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```---
title: "Data Assignment 1"
subtitle: "States, Regimes and Institutions"
author: "Pablo Pardavila Romero"
format: pdf
editor: visual
---

1.  **We want to check the growth of democratic regimes after WWI (1900-20) and the collapse of the Soviet Union (1986-1994). Generate graphics that show the evolution of the number of democracies by year using `e_boix_regime` (Boix, Miller and Rosato's measurement of democracy).**

```{r}
#| echo: FALSE
#| message: false
#| warning: false
#| results: hide
library(tidyverse)

#First of all, it is necessary to know what the variable is measuring. According to the codebook e_boix_regime is a ``dichotomous democracy measure based on contestation and participation. Countries coded democratic have (1) political leaders that are chosen through free and fair elections and (2) a minimal level of suffrage."

#My first intuition is to do a graph like this. But, because of the nature
#of the data, it comes up with just an average of the variable for 1800-2015.
```

```{r}
#| echo: false

#| message: false
#| warning: false
#| results: hide

#For that reason it is first necessary to filter the data, (first for the post WWI
#period and then for the collapse of the USSR) ONLY
#for democracies (i.e., e_boix_regime == 1)

#Post WWI (1900-1920)
democracy_counts_1900_1920 <- vdem |>
filter(year >= 1900, year <= 1920, e_boix_regime == 1) |>
group_by(year) |>
summarise(num_democracies = n())

ggplot(data = democracy_counts_1900_1920, aes(x = year, y = num_democracies)) +
geom_line() +
labs(x = "Year", y = "No. of democracies",
title = "Evolution of No. of democracies (1900-1920)")

#Collapse USSR (1986-1994)

#| fig-width: 7
#| fig-height: 5
democracy_counts_1986_1994 <- vdem |>
filter(year >= 1986, year <= 1994, e_boix_regime == 1) |>
group_by(year) |>
summarise(num_democracies = n())

ggplot(data = democracy_counts_1986_1994, aes(x = year, y = num_democracies)) +
geom_line() +
labs(x = "Year", y = "No. of democracies",
title = "Evolution of No. of democracies (1900-1920)")
```

2.  **Check the regression coefficient between log of GDPp (`e_migdppcln`) and V-Dem polyarchy (`v2x_polyarchy`) by periods of 20 years starting in 1860-79. Represent graphically the temporal evolution of the coefficient (do not include any control, or the lag of the dependent variable, this is the sheer correlation). Do the same but with region of the world (`e_regionpol_6C`) instead of time periods. Interpret the results.**

`coef(lm(e_migdppcln ~ v2x_polyarchy)` (regression 1.1) and `coef(lm(v2x_polyarchy ~ e_migdppcln)` (regression 1.2)

```{r}
#| echo: false

#To generate a regression coefficient it is first necessary to create a new
#variable with 20-year-periods from 1860 to 1879 for both variables.
vdem <- vdem |>
mutate(period = cut(year, breaks = seq(1859, max(year), by = 20), labels = FALSE))

#Once we have the variable, we can run a regression for each of those periods:
reg11 <- vdem |>
group_by(period) |>
summarise(
coefficient = coef(lm(e_migdppcln ~ v2x_polyarchy))[2],
period_start = min(year),
period_end = max(year)
)

reg12 <- vdem |>
group_by(period) |>
summarise(
coefficient = coef(lm(v2x_polyarchy ~ e_migdppcln))[2],
period_start = min(year),
period_end = max(year)
)

print(reg11)
print(reg12)
```

Graphically:

```{r}
#| echo: false
ggplot(data = reg11, aes(x = period_start, y = coefficient)) +
geom_line() +
labs(
x = "Start Year of Period",
y = "Coefficient",
title = "Evolution of Coefficients Over Time (Regression 1.1)",
subtitle = "y = GDPpc (log), x = Polyarchy"
)

ggplot(data = reg12, aes(x = period_start, y = coefficient)) +
geom_line() +
labs(
x = "Start Year of Period",
y = "Coefficient",
title = "Evolution of Coefficients Over Time (Regression 1.2)",
subtitle = "y = Polyarchy, x = GDPpc (log)"
)
```

`lm(e_migdppcln ~ v2x_polyarchy)` (regression 2.1) by region

```{r}
#| echo: false
reg21 <- vdem |>
group_by(e_regionpol_6C) |>
do(model = lm(e_migdppcln ~ v2x_polyarchy, data = .)) |>
summarise(
region = e_regionpol_6C,
coefficient = coef(model)[2],
r_squared = summary(model)\$r.squared
)

print(reg21)
```

Graphically

```{r}
#| echo: false

region_names <- c("E. Eur/C. Asia", "L. America", "M. East", "Sub-Sah. Africa", "Eur/Amer", "Asia & Pacific")

ggplot(reg21, aes(x = factor(region, levels = 1:6, labels = region_names), y = coefficient)) +
geom_bar(stat = "identity") +
labs(x = "Region", y = "Coefficient") +
ggtitle("Corr. Coefficient (reg21) by Region")
```

For the relation between democracy and GDP per capita over time, democracy seems to explain changes in GDPpc mostly at the end of the \$19^{th}\$ century, with a steep decrease at the beggining of the \$20^th\$ century. The correlation is stronger in the period ranging from 1900 to 1939 than for any other period.

When we look at the average effect of GDPpc in democracy this relation increases from 1800 to the post WWI period and then it starts decreasing.

For the relation between democracy and GDP per capita, in general, for every unit increase in the measure of democracy, the logarithm of GDP per capita is expected to increase more in Europe/America than in the rest of world regions. The r-square indicates that the % of variation of GDP is can be explained by democracy more in Europe/America, Latin America, and, to a lesser extent in East Europe and Central Asia. In the Sub-Saharan Africa and in the Middle East this explanatory power is almost absent.```