Knowledge that Transforms

CHARLES BABBAGE deserves full membership in the club of mathematicians who have made significant contributions to economics, a club which began with Daniel Bernoulli (1738) and reaches at least to John von Neumann (1944). It is appropriate that Babbage's contributions were wholly nonmathematical, for his talents were richly varied and his behavior wonderfully eccentric. The invention of those ancestors of the modern computer, the Difference Machine and the Analytical Machine, is of course his greatest claim to fame: they are prodigies of both theoretical creativity and mechanical implementation. The Difference Machine was designed to produce and print mathematical tables by the use of finite differences. By 1822 Babbage had a small working model and was promising soon to produce logarithmic tables as cheap as potatoes. In building a large machine-which continually grew in power and complexity-he encountered and overcame innumerable analytical and mechanical problems. The work on the machine ground to a halt about 1832, after the Treasury refused to add to its previous grants of E12,000. Soon Babbage turned to the Analytical Machine, which consisted of two parts:

Michael L. Wachter, William L. Wascher, Leveling the Peaks and Troughs of the Demographic Cycle: An Application to School Enrollment Rates: A Reply, The Review of Economics and Statistics, Vol. 73, No. 3 (Aug., 1991), pp. 575-576

It also differs from the Dutkowsky-Foote estimate because of their use of unseasonally adjusted money stock data and an ending date which is not the ending date reported in their paper. Our dynamic simulations of equations (1) and (2) are shown in figure 2. It is immediately apparent that something has gone very badly awry. Our simulations indicate that the Dutkowsky-Foote model overpredicts money demand over the simulation period January 1975 to June 1985 even more than the standard money demand function; the root mean squared error of the Dutkowsky-Foote model is 0.152 compared to 0.111 for the standard money demand function. Our attempts to replicate both the Dutkowsky-Foote estimates and their dynamic simulations convince us that the authors were not running comparable simulations. For the standard money demand function, they do indeed run a post-sample dynamic simulation. For their own model, however, they run a non-dynamic or static simulation. Given their estimated coefficient for the lagged dependent variable of 0.999, this is virtually equivalent to using the actual lagged money stock. Indeed, we recreated the original Dutkowsky-Foote figure 1 by plotting the actual lagged money stock in lieu of their simulated result; the figures are almost identical. Dutkowsky and Foote (1988, p. 90) state that . . post-sample forecasting ability has become the acid test for money demand models. It is just not cricket, however, to compare a post-sample dynamic simulation of one model with a static simulation of another, as they do. On a level playing field, their model fails the acid test by an even wider margin than the standard money demand model.