Skip to main content
SpringerLink
Log in

City Size Distribution in Colombia and Its Regions, 1835–2005

  • Chapter
  • First Online:
Population Change and Impacts in Asia and the Pacific

Part of the book series: New Frontiers in Regional Science: Asian Perspectives ((NFRSASIPER,volume 30))

Abstract

By using census data from 1835 to 2005, this chapter studies the urban hierarchy in Colombia and its regions. The chapter focuses on three issues: firstly, the city size distribution by means of Zipf’s law and Gibrat’s law; secondly, evolution in the population growth models; and, thirdly, the empirical validation of the point made by Gabaix (Q J Econ 114(3):739–767, 1999b) on the coincidence between national and regional population patterns. Using the adjusted rank–size relationship and non-parametric techniques, we find that city size distributions follow Zipf’s power law, and also that Gibrat’s law holds at the national level and partially for the regions over the second half of the twentieth century. These results are consistent with changes in the population growth model from the mid-fifties at national and regional levels.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Zipf (1949) was the first to formally suggest that city size follows a Pareto distribution. Nevertheless, Auerbach (1913) was the first to note this empirical regularity.

  2. 2.

    Duranton (2006, 2007) develops a mechanism through which the agglomeration of firms is related to Zipf’s law. The argument is based on the proportional relationship between migration and the quantity of goods produced in a city or region, and also the relationship between investment in innovation and the number of firms. Under this scenario, small and discreet innovations will result in proportional population growth which, in turn, generates a Pareto distribution.

  3. 3.

    The mechanism through which the deterministic growth model is related to the quality of life is given by the relationship between the agglomeration and the cities’ growth. The agglomeration of firms within particular cities or regions implies positive effects on income and employment.

  4. 4.

    Almost half of the territory, the southeast of Colombia has historically been occupied by rain forest and jungle, where only about 4% of the population lives.

  5. 5.

    This expression indicates that it is possible to empirically estimate, through a linear regression, the coefficient a, from which we can then derive whether or not the Zipf’s law holds.

  6. 6.

    In this case, if the growth of all cities is proportional, such as predicted by Gibrat’s law, the straight line with slope equal to 1 predicted by Zipf’s Law should move in a parallel fashion (Goerlich and Mas 2010).

  7. 7.

    These arguments lead the author to assert that, when analyzing the upper tail of the city size distribution, the hypothesis testing power is low when the intention is to distinguish between a lognormal and a Pareto distribution (see Eeckhout’s (2009) response to Levy (2009)).

  8. 8.

    Härdle (1990) presents a detailed description on the computation of non-parametric estimates of the mean and variance.

  9. 9.

    In order to confirm the robustness of the results with respect to different bandwidths, additional exercises were carried out using the Silverman’s (1986) optimal bandwidth and similar results were found. For Germany, Giesen and Südekum (2011) also found, in a similar exercise, similar results using these two bandwidths.

  10. 10.

    Other administrative units are the metropolitan areas. However, in Colombia they are only 10.

  11. 11.

    Some recent studies have argued that using a truncated population distribution may give rise to biased Pareto coefficients (Giesen et al. 2010; Ioannides and Skouras 2013; González-Val et al. 2013).

  12. 12.

    In Colombia in 2015, approximately 76% of the population was living in the urban areas.

  13. 13.

    In order to test the robustness of the results, two alternatives were also used: those including the municipalities within 90 and 95 percentiles of the population distribution. The results were similar in magnitude and significance.

  14. 14.

    An arbitrary city size is taken in order to facilitate visualization of changes in the number and size of cities over time.

  15. 15.

    This relationship holds as long as particular statistical conditions holds (Gabaix 1999b; Skouras 2009).

  16. 16.

    Notice, for instance, that in the Caribbean region Zipf’s Law began to hold before it did in the other regions. Although this chapter does not pretend to answer the question why this is so, one possible explanation is that, historically, this region was one of the first to be populated, mainly due to its importance as a seaport and a “hot spot” for international trade.

  17. 17.

    The results are only given for this particular period because for all regions and for the rest of the series the hypotheses of constant means and variances were rejected. Additionally, it is of major interest to check the results for Gibrat’s and Zipf’s laws only for the periods where the latter law holds.

