Interpretation of intercept-only fixed effect model

[shenflow]

Suppose we have a fixed effect model for a panel of i firms and t periods. The model includes a fixed effect for the firms i and a constant as the independent variables and some dependent variable (say e.g. firm cashflows). No further independent variables! Put differently, it is an intercept only fixed effects model.

How do we interpret the constant (intercept) in this model? Without the fixed effect, the constant would simply be the average of the dependent variable across firms i and periods t. But what does the fixed effect change exactly?

[PaigeMiller · Accepted solution]

The fixed effect plus the intercept estimates the mean response for each firm. Simple example, heights of people by gender

Intercept  67.5

Males 5

Females 0

Thus, the estimated mean height for males is 72.5.