Quantitative Research Methods: Introduction to Applied Statistics

• From ideas to regression models
• Regression diagnostics (recap)

• Remember that replication is a cornerstone for the quantitative (social) science
• Acemoglu, D., Johnson, S., Robinson, J. A., & Yared, P. (2008). Income and democracy. American Economic Review, 98(3), 808-42.

• To slightly paraphrase Acemoglu and colleagues,
  • Why are all OECD countries democracies, whilst most of non-democracies are located in sub-Saharan Africa or Southeast Asia?
• Influential modernization theory tries to answer this question:
  • Specifically, higher per-capita income causes the country to become a democracy

• Therefore, our hypothesis would be as follows:
  • Higher GDP should be associated to increased democracy in the countries
• In this very example, we will use replication data from Acemoglu et al.
  • DV: Freedom House Democracy score by country;
  • IV: Logged GDP per capita by country
  • We look at average figures characterizing countries in the 1990s

Now, let's load the data:

### Download it from this link: https://goo.gl/6vhv55 or ask for the flash drive
figure1 <- read.csv("figure1.csv", stringsAsFactors = FALSE)

• DV: variable $fhpolrigaug$
• IV: variable $lrgdpch$
• We expect that GDP predicts democracy scores

First, let's visualize relationship

ggplot(figure1, aes(x=lrgdpch, y=fhpolrigaug))+
  geom_text(aes(label=code), size=2)+
  geom_smooth(method="lm")+
  labs(x="Log GDP per Capita (Penn World Tables)",
       y="Freedom House Measure of Democracy",
       title="Figure 1",
       subtitle="Democracy and Income, 1990s")

Looks promising, so let's run the model:

acem <- lm(fhpolrigaug~lrgdpch, data=figure1)

summary(acem)

acem$r.squared

• R-squared measures how much of the variation in the dataset is explained by our model
• R-squared changes between 0 and 1:
  • 0 means that the model explains none of the variation in the dataset

• Linearity
• Homoscedasticity
• Independence
• Normal distribution

par(mfrow=c(2,2))

plot(acem)

mean(acem$residuals)

• How would you interpret the results?
• Potentially, what would be better model to assess the effect of economic development on democracy?

• Well, in theory, change into GDP should predict the change in democracy scores
• Let's check this assumption!

Now, let's load the data:

### Download it from this link: https://goo.gl/ygPv3j or ask for the flash drive
figure1 <- read.csv("figure2.csv", stringsAsFactors = FALSE)

acem2 <- lm(democ~growth, data=figure2)

summary(acem2)

• How would you interpret the results?
• What would be the problem with this analysis?
  • Forget statistics, just think from the conceptual perspective

• Incorporation of additional variables into our model almost removes the effect of GDP on democracy
  • Constraint on the executive at independence
  • Year of independence/100
  • catholics % of population
  • muslim % of population
  • protestant % of population

### data can be loaded from here: https://goo.gl/uWMEuc
figure3 <- read.csv("figure3.csv", stringsAsFactors = FALSE, sep="\t")

democracy <- lm(democ~consfirstaug+indcent+
              rel_catho80+rel_muslim80+rel_protmg80, 
              data=figure3)
growth <- lm(growth~consfirstaug+indcent+
               rel_catho80+rel_muslim80+rel_protmg80, 
             data=figure3)
democracy$residuals <- as.numeric(democracy$residuals)
growth$residuals <- as.numeric(growth$residuals)

residuals <- as.data.frame(cbind(democracy$residuals, growth$residuals))

names(residuals) <- c("democracy", "growth")

ggplot(residuals, aes(x=growth, y=democracy))+
  geom_point()+
  geom_smooth(method="lm")+
  labs(x="Change in Log GDP per Capita, Independent of Historical Factors",
       y="Change in Democracy Independent of Historical Factors",
       title="Change in Democracy and Change in Income, 1500-2000",
       subtitle="Conditional on Historical Factors")

• Interesting?