Compression techniques for deep learning have become increasingly popular, particularly in settings where latency and memory constraints are imposed. Several methods, such as pruning, distillation, and quantization, have been adopted for compressing models, each providing distinct advantages. However, existing literature demonstrates that compressing deep learning models could affect their fairness. Our analysis involves a comprehensive evaluation of pruned, distilled, and quantized language models, which we benchmark across a range of intrinsic and extrinsic metrics for measuring bias in text classification. We also investigate the impact of using multilingual models and evaluation measures. Our findings highlight the significance of considering both the pre-trained model and the chosen compression strategy in developing equitable language technologies. The results also indicate that compression strategies can have an adverse effect on fairness measures.