Modeling heterogeneity among firms, workers, or countries ensures robust empirical analysis and also provides a measurement of important, but latent, economic forces. However, to model with economic theory alone is challenging and leaves room for data-driven econometric methods to assist. Furthermore, in contrast to a single cross-section, panel data offer more observations to model heterogeneity flexibly, to sharpen estimates' precision, and to reduce estimates' finite-sample bias. This dissertation develops data-driven econometric panel methods to account for heterogeneity and applies them to estimate the firm's production function for policy analysis. And there are three substantive chapters. The second chapter proposes an estimator for the partially linear model with additive time-varying grouped fixed effects. Popular empirical methods, such as regression discontinuity and control functions, employ the partially linear model. The addition of grouped fixed effects allows time-varying heterogeneity, which is a natural extension in the panel environment. The second chapter's estimator combines the use of the series approximation and the K-mean algorithm. Furthermore, I provide sufficient conditions to characterise the estimator's asymptotic performance - under large $N$ and $T$ but with $N$ as comparatively larger than $T$. The third chapter studies an Olley-Pakes type (proxy variable) estimator for the firm's production function. Empirical economic literature extensively uses the proxy variable approach to answer policy questions on the economy's productivity and the market's competitiveness. By using the partially linear model with Grouped Fixed Effects, the third chapter extends the proxy variable approach to allow differences in firms' productivity dynamics by finitely many groups. The extension provides a new framework for empirical research to identify intrinsic differences in firms' technologies and study the inequalities among firms' performances. Using Chilean manufacturing data, I find the productivity dynamics groups explain the firm's performance in market share and the ability to export. The fourth chapter, co-authored with Xu Cheng and Frank Schorfheide, studies multidimensional latent heterogeneity in a GMM framework. We present a generalised K-mean algorithm to account for multidimensional heterogeneity in our nonlinear GMM framework. Similarly, we provide sufficient conditions to characterise the estimator's asymptotic performance - under large $N$ and $T$ but with $N$ as comparatively larger than $T$. For application, we consider the dynamic panel estimation of the firm's production function. Here, the firms have latent heterogeneity in their output elasticities and mean productivity levels. The fourth chapter concludes in applying our estimator to document the rise of aggregate mark-up in the US economy.