ECON 266: Multivariate Ordinary Least Squares (OLS)

In the context of Ordinary Least Squares (OLS) estimation, which of the following conditions, when violated, would MOST directly lead to biased coefficient estimates, even with a large sample size?

Consider an econometric model where one suspects a high degree of multicollinearity. Which of the following is the MOST reliable strategy to address multicollinearity's impact on coefficient estimates, while preserving interpretability and statistical validity?

Suppose an econometrician is estimating a Cobb-Douglas production function: $\ln(Q_i) = \beta_0 + \beta_1\ln(K_i) + \beta_2\ln(L_i) + \epsilon_i$, where $Q$ is output, $K$ is capital, and $L$ is labor. To test for constant returns to scale, what null hypothesis should be tested using an F-test?

In the context of simultaneous equation models, which identification strategy is MOST appropriate when an instrumental variable is correlated with the endogenous explanatory variable but is uncorrelated with the structural error term?

Consider a scenario involving an autoregressive distributed lag (ADL) model. Under what specific circumstances would one need to employ a unit root test (e.g., Augmented Dickey-Fuller test) and subsequently estimate the model in differences or with an error correction mechanism (ECM)?

Imagine you are analyzing a time series dataset and suspect the presence of a structural break. Which econometric technique is MOST appropriate for formally testing the null hypothesis of no structural break at an unknown breakpoint?

In the context of panel data analysis, what is the PRIMARY distinction between a fixed effects model and a random effects model, and under what condition is a fixed effects model generally preferred?

When using instrumental variable regression (IV), what statistical test is MOST appropriate for assessing the strength and validity of the instruments in the presence of multiple instruments for a single endogenous variable?

Consider an econometrician estimating a dynamic panel data model with lagged dependent variables. Which estimation technique is MOST appropriate to address the Nickell bias that arises due to the correlation between the lagged dependent variable and the error term?

Suppose you are estimating a model and you standardize the variables. By how much do you need to multiply $b_j$ to convert the effect back into the original units of $Y$?

Which of the following statements accurately describes the implications of the Gauss-Markov theorem for OLS estimators under classical assumptions?

In the context of conducting hypothesis tests on multiple coefficients using an F-test, which of the following scenarios represents a valid null hypothesis?

According to the content, what distribution-specific assumption is explicitly listed as a requirement for ensuring that Ordinary Least Squares (OLS) estimators are Best Linear Unbiased Estimators (BLUE)?

In the context of multicollinearity, which of the following statements accurately describes the potential consequences for Ordinary Least Squares (OLS) regression analysis and hypothesis testing?

Consider a regression model where you suspect the exogeneity assumption is violated. Which of the following conditions must hold for an instrumental variable (Z) to be considered valid?

How does standardization impact the interpretation of regression coefficients?

In time series analysis, what is the primary purpose of stationarity tests such as the Augmented Dickey-Fuller (ADF) test, and what action should be taken if a series is found to be non-stationary?

In the context of regression diagnostics, what does a Breusch-Pagan test primarily assess, and what corrective action is typically taken if the test indicates a statistically significant violation of its null hypothesis?

Consider a scenario in which a researcher standardizes all the independent variables in a multiple regression model before estimation. What is the MOST accurate interpretation of the resulting standardized coefficients?