References

  • Anderson G, Ge Y (2005) The size distribution of Chinese cities. Reg Sci Urban Econ 35(6):756–776

    Article  Google Scholar 

  • Auerbach F (1913) Das gesetz der bevölkerungskonzentration. Petermanns Geographische Mitteilungen 59:74–76

    Google Scholar 

  • Basu B, Bandyapadhyay S (2009) Zipf’s law and distribution of population in Indian cities. Indian J Phys 83(11):1575–1582

    Article  Google Scholar 

  • Bejarano J (1994) El despegue cafetero (1900-1928). In: J. A. Ocampo (compilador) Histórica Económica de Colombia. TM Editores-Fedesarrollo, Bogotá, pp 173–207

    Google Scholar 

  • Benguigui L, Blumenfeld-Lieberthal E (2011) The end of a paradigm: is Zipf’s law universal? J Geogr Syst 13(1):87–100

    Article  Google Scholar 

  • Bernal G, Nieto C (2006) Evolución del coeficiente de Zipf para Colombia en el siglo XX, Documentos de economía no. 5, Universidad Javeriana-Departamento de Economía

    Google Scholar 

  • Bonet J, Meisel A (1999) La convergencia regional en Colombia: una visión de largo plazo, 1926–1995. Documentos de trabajo sobre economía regional no. 8, Banco de la República-Cartagena

    Google Scholar 

  • Champernowne DG (1953) A model of income distribution. Econ J 63(250):318–351

    Article  Google Scholar 

  • Cheshire P (1999) Trends in sizes and structures of urban areas. In: Cheshire PC, Mills ES (eds) Handbook of regional and urban economics, vol 3. North-Holland, Amsterdam, pp 1339–1373

    Google Scholar 

  • Dimou M, Schaffar A (2009) Urban hierarchies and city-growth in the Balkans. Urban Stud 46(13):2891–2906

    Article  Google Scholar 

  • Dobkins L, Ioannides Y (2001) Spatial interactions among US cities: 1900-1990. Reg Sci Urban Econ 31(6):701–731

    Article  Google Scholar 

  • Duranton G (2006) Some foundations for Zipf’s law: product proliferation and local spillovers. Reg Sci Urban Econ 36(4):542–563

    Article  Google Scholar 

  • Duranton G (2007) Urban evolutions: the fast, the slow, and the still. Am Econ Rev 97(1):197–221

    Article  Google Scholar 

  • Eeckhout J (2004) Gibrat’s law for (all) cities. Am Econ Rev 94(5):1429–1451

    Article  Google Scholar 

  • Eeckhout J (2009) Gibrat’s law for (all) cities: reply. Am Econ Rev 99(4):1676–1683

    Article  Google Scholar 

  • Firdaus M, Fitria A (2010) Does the rank-size rule matter in Indonesia? Determinants of the size distribution of cities. J Indones Econ Business 25(1):114–120

    Google Scholar 

  • Gabaix X (1999a) Zipf’s law and the growth of cities. Am Econ Rev 89(2):129–132

    Article  Google Scholar 

  • Gabaix X (1999b) Zipf’s law for cities: an explanation. Q J Econ 114(3):739–767

    Article  Google Scholar 

  • Gabaix X (2016) Power laws in economics: an introduction. J Econ Perspect 30(1):185–205

    Article  Google Scholar 

  • Gabaix X, Ibragimov R (2011) Rank-1/2: a simple way to improve the OLS estimation of tail exponents. J Business Econ Stat 29(1):24–39

    Article  Google Scholar 

  • Gibrat R (1931) Les inégalités économiques. Recueil Sirey, Paris

    Google Scholar 

  • Giesen K, Südekum J (2011) Zipf’s law for cities in the regions and the country. J Econ Geogr 11(4):667–686

    Article  Google Scholar 

  • Giesen K, Zimmermann A, Suedekum J (2010) The size distribution across all cities—double Pareto lognormal strikes. J Urban Econ 68:129–137

    Article  Google Scholar 

  • Goerlich F, Mas M (2010) La distribución empírica del tamaño de las ciudades en España, 1900-2001. Quién verifica la Ley de Zipf, Revista de Economía Aplicada XVIII 54:133–159

    Google Scholar 

  • González-Val R (2010) The evolution of U.S. city size distribution from a long-term perspective (1900–2000). J Reg Sci 50(5):952–972

    Article  Google Scholar 

  • González-Val R, Ramos A, Sanz-García F, Vera-Cabello M (2013) City distribution for all cities: which one is best. Pap Reg Sci 94(1):177–196

