-BW 0.008537 25 0.6566 0.3613 1.817
## Double-BW 0.034148 70 0.2512 0.1649 1.523
## Pr(>|z|)
## LATE 0.20204
## Half-BW 0.06919 .
## Double-BW 0.12768
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 1.061 7 38 0.8137
## Half-BW 1.874 7 17 0.2749
## Double-BW 1.188 7 62 0.6458##
## Call:
## RDestimate(formula = pca ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.06049 103 0.07464 0.03883 1.9221
## Half-BW 0.03024 64 0.02300 0.03532 0.6512
## Double-BW 0.12098 4081 0.15705 0.03796 4.1374
## Pr(>|z|)
## LATE 5.459e-02 .
## Half-BW 5.149e-01
## Double-BW 3.513e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 23.33 7 95 0.000e+00
## Half-BW 21.81 7 56 1.383e-13
## Double-BW 22.42 7 4073 0.000e+00##
## Call:
## RDestimate(formula = varcred ~ indicador | ihh_cred + pib + npl +
## selic, data = dados3, cutpoint = 0.1)
##
## Type:
## sharp
##
## Estimates:
## Bandwidth Observations Estimate Std. Error z value
## LATE 0.02703 57 0.000222 0.008906 0.02493
## Half-BW 0.01352 34 -0.008711 0.010785 -0.80769
## Double-BW 0.05406 89 -0.005334 0.008368 -0.63750
## Pr(>|z|)
## LATE 0.9801
## Half-BW 0.4193
## Double-BW 0.5238
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## F-statistics:
## F Num. DoF Denom. DoF p
## LATE 10.206 7 49 1.659e-07
## Half-BW 6.208 7 26 4.899e-04
## Double-BW 11.579 7 81 8.327e-10O resultado apresenta consistência quando incorporamos controles que claramente poderiam reduzir o vies, como é o caso da selic, concentração bancária e pib.
Notemos que o resultado inidica um aumento da ineficiência em 9% quando analisamos por componentes principais, cuja métrica de avaliação é um mix de3.
Quando analisamos apenas os custos de serivços, o resultado é de que há um aumento de 3% destes custos.
Assim, o impacto regulatório da Resolução pode ser medida em escala de bilhões. Pois basta multiplicar o efeito médio, pela receita média de servicos. Que dará
receita<-c(dados3$rec_s[dados3$indicador>0.1])
sum(receita)*0.03## [1] 0.4582079hist(dados3$pca[dados3$pca>0 & dados3$pca<1])
Comparando os resultados.
Agora, analisando os resultados de OLS, Diff-in-Diff e RDD.
library(lubridate)
dados2 <- read.csv2("dados.csv")
dados2$ind<-c(dados2$indicador>=0.1)
dados2$tem<-c(as_date(dados2$data)>=as_date('2015-10-29'))
var<-c("marfi", "pca", "rec_s", "roa", "roe", "spread")
marfi_1<-lm( marfi ~ind+ihh_cred+ pib+ npl+selic, dados2)
marfi_2<-lm(marfi ~ind + tem + ind*tem+ihh_cred+ pib+ npl+selic, dados2)
stargazer(marfi_1,marfi_2, type="html")##
## <table style="text-align:center"><tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="2"><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="2" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td colspan="2">marfi</td></tr>
## <tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">ind</td><td>-0.174</td><td>0.213</td></tr>
## <tr><td style="text-align:left"></td><td>(1.330)</td><td>(1.710)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">tem</td><td></td><td>2.233<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.942)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">ihh_cred</td><td>0.001</td><td>-0.005</td></tr>
## <tr><td style="text-align:left"></td><td>(0.003)</td><td>(0.004)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pib</td><td>0.008</td><td>-0.024</td></tr>
## <tr><td style="text-align:left"></td><td>(0.133)</td><td>(0.134)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">npl</td><td>-3.408</td><td>-3.466</td></tr>
## <tr><td style="text-align:left"></td><td>(2.633)</td><td>(2.632)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">selic</td><td>-0.096</td><td>-0.110</td></tr>
## <tr><td style="text-align:left"></td><td>(0.134)</td><td>(0.134)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">indTRUE:tem</td><td></td><td>-1.000</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(2.718)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>-0.554</td><td>8.481</td></tr>
## <tr><td style="text-align:left"></td><td>(5.078)</td><td>(6.379)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>4,094</td><td>4,094</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.001</td><td>0.002</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>-0.0003</td><td>0.001</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>16.439 (df = 4088)</td><td>16.432 (df = 4086)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>0.718 (df = 5; 4088)</td><td>1.318 (df = 7; 4086)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="2" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>pca_1<-lm(pca ~ind+ihh_cred+ pib+ npl+selic, dados2)
pca_2<-lm(pca ~ind + tem + ind*tem+ ihh_cred+ pib+ npl+selic, dados2)
