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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9 views

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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31 views

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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28 views

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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58 views

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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64 views

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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9 views

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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32 views

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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57 views

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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Is Instrumental Variable Estimation using delayed inputs unbiased?

Assuming the following system: $y(k) = \frac{B(z)}{A(z)} * u(k) + e(k)$ where e is zero-mean white noise and $A(z, θ) = 1 + a_1 z^{−1} + a_2 z^{−2} ...$ and $B(z, θ) = b_1 z^{−1} + b_2 z^{−2} ......
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49 views

Condition for nonlinear IV

Consider the linear model $$y=x\beta+\epsilon.$$ A necessary condition for $z$ to be a valid instrument for $x$ is that $E[x'z]\neq0$, right? What if we have a nonlinear regression of the form $y=g(x,\...
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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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38 views

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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66 views

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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146 views

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 ...
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Difference GMM: is it possible to build valid instruments with X that is (mostly) time invariant?

I have a theoretical question regarding the estimation of Difference GMM (Arellano Bond). I have a panel with 90 countries and 27 years and am trying to estimate a model similar to the following $y_{i,...
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Intuition dealing with partially observed correlated errors

I have a situation where I have a predictor and an outcome that are confounded by a partially observed confounder. The setup is as follows: We have a set of correlated errors that are drawn from the ...
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Fuzzy Regression Discontinuity Design - small probability of treatment

I am doing a Fuzzy RDD and in my regressions I obtain strangely large coefficients. Does anyone have a suggestion how to interpret these? An example: From the second stage of an IV regression, I get ...
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35 views

Proof that Sargan test statistic is distributed $\chi^2$

Assume that $$\textbf{y} = X\boldsymbol\beta + \boldsymbol\varepsilon $$ , where $\boldsymbol\varepsilon$ is an $n \times 1$ random vector and that X is an $n \times k$ matrix of regressors; $m$ of ...
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Does endogeneity problem matter when proving the existence of association/causality relationship?

In social science field (particularly Finance and Operations Management), we usually need to prove or disprove hypotheses of the type: X are positively associated with Y. One of the typical method to ...
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19 views

interpretation of odds ratio in mendelian randomization analysis

I want to do a two-sample Mendelian Randomization (MR) study using summary data to estimate the effect of a continuous exposure on a binary outcome. The genetic associations with the exposure are ...
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OLS and 2SLS normal equations

For a system of equations with $M=2$ endogenous variables, $ Y=\begin{bmatrix} y_1 & y_2 \end{bmatrix}$ and $K=3$ exogenous variables, $X=\begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}$. ...
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161 views

How can I identify and choose instrumental variables?

I am interested in what effect civilian funding of rebel groups (X) has on their degree of violence (Y). There might be an endogeneity problem due to omitted variable bias and reserve causality. Hence,...
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49 views

How to instrument categorical dummy variables

Suppose that X is a categorical variables for 4 possible regions. Suppose that we want to evaluate the effect of X on an outcome Y, but we believe X is correlated with unobservables. I separate ...
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A nonmonoton Continuous Instrumental Variable (Can we use nonmonoton continuous instruments?)

I would like to ask " Can a continuous (nonbinary) instrumental variable can be nonmonotonic or not ?" Background of the problem : What do I mean? I want to give an example over an article. At an ...
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24 views

IV - choosing among valid instruments

I am using an instrument variable approach where I have access to several valid (but many times weak instruments) to instrument for a singe endogenous variable. My question is how to think about which ...
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22 views

Simultaneous equation model with endogenous regressors

Let's assume four dependent variables $Y_1$, $Y_2$ and $Y_3$ that are correlated. I want to evaluate the impact of several regressors: $X_1$, $X_2$ and $X_3$ on these 3 dependent variables using a ...
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32 views

PCA of many weak IVs in 2SLS

"Instrumental variable estimators can be severely biased in finite samples when the degree of overidentification is high or when the instruments are weakly correlated with the endogenous regressors." ...
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22 views

Strict exogeneity is violated: consequences

What are the consequences for the OLS estimator when weak exogeneity holds but strict exogeneity does not? Thank you.
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Lagged variables as IVs

I want to run a endogeneity check on a particular explanatory variable. My dependent variables has value added of services in manufacturing exports, while my suspected endogenous variable is overall ...
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Two-stage residual inclusion when having two endogenous variables

I am using residual inclusion to deal with the potential endogeneity of two regressors. The coefficient of these two variables vary widely in the structural equation depending on whether one or both ...
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257 views

Can I ignore the negative R-squared value when I am using instrumental variable regression?

I am running an instrumental variable regression using 'ivreg' command in R program. I find that all my validity tests related to endogeneity are satisfied only except the R-squared value which is ...
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1answer
55 views

Instrumental variable totally changed the endogenous variables's coefficient

I have a set of panel data and I am adding one instrumental variable to the panel regression. The coefficient for the endogenous variable is -3.8% (p<0.0001) with R^2=20% but after adding the IV ...
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35 views

Repeated measures design (2x2 within subject variables) with one continuous variable and one covariate

I have a repeated measures design (one DV measured twice, both times in two different conditions) with one continuous IV and one (continuous) covariate. I'm trying to see if there is an interaction ...
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201 views

Do I need Sargan test with equal numbers of instruments and endogenous variables when one instrument can affect more than one endogenous variables?

I have a instrumental variable logistic regression I run with three instruments (z1, z2, z3) and three endogenous variables (k1, k2, k3). Therefore, since the number of instruments "3" equals the ...
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29 views

Equivalency of the control function approach and IV

I am trying to see how these two are equivalent. So say Y = BX1 + e1, and x1 is endogenous. and say I have a Z s.t. E[Z'e]=0, and say the linear project of x1 onto z is given by X1= piZ + N. Now, if ...
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44 views

Instrumental variables analysis with exclusion restriction violation

I am working with data from a randomized experimental study in which the random assignment of units is used as an instrument. However, there are four endogenous variables (treatments) which are ...
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82 views

Combining categories by Weight of Evidence

When calculating Information Value and Weight of Evidence, it's possible to draw a chart of WoE for each variable to study its effect on the state of the target variable. Now, I know it's possible to ...
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22 views

What is “instrument contamination”?

When going through instrumental variable literature sometimes, but rather rarely, I happen to find expression "instrument contamination". What does it mean? Is this another expression for ...
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30 views

Proving that average treatment effect for RDD with multiple cutoffs is a weighted average of the causal effect at each cutoff

Let $Xi$ denote the original running variable and $Ci$ be the cutoff that unit $i$ faces (e.g., the nearest cutoff). For simplicity, I consider a case where the binary treatment is assigned if $Xi$ ...
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Strangely identical Probit and IVProbit results

I'm currently running 3 probit regressions, each of which have IV variants. In each model the regressors and instruments are identical (the coding essentially looks exactly the same for each model, ...

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