Asymptotic Properties of OLS Estimator
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Questions and Answers

What is the name of the test that is used to detect multiplicative heteroskedasticity?

  • White test
  • T-test
  • F-test
  • Breusch-Pagan test (correct)
  • Heteroskedasticity is a type of autocorrelation.

    False

    What is the purpose of weighted least squares (WLS) in the context of heteroskedasticity?

    To give more weight to observations with lower variance

    The standard errors of the OLS estimates can be adjusted for heteroskedasticity using ____________________ standard errors.

    <p>Heteroskedasticity-consistent</p> Signup and view all the answers

    Match the following tests with their purposes in detecting heteroskedasticity:

    <p>Breusch-Pagan test = Detecting multiplicative heteroskedasticity White test = Detecting non-normality of errors F-test = Comparing the means of two groups T-test = Comparing the means of two groups</p> Signup and view all the answers

    What is the purpose of testing for heteroskedasticity in a linear regression model?

    <p>To determine if the variance of the errors is constant</p> Signup and view all the answers

    What is the purpose of testing for first-order autocorrelation?

    <p>To determine if the error terms are correlated</p> Signup and view all the answers

    Higher-order autocorrelation occurs when the error terms are correlated with each other, but with a lag of more than one period.

    <p>True</p> Signup and view all the answers

    What is the name of the test used to detect first-order autocorrelation?

    <p>The Durbin-Watson test</p> Signup and view all the answers

    Autocorrelation occurs when the error terms are correlated with each other, which can lead to _______________ in the parameter estimates.

    <p>bias</p> Signup and view all the answers

    Match the following autocorrelation patterns with their descriptions:

    <p>First-order Autocorrelation = Correlation between error terms and their lagged values by one period Higher-order Autocorrelation = Correlation between error terms and their lagged values by more than one period Moving Average Errors = Type of error term that is a combination of current and past errors</p> Signup and view all the answers

    Heteroskedasticity and autocorrelation are the same phenomenon.

    <p>False</p> Signup and view all the answers

    What is the consequence of heteroskedasticity on the OLS estimator?

    <p>It leads to biased and inefficient estimates</p> Signup and view all the answers

    Heteroskedasticity is a type of autocorrelation.

    <p>False</p> Signup and view all the answers

    What is the alternative estimator derived to address heteroskedasticity?

    <p>A robust estimator or a weighted least squares estimator</p> Signup and view all the answers

    Heteroskedasticity is a situation where the variability of the ____________ is not constant.

    <p>error term</p> Signup and view all the answers

    Which of the following is a test for heteroskedasticity?

    <p>Breusch-Pagan test</p> Signup and view all the answers

    Autocorrelation is a type of heteroskedasticity.

    <p>False</p> Signup and view all the answers

    What is the consequence of autocorrelation on the OLS estimator?

    <p>It leads to inefficient and biased estimates</p> Signup and view all the answers

    Autocorrelation is a situation where the error terms are ____________ with each other.

    <p>correlated</p> Signup and view all the answers

    Match the following concepts with their definitions:

    <p>Heteroskedasticity = A situation where the error terms are correlated with each other Autocorrelation = A situation where the variability of the error term is not constant</p> Signup and view all the answers

    Which of the following is a reason for using robust estimation methods?

    <p>To address heteroskedasticity</p> Signup and view all the answers

    Study Notes

    Asymptotic Properties of the OLS Estimator

    • Consistency of the OLS estimator is discussed in section 2.6.1
    • Asymptotic normality of the OLS estimator is discussed in section 2.6.2
    • Small samples and asymptotic theory are discussed in section 2.6.3

    Illustration: The Capital Asset Pricing Model

    • CAPM is presented as a regression model in section 2.7.1
    • Estimating and testing the CAPM is discussed in section 2.7.2
    • A real-world example of the largest hedge fund is given in section 2.7.3

    Multicollinearity

    • Multicollinearity is discussed in section 2.8
    • An example of individual wages is used to illustrate multicollinearity in section 2.8.1

    Missing Data, Outliers, and Influential Observations

    • Outliers and influential observations are discussed in section 2.9.1
    • Robust estimation methods are presented in section 2.9.2
    • Missing observations are discussed in section 2.9.3

    Prediction

    • Prediction is discussed in section 2.10

    Interpreting and Comparing Regression Models

    • Interpreting the linear model is discussed in section 3.1
    • Selecting the set of regressors is discussed in section 3.2
    • Misspecifying the set of regressors is discussed in section 3.2.1
    • Selecting regressors is discussed in section 3.2.2
    • Comparing non-nested models is discussed in section 3.2.3

    Misspecifying the Functional Form

    • Nonlinear models are discussed in section 3.3.1
    • Testing the functional form is discussed in section 3.3.2
    • Testing for a structural break is discussed in section 3.3.3

    Illustrations

    • Explaining house prices is discussed in section 3.4
    • Predicting stock index returns is discussed in section 3.5
    • Explaining individual wages is discussed in section 3.6

    Heteroskedasticity and Autocorrelation

    • Consequences for the OLS estimator are discussed in section 4.1
    • Deriving an alternative estimator is discussed in section 4.2
    • Heteroskedasticity is discussed in section 4.3
    • Testing for heteroskedasticity is discussed in section 4.4
    • Autocorrelation is discussed in section 4.6
    • Testing for first-order autocorrelation is discussed in section 4.7

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    Description

    This quiz covers the asymptotic properties of the Ordinary Least Squares (OLS) estimator, including consistency and asymptotic normality.

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