Text as Priors

This paper studies how textual information can be used as prior information in high-dimensional penalized estimation. Rather than treating text as an additional set of regressors, we use textual analysis to construct two classes of priors: linkage priors, which encode the relative relevance of covariates, and direction priors, which encode prior information about coefficient signs. We incorporate these priors through weighted and asymmetric LASSO procedures. We show that, when the priors are sufficiently informative, they improve variable selection by relaxing the irrepresentable condition required for selection consistency of the standard LASSO, especially in settings with strongly correlated covariates. We illustrate the framework in three applications based on Chinese financial news: cross-firm return prediction, large precision matrix estimation for portfolio construction, and high-dimensional text regression with sentiment-based sign restrictions. Overall, the results show that text can enhance high-dimensional estimation not only as data, but also as a source of economically meaningful prior information.