Models with high dimensional sets of fixed effects are frequently used to examine, among others, linked employer-employee data, student outcomes and migration. Estimating these models is computationally difficult, so simplifying assumptions that are likely to cause bias are often invoked to make computation feasible and specification tests are rarely conducted. I present a simple method to estimate large two-way fixed effects (TWFE) and worker-firm match effect models without additional assumptions. It computes the exact OLS solution including estimates of the fixed effects and makes testing feasible even with multi-way clustered errors. An application using German linked employer-employee data illustrates the advantages: The data reject the assumptions of simpler estimators and omitting match effects biases estimates including the returns to experience and the gender wage gap. Specification tests detect both problems. The results suggest that firm fixed effects, not match effects, are the main channel through which job transitions drive wage dynamics, which underlines the importance of firm heterogeneity for labor market dynamics.