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The self-attention module is a key component of Transformer-based models, wherein each token pays attention to every other token. Recent studies have shown that these heads exhibit syntactic, semantic, or local behaviour. Some studies have also identified promise in restricting this attention to be local, i.e., a token attending to other tokens only in a small neighbourhood around it. However, no conclusive evidence exists that such local attention alone is sufficient to achieve high accuracy on multiple NLP tasks. In this work, we systematically analyse the role of locality information in learnt models and contrast it with the role of syntactic information. More specifically, we first do a sensitivity analysis and show that, at every layer, the representation of a token is much more sensitive to tokens in a small neighborhood around it than to tokens which are syntactically related to it. We then define an attention bias metric to determine whether a head pays more attention to local tokens or to syntactically related tokens. We show that a larger fraction of heads have a locality bias as compared to a syntactic bias. Having established the importance of local attention heads, we train and evaluate models where varying fractions of the attention heads are constrained to be local. Such models would be more efficient as they would have fewer computations in the attention layer. We evaluate these models on 4 GLUE datasets (QQP, SST-2, MRPC, QNLI) and 2 MT datasets (En-De, En-Ru) and clearly demonstrate that such constrained models have comparable performance to the unconstrained models. Through this systematic evaluation we establish that attention in Transformer-based models can be constrained to be local without affecting performance.