Part 1 Comprehension

The Colonial Origins of Comparative Development: An Empirical Investigation.

1. What is the central point of the paper?

The paper by Acemoglu, Johnson and Robinson essentially argues that of key importance in estimating the causes of difference in income per capita across countries is the effect of better ‘institutions’. Amongst other things, these institutions define and enforce property rights, encouraging investment in human and physical capital within economies. What is difficult however, is estimating the size of this causal impact – that is, trying to determine how much of the difference between different country’s incomes is determined by the strength of their institutions. The central point of this paper is that Acemoglu et al. argue that through the use of historical settler mortality rates in European colonies as an instrumental variable, it is possible to tease out the size of this institutional impact on their dependent variable, GDP per capita.

2. What variables do the authors use to proxy for current institutions?

The main proxy variable that the authors use for a measure of institutional effectiveness is a variable called ‘average protection against expropriation risk 1985-95’ which is formed from the mean value of each country’s 0-10 (a score of 0 being the lowest amount of protection) score on an index of protection against expropriation from information collected in ‘Political Risk Services’ in ‘A business guide to political risk for international decisions’, by Coplin, O’leary and Sealy.

3. Why can’t we just look at the simple relationship between these variables and today’s development? Isn’t that the causal relationship?

There are several reasons that performing a OLS estimate regressing income per capita on the mean of ‘average protection against expropriation risk’ does not provide a valid estimate of the causal impact of institutions. Acemoglu et al. identify the issue of reverse causality – that wealthier countries may be able to afford and/or prefer better institutions. They also point to a potential myriad of confounding variables that may simultaneously affect GDP per capita and a country’s institutional effectiveness score, causing irreconcilable endogeneity problems in the model. Finally they point to the fact that the data on institutional effectiveness is collected ex post and therefor has the potential to demonstrate some bias on the part of those collecting the data to better institutions in richer countries.

4. What is the instrumental variable the authors describe?

To overcome this problem the authors identify an instrumental variable in the mortality rates of European settlers in different countries, using data on the mortality rates of soldiers, bishops, and sailors stationed in the colonies be- tween the seventeenth and nineteenth centuries.. The argument goes something like this:

  1. That the differences in mortality rates of European settlers in the Colonies are directly correlated with the density of European settlement (With settlers preferring to settle in areas with lower mortality rates).
  2. That the Colonies with higher density of European settlement created more effective institutions at the time of settlement.
  3. That the performance of these institutions is directly correlated with the performance of current institutions.
  4. That GDP per capita in different countries is correlated with the performance of these institutions.

Through this reasoning, the authors proceed to estimate the impact of settler mortality rates on country’s institutional effectiveness scores. Performing the first stage of a 2SLS estimate.

5. What is their exclusion restriction? Do you find it plausible?

The implied (and explicitly acknowledged) exclusion restriction required to validate the use of this instrumental variable is that settler mortality rates do not directly, or through another variable other than institutional effectiveness, have any impact on countries GDP per capita. Acemoglu et al. perform several tests to support their exclusion restriction, including controlling for colonial origin, religion, climate and other geographical characteristics, pre-existing “European culture” and finally the general effect of disease on development that maybe being captured in the instrument. All in all, the authors provide substantial testing to defend their instrument against claims that it is inaccurately attributing 100% of the causal impact of settler mortality rates to its impact on the establishment of effective institutions.

While the testing and arguments that the authors provide in defence of their exclusion restriction are exhaustive and on the whole, very persuasive, I remain skeptical for one key reason. This reason is identified very early on in the paper when the authors describe the approach of the colonizing powers to colonies that presented less habitable environments with higher mortality rates. The authors describe these colonies as “extractive states… the main purpose of [which] was to transfer as much of the resources to the colony to the colonizer”. This implies that colonies that presented colonizing powers with high mortality rates became subjected to direct and substantial resource extraction. As a result, I am skeptical of the author’s conclusion. In order to estimate effectively the impact of settler mortality rates on GDP per capita through their impact on the establishment of effective institutions, the counter-factual position needs to be the level of institutional effectiveness in countries without the impact of colonizing powers. In this study, the counterfactual position is estimated through the observation of countries whose resources were aggressively “extracted” by the colonizing powers. As such, the exclusion restriction could be seen as violated through the following reasoning:

  1. Countries with high settler mortality rates were subjected to higher levels of resource extraction.
  2. Historical prolonged, deliberate and aggressive resource “extraction” is negatively correlated with current GDP per capital.

