In the discussions of trading, unemployment and income distribution inequality, this question is raised by economists that in economic development of developing and developed countries, which policy is necessary in the first stage. Is trading liberalization the pre-requirement of transfer from a close economy to a relative open economy and is it necessary for the developed economy compared to other policies, or after achieving an economic growth level and reduction of class difference, poverty and unemployment, the countries should start trade liberalization. By this pre-requirement, a two-stage systematic generalized method of moments technique (GMM) presented by Blundell & bond (1998) during 1991-2008 is applied to evaluate the relationship between three main indices for both groups of selected developed and developing countries. The results of study show that in both groups of countries, high production and increasing foreign direct investment provide open economy and can create employment and reduce unemployment but by increasing population growth rate, unemployment and inflation in both groups of countries, household income inequality is increased. The turning point of this study is regarding household income inequality as increased by increasing economic growth rate and control of open economy in developing counties but in developed countries, increasing economic growth rate and open economy, household income distribution is improved. JEL Classification: C33, C36, D31, F43.