Deep neural networks are computationally expensive which has motivated the development of model compression techniques to reduce the resource consumption. Nevertheless, recent studies have suggested that model compression can have an adverse effect on algorithmic fairness, amplifying existing biases in machine learning models. With this work we aim to extend those studies to the context of facial expression recognition. To do that, we set up a neural network classifier to perform facial expression recognition and implement several model compression techniques on top of it. We then run experiments on two facial expression datasets, namely the Extended Cohn-Kanade Dataset (CK+DB) and the Real-World Affective Faces Database (RAF-DB), to examine the individual and combined effect that compression techniques have on the model size, accuracy and fairness. Our experimental results show that: (i) Compression and quantisation achieve significant reduction in model size with minimal impact on overall accuracy for both CK+ DB and RAFDB; (ii) in terms of model accuracy, the classifier trained and tested on RAF-DB is more robust to compression compared to the CK+ DB; and (iii) for RAF-DB, the different compression strategies do not increase the gap in predictive performance across the sensitive attributes of gender, race and age which is in contrast with the results on the CK+ DB where compression seems to amplify existing biases for gender.