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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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IV-estimation vs. Heckman's selection model

I am trying to grasp the difference between IV-estimation and Heckman's selection model. I do that by considering the following set-up. My outcome if interest is y ...
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2SLS - With the same X's and Z's but 3 different Y's, Over-identification and Hausman tests give different results

Dear Stack Exchange users, Let's say that my independent variable of interest is expected to be endogenous and that I want to investigate its effect on 3 separate outcomes. I run separate 2SLS's (one ...
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weighted IV estimation by plm

I apply plm package to do fixed effects IV regression but find something which I couldn't understand. Theoretically, if we only have one endogenous variable and one IV, the IV estimator should be ...
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Is it ok to include endogenous explanatory variables in control function approach?

I am using control function approach (Woolridge 2010, 128-29) with the goal of correctly estimating the effect of my endogenous explanatory variable y2 on the outcome variable y1. Because y1 is a ...
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2SLS: Residual in first stage to handle a unique endogeity problem?

I am interested in the following model: $y = f(x)\beta + e$, where $x = x'+x''$, $f()$ is a nonlinear transformation, and $cov(x,e) \neq 0$. Suppose I have an instrument $z$ that satisfies the ...
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Instrumental variable analysis: ivreg (R) vs. naive estimation

Short version of my question: Is it true that the naive, 2-step instrumental variable approach overestimates the standard errors (I expected an underestimation)? Long version: I am working with an ...
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Solving correlation between explanatory variables using instrumental variables

I am currently stuck on a task where I am interested in estimating the production function for agricultural output as follows: \begin{equation} y_{i} = x_{i}\beta + \alpha_i + \epsilon_{i} \end{...
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Is Hausman-Taylor Estimator with different within- and between-group effects biased?

Background Assume the simple two-level linear model $$y_{ij}=\beta_0 + \beta_1X_{ij}+\beta_2X_{ij}^{end}+\beta_3Z_j+\beta_4Z_j^{end}$$ where $X_{ij}$ and $Z_j$ are exogenous and $X^{end}_{ij}$ and $Z^...
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Standard errors of *partial* two stage least squares coefficients

Here partial 2SLS (I coined this term and found it descriptive) is the approach that SAS uses for 2SLS. Compared to "ordinary" 2SLS which in the first stage projects all explanatory variables $X$ onto ...
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GMM Distance and/or Davidson-Mackinson endogeneity test in R

I'm looking for alternative Durbin-Wu-Hausman test of endogeneity in R for triangulation purposes. I have found GMM distance test in ivreg2 package in Stata (http://fmwww.bc.edu/ec-p/wp667.pdf) but ...
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How to prove the distribution of Generalised Instrumental Variables Estimator

$\hat { \beta } _ { GI V } = ( X ^ { \prime } Z ( Z ^ { \prime } Z ) ^ { - 1 } Z ^ { \prime } X ) ^ { - 1 } X ^ { \prime } Z ( Z ^ { \prime } Z ) ^ { - 1 } Z^ { \prime }y\hspace{35pt}(a)$ $(a)$ is ...
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Interpretation of correlation in endogenous regression model

Suppose you have a linear regression with an endogenous regressor $x$ that can be represented as follows: $x = z'\delta + \epsilon_1$ $y = \beta x + w'\gamma + \epsilon_2$ where $\begin{pmatrix}\...
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Can I use an instrumental variable to control for treatment endogeneity in differences-in-differences model?

