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Questions tagged [omitted-variable-bias]

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A model suffering from omitted variable bias can be said to be unidentified?

If my regression model $$ y_i = \alpha + \beta x_i + \epsilon_i $$ suffers from OVB the error contains one variable which we assume correlated with $$ \epsilon_i = \gamma w_i + u_i $$ my estimate of $\...
Three Diag's user avatar
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Under what conditions are the remaining coefficients of a regression with a variable omitted "scaled" relative to those in the complete regression?

I was reading this article that discusses the impact of ommitting variable from a regression equation, and analyzes the impact it will have. Here is some notation they use: given a data matrix $X$, ...
Paul's user avatar
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How to deal with possibly important predictors omitted during the building of an OLS multivariate linear regression model?

I am building a descriptive model using OLS multivariate linear regression. I have a couple dozen candidate predictors, but only around 200 cases. Since I wanted at least 10 cases / variable for the ...
jorvaor's user avatar
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Endogeneity or omitted variable bias in a causal model

I am estimating a regression of the form: My variable of interest is "X1", and based on the information here I can confidently say that the goal of my analysis is a causal inference. Now to ...
mpinzonc's user avatar
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Specific question about the effect of an omitted variable on a regression model

Suppose an independent variable that is influential in the data generating process for some dependent variable is omitted. The omitted variable has the following characteristics: It is NOT correlated ...
Patrick C's user avatar
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Expression for Omitted Variable Bias in Particular Coefficient [duplicate]

Suppose the true model is $y_i=\beta_0+\beta_1x_{1i}+\beta_2x_{2i}+\epsilon_i$, but $x_2$ is not observable. If we run a regression instead on the model $y_i=\beta_0+\beta_1x_{1i}+\eta_{1i}$, what is ...
user624173's user avatar
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Endogenous omitted variable in the model

If I know about an omitted variable in the regression and the data for it is available. But I also know that this omitted variable is endogenous, because the dependent variable and the omitted ...
Marlon Brando's user avatar
2 votes
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Why is there a negative bias in this example of omitted variable bias?

I was learning the mechanics of omitted variable bias in the context of linear regression. I built the following simple model with R: ...
Bobby's user avatar
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How to prove OLS estimator still unbiased if omitted variable(s) are independent of included variables

Using the usual matrix notation for Ordinary Linear Regression, suppose for $X_{n\times p}, Y_{n\times1}, B_{p\times1}$ and $e\sim MVN(0,I_{n\times n})$, we know the 'true' relationship is: $$Y=XB+e$$ ...
Eric's user avatar
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biased estimation of variable correlated with endogenous variable

I have the following model: $ X = \alpha_1 + aZ + \epsilon_1 \\ Y = \alpha_2 + bZ + cX + \epsilon_2 $ Suppose that $Z$ is randomly assigned but $X$ is correlated with the error term $\epsilon_2$, in ...
Eaman's user avatar
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Omitted variable bias: 3 correlated variables and 1 omitted (R simulation)

I get weird results when trying to analyze omitted variable bias in R. If I try to analyze the bias for coefficient $\beta_j$ of variable $x_j$ in case of one omitted variable from set of two ...
Athaeneus's user avatar
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Test an instrument's correlation with unobservable when it's redundant in structural equation

I'm working on Wooldridge's โ€œEconometric Analysis of Cross Section and Panel Dataโ€ and I don't fully get why this test would not work. I'll share my work with screenshots so it's clearer hope that's ...
Facundo Arcusa's user avatar
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1 answer
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Model without interaction terms: how wrong is it?

Suppose we have the following DGP: $ y = 10 x_1 + 20 x_2 + 30 x_1 x_2 $ Suppose we sample from the population, and we estimate the following models: $ y = \alpha_1 x_1 + \beta_1 x_2 $ $ y = \alpha_2 ...
robertspierre's user avatar
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How is the omitted variable bias formula derived?

I see it is often quoted that the omitted variable bias formula is $$ \text{Bias}\left(\widehat{\beta_1}\right) = \beta_2 \cdot \text{Corr}\left(X_2,X_1\right) $$ where $\widehat{\beta_1}$ is the ...
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Omitted variable problem

I'm studying the cases in which the endogeneity problem arises in OLS regression. Suppose we have the following population equation: $y=\beta_0 +\beta_1 x_1 + ... + \beta_k x_k + \gamma q + \epsilon$ ...
John M.'s user avatar
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What would it take for the omitted-variable bias from multiple omitted variables to cancel out?

