This paper merges two isolated bodies of literature: the Markov chain model with macro data, formally described in detail by MacRae in 1977, and the Ecological inference model, the pitfalls of which were discussed by Robinson in 1950. Both are choice models. They have the same likelihood function and the same regression equation.
Decades ago, this likelihood function was computationally demanding. This has led to the use of several approximate methods, in particular with the Ecological inference model. Due to the improvement in computer hardware and software since Macrae (1977), the exact maximum likelihood should now be the preferred estimation method.
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