Week 6
Matthew Kourlinis, Jack Nguyen, Nick Russell, Nicola Simpson
7 September 2015
Part 1 : Comprehension
What is the central point of the paper?
The central point of the paper is to analyse whether a countries economic development is affected by whether a region was colonized with European settlement or if an extraction regime was set up.
European mortality rates in colonies are a good proxy for institutional development. It is hypothesized that colonies where European mortality rates were high had extractive institutions that have persisted to the present day, in contrast to more favourable climates where Europeans settled and brought with them a desire for strong institutions, property rights and checks against government powers {Australia’s Rum Rebellion in the early 1800’s is a good example}. Locations of high European mortality where regions where malaria and yellow fever were prevalent, due to a lack of exposure during infancy Europeans were much more susceptible to these diseases than indigenous peoples. However European’s brought with them new diseases which also wiped out native people’s such as Pissaro’s conquest of the Inca’s in South America in the 1500’s, a small band on Spanish brough disease that wiped out around 50 - 80% of the Incans at the time.
What Variables do the authors use to proxy for current institutions?
The authors use the proxies of European colonizer mortality as a proxy for whether a geographic location was suitable for colonization and therefore more likely to have institutions developed. The authors look at whether the institutional development during colonisation had a persisting effect and whether it still affects GDP and how developed the institutions of the country are today.
The authors look at other variables that have been theorised as affecting development including:
GDP
latitude economists have suggested proximity to the equator determined a country’s colonisation with countries close to the equator being more extraction due to the increased European mortality in those areas.
Exclusion of outliers such as“neo Europeans” such as the USA, Canada, Australia and New Zealand.
The Eurpoean coloniser is controlled for - France & England in particular & whether the type of institutions varied with the cultural variance. Studies found that British institutions were stronger, but it has a small weak effect and the British tended to colonise areas where colonial settlement was possible
Religion is controlled for, with little effect on institutional development
Temperature and humidity are controlled for
Soil type & quality,
Whether the colony was landlocked or not
Enthnolinguistic fragmentation, which is interesting because the Inca’s persuaded other groups to join their empire to take advantage of their farming techniques, whereas European used force to gain compliance. Inca’s had a very diverse range of ethnicities within its Empire.
Why can’t we just look at the simple relationship between these variables and today’s development? Isn’t that the casual relationship?
The institutions that were developed continued to be used in the colonies post independence from the Coloniser. The authors find that in extractive colonies such as in Latin America, slave labour and monopoly markets persisted into the 20th century in cases such as Guatemala, until 1886 in Brazil and 1910 in Mexico.
A causal relationship is one that a behaviour or outcome is the result of an event taking place. The authors find that these variables are not independent of the institutional development variable and that the only variable that matters is whether the Europeans could safely settle in an area. Where they could not settle they did not develop strong institutions.
European mortality is an exogenous variable and has a high correlation between European settlement, early institutional development and the institutions today.
What is the instrumental variable the authors describe?
The instrumental variable that authors describe is mortality of European settlers in colonisation (M).
What is their exclusion restriction? Do you find it plausible?
The exclusion restriction is that protection against expropriation variable R is treated as endogenous and does not appear in \(log y = \mu + \alpha R + \chi\gamma + \epsilon\)
This suggests that mortality is excluded from the process of extracting resources. I don’t find it particularly plausible as European mortality had a significant effect on determining where colonisation or extraction would occur. Indeed the British considered setting up a penal colony on an island in Africa, but the obscenely high mortality rates dissuaded them from that idea.
Part 2 : Using Acemoglu Johnson and Robinson’s data to update our model from last week
# Load the libraries
library(ggplot2); library(dplyr)##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Read the data
pwt <- read.csv("pwt71.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 parameter mod2 estimates
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] 0.06628292Task 1
# Task 1, introducing ajr.RData -------------------------------------------
load("ajr.RData")
dataset3 <- left_join(pwt.2, acemoglu) #joining dataset pwt.2 and acemoglu together## Joining by: "isocode"## Warning in left_join_impl(x, y, by$x, by$y): joining character vector and
