Instrumental Variable Analysis
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Questions and Answers

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 ______

<p>Xi</p> Signup and view all the answers

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

<p>identify</p> Signup and view all the answers

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

<p>D</p> Signup and view all the answers

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

<p>collider</p> Signup and view all the answers

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

<p>causal</p> Signup and view all the answers

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 ______.

<p>Zi</p> Signup and view all the answers

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

<p>covariates</p> Signup and view all the answers

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

<p>correlated</p> Signup and view all the answers

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

<p>D</p> Signup and view all the answers

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

<p>U</p> Signup and view all the answers

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

<p>IV</p> Signup and view all the answers

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

<p>Instrumental</p> Signup and view all the answers

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

<p>want</p> Signup and view all the answers

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

<p>identify</p> Signup and view all the answers

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

<p>just-identified</p> Signup and view all the answers

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

<p>endogenous</p> Signup and view all the answers

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 ______

<p>OLS</p> Signup and view all the answers

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

<p>want</p> Signup and view all the answers

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 ______

<p>want</p> Signup and view all the answers

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

<p>causal</p> Signup and view all the answers

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

<p>identify</p> Signup and view all the answers

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

<p>D</p> Signup and view all the answers

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.

<p>Instrumental Variables (IV)</p> Signup and view all the answers

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.

<p>IV</p> Signup and view all the answers

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 ______.

<p>IV</p> Signup and view all the answers

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 ______.

<p>Z</p> Signup and view all the answers

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 ______.

<p>compliance</p> Signup and view all the answers

Adjusting for X allows to identify the ______ effect.

<p>causal</p> Signup and view all the answers

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

<p>earnings</p> Signup and view all the answers

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

<p>open</p> Signup and view all the answers

In IV, not ______ is manipulated, but Z.

<p>X</p> Signup and view all the answers

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

<p>X</p> Signup and view all the answers

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

<p>identify</p> Signup and view all the answers

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

<p>variables</p> Signup and view all the answers

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

<p>Y</p> Signup and view all the answers

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 ______.

<p>want</p> Signup and view all the answers

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

<p>applies</p> Signup and view all the answers

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

<p>Causal effect</p> Signup and view all the answers

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

<p>Random part not controlled for by covariates</p> Signup and view all the answers

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

<p>Excludes direct effect of Z on Y</p> Signup and view all the answers

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

<p>Controls for endogeneity</p> Signup and view all the answers

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

<p>Enables unbiased estimates of effects</p> Signup and view all the answers

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

<p>To demonstrate the mechanics of IV and when it fails</p> Signup and view all the answers

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

<p>The random part of potential outcomes remaining after controlling for observed variables</p> Signup and view all the answers

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

<p>It indicates that the outcome variable is only affected by the instrument</p> Signup and view all the answers

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

<p>Remove correlation between potential outcomes and treatment by using instrumental variables</p> Signup and view all the answers

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

<p>To express the sample analog of Cov(Y, Z)/Var(Z) = Cov(D, Z)/Var(Z)</p> Signup and view all the answers

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

<p>Decomposes the treatment variable into two parts, one uncorrelated with potential outcomes and one correlated with them</p> Signup and view all the answers

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

<p>It provides an estimate of the coefficient of interest in IV models</p> Signup and view all the answers

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

<p>It is correlated with potential outcomes only through the treatment variable</p> Signup and view all the answers

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

<p>To eliminate bias in estimating causal effects</p> Signup and view all the answers

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

<p>It accounts for potential endogeneity issues by using instrumental variables</p> Signup and view all the answers

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

<p>To remove the correlation between potential outcomes and the treatment</p> Signup and view all the answers

Why is a good instrument crucial in instrumental variable analysis?

<p>To ensure random assignment</p> Signup and view all the answers

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

<p>The instrument has no effect on the outcome variable</p> Signup and view all the answers

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

<p>To test hypotheses about coefficients in a model</p> Signup and view all the answers

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

<p>Because X may be correlated with unobservables affecting the outcome</p> Signup and view all the answers

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

<p>To remove the correlation between potential outcomes and the treatment</p> Signup and view all the answers

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

<p>Testing the significance of coefficients in the regression model</p> Signup and view all the answers

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

<p>Conditional independence of potential outcomes on covariates given instruments</p> Signup and view all the answers

How does 2SLS differ from OLS regression?

<p>2SLS involves two distinct regression stages</p> Signup and view all the answers

What distinguishes Wald estimation in IV from other methods?

<p>It accounts for both endogeneity and exogeneity simultaneously</p> Signup and view all the answers

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

<p>To control for omitted variables that are correlated with the treatment</p> Signup and view all the answers

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

<p>The only reason for correlation between the outcome variable (Y) and Z is through D</p> Signup and view all the answers

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

<p>It is used for calculating the standard error of IV estimates</p> Signup and view all the answers

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

<p>Z helps identify the causal effect by being correlated with the treatment variable</p> Signup and view all the answers

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

<p>It represents a confounding path that needs to be controlled for in IV analysis</p> Signup and view all the answers

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

<p>It represents the random part of potential outcomes left after controlling for Z.</p> Signup and view all the answers

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

<p>The causal effect</p> Signup and view all the answers

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

<p>The instrumental variable (Z)</p> Signup and view all the answers

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

<p>To assess the significance of the instrumental variable</p> Signup and view all the answers

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

<p>To allow for identification of the causal effect</p> Signup and view all the answers

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

<p>It leads to biased estimates of the causal effect</p> Signup and view all the answers

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

<p>It uses only the uncorrelated part of D in the second stage</p> Signup and view all the answers

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