Following this line of argument, the estimated impact of settler mortality rates on GDP per capita, and by implication the effect of institutions on GDP per capita could be substantially overstated. Furthermore, along a similar line of argument, I suspect that there are many more side effects of this “extraction” approach to colonization that could potentially be correlated with GDP per capita.

Part 2: Using Acemoglu Johnson and Robinson’s data to update our model from last week.

Task 1

# Load the libraries
library(ggplot2); library(dplyr); library(AER)
# Read the data
pwt <- read.csv("pwt71_wo_country_names_wo_g_vars.csv")

# Filter out the observations outside the period I'm interested in
pwt.ss <- pwt %>% filter(year<=2010 & year>=1985)

# Generate our data for the regression
pwt.2 <- pwt.ss  %>% group_by(isocode) %>% # For each country
  summarise(s = mean(ki), # What was the average investment?
            y = last(y), # The last GDP per person relative to the US?
            n = 100*log(last(POP)/first(POP))/(n() - 1)) %>% # Population growth rate?
  filter(!is.na(s)) %>% # Get rid of missing rows of s
  mutate(ln_y = log(y), # Create new columns- log of y
         ln_s = log(s), # Log of s
         ln_ngd = log(n + 1.6 + 5)) # Log of n + g + delta

# Modelling! --------------------------------------------------------------

# Run the linear model (unrestricted)
mod1 <- lm(ln_y ~ ln_s + ln_ngd, data = pwt.2)
# Take a look at the parameter estimates
summary(mod1)
## 
## Call:
## lm(formula = ln_y ~ ln_s + ln_ngd, data = pwt.2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.59258 -0.73868  0.00282  0.64383  3.06444 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  11.9528     1.6039   7.453 5.90e-12 ***
## ln_s          0.9987     0.1925   5.187 6.56e-07 ***
## ln_ngd       -5.8616     0.6588  -8.898 1.36e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.001 on 156 degrees of freedom
## Multiple R-squared:  0.4482, Adjusted R-squared:  0.4411 
## F-statistic: 63.35 on 2 and 156 DF,  p-value: < 2.2e-16
# Run the restricted parameter model
mod2 <- nls(ln_y ~ A + (alpha/(1-alpha))*ln_s - (alpha/(1-alpha))*ln_ngd, 
            data = pwt.2,
            start = list(A = 11, alpha = 0.3))
# Take a look at the parameters
summary(mod2)
## 
## Formula: ln_y ~ A + (alpha/(1 - alpha)) * ln_s - (alpha/(1 - alpha)) * 
##     ln_ngd
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## A      1.17489    0.21144   5.557 1.15e-07 ***
## alpha  0.60966    0.02999  20.328  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.134 on 157 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.969e-07
# Simulate a new country called Straya -----------------------------------------------

# Exogenous variables
s_current <- 26
n_current <- 1.6

# Parameters of the model
A <- coef(mod2)[1]
alpha <- coef(mod2)[2]
se <- 1.134 # From the summary command


# Simulate new country 1000 times (benchmark/baseline/BAU)

straya_1 <- rnorm(100000, # Generate 100k new observations
                  mean = A + (alpha/(1-alpha))*log(s_current) - (alpha/(1-alpha))*log(n_current + 1.6 + 5),
                  sd = se)

# Plot a histogram
hist(exp(straya_1), xlim = c(0, 200), breaks = 100)

# Simulate with new savings rate
s_new <- 27

straya_2 <- rnorm(100000,
                  mean = A + (alpha/(1-alpha))*log(s_new) - (alpha/(1-alpha))*log(n_current + 1.6 + 5),
                  sd = se)
hist(exp(straya_2), xlim = c(0, 200), breaks = 100)

# What is the difference in median simulations between the scenarios? 
median(straya_2) - median(straya_1)
## [1] 0.06345584

Calculating for institutions.

\[\ln(A_{i}) = \bar{A} + \delta_{i}\mbox{aveexpr}_{i} + \eta_{i}\]