Let's stick to ordinary least squares linear regression for now, and assume the typical conditions for the Gauss-Markov theorem. If it is helpful to assume Gaussian errors, that's fine. In such a ...
Dave's user avatar
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Omitted variables problem

I'm studying the omitted variables problem. My model is: $E[y|x_1,x_2,...,x_k,q]=\beta_0+\beta_1x_1+...+\beta_k x_k + \gamma q$ From the first equation, I write the population model as $y= \beta_0+\...
John M.'s user avatar
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Comparing IV and OLS results to get infomation about the omitted variable correlation

Very often in seminars people compare the (biased because of endogeneity) results of their OLS estimation with those (unbiased) from an IV strategy estimation. Assuming everything is ok with the IV ...
Francesco Armillei's user avatar
2 votes
1 answer
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Difference between the concept of omitted variable bias in econ and epidemiology/social sciences (Elwert and Winship)

I am currently reading the article by Elwert and Winship's Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable. However, I am however quite perplexed by the definition of ...
Lydia Palumbo's user avatar
1 vote
2 answers
266 views

control "for post-treatment" variables vs omitted variable bias

in chapter 9 of gelman's data analysis using regression and multilevel/hierarchical models, page 170 presents a simple example on the bias of an omitted variable $x$ from a regression of an outcome $y$...
Palace Chan's user avatar
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Does Omitted Variable Bias Matter for Prediction? [duplicate]

In the context of linear models, I can see why omitted variable bias may matter, as often we are interested in causal effects. In the context of time series models, we are often interested in ...
Student's user avatar
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Variance of linear regression model with omitted variable bias

Suppose we have the following data generation process: \begin{align*} U &= N_{U}\\ X_{1} &= \alpha_{1}U + N_{1}\\ X_{2} &= \alpha_{2}U + N_{2}\\ X_{3} &= \alpha_{3}U + ...
Sergio's user avatar
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2 votes
2 answers
591 views

Adjusting for confounding in linear regression model

I am wondering how would the slope and intercept change after adjusting for a confounder factor. After adjustment, would the slope be lower, or higher, and the value for the intercept? Is there any ...
COCONUT's user avatar
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1 answer
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Does omitted variable bias affects coefficients for those variables that are not correlated with the error term? (When their is one variable that is)

Does omitted variable bias affects coefficients for those variables that are not correlated with the error term? (When there is one variable that is.) I found two answers, but they appear to be ...
Richard Boylan's user avatar
1 vote
1 answer
77 views

My instrument (z) only affects y through x, but y affects z directly. Is my instrument valid?

I'm running a regression model to test whether unionisation rates have an impact on wages. I've introduced an instrumental variable: public support for unions. As far as I can tell, this instrument ...
fredhill_'s user avatar
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247 views

Question about statement in Oster (2019): variation in a control

In Oster (2019), she discusses how authors typically include controls and examine coefficient stability as a way to test for presence of confounding, and points out that researchers should consider ...
Steve's user avatar
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Do insignificant variables result in a specification error?

I am trying to understand omitted variable bais better. I know that it detects irrelevant variables, but are irrelevant variables and insignificant variables synonymous here? If I have a regression ...
rabito's user avatar
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4 votes
2 answers
391 views

Using a DAG to understand omitted variable bias in OLS vs Binary Dependent Variable Regression

Suppose I have three variables. $A$ and $U$ are continuous variables but $U$ is unobserved. $Y$ is the binary outcome. $A$ and $U$ are independent. Let the true model be from the typical probit or ...
Pburg's user avatar
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Instrument validity: does a positive and significant coefficient on Z in a regression of Y on X and Z pose a problem?

I have an initial regression of Y on X and Z. Both of my coefficients on X and Z are non-zero and strongly statistically significant. X and Z are correlated but I am told collinearity shouldn't be an ...
Michael's user avatar
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2 votes
1 answer
47 views

Should I adjust for a confounder when it is colinear with a predictor?

Suppose the DAG in the population is as follows: We observe both $X_1$ and $X_2$. We are interested in the effect of $X_1$ on $Y$. We want to use OLS to estimate the relationship. Now if I take $X_2$ ...
robertspierre's user avatar
2 votes
1 answer
200 views

Trade-off between omitting variables or dropping observations in multivariate logistic regression

Say you are selecting $n$ observations from a complex survey of $N$ individuals to create an analytical sample of relevant observations; and that you intend to fit a binomial multivariate logistic ...
atuin's user avatar
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0 votes
1 answer
389 views

VAR model variable selection

I'm required to use two time series models in my exam project. I want to use a stock price of an energy company, and then explain it first using ARIMA, and then adding other variables and using VAR. ...
Rakamakafon's user avatar
1 vote
2 answers
206 views

Is omitted variable bias possible with a perfectly correlated dependent and independent variable?

