Laboratorio Bio-demografico

class: center, middle, inverse, title-slide

# Laboratorio Bio-demografico
## Lezione 17 - Fecondità e Indice Sviluppo Umano
### Nicola Barban Alma Mater Studiorum Università di Bologna Dipartimento di Scienze Statistiche
### 24 Marzo 2021 <img src="../img/UniBo-Universita-di-Bologna.png" style="width:20.0%" />

---

# Advances in development reverse fertility declines

### Mikko Myrskyla, Hans-Peter Kohler & Francesco C. Billari
### *Nature* 460(6) 741-743

---
# Fecondità e Sviluppo Umano

>...The negative association of fertility
with economic and social development has  become one
of the most solidly established and generally accepted empirical
regularities in the social sciences

> more than
half of the global population now lives in regions with below-
4 replacement fertility (less than 2.1 children per woman)

> ..Our analyses show that at advanced HDI levels, **further development can reverse the declining trend in fertility**

---
# Human Development Index

L'indice di sviluppo umano (HDI-Human Development Index) è un indice comparativo dello sviluppo dei vari paesi calcolato tenendo conto di:

1. tassi di aspettativa di vita
2. istruzione
3. reddito nazionale lordo procapite

È divenuto uno strumento standard per misurare il benessere di un paese.

---
# Carico i dati

```r
hdi <- read_csv("nature08230-s2.csv") %>%
 select(1:32) %>% 
 pivot_longer(cols=-"country", names_to="year", values_to="hdi", names_prefix="HDI.") %>% mutate(year = year %>% as.numeric())
```
---

```r
hdi %>%  ggplot(aes(x=year, y=hdi, group=country))+
  geom_line(col="grey", alpha=.5)+geom_line(data= hdi %>% filter(country=="Ireland") , aes(col="Ireland"), size=1.1)+
  scale_color_manual("Country", values="darkred")+labs(y="Human Development Index")
```

<img src="lezione17_files/figure-html/unnamed-chunk-2-1.png" width="50%" />
---
# Top 10 countries

```r
hdi_top2005<- hdi %>% 
 filter(year==2005) %>% 
 arrange(-hdi) %>% head(n=10)

kable(hdi_top2005)
```

|country    | year|       hdi|
|:----------|----:|---------:|
|Australia  | 2005| 0.9656471|
|Norway     | 2005| 0.9613572|
|Iceland    | 2005| 0.9563735|
|Ireland    | 2005| 0.9497891|
|Luxembourg | 2005| 0.9492867|
|Sweden     | 2005| 0.9474523|
|Canada     | 2005| 0.9455638|
|NL         | 2005| 0.9451833|
|Finland    | 2005| 0.9448557|
|France     | 2005| 0.9447272|
---

```r
hdi_top1975<- hdi %>% 
 filter(year==1980) %>% 
 arrange(-hdi) %>% head(n=10)

kable(hdi_top1975)
```

|country     | year|       hdi|
|:-----------|----:|---------:|
|Canada      | 1980| 0.9019683|
|NL          | 1980| 0.8933627|
|USA         | 1980| 0.8903073|
|Switzerland | 1980| 0.8880443|
|Norway      | 1980| 0.8874847|
|Denmark     | 1980| 0.8767196|
|France      | 1980| 0.8749357|
|Sweden      | 1980| 0.8744130|
|Finland     | 1980| 0.8731324|
|Iceland     | 1980| 0.8721067|

---

```r
hdi<- hdi %>% 
 group_by(year) %>% 
 arrange(-hdi) %>% 
 mutate(rank=row_number())

hdi %>% filter(year==2005, country=="Ireland") %>% 
   select(country, rank)
```

```
## # A tibble: 1 x 3
## # Groups: year [1]
## year country rank
## <dbl> <chr> <int>
## 1 2005 Ireland 4
```

```r
 hdi %>% filter(year==1975, country=="Ireland") %>% 
   select(country, rank)
```

```
## # A tibble: 1 x 3
## # Groups: year [1]
## year country rank
## <dbl> <chr> <int>
## 1 1975 Ireland 23
```
---
# Tasso di fecondità totale

* Il tasso di fecondità totale (Total Fertility Rate) esprime il numero medio di figli per donna in età feconda (15-49 anni).

