  Estimating weights in the synthetic control method, typically resulting in
sparse weights where only a few control units have non-zero weights, involves
an optimization procedure that simultaneously selects and aligns control units
to closely match the treated unit. However, this simultaneous selection and
alignment of control units may lead to a loss of efficiency. Another concern
arising from the aforementioned procedure is its susceptibility to
under-fitting due to imperfect pre-treatment fit. It is not uncommon for the
linear combination, using nonnegative weights, of pre-treatment period outcomes
for the control units to inadequately approximate the pre-treatment outcomes
for the treated unit. To address both of these issues, this paper proposes a
simple and effective method called Synthetic Regressing Control (SRC). The SRC
method begins by performing the univariate linear regression to appropriately
align the pre-treatment periods of the control units with the treated unit.
Subsequently, a SRC estimator is obtained by synthesizing (taking a weighted
average) the fitted controls. To determine the weights in the synthesis
procedure, we propose an approach that utilizes a criterion of unbiased risk
estimator. Theoretically, we show that the synthesis way is asymptotically
optimal in the sense of achieving the lowest possible squared error. Extensive
numerical experiments highlight the advantages of the SRC method.
