Questions tagged [omitted-variable-bias]

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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: $y=\beta_0 +\beta_1 x_1 + ... + \beta_k x_k + \gamma q + \epsilon$ ...
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Can I use DiD for a RDD design? (treatment determined by threshold)

is it possible to apply a Difference-in-Differences method for a quasi-experiment that determines treatment by a threshold? All schools below a certain API rank are treated the rest is not (control). ...
Schwa97's user avatar
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2 answers
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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
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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
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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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Omitted Variables Bias and time-invariant variables

In empirical research, when working with panel data sets, it is common to include time fixed effects (e.g., year dummies) into your regression model to account for unobserved heterogeneity across time,...
Max'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 + ...
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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 ...
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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
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1 answer
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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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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 ...
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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 ...
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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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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
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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 ...
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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
128 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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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 ${(π‘Œ_i , 𝑋_{1,i} , 𝑋_{2,i} ): 𝑖 = 1, ... , 𝑛}$. You want to estimate the causal effect of $𝑋_1$ on $π‘Œ$. You first run a regression $π‘Œ_i = 𝛼_0 + 𝛼_1𝑋_{1,i} +...
gggg's user avatar
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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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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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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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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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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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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 answer
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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
25 votes
3 answers
2k 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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1 answer
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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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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
4k 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
2 votes
0 answers
124 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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