Exam 1 Quizzes Flashcards
(12 cards)
Draw the main instrumental variables DAG, ensuring that you denote the independent variable (X), the instrumental variable (Q), dependent variable (Y), and a confounding variable (Z).
The Q is to be able to overcome reverse causal relationship between x and y. (Q influences X, which influences Y, and Z influences X and Y).
What is the central question in Acemoglu, Johnson, and Robinson (2001)?
The central question waas whether early institutions had a relationship to the income (GDP) of a country today (based on the colonizer country’s style).
This was explored through the instrumental variable of high mortality rates which basically showed that areas with this high rate were note settled in to create those proper institutions and instead became resource extractive states. Those that did get settlements that created proper institutions (aka areas of low mortality rate) were seen to have higher income today. When they controlled for other variables their effects did not drastically change, which is good.
What are the 5 main assumptions necessary for instrumental variables estimation, and how do they apply to Kocher, Pepinshy, and Kalyvas (2011)?
1) 1st stage relationship - previous VC control (Q) -> bombed (X) used to be able to estimate Y
2) Ignorability - Q is (conditionally) randomized with respect to Y and X
3) SUTVA - only 1 unit of X (i.e. bombed, not 1/2 bombed), units must not interfere with each other (i.e. one bombed hamlet not affecting neighbor)
4) Monotonicity - Q shifts X in same direction (i.e. VC control leads to more bombing not less bombing)
5) Exclusion Restriction - Q -> Y (vc control)
Are most of the non-compliance problems in Slough and Fariss (2021) related to ignorability or positivity?
Positivity
Provide the rationale for your answer in question 1 (Slough and Fariss (2021)), making sure to a) define ignorability and positivity from an internal validity perspective; and b) explain how they relate to this specific case.
Ignorability: no unmeasured Z or unintentionally open back door paths between X & Y which may arise from S (selection bias)
Positivity: whether different manifestations of X overlap across subgroups/strata of treatment and control, taking into account S(selection bias) that can result in under or over coverage
This relates to why most were positivity because most reasons for noncompliance were outside eligibility restrictions (aka their stratas wouldn’t have the TC) and that is a problem.
One was ignorability because couldn’t find records - confounder that would impact treatment or control.
Define ignorability and positivity from an external validity perspective and explain how they relate to Slough and Fariss (2021).
Ignorability: no unaccounted for S (selection bias) that generate sample-population difference via V (modifier)
Positivity: whether different manifestations of X overlap across sample + population, taking into account S (selection bias) that can result in under or over coverage
They relate because if the sample is too biased (i.e. all chronic smokers) then it does not reflect the general population; in this case, the sample had way more of certain inmates receiving the service than other groups, meaning the generalizability was skewed (undercoverage) meaning the problem is that we can’t ignore it.
Draw the potential DAG(s) that standard natural experiments generally take, and explain why they take this/these form(s).
An experiment DAG = Z and X influence Y
A fork DAG = X influences Y, Z influences X and Y
The experiment DAG is possible because 𝑍 is irrelevant is 𝑋 is randomly assigned—even if the researcher doesn’t control it in a natural experiment. The fork DAG is possible because the as-if random assignment is not always perfect in natural experiments, so it is often necessary to control for 𝑍.
Explain in detail at least one limitation of standard natural experiments.
- Nature doesn’t assign every treatment as-if randomly:
a. Randomized experiments have similar problem:
* Not everything can be randomly assigned for ethics or feasibility reasons
b. Many major social science phenomena not assigned as-if randomly:
* Democracy/autocracy (political science)
* Social capital (sociology)
* GDP (economics) - Overclaiming
a. Everyone wants to say that their treatment is as-if randomly assigned
* It makes life easy when we can ignore the confounding (𝑍) variables, but that is frequently not the case
b. Standard natural experiments are hard to verify
* They necessitate great qualitative knowledge of treatment assignment CPOs. Otherwise, if we can’t show that the treatment assignment is as good as random through qualitative knowledge of the case, it is really not a natural experiment.
* Balance tables are the main method that we have to show that observations are assigned as-if randomly, but balance tables are only useful if
(i) we have access to all of the potential 𝑍 variables; and (ii) they are measured correctly. Often, we can’t meet those two criteria
Why does the Balcells and Torats-Espinosa (2018) article qualify as a standard natural experiment? Please provide lots of details.
Ostensibly, terrorist attacks are not randomly assigned. However, the combination of terrorist attacks happening and nationally-representative public opinion polls on whether people aim to vote in the next election could be construed as good as randomly assigned—i.e., a natural experiment. So what @BalcellsTorratsEspinosa2018 did
is compare people’s interest in voting the next election in polls directly 1, 3, and 5 days after the terrorist attacks compared to public opinion polls conducted outside those windows from 1989-1997. Basically, this is too much of coincidence for it not to be natural experiment
Draw the main instrumental variable DAG, ensuring that you denote the independent variable (𝑋), instrumental variable (𝑄), dependent variable (𝑌), and a confounding variable (𝑍).
Q influences X which influences Y. Z influences X and Y.
Load libraries
library(ggdag)
library(tidyverse)
# Define the DAG with custom coordinates
instrument <- dagify(
Y ~ X + Z, # y is influenced by x and z
X ~ Z + Q, # x is influenced by z
exposure = “X”,
outcome = “Y”,
coords = list(
x = c(Q = -1, X = 0, Z = 0, Y= 1), # Horizontal positions
y = c(Q = 0, X = 0, Z = 1, Y = 0) # Vertical positions))
# Plot the DAG
ggdag_status(instrument) +
labs(title = “Instrumental Variable”) +
theme_dag()
What is the central question in Acemoglu, Johnson, and Robinson (2001)?
Do institutions cause development? At a lower level, does average protection against expropriation increase GDP per capita?
What are the 5 main assumptions necessary for instrumental variables estimation, and how do they apply to Kocher, Pepinsky, and Kalyvas (2011)?
First-Stage Relationship: There must be a relationship between the endogenous 𝑋 variable (bombing) and the instrumental variable 𝑄 (previous VC control).
– This assumption, which some also call the relevance assumption, must be empirically tested. Usually, the threshold for having a strong enough instrument to pass the first stage is an 𝐹 -statistic of greater than 10 or 11.
* Stable Unit Treatment Value Assumption (SUTVA): There is only version of the treatment 𝑋 (i.e., bombed), and units must not interfere with each other (e.g., getting bombed in one Hamlet should not affect neighboring Hamlets).
* Monotonocity: The instruments 𝑄 (previous VC territorial control) shifts the treatment 𝑋 (bombing) in the same direction—i.e, there are no defiers, who do the opposite of their treatment assignment. In other words, Hamlet territorial control must usually lead to more bombing, not less, which is logical here: there is no need to bomb if there are not territorial control issues.
* Exclusion Restriction: The instrumental variables 𝑄 and 𝑅 (previous VC territorial control) must not be directly related to the outcome 𝑌 (more current VC territorial control). This assumption is more questionable, because it is hard to imagine that previous territorial control and current territorial control not being related, especially given that the measurements are only 6 months apart.
* Ignorability: The instrument 𝑄 (previous VC control) should be randomized or conditionally randomized (based on 𝑍) with respect to the outcome 𝑌 (VC control) and treatment variable 𝑋 (bombing).
– This is about closing the backdoor paths and not having reverse causality.
