Question 1

A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.

Accepted Answer

A pooled model typically assumes that the error term is uncorrelated with the independent variables. Bias in coefficient estimates arises when there is correlation between the error term and the independent variables, not when there is no correlation.

Question 2

The fixed effect ($\alpha$) is the part of the unobserved error and it is different for every observation for unit i.

Accepted Answer

The fixed effect is not part of the unobserved error; rather, it represents unobserved individual characteristics that are constant over time for each unit but vary across units.

Question 3

The value of the $\alpha$_iparameter can potentially take on a different value for each unit i.

Accepted Answer

The parameter F1F1F1S1αF1F1F10_i can potentially take on a different value for each unit i, as it is specified with the subscript i.

Question 4

When dealing with fixed effects, a de-meaned model approach is superior to the LSDV approach because the de-meaned model gives us more accurate coefficient estimates.

Accepted Answer

Both the de-meaned model approach and the Least Squares Dummy Variable (LSDV) approach yield identical coefficient estimates for the variables of interest in fixed effects models; the choice between them is often based on computational convenience rather than accuracy of the estimates.

Question 5

Having a model that controls for fixed effects even when the fixed effects are 0 ($\alpha$_i=0 for all units) will not cause bias.

Accepted Answer

Controlling for fixed effects when they are all 0 does not introduce bias in the model. It simply means that the fixed effects are not having any impact on the dependent variable.

Question 6

Which of the following is true about fixed effects models? A) We cannot use fixed effects models when we suspect there are fixed effects but no such effect exists ($\alpha$_i=0 for all units) B) Fixed effects models cannot generate a coefficient on a variable that is constant within all units. C) Fixed effects will generate a coefficient on a variable as long as that variable differs across units. D) A fixed effects model is not possible when there are a large number of units in the model.

Accepted Answer

Fixed effects models eliminate the effect of any variable that is constant within a unit, so it cannot generate a coefficient on such a variable. A is incorrect as fixed effects models can still be used even if there are no fixed effects. C is partially correct in that fixed effects will generate a coefficient on a variable as long as it differs across units, but this is not the only condition. D is incorrect as fixed effects models can handle a large number of units, although computational limitations may become an issue.

Question 7

Pooled OLS models are biased when:
A) When the fixed effects are correlated with the independent variable.
B) When the fixed effects are correlated with the dependent variable.
C) When the fixed effects model is used when in reality there are no fixed effects in the data.
D) When we don't know the direction of the fixed effects.

Accepted Answer

Pooled OLS models are biased when the fixed effects (unobserved individual-specific attributes) are correlated with the independent variables. This correlation means that the omitted variable bias is present, as the model fails to account for these fixed effects, leading to biased and inconsistent estimates.

Question 8

In order to run a two-way fixed effect model, we can use:
A) A de-meaned approach
B) A LSDV approach
C) Both a and b
D) None of the above.

Accepted Answer

Both a de-meaned approach and a LSDV approach can be used to run a two-way fixed effect model. The de-meaned approach subtracts the group means from each observation, while the LSDV approach creates binary variables for each group and includes them in the regression equation. Using both approaches can provide additional robustness to the results.

Question 9

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who got the treatment before they received it is: A) B0+B1+B2+B3 B) B0+B1+B3 C) B0+B1 D) B0+B1+B2

Accepted Answer

When determining the expected value of the dependent variable for those who got the treatment before they received it, we are essentially setting the Treated_i equal to 0. This means that the second and fourth terms in the equation become 0, leaving only B0+B1 as the expected value. Therefore, the best choice is C.

Question 10

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who in the control group after the treatment was administered is: A) B0+B1+B2+B3 B) B0+B1+B3 C) B0+B1 D) B0+B2

Accepted Answer

The expected value for the control group after the treatment is administered includes the intercept (B0) and the effect of being in the control group after the treatment (B2), without the treatment effect (B1) or the interaction term (B3).

