Suppose we omit X2 from the following in a bivariate model Yi = $\beta$ 0 + $\beta$1X1i + $\varepsilon$ i And suppose X2 is negatively related to X1 and $\beta$2 is positive, while $\beta$1 is positive. What is the likely effect of omitting X2 on our estimate of $\beta$1?

A) No effect; $\beta$1hat will be unbiased. B) $\beta$1hat will be more positive than it should be. C) $\beta$1hat will be less positive than it should be. D) $\beta$1hat will equal zero. A) No effect; $\beta$1hat will be unbiased. B) $\beta$1hat will be more positive than it should be. C) $\beta$1hat will be less positive than it should be. D) $\beta$1hat will equal zero. C

Suppose we omit X3 (a variable that actually affects Y) from the following in a bivariate model Yi = $\beta$ 0 + $\beta$1X1i + $\beta$2X2i + $\varepsilon$ i And suppose each of the independent variables are correlated with the other independent variables. What is the consequence of omitting X3 on $\beta$1hat?

A) No effect; $\beta$1hat will be unbiased. B) The bias will depend only on the correlation of X1 and X3. C) The bias will depend on the correlations of all the independent variables. D) The bias will depend only on the correlation of X1 and X2. A) No effect; $\beta$1hat will be unbiased. B) The bias will depend only on the correlation of X1 and X3. C) The bias will depend on the correlations of all the independent variables. D) The bias will depend only on the correlation of X1 and X2. C

9. Suppose that X1 is measured with error. Yi = $\beta$ 0 + $\beta$1X1i + $\varepsilon$ i Xi = X*1i + $\nu$ i In which of the following cases will the bias be most severe?

A) The variance of the independent variable ($\sigma$x*) is much smaller than the variance of the error measurement error ($\sigma$$\nu$). B) The variance of the independent variable ($\sigma$x*) is much larger than the variance of the error measurement error (($\sigma$$\nu$). C) The variance of the error measurement error (($\sigma$$\nu$) is zero. D) There will be no bias. A) The variance of the independent variable ($\sigma$x*) is much smaller than the variance of the error measurement error ($\sigma$$\nu$). B) The variance of the independent variable ($\sigma$x*) is much larger than the variance of the error measurement error (($\sigma$$\nu$). C) The variance of the error measurement error (($\sigma$$\nu$) is zero. D) There will be no bias.

Suppose we omit X2 from the following in a bivariate model Yi = $\beta$ 0 + $\beta$1X1i + $\varepsilon$ i And suppose X2 is positively related to X1 and $\beta$2 is positive, while $\beta$1 is negative. What is the likely effect of omitting X2 on our estimate of $\beta$1?

A) No effect; $\beta$1 hat will be unbiased. B) $\beta$1 hat will be more negative than it should be. C) $\beta$1 hat will be less negative than it should be. D) $\beta$1 hat will be biased toward zero. A) No effect; $\beta$1 hat will be unbiased. B) $\beta$1 hat will be more negative than it should be. C) $\beta$1 hat will be less negative than it should be. D) $\beta$1 hat will be biased toward zero.

10. Suppose that X1 is measured with error. Yi = $\beta$ 0 + $\beta$1X1i + $\varepsilon$ i Xi = X*1i + $\varepsilon$ i Which of the following is most accurate?

A) The estimate of $\beta$1hat will be larger than it should be. B) The estimate of $\beta$1hat will be smaller than it should be. C) $\beta$1hat will be biased toward zero. D) We know $\beta$1hat will be biased, but do not know which direction. A) The estimate of $\beta$1hat will be larger than it should be. B) The estimate of $\beta$1hat will be smaller than it should be. C) $\beta$1hat will be biased toward zero. D) We know $\beta$1hat will be biased, but do not know which direction.

Exam 14: Advanced Ols

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is negatively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is positive. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

Suppose we omit X₃ (a variable that does not affect Y) from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\beta$ ₂X₂_i + $\varepsilon$ _i And suppose each of the independent variables are correlated with the other independent variables. What is the consequence of omitting X₃on $\beta$ ₁hat?

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

Suppose we omit X₃ (a variable that actually affects Y) from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\beta$ ₂X₂_i + $\varepsilon$ _i And suppose each of the independent variables are correlated with the other independent variables. What is the consequence of omitting X₃on $\beta$ ₁hat?