    Google Scholar 

  • Härdle W (1990) Applied nonparametric regression. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Ioannides Y, Overman H (2003) Zipf’s law for cities: an empirical examination. Reg Sci Urban Econ 33(2):127–137

    Article  Google Scholar 

  • Ioannides Y, Skouras S (2013) US city size distribution: robustly Pareto, but only in the tail. J Urban Econ 73:18–29

    Article  Google Scholar 

  • Krugman P (1990) Increasing returns and economic geography. Working paper no. w3275. National Bureau of Economic Research

    Google Scholar 

  • Levy M (2009) Gibrat’s law for (all) cities: comment. Am Econ Rev 99(4):1672–1675

    Article  Google Scholar 

  • Matlaba VJ, Holmes MJ, Mccann P, Poot J (2013) A century of the evolution of the urban system in Brazil. Rev Urban Reg Dev Stud 25(3):129–151

    Article  Google Scholar 

  • Melo J (1994) Las vicisitudes del modelo liberal (1850-1899). In: J. A. Ocampo (compilador) Histórica Económica de Colombia. TM Editores-Fedesarrollo, Bogotá, pp 119–172

    Google Scholar 

  • Moura NJ, Ribeiro MB (2006) Zipf’s law for Brazilian cities. Phys A Stat Mech Appl 367:441–448

    Article  Google Scholar 

  • Nadaraya E (1964) On estimating regression. Theor Probab Appl 9:141–142

    Article  Google Scholar 

  • Nota S, Song F (2006) Further analysis of the Zipf’s law: does the rank-size rule really exist, UNR Joint Economics Working Paper Series, No. 07-2006. University of Nevada, Reno

    Google Scholar 

  • Ocampo J, Bernal J, Avella M, Errázuriz M (1994) La consolidación del capitalismo moderno (1945-1986). In: J. A. Ocampo (compilador) Histórica Económica de Colombia. TM Editores-Fedesarrollo, Bogotá, pp 243–334

    Google Scholar 

  • Pérez GJ (2005) Dimensión espacial de la pobreza en Colombia. Revista ensayos sobre política económica 48:234–293

    Article  Google Scholar 

  • Pérez GJ (2006) Población y Ley de Zipf en Colombia y la Costa Caribe, 1912–1993, Documentos de trabajo sobre economía regional no. 71, Banco de la República–CEER

    Google Scholar 

  • Rosen K, Resnick M (1980) The size distribution of cities: an examination of the Pareto law and primacy. J Urban Econ 8(2):165–186

    Article  Google Scholar 

  • Schaffar A, Dimou M (2012) Rank-size city dynamics in China and India, 1981–2004. Reg Stud 46(6):707–721

    Article  Google Scholar 

  • Silverman B (1986) Density estimation for statistics and data analysis. Chapman and Hall, New York

    Book  Google Scholar 

  • Simon H (1955) On a class of skew distribution functions. Biometrika 42(3-4):425–440

    Article  Google Scholar 

  • Skouras S (2009) Explaining Zipf’s law for US cities. Available at SSRN 1527497

    Google Scholar 

  • Song S, Zhang K (2002) Urbanization and city-size distribution in China. Urban Stud 39(12):2317–2327

    Article  Google Scholar 

  • Soo K (2005) Zipf’s law for cities: a cross-country investigation. Reg Sci Urban Econ 35(3):239–263

    Article  Google Scholar 

  • Watson G (1964) Smooth regression analysis. Sankhya 26:359–376

    Google Scholar 

  • Ye X, Xie Y (2012) Re-examination of Zipf’s law and urban dynamic in China: a regional approach. Ann Reg Sci 49(1):135–156

    Article  Google Scholar 

  • Zhou Y, Ma L (2003) China’s urbanization levels: reconstructing a baseline from the fifth population census. China Q 173:176–196

    Article  Google Scholar 

  • Zipf G (1949) Human behavior and the principle of least effort. Addison-Wesley, Cambridge, MA

    Google Scholar 

Download references

Disclaimer

A Spanish version of this research was published in Revista de Historia Económica/Journal of Iberian and Latin American Economic History (New Series), Volume 32/Issue 02/September 2014, pp 247–286.

Author information

Authors and Affiliations

  1. Center for Regional Economics Studies, Banco de la República, Cartagena de Indias, Colombia

    Gerson Javier Pérez-Valbuena

  2. Universidad del Norte, Barranquilla, Colombia

    Adolfo Meisel-Roca

Authors
  1. Gerson Javier Pérez-Valbuena
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adolfo Meisel-Roca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerson Javier Pérez-Valbuena .

