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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Simulating a bimodal biased IV estimator

How can I simulate a bimodal biased IV estimator? The common unimodal heavy-tailed biased estimator would be something like this: ...
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30 views

Estimating finite sample bias for Instrumental Variables

Are there ways to estimate the finite sample bias with instrumental variables? I guess this would be conditional on assuming some structure to the problem and also would involve simulation, but, at ...
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52 views

probit two stage least squares

I was told that it's possible to run a 2 stage iv regression where the first stage is a probit and the second stage is an OLS. Is it possible use 2sls if the first stage is a probit but th second ...
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13 views

Standardized coefficients and IV method

In a multivariate regression, suppose we want to calculate the metric coefficients from the standardized ones. Is the method (standardized coeffcient times standard deviation of the dependent ...
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21 views

MLE or instrumental variables

I'm trying to estimate a model in which one of the explanatory variables is correlated with the error term. As I see it there are two alternatives, specify the likelihood function and maximize it to ...
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80 views

How do instrumental variables address selection bias?

I'm wondering how an instrumental variable addresses selection bias in regression. Here's the example I'm chewing on: In Mostly Harmless Econometrics, the authors discuss and IV regression relating ...
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33 views

2-stage Heckman instrumental variable estimation

I am working on my thesis. My main regression model is the following: $Y=x_1*{\rm Payment}+x_2*{\rm Country}+x_3*{\rm Industry}...$ All independent variables are dummy / binary variables. In a next ...
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58 views

Estimated standard errors for weak instrumental variable

I would like an explanation on the statement in bold below. At first glance, I'd think that a weak instrumental variable would yield a even bigger standard error estimate. "When instruments are ...
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31 views

How to run a instrumental variable regression for the dependent variable

probably a very stupid question but I did not find any solution so far: I would like to test the following: If performance was bad in t-1 ($per_{t-1}$), then managers increase risk ($\Delta risk_t$) ...
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1answer
64 views

Optimal weighting matrix instrumental variables estimator

The formula for the optimal weighting matrix when you perform regression with more instrumental variables than endogenous predictors is the following: $W_{opt} = (\frac{1}{N}Z'Z)^{-1} $ This tells ...
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1answer
55 views

Testing for weak instrument: include intercept in regression of instrument?

When you want to use the IV (instrumental variable) estimator, you typically first test if you have a strong instrument. You do so by regressing the (endogenous) predictor against the instrument. ...
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48 views

Testing “weak” instruments - F test

I would like to address the endogeneity problem in my model. Let me go step by step. I have panel data for 19 countries, 1995-2010. My regression model: ...
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23 views

Adjusting regression for correlated errors-in-variables

I have a set of data points $\{x_i\}$. These data points are grouped so that (say) $i\in\{1,2,3\}$ is group $A$, $i\in\{4,5,6,7\}$ is group $B$, etc. I would like to test the null hypothesis of no ...
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How do you determine if an instrumental variable is randomly assigned?

For an IV to be valid, it must be: Randomly assigned Correlated with the endogenous variable in the model Uncorrelated with the dependent variable in the model What does the random assignment of ...
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73 views

Use of different outputs in a meta-analysis?

I'm interested in performing a meta-analysis of instrumental variables analyses from a handful of different studies, asking for the same set of model results from all study investigators. However, at ...
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84 views

IV (2SLS) with ordered/binary dependent and endogenous variable

thanks for taking time to read this first of all. I am looking for an IV procedure if the endogenous variable is binary or ordinal (0 to 5). I see the problem of using 2SLS if the endogenous variable ...
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146 views

Instrumental variables and mixed/multilevel models

I want to estimate a growth model to model the growth trajectories of individuals $j$ over multiple time points $t$ by applying a standard mixed/mutilevel model (also known as random coefficient ...
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1answer
72 views

IV estimator: efficient implementation?

