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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19 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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55 views
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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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How can I get goodness-of-fit measures for “ivglm” from “ivtools” package in R?

I am trying to get the goodness-of-fit measures, such as R-square, chi-square, etc. from the "ivglm" code in the "ivtools" package in R programming. However, I could not find a way to get these from ...
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19 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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17 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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17 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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19 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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13 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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5 views

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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12 views

Hausman test statistic - to multiply or not to multiply by n

I am having some serious doubts regarding the formula of the Hausman statistic for the case in which I compare OLS and IV estimates. I am getting confused with what my references are giving me. What ...
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8 views

Marginal Treatment Effect with a continuous treatment variable

I am totally new to the concept, but I would like to apply a MTE estimation within the following simultaneous equation model (if it is even possible) : \begin{cases} Y_i = \alpha_0 + \alpha_1. A_i + ...
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Exogenous/control varible not include in IV when runing reg3

I have the following two-equation system. $$y_1=c_{10}+c_{11} y_2+c_{12} x_1+c_{12} x_3+e_1$$ $$y2=c_{20}+c_{21} y_{1}+c_{22} x_2+c_{23} x_3+e_2$$ where, $y_1$, $y_2$ are endogenous variables, $x_1$,$...
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Does direction of causality between instrument and variable matter?

The standard scheme of instrumental variable in terms of causality (->) is: Z -> X -> Y Where Z is an instrument, X ...
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31 views

The Durbin-Wu-Hausman test and its interpretation

I'm currently working out the interpretation of a Durbin-Wu-Hausman test. I have a linear regression which regresses the body mass index of an individual, "BMI", on different variables such as the ...
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Correction function to correct endogeneity without instrumental variable

What happens if the disturbances are divided into residuals? This could be a solution to correct endogeneity without instrumental variable?
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8 views

overidentification test

Dears, i have to run overidentification test using ivreg. the summary gave me this result: Diagnostic tests: df1 df2 statistic p-value Weak instruments 1 45 45.158 2.65e-08 **...
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12 views

Endogeneity Problems without instrumental variable

Before Philip G. Wright proposed the method of Instrumental Variables in 1928 as solution to endongenity problems, how did econometricians and statisticians solve economics models with endogeneity? ...
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39 views

Unbiasedness of Intrumental Variable Estimator

is instrumental variable estimator unbiased in the case of stochastic regressor X and how can i show this? (I know how to show consistency, i need to show unbiasedness)
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32 views

How to interpret the tests for weak instrument in R?

Stock & Yogo (2005) provide the rule-of-thumb that the first-stage F-test of an IV regression should be above 10 for the bias of the instrument to be less than 10%, and suggest to call weak an ...
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Why ivmodelFormula and ivmodel give different results in R?

I stumbled upon an issue with the ivmodel package: when exogenous covariates are included in the model, the ivmodel function ...
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16 views

Treatment effect on the non treated if there are no never-takers and no defiers

$Y$ is my outcome variable, $D$ is the treatment, $Z$ is the instrument, $Y_i$ is the outcome when $D=i$, $D_i$ is the treatment when $Z=i$ I don't understand the following result : when ...
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14 views

Direction of bias when changing from OLS to IV

If when using an instrumental variable it increases the size of the coefficient and changes the direction of the relationship compared to OLS --> what direction of bias does it suggest in the OLS ...
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Simulation in Stata: instrumental variables with endogenous nonlinear regressor

I'm doing an exercise from Microeconometrics Using Stata, by Cameron and Trivedi, Exercise 11 of Chapter 6 (page 204). "When an endogenous variable enters the regression nonlinearly, the obvious IV ...
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Intuition for Instrumental Variable estimator in Linear Regression Model

Suppose we have the linear regression model given by $y=X\beta+\epsilon$, but we have a violation of assumptions where $X$, the regressor matrix, and $\epsilon$ are correlated. Also, suppose there is ...
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How to find an instrumental variable

Let's consider the linear model with endogenous errors: $$ y_t = \beta x_t + e_t $$ with $E[x_t e_t] \neq 0$. How do we find in practice an instrumental variable (IV)? i.e. a variable $z_t$ that ...
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How to think of compliance (and IV and LATE) in phase-in RCT designs

How should we think of compliance in a phase-in RCT design? What are the assumptions recovering the LATE by instrumental variables in this case? Details: In a traditional (simultaneous) RCT, in case ...
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75 views

F-statistic in two-stage least-squares with many instruments

There is this rule of thumb that the first stage F-statistic should be >10 in instrumental variable analysis to rule out weak instruments. Is this "rule" for one instrument only or also valid if I ...
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Instrumental Variables with Missing Observations in the Endogneous Regressor

I have 10k observations for a dependent variable $Y$ and an endogenous regressor $X$ with many missing observations (90%). I also have an instrument $Z$ without missings. I know that the values for $X$...
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Dealing with endogeniety in an entire regression

I am using OLS to test the statistical significance of a state-wide(US states) sentiment variable that was calculated based on Twitter data. I use macro-variables(gdp, unemployment etc.) as controls. ...
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How do I use GAMs in instrumental variable analysis?

