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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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Cannot get goodnes-of-fit measures from ivprobit output (in ivprobit package)

I am using the ivprobit function from the ivprobit package in R. This ivprobit function is a binary regression with instrumental variables. However, I could not find a way to derive any goodness-of-...
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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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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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35 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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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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63 views

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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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
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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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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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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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1answer
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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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105 views

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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1answer
253 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 ...