Question 11

Which of the following is a reason why fixed effect models can't estimate coefficients on variables that do not vary within unit?
A) Because no fixed effects exists in such a case.
B) The de-meaned variables will not vary.
C) We can estimate such a variable with fixed effects.
D) The errors will be homoscedastic.

Accepted Answer

Fixed effect models involve de-meaning the variables within each unit, which means that any variable that does not vary within a unit will have a constant value of zero after de-meaning. This means that it is impossible to estimate the effect of such a variable using a fixed effect model.

Question 12

In order to employ the LSDV approach in a one-way fixed effects model, we have to:
A) Create a dummy variable for every unit and include it in the model.
B) Create a dummy variable for every unit and include all but one in the model.
C) Subtract the unit specific averages from both the dependent and independent variables.
D) Create dummy variables for every unit and subtract the unit specific average from the dependent variable.

Accepted Answer

The LSDV (Least Squares Dummy Variable) approach in a one-way fixed effects model involves creating a dummy variable for each unit (e.g., individual, firm, country) in the panel data, but one must be excluded to avoid the dummy variable trap, which occurs when the dummy variables are perfectly multicollinear with the intercept.

Question 13

The benefit of the de-meaned approach over the LSDV approach is:
A) It gives more accurate coefficient estimates.
B) The coefficient estimates have a lower standard error.
C) Easier to implement if there are a lot of different units.
D) We will be able to estimate coefficients on variables that do not vary within unit.

Accepted Answer

The de-meaned approach is easier to implement when there are a lot of different units because it avoids the need to estimate individual intercepts for each unit, which can be computationally intensive. This approach does not necessarily give more accurate coefficient estimates or lower standard errors compared to the LSDV approach, and it may not be suitable for estimating coefficients on variables that do not vary within unit.

Question 14

Which of the following factors could lead us to believe that a fixed effect model is necessary to control for endogeneity when examining the relationship between corruption (dependent) and regime type (independent) across countries over time?
A) Religion
B) Culture
C) External threat
D) All of the above.

Accepted Answer

Religion, culture, and external threat are all factors that could potentially lead to endogeneity when examining the relationship between corruption and regime type over time. These factors may affect both corruption and regime type, making it difficult to disentangle their effects without controlling for them through a fixed effects model.

Question 15

Which of the following is most likely not a factor that would cause endogeneity (fixed effect is zero) when examining the relationship of bilateral trade (dependent) and trade alliances (independent).
A) Shared language
B) Distance between trading partners
C) Regime type
D) Inflation rate

Accepted Answer

Inflation rate is unlikely to cause endogeneity in the relationship between bilateral trade and trade alliances because it is not directly related to either variable. Shared language, distance between trading partners, and regime type are all factors that could potentially affect both bilateral trade and trade alliances, creating endogeneity in the relationship between the two variables.

Question 16

List and provide a brief explanation of three potential fixed effects that could bias a model in the analysis of the relationship between attendance at a private school and test scores.

Accepted Answer

The answer of List and provide a brief explanation of...

Question 17

Describe the issues involved with using a pooled model and given an example of why a pooled model could lead to biased results.

Accepted Answer

The answer of Describe the issues involved with using a...

Question 18

Explain why a fixed effects model is not necessary in a case where fixed effects exist but the fixed effects are not correlated with the independent variable.

Accepted Answer

The answer of Explain why a fixed effects model is...

Question 19

Write down and explain the basic difference in difference equation. Point out which of the coefficients we are most interested in.

Accepted Answer

The answer of Write down and explain the basic difference...

Question 20

Explain why coefficients on variables that do not vary within the unit cannot be estimated in a fixed effects model.

Accepted Answer

The answer of Explain why coefficients on variables that do...

Quiz 8: Using Fixed Effects to Fight Endogeneity in Panel Data and Difference-In-Difference Models

A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.

The fixed effect ( $\alpha$ ) is the part of the unobserved error and it is different for every observation for unit i.

The value of the $\alpha$ _iparameter can potentially take on a different value for each unit i.

When dealing with fixed effects, a de-meaned model approach is superior to the LSDV approach because the de-meaned model gives us more accurate coefficient estimates.

