We propose a new likelihood-based estimation method for the sequential search model. By allowing search costs to be heterogeneous across consumers and products, we can directly compute the joint probability of the search sequence and the purchase decision when consumers are searching for the idiosyncratic preference shocks in their utility functions. Under this procedure, one recursively makes random draws for each dimension that requires numerical integration to simulate the probabilities associated with the purchase decision and the search sequence under the sequential search algorithm. We then present details from an extensive simulation study that compares the proposed approach with existing estimation methods recently used for sequential search model estimation, viz., the kernel-smoothed frequency simulator (KSFS) and the crude frequency simulator (CFS). In the empirical application, we apply the proposed method to the Expedia dataset from Kaggle which has previously been analyzed using the KSFS estimator and the assumption of homogeneous search costs. We demonstrate that the proposed method has a better predictive performance associated with differences in the estimated effects of various drivers of clicks and purchases, and highlight the importance of the heterogeneous search costs assumption even when KSFS is used to estimate the sequential search model. Lastly, from a managerial perspective, we show that sorting products by their expected utilities can enhance consumer welfare and increase the number of transactions.