We study in this work the importance of depth in convolutional models for text classification, either when character or word inputs are considered. We show on 5 standard text classification and sentiment analysis tasks that deep models indeed give better performances than shallow networks when the text input is represented as a sequence of characters. However, a simple shallow-and-wide network outperforms deep models such as DenseNet with word inputs. Our shallow word model further establishes new state-of-the-art performances on two datasets: Yelp Binary (95.9\%) and Yelp Full (64.9\%). Do Convolutional Networks need to be Deep for Text Classification ?