The multicountry model was developed in the early 1980s by Ray Fair, and the first complete description of it is in
Fair (1984), Specification, Estimation, and Analysis of Macroeconometric Models.
The latest version of the model is the MCJ model. The MCJ model consists of estimated structural equations for 37 countries. There are also estimated trade share equations for 56 countries plus an "all other" category, labelled "AO". The trade share matrix is thus 57 x 57. The data for the non US countries begin in 1960. Some of the country models are annual rather than quarterly. The estimation periods vary from country to country. They end at late as 2017:4. The model can be solved through 2016:4. The estimation technique for all the countries is two stage least squares except when there are too few observations to make the technique practical, where ordinary least squares is used. A complete description of the MCJ model is in Macroeconometric Modeling: 2018.