Can macro F1 score be greater than micro F1 score?
Yes, it can.

Example with Precision


Class A: 1 TP and 1 FP
Class B: 10 TP and 90 FP
Class C: 1 TP and 1 FP
Class D: 1 TP and 1 FP


Here, $P_A = P_C = P_D = 0.5$, $P_B = 0.1$

Macro-F1 is: $P_M = \frac{P_A + P_B + P_C + P_D}{4} = 0.4 $,
while micro-F1 is: $P_m=\frac{TP_A+TP_B+TP_C+TP_D}{TP_A+TP_B+TP_C+TP_D+FP_A+FP_B+FP_D+FP_D} = 0.123$, hence $P_M &gt; P_m$.