I had a funny night. Most of my dreams had to do with economic research focusing on mathematics. One of the dreams revisited the research leading up to my doctoral dissertation at MIT. I woke up in the middle of the night, but the dream kind of continued. By and by, I was not sure whether I was dreaming or not. And then I realized that I had missed a wonderful opportunity to round off my doctoral research. So many years later, I could not imagine such a gaping hole in my work. I even thought of doing something about it right now, and as soon as possible, but I gave up the idea before dawn. It was too late. Besides, someone could have done what I failed to do in the intervening years. Anyhow, it took me a while to fall asleep again. My research showing glaring errors of Wassily Leontief’s work kept returning to my mind (“Who is Afraid of Wassily Leontief?” November 21, 1990).

When I started working on multiregional input-output analysis, there were three mathematical models underlying it. They were the column-coefficient model, the row-coefficient model, and the gravity coefficient model combining the two. They were known by the names of their authors as the Chenery-Moses, Polenske, and Leontief-Strout models, respectively. My doctoral dissertation set up conditions these models had to satisfy to guarantee macroeconomic stability.[1] The dissertation also struck down the Polenske model as economically unstable. Several years later, I showed that the Leontief-Strout model was economically unstable, as well.[2] My work was crowned with a new version of the row-coefficient model, which I showed to be economically stable.[3] The Bon-Polenske model was my last step in a long series of contributions to regional science.

What I realized in the middle of last night was that I failed to come up with a new version of the gravity coefficient model that would satisfy my own conditions of economic stability. And it was within easy reach at the time. The Bon-Leontief-Strout model would have been the real crown of my work some forty years ago. I would have left the field with three multiregional input-output models once again rather than with only two. And two of them would have my own name attached to them. The Chenery-Moses and Bon-Polenske models are the key to the field, but the Bon-Leontief-Strout model would have been a wonderful addition to it. Again, someone has most likely come up with such a model in the meanwhile, but I just could not believe my own failure. Yet another one, too! And it would have been quite important in view of the fact that models of this kind could provide the basis for global input-output analysis, one of the underpinnings for guiding the global economic policy (“Wassily Leontief and I,” May 4, 2014). Alas, what an incredible night!

Footnotes

1. “Some Conditions of Macroeconomic Stability of Multiregional Input-Output Models,” Economic Analysis, Vol. 16, Nos. 1-2, 1977, pp. 65-87 (also published by the US Department of Transportation, September 1975),

2. “Comparative Stability Analysis of Multiregional Input-Output Models: Column, Row, and Leontief-Strout Gravity Coefficient Models,” Quarterly Journal of Economics, Vol. 99, No. 4, pp. 791-815.

3. “Supply-Side Multiregional Input-Output Model,” Journal of Regional Science, Vol. 28, No. 1, 1988, pp. 41-50.