The assumption of group heterogeneity has become popular in panel data models. Instead of modeling heterogeneity via unit-specific coefficients, the cross-sectional units are assumed to cluster into groups, and within each group, units share the same coefficients. This thesis develops an econometric framework to incorporate prior knowledge of groups, which is considered additional information that does not enter the likelihood function. The prior knowledge aids in clustering units into groups and sharpens the inference of group-specific parameters, particularly when units are not well-separated. In the first chapter, Incorporating Prior Knowledge of Latent Group Structure in Panel Data Models, we develop a constrained Bayesian grouped estimator that exploits researchers' prior beliefs on groups in a form of pairwise constraints, indicating whether a pair of units is likely to belong to the same group or different groups. We propose a prior to incorporate the pairwise constraints with varying degrees of confidence in the panel data models. In the second chapter, Heterogeneous Effect of Income on Democracy, we revisit the relationship between a country's income and its democratic transition. The proposed framework uncovers a group structure with a moderate number of groups, each exhibiting a unique and distinct trajectory toward democracy. Furthermore, we identify heterogeneous income effects on democracy and, contrary to the initial findings, show that a positive income effect persists in some groups of countries, though quantitatively small. In the third chapter, Forecast US CPI Inflation of Sub-Indices, we predict the inflation of the U.S. CPI sub-indices. The results indicate that the proposed predictor generates more precise density forecasts than standard models, which can be primarily attributed to three key features: the nonparametric Bayesian prior, an a priori belief on group structure, and grouped cross-sectional heteroskedasticity. The three chapters are closely interrelated. Chapter one introduces a novel nonparametric Bayesian prior for panel data models, enabling the estimation of group heterogeneity while considering prior information on the underlying group structure. Chapter two delves into the applied question of income's effect on democracy, where researchers have prior knowledge about the group. This serves as an ideal case study to illustrate the improvement of posterior inference through the use of prior group information. Chapter three focuses on forecasting, exploring the benefits of incorporating prior group knowledge into predictions. Collectively, these chapters provide a comprehensive understanding of analyzing group heterogeneity in panel models while incorporating prior knowledge.