The efficiency of physical capital accumulation plays a critical role for economic growth. This paper aims at examine if economic freedom promotes economic growth via physical capital accumulation. This is done by estimating a production function by replacing the inputs with institutional indices. The first input is GDP per capital growth rate which serve as a proxy for institutional aspects and the other input are the economic freedom indexes which will serve as proxies for physical capital accumulation. This is done by applying the augmented mean group (AMG) estimator that is designed for dealing with macro panel data analysis, including twenty developing countries where the economies have experienced a rapid growth, and the time period are between 1995 and 2017. The theoretical framework is based on the Solow growth model, institutional theory and marginal efficiency of capital (MEC). The results show that economic freedom promotes economic growth via physical capital accumulation where GDP per capital growth rate served as a proxy for institutional aspects and economic freedom indexes as proxies for physical capital accumulation. The results also show that the AMG estimator is the best fit for macro panel data analysis since it are designed for dealing with heterogeneity.