This paper presents an empirical analysis of the impact of institutions on the economic growth of 27 developing countries during the period 1990-2014. Many creative models of panel data allow variations in slope coefficients both across time and cross-sectional units. All models were established in a Bayesian structure and their performance was tested by using an interesting application of the effect of institution on GDP. Technical details of all these models are given and tools are presented to compare their performance in the Bayesian system. Besides, panel data models and posterior model pools are provided for an insight into the institution's relationship with economic development. The derivation of Bayesian panel data models is included. The previous data has been used in this study and normal gamma prior is used for the models of panel data. 2SLS estimation technique has been used to analyze the classical estimation of panel data models. In the paper, developing countries were viewed as a whole. The study's evaluated results have shown that panel data models are valid Bayesian methodology models. In the Bayesian approach, the results of all independent variables affect the dependent variable significantly and positively. Based on all model standard defects, it is necessary to say that the Fixed Effect Model is the best in Bayesian panel data estimation methods. It was also shown that in comparison to other models, the fixed-effect model has the lowest standard error value.