Comparison Gravity and Polynomial Models

Using the same method that produced the test data and gravity model described above, we generated a new set of Monte Carlo data and then estimated the sales-distance relationship using the gravity model. Although the gravity model worked well in this case, it (of course) did not explain all the variations in the data. Could a polynomial model work better?

Figure 13-10, "Gravity vs. polynomial specifications," shows the result of this exercise. Using the MATLAB basic curve-fitting tool, we were able to quickly overlay a cubic (third degree) polynomial equation onto the data. Eyeballing the data indicates that the cubic polynomial does a better job of explaining the variations for almost all of the ranges. The little hump upward and the tail downward in the cubic curve bring it closer to the distribution of the test data.

Goodness of Fit and Understanding the Market

This raises a fundamental question about using statistical methods to estimate a behavioral relationship. Is the objective of such an exercise to get the best fit, or to get the best model?

Going back to our first maxim, we clearly believe it is more important to understand the market and to properly model the underlying behavior than to get the best fit with any single data set. Getting the model right means understanding not just one situation, but an entire market.

Furthermore, keep in mind the well-known result from econometrics: the goodness of fit of any equation can be improved simply by adding more explanatory variables, even if these variables are meaningless.351

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