Discussion 9. Instrumental Variable

STSCI/INFO/ILRST 3900: Causal Inference

November 11, 2026

• You can download the slides for this week’s discussion

• Read the paper “The Colonial Origins of Comparative Development: An Empirical Investigation.” in American economic review, by Daron Acemoglu, Simon Johnson, and James A. Robinson.

• Download the .Rmd

• Answer the questions and hand in the in-class assignment

How are institutions and economic development related?

In this lab we will be examining the following question: what is the effect of institutions on economic performance? We will use data from “The Colonial Origins of Comparative Development: An Empirical Investigation.”.

Load the data

Let’s begin by loading the data. For this we will use a package called ivdoctr, which you might need to install using install.packages(ivdoctr). Then load the data which is called colonial.

library(ivdoctr)
data(colonial)

# Take a look at the data
head(colonial)

##    shortnam africa  lat_abst rich4   avexpr logpgp95
##      <char>  <num>     <num> <num>    <num>    <num>
## 1:      AGO      1 0.1366667     0 5.363636 7.770645
## 2:      ARG      0 0.3777778     0 6.386364 9.133459
## 3:      AUS      0 0.3000000     1 9.318182 9.897972
## 4:      BFA      1 0.1444445     0 4.454545 6.845880
## 5:      BGD      0 0.2666667     0 5.136364 6.877296
## 6:      BHS      0 0.2683333     0 7.500000 9.285448
##      logem4  asia   loghjypl
##       <num> <num>      <num>
## 1: 5.634789     0 -3.4112477
## 2: 4.232656     0 -0.8722738
## 3: 2.145931     0 -0.1707883
## 4: 5.634789     0 -3.5404594
## 5: 4.268438     1 -2.0635681
## 6: 4.442651     0         NA

In the data, our variables of interest are the following:

• logpgp95: Log GDP per capita in 1995 (outcome variable)
• avexpr: Average protection against the risk of expropriation (measure of institutional quality)
• logem4: Log European settler mortality (instrumental variable)

Estimate the causal effect of institutions

We will estimate the causal effect of institutional quality (avexpr) on economic development (logpgp95) using the instrumental variable, European settler mortality (logem4).

Manually implementing Two-Stage Least Squares

Follow the steps of two-stage least square on the slides:

First stage:

In the first stage, we use the IV to predict the treatment by regressing institutional quality (avexpr) on our instrument (logem4)

first_stage <- lm(avexpr ~ logem4, data = colonial)

# Obtain predicted institutional quality
avexpr_hat <- fitted(first_stage)

Second stage:

In the second stage, we regress the outcome on the predicted treatment from stage 1, i.e. regress economic development (logpgp95) on the predicted institutional quality (avexpr_hat).

second_stage <- lm(logpgp95 ~ avexpr_hat, data = colonial)

summary(second_stage)

## 
## Call:
## lm(formula = logpgp95 ~ avexpr_hat, data = colonial)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7545 -0.5386  0.1412  0.4607  1.4059 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.9097     0.8233   2.320   0.0237 *  
## avexpr_hat    0.9443     0.1255   7.523 2.66e-10 ***
## ---
## Signif. codes:  
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7604 on 62 degrees of freedom
## Multiple R-squared:  0.4772, Adjusted R-squared:  0.4688 
## F-statistic:  56.6 on 1 and 62 DF,  p-value: 2.659e-10

The coefficient on avexpr_hat is our manually calculated 2SLS estimate.

Two-Stage Least Squares (2SLS) using ivreg()

We can estimate the causal effect using the ivreg() function from the AER package. You will need to create a formula specifying the outcome variable, endogenous explanatory variable, and instrument. The formula has the following structure: outcome ~ endogenous_variable | instrument

library(AER)

iv_formula <- ... ~ ... | ...

iv_model <- ivreg(
  formula = iv_formula,
  data = colonial
)

summary(iv_model)

The coefficient on avexpr is the IV estimate of the causal effect of institutional quality on economic development.

The IV estimate obtained using ivreg() should be identical to the coefficient obtained from the manual two-stage procedure.

Note: The conventional standard errors reported by the second-stage OLS regression are not the correct 2SLS standard errors. The ivreg() function calculates the appropriate IV standard errors.