I would like to implement (in R) an instrumental variable (IV) estimator, that takes the most general form (here not 2SLS or GMM!): $$ \beta_{IV} = (Z'X)^{-1}Z'Y $$ I could code this in the naive ...
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1answer
1k views

Fuzzy regression discontinuity design in Stata

I am currently running computations through a "Fuzzy" Regression discontinuity Design. Suppose my data are in the following form: $Z$: assignment variable; if $Z > Z_0$ then the person is ...
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1answer
191 views

Applying Frisch-Waugh-Lovell theorem to IV regression in R

I am estimating an instrumental variables linear regression that has a large number of indicator (factor) variables. I don't particularly care about the coefficient estimates on those indicator ...
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67 views

valid instrument for oil consumption in IV model

I want to run a gdp vs. oil consumption model where oil consumption is suspected to be endogenous - correlated with the error terms. Can a variable correlated with world oil price but not with the gdp ...
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110 views

Derivation of IV estimator?

Assume, the model we are trying to estimate is: $Y=\beta_ß+\beta_1X+U$ where x and u are correlated: $Cov(X,U)\neq 0$ Then OLS is inconsistent: ...
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422 views

Econometrics: Sargan test

Here are 3 questions about econometrics and R codes. Test the endogeneity of the variable EDUC: ...
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4answers
3k views

What do “endogeneity” and “exogeneity” mean substantively?

I understand that the basic definition of endogeneity is that $$ X'\epsilon=0 $$ is not satisfied, but what does this mean in a real world sense? I read the Wikipedia article, with the supply and ...
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2answers
161 views

Where do I put the control variables in 2SLS?

When I am running a 2 stage least squares, where do I put the control variables? Should I put the control variables in the first stage? The second stage? Both? Can someone explain why?
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262 views

Testing for weak instruments in panel data

Suppose I have hierarchical data such as students clustered into classrooms. I want to use a two stage least squares regression with an instrument that affects students at the classroom level to test ...
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1answer
217 views

Limited Information Maximum Likelihood (LIML) estimation in R?

Curious whether anyone knows a package, or has written an implementation themselves, for conducting instrumental variables regressions using LIML in R. All of the R packages I have seen for IV ...
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205 views

Discussion about proxy- and instrument variables and endogeneity in the context of a multi equation model

Assume two equations $Y_1 = X_1\beta_1 + X_2\beta_2 + U_1$ $Y_2 = X_1\alpha_1 + X_2\alpha_2 + U_2$ Further assume that $ \ U_1 = X_4 + E_1$ and $U_2 = X_4 + E_2$ with $ \ corr(Y_1,X_4)\ne 0, \ \ ...
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Question about Hausman-test for endogeneity with two endogenous regressors with potential heteroscedasticity

First question: Is the following example of computing the Hausman-test for endogenity with two endogenous regressors adequate? Second question: Is it true that in case of heteroscedasticity, i.e. ...
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1answer
109 views

First stage of TSLS and the matrix of instruments W

If we assume we have 2 equations and each equation contains the other dependent variable. $y_1 = \beta_0 + \beta_1 y_2 + \beta_2 z_1 + u_1$ $y_2 = \alpha_0 + \alpha_1 y_1 + \alpha_2 z_2 + u_2$ For ...
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290 views

When are the asymptotic variance of OLS and 2SLS equal?

Assume the model $ \ y = X\beta + u \ $ with $\ W \ $ is a $ \ n\times l \ $ so called matrix of instruments. The following assumptions hold. There is a law of large numbers (LLN) for 1.,2.,3. and ...
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387 views

Mixed thoughts about the Durbin-Wu-Hausman Test. Is it really feasible?

I just studied (again) some statements of the DWH test. After I thought about the theory behind the DWH test, is it not basically kind of useless since I cannot tell if there's actually a problem ...
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170 views

Definition of “optimal” instruments

The book I read (Davidson,MacKinnon - Econometric Theory and Methods) describes the definition of "optimal instrument variables" as the following: Usually, and this is seen very often in other ...
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185 views

Limiting distribution of Hansen Sargan J statistic

I was reading about instrumental variables, where I found description of the Hansen Sargen J statistic. The model is the usual $y=X\beta+\epsilon$, where $X\in \mathbb{R}^{N\times K}$, ...
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76 views

Are variables, which linear combination results in a endogenous variable, endogenous?