## factor, coercing into character vectordataset4 <- dataset3 %>% filter(!is.na(avexpr)) %>% # Get rid of missing rows of avexpr, in new dataset dataset4
filter(!is.na(logem4)) #Get rid of missing rows of logem4
mod3 <- lm(ln_y ~ ln_s + ln_ngd + avexpr, data = dataset4) #creating a linear model including the variable of institutional quality
summary(mod3) #summary of mod3##
## Call:
## lm(formula = ln_y ~ ln_s + ln_ngd + avexpr, data = dataset4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20719 -0.42763 -0.02798 0.49676 1.32809
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.84434 2.46420 3.183 0.00218 **
## ln_s 0.76539 0.23815 3.214 0.00199 **
## ln_ngd -4.85618 0.93961 -5.168 2.19e-06 ***
## avexpr 0.39884 0.05701 6.996 1.35e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6587 on 69 degrees of freedom
## Multiple R-squared: 0.7504, Adjusted R-squared: 0.7395
## F-statistic: 69.13 on 3 and 69 DF, p-value: < 2.2e-16#run unrestricted parameter model inputting delta * avexpr as a new expression
mod4 <- nls(ln_y ~ A + (alpha/(1-alpha))*ln_s + delta*avexpr - (alpha/(1-alpha))*ln_ngd,
data = dataset4,
start = list(A = 11, alpha = 0.3, delta = 1))
#summary of mod4
summary(mod4)##
## Formula: ln_y ~ A + (alpha/(1 - alpha)) * ln_s + delta * avexpr - (alpha/(1 -
## alpha)) * ln_ngd
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## A -1.74786 0.36606 -4.775 9.56e-06 ***
## alpha 0.55599 0.04403 12.626 < 2e-16 ***
## delta 0.46850 0.05951 7.873 3.13e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7234 on 70 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.793e-08straya1 <- dataset4 %>% filter(isocode == "AUS") #creating new data with only country australia
s_straya <- straya1 %>% select(s) %>% sum() #selecting only australia's value of S as a value
n_straya <- straya1 %>% select(n) %>% sum() #selecting only australia's value of n as a value
avexpr_aus <- straya1 %>% select(avexpr) %>% sum() #creating new value of just australia's avexpr
#model parameters
A2 <-coef(mod4)[1] #taking the coefficient 1 from mod4, which gave us the estimate of A, and naming it as value A2
alpha2 <- coef(mod4)[2] #taking the coefficient 2 from mod4, which gave us the estimate of alpha, and naming it as value alpha2
delta <- coef(mod4)[3] #taking the coefficient 3 from mod4, which gave us the estimate of delta, and naming it as value delta
se2 <- 0.7234 # From the summary command
straya_3 <- rnorm(100000, # Generate 100k new observations
mean = A2 + delta * avexpr_aus + (alpha2/(1-alpha2))*log(s_straya) - (alpha2/(1-alpha2))*log(n_straya + 1.6 + 5),
sd = se2)
hist(exp(straya_3), xlim = c(0, 500), breaks = 150) #create historgram of straya_3 observations
s_straya1 <- s_straya + 1 #increase savings rate of australia by 1
straya_4 <- rnorm(100000, # Generate 100k new observations of australia with increased savings rate
mean = A2 + delta*avexpr_aus + (alpha2/(1-alpha2))*log(s_straya1) - (alpha2/(1-alpha2))*log(n_straya + 1.6 + 5),
sd = se2)
hist(exp(straya_4), xlim = c(0, 500), breaks = 150) #create historgram of straya_4 observations
median(straya_4)-median(straya_3)## [1] 0.04151714Task 2
# Task 2 ------------------------------------------------------------------
library(AER) #open library AER for use in task 2## Loading required package: car
## Loading required package: lmtest
## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Loading required package: sandwich
## Loading required package: survival# Run the linear model (unrestricted) with proxies (logem4)
task2_mod1 <- lm(ln_y ~ ln_s + ln_ngd + logem4,
data = dataset4)
summary(task2_mod1)##
## Call:
## lm(formula = ln_y ~ ln_s + ln_ngd + logem4, data = dataset4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.89277 -0.49977 0.09557 0.49210 1.52387
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.82426 2.64072 4.478 2.91e-05 ***
## ln_s 0.80430 0.27254 2.951 0.004323 **
## ln_ngd -4.70480 1.14318 -4.116 0.000105 ***
## logem4 -0.39129 0.08351 -4.686 1.36e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.75 on 69 degrees of freedom
## Multiple R-squared: 0.6763, Adjusted R-squared: 0.6622
## F-statistic: 48.05 on 3 and 69 DF, p-value: < 2.2e-16# Used ivreg to estimate (unrestricted) model with logem4
task2_mod2 <- ivreg(ln_y ~ ln_s + ln_ngd | ln_ngd + logem4,
data = dataset4)
summary(task2_mod2)##
## Call:
## ivreg(formula = ln_y ~ ln_s + ln_ngd | ln_ngd + logem4, data = dataset4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4519 -1.5995 0.2763 1.2965 6.3358
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -23.061 24.674 -0.935 0.3532
## ln_s 7.007 3.751 1.868 0.0659 .
## ln_ngd 2.120 6.551 0.324 0.7472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.172 on 70 degrees of freedom
## Multiple R-Squared: -1.754, Adjusted R-squared: -1.832
## Wald test: 8.076 on 2 and 70 DF, p-value: 0.0006982# Used ivreg to estimate (unrestricted) model with avexpr
task2_mod3 <- ivreg(ln_y ~ ln_s + ln_ngd | ln_ngd + avexpr,
data = dataset4)
summary(task2_mod3)##
## Call:
## ivreg(formula = ln_y ~ ln_s + ln_ngd | ln_ngd + avexpr, data = dataset4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2815 -2.0909 0.1943 1.7075 9.1022
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -42.015 39.925 -1.052 0.296
## ln_s 9.962 6.103 1.632 0.107
## ln_ngd 6.869 10.474 0.656 0.514
##
## Residual standard error: 3.11 on 70 degrees of freedom
## Multiple R-Squared: -4.645, Adjusted R-squared: -4.806
## Wald test: 4.421 on 2 and 70 DF, p-value: 0.01556