Here we present a Joint-Tissue Imputation (JTI) approach and a Mendelian Randomization (MR) framework for causal inference, MR-JTI. JTI borrows information across transcriptomes of different tissues, leveraging shared genetic regulation, to improve prediction performance in a tissue-dependent manner. Notably, JTI includes single-tissue imputation PrediXcan as a special case and outperforms other single-tissue approaches (BSLMM and Dirichlet Process Regression). MR-JTI models variant-level heterogeneity (primarily due to horizontal pleiotropy, addressing a major challenge of TWAS interpretation) and performs causal inference with type-I error control. We make explicit the connection between the genetic architecture of gene expression and of complex traits, and the suitability of MR as a causal inference strategy for TWAS. We provide a resource of imputation models generated from GTEx and PsychENCODE panels. Analysis of biobanks and meta-analysis data and extensive simulations show substantially improved statistical power, replication, and causal mapping rate for JTI relative to existing approaches.