Zipf's Law for Cities and Beyond: The Case of Denmark

By Knudsen, Thornbjorn | The American Journal of Economics and Sociology, January 2001 | Go to article overview

Zipf's Law for Cities and Beyond: The Case of Denmark


Knudsen, Thornbjorn, The American Journal of Economics and Sociology


THORNBJORN KNUDSEN [*]

ABSTRACT. Zipf's law for cities is one of the most conspicuous and robust empirical facts in the social sciences. It says that for most countries, the size distribution of cities must fit the power law: the number of cities with populations greater than S is inversely proportional to S. The present paper answers three questions related to Zipf's law: (1) does the Danish case refute Zipf's law for cities?, (2) what are the implications of Zipf's law for models of local growth?, and (3) do we have a Zipf's law for firms? Based on empirical data on the 61 largest Danish cities for year 2000, the answer to (1) is NO--the Danish case is not the exception which refutes Zipf's law. The consideration of (2) then leads to an empirical test of (3). The question of the existence of Zipf's law for firms is tested on a sample of 14,541 Danish production companies (the total population for 1997 with 10 employees or more). Based on the empirical evidence, the answer to (3) is YES in the sense that the growth pattern of Dani sh production companies follows a clean rank-size distribution consistent with Zipf's law.

PREDICTION IN ECONOMICS, and in the social sciences generally, is a rather scarce commodity (Reder 1999) and perhaps an unattainable ideal (Aumann 2000). According to Aumann, the value of a good theory lies in its usefulness in structuring reasoning and, therefore, one empirical fact to be cited in favour of a theory is its diffusion in some population of scientists. In other words, the more use of a particular theory, the better. As Reder notes, economists tend to place higher value on technique than content; clever theoretical ideas are valued over the assiduous gathering and careful presentation of data. And since mainstream economics, in any case, has a sufficiently flexible theoretical basis to rationalize contrary empirical facts also, data do not play the prominent role they do in the natural sciences. As important reasons for the gap between theory and applied work, Reder points to the rather low status of empirical facts and the tendency to use the term "prediction" when "retrodiction" would be more suitable (pp. 27-29). In contrast to this generally disappointing state of affairs (see, e.g., Reder 1999), there exists one exceptional case, a notable empirical success story in which theory must bow to facts. This case is zipf's law for cities, which has important implications for the admissibility of theoretical growth models. In economics one very rarely finds empirical relationships which deserve to be called laws. Zipf's law for cities, however, is one of the most conspicuous empirical facts in economics and in the social sciences in general (Brakman et al. 1999). It is surely an outstanding empirical regularity deserving the status of an experimental law (Gabaix 1999).

According to Zipf's law, the growth pattern of cities almost everywhere follows the power law--the number of cities with populations greater than S is proportional to 1/S. Put differently, if we rank a sample of cities according to population size, and then place the log of the size on the X-axis and the corresponding log of the rank on the Y-axis, there should appear a straight line with slope -1. Should the numerical value of the slope exceed 1, cities are more dispersed than predicted whereas a slope less than one indicates that cities are more even sized than the prediction. Surprisingly, we actually see a slope of about 1 when data on American metropolitan areas are used. Both Gabaix (1999) and Krugman (1996) obtained a slope of -1.005 (std.dev. 0.010) and an [R.sup.2] of .986 for the 135 American metropolitan areas listed in the Statistical Abstract of the United States for 1991. Similar results have been reported for most countries in contemporary times (Rosen and Resnick 1980). The support of Zipf's law for previous periods has included samples of cities in India (Zipf 1949), China (Rozman 1990), the Netherlands (Brakman et al. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Zipf's Law for Cities and Beyond: The Case of Denmark
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Author Advanced search

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.