Question 1

Autocorrelation causes bias in a model with fixed effects.

Accepted Answer

Autocorrelation occurs when the errors in a model are correlated with each other over time, violating the assumption of independence. This can lead to biased and inconsistent estimates of the fixed effects in the model.

Question 2

Autocorrelation causes bias in a model without fixed effects.

Accepted Answer

False

Question 3

A biased coefficient is always worse than an unbiased coefficient.

Accepted Answer

A biased coefficient is not always worse than an unbiased coefficient because in some contexts, especially when dealing with high variance or overfitting, a slight bias can lead to a lower mean squared error (MSE) and better generalization to unseen data.

Question 4

Random effects models are biased if the random effects error term is correlated with X.

Accepted Answer

If the random effects error term is correlated with X, it violates the assumptions of the random effects model and leads to biased estimates. This is known as the incidental parameter problem. In such cases, fixed effects models may be more appropriate.

Question 5

Random effects models are appropriate only when their coefficients are similar to coefficients produced by fixed effects models.

Accepted Answer

Random effects models are appropriate when the coefficients of interest vary randomly across units, and this variation is not of primary interest. In contrast, fixed effects models are appropriate when the coefficients of interest are fixed and do not vary across units. Therefore, random effects models are appropriate only when their coefficients are not similar to coefficients produced by fixed effects models.

Question 6

Which of the following is a proper procedure for testing for autocorrelation in a panel data model without a lagged dependent variable?&#10;A) Run a model that does not address autocorrelation and test for autocorrelated errors based on the residuals from that model.&#10;B) Run a $\rho$-transformed model and test for autocorrelated errors based on the residuals from that model.&#10;C) Assess whether there is a different intercept for each unit.&#10;D) Run a probit or logit model and test for autocorrelated errors based on the residuals from that model.

Accepted Answer

Running a model that does not address autocorrelation and testing for autocorrelated errors based on the residuals from that model is a common approach for testing for autocorrelation in panel data models without a lagged dependent variable. This can be done using standard tests such as the Durbin-Watson test or the Breusch-Godfrey test. Option B is not a standard procedure for testing autocorrelation in panel data models. Option C is a way to test for fixed effects, not autocorrelation. Option D is not applicable as probit and logit models are used for binary dependent variables, and testing for autocorrelation in their residuals is not relevant.

Question 7

Under what conditions is the bias caused by autocorrelaed errors in a fixed effect model the most severe?&#10;A) We have many observations for each unit.&#10;B) We have few observations for each unit.&#10;C) We have many observations for each time period.&#10;D) We have few observations for each time period.

Accepted Answer

The answer of Under what conditions is the bias caused...

Question 8

Suppose that we have the following results from a model with lagged dependent variable
Y_i_t = 0.9Y_i_,t-1 + 2X_1i_t
Which of the following is most accurate?

A) The short-term effect of a one unit change in X will be a 2.9 unit change in Y.
B) The long-term effect of a one unit change in X will be a 20 unit change in Y.
C) The long-term effect of a one unit change in X will be a 4 unit change in Y.
D) Y will keep getting smaller and smaller over time.

Accepted Answer

The long-term effect of a one unit change in X on Y in models with lagged dependent variables is calculated by dividing the coefficient of X by (1 minus the coefficient of the lagged dependent variable). The choice indicating a 20 unit change suggests a calculation that accounts for the cumulative effect over time, which is characteristic of the long-term effect in such models.

Question 9

Suppose that we are comparing results in the following two models
Model A: Y_i_t = 0.9Y_i_,t-1 + 2X_1i_t
Model A: Y_i_t = 0.8Y_i_,t-1 + 2X_1i_t
Which of the following is true?

A) The long-term effect of a one unit change in X will be 10 times bigger in Model A than in Model
B) The long-term effect of a one unit change in X will be 10 percent bigger in Model A than in Model
C) The short-term effect of a one unit change in X will be bigger in Model A than in Model
D) The short-term effect of a one unit change in X will be smaller in Model A than in Model

Accepted Answer

In Model A, the coefficient on X_1i_t is 10 times larger than in Model B (F1F1F1S1F1F1F10X_1i_t), therefore a one unit change in X will have a 10 times bigger effect on Y in the long run in Model A compared to Model B.

Question 10

What usually happens to autocorrelation when we add a lagged dependent variable to the model?&#10;A) Autocorrelation gets bigger.&#10;B) Autocorrelation gets smaller.&#10;C) Autocorrelation stays the same.&#10;D) We cannot test for autocorrelation when a lagged dependent variable is included in the model.

Accepted Answer

Adding a lagged dependent variable to the model can help to reduce autocorrelation in the residuals, as it accounts for some of the serial correlation that may be present in the data. By including the lagged dependent variable, the model is better able to capture any patterns or trends in the data, which can help to reduce autocorrelation.

Question 11

What usually happens to autocorrelation when we add a lagged dependent variable to the model?&#10;A) Autocorrelation gets bigger.&#10;B) Autocorrelation gets smaller.&#10;C) Autocorrelation stays the same.&#10;D) We cannot test for autocorrelation when a lagged dependent variable is included in the model.

Accepted Answer

The answer of What usually happens to autocorrelation when we...

Question 12

OLS coefficients are biased when there is a lagged dependent variable and fixed effects in the same model. Which of the following statements is most accurate about using OLS when there is a lagged dependent variable and fixed effects in the same model?

A) We should never use OLS in this situation.
B) Instrumental variables are easier to use OLS in this situation.
C) OLS can produce coefficient estimates that are biased, but still on average closer to the true values in this situation.
D) OLS performs worse in this situation when we have many observations for each unit.

Accepted Answer

The answer of OLS coefficients are biased when there is...

Question 13

What factor is associated with lower bias in a model with a lagged dependent variable and fixed effects?&#10;A) Large number of observations for each period.&#10;B) Large number of time periods.&#10;C) A large coefficient on the lagged dependent variable.&#10;D) Using multiple lags (e.g., the dependent variable from the previous period and the period before that).

Accepted Answer

The answer of What factor is associated with lower bias...

Question 14

Describe the potential trade-off between bias and accuracy using an example of an estimator that is biased, but accurate and one that is unbiased, but inaccurate.

Accepted Answer

The answer of Describe the potential trade-off between bias and...

Question 15

Describe when it is appropriate to use random effects models.

Accepted Answer

The answer of Describe when it is appropriate to use...

Question 16

Explain why a model with a lagged dependent variable and fixed effects will be biased.

Accepted Answer

The answer of Explain why a model with a lagged...

Question 17

Explain why it is important to test for autocorrelation when using a model with a lagged dependent variable and no fixed effects.

Accepted Answer

The answer of Explain why it is important to test...

Deck 15: Advanced Panel Data