Estimación por variables instrumentales (IV)

class: center, middle, inverse, title-slide

.title[
# Estimación por variables instrumentales (IV)
]
.author[
### Erika R. Badillo <br> <span class="notbold" style="font-size:65%"><a href="mailto:erika.badilloen@unaula.edu.co" class="email">erika.badilloen@unaula.edu.co</a></span> <br> <br> <br> <br> <br> <br> <br> <br> <br>
]
.date[
### <span class="notbold" style="font-size:65%">Econometría II <br> Programa de Economía <br> Universidad Autónoma Latinoamericana</span>
]

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# <span style="font-size:80%">En este tema</span>

- <span style="font-size:150%"> [<span style="color:black">Ejercicio aplicado en R: efectos de la educación de la mujer sobre la fertilidad](#ejercicio)</span>

---
# <span style="font-size:80%">Lecturas adicionales</span>
- <span style="font-size:150%">Wooldridge, J. (2010). *Econometric Analysis of Cross Section and Panel Data*. 2a edición. MA: MIT Press. <span style="color:blue">Cap 5 <br> <br>

- <span style="font-size:150%"> Greene, W. H. (2018). *Econometric Analysis*. 8th ed. NY: Pearson. <span style="color:blue">Cap 8

---
name: ejercicio
# <span style="font-size:70%">Ejercicio aplicado: efectos de la educación de la mujer sobre la fertilidad</span>

**Las mujeres más educadas tienen menos hijos?**

Numerosos estudios indican que la educación de las mujeres tiene un efecto negativo sobre la fertilidad. Varias son las posibles explicaciones:
- la escolarización aumenta el coste de oportunidad de tener un hijo
- aumenta la eficiencia del control de fertilidad  
- simplemente reduce la preferencia por los hijos

En este ejercicio vamos a estudiar este posible efecto negativo.  El siguiente ejercicio se basa en el paper: McCrary, J y Royer, H. (2011). "The Effect of Female Education on Fertility and Infant Health: Evidence from School Entry Policies Using Exact Date of Birth". *American Economic Review*, 101: 158-195.

Los datos para este ejercicio proviene de la *General Social Survey (GSS)* de los Estados Unidos. En los siguientes links se encuentran los datos, la descripción detallada de los datos y el código utilizado en R:
- [Datos](https://ebadilloe.github.io/EconometriaII/IV/GSS2012_2018.dta)
- [Descripción de la información](https://gss.norc.org/get-the-data/stata)
- [Código en R](https://ebadilloe.github.io/EconometriaII/IV/IV_clase.R)

---
# <span style="font-size:70%">Ejercicio aplicado: efectos de la educación de la mujer sobre la fertilidad</span>
.small-code[
Cargando las librerías

``` r
library(devtools); library(haven); library(dplyr); library(cragg); library(AER); library(tidyverse); library(stargazer); library(modelsummary)
library(gt); library(knitr); library(kableExtra); library(tibble)
```

Leyendo los datos y procesando la información

``` r
setwd("C:/Users/USUARIO/OneDrive - Universidad Autónoma Latinoamericana/1 Econometria/1 Econometria II-UNAULA/Clases/IV")
data <- read_dta("GSS2012_2018.DTA") %>% # Leyendo el archivo .dta
  select(year, age, sex, race, educ, childs, paeduc, maeduc, wrkstat, marital) %>% # Seleccionando variables de la base      
  filter(sex==2, year>=2014 & year<=2018, age>=35 & age<=55) %>% # Filtrando la base para mujeres y años
  mutate(age2 = age*age, afroa = case_when(race == 1 ~ 1,
                                           race == 2 ~ 0), 
                         working = case_when(wrkstat >= 1 & wrkstat<= 2 ~ 1,
                                             wrkstat >= 3 & wrkstat<= 8 ~ 0),
                         casado = case_when(marital == 1 ~ 1,
                                            marital != 1 ~ 0)) %>% # Creando variables 
  drop_na() # Borrando missings de toda la base
```