stargazer(pca_1,pca_2, type="html")##
## <table style="text-align:center"><tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="2"><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="2" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td colspan="2">pca</td></tr>
## <tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">ind</td><td>0.149<sup>*</sup></td><td>0.207<sup>*</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.089)</td><td>(0.114)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">tem</td><td></td><td>0.146<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.063)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">ihh_cred</td><td>0.001<sup>***</sup></td><td>0.0001</td></tr>
## <tr><td style="text-align:left"></td><td>(0.0002)</td><td>(0.0002)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pib</td><td>0.012</td><td>0.010</td></tr>
## <tr><td style="text-align:left"></td><td>(0.009)</td><td>(0.009)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">npl</td><td>-2.116<sup>***</sup></td><td>-2.119<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.176)</td><td>(0.176)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">selic</td><td>0.009</td><td>0.009</td></tr>
## <tr><td style="text-align:left"></td><td>(0.009)</td><td>(0.009)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">indTRUE:tem</td><td></td><td>-0.147</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.182)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>-0.778<sup>**</sup></td><td>-0.204</td></tr>
## <tr><td style="text-align:left"></td><td>(0.341)</td><td>(0.428)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>4,081</td><td>4,081</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.037</td><td>0.038</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>0.036</td><td>0.037</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>1.100 (df = 4075)</td><td>1.100 (df = 4073)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>31.254<sup>***</sup> (df = 5; 4075)</td><td>23.151<sup>***</sup> (df = 7; 4073)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="2" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>rec_s_1<-lm(rec_s ~ind+ihh_cred+ pib+ npl+selic, dados2)
rec_s_2<-lm(rec_s ~ind + tem + ind*tem+ ihh_cred+ pib+ npl+selic, dados2)
stargazer(rec_s_1,rec_s_2, type="html")##
## <table style="text-align:center"><tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="2"><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="2" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td colspan="2">rec_s</td></tr>
## <tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">ind</td><td>0.042<sup>***</sup></td><td>0.049<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.007)</td><td>(0.009)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">tem</td><td></td><td>0.011<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.005)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">ihh_cred</td><td>0.0001<sup>***</sup></td><td>0.00004<sup>*</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.00001)</td><td>(0.00002)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pib</td><td>0.001</td><td>0.001</td></tr>
## <tr><td style="text-align:left"></td><td>(0.001)</td><td>(0.001)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">npl</td><td>0.011</td><td>0.010</td></tr>
## <tr><td style="text-align:left"></td><td>(0.014)</td><td>(0.014)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">selic</td><td>-0.001</td><td>-0.001</td></tr>
## <tr><td style="text-align:left"></td><td>(0.001)</td><td>(0.001)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">indTRUE:tem</td><td></td><td>-0.019</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.015)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>-0.046</td><td>-0.002</td></tr>
