CGD just posted my new working paper that explains the theory and practice of Maximum Likelihood estimation of fully observed recursive mixed-process equation systems.
Why should you care? It relates directly to a study I mentioned before, which is one of the most important evaluations of the impact of microcredit on borrowing households. Mark Pitt of Brown University and Shahidur Khandker of the World Bank wrote it, and published it in the prestigious Journal of Political Economy in 1998. Analyzing data from surveys of some 1,800 households in Bangladesh in 1991-92, they concluded that "annual household consumption expenditure increases 18 taka for every 100 additional taka borrowed by women…compared with 11 taka for men." I.e., microcredit reduces poverty, especially when given to women. Via some extrapolations in Khandker's book, the paper is the source of a figure Muhammad Yunus has cited: 5% of Grameen borrowers climb out of poverty each year.
To reach this conclusion, Pitt and Khandker apply a sophisticated statistical technique, what they call "Weighted Exogenous Sampling Maximum Likelihood–Limited Information Maximum Likelihood–Fixed Effects." I am certain now that few readers fully understood what they did, let alone could imitate it...
Until now. Well, actually until the fall of 2007, when I released a computer program called "cmp" that lets users of a popular statistical software package called Stata apply the same techniques. This January I wrote up the theory and documented the program in this new paper.
I wrote the program in order to end a lingering controversy over the Pitt and Khandker work, as part of my quest to understand what we know about the impacts of microfinance. In 1999, Jonathan Morduch questioned Pitt and Khandker's methods and results. Pitt fired back. Neither economist used the other's methods, so there was no effective attempt to directly reconcile the contradictory results. And the arguments were so technical that it was hard for non-experts to know what to make of it all.
Using the new program, I believe I have untangled the controversy. But it seems best for me to say no more for now. I apologize for violating the spirit of this "open book" blog. I hope to drop the other shoe in a few weeks.
I went through a similar exploration some years ago to come to terms with the statistical literature on whether foreign aid reliably raises economic growth in receiving countries. In order to judge some of the papers, I wrote another Stata program, and a paper about it. Then I concluded that most aid-growth studies (including ones that use my program!) are flawed.