Reply to kelly, cutright, and hittle

The major thrust of Kelly et al.'s "Comment" is that the relationship found by me between level of social security and fertility is not at all causal but entirely spurious, and that it is eliminated when level of economic development is properly controlled. They demonstrated this by developing a "modernization index" and then controlling for this index. The resulting partial correlation coefficients are both small and statistically insignificant. In contrast, I controlled for infant mortality, per capita gross domestic product, and per capita newspaper circulation and found sizeable betas that were sometimes statistically significant. As a general rule, if the relationship between two variables becomes significant when nonintervening variables are controlled, the relationship between the original two variables is believed to be spurious. Accordingly, the work of Kelly et al. appears quite compelling. The work of Kelly et al. should be scrutinized, however, just as my work was properly scrutinized. Initially, the focus of my scrutiny shall be on the "modernization index." From an intuitive or theoretical standpoint, it is not a compelling index for several reasons. First, it includes at least one measure that is correlated with fertility, but not causally so. For example, it seems unlikely that the natural logarithm of telephones per 1000 persons is causally related to fertility. Thus, in an effort to demonstrate spuriousness, Kelly et al. partially control for variables which themselves are spuriously related to fertility. Frankly, this process seems both peculiar and suspect. To the credit of Kelly et al., the logarithm of telephones is being used as a measure of economic development, but others (cf. Rummel, 1972) have indicated that the gross national product (GNP) per capita or gross domestic product (GDP) per capita, which I used, are better measures. Second, the Kelly index ignores variables known to be causally important (e.g., infant mortality). Third, it standardizes the five components and then sums them. In so doing, it weighs all the components equally. In general, several separate variables will explain a greater amount of variance than will an index of those variables, and, more crucially, simultaneously controlling for several variables is a better test of spuriousness than is controlling for a single index. In sum, from a theoretical standpoint, controlling for the modernization index is perhaps less compelling than controlling for infant mortality, GDP per capita, and per capita newspaper circulation. However, to the credit of Kelly et al., it must be recognized that when they control for the modernization index, the relationship between social security and fertility is negligible, whereas when I control for my three measures of development, the relationship is not negligible. Logically, of course, there are two possibilities: (a) the relationship between social security and fertility may be entirely spurious, and I simply failed to adequately control for other variables; or (b) social security may causally affect fertility, and Kelly et al. simply obscured that relationship. In sum, either study may be correct, but, at this point, it is clearly my responsibility to provide further evidence to support my position. Since both my conclusion and that of Kelly et al. are based upon the same data sets, both suffer from the flaws of those