Questions tagged [omitted-variable-bias]
20 questions
25
votes
3 answers
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 to the confounding factor Z, I could conclude…
Franco
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8
votes
1 answer
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
$$
Y = \beta_{0} + \beta_{1}X_{1} + \varepsilon
$$
however, there is another variable…
gtoques
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7
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1 answer
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 causally related to both $X$ and $Y$ with a…
Rob G.
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7
votes
2 answers
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 if I don't put both I will suffer from omitted…
Maverick Meerkat
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3
votes
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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 how $R^2$ moves with the addition of controls as…
Steve
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3
votes
2 answers
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 logit setup,
$$Y = \mathbf{1}\{\beta_0 + \beta_1A +…
Pburg
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2
votes
1 answer
Trade-off between omitting variables or dropping observations in multivariate logistic regression
Say you are selecting $n$ observations from a complex survey of $N$ individuals to create an analytical sample of relevant observations; and that you intend to fit a binomial multivariate logistic regression to the data, where:
$$
Y = \beta_0 +…
atuin
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2
votes
1 answer
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 {( , , ): = 1, ... , }. You want to estimate the causal effect
of 1 on . You first run a regression = 0 + 1i + i and get the following result:
where the numbers in parentheses are standard errors.
Now, suppose…
gggg
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2
votes
0 answers
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 (exogenous) instrument $z_1$, that is only expected to…
Tom
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2
votes
1 answer
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
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2
votes
0 answers
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 dependent variable of interest, "service time per…
Mr. A
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1
vote
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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 with insignificant (p < .05) variables then do I…
rabito
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1
vote
1 answer
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 overwhelming issue, OVB would be a stronger one,…
Michael
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1
vote
1 answer
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 $X_2$ into account:
$Y=\beta_0 + \beta_1 X_1 + \beta_2…
robertspierre
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vote
2 answers
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 struggling to construct an example. If it is possible,…
Data
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