Suppose $X$ and $Y$ are perfectly correlated, and we fit a model $Y=a+bX+\epsilon$. Is it possible that there would be omitted variable bias in this situation? Intuitively, I think so, but I'm ...
Data's user avatar
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3 votes
2 answers
726 views

How to test whether OVB by examining two regressors (X_1, X_2) using hypothesis test with null hypothesis H0: corr(X_1,X_2) = 0

Suppose you have an i.i.d. sample ${(๐‘Œ_i , ๐‘‹_{1,i} , ๐‘‹_{2,i} ): ๐‘– = 1, ... , ๐‘›}$. You want to estimate the causal effect of $๐‘‹_1$ on $๐‘Œ$. You first run a regression $๐‘Œ_i = ๐›ผ_0 + ๐›ผ_1๐‘‹_{1,i} +...
gggg's user avatar
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10 votes
1 answer
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Difference Omitted Variable Bias and Confounding?

Is there a difference between omitted variable bias and confounding bias in linear models? To my knowledge, when investigating the causal effect of $X$ on $Y$, a confounder is a variable $Z$ that is ...
Rob G.'s user avatar
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0 votes
1 answer
658 views

Endogeneity coming from omitted variable vs measurement error

Can someone explain more clearly what is a measurement error and how is it different from omitted variable. I know the theoretical implications, but I don't really know how to tell which problem I'm ...
LFG's user avatar
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9 votes
1 answer
2k views

Omitted Variable Bias (OVB) and multicollinearity

In a linear regression model, the reason we control for variables is to prevent the omitted variable bias (OVB). That is, suppose we are trying to fit the model $$ Y = \beta_{0} + \beta_{1}X_{1} + \...
gtoques's user avatar
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2 votes
0 answers
43 views

Derivation of Neuhaus, Jewell(1993)

I wish to ask a derivation problem in Neuhaus, Jewell(1993) - "A geometric approach to assess bias due to omitted covariates in generalized linear models" The statistical True model dealt in ...
Kyuseong Choi's user avatar
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0 answers
21 views

Question about regression and deriving omitted variables

usually when I see derivations of ommited variable bias, I see something of the sort: from y=xb + $\eta$, and looking at the for formula for the slope estimate: $cov(x,y)$$/var(x)$ $cov(x,xb+\eta )$$/...
Steve's user avatar
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2 votes
0 answers
60 views

Using an IV when there is more than one omitted variable

I am trying to estimate the following model: $$y=B_0 + B_1x_1 + B_2x_2 + B_3x_3 + e$$ However, I have an omitted variable bias because $x_2$ and $x_3$ are not observed. Situation 1 If I have an (...
Tom's user avatar
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1 vote
1 answer
368 views

Omitted variable bias in ordered logistic regression query

Including too few variables in OLS regression means that the coefficient estimates can be biased, e.g. if we aren't controlling for a variable in a model that should be there, it is instead captured ...
user avatar
26 votes
3 answers
3k views

Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)

I'm a rookie with statistics, and I'm struggling to understand this: it is well known that a confounding factor can cause a spurious association, leading to rejecting a true null hypothesis (i.e. due ...
Franco's user avatar
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3 votes
1 answer
2k views

Does confounding always imply endogeneity?

I'm a bit confused with the definitions regarding causal inference. My question is whether we can call measured confounding an endogeneity problem?
Anita 's user avatar
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0 answers
189 views

Are coefficients that are zero omitted variable bias?

If a regression coefficient is essentially zero, doesn't that imply that there is (massive) omitted variable bias? That is, the change must then exist in the error term. The classic definition of OVB ...
Frans's user avatar
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10 votes
2 answers
5k views

Omitted variable bias vs. Multicollinearity

There's seems to be a bit like catch 22: suppose I am doing linear regression, and I have 2 variables that are highly correlated. If I use both in my model, I will suffer from multicollinearity, but ...
Maverick Meerkat's user avatar
3 votes
1 answer
142 views

Can an omitted random variable cause "omitted variable bias"?

Suppose we have a linear regression: Y = mx + b where X is the independent variable of interest, in this case "scoops of ice cream per order" at an ice cream shop, b is the error term, and Y is the ...
Mr. A's user avatar
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