  In the data-rich environment, using many economic predictors to forecast a
few key variables has become a new trend in econometrics. The commonly used
approach is factor augment (FA) approach. In this paper, we pursue another
direction, variable selection (VS) approach, to handle high-dimensional
predictors. VS is an active topic in statistics and computer science. However,
it does not receive as much attention as FA in economics. This paper introduces
several cutting-edge VS methods to economic forecasting, which includes: (1)
classical greedy procedures; (2) l1 regularization; (3) gradient descent with
sparsification and (4) meta-heuristic algorithms. Comprehensive simulation
studies are conducted to compare their variable selection accuracy and
prediction performance under different scenarios. Among the reviewed methods, a
meta-heuristic algorithm called sequential Monte Carlo algorithm performs the
best. Surprisingly the classical forward selection is comparable to it and
better than other more sophisticated algorithms. In addition, we apply these VS
methods on economic forecasting and compare with the popular FA approach. It
turns out for employment rate and CPI inflation, some VS methods can achieve
considerable improvement over FA, and the selected predictors can be well
explained by economic theories.