I have panel data with two time periods (pre and post) and two groups (treatment and control). I have a differences-in-differences model with the standard estimating equation: \begin{equation} y_{it} ...
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20 views

Test for exogenity

I have a few questions about this alternative test for exogeneity. The first question is about the auxiliary regression? I have tried to google it and still don't understand the meaning of it. What ...
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Double Mendelian Randomization: Reasonableness & False Positive Concerns

I've been interested in mendelian randomizations (a form of instrument variable analyses) as a method for gaining insight into causal relationships between risk factors and outcomes. An example i ...
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32 views

hausman test for exogenity

Can someone explain the intuition behind the Haussman test for exogenity and the equation for H. what does it mean, that "it is normalised by the covariance of the difference".
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instrumental variables property

How can I show that the instrumental variables (IV) estimator is consistent from this equation using the two stage least squares method? Where does this equation come from?
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2SLS IV with endogenous interaction in Stata: Difference between ivreg2 and manual estimates

I want to estimate 2SLS in Stata with two endogenous, continuous variables: $X_1$ and the interaction term $X_1*X_2$. The other IVs $X_2...X_N$, including the quadratic $X_2^2$, are all exogenous. I ...
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Instrumental variables with non-normal endogenous

Does it make sense to conduct an instrumental variables model where the endogenous variable of interest is continuous but not normally distributed? I know for normal regression purposes, there is no ...
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Is there any statistical problem on instrumental variable analysis with binary exposure and binary outcome?

I would like to conduct an instrumental variable (IV) analysis (a.k.a Mendelian Randomization analysis due to my IV is a genetic variant). In many cases as I searched before, an IV analysis was ...
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What is difference between mediation analysis and mendelian randomization analysis?

I would like to know what the difference between mediation analysis and mendelian randomization (MR) analysis is. As I know, instrumental variable (IV) in mediation analysis is almost similar to IV (=...
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Is there any problem to conduct instrumental variables analysis with binary endogenous variable and binary outcome?

I would like to introduce "instrumental variables" in my study. In many cases, the outcome (dependent variable; DV) is a continuous variable. However, my study design has binary outcome (DV) and ...
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Do we keep the instrument in the OLS, if Wu-Hausman test (using that instrument) fails to reject that OLS is consistent?

If two instrument variables (for example $Z_1$ and $Z_2$) are both exogenous and relevant. And we found Wu-Hausman test fails to reject the $H_0$: Both IV regression and OLS are consistent. When we ...
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How should an author convince readers that weak instruments are not a problem?

I see in a lot of instrumental variables papers that authors will often discuss first stage $R^2$ values or $F$ statistics to assuage concerns that they are working with a weak instrument. This seems ...
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2SLS overidentification test - Why is it the test only helps deciding if the added IV is endogenous? And why adjust for d.o.f?

I heard from a lecture that if we test for overidentification, the output will only help us to determine whether the added IV is exogenous. It however won't help in telling, and in fact we can never ...
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Comparing adjacent categories of a IV in logistic regression

I have 200 subjects with a dependant variable (positive/negative) and I want to test them with an independent variable (IV) of 4 categories (age). So, the 200 individuals are dealt among the 4 ...
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Weak instrument problem, how can a “false experiment” serve as an identification check?

In their 2004 paper, Miguel et al. investigate the role of income growth by using current and lagged rainfall as an instrument. However, the instruments are somewhat weak: the joint F-statistic is ...
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How come p-value for ivreg and manual lm differs so much?

Can anyone tell me why the p-values for two stage least squares for manual lm vs ivreg way ...
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152 views

F-stat in instrumental variable regression is too large

I have been getting an F-stat in the thousands when performing an instrumental variable regression. Is that a problem? Why is it that large and what might that be indicating? Anybody has run into ...
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IV regression: endogenous variable is sum of exogenous and endogenous

Suppose I construct the variable $U_i = S_i + T_i $, and I want to estimate the equation $$ Y_i = \alpha + \beta U_i + \gamma X_i + \epsilon _i $$ Suppose $X_i$ and $S_i$ are exogenous, but $T_i$ is ...
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Differences between xtreg and xtivreg affecting nesting of clusters

This post is cross posted in a reply on statlist here I'm working with panel regression (fe = id year). I cluster on a regional variable, land, but my clusters are not nested. So I sorted out the ...
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How is instrumental variables with many exogenous predictors related to propensity scoring?