Having a model that controls for fixed effects even when the fixed effects are 0 ( $\alpha$ _i=0 for all units) will not cause bias.

Which of the following is true about fixed effects models?

Pooled OLS models are biased when:

In order to run a two-way fixed effect model, we can use:

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who got the treatment before they received it is:

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who in the control group after the treatment was administered is:

Which of the following is a reason why fixed effect models can't estimate coefficients on variables that do not vary within unit?

In order to employ the LSDV approach in a one-way fixed effects model, we have to:

The benefit of the de-meaned approach over the LSDV approach is:

Which of the following factors could lead us to believe that a fixed effect model is necessary to control for endogeneity when examining the relationship between corruption (dependent) and regime type (independent) across countries over time?

Which of the following is most likely not a factor that would cause endogeneity (fixed effect is zero) when examining the relationship of bilateral trade (dependent) and trade alliances (independent) .

List and provide a brief explanation of three potential fixed effects that could bias a model in the analysis of the relationship between attendance at a private school and test scores.

Describe the issues involved with using a pooled model and given an example of why a pooled model could lead to biased results.

Explain why a fixed effects model is not necessary in a case where fixed effects exist but the fixed effects are not correlated with the independent variable.

Write down and explain the basic difference in difference equation. Point out which of the coefficients we are most interested in.

Explain why coefficients on variables that do not vary within the unit cannot be estimated in a fixed effects model.

Quiz 8: Using Fixed Effects to Fight Endogeneity in Panel Data and Difference-In-Difference Models

A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.

The fixed effect ( α\alphaα ) is the part of the unobserved error and it is different for every observation for unit i.

The value of the α\alphaα i parameter can potentially take on a different value for each unit i.

When dealing with fixed effects, a de-meaned model approach is superior to the LSDV approach because the de-meaned model gives us more accurate coefficient estimates.

Having a model that controls for fixed effects even when the fixed effects are 0 ( α\alphaα i=0 for all units) will not cause bias.

Which of the following is true about fixed effects models?

Pooled OLS models are biased when:

In order to run a two-way fixed effect model, we can use:

Given Yit = B0 + B1Treatedi + B2Aftert + B3(Treatedi*Aftert) + eit, the expected value of the dependent variable for those who got the treatment before they received it is:

Given Yit = B0 + B1Treatedi + B2Aftert + B3(Treatedi*Aftert) + eit, the expected value of the dependent variable for those who in the control group after the treatment was administered is:

Which of the following is a reason why fixed effect models can't estimate coefficients on variables that do not vary within unit?

In order to employ the LSDV approach in a one-way fixed effects model, we have to:

The benefit of the de-meaned approach over the LSDV approach is:

Which of the following factors could lead us to believe that a fixed effect model is necessary to control for endogeneity when examining the relationship between corruption (dependent) and regime type (independent) across countries over time?

Which of the following is most likely not a factor that would cause endogeneity (fixed effect is zero) when examining the relationship of bilateral trade (dependent) and trade alliances (independent) .

List and provide a brief explanation of three potential fixed effects that could bias a model in the analysis of the relationship between attendance at a private school and test scores.

Describe the issues involved with using a pooled model and given an example of why a pooled model could lead to biased results.

Explain why a fixed effects model is not necessary in a case where fixed effects exist but the fixed effects are not correlated with the independent variable.

Write down and explain the basic difference in difference equation. Point out which of the coefficients we are most interested in.

Explain why coefficients on variables that do not vary within the unit cannot be estimated in a fixed effects model.

The fixed effect ( $\alpha$ ) is the part of the unobserved error and it is different for every observation for unit i.

The value of the $\alpha$ _iparameter can potentially take on a different value for each unit i.

Having a model that controls for fixed effects even when the fixed effects are 0 ( $\alpha$ _i=0 for all units) will not cause bias.

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who got the treatment before they received it is:

Given Y_it= B₀+ B₁Treated_i+ B2After_t+ B3(Treated_i*After_t) + e_it, the expected value of the dependent variable for those who in the control group after the treatment was administered is: