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Multi-touch attribution (MTA), aiming to estimate the contribution of each advertisement touchpoint in conversion journeys, is essential for budget allocation and automatically advertising. Existing methods first train a model to predict the conversion probability of the advertisement journeys with historical data and calculate the attribution of each touchpoint using counterfactual predictions. An assumption of these works is the conversion prediction model is unbiased, i.e., it can give accurate predictions on any randomly assigned journey, including both the factual and counterfactual ones. Nevertheless, this assumption does not always hold as the exposed advertisements are recommended according to user preferences. This confounding bias of users would lead to an out-of-distribution (OOD) problem in the counterfactual prediction and cause concept drift in attribution. In this paper, we define the causal MTA task and propose CausalMTA to eliminate the influence of user preferences. It systemically eliminates the confounding bias from both static and dynamic preferences to learn the conversion prediction model using historical data. We also provide a theoretical analysis to prove CausalMTA can learn an unbiased prediction model with sufficient data. Extensive experiments on both public datasets and the impression data in an e-commerce company show that CausalMTA not only achieves better prediction performance than the state-of-the-art method but also generates meaningful attribution credits across different advertising channels.