## <tr><td style="text-align:left"></td><td>(0.028)</td><td>(0.035)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>4,091</td><td>4,091</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.018</td><td>0.020</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>0.017</td><td>0.018</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>0.090 (df = 4085)</td><td>0.090 (df = 4083)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>15.121<sup>***</sup> (df = 5; 4085)</td><td>11.657<sup>***</sup> (df = 7; 4083)</td></tr>
## <tr><td colspan="3" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="2" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>roa_1<-lm(roa ~ind+ihh_cred+ pib+ npl+selic, dados2)
roa_2<-lm(roa ~ind + tem + ind*tem+ ihh_cred+ pib+ npl+selic, dados2)
roe_1<-lm(roe ~ind+ihh_cred+ pib+ npl+selic, dados2)
roe_2<-lm(roe ~ind + tem + ind*tem+ ihh_cred+ pib+ npl+selic, dados2)
spread_1<-lm(spread ~ind+ihh_cred+ pib+ npl+selic, dados2)
spread_2<-lm(spread ~ind + tem + ind*tem+ ihh_cred+ pib+ npl+selic, dados2)
stargazer(marfi_1,marfi_2,spread_1,spread_2,pca_1,pca_2,roa_1,roa_2,roe_1,roe_2,rec_s_1,rec_s_2, type="html")##
## <table style="text-align:center"><tr><td colspan="13" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td colspan="12"><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="12" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td colspan="2">marfi</td><td colspan="2">spread</td><td colspan="2">pca</td><td colspan="2">roa</td><td colspan="2">roe</td><td colspan="2">rec_s</td></tr>
## <tr><td style="text-align:left"></td><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td><td>(6)</td><td>(7)</td><td>(8)</td><td>(9)</td><td>(10)</td><td>(11)</td><td>(12)</td></tr>
## <tr><td colspan="13" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">ind</td><td>-0.174</td><td>0.213</td><td>-0.020</td><td>0.011</td><td>0.149<sup>*</sup></td><td>0.207<sup>*</sup></td><td>0.004</td><td>0.007</td><td>0.077</td><td>0.031</td><td>0.042<sup>***</sup></td><td>0.049<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(1.330)</td><td>(1.710)</td><td>(0.082)</td><td>(0.105)</td><td>(0.089)</td><td>(0.114)</td><td>(0.006)</td><td>(0.007)</td><td>(0.393)</td><td>(0.504)</td><td>(0.007)</td><td>(0.009)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">tem</td><td></td><td>2.233<sup>**</sup></td><td></td><td>0.123<sup>**</sup></td><td></td><td>0.146<sup>**</sup></td><td></td><td>0.012<sup>***</sup></td><td></td><td>0.140</td><td></td><td>0.011<sup>**</sup></td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(0.942)</td><td></td><td>(0.058)</td><td></td><td>(0.063)</td><td></td><td>(0.004)</td><td></td><td>(0.279)</td><td></td><td>(0.005)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">ihh_cred</td><td>0.001</td><td>-0.005</td><td>0.0002</td><td>-0.0002</td><td>0.001<sup>***</sup></td><td>0.0001</td><td>0.00002<sup>**</sup></td><td>-0.00001</td><td>-0.001</td><td>-0.001</td><td>0.0001<sup>***</sup></td><td>0.00004<sup>*</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.003)</td><td>(0.004)</td><td>(0.0002)</td><td>(0.0002)</td><td>(0.0002)</td><td>(0.0002)</td><td>(0.00001)</td><td>(0.00002)</td><td>(0.001)</td><td>(0.001)</td><td>(0.00001)</td><td>(0.00002)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">pib</td><td>0.008</td><td>-0.024</td><td>0.005</td><td>0.003</td><td>0.012</td><td>0.010</td><td>0.001<sup>**</sup></td><td>0.001<sup>*</sup></td><td>0.020</td><td>0.018</td><td>0.001</td><td>0.001</td></tr>
## <tr><td style="text-align:left"></td><td>(0.133)</td><td>(0.134)</td><td>(0.008)</td><td>(0.008)</td><td>(0.009)</td><td>(0.009)</td><td>(0.001)</td><td>(0.001)</td><td>(0.040)</td><td>(0.040)</td><td>(0.001)</td><td>(0.001)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">npl</td><td>-3.408</td><td>-3.466</td><td>0.621<sup>***</sup></td><td>0.618<sup>***</sup></td><td>-2.116<sup>***</sup></td><td>-2.119<sup>***</sup></td><td>-0.154<sup>***</sup></td><td>-0.154<sup>***</sup></td><td>5.264<sup>***</sup></td><td>5.261<sup>***</sup></td><td>0.011</td><td>0.010</td></tr>
## <tr><td