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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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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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Ramsey's RESET test vs Rainbow test for omitted variable bias tests

I am trying to provide some statistical proof about the omitted variable bias in my regression model. I have used the following two omitted variable bias tests for this purpose: (1) Ramsey's RESET ...
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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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2SLS in Fuzzy Regression Discontinuity

What is the logic of conducting an IV-2SLS in Fuzzy Regression Discontinuity Design? Why can't we run a regression just like in Sharp RD?
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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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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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294 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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143 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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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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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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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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25 views

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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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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Logistic regression including instrumental variable (“ivprobit” in R) has coefficients with much reduced significance

I am trying to run a logistic regression including instrumental variables by using "ivprobit" function in R from the package called "ivprobit". If I do not include the instrumental variable, the "glm"...
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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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51 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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47 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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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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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 ...
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Meta analysis of multiple IV-regressions

For simplicity let us consider a single output Y and a single endogenous regressor of interest S. Suppose we have run multiple experiments over different periods in time, where we in each experiment, ...
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Why not use instrumental variable directly as a covariate in the regression?

I know this is a silly question, as I know the theory of instrumental variables and two stage regression. Still, I never saw a clear answer to the following: assume you have endogeneity due to ...
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Is this causal effect identifiable? It includes a mixture of observational and interventional data with selection effects

The DAG of the model is below. We wish to estimate P(attitude | do(exposed)). moving up from the bottom of the dag: we ...
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Instrument only relevant for endogenous subsample

I have a panel of person-year observations and I run the following regression reg y x where y is some measure of a person's performance in a certain project in a ...
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43 views

Instrument systematically underpredicting endogenous variable based on values of outcome variable

Consider the following linear regression model: $$ y_{i}=x_{i}\beta+\epsilon_{i} $$ In the above, the error term is not conditionally mean independent of $x_{i},$ that is $\mathbb{E}\left(\epsilon_{i}|...
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Bootstrap confidence interval for just-identified IV estimator

Assume we have a regression model \begin{equation} y_{i} = z_{i}' \delta + \epsilon_{i} \end{equation} with dependent variable $y_{i}$, L regressors $z_{i}$ and K instruments $x_{i}$, and assumptions ...
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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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1answer
91 views

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 ...