I'm a little bit confused.... Lets say I assume $x$ to be endogenous and I observe that $x = a v_1 + b v_2 + c v_3$ so that $x$ can be expressed as the perfect linear combination of $v_1, v_2, ...
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179 views

When we are dealing with instrumental variables is this correct?

If I'm to find an instrumental variable for an equation, am I getting this idea right? I have this regression: ...
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105 views

Two-stage least squares approach to Deming regression

I am interested in statistical inference for the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are nonrandom fixed numbers, ...
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Comparing fuzzy RD estimates to an “OLS” analogue

In IV, I've sometimes seen the estimates compared to OLS to give a sense of how the LATE may compare to ATE. What would the analogue be in fuzzy RD? What is the benchmark estimate? I'd imagine ...
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430 views

Fuzzy regression discontinuity design and exclusion restriction

In a fuzzy regression discontinuity design, what does the exclusion restriction look like in terms of a conditional expectation between the instrument in the first stage and the error term in the ...
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1answer
729 views

How to do an instrumental variables regression with an instrumented interaction term in Stata?

I'm having a bit of a problem with Stata syntax. I need to do the following regression: $$y = ax + bz + c(xz) + e$$ where both $x$ and $z$ are instrumented and also the interaction term $xz$ uses ...
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186 views

How to account for a regressand affecting a regressor?

I forget the terminology, but this happens when you regress, say, $Y$ on a list of variables, and you suspect that $Y$ affects, say, $x_3$ in addition to $x_3$ affecting $Y.$ I forget how this is ...
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126 views

Legitimate IV for panel?

In a panel regression using fixed effects, is it correct to use an instrument that does not vary by year? To use an old but simple example, Angrist and Kruger 1991 use quarter of birth as an ...
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1answer
358 views

Is there any identification assumption for IV?

I am asking this because I know there are IA's for cross sectional estimators and D-in-D estimators, but am unsure if there are any for IV estimation. Does anyone know if there is or isn't, and if ...
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1answer
173 views

Being totally stuck at my master thesis: cant figure out this 3 equation SEM

I got smth which looks like this $y_1 = \alpha_1\cdot y_2 + \alpha_2\cdot y_3 + X\cdot\alpha_3 + u_1$ $y_2 = \beta_1\cdot y_1 + \beta_2\cdot y_3 + X\cdot\beta_3 + u_2$ $y_3 = \gamma_1\cdot y_1 + ...
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3answers
582 views

Random assignment: why bother?

Random assignment is valuable because it ensures independence of treatment from potential outcomes. That is how it leads to unbiased estimates of the average treatment effect. But other assignment ...
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3answers
249 views

Formal definition of random assignment

I am looking for a formal definition of random assignment. Let $\mathbf{Z}$ be a vector of treatment assignments in which each element is 0 (unit not assigned to treatment) or 1 (unit assigned to ...
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57 views

Linearity and ordinal variables in nonparametric setting

I am using the np package in R with the npregiv command. The program is in beta, and I cannot call ordered(var) on one of my instruments (a bug in the program I am ...
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58 views

About Identification in a 3 equation SEM

I got this example and I was wondering about a certain statement: $$ \begin{aligned} y_1 &= \alpha_{12}y_2 + \alpha_{13}y_3 + \beta_{11}z_1 + u_1 \\ y_2 &= \alpha_{21}y_1 + \beta_{21}z_1 + ...
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343 views

How do I identify this simultaneous equations model?

I have the following model (which is in this form is not identifiable if the $y$'s are indeed endogenous): (1) $y_1 = a_0 + a_1y_2 + a_2y_3 + \boldsymbol{Xa} + \boldsymbol{u}$ (2) $y_2 = b_0 + ...
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Average Structural Function Calculation

EDIT: I have solved this problem myself. The problem with the simulation below is that the omitted variable should not be included in the 'true model'. I have written a blog post with a more detailed ...