.pull-left-30[

``` r
data[,c("race","afroa")]
```

```
# A tibble: 935 × 2
   race      afroa
   <dbl+lbl> <dbl>
 1 1 [white]     1
 2 1 [white]     1
 3 1 [white]     1
 4 1 [white]     1
 5 2 [black]     0
 6 1 [white]     1
 7 1 [white]     1
 8 1 [white]     1
 9 1 [white]     1
10 2 [black]     0
# ℹ 925 more rows
```
]

.pull-left-30[

``` r
data[,c("wrkstat","working")]
```

```
# A tibble: 935 × 2
   wrkstat              working
   <dbl+lbl>              <dbl>
 1 7 [keeping house]          0
 2 1 [working fulltime]       1
 3 3 [temp not working]       0
 4 1 [working fulltime]       1
 5 1 [working fulltime]       1
 6 1 [working fulltime]       1
 7 1 [working fulltime]       1
 8 1 [working fulltime]       1
 9 1 [working fulltime]       1
10 1 [working fulltime]       1
# ℹ 925 more rows
```
]

.pull-left-30[

``` r
data[,c("marital","casado")]
```

```
# A tibble: 935 × 2
   marital           casado
   <dbl+lbl>          <dbl>
 1 5 [never married]      0
 2 5 [never married]      0
 3 5 [never married]      0
 4 4 [separated]          0
 5 5 [never married]      0
 6 1 [married]            1
 7 5 [never married]      0
 8 1 [married]            1
 9 1 [married]            1
10 5 [never married]      0
# ℹ 925 more rows
```
]
]
---
# <span style="font-size:70%">Ejercicio aplicado: efectos de la educación de la mujer sobre la fertilidad</span>
.small-code[
.pull-left-50[
Estimación por OLS

``` r
ols <- lm(childs ~ educ+age+I(age2)+casado+afroa+working, data=data)

summary(ols)
```

```

Call:
lm(formula = childs ~ educ + age + I(age2) + casado + afroa + 
    working, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6795 -0.8997 -0.0462  0.7965  5.6386

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.231814   2.675422  -0.087  0.93097    
educ        -0.136673   0.015867  -8.614  < 2e-16 ***
age          0.204314   0.119975   1.703  0.08891 .  
I(age2)     -0.002341   0.001328  -1.763  0.07820 .  
casado       0.471561   0.091202   5.171 2.86e-07 ***
afroa       -0.196362   0.124672  -1.575  0.11559    
working     -0.259425   0.098934  -2.622  0.00888 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.345 on 928 degrees of freedom
Multiple R-squared:  0.1132,	Adjusted R-squared:  0.1075 
F-statistic: 19.75 on 6 and 928 DF,  p-value: < 2.2e-16
```
]

.pull-right-50[
Estimación por 2SLS

``` r
iv <- ivreg(childs ~ educ+age+I(age2)+casado+afroa+working |
                           age+I(age2)+casado+afroa+working+paeduc+maeduc, data=data)

summary(iv)
```

```

Call:
ivreg(formula = childs ~ educ + age + I(age2) + casado + afroa + 
    working | age + I(age2) + casado + afroa + working + paeduc + 
    maeduc, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-4.01831 -0.89164 -0.05782  0.79643  5.53646

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.176497   2.699724   0.065   0.9479    
educ        -0.179672   0.032775  -5.482 5.42e-08 ***
age          0.212482   0.120572   1.762   0.0784 .  
I(age2)     -0.002446   0.001335  -1.832   0.0672 .  
casado       0.506371   0.094453   5.361 1.04e-07 ***
afroa       -0.200423   0.125194  -1.601   0.1097    
working     -0.196300   0.107859  -1.820   0.0691 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.351 on 928 degrees of freedom
Multiple R-Squared: 0.1062,	Adjusted R-squared: 0.1004 
Wald test: 12.33 on 6 and 928 DF,  p-value: 2.171e-13 
```
]
]
---
# <span style="font-size:70%">Ejercicio aplicado: efectos de la educación de la mujer sobre la fertilidad</span>
<font size = "3">
.medium-code[
Utilizamos el paquete [```modelsummary```](https://vincentarelbundock.github.io/modelsummary/articles/modelsummary.html) para generar tablas editadas (Word, tex, text, png, html...)

``` r
modelos <- list("OLS" = lm(childs ~ educ+age+I(age2)+casado+afroa+working, data=data),
                "IV"  = ivreg(childs ~ educ+age+I(age2)+casado+afroa+working |
                              age+I(age2)+casado+afroa+working+paeduc+maeduc, data=data))
cm <- c( '(Intercept)' = 'Constante', 'educ' = 'Educación', 'age' = 'Edad', 'I(age2)' = 'Edad2', 'casado' = 'Casado', 'afroa' = 'Afroamericano', 'working' = 'Empleado (=1)')
cap <- 'Tabla 1. Determinantes de la fertilidad'
modelsummary(modelos, output = 'gt', coef_map = cm, stars = c('*'=.1, '**'=.05, '***'=.01), statistic = "std.error", title = cap,
             gof_omit = 'IC|Log', coef_omit = "[^educ]") %>%
    tab_style(style = cell_text(size = 'medium'), locations = cells_body(rows = 1:6)) %>%
    tab_style(style = cell_text(color = 'red'), locations = cells_body(rows = 1)) %>% 
    tab_source_note(source_note = "Nota: Errores estándar en paréntesis") %>%
    tab_style(style = cell_text(color = "black", size = "x-small"), locations = cells_source_notes())
```

