77 Questions
The initial focus on constant effects in IV is to explain the mechanics of IV - how it works and when it ______
fails
IV is used when sometimes the regression we have is not the regression we ______
want
If the Di and Ui are correlated, then controlling for X is not sufficient for identifying τ because the regression we get is not the regression we ______
want
The error term Ui represents the random part of potential outcomes left after controlling for ______
Xi
Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E
identify
In the IV framework, not ______ is manipulated, but Z.
D
There is no open back-door path Z → D ← U → Y because D is a ______ on this path and not controlled for.
collider
The ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) gives the ______ effect.
causal
Cov(Yi, Zi) = {E[Yi |Zi = 1] − E[Yi |Zi = 0]}p(1 − p) with an analogous formula for Cov(Di, Zi) demonstrates the relationship between Yi, Di, and the dummy variable ______.
Zi
Two-stage least squares (2SLS) in practice allows the addition of exogenous ______ and the use of multiple instruments.
covariates
An Instrumental Variable (IV) is a variable that is ______ with the causal variable of interest (Di)
correlated
The exclusion restriction in IV states that the only reason Y is correlated with Z is through ______
D
Assumption 2 in the IV DAG is shown by the absence of an arrow between Z and ______
U
The IV estimator is the sample analog of the expression Cov(Y, Z)/Var(Z) = Cov(D, Z)/Var(Z), where RF stands for regression of Y on Z and '1st' stands for regression of D on Z. This expression represents the fundamental idea behind ______ estimation
IV
In IV and 2SLS, the causal chain goes from Z through D to Y, highlighting the role of Z as an ______ variable that helps identify the causal effect
Instrumental
IV is used when the regression we have is not the regression we ______
want
Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E
identify
Just-identified 2SLS is a case where the number of instruments is equal to the number of endogenous variables, making the model ______
just-identified
In IV, the exclusion restriction assumes that the instrument only affects the outcome variable through the ______ variable
endogenous
Manual 2SLS involves estimating the first stage yourself, generating fitted values of the endogenous variable, and plugging these values into the second stage equation before running ______
OLS
IV is used when sometimes the regression we have is not the regression we ______
want
If the Di and Ui are correlated, then controlling for X is not sufficient for identifying τ because the regression we get is not the regression we ______
want
The ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) gives the ______ effect.
causal
Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E
identify
In the IV framework, not ______ is manipulated, but Z.
D
Stage Y = α + τ D̂i + [Ui + τ ξi ] = α + τ D̂i + ei = α + τ (π̂0 + π̂1 Zi ) + ei = (α + τ π̂0 ) + τ (π̂1 Zi ) + ei Cov(Y, π̂1 Z) π̂1 · Cov(Y, Z) = V ar(π̂1 Z) π̂12 · V ar(Z) V ar(Z) Cov(Y, Z) 1 Cov(Y, Z) = = π̂1 V ar(Z) Cov(D, Z) V ar(Z) Cov(Y, Z) = Cov(D, Z) τ= 13 / 40 IV and 2SLS Two-stage least squares (2SLS) Intuitively, what does 2SLS do?It decomposes D into two parts: 1 2 the part that is uncorrelated with U , D̂, which is a function of Z and X, both assumed to be uncorrelated with U the part that is correlated with U , ξˆ1i For identification in the second stage, only the uncorrelated part D̂ is used In other words, 2SLS removes the correlation between the potential outcomes and the treatment The precise connection between IV and potential outcomes will be discussed in the second part of the IV section 14 / 40 IV and 2SLS Two-stage least squares (2SLS) Where does a good instrument come from?Ideally, it is as good as randomly assigned Random assignment, e.g.lotteries, with partial compliance Random events like date of birth, combined with legislation referring to age Gender of children If the instrument is non-random we need a further assumption: conditional on X potential outcomes are independent of Z 15 / 40 IV and 2SLS 2SLS with random instrument and partial compliance Despite random assignment some agents choose not to get treated.This decision is a function of observables X and unobservables, shown by the dashed arrow.
Instrumental Variables (IV)
2SLS removes the correlation between the potential outcomes and the treatment. The precise connection between ______ and potential outcomes will be discussed in the second part of the IV section.
IV
For identification in the second stage of 2SLS, only the uncorrelated part D̂ is used, which is a function of Z and X, both assumed to be uncorrelated with U, the part that is uncorrelated with U is known as ______.
IV
Where does a good instrument come from? Ideally, it is as good as randomly assigned. Random assignment examples include lotteries, with partial compliance, random events like date of birth, combined with legislation referring to age, and gender of children. If the instrument is non-random, a further assumption is needed: conditional on X potential outcomes are independent of ______.
Z
Despite random assignment, some agents choose not to get treated. This decision is a function of observables X and unobservables. This situation is shown by the dashed arrow in the context of 2SLS with random instrument and partial ______.
compliance
Adjusting for X allows to identify the ______ effect.
causal
Angrist (1990) studied the effect of military service on ______.
earnings
The back-door path Z ← X → Y is ______.
open
In IV, not ______ is manipulated, but Z.