* In un’ottica generazionale il tasso di fecondità che assicura ad una popolazione la possibilità di riprodursi mantenendo costante la propria struttura è pari a 2,1 figli per donna.

* **Low fertility** TFR>1,5
* **Very Low Fertility** TFR>1,3

www.humanfertility.org
---

```r
tfr <- read_csv("nature08230-s2.csv") %>%
 select(1,32:63) %>% 
 pivot_longer(cols=-"country", names_to="year", values_to="tfr", names_prefix="TFR.") %>% mutate(year = year %>% as.numeric())
```
---
# Fertility and development

>For example, the 2005 TFR levels for countries with an HDI between 0.9 and 0.92 is on average 1.24; in contrast, the average TFR is 1.89 in countries at the highest levels of development (HDI . 0.95).
These differential fertility levels at intermediate and very advanced development stages have markedly different long-term implications: the former, **if prevailing in the long term in the absence of migration, indicates a halving of the population and birth cohort approximately every 40–45 years;** in contrast, the latter level can sustain population replacement with relatively modest levels of in-migration

---

```r
tfr %>%  ggplot(aes(x=year, y=tfr, group=country))+
  geom_line(col="grey", alpha=.5)+geom_line(data= tfr %>% filter(country=="Italy") , aes(col="Italy"), size=1.1)+
  scale_color_manual("Country", values="darkred")+labs(y="Total Fertility Rate")  
```

---
# Merge datasets

```r
codes<-read_csv("codes.csv")

df<-left_join(tfr, hdi, by=c("year", "country")) %>% 
 filter(year>0)

df %>% ggplot(aes(x=hdi, y=tfr))+geom_point(col="grey", alpha=.5)
```

<img src="lezione17_files/figure-html/unnamed-chunk-8-1.png" width="60%" />
---
# Trasformo HDI e TFR

```r
transf.hdi <- function(x) -log(1-x)
transf.tfr <- function(x, mu=31,prop.fem=.4886) log(prop.fem * x)/mu

library(scales)
hdi.transf <- trans_new("transf.hdi",
 function(x) -log(1-x),
 function(y) 1-exp(-y),
 domain=c(0, Inf),
 breaks=c(0.3,.6,.8,.9,.95))

tfr.transf <- trans_new("transf.tfr",
 function(x) log(.4886 * x)/31,
 function(y) exp(y*31)/.4886,
 domain=c(1, Inf),
 breaks=c(1.2,1.5,2,3,4,6,8))
```

---
# Creo il grafico  base

```r
baseplot<-df %>% filter(year==1975 |year==2005) %>% 
 ggplot(aes(x=hdi, y=tfr, col=as.factor(year), pch=as.factor(year)))+
 coord_trans(y = tfr.transf, x=hdi.transf)+
 scale_y_continuous(breaks = c(1.2,1.5,2,3,4,6,8),limits=c(1.15,9))+
 scale_x_continuous(breaks = c(0.3,.6,.8,.9,.95))+
 theme_minimal()+
 labs(title="Human Development Index and Fertility",
 x="Human development index",
 y="Total fertility rate",
 caption="Source: Myrskyla et al., 2009")+
 theme(axis.line = element_line(colour = "black"),
 panel.grid.major = element_blank(),
 panel.grid.minor = element_blank(),
 panel.border = element_blank(),
 panel.background = element_blank()) 
```
---

```r
baseplot
```

<img src="lezione17_files/figure-html/unnamed-chunk-11-1.png" width="60%" />
---
# Aggiungo rettangolo

```r
plot1<-baseplot+geom_rect(aes(xmin=.85, xmax=.9, ymin=-Inf, ymax=Inf),fill="grey",col=NA, alpha=.1, show.legend = FALSE)
```
---

```r
plot1
```

<img src="lezione17_files/figure-html/unnamed-chunk-13-1.png" width="60%" />
---
# Aggiungo punti e trend

```r
plot2<- plot1 +
 geom_point()+
 geom_smooth( method="loess", se=FALSE, show.legend=FALSE, span=c(.45))
```
---

```r
plot2
```

