Research Skills Part 4 Flashcards
y = a + ßD > Give the mean for D = 0 and D = 1
y = a + ßD
mean D=0: a
mean D=1: a + ß
Mean of group 0 is significantly different from mean of group 1 if t-stat of ß is significant.
Give mean for: y = ß1 + ß2D2 + ß3D3 + ß4D4
y = ß1 + ß2D2 + ß3D3 + ß4D4
base group: ß1
group 2: a + ß2
group 3: a + ß3
group 4: a + ß4
Give the mean and intercepts: y = ß1 + ß2D + ß3X + ß4(X*D)
y = ß1 + ß2D + ß3X + ß4(X*D)
Now, the effect of X depends on D and vice versa. This means that the slope for each group is different.
D=0 > y = ß1 + ß3X
ß1 = intercept
ß3 = slope
D=1 > y = (ß1 + ß2) + (ß3 + ß4)X
(ß1 + ß2) = intercept
(ß3 + ß4) = slope
There’s a difference in marginal effect if ß4 is unequal to 0!
What are the benefits of panel data?
- Panel data methods can reduce the omitted variables bias
- Possibility to control for unobserved common components
- Precision of estimates increase by using more data
- More flexibility to model dynamics at individual level
What are the drawbacks of panel data?
- Regression assumptions are easily violated > we should worry more about cross-sectional correlations between observations.
- Econometric methods are more complicated
What are the drawbacks of using a standard pooled OLS estimator? And what can we do to fix this?
- It does not account for cross-sectional / time-series correlation between different residuals > S.E. are too small
- It is biased if omitted variables are correlated with indep vars.
We can use a pooled OLS regression with clustered (panel-robust) standard errors
- we can allow the errors to be correlated over time within the same i (firm) (e.g. y = firm leverage)
- allow the errors to be correlated across firms within the same period (e.g. y = stock return)
- or both
We can also use fixed effects (FE) in a panel model. When do you include fixed effects?
Example: control for individual effects by adding dummy for each firm, where D1i is dummy equal to one for all observations on first unit (i.e. i = 1) and zero otherwise, etc.
If the firm effects vary RANDOMLY across firms, unrelated to Xit we can treat them as part of the error term. In this case pooled OLS with (panel-robust) standard errors is fine.
The Hausman Test tests if fixed effects are needed. If it rejects, we need fixed effects.
What is the difference between random effects and fixed effects?
A random-effects model assumes that explanatory variables have fixed relationships with the response variable across all observations, but that these fixed effects may vary from one observation to another. For example, let’s say you might be interested in studying how different levels of stress affect heart rate and blood pressure; here the assumption is that there is a fixed difference (i.e., slope) between each level of stress and its corresponding outcome (i.e., heart rate or blood pressure). However, this fixed difference can vary across individuals (e.g., some people might experience more stress than others when exposed to the same level of stress).
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Fixed effect models assume that the explanatory variable has a fixed or constant relationship with the response variable across all observations.
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An advantage of random effects is that you can include time invariant variables (i.e. gender). In the fixed effects model these variables are absorbed by the intercept.
Why is the random effects estimator (GLS) more efficient than OLS?
The random effects estimator (GLS) is more efficient because it exploits the error structure (and assumes homoskedasticity).
What’s the difference between firm fixed effects and time fixed effects?
Firm fixed effects allow intercepts to vary across firms
- Removes omitted variable bias due to (non-random) individual effects
- Removes bias in std. errors due to autocorrelation in error terms
- Con: cannot include time-invariant (constant) indep vars
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Time fixed effects allow intercepts to vary over time. Including time dummies removes the omitted variable bias due to unobserved time effects and removes bias in S.E.s due to cross-sectional correlation (within period correlation).
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Time fixed effects capture cross-sectional correlation, while firm fixed effects capture autocorrelation
Assume we wish to estimate the impact of X on Y, separately for firms with D=1 and D=0. How do we do this in one regression?
A. Y = X + D
B. Y = X + XD
C. Y = X + D + XD
D. Y = D + X*D
C
When estimating a panel model with firm fixed effects…
A. … we obtain more precise estimates of the slope coefficients
B. … we cannot include firm-invariant explanatory variables
C. … we cannot include time-invariant explanatory variables
D. … we cannot use standard errors clustered by firm
C
What is/are the main reason(s) to include firm fixed effects in a panel regression?
A. improving precision of the estimation of the slope coefficients
B. obtaining appropriate standard errors for the slope coefficients
C. controlling for time-invariant firm-specific factors
D. reducing bias in the estimation of the slope coefficients
C & D
Consider a linear probability model, explaining failing (y=1) the MSc. The coefficient for female is -0.03. What does this mean?
A. female students are 0.03% less likely to fail
B. male students are 3% more likely to pass
C. female students are 3% more likely to pass
C
Consider a logit model, explaining failing (y=1) the MSc. The coefficient for female is -0.03. What does this mean?
A. female students are more likely to pass
B. male students are more likely to pass
C. female students are 3% more likely to pass
D. don’t know. need to calculate marginal effects
A
