This vignette illustrates how to
use the ivdoctr
package in practice. This example comes
from “The
colonial origins of comparative development: An empirical
investigation” by Acemoglu, Johnson, and Robinson (2001).
The authors study the effect of institutions on GDP per capita across 64 countries. Since institutional quality is endogenous, they use differences in mortality rates of early western settlers across colonies as an instrumental variable. The regression specification is as follows:
The authors state that there is likely a positive correlation between
institutional quality and the error term (u), which could come from reverse
causality (e.g., wealthier societies can afford better institutions) or
omitted variables (e.g., rule of law or British culture are positively
correlated with present-day institutional quality). This positive
correlation is a researcher belief that can be input into
ivdoctr
using the r_TstarU_restriction
argument that accepts a 2-element vector of bounds. For the exercise, we
use 0.9 as the conservative upper bound on the extent of the
endogeneity.
The authors also state that up to 40% of the measure of “institutions” is noise. Measurement error is 1 − κ, so κ ∈ [0.6, 1] is the translation of this belief. The code below runs the estimation given these beliefs:
library(ivdoctr)
endog <- c(0, 0.9)
meas <- c(0.6, 1)
colonial_example1 <- ivdoctr(y_name = "logpgp95", T_name = "avexpr",
z_name = "logem4", data = colonial,
controls = NULL, robust = FALSE,
r_TstarU_restriction = endog,
k_restriction = meas,
example_name = "Colonial Origins")
Let’s say the reader wants to examine how these results might change if the measurement error is worse than the researchers allowed for. The following code implements the worst case scenario, allowing for all information to be noise (we need to be just a little away from 0 to prevent computation errors).
endog <- c(0, 0.9)
meas <- c(0.001, 0.6)
colonial_example2 <- ivdoctr(y_name = "logpgp95", T_name = "avexpr",
z_name = "logem4", data = colonial,
controls = NULL, robust = FALSE,
r_TstarU_restriction = endog,
k_restriction = meas,
example_name = "Colonial Origins")
Now, we can generate the LaTeX summary table illustrating these
estimation results using makeTable()
and save it to
colonial.tex
.
This generates the following table:
To explore the surface of estimates consistent with Autor et al.’s
beliefs, ivdoctr
also generates an interactive 3D plot of
the surface, which can be rotated and zoomed using the mouse:
This package exports three main functions:
ivdoctr()
: Generates list of estimates, including OLS
and IV regression objectsmakeTable()
: Generates the TeX code for a stand-alone
regression table and saves it to the specified file.plot_3d_beta()
: Generates an interactive 3D plot
illustrating the relationship between the causal estimates, instrument
endogeneity, instrument invalidity, and measurement error.Both ivdoctr
and plot_3d_beta
use the same
primary inputs. Users input the name of the dataset (data
),
the name of the dependent variable (y_name
), the name of
the treatment variable(s) (T_name
), the name(s) of the
instrument(s) (z_name
), and the names of the control
variables (controls
). Without any additional arguments, the
functions will output the identified set. If users have beliefs over
measurement error and/or instrument endogeneity, they can specify those
using k_restriction
and r_TstarU_restriction
,
respectively.