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</style>
<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <caption class='gt_caption'>Tabla 1. Determinantes de la fertilidad</caption>
  <thead>
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a-"> </th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="OLS">OLS</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="IV">IV</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td headers=" " class="gt_row gt_left" style="font-size: medium; color: #FF0000;">Educación</td>
<td headers="OLS" class="gt_row gt_center" style="font-size: medium; color: #FF0000;">-0.137***</td>
<td headers="IV" class="gt_row gt_center" style="font-size: medium; color: #FF0000;">-0.180***</td></tr>
    <tr><td headers=" " class="gt_row gt_left" style="border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: #000000; font-size: medium;"></td>
<td headers="OLS" class="gt_row gt_center" style="border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: #000000; font-size: medium;">(0.016)</td>
<td headers="IV" class="gt_row gt_center" style="border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: #000000; font-size: medium;">(0.033)</td></tr>
    <tr><td headers=" " class="gt_row gt_left" style="font-size: medium;">Num.Obs.</td>
<td headers="OLS" class="gt_row gt_center" style="font-size: medium;">935</td>
<td headers="IV" class="gt_row gt_center" style="font-size: medium;">935</td></tr>
    <tr><td headers=" " class="gt_row gt_left" style="font-size: medium;">R2</td>
<td headers="OLS" class="gt_row gt_center" style="font-size: medium;">0.113</td>
<td headers="IV" class="gt_row gt_center" style="font-size: medium;">0.106</td></tr>
    <tr><td headers=" " class="gt_row gt_left" style="font-size: medium;">R2 Adj.</td>
<td headers="OLS" class="gt_row gt_center" style="font-size: medium;">0.107</td>
<td headers="IV" class="gt_row gt_center" style="font-size: medium;">0.100</td></tr>
    <tr><td headers=" " class="gt_row gt_left" style="font-size: medium;">F</td>
<td headers="OLS" class="gt_row gt_center" style="font-size: medium;">19.747</td>
<td headers="IV" class="gt_row gt_center" style="font-size: medium;"></td></tr>
    <tr><td headers=" " class="gt_row gt_left">RMSE</td>
<td headers="OLS" class="gt_row gt_center">1.34</td>
<td headers="IV" class="gt_row gt_center">1.35</td></tr>
  </tbody>
  <tfoot class="gt_sourcenotes">
    <tr>
      <td class="gt_sourcenote" style="color: #000000; font-size: x-small;" colspan="3">* p < 0.1, ** p < 0.05, *** p < 0.01</td>
    </tr>
    <tr>
      <td class="gt_sourcenote" style="color: #000000; font-size: x-small;" colspan="3">Nota: Errores estándar en paréntesis</td>
    </tr>
  </tfoot>
  
</table>
</div>
]