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

Even if we don't observe a variable, we can make informed speculations about the effect of omitting the variable on coefficients on variables we do observe.

(True/False)

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Question 4

Please explain, in words and using equations, why B1hat is a random variable.

(Essay)

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Question 5

Which assumption is necessary for the expected value of b1hat to equal b1?

(Multiple Choice)

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Question 6

The conditions for omitted variable bias can be derived by substituting the true value of Y into the B1hat equation for the model where X2 is omitted.

(True/False)

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Question 7

If the errors are not homoscedastic and uncorrelated with each other, then OLS estimates are biased and but the easy-to-use standard OLS equation for the variance of B1hat is still appropriate.

(True/False)

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Question 8

Which assumption is not necessary for the following equation to correctly characterize the standard error of $\beta$ 1hat?

(Multiple Choice)

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Question 9

We derive the B1hat equation by setting the sum of squared residuals equation to 0 and solving for B1hat.

(True/False)

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Question 10

Derive the equation for attenuation bias due to a measurement error in the independent variable in a case where there is only one independent variable.

(Essay)

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Question 11

_9.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\nu$ _i In which of the following cases will the bias be most severe?

(Multiple Choice)

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Question 12

In which of the following will omitted variable bias be the most severe? Treat X2 as the omitted variable in a bivariate model of Y_i = $\beta$ ₀ + $\beta$ ₁X₁_i + $\varepsilon$ _i

(Multiple Choice)

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Question 13

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is positively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is negative. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

(Multiple Choice)

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Question 14

Derive the equation for the omitted variable bias condition.

(Essay)

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Question 15

A single poorly measured independent variable will not cause other coefficients to be biased.

(True/False)

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Question 16

Since a lot of times we do not have the values for X2, and X2 could be correlated both with X1 and Y, we will have to anticipate the sign of the bias, but we won't necessarily know the magnitude of the bias. Provide a list/table that gives the anticipated sign of the bias based on the relationship between X2 and X1 as well as the relationship between X2 and Y.

(Essay)

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Question 17

_10.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\varepsilon$ _i Which of the following is most accurate?

(Multiple Choice)

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Question 18

Show the steps in involved in deriving the OLS estimates for B1hat, and describe the assumption that is necessary for B1hat to be an unbiased estimator of B1.

(Essay)

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Question 19

Suppose we omit X₃ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\beta$ ₂X₂_i + $\varepsilon$ _i And suppose each of the independent variables is completely uncorrelated with the other independent variables (i.e., they have been randomly chosen in a randomized experiment). What is the consequence of omitting X₃on $\beta$ ₁hat?

(Multiple Choice)

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Question 20

Showing 1 - 20 of 20

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is negatively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is positive. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

Even if we don't observe a variable, we can make informed speculations about the effect of omitting the variable on coefficients on variables we do observe.

Please explain, in words and using equations, why B1hat is a random variable.

Which assumption is necessary for the expected value of b1hat to equal b1?

The conditions for omitted variable bias can be derived by substituting the true value of Y into the B1hat equation for the model where X2 is omitted.

If the errors are not homoscedastic and uncorrelated with each other, then OLS estimates are biased and but the easy-to-use standard OLS equation for the variance of B1hat is still appropriate.

Which assumption is not necessary for the following equation to correctly characterize the standard error of $\beta$ 1hat?

We derive the B1hat equation by setting the sum of squared residuals equation to 0 and solving for B1hat.

Derive the equation for attenuation bias due to a measurement error in the independent variable in a case where there is only one independent variable.

_9.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\nu$ _i In which of the following cases will the bias be most severe?

In which of the following will omitted variable bias be the most severe? Treat X2 as the omitted variable in a bivariate model of Y_i = $\beta$ ₀ + $\beta$ ₁X₁_i + $\varepsilon$ _i

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is positively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is negative. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

Derive the equation for the omitted variable bias condition.

A single poorly measured independent variable will not cause other coefficients to be biased.

_10.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\varepsilon$ _i Which of the following is most accurate?

Show the steps in involved in deriving the OLS estimates for B1hat, and describe the assumption that is necessary for B1hat to be an unbiased estimator of B1.

