Message-level and word-level polarity classification are two popular tasks in Twitter sentiment analysis. They have been commonly addressed by training supervised models from labelled data. The main limitation of these models is the high cost of data annotation. Transferring existing labels from a related problem domain is one possible solution for this problem. In this paper, we study how to transfer sentiment labels from the word domain to the tweet domain and vice versa by making their corresponding instances compatible. We model instances of these two domains as the aggregation of instances from the other (i.e., tweets are treated as collections of the words they contain and words are treated as collections of the tweets in which they occur) and perform aggregation by averaging the corresponding constituents. We study two different setups for averaging tweet and word vectors: 1) representing tweets by standard NLP features such as unigrams and part-of-speech tags and words by averaging the vectors of the tweets in which they occur, and 2) representing words using skip-gram embeddings and tweets as the average embedding vector of their words. A consequence of our approach is that instances of both domains reside in the same feature space. Thus, a sentiment classifier trained on labelled data from one domain can be used to classify instances from the other one. We evaluate this approach in two transfer learning tasks: 1) sentiment classification of tweets by applying a word-level sentiment classifier, and 2) induction of a polarity lexicon by applying a tweet-level polarity classifier. Our results show that the proposed model can successfully classify words and tweets after transfer.