This dissertation examines the relationship between productivity growth and research activities of heterogeneous firms, and the contribution of firm heterogeneity to business cycle fluctuations. The first chapter uses a dynamic model to study firms' decisions on whether to conduct research in house, with external units or via both modes. Productivity is modeled to evolve endogenously according to Research and Development (R&D) modes, and the costs of starting and continuing research are random and mode specific. Model estimates from a panel of Chinese manufacturing firms show that in-house R&D is more effective and costs less to maintain, but smaller firms choose external R&D because of its lower startup cost. These estimates are consistent with the observed cross-sectional differences in firm size by research status, and can match the persistence and transition dynamics in R&D modes. Simulation exercises show that continuation cost reduction induces more changes in R&D decisions, but start up cost reduction leads to most of the aggregate productivity gain. The second chapter investigates the impact of innovation on firm level prices. This impact depends on how innovation affects quality and efficiency and how the firm passes these changes onto prices. Estimation results of the empirical model with a panel of Spanish firms show that firms take advantage of process innovations to enlarge markups by not completely passing onto prices the decrease in cost. Product innovations could increase or decrease cost but they do not affect markups, thus we do not find prices to change systematically with them. The third chapter examines the contribution of firm level shocks to output fluctuations for four OECD countries (US, Germany, Canada and the UK). Recent studies stemming from Gabaix (2011) show that when few firms account for a disproportionately large share of production, shocks to these firms can propagate to generate business cycle fluctuations. However, we find that while firm size distribution is highly skewed in these four economies, the ability of the largest firms to transmit shocks is not universal and thus should not be taken for granted.