Rank-Size Rule (also known as Zipf’s Law) states that a city’s population size tends to be proportional to the largest city’s population divided by the city’s rank (its position in population size hierarchy).

Mathematically:
City Population = Largest City’s Population / Rank of City

For instance, if the largest city in a country or region has a population of 1.2 million, the sizes of other cities should theoretically follow this distribution.

Explanation of the Theoretical Model

Xavier/Gabaix’s Explanation:

  1. Initial Growth: The development of cities begins in a random fashion.
  2. Long-Term Stabilization: Over time, growth rates stabilize and regress toward the mean. This is due to a relatively equal distribution of new and existing job opportunities across cities.
  3. Uniform Volatility: Deviations from average growth rates are characterized by uniform variability for all cities. However, larger cities tend to have more diversified economies, leading to less fluctuation in their growth rates.

These assumptions, when modeled mathematically, lead to the rank-size rule over the long term.

Practical Observations

In reality, there are fewer small cities than the rule predicts. This discrepancy arises because a city requires a critical mass to sustain itself. Smaller cities may decline or fail due to higher volatility in their growth rates.

Additionally, the mathematical model does not fully explain why the hierarchy of cities remains stable over long periods or why rank changes are rare, occurring only due to major systemic shifts.

Source:

Zipf’s Law for Cities: An Explanation, Harvard/MIT Working Paper, 1998
Referenced in the book Commercial Real Estate Analysis and Investments by D. M. Geltner, N. G. Miller, J. Clayton, and P. Eichholtz.

Observations for Georgia and Similar Countries

I was curious to see how well this rule applies to Georgia and comparable European countries with similar sizes and landscapes. Data sourced with the help of Copilot/ChatGPT may lack full accuracy:

  • Closest Match to Zipf’s Law: Switzerland
  • Followed by: Slovakia
  • Deviating Structures: Georgia, Austria, and Serbia exhibit more “primate city” structures, where one city disproportionately dominates.

Explanation for Primate Structures

Such structures are often attributed to the historical significance and age of capital cities, which enabled their early development. Subsequent systemic changes have not been sufficient to alter the proportional relationships between cities.

Investment-Relevant Statistics

Source: geostat.ge