Survivor: Is There an Optimal Country Size?

Abstract

Contemporary manifestations of international integration and national disintegration have stimulated speculation on the optimal size of a country. Economic theories focus on efficient resource allocation, and empirical work on partial equilibrium tests correlating size with variables (limited by data availability to recent times) selected from theoretical models of optimal size. This article questions the assumption that there is an optimal size, offering a test using data covering 500 years. The existence of an optimum, determined by efficiency or other goals, will be revealed by a size category generating an increasing proportion of world income, as more states move into that category. The results of this “survivor” test do not indicate the emergence of an optimal country size, despite data limitations that prevent cross-sectional analysis over a long time period. The absence of evolution toward optimal size suggests alternative directions in the research on country size.

KEYWORDS:

• optimal size
• income
• evolution
• efficiency
• population

Notes

1. Recent surveys may be found in Alesina and Spolaore (2005), Drazen (2000), Lake and O'Mahony (2004), and Ruta (2005).

2. An efficiency case for redistribution based on cardinal utility requires interpersonal comparisons of utility, an exercise that is arbitrary or empirically unattainable outside of an experimental setting. Ordinal utility allows the specification of redistributions that are both efficient and Pareto optimal (at least one person gains and no one loses) or “superfair” (envy free), but an efficient country size need not be Pareto optimal or superfair.

3. If population is spread evenly across the area of a circular country, the rate of increase of the area with respect to radius (r) is 2πr and the rate of increase of the circumference is 2π. Per capita defense costs will decrease with size, assuming total costs are a function of the perimeter.

4. Secession by referendum may not be easy if the beneficiaries of redistribution outnumber those desiring to leave, as the San Fernando Valley discovered when it tried to leave Los Angeles in 2002. Other goals may complicate calculations; some Québec voters want to leave Canada despite net transfers into the province.

5. Rational expectations is the assumption that the expected value of a random variable is normally distributed around its actual value (i.e., most people have enough information to make good predictions).

6. Higher risk exposure might be a reason for having a larger country, if citizens are risk averse (as noted earlier), but in that case the rationale is insurance, not scale economies.

7. The technique was set out by Stigler (1958) and developed by, among others, Saving (1961) and Weiss (1964).

8. Maddison (2003) lists Soviet republics separately in his data for 1973 but only the Soviet Union for 1950, most likely for lack of data. Though these republics had more administrative significance in 1973 than in 1950, there is some unavoidable arbitrariness. The number of observations is large enough that any such measurement errors should not significantly bias the results.

9. Scherer and Ross (1990, pp. 141–146) explain the process in the context of industrial concentration. The distribution is quite robust and may still be attained when the assumptions of Gibrat's Law are violated (e.g., serial correlation in year to year growth rates).

10. Using 95% critical values of the Shapiro-Wilk test described in the STATA manuals.

11. Combining the National Material Capabilities dataset (see Appendix) with Maddison's GDP data, the simple correlation of energy consumption and GDP is 0.93 for the period 1820 to 2001.

12. The Herfindahl measures of concentration in energy consumption by both population and area deciles declined from 1820 to 1870, rose to 1950, and fell thereafter.

13. An exception is Friedman's (1977) index of linguistic homogeneity for European countries from 1140 to 1950, a possible proxy for homogeneity of demand,.

14. A survey of capital structure theories and applications to international politics may be found in Conybeare (1994).