ECON 266: Bivariate OLS and Unbiasedness

In the context of Ordinary Least Squares (OLS) estimation, which statement best describes the implication of the exogeneity condition being satisfied?

How does increasing the sample size (N) and variance of the independent variable (var(X)) affect the variance of the OLS estimator $b_1$, assuming other factors remain constant?

Within the framework of OLS regression, what impact does the condition of homoskedasticity truly have on the properties of the estimator?

What is the precise interpretation of the probability limit ('plim') in the context of the consistency of an estimator, such as the OLS estimator $b_1$?

In a bivariate OLS regression, how does the presence of autocorrelation in the error term affect the properties of the OLS estimator $b_1$?

Given an OLS regression model, under what conditions should one prioritize addressing heteroskedasticity over autocorrelation when both are detected in the residuals?

In the context of assessing the 'Goodness of Fit' in an OLS regression model, which technique offers the most nuanced understanding of the model's predictive power, beyond simply considering the $R^2$?

How do outliers impact the OLS estimation, and under which specific condition is their effect most pronounced, necessitating particularly vigilant detection and handling?

Consider an OLS regression where the residuals exhibit a clustering pattern. What is the most accurate characterization of the consequence of this clustering?

What conditions must be met to ensure the variance of $b_1$ for OLS is as expected?

Within the context of OLS assumptions, what scenario could lead to a violation of the assumption of uncorrelated errors, thereby compromising the validity of statistical inference?

In the framework of OLS regression, if one observes that, conditional on X, $E[\epsilon | X] \neq 0$, how does this affect the OLS estimator, and what is the most appropriate course of action?

Consider a scenario in which you are performing OLS on a dataset and discover that the true model is $y = x^2 + \epsilon$, but you estimate $y = x + \epsilon$. What problem is present and what is its consequence for interpreting $b_1$?

Under what specific circumstance is applying a variance stabilizing transformation theoretically justified to achieve more efficient OLS estimation?

In the context of OLS regression, what is the most precise definition of 'consistency' of an estimator, such as $b_1$?

If the primary objective is to obtain unbiased estimates of the coefficients in a linear regression model, what assumption should be prioritized above all others?

Suppose you estimate a linear regression and suspect the presence of heteroskedasticity. What impact does heteroskedasticity have on the OLS estimator and what is an effective strategy for obtaining valid statistical inferences given this problem?

How can a researcher effectively discern whether high leverage points or influential outliers pose a greater threat to the validity of an OLS regression model?

If one suspects that their OLS regression suffers from omitted variable bias, under what specific condition can simply adding the omitted variable to the model not resolve the problem?

A researcher finds that the Durbin-Watson statistic in their OLS regression is very close to 0. What is the most precise interpretation of this result, and what are the immediate consequences for the validity of their model?

Under what precise conditions would one choose Feasible Generalized Least Squares (FGLS) over Ordinary Least Squares (OLS) for estimating a linear regression model?

In the context of assessing potential multicollinearity in a multiple regression model, what threshold for Variance Inflation Factor (VIF) generally signals substantial multicollinearity warranting remedial action?

Consider the scenario where an econometrician is modeling the daily sales of ice cream as a function of temperature and finds a significant outlier observation corresponding to a day with an unusually high number of sales due to a local festival. Which approach should be prioritized?

In a time series regression, the Augmented Dickey-Fuller (ADF) test yields a test statistic that is less (more negative) than the critical value at a 5% significance level. Without detrending, what conclusion can be accurately drawn from this result?

In the context of hypothesis testing in OLS regression, what is the best way to interpret the statement 'If $\beta_1 = 0$, the probability of observing values of $b_1$ that are closer to zero is high while the probability of obtaining values very different from zero is low'?