In a large (many exogenous predictors) instrumental variables regression, with covariate matrix $X$, outcome $Y$ and binary treatment indicator $T$, a two-stage least-squares approach might be like ...
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Second stage in TS2SLS

I am working with a Two Stages Two Steps Least Squares (TS2SLS) in a Diff-in-Diff context, with cross-section data. I have a large sample where I observe the binary outcome Y as well as the ...
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Testing for the exogeneity of the subsets of instruments

Suppose that there is one endogenous variable and two instruments. The aim is to test whether instrument 2 is an exogenous instrument. The relevant statistic is the C statistic which is also called ...
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Testing the exogeneity of the subsets of instruments

Suppose that there is one endogenous variable and three instruments. The aim is to test whether instrument_3 is an exogenous instrument. The relevant statistic is the C statistic which is also called ...
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Correlation between the dependent variable and the instrument

In the case of a single endogenous variable and a single instrumental variable, the IV estimator is given by $b_{IV} = \frac{cov(z,y)}{cov(z,x)}$ It is often mentioned that "the instrument should ...
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Why does instrument exogeneity imply conditional mean zero?

On slide 14 here: https://www.uio.no/studier/emner/sv/oekonomi/ECON4150/v14/undervisningsmateriale/lecture16_instrumental_variables.pdf it says that "instrument exogeneity implies $E[u_i \mid Z_i]=0$" ...
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When is it justifiable to ignore explanatory variable endogeneity in a regression model?

I have three related questions: Is there a way to conduct a back of the envelop calculation that informs the reader on the degree of endogeneity we should have to bias the OLS estimates in a ...
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Set of instrumental dummy variables for a discrete endogenous variable - monotonicity assumption, overidentification and balance tests

One of the most recent critics to the 2SLS is that the instrument seldom fulfills the monotonicity assumption, that is, that the instrument should affect the instrumented variable in the same ...
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IV: Can I use different samples in first and second stages?

I want to run an IV regression, where in the first stage I use different sample (size) compared to the second stage. The approximate logic is as follows. I want to study how trading volume affects ...
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174 views

Endogeneity bias in cross sectional data

My supervisor asked to use 2SLS in thesis titled : Does Women's Autonomy affect child health survival" I used stata and found women's autonomy as endogenous variable, while women's education was ...
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Panel Data IV for a binary (one-time single cross) variable

I have a panel dataset. The endogenous variable is binary and has the following nature: single cross: change at most on time one direction change: only from 0 to 1 So, this endogenous variable $X$ ...
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Proliferation of Instruments in DPD GMM, with large T and small N

I want to estimate a dynamic panel data model, by using the GMM. To best of my knowledge there are two main estimators, the difference GMM and the system GMM. I am working with a long panel, my T is ...
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Optimal instrument in panel IV

I am estimating demand elasticity in panel data instrumenting log price with a cost variable. I have 3 versions of the model: In which I used the cost variable directly In which I used a log of the ...
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Is it true that if one coefficient in a linear model is endogenous, then any individual coefficient will be inconsistent?

This question is related to Bias of more than one endogenous variables, and I am essentially asking for some help regarding proving the results of the answer algebraically along with some related ...
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Instrumental Variable in Panel data

Assume that I have an endogeneity issue in my data and in my panel data is not balanced panel data ($T>N$). In this case, what are the most efficient panel estimation approaches when $T>N$?
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References Instrumental Variables

is anyone an well-informed about instrumental variable in economics ? I'd like to have a list of good papers or books (i don't know how to identify them) such that f i read and understand completely ...
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Instrumenting the Treatment in a Difference-in-Differences Design

I have come across a problem for which the CrossValidated archive did not provide an adequate answer. Consider that we estimate treatment effects in a fixed effects difference-in-differences design (...
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Is instrument variable valid if it affect endogenous treatment’s effect?

Let say I have a really simple model $y=x+controls+u$, x is the treatment and is endogenous dummy variable, and z is an instrument variable for x. I want to test the casual relationship between x and ...
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313 views

Testing for significant difference between coefficients from 2 different IV regressions (Stata or in general)

I'm running two different IV models in Stata that share the same DV and controls but have different instruments for the independent variable of interest. ...