01:220:322 Chap.8 Dummy Variables and Qualitative Information
Dummy Variables and Qualitative Information
Coding categories
A dummy variable equals one for a category and zero otherwise, and it is named after the category coded one. In a regression with only a dummy, its coefficient is the difference between the two group means and its t statistic tests whether they are equal.
Base groups and the trap
Every dummy coefficient is measured relative to the base group coded zero.
With several categories, include one fewer dummy than categories.
Including a full set with an intercept is the dummy variable trap, a case of perfect collinearity that software resolves by dropping a variable.
Log outcomes
When the outcome is in logs, one hundred times a dummy coefficient is an approximate percentage gap, and the exponential gives the exact gap, which matters for larger coefficients.
Interactions
Two dummies and their product define four groups; each group mean is the intercept plus every coefficient that switches on for that group, and the interaction is the difference between two premia.
Interacting a dummy with a continuous variable lets the slope differ by group, and a claim of no group difference then needs a joint F test on every term involving the dummy.
The linear probability model
With a binary outcome, OLS estimates probabilities: each slope is a change in probability measured in percentage points.
The model can predict probabilities below zero or above one, forces constant effects, and is heteroskedastic by construction, so robust standard errors are required.
Comparing two non-base groups
With several categories each coefficient compares one group with the base. To compare two other groups, test the difference of their coefficients with lincom, or rerun the regression with one of them as the base.
Both routes give the same estimate and standard error.
Different slopes by group
An interaction between a dummy and a continuous variable lets each group have its own slope. The main-effect coefficient on the dummy is then the gap when the continuous variable equals zero, so centring that variable at a meaningful value makes the gap interpretable.
What this chapter covers
- 01
Dummy coefficients as group differences
- 02
Base groups and the dummy variable trap
- 03
Percentage gaps with log outcomes
- 04
Several categories and ordinal variables
- 05
Dummy interactions and cell means
- 06
Linear probability model and its limits
Worked example · free
Reading a linear probability model
- 2Each extra study hour raises the pass probability by 5.8 percentage points, holding tutoring fixed.
- 2Tutored students are 11 percentage points more likely to pass at the same study hours.
- 2Prediction: 0.21 + 0.058(16) + 0.11 = 1.248, above one, a known shortcoming of the model.
Key terms
- Dummy Variable
- A variable equal to one for a category and zero otherwise.
- Base Group
- The category coded zero on every dummy, against which dummy coefficients are measured.
- Dummy Variable Trap
- Including a dummy for every category along with an intercept, which creates perfect collinearity.
- Linear Probability Model
- A regression with a binary outcome in which each slope is a change in probability.
- Ordinal Variable
- A variable whose categories have a meaningful order but not meaningful spacing.
- Interaction Coefficient
- The change in one variable's effect when another variable switches on or rises by one unit.
Dummy Variables and Qualitative Information FAQ
Why can I not include both a male and a female dummy?
With an intercept in the model the two dummies add up to one for everyone, an exact linear relation with the constant. That is perfect collinearity, and software will drop one of them.
How do I get the mean for a group from a model with two dummies and an interaction?
Start from the intercept and add every coefficient whose variables equal one for that group. The interaction is added only for the group where both dummies are one.
What are the main weaknesses of the linear probability model?
Predictions can fall outside the zero to one range, every regressor has the same effect at all levels, and the error variance depends on the regressors, which is why robust inference is needed.
How is a dummy coefficient read when the outcome is in logs?
Multiply it by one hundred for an approximate percentage gap relative to the base group. For coefficients above about 0.1 in size, report the exact gap using the exponential, which can differ by several points.
Why are interaction coefficients so often insignificant?
They measure a difference between two effects, each estimated with error, and they rely on fewer observations in the relevant cells. Wide standard errors are common, which is one reason joint tests of all group terms are useful.
Exam move
For every dummy regression, write out each group's predicted mean in a small table before interpreting any single coefficient.
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