Zipf's Law in the Case of Moroccan Cities

Abstract

In this paper, we explore the validity of rank‐size rule in the Moroccan urban system. We use data from the 1982, 1994, and 2004 censuses. Three thresholds are considered to truncate the data: 5000, 50000, and 100000 residents. Power law states that the rank (r) of a city is proportional to a power of its size (Sr), that is, r ̴ S•α. The ordinary least squares (OLS) method is used to estimate α. Using OLS method without Gabaix‐Ibragimov correction (GIC) provides evidence of the validity of Zipf's law for cities of more than 100 000 dwellers.When the GIC is used, it appears that the zipfian distribution (α = ‐1) is also valid for cities of more than 50000 inhabitants. Over the period 1982–2004, it seems likely that intermediate cities grew more rapidly than other cities. This may lead to a more balanced distribution of the Moroccan urban system.

Zipf’s law and city size distribution: A survey of the literature and future research agenda

“…Gligor and Gligor [66] supported the Zipf's law for 265 large and medium urban settlements of Romania for the census year 2002. Ezzahid and ElHamdani [67] explored the Zipf's law for Moroccan cities for the census years 1982, 1994, and 2004. Zipf's law holds for Moroccan cities with more than 50,000 inhabitants 3 .…”

“…It was significantly different from one from 2007 onward 4 . Giesen and Südekum [65] Germany Cities with more than 100,000 inhabitants Gligor and Gligor [66] Romania 265 large and medium urban settlements Ezzahid and ElHamdani [67] Morocco Cities with more than 50,000 inhabitants Rastvortseva and Manaeva [69] Russia City size distribution does not conform to Zipf's law Lalanne [70] Canada 152 largest urban areas Dubé and Polèse [71] 135 largest urban areas Lanaspa, Pueyo and Sanz [72] Spain Le Gallo and Chasco [6] 722 Spanish municipalities City size distribution approaches to Zipf's law as countries experience urbanization Gangopadhyay and Basu [47] India Different samples; minimum threshold is the cities above 10,000 inhabitants in the census year 2001 Gangopadhyay and Basu [48] Cities above 212,523 inhabitants in the census year 2011 Luckstead and Devadoss [56] 58 largest cities from 1950 to 2010 Moura and Ribeiro [73] Brazil Cities with 30,000 inhabitants or more Matlaba, Holmes, McCann and Poot [74] 185 largest functionally defined urban areas Ignazzi [5] Census years data from 1871 to 2010 City size distribution may evolve away from Zipf's law over time Soo [75] Malaysia Cities with more than 10,000 inhabitants Pérez-Campuzano, Guzmán-Vargas and Angulo-Brown [7]…”

Rank-size Distribution of Cities and Municipalities in Bangladesh

“…Alternatively, when a truncated sample of only larger cities was considered, this trend was reversed, with an increased evenness in the distribution of population among the larger cities [52]. For cities in Morocco, the adherence to Zipf's law was examined based on three truncated population census data at three different years, from 1982 to 2004 [53]. The results from this study concluded that even though the Pareto coefficient for the cities at these levels was not statistically different from 1, the urban system for Morocco tended towards a more balanced distribution over time [53].…”

Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan

“…Extant literature has examined the empirical validation of Zipf's law for city size distribution and largely reports mixed and controversial evidence. One strand of the literature argues that the size distribution of cities obeys Zipf's law and tries to establish that Zipf's law for city size distribtuion is universal [17][18][19][20][21][22][23][24]. In contrast, another strand of the literature finds that Zipf's law either does not exactly hold [5,[25][26][27][28][29][30] or the city size distribution may tilt away from Zipf's law over time [31][32][33][34] and rejects the hypothesis that Zipf's law is universal (see, for example, the recent literature survey on Zipf's law and city size distribution by Arshad, Hu and Ashraf [35]).…”

“…France [18], Germany [21], Canada [29], Brazil [50][51][52], Morocco [24], Malaysia [31], Mexico [34] and Turkey [32], it comes to us as a surprise that to date no major effort has been made to study the city size distribution of Pakistan.…”