The Quest for Causality

Stats in the Wild: Good Data Practices

Bivariate Ols: the Foundation of Econometric Analysis

Hypothesis Testing and Interval Estimation: Answering Research

Multivariate Ols: Where the Action Is

Dummy Variables: Smarter Than You Think

Specifying Models

Using Fixed Effects Models to Fight Endogeneity in Panel Data a

Instrumental Variables: Using Exogenous Variation to Fight Endogen

Experiments: Dealing With Real-World Challenges

Regression Discontinuity: Looking for Jumps in Data

Dummy Dependent Variables

Time Series: Dealing With Stickiness Over Time

Advanced Panel Data

Filters

Exam 14: Advanced Ols

Suppose we omit X2 from the following in a bivariate model Yi = β\betaβ 0 + β\betaβ 1X1i + ε\varepsilonε i And suppose X2 is negatively related to X1 and β\betaβ 2 is positive, while β\betaβ 1 is positive. What is the likely effect of omitting X2 on our estimate of β\betaβ 1?

Even if we don't observe a variable, we can make informed speculations about the effect of omitting the variable on coefficients on variables we do observe.

Please explain, in words and using equations, why B1hat is a random variable.

Which assumption is necessary for the expected value of b1hat to equal b1?

The conditions for omitted variable bias can be derived by substituting the true value of Y into the B1hat equation for the model where X2 is omitted.

If the errors are not homoscedastic and uncorrelated with each other, then OLS estimates are biased and but the easy-to-use standard OLS equation for the variance of B1hat is still appropriate.

Which assumption is not necessary for the following equation to correctly characterize the standard error of β\betaβ 1hat?

We derive the B1hat equation by setting the sum of squared residuals equation to 0 and solving for B1hat.

Derive the equation for attenuation bias due to a measurement error in the independent variable in a case where there is only one independent variable.

9. Suppose that X1 is measured with error. Yi = β\betaβ 0 + β\betaβ 1X1i + ε\varepsilonε i Xi = X*1i + ν\nuν i In which of the following cases will the bias be most severe?

In which of the following will omitted variable bias be the most severe? Treat X2 as the omitted variable in a bivariate model of Yi = β\betaβ 0 + β\betaβ 1X1i + ε\varepsilonε i

Suppose we omit X2 from the following in a bivariate model Yi = β\betaβ 0 + β\betaβ 1X1i + ε\varepsilonε i And suppose X2 is positively related to X1 and β\betaβ 2 is positive, while β\betaβ 1 is negative. What is the likely effect of omitting X2 on our estimate of β\betaβ 1?

Derive the equation for the omitted variable bias condition.

A single poorly measured independent variable will not cause other coefficients to be biased.

10. Suppose that X1 is measured with error. Yi = β\betaβ 0 + β\betaβ 1X1i + ε\varepsilonε i Xi = X*1i + ε\varepsilonε i Which of the following is most accurate?

Show the steps in involved in deriving the OLS estimates for B1hat, and describe the assumption that is necessary for B1hat to be an unbiased estimator of B1.

The Quest for Causality

Stats in the Wild: Good Data Practices

Bivariate Ols: the Foundation of Econometric Analysis

Hypothesis Testing and Interval Estimation: Answering Research

Multivariate Ols: Where the Action Is

Dummy Variables: Smarter Than You Think

Specifying Models

Using Fixed Effects Models to Fight Endogeneity in Panel Data a

Instrumental Variables: Using Exogenous Variation to Fight Endogen

Experiments: Dealing With Real-World Challenges

Regression Discontinuity: Looking for Jumps in Data

Dummy Dependent Variables

Time Series: Dealing With Stickiness Over Time

Advanced Panel Data

Filters

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is negatively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is positive. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

Which assumption is not necessary for the following equation to correctly characterize the standard error of $\beta$ 1hat?

_9.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\nu$ _i In which of the following cases will the bias be most severe?

In which of the following will omitted variable bias be the most severe? Treat X2 as the omitted variable in a bivariate model of Y_i = $\beta$ ₀ + $\beta$ ₁X₁_i + $\varepsilon$ _i

Suppose we omit X₂ from the following in a bivariate model Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i And suppose X₂ is positively related to X₁ and $\beta$ ₂ is positive, while $\beta$ ₁is negative. What is the likely effect of omitting X₂ on our estimate of $\beta$ ₁?

_10.Suppose that X₁ is measured with error. Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\varepsilon$ _i X_i = X*_1i + $\varepsilon$ _i Which of the following is most accurate?