What is the linear regression formula?
Yi = a + ß1X1i + ß2X21 + ….,
Where:
Yi = Dependent variable for observation i
Xti = Independent variable for observation i
A,ß = coefficients to be estimated
Example: If independent variables are # of experience and job description:
Wage = a + ß# of years of experience + ß job description
What are the 5 outputs in R of linear regressions?
- Estimate: point estimate of ß
- Std. Error: Precision of estimate
- T value = Estimate / std error
- Pr (>|t|) = p-value (significance)
- R-squared: fraction of variance explained
What are three types of data in panel regression?
- Cross-section
Structure: many units, one period - Time series
Structure: one unit, many periods - Panel
Structure: many units, many periods
What is a balanced panel?
same number of observations per unit
What is an unbalanced panel?
not same number of observations per unit
What is a pooled regression model?
running a linear OLS regression model with panel data
What are the two main problems with pooled regression models?
- Technical: violation of uncorrelated errors of OLS is violated as observations within units are often correlated. Leads to biased coefficients and standard errors
- Conceptual: pooled OLS estimates bunches together across and within unit variation of variables.
Give two reasons errors are often correlated within units in a pooled regression model?
- Unobserved unit- or time-constant variables impacting the dependent variable and possibly the independent variables
- Unobserved unit- or time-variables: Variables that have a constant impact over time within units but are not measured in the dataset.
What are the two types of variation within panel data?
- Across unit variation: different values for x and Y with a certain relationship
- Within unit variation: relationship between X and Y within each unit.
Which type of variation is more credible to establish causality?
Within unit variation is more credible to establish how X causes & to change because, comparing the same unit against itself over time is more comprehensive to establish causal effects of X on Y
How does the regression formula look when using only within unit variation?
Yi = a + ß1X1i + … ßnXn1 + ci + ei, where:
Ci = a constant that is different for each unit to be considered an intercept different for each unit. This is called the fixed effect
What are three ways of runing regressions using within unit variation?
- Estimate separate dummy variables for each unit
- Demean Y and X variables by using unit level averages (within transformation)
- Estimate statistical distribution for fixed effects (Random effect)
How do regressions of panel data work when using seperate dummy variables?
If one uses separate dummy variables for each unit, each dummy is just another line in the R output with the Estimate, Std. Error, t value and significance. This shows the effect of the variation within units.
What is the main drawback of using seperate dummy variables for each unit in panel data regressions?
Drawback of using separate dummy variables for each unit: not suitable for larger datasets. That is what you would use within transformation for.
What are the steps of within transformation regressions? And give three benefits of within transformation method?
- Determine the mean value of dependent variable (Y) over the different time t units
- For each time unit: Y – Mean(Y)
This will remove from your dataset all units that have only one observation (time t) as they do not contain any variation
Time fixed effects are accounted for with wave (all different time units observed in dataset)
You can combine different fixed effects too in order to capture effects that are constant within both parameter 1 and parameter 2.
What is meant with clustering standard errors?
Clustering standard errors: this is a solution for accounting for correlation in error terms. Clusters should be made on the same level as your fixed effects.
What are three characteristics of panel regression outcomes?
- Controls for unobserved unit-specific effects that are constant over time
- Looks only at within-unit variation
- Makes panel regression better at answering questions such as ‘did X cause Y’ compared to standard OLS regression
Give two things panel regression cannot be used for?
- Control for unobserved unit-specific effects that vary over time
- Solve all issues of answering ‘did X cause Y’?
