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14 questions · 1 formulas

Omitted variable bias — two conditions

Bias if Z affects Y AND Z is correlated with an included X

Trap: Only one condition → no bias.

Omitted Variable BiasD–A level★ High priority — official Canvas example

If an omitted variable is a determinant of Y, when is the OLS estimator of included X biased?

→ D) The OLS estimator is biased if the omitted variable is correlated with the included variable.

Canvas Example MCQ — Q75

A) You cannot measure the omitted variable's effect, but included-variable estimators are unaffected.
B) There is no effect on included-variable estimators because the other variable is not included.
C) The OLS estimator of the included variable is always biased.
D) The OLS estimator is biased if the omitted variable is correlated with the included variable.

OVB requires both relevance for Y and correlation with included X.

Rule: Memorize the two-condition rule.

Omitted Variable BiasD–A level★ High priority — official Canvas example

When does omitted-variable bias exist?

→ D) exists if the omitted variable is correlated with an included regressor and is a determinant of Y.

Canvas Example MCQ — Q76

A) is always present whenever R-squared < 1.
B) is always present but negligible in almost all economic examples.
C) exists if the omitted variable is correlated with an included regressor but is not a determinant of Y.
D) exists if the omitted variable is correlated with an included regressor and is a determinant of Y.

This is the two-condition rule stated directly.

Rule: Both conditions, not either one.

Omitted Variable BiasD–A level★ High priority — official Canvas example

OVB occurs when an omitted variable...

→ B) affects the dependent variable and is correlated with at least one included regressor.

Canvas Example MCQ — Q78

A) is unrelated to both the dependent variable and the included regressors.
B) affects the dependent variable and is correlated with at least one included regressor.
C) is correlated with an included regressor but has no effect on the dependent variable.
D) affects the dependent variable but is uncorrelated with all included regressors.
E) None of the above.

That statement contains both required conditions.

Rule: Two conditions.

Omitted Variable BiasD–A level★ High priority — official Canvas example

An omitted variable affects Y but is uncorrelated with all included regressors. Does it create OVB?

→ C) No, because correlation with an included regressor is also required.

Canvas Example MCQ — Q79

A) Yes, always.
B) Yes, if the sample size is small.
C) No, because correlation with an included regressor is also required.
D) No, because omitted variables can never cause bias.
E) None of the above.

Condition 1 holds but condition 2 does not.

Rule: One condition alone is insufficient.

Omitted Variable BiasD–A level★ High priority — official Canvas example

An omitted variable is correlated with X1 but has no effect on Y. Does it bias the estimated coefficient on X1?

→ C) No, because the omitted variable must also be a determinant of Y.

Canvas Example MCQ — Q80

A) Yes, always.
B) Yes, because correlation with X1 is sufficient.
C) No, because the omitted variable must also be a determinant of Y.
D) No, unless X1 is a dummy variable.
E) None of the above.

Condition 2 holds but condition 1 does not.

Rule: Correlation alone is insufficient.

Omitted Variable BiasD–A level★ High priority — official Canvas example

Which two conditions are required for OVB?

→ B) The omitted variable must affect Y and be correlated with an included regressor.

Canvas Example MCQ — Q81

A) The omitted variable must have a large variance and a non-zero mean.
B) The omitted variable must affect Y and be correlated with an included regressor.
C) The omitted variable must be normally distributed and correlated with Y.
D) The omitted variable must be statistically significant and correlated with the error term.
E) None of the above.

Exactly the two-condition rule.

Rule: Memorize verbatim.

Omitted Variable BiasD–A level★ High priority — official Canvas example

True/False: if omitted variable affects Y but is uncorrelated with every included regressor, omission does not create OVB in OLS slopes.

→ A) True

Canvas Example MCQ — Q82

A) True
B) False
C) True only in large samples
D) True only if R-squared is high
E) None of the above.

No correlation with included X means the omission does not systematically contaminate the included slope coefficients through OVB.

Rule: Effect on Y alone is not enough.

Omitted Variable BiasD–A level★ High priority — official Canvas example

House prices are regressed on floor area; neighbourhood quality is omitted. When is OVB likely?

→ A) Neighbourhood quality affects house prices and is correlated with floor area.

Canvas Example MCQ — Q83

A) Neighbourhood quality affects house prices and is correlated with floor area.
B) Neighbourhood quality affects house prices but is completely unrelated to floor area.
C) Neighbourhood quality is correlated with floor area but does not affect house prices.
D) Neighbourhood quality is measured in categories rather than numbers.
E) None of the above.

Both required conditions are satisfied.

Rule: Apply the two conditions to the story.

Model Fit & RMSED–A level★ High priority — official Canvas example

A multiple regression has adjusted R² = 0.68. Closest interpretation?