<img src="lezione17_files/figure-html/unnamed-chunk-15-1.png" width="60%" />
---
 Aggiungo la legenda

```r
plot_final<-plot2+
 scale_color_manual("", values=c("blue", "red"), labels=c("1975", "2005") )+
 scale_shape_manual(name = "", values=c(15,17), labels=c("1975", "2005") )+
 theme(legend.position = c(0.8, .9))
```
---

```r
 plot_final
```

```r
 ggsave(filename="Fig1.pdf",width=10, height=10, units = "cm" )
```
---
# Grafico 2
### Seleziono paesi che raggiungono HDI alto nel 2005

```r
countries_high_hdi<-df %>% 
 filter(year==2005 & hdi>=.9 & country!="Slovenia") %>% 
 select(country) %>% as_vector()
```
---
# Preparo i dati

```r
df_refs<-df %>% 
 filter(year>0, country %in% countries_high_hdi) %>% 
 group_by(country) %>% 
 mutate(high_hdi=(hdi>=.85 & hdi<=.9),
 year_high=year*high_hdi) %>% 
 filter(year_high>0) %>% 
 mutate(ref_tfr=min(tfr),
 ref_year= max(0, year*(tfr==ref_tfr)),
 ref_hdi=max(0, hdi*(tfr==ref_tfr))) %>% 
 group_by(country) %>% 
 select(country,ref_year, ref_tfr, ref_hdi ) %>% 
summarize_all(max)
```
---
# Creo dataset per fig2

```r
df_plot <- df %>% 
 left_join(df_refs) %>% 
 filter( country %in% countries_high_hdi) %>% 
 mutate(change_tfr=tfr-ref_tfr,
 change_hdi=hdi-ref_hdi)
```
---
# Scheletro grafico

```r
plot0<-df_plot %>% 
 filter(year==2005 | year==1975) %>% 
 ggplot(aes(x=change_hdi, y=change_tfr, col=country))+
 scale_y_continuous(breaks = c(-.5, 0, .5, 1),limits=c(-.55,1.1))+
 scale_x_continuous(breaks = c(-.10, -.05, 0, .05, .1),limits=c(-.11,.11))+
 theme_minimal()+
 labs( x="Change in HDI compared to reference year",
 y="Change in TFR compared to reference year",
 caption="Source: Myrskyla et al., 2009")+
 theme(axis.line = element_blank(),
 panel.grid.major = element_blank(),
 panel.grid.minor = element_blank(),
 panel.border = element_rect(colour = "black", fill=NA, size=1),
 panel.background = element_blank()) +
 geom_hline(yintercept=0, lty=2)+
 geom_vline(xintercept=0, lty=2)
```
---

```r
plot0
```

---
# Aggiungo punti e segmenti

```r
plot1<-plot0+
 geom_point(data=df_plot %>% 
 filter(year==2005 | year==1975) %>% 
 filter(is.na(hdi)==F & is.na(tfr)==F),
 show.legend = FALSE)+
 geom_segment(data=df_plot %>% filter(year==2005 | year==1975), aes( xend = 0, yend = 0, colour = country),lty=4, show.legend = FALSE)
```
---

```r
plot1
```

<img src="lezione17_files/figure-html/unnamed-chunk-24-1.png" width="60%" />
---
# Aggiungo linee paesi

```r
countries_lines<-c("USA", "NL", "Japan", "Norway")
plot_final<-plot1+
 geom_line(data=df_plot %>% filter(country %in% countries_lines), show.legend = FALSE, size=1.5 )
```
---
# Figura 2

```r
library(plotly)
ggplotly(plot_final)
```

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country: Luxembourg","change_hdi: 0.084117338 change_tfr: 0.320000 country: Luxembourg"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,180,240,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(0,180,240,1)"}},"hoveron":"points","name":"Luxembourg","legendgroup":"Luxembourg","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[-0.010295137,0.0750736790000001],"y":[0.411,0.0800000000000001],"text":["change_hdi: -0.010295137 change_tfr: 0.411000 country: New Zealand","change_hdi: 0.075073679 change_tfr: 0.080000 country: New Zealand"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,169,255,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(0,169,255,1)"}},"hoveron":"points","name":"New Zealand","legendgroup":"New 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---
# Modello di regressione
> We use a differences-in-differences regression model with time fixed-effects and a structural change in the HDI–fertility relationship at a critical HDI level that is estimated from the data.

