We study the problem of predicting regional economy of U.S. counties with open migration data collected from U.S. Internal Revenue Service (IRS) records. To capture the complicated correlations between them, we design a novel Attentional Multi-graph Convolutional Network (AMCN), which models the migration behavior as a multi-graph with different types of edges denoting the migration flows collected from heterogeneous sources of different years and different demographics. AMCN extracts high quality feature from the migration multi-graph by first applying customized aggregator functions on the induced subgraphs, and then fusing the aggregated features with a higher-order attentional aggregator function. In addition, we address the data sparsity problem with an important neighbor discovery algorithm that can automatically supplement important neighbors that are absent in the empirical data. Experiment results show our AMCN model significantly outperforms all baselines in terms of reducing the relative mean square error by 43.8% against the classic regression model and by 12.7% against the state-of-the-art deep learning baselines. In-depth model analysis shows our proposed AMCN model reveals insightful correlations between regional economy and migration data.