I have an outcome $Y$, a risk factor $X$, and an instrument $Z$. In a two-stage least squares (2SLS) setting, the first stage is $$ X=Z + \varepsilon $$ and the second stage uses predictions from ...
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Interpreting the relationship between my instrumented variable (X1), X2, and Y (IV regression)

I have run an IV regression with a dichotomous outcome (Y) and my endogenous ("instrumented") regressor (X1) is also dichotomous. I am assessing whether continuous variable (X2) is moderating the ...
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Comparing raw and log-transformed regression coefficients

I'm attempting to perform a power-calculation for a two-sample Mendelian randomization study using genome-wide association study (GWAS) summary statistics, with a binary outcome [http://cnsgenomics....
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357 views

Does the Heckman correction with an exclusion restriction provide causal inference?

I think I might be getting instrumental variables estimation and the Heckman correction with an exclusion restriction confused. I know that instrumental variables estimation is way to show causal ...
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1answer
167 views

Does the direction of correlation matter for Instrumental Variable?

For a valid instrumental variable: (1) the instrument must be correlated with the endogenous explanatory variables, and, (2) the instrument cannot be correlated with the error term in the ...
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10 views

Instrumental variables and GARCH

Can you use the predicted value from the first stage (as estimated using 2SLS) to replace the endogenous variable in a GARCH model? Or, what would be a different way of using instrumental variables in ...
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31 views

Bias/variance of IV estimation

I'm studying IV estimation by myself and have some confusion about the basics. Let $y=X\beta_0 + u$ be a linear model with endogenous variable $X$, and $Z$ be an instrument, meaning that $Z$ and $u$ ...
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33 views

Interpreting results of a placebo test

I am using an instrumental variables model to analyze the impact of internet use on hours worked. As part of my analysis, I conduct a placebo test using data from the pre-internet era. Unfortunately,...
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1answer
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Is the IV approach applicable to endogenous count variable in a linear regression?

In a linear regression setting, one of the regressors (independent variables) is endogeneous. However, strictly speaking it is not continouus, but a count variable. A continouus instrumental variable ...
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Overidentified vs just identified models

Why go with overidentified models as opposed to just-identified? If you can go with over-identified models, how many instrumental variables can you have at max in a 2SLS model?
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Instrumental variables - alternatives to 2SLS: not using exogenous variables in the first stage

I think that everyone knows how 2SLS works. say that we have: $y_t=a_1 +a_2X_t+a_3W^1_t+a_4W^2_t+e_t$ Let's call this equation equation (1), where $X_t$ is an endogenous ...
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Different standard errors from ivreg and ivregress 2sls commands

In stata 15, I accidentaly used the command ivreg without specifying 2sls. In the output, it declared that 2sls was being used so I proceeded. However, later when double-checking my results I used the ...
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32 views

Instrumental Variables for Foreign Direct Investment

I'm trying to estimate a fixed-effect regression model. Basically my Y is tertiary education enrollment (I'm trying to see the effect of FDI investment in host country, to the extent that whether ...
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Convergence in distribution of the $2SLS$ estimator for some $\pi = \frac{h}{\sqrt{n}}$

Consider the following IV model. $$y_{1,i} = y_{2,i} \beta + u_i$$ $$y_{2,i} = z_{i}' \pi + v_{2,i}$$ with $(z_i', u_i, v_{2,i})$ iid and $\begin{pmatrix} u_i \\ v_{2,i} \end{pmatrix} \sim N(0_{...
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17 views

Would my exclusion restriction be satisfied with this instrument?

I want to estimate the impact of home internet use on hours worked. Due to endogeneity concerns, I was thinking to use an IV approach. One instrument I have seen in similar literature and was ...
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25 views

Instrumental variable predicts endogenous variable in an unexpected direction

I am trying to estimate a causal relationship between two variables. I'm concerned about endogeneity, so I'm using an instrument. The instrument strongly predicts the endogenous regressor, however it ...
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90 views

What 'level' of fixed effects should I be using?

I'm trying to see the impact of using the internet at home on individuals' hours worked. To address endogeneity concerns, I am using terrain slope as an instrument, as slope makes it more costly for ...
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1answer
55 views

Derivation of IV estimator using Linear Algebra

Im aware of the question Derivation of IV estimator? on this site. Im interested however in obtaining the way we derive it using linear algebra. $$\beta^{IV}=(Z'X)^{-1}Z'Y$$ the reason why I ask ...
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IV with LIML yield Zero cefficients

I am using stata to run "IVREG LIML" which is a 2sls with Limited Maximum Likelihood estimator. However, some of the coefficients are zeros with p-value equal 1. I wonder what cause this issue. I ...
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43 views

Error Using Interaction Effect Between Individual and Time Fixed Effects

I am trying to run a two-way fixed effects model with an instrument using the plm function: ...
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5 views

Higher moments / internal IV regression

I have a set of data and am trying to look at the relative importance of two different variables in predicting an outcome: $Y \sim X_1 + X_2 + \epsilon$ but the variable $X_1$ is endogenous and ...