This paper seeks to device and estimate an accounting framework for international comparison of income that takes into account relevant features of poor countries that are often disregarded in the more traditional single-good, Cobb-Douglas accounting framework. Our framework allows for multiple sectors, namely agriculture, manufacturing and services, as well as the possibility of home production. As poor countries are mainly agricultural and their home production could be potentially large, we consider these two features critical to correctly assess the contribution of factors of production versus TFP. Sectorial production functions can either be Cobb-Douglas with different capital shares, but we also study more general CES production functions. We assess how well a single-good, Cobb-Douglas framework performs compared with ours. We show that the standard framework could significantly downplay the role of factors of production, particularly for poor countries, if factor shares are significantly different across sectors. Given the critical importance of sectorial factor shares and the poor basis for any calibration, especially for poor countries, we proceed to estimate these and other parameters of the model under different identifying assumptions. The estimation exploits sectorial information on outputs and inputs.