Demonstrating the Bias Toward Negative Quadratic Effects

To recapitulate, unless one firmly believes that too many doctors, tele­phones, and/or R&D technicians reduce growth, one should be suspicious of cross-country regressions showing that too much finance does so.

This inherent quadratic coefficient bias can be seen more intuitively, however, in figure 6.1. The natural logarithm of ppp per capita income is on the horizontal axis. The primary relationship of growth to per capita income is shown by the downward-sloping convergence line, g. Some other variable related positively to per capita income, such as financial depth or doctors per capita, is shown on the upward-sloping line z, against an appro­priate scale on the right-hand vertical axis. Suppose the units for this other variable are chosen such that at income level B, where the two lines inter­sect, the value of the variable z will be the same as the growth rate g. Then if a regression of gon ln y is augmented by including terms zand z2, a positive contribution from those two terms will tend to be needed in the zone AB, but a negative contribution will be needed in the zone BC where the g line lies below the z line. The only way for the contribution to shift from positive to negative will be for the coefficient on z to be positive and the coefficient on z² to be negative.