  The spatial autoregressive (SAR) model has been widely applied in various
empirical economic studies to characterize the spatial dependence among
subjects. However, the precision of estimating the SAR model diminishes when
the sample size of the target data is limited. In this paper, we propose a new
transfer learning framework for the SAR model to borrow the information from
similar source data to improve both estimation and prediction. When the
informative source data sets are known, we introduce a two-stage algorithm,
including a transferring stage and a debiasing stage, to estimate the unknown
parameters and also establish the theoretical convergence rates for the
resulting estimators. If we do not know which sources to transfer, a
transferable source detection algorithm is proposed to detect informative
sources data based on spatial residual bootstrap to retain the necessary
spatial dependence. Its detection consistency is also derived. Simulation
studies demonstrate that using informative source data, our transfer learning
algorithm significantly enhances the performance of the classical two-stage
least squares estimator. In the empirical application, we apply our method to
the election prediction in swing states in the 2020 U.S. presidential election,
utilizing polling data from the 2016 U.S. presidential election along with
other demographic and geographical data. The empirical results show that our
method outperforms traditional estimation methods.
