Asymptotic Properties of OLS Estimator
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What is a consequence of heteroskedasticity on the OLS estimator?

  • It makes the OLS estimator inconsistent.
  • It has no effect on the OLS estimator.
  • It leads to unbiased estimates but inefficient.
  • It increases the variance of the OLS estimator. (correct)

    • What is a characteristic of the alternative estimator derived in the presence of heteroskedasticity?

  • It is more efficient than the OLS estimator. (correct)
  • It is only applicable to small samples.
  • It is less efficient than the OLS estimator.
  • It is unbiased and consistent.

    • What is the primary concern of autocorrelation in regression analysis?

  • It affects the consistency of the OLS estimator. (correct)
  • It leads to biased estimates.
  • It invalidates the use of R-squared.
  • It has no impact on the regression analysis.

    • Which of the following is a common cause of heteroskedasticity?

    <p>Changes in the variance of the error term over time.</p> Signup and view all the answers

    What is the effect of multicollinearity on the OLS estimator?

    <p>It increases the variance of the OLS estimator.</p> Signup and view all the answers

    What is a common test for heteroskedasticity?

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

    What is an implication of heteroskedasticity on hypothesis testing?

    <p>It leads to incorrect test statistics.</p> Signup and view all the answers

    Which of the following is a characteristic of autoregressive conditional heteroskedasticity (ARCH)?

    <p>It models the variance of the error term as a function of past errors.</p> Signup and view all the answers

    What is a consequence of ignoring heteroskedasticity in regression analysis?

    <p>It results in inefficient estimates.</p> Signup and view all the answers

    What is a common remedy for autocorrelation in time series data?

    <p>Differencing the data.</p> Signup and view all the answers

    What is the primary concern when dealing with heteroskedasticity in linear regression?

    <p>Inconsistent standard errors</p> Signup and view all the answers

    Which test is commonly used to detect multiplicative heteroskedasticity?

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

    What is the purpose of using weighted least squares with arbitrary weights?

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

    What is the main difference between the Breusch-Pagan test and the White test?

    <p>The Breusch-Pagan test is a Lagrange multiplier test, while the White test is a Wald test</p> Signup and view all the answers

    When should you use heteroskedasticity-consistent standard errors for OLS?

    <p>When there is a suspicion of heteroskedasticity</p> Signup and view all the answers

    What is the consequence of ignoring heteroskedasticity in linear regression?

    <p>All of the above</p> Signup and view all the answers

    What is the primary issue with autocorrelation in a regression model?

    <p>It results in inconsistent estimates of the coefficients</p> Signup and view all the answers

    What is the main purpose of the Durbin-Watson test?

    <p>To test for first-order autocorrelation in the residuals</p> Signup and view all the answers

    If the Durbin-Watson statistic is close to 2, what can be concluded about the residuals?

    <p>There is no autocorrelation in the residuals</p> Signup and view all the answers

    What is the main difference between first-order autocorrelation and higher-order autocorrelation?

    <p>First-order autocorrelation affects the current error term, while higher-order autocorrelation affects lagged error terms</p> Signup and view all the answers

    What is the consequence of ignoring autocorrelation in a regression model?

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

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

    <p>To ensure that the estimates are consistent and efficient</p> Signup and view all the answers

    If the residuals of a linear regression model are found to be homoskedastic, weighted least squares with arbitrary weights can still provide more efficient estimates than OLS.

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

    The Breusch-Pagan test and the White test are equivalent and will always produce the same results.

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

    Heteroskedasticity-consistent standard errors for OLS are only required when the regression model includes a lagged dependent variable.

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

    Autocorrelation in a regression model can be detected using the Durbin-Watson test, but it cannot be corrected.

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

    Multiplicative heteroskedasticity can be tested using the Breusch-Pagan test.

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

    Ignoring autocorrelation in a regression model will always lead to inflated standard errors.

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

    The presence of heteroskedasticity always leads to inconsistent OLS estimates.

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

    The Durbin-Watson test is a diagnostic test for heteroskedasticity.

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

    First-order autocorrelation is a type of moving average error.

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

    The presence of heteroskedasticity in a linear regression model implies that the ordinary least squares (OLS) estimator is biased.

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

    Autocorrelation is a concern only in time series data.

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

    Heteroskedasticity can be detected using the Durbin-Watson test.

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

    Autocorrelation in a regression model is a characteristic of the error term only.

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

    Higher-order autocorrelation is a type of autocorrelation that occurs when the error term is correlated with a lag of more than one period.

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

    The Breusch-Pagan test is a statistical test used to detect multiplicative heteroskedasticity.

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

    The Durbin-Watson test is a statistical test used to detect higher-order autocorrelation.

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

    Heteroskedasticity-consistent standard errors are always required when using weighted least squares.

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

    Autocorrelation in a regression model implies that the error term is not normally distributed.

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

    The presence of heteroskedasticity in a linear regression model implies that the OLS estimator is inconsistent.

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

    The primary concern of autocorrelation in regression analysis is that it can lead to biased estimates.

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

    The White test is a statistical test used to detect autocorrelation in a regression model.

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

    Ignoring heteroskedasticity in a linear regression model can lead to overestimation of the variance of the OLS estimator.

    <p>True</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

    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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