# Questions tagged [instrumental-variables]

Instrumental variables (IV) are used for causal inference with observational data in the presence of endogeneity when standard regression methods yield biased and inconsistent estimates.

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### Weak IV test- one endogenous regressor and two IVs

I wanted to know what would be the relevant weak IV tests among the following in case of one endogenous regressor and 2 IVs. i) Comparing Cragg-Donald F-statistic to Stock-Yogo table ii) Kleibergen-...
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### I am unable to create this variable [migrated]

How do I create a variable in R, which takes a value of 0 60% of the time and a value of 1 otherwise?
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### Where do the coefficients from regression of the instrument on VAR innovation come from in this setting?

I am studying VAR identification strategy with instrumental variable. The main clam is that the fitted value ($\Pi$) of a regression of the instrument ($w_t$) on the innovations ($\upsilon_t$) ...
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### Estimating post treatment outcome of IV

In the Angrist, Mastering metrices book (page 118, chapter 3, Instrumental variable) Angrist calculated "recidivism was greater among suspects assigned to be coddled than among those assigned to be ...
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### What statistical method to use to compare only two (of multiple) groups with respect to a binary outcome?

$n$ patients are randomly given treatment $A$ or treatment $B$ (with 50% of patients receiving each). Some patients from either group may then choose to ignore the treatment (i.e. a third option $C$). ...
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### Measuring difference in effect on output between two values of input variable

I have the following scenario: Of n patients, half are randomly assigned a label 0 and the rest are assigned ...
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### Why do estimates differ so much between Instrumental Variable (ivreg) vs 2SLS (lm)?

I am working with some messy pilot data to figure out whether Instrumental Variable analysis will help interpret the results of a randomized controlled trial I am preparing. Treatment compliance in ...
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### Interpretation of Hausman test - IV models

I ran two IV models: 1) ivreg 2sls y x1 (x2=z1) 2) ivreg 2sls y x1 (x2=z1 z2) than I did a Hausman test, and it was not significant, so I could not reject the null. What does that mean? Is z2 a valid ...
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### R-square and Intrumental Regression

Given that a linear regression model has been estimated using instruments can R-square then be interpreted in the usual fashion (as in linear regression without instruments)?
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### Hierarchical/Multilayer/Nested Instrumental Variable Regression

If we can view classical instrumental variable regression as "two-layer" (from instrumental variable to covariate and then to the response), is there any "hierarchical/multilayer/nested" version of ...
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### How to decide which variables belong in the first and second stage of the 2SLS method

Let's assume I want to estimate the model: Income = Education + Gender + u Let's say I would like to use the occurrence of two events with ...
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### How to conceptually think about repeated sampling with instrumental variables?

Say I am using rainfall during a protest as an instrument for political participation on some outcome y. When thinking conceptually about the sampling distribution, what does this mean here? Is it ...
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### Clinically meaningful explanation of marginal treatment effect (MTE) in instrument variable study

I am working on an instrumental variable application using clinical data. We will use a so-called preference-based instrument. We may include this as a continuous variable. With a continous instrument,...
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### Not recovering true coefficient with recursive bivariate probit model on simulated data

I have built a simulated dataset to try to build my intuition about the recursive bivariate probit model. The challenge I'm running into is that I'm unable to recover the true coefficient in my ...
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### Instrument Validity Is Not Empirically Testable

BACKGROUND Suppose we want to use a random sample to estimate $\beta$ in the following regression model: $$Y_i=\alpha+\beta X_i+\epsilon_i.$$ The OLS estimator of $\beta$ is inconsistent if the ...
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### How to prove that one-sided non-compliance implies $E\left ( y|z=0 \right )=E\left ( y_{0}|z=0 \right )$?

Let $d \in \left \{ 0,1 \right \}$ denote the treatment status with unity indicating that the individual has been treated and let $z \in \left \{ 0,1 \right \}$ denote a binary indicator for whether ...
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### OLS, IV applied to basic macro model

I am preparing for my final in Econometrics but I am confused over a new problem I encountered. I think I have solved it but I am unsure whether I am not making any gross mistakes. This is the study ...
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### Explaining instrumental variable 2SLS in a simple yet precise way

I am trying to explain IV 2SLS in a non-technical yet precise way. However, I still think I can improve, and I would highly appreciate input that could make some points clearer. One of the sticking ...
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### Instrumental variables with interactions between endogenous variables

I have two endogenous variables $x_1$ and $x_2$ and am trying to estimate the following model: $$y = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_{12} x_{12}$$ where $x_{12} = x_1\times x_2$. I'm ...
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### When using multiple continuous instruments do I get a weighted Local Average Treatment Effect?

I have the following model: $y_i = \alpha + \beta d_i + g(x_i)+e_i$ Since I have reason to believe that $d_i$ is endogenous, I am using 3 plausibly exogenous variables ($z_1,z_2,z_3$) to instrument ...
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### Interpretation of the Hausman test (overidentification in relation to IV's) for large samples

I am using survey data with a huge amount of observations, such as the World Value Surveys. Large sample sizes are obviously very nice, but I have have encountered some downsides as well. To give an ...
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### What control variables do we need for IV regression?

I am running and IV regression and I need help on what control variables to include in the IV regression. I believe that I have to control for potential variable that are correlated with both the ...