#load new data
load("ajr.RData")
#Join the datasets
dataset3 <- left_join(pwt.2, acemoglu)
## Joining by: "isocode"
# Run the linear model (unrestricted). aveexpr is a score of the average protection against expropriation risk from 1985-1995. We'll use this variable as a proxy for institutional quality.
mod3 <- lm(ln_y ~ ln_s + ln_ngd + avexpr, data = dataset3)
# Take a look at the parameter estimates
summary(mod3)
## 
## Call:
## lm(formula = ln_y ~ ln_s + ln_ngd + avexpr, data = dataset3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.91042 -0.46412  0.03536  0.43753  2.07754 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.08682    1.74192   1.772   0.0792 .  
## ln_s         1.14396    0.19254   5.941 3.57e-08 ***
## ln_ngd      -3.11426    0.68606  -4.539 1.48e-05 ***
## avexpr       0.38437    0.04704   8.170 6.66e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7312 on 107 degrees of freedom
##   (48 observations deleted due to missingness)
## Multiple R-squared:  0.7339, Adjusted R-squared:  0.7264 
## F-statistic: 98.35 on 3 and 107 DF,  p-value: < 2.2e-16
# Run the restricted parameter model
mod4 <- nls(ln_y ~ A + delta*avexpr + (alpha/(1-alpha))*ln_s - (alpha/(1-alpha))*ln_ngd, 
            data = dataset3,
            start = list(A = 11, alpha = 0.3, delta = 1))
# Take a look at the parameters
summary(mod4)
## 
## Formula: ln_y ~ A + delta * avexpr + (alpha/(1 - alpha)) * ln_s - (alpha/(1 - 
##     alpha)) * ln_ngd
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## A     -1.61506    0.28494  -5.668 1.21e-07 ***
## alpha  0.56647    0.03543  15.986  < 2e-16 ***
## delta  0.44143    0.04341  10.170  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7528 on 108 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.507e-07
##   (48 observations deleted due to missingness)

\(\alpha\) is 0.56647, down from 0.60966 in the initial model.

# Simulate a new country called Straya -----------------------------------------------

# Exogenous variables, saving increased by 1% from straya_2
s_current <- 26
n_current <- 1.6
# Parameters of the model
A <- coef(mod4)[1]
alpha <- coef(mod4)[2]
se <- 0.7528 # From the summary of mod4
delta <- 0.44143  #From the summary of mod4

# Simulate new country 1000 times (benchmark/baseline/BAU). AUS's avexpr is 9.318182

straya_3 <- rnorm(100000, # Generate 100k new observations
                  mean = A + delta*9.318182 + (alpha/(1-alpha))*log(s_current) - (alpha/(1-alpha))*log(n_current + 1.6 + 5),
                  sd = se)

# Plot a histogram
hist(exp(straya_3), xlim = c(0, 200), breaks = 100)

# Simulate with new savings rate
s_new <- 27

straya_4<- rnorm(100000,
                  mean = A + delta*9.318182 + (alpha/(1-alpha))*log(s_new) - (alpha/(1-alpha))*log(n_current + 1.6 + 5),
                  sd = se)
hist(exp(straya_4), xlim = c(0, 200), breaks = 100)

# What is the difference in median simulations between the scenarios? 
median(straya_4) - median(straya_3)
## [1] 0.05298765

Task 2

mod_5 <- ivreg(ln_y ~ avexpr + ln_s + ln_ngd | logem4 + ln_s + ln_ngd, data = dataset3)

summary(mod_5)
## 
## Call:
## ivreg(formula = ln_y ~ avexpr + ln_s + ln_ngd | logem4 + ln_s + 
##     ln_ngd, data = dataset3)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -2.067414 -0.584478 -0.005362  0.496341  1.962222 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.002849   4.889020  -0.001   0.9995    
## avexpr       0.833978   0.212263   3.929   0.0002 ***
## ln_s         0.436080   0.356334   1.224   0.2252    
## ln_ngd      -2.055080   1.801921  -1.140   0.2580    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8945 on 69 degrees of freedom
## Multiple R-Squared: 0.5396,  Adjusted R-squared: 0.5196 
## Wald test: 33.78 on 3 and 69 DF,  p-value: 1.501e-13

ln_s & ln_ngd are much closer together, while still implying different \(\alpha\)s it is a better model. Cannot say that ln_s & ln_ndg are different from zero.