26.10.2023 Regression#

Intro#

Dependent Variable = intercept + ß explanatory variable + error

\[ y = \alpha + \beta x + \mu \]

  • \(\beta\) estimated with Ordinary Least Squares (OLS)

  • explanatory variable = should be exogenous

Acemoglus Regression#

Formula

\[ \log y_i = \mu + aR_i+\bf{X}_i \gamma+ \epsilon \]

Figure:

Table:

img

  • empty lines = not included in regression

    • every new sample = broader regression formula with dummies etc.

  • \(R^2 = 0.62\): goodness of fit of regression line

    • quite good here (explains 62% of the variance)

  • Sample 7/8 new dependent variable to make it more solid

Interlude: Regression Interpretation#

Modell

Abhängige Var.

Erklärende Var.

Interpretation

Level-Level

y

\(x_j\)

\(\Delta \hat{y} = \beta_j \Delta x_j\)

Level-Log

y

\(log(x_j)\)

\(\Delta \hat{y} = \frac{\beta_j}{100} \% \Delta x_j\)

Log-Level

log(y)

\(x_j\)

\(\% \Delta \hat{y} = 100 \beta_j \Delta x_j\)

Log-Log

log(y)

log(x)

\(\% \Delta \hat{y} = \beta_j \% \Delta x_j\)

=> ours is log-level

Recreation of the Table#

library(stargazer)
load("data/dataset_AJR2001.Rdata")
head(data)

Table 2: Estimation of Models 1-4 for both datasets

Table Column Names:

  • logpgp95= Log GDP per capita, PPP, 1995

  • avexpr = Average protection against expropriation risk, 1985-1995

  • baseco = Dummy variable for countries in the base sample (colonized)

  • lat_abst = Absolute value of latitude

  • loghjypl = Log output per worker in 1988 (US normalized to 1)

m_T2_world_1 <- lm(logpgp95 ~ avexpr, data=data)
m_T2_base_1 <- lm(logpgp95 ~ avexpr, data=data[which(data$baseco==1),])

#latitude added
m_T2_world_2 <- lm(logpgp95 ~avexpr + lat_abst,data=data)
m_T2_base_2 <- lm(logpgp95 ~ avexpr + lat_abst, data=data[which(data$baseco==1),])

# continent dummies
m_T2_world_3 <- lm(logpgp95 ~avexpr + lat_abst + asia + africa + other,data=data)
m_T2_base_3 <- lm(logpgp95 ~ avexpr + lat_abst + asia + africa + other, data=data[which(data$baseco==1),])

# other dependent variable
m_T2_world_4 <- lm(loghjypl ~avexpr, data=data)
m_T2_base_4 <- lm(loghjypl ~ avexpr, data=data[which(data$baseco==1),])

Summary of the first Regression

summary(m_T2_world_1)

Now we have the Regression Models, but until now no Table to present these

#| results: asis
all_res <- list(
  m_T2_world_1, m_T2_base_1,
  m_T2_world_2, m_T2_base_2,
  m_T2_world_3, m_T2_base_3,
  m_T2_world_4, m_T2_base_4
  )
coef_names <- c("Average Protection", "Latittude","Asia dummy", "Africa dummy", "Other")
note <- "Nitzuen lorem"
stargazer(all_res, 
          type="html", 
          out="data/Table2_stargazer.html", omit = "Constant",
          notes.label = note,
          dep.var.labels = c("log GDP per Capita", "log output per worker"),
          covariate.labels = coef_names
          )