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

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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.

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

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We are most interested in B3, the coefficient that indicates that after taking into account the fact that the treated units may be different (B1) and that the post-treatment period may be different than the pre-treatment period for all units (B2) there are differences in the treated units in the post-treatment period
Yit=β0+β1 Treated i+β2 After t+β3( Treated i× After t)+ϵitY _ { i t } = \beta _ { 0 } + \beta _ { 1 } \text { Treated } _ { i } + \beta _ { 2 } \text { After } _ { t } + \beta _ { 3 } \left( \text { Treated } _ { i } \times \text { After } _ { t } \right) + \epsilon _ { i t }

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

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Pooled OLS models are biased when:

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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.

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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:

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

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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.

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Which of the following is true about fixed effects models?

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

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

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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).

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

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

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

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

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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?

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

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

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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:

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