* `differences-in-differences` = metodo di regressione che confronta dati prima e dopo **trattamento.**
* `time fixed-effects` = dummy variables (year)
*  `structural change` = trend separati per prima e dopo **trattamento**

---
# Modello di regressione

>The starting point of our statistical model linking development to fertility is the relationship

`\(TFR_it = (\alpha^{pre} + \beta^{pre} \times HDI_{it}) \times B^{pre} + (\alpha^{post} + \beta^{post} \times HDI_{it}) \times B^{post} + \epsilon_{it}\)`

`\(\epsilon_{it}\)` contiene caratteristiche *time invariant* del paese

### Modello di regressione
**Analisi delle differenze:**

`\(\Delta TFR_{it} = \alpha \Delta B^{post} + \beta^{pre}  \Delta HDI^{pre} + \beta^{post} \Delta HDI^{post} + \Delta \gamma_t + \Delta \eta_{it}\)`

---
# Preparo dati per modello di regressione

```r
countries_models<- df %>% 
 filter(year==2005 & hdi>=.86) %>% 
 select(country) %>% as_vector()
```
---
# Calcolo dummies pre- e post- trattamento

```r
 df_models.0<-df %>% 
 filter(year>0, country %in% countries_models) %>% 
 mutate(high_hdi=ifelse(hdi>=.86, 1,0 ),
 year_high=year*high_hdi,
 year_high=na_if(year_high,0)) %>% 
 group_by(country) %>% 
 mutate(break_year=min(year_high, na.rm=T) ,
 post=ifelse(year>=break_year,1,0),
 pre=ifelse(year<break_year,1,0))
```
---
# preparo variabili per regressione pre- post- trattamento

```r
 df_models.1 <- df_models.0 %>% 
 group_by(country) %>% 
 arrange(country, year) %>% 
 mutate(diff_tfr=c(0,diff(tfr)),
 diff_hdi=c(0,diff(hdi)),
 diff_post=c(0,diff(post)),
 diff_pre=c(0,diff(pre)),
 dhdi_pre=diff_hdi*pre,
 dhdi_post=diff_hdi*post
 )
```
---
# Modello 1

```r
library(broom)
mod1<- lm(diff_tfr~diff_post +dhdi_pre + dhdi_post +factor(year), data=df_models.1)

tidy(mod1) %>%  filter(term %in% c("dhdi_pre", "dhdi_post")) %>% 
  kable(digits =2)
```

|term      | estimate| std.error| statistic| p.value|
|:---------|--------:|---------:|---------:|-------:|
|dhdi_pre  |    -1.80|      0.81|     -2.22|    0.03|
|dhdi_post |     3.86|      0.94|      4.08|    0.00|
---
# Preparo dati per modello 2

```r
 df_models.2 <- df_models.1 %>% 
 group_by(country) %>% 
 mutate(lag_hdi_pre=lag(dhdi_pre, 1),
 lag_hdi_post=lag(dhdi_post, 1))
```
---
# Modello 2

```r
mod2<- lm(diff_tfr~lag_hdi_pre +lag_hdi_post + diff_post+ factor(year)-1, data=df_models.2 )

tidy(mod2) %>%  
  filter(term %in% c("lag_hdi_pre", "lag_hdi_post")) %>% 
  kable(digits =2)
```

|term         | estimate| std.error| statistic| p.value|
|:------------|--------:|---------:|---------:|-------:|
|lag_hdi_pre  |    -1.11|      0.84|     -1.32|    0.19|
|lag_hdi_post |     4.05|      0.97|      4.16|    0.00|
---
# Conclusioni

> The existence of a positive HDI–fertility relationship at advanced development stages indicates that further development has the potential to reverse earlier fertility declines once countries reach very high HDI levels

1. **investigate the different mechanisms that may underlie this reversal**

* labour-market flexibility,
  * social security and individual welfare, 
  * gender and economic equality, 
  * human capital and social/family policies
  
  can facilitate relatively high levels of fertility

2. Policies targeted at further increasing HDI levels in advanced societies may therefore be suitable as a general strategy to reduce demographic imbalances caused by very low fer- tility levels.