Which of the following can cause the usual OLS t statistics...

Which of the following can cause the usual OLS $t$ statistics to be invalid (that is, not to have $t$ distributions under $\mathrm{H}_{0}$ )? i. Heteroskedasticity. ii. A sample correlation coefficient of .95 between two independent variables that are in the model. iii. Omitting an important explanatory variable.

Which of the following can cause the usual OLS $t$ statistics to be invalid (that is, not to have $t$ distributions under $\mathrm{H}_{0}$ )?
i. Heteroskedasticity.
ii. A sample correlation coefficient of .95 between two independent variables that are in the model.
iii. Omitting an important explanatory variable.

Key Concepts

Heteroskedasticity

This concept refers to the situation where the variance of the error terms in a regression model is not constant across observations. Under the classical assumptions of OLS, constant error variance is crucial for the standard formulas for standard errors and for the t-statistic to follow a t-distribution under the null hypothesis. When heteroskedasticity is present, the usual OLS standard errors are inconsistent, and thus the t-statistics used for hypothesis testing may not follow the t-distribution, leading to invalid inference.

Multicollinearity

Multicollinearity occurs when two or more independent variables in a regression model are highly correlated. This can inflate the variances of the coefficient estimates and make them unstable, leading to less reliable estimates. However, while multicollinearity affects the precision of the estimates (making hypothesis testing less powerful), it does not in itself invalidate the t-statistics or alter their theoretical t-distribution under the null hypothesis when all other assumptions hold.

Omitted Variable Bias

Omitted variable bias arises when a relevant explanatory variable is left out of the regression model. This omission can lead to biased and inconsistent coefficient estimates if the omitted variable is correlated with one or more included regressors. Since the bias affects the expected values of the estimates and the standard errors, it violates the assumptions underlying the t-distribution of the test statistics, leading to invalid inference under the null hypothesis.

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