X
The error term Ui represents the random part of potential outcomes left after controlling for ______.
X
Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E.
identify
Two-stage least squares (2SLS) allows the addition of exogenous ______ and the use of multiple instruments.
variables
In the IV framework, not ______ is manipulated, but Z.
Y
If the Di and Ui are correlated, then controlling for X is not sufficient for identifying τ because the regression we get is not the regression we ______.
want
The initial focus on constant effects in IV is to explain the mechanics of IV - how it works and when it ______.
applies
What does the ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) represent in the IV framework?
Causal effect
How is the error term Ui defined in the context of potential outcomes and the IV framework?
Random part not controlled for by covariates
What is the role of the exclusion restriction in the context of IV and causal inference?
Excludes direct effect of Z on Y
In Two-Stage Least Squares (2SLS), what is the function of the uncorrelated part D̂ used for identification in the second stage?
Controls for endogeneity
What is the significance of using exogenous covariates and multiple instruments in Two-Stage Least Squares (2SLS)?
Enables unbiased estimates of effects
What is the primary purpose of the initial focus on constant effects in Instrumental Variables (IV)?
To demonstrate the mechanics of IV and when it fails
In the context of Two-Stage Least Squares (2SLS), what does the error term Ui represent?
The random part of potential outcomes remaining after controlling for observed variables
What role does the exclusion restriction play in Instrumental Variables (IV)?
It indicates that the outcome variable is only affected by the instrument
What does Two-Stage Least Squares (2SLS) do in the context of instrumental variables?
Remove correlation between potential outcomes and treatment by using instrumental variables
What is the fundamental idea behind the Wald estimator in Instrumental Variables (IV)?
To express the sample analog of Cov(Y, Z)/Var(Z) = Cov(D, Z)/Var(Z)
What does 2SLS do in the context of instrumental variables (IV)?
Decomposes the treatment variable into two parts, one uncorrelated with potential outcomes and one correlated with them
What is the role of the Wald estimator in instrumental variables (IV)?
It provides an estimate of the coefficient of interest in IV models
How does a good instrument differ from a random assignment in IV?
It is correlated with potential outcomes only through the treatment variable
Why is conditional independence of potential outcomes on observed variables crucial in IV?
To eliminate bias in estimating causal effects
In what way does 2SLS differ from simple regression techniques in estimating causal effects?
It accounts for potential endogeneity issues by using instrumental variables
What is the purpose of 2SLS in the context of instrumental variables?
To remove the correlation between potential outcomes and the treatment
Why is a good instrument crucial in instrumental variable analysis?
To ensure random assignment
In the context of instrumental variables, what does the exclusion restriction assume?
The instrument has no effect on the outcome variable
What is the main function of the Wald estimator in instrumental variable analysis?
To test hypotheses about coefficients in a model
Why is controlling for X insufficient for identifying causal effects in instrumental variable analysis?
Because X may be correlated with unobservables affecting the outcome
What is the purpose of 2SLS in instrumental variable regression?
To remove the correlation between potential outcomes and the treatment
In IV estimation, what does the Wald estimator primarily focus on?
Testing the significance of coefficients in the regression model
What is a crucial assumption related to instrumental variables in 2SLS?
Conditional independence of potential outcomes on covariates given instruments
How does 2SLS differ from OLS regression?
2SLS involves two distinct regression stages
What distinguishes Wald estimation in IV from other methods?
It accounts for both endogeneity and exogeneity simultaneously
What is the purpose of using Instrumental Variables (IV) in causal inference?
To control for omitted variables that are correlated with the treatment
In the context of IV and 2SLS, what does the exclusion restriction imply?
The only reason for correlation between the outcome variable (Y) and Z is through D
What is the significance of the Wald estimator in instrumental variable analysis?
It is used for calculating the standard error of IV estimates
When applying Two-Stage Least Squares (2SLS), what role does Z play in the analysis?
Z helps identify the causal effect by being correlated with the treatment variable
What does the back-door path Z ← X → Y indicate in causal inference?
It represents a confounding path that needs to be controlled for in IV analysis
What is the significance of the error term Ui in the context of potential outcomes and the IV framework?
It represents the random part of potential outcomes left after controlling for Z.
What does the ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) represent in the IV framework?
The causal effect
In the IV framework, what is manipulated instead of the causal variable of interest (Di)?
The instrumental variable (Z)
What is the role of the Wald estimator in IV and 2SLS?
To assess the significance of the instrumental variable
Why is it crucial to adjust for X in certain cases in IV?
To allow for identification of the causal effect
What problem arises if Di and Ui are correlated and X is not adjusted for in IV?
It leads to biased estimates of the causal effect
What does 2SLS do to ensure identification in the second stage?
It uses only the uncorrelated part of D in the second stage
Learn about the significance of Z⊥⊥U in instrumental variable analysis and how it relates to the error term U. Discover how instrumental variables help in estimating treatment effects by minimizing biases caused by omitted variables.
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