style="text-align:left"></td><td>(2.633)</td><td>(2.632)</td><td>(0.163)</td><td>(0.163)</td><td>(0.176)</td><td>(0.176)</td><td>(0.011)</td><td>(0.011)</td><td>(0.780)</td><td>(0.780)</td><td>(0.014)</td><td>(0.014)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">selic</td><td>-0.096</td><td>-0.110</td><td>0.011</td><td>0.010</td><td>0.009</td><td>0.009</td><td>0.001<sup>**</sup></td><td>0.001<sup>**</sup></td><td>0.017</td><td>0.017</td><td>-0.001</td><td>-0.001</td></tr>
## <tr><td style="text-align:left"></td><td>(0.134)</td><td>(0.134)</td><td>(0.008)</td><td>(0.008)</td><td>(0.009)</td><td>(0.009)</td><td>(0.001)</td><td>(0.001)</td><td>(0.040)</td><td>(0.040)</td><td>(0.001)</td><td>(0.001)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">indTRUE:tem</td><td></td><td>-1.000</td><td></td><td>-0.080</td><td></td><td>-0.147</td><td></td><td>-0.007</td><td></td><td>0.116</td><td></td><td>-0.019</td></tr>
## <tr><td style="text-align:left"></td><td></td><td>(2.718)</td><td></td><td>(0.167)</td><td></td><td>(0.182)</td><td></td><td>(0.012)</td><td></td><td>(0.804)</td><td></td><td>(0.015)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>-0.554</td><td>8.481</td><td>-0.280</td><td>0.214</td><td>-0.778<sup>**</sup></td><td>-0.204</td><td>-0.030</td><td>0.016</td><td>0.567</td><td>1.164</td><td>-0.046</td><td>-0.002</td></tr>
## <tr><td style="text-align:left"></td><td>(5.078)</td><td>(6.379)</td><td>(0.314)</td><td>(0.394)</td><td>(0.341)</td><td>(0.428)</td><td>(0.022)</td><td>(0.028)</td><td>(1.504)</td><td>(1.891)</td><td>(0.028)</td><td>(0.035)</td></tr>
## <tr><td style="text-align:left"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr>
## <tr><td colspan="13" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>4,094</td><td>4,094</td><td>4,089</td><td>4,089</td><td>4,081</td><td>4,081</td><td>4,095</td><td>4,095</td><td>4,092</td><td>4,092</td><td>4,091</td><td>4,091</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.001</td><td>0.002</td><td>0.004</td><td>0.006</td><td>0.037</td><td>0.038</td><td>0.044</td><td>0.046</td><td>0.012</td><td>0.012</td><td>0.018</td><td>0.020</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>-0.0003</td><td>0.001</td><td>0.003</td><td>0.004</td><td>0.036</td><td>0.037</td><td>0.043</td><td>0.044</td><td>0.011</td><td>0.010</td><td>0.017</td><td>0.018</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>16.439 (df = 4088)</td><td>16.432 (df = 4086)</td><td>1.015 (df = 4083)</td><td>1.014 (df = 4081)</td><td>1.100 (df = 4075)</td><td>1.100 (df = 4073)</td><td>0.071 (df = 4089)</td><td>0.071 (df = 4087)</td><td>4.868 (df = 4086)</td><td>4.869 (df = 4084)</td><td>0.090 (df = 4085)</td><td>0.090 (df = 4083)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>0.718 (df = 5; 4088)</td><td>1.318 (df = 7; 4086)</td><td>3.635<sup>***</sup> (df = 5; 4083)</td><td>3.247<sup>***</sup> (df = 7; 4081)</td><td>31.254<sup>***</sup> (df = 5; 4075)</td><td>23.151<sup>***</sup> (df = 7; 4073)</td><td>37.487<sup>***</sup> (df = 5; 4089)</td><td>27.975<sup>***</sup> (df = 7; 4087)</td><td>9.717<sup>***</sup> (df = 5; 4086)</td><td>6.980<sup>***</sup> (df = 7; 4084)</td><td>15.121<sup>***</sup> (df = 5; 4085)</td><td>11.657<sup>***</sup> (df = 7; 4083)</td></tr>
## <tr><td colspan="13" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td colspan="12" style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>Referências
Yeager et al. (2011)
Dimmery (2016)
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Boyle, John, Michael Bucuvalas, Linda Piekarski, and Andy Weiss. 2009. “Zero Banks: Coverage Error and Bias in Rdd Samples Based on Hundred Banks with Listed Numbers.” Public Opinion Quarterly 73 (4): 729–50.
de Blasio, Guido, Stefania De Mitri, Alessio D’Ignazio, Paolo Finaldi Russo, and Lavinia Stoppani. 2018. “Public Guarantees to SME Borrowing. A RDD Evaluation.” Journal of Banking & Finance 96: 73–86.
Dimmery, Drew. 2016. “Package Rdd.” Manual for the Statistical Software R.
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Yeager, David S, Jon A Krosnick, LinChiat Chang, Harold S Javitz, Matthew S Levendusky, Alberto Simpser, and Rui Wang. 2011. “Comparing the Accuracy of Rdd Telephone Surveys and Internet Surveys Conducted with Probability and Non-Probability Samples.” Public Opinion Quarterly 75 (4): 709–47.