Instrumental Variable Analysis

The initial focus on constant effects in IV is to explain the mechanics of IV - how it works and when it ______

IV is used when sometimes the regression we have is not the regression we ______

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 ______

The error term Ui represents the random part of potential outcomes left after controlling for ______

Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E

In the IV framework, not ______ is manipulated, but Z.

There is no open back-door path Z → D ← U → Y because D is a ______ on this path and not controlled for.

The ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) gives the ______ effect.

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 ______.

Two-stage least squares (2SLS) in practice allows the addition of exogenous ______ and the use of multiple instruments.

An Instrumental Variable (IV) is a variable that is ______ with the causal variable of interest (Di)

The exclusion restriction in IV states that the only reason Y is correlated with Z is through ______

Assumption 2 in the IV DAG is shown by the absence of an arrow between Z and ______

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

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

IV is used when the regression we have is not the regression we ______

Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E

Just-identified 2SLS is a case where the number of instruments is equal to the number of endogenous variables, making the model ______

In IV, the exclusion restriction assumes that the instrument only affects the outcome variable through the ______ variable

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 ______

IV is used when sometimes the regression we have is not the regression we ______

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 ______

The ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) gives the ______ effect.

Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E

In the IV framework, not ______ is manipulated, but Z.

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.

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.

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 ______.

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 ______.

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 ______.

Adjusting for X allows to identify the ______ effect.

Angrist (1990) studied the effect of military service on ______.

The back-door path Z ← X → Y is ______.

In IV, not ______ is manipulated, but Z.

The error term Ui represents the random part of potential outcomes left after controlling for ______.

Causal effect is not identified by assuming CIA (conditioning on X), which means CIA does not ______ AT E.

Two-stage least squares (2SLS) allows the addition of exogenous ______ and the use of multiple instruments.

In the IV framework, not ______ is manipulated, but Z.

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 ______.

The initial focus on constant effects in IV is to explain the mechanics of IV - how it works and when it ______.

What does the ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) represent in the IV framework?

How is the error term Ui defined in the context of potential outcomes and the IV framework?

What is the role of the exclusion restriction in the context of IV and causal inference?

In Two-Stage Least Squares (2SLS), what is the function of the uncorrelated part D̂ used for identification in the second stage?

What is the significance of using exogenous covariates and multiple instruments in Two-Stage Least Squares (2SLS)?

What is the primary purpose of the initial focus on constant effects in Instrumental Variables (IV)?

In the context of Two-Stage Least Squares (2SLS), what does the error term Ui represent?

What role does the exclusion restriction play in Instrumental Variables (IV)?

What does Two-Stage Least Squares (2SLS) do in the context of instrumental variables?

What is the fundamental idea behind the Wald estimator in Instrumental Variables (IV)?

What does 2SLS do in the context of instrumental variables (IV)?

What is the role of the Wald estimator in instrumental variables (IV)?

How does a good instrument differ from a random assignment in IV?

Why is conditional independence of potential outcomes on observed variables crucial in IV?

In what way does 2SLS differ from simple regression techniques in estimating causal effects?

What is the purpose of 2SLS in the context of instrumental variables?

Why is a good instrument crucial in instrumental variable analysis?

In the context of instrumental variables, what does the exclusion restriction assume?

What is the main function of the Wald estimator in instrumental variable analysis?

Why is controlling for X insufficient for identifying causal effects in instrumental variable analysis?

What is the purpose of 2SLS in instrumental variable regression?

In IV estimation, what does the Wald estimator primarily focus on?

What is a crucial assumption related to instrumental variables in 2SLS?

How does 2SLS differ from OLS regression?

What distinguishes Wald estimation in IV from other methods?

What is the purpose of using Instrumental Variables (IV) in causal inference?

In the context of IV and 2SLS, what does the exclusion restriction imply?

What is the significance of the Wald estimator in instrumental variable analysis?

When applying Two-Stage Least Squares (2SLS), what role does Z play in the analysis?

What does the back-door path Z ← X → Y indicate in causal inference?

What is the significance of the error term Ui in the context of potential outcomes and the IV framework?

What does the ratio of changes in D (first stage, π1) and Y (reduced form, π1 × τ) represent in the IV framework?

In the IV framework, what is manipulated instead of the causal variable of interest (Di)?

What is the role of the Wald estimator in IV and 2SLS?

Why is it crucial to adjust for X in certain cases in IV?

What problem arises if Di and Ui are correlated and X is not adjusted for in IV?

What does 2SLS do to ensure identification in the second stage?