  We highlight that match fixed effects, represented by the coefficients of
interaction terms involving dummy variables for two elements, lack
identification without specific restrictions on parameters. Consequently, the
coefficients typically reported as relative match fixed effects by statistical
software are not interpretable. To address this, we establish normalization
conditions that enable identification of match fixed effect parameters as
interpretable indicators of unobserved match affinity, facilitating comparisons
among observed matches. Using data from middle school students in the 2007
Trends in International Mathematics and Science Study (TIMSS), we highlight the
distribution of comparable match fixed effects within a specific school.
