Ethnicity and race are vital for understanding representation, yet individual-level data are often unavailable. Recent methodological advances have allowed researchers to impute racial and ethnic classifications based on publicly available information, but predictions vary in their accuracy and can introduce statistical biases in downstream analyses. We provide an overview of common estimation methods, including Bayesian approaches and machine learning techniques that use names or images as inputs. We propose and test a hybrid approach that combines surname-based Bayesian estimation with the use of publicly available images in a convolutional neural network. We find that the proposed approach not only reduces statistical bias in downstream analyses but also improves accuracy in a sample of over 16,000 local elected officials. We conclude with a discussion of caveats and describe settings where the hybrid approach is especially suitable.