This paper uses Tanzanian annual time series data for the period 2007-2016 in a Bayesian MCMC (Markov Chain Monte Carlo) to establish and compare the impact of natural gas revenues and institutional quality in the economy. We found that, the interaction effect between natural gas revenues and institutional quality as contributors to the economy was wide. This difference seems to be largely explained by institutional quality. This suggests that strengthening institutional quality structures in the country will reshape natural gas revenues, providing higher national economic growth. The results are robust due to combinations of prior distribution and likelihood function. These findings have important implications for Tanzania, while also suggesting developing countries with natural resources need to ensure they have implemented appropriate policy measures to improve institutional quality.