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We analyze the properties of a number of data-rich methods that are widely used in macroeconomic forecasting, in particular, principal components (PC) and Bayesian regression, as well as a lesser-known alternative, partial least squares (PLS) regression. In the latter method, linear, orthogonal combinations of a large number of predictor variables are constructed such that the covariance between a target variable and these common components is maximized. Existing studies have focused on modeling the target variable as function of a finite set of unobserved common factors that underlies a large set of predictor variables, whereas we assume that this target variable depends directly on the whole set of predictor variables. Given this set-up, we show theoretically that under a variety of different unobserved factor structures, PLS and Bayesian regression provide asymptotically the best fit for the target variable of interest. This includes the case of an asymptotically weak factor structure for the predictor variables, for which it is known that PC regression becomes inconsistent. Monte Carlo experiments confirm our theoretical results that PLS regression is close to Bayesian regression when the data have a factor structure. When the factor structure in the data becomes weak, PLS and Bayesian regression outperform PC regression. Finally, we apply PLS, principal components, and Bayesian regressions on a large panel of monthly U.S. macroeconomic data to forecast key variables across different subperiods, and PLS and Bayesian regression usually have the best out-of-sample performances.