→ A) Approximately 68% of the variation in the dependent variable is explained by the model, after adjusting for the number of estimated parameters.

Canvas Example MCQ — Q87

A) Approximately 68% of the variation in the dependent variable is explained by the model, after adjusting for the number of estimated parameters.
B) 68% of the explanatory variables are statistically significant.
C) The model predicts the dependent variable correctly for exactly 68% of observations.
D) The remaining 32% must be caused by omitted-variable bias.
E) None of the above.

This is the source’s approximate interpretation. It is not 68% significant variables and not 68% correctly predicted observations.

Rule: Do not confuse fit with significance or classification accuracy.

Regression BasicsD–A levelVery high priority

In econometric modelling the assumption of strict exogeneity implies that_____

→ A) cov(xi, ej) = 0: there is no correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.

Old Exam — Dec 2021 re-exam, Q19

A) cov(xi, ej) = 0: there is no correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.
B) cov(xi, ej) ≠ 0: there is positive or negative correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.
C) cov(xi, ej) > 0: there is strict positive correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i
D) cov(xi, ej) < 0: there is strict negative correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i
E) None of the above (A, B, C, D) is correct.

Strict exogeneity means no correlation between regressors and errors across all observations/time periods: Cov(x_i,e_j)=0 -> A.

Rule: Identify model units and form before calculating. Never confuse coefficient size, significance, R2 and prediction accuracy.

Regression BasicsD–A levelVery high priority

In econometric modelling the assumption of strict exogeneity implies that_____

→ A) cov(xi, ej) = 0: there is no correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.

Old Exam — Oct 2021, Q16

A) cov(xi, ej) = 0: there is no correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.
B) cov(xi, ej) ≠ 0: there is positive or negative correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i.
C) cov(xi, ej) > 0: there is strict positive correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i
D) cov(xi, ej) < 0: there is strict negative correlation between the omitted factors (variables) associated with the observation j and the value of the explanatory variable for observation i
E) None of the above (A, B, C, D) is correct.

Strict exogeneity requires regressors to be uncorrelated with the error in every time period: Cov(x_i,e_j)=0 -> A.

Rule: Identify model units and form before calculating. Never confuse coefficient size, significance, R2 and prediction accuracy.

Regression BasicsE-levelVery high priority

In a multiple regression, the coefficient βj measures the change in expected Y for a one-unit change in Xj, holding other included regressors constant. Is this partial effect automatically a causal effect?

→ A) False — it is a conditional association and is causal only under additional identification assumptions

Computer Lab 4 — Exercise 2, Task 2

A) False — it is a conditional association and is causal only under additional identification assumptions
B) True — any regression coefficient is causal by construction
C) True, but only when R² exceeds 0.70
D) False — coefficients from regression are always meaningless

Holding the other included regressors constant removes their confounding influence only, not all possible confounding from omitted variables; causal interpretation requires further assumptions (e.g., no omitted confounders, correct functional form).

Rule: Partial association ≠ causal effect unless identification assumptions hold.

Omitted Variable BiasE-levelHigh priority

For an omitted variable to cause omitted variable bias (OVB) in the estimated STR coefficient, which two conditions must both hold for the omitted variable?

→ A) It must affect the dependent variable (test scores) AND be correlated with an included regressor (e.g., STR)

Computer Lab 4 — Exercise 2, Task 5

A) It must affect the dependent variable (test scores) AND be correlated with an included regressor (e.g., STR)
B) It must be measured in the same units as STR
C) It must be correlated with the dependent variable only
D) It must be uncorrelated with all included regressors

OVB requires the omitted factor to (1) influence Y and (2) be correlated with an included regressor; if either condition fails, omitting it does not bias that coefficient.

Rule: Two OVB conditions: affects Y AND correlated with an included regressor — both must hold.

Omitted Variable BiasD–A levelHigh priority

The STR coefficient falls in magnitude from -2.280 (Model 1, no controls) to -1.014 (Model 5, with controls), while its sign stays negative. What is the best interpretation?

→ A) This pattern is consistent with omitted variable bias in Model 1, but the coefficient change alone does not prove STR's effect is causal

Computer Lab 4 — Exercise 2, Task 6 (comparison)

A) This pattern is consistent with omitted variable bias in Model 1, but the coefficient change alone does not prove STR's effect is causal
B) This proves Model 1 was causal and Model 5 is biased
C) This proves STR has no real relationship with test scores
D) This change in magnitude automatically makes the Model 5 coefficient statistically insignificant

A shrinking coefficient magnitude after adding plausible confounders is consistent with OVB in the simpler model, but establishing causality requires more than observing a coefficient change; significance must be checked separately using SEs/t-stats.

Rule: Coefficient movement across specifications is suggestive of OVB, not conclusive proof of causality or (in)significance.