Editor information

Editors and Affiliations

  1. Department of Spatial Economics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, National Institute of Demographic and Economic Analysis (NIDEA), University of Waikato, Hamilton, New Zealand

    Jacques Poot

  2. School of Economics and Finance, Massey University, Auckland, New Zealand

    Matthew Roskruge

Appendices

Appendix 1

Descriptive statistics of the Colombian cities, 1835–2005 (Municipalities representing 100% of the population)

Year

Number of cities

Mean

Standard deviation

Median

Minimum size

Maximum size

Gini index

1835

749

2.070

2.270

1.512

34

39.442

0.468

1843

751

2.360

2.355

1.846

63

40.086

0.445

1851

802

2.617

2.461

2.010

37

29.649

0.459

1870

739

3.624

3.045

2.845

58

40.883

0.392

1905

762

5.616

6.004

4.175

97

100.000

0.423

1912

767

6.486

6.759

5.054

33

121.257

0.387

1918

806

7.056

7.955

5.408

160

143.994

0.411

1938

809

10.745

17.079

7.309

399

355.502

0.442

1951

827

13.944

33.148

8.330

347

715.250

0.508

1964

879

19.875

71.058

10.093

294

1.697.311

0.581

1973

1020

22.403

106.622

10.118

85

2.861.913

0.635

1985

1024

29.352

153.862

12.000

797

4.236.490

0.669

1993

1061

31.206

175.391

11.343

78

4.945.448

0.701

2005

1113

38.524

233.820

12.626

225

6.840.116

0.726

  1. Source: Authors’ calculations based on Census data

Appendix 2

Descriptive statistics of the Colombian regions, 1835–2005 (Municipalities representing 100% of the population)

Year

Number of cities

Mean

Standard deviation

Median

Minimum size

Maximum size

Gini index

(a) Caribbean region

1835

182

1.236

1.480

765

74

11.929

0.512

1843

187

1.269

1.416

761

70

10.145

0.497

1851

189

1.344

1.475

791

93

9.896

0.498

1870

126

2.595

2.051

1.950

390

11.595

0.387

1905

145

3.641

4.466

2.506

97

40.115

0.462

1912

118

6.277

6.270

4.473

184

48.907

0.403

1918

119

7.018

8.202

4.472

726

64.543

0.448

1938

113

12.707

17.967

8.177

1.412

152.348

0.481

1951

117

16.541

29.526

10.663

1.970

283.238

0.512

1964

128

25.490

50.441

14.614

2.318

498.301

0.535

1973

161

28.693

64.513

15.206

2.624

703.488

0.562

1985

161

38.933

89.988

18.962

3.676

927.233

0.580

1993

162

42.404

99.832

19.631

3.840

993.759

0.595

2005

194

46.861

117.517

19.065

2.721

1.146.498

0.628

(b) Central region

1835

127

2.300

1.895

1.911

79

10.280

0.418

1843

135

2.661

1.887

2.276

66

9.118

0.370

1851

156

2.876

2.229

2.344

198

13.755

0.397

1870

159

3.949

3.258

3.336

281

29.765

0.388

1905

176

7.516

6.191

5.566

464

53.936

0.375

1912

184

8.257

7.109

6.396

547

71.004

0.368

1918

203

8.665

7.896

6.454

276

79.146

0.390

1938

211

13.004

14.809

9.755

474

168.266

0.408

1951

217

16.970

28.290

11.615

1.255

363.865

0.461

1964

236

22.435

55.056

13.303

2.297

772.887

0.526

1973

270

23.692

75.289

12.897

918

1.163.868

0.566

1985

273

29.656

96.443

14.922

2.005

1.480.382

0.593

1993

273

31.748

107.418

14.858

2.329

1.630.009

0.623

2005

278

39.136

143.948

16.079

2.690

2.214.494

0.663

(c) Eastern region

1835

315

2.590

2.813

2.006

71

39.442

0.425

1843

306

2.923

2.891

2.454

63

40.086

0.399

1851

321

3.338

2.847

2.766

51

29.649

0.407

1870

314

4.174

3.358

3.446

58

40.883

0.362

1905

322

5.350

6.268

4.280

262

100.000

0.379

1912

323

5.870

7.261

4.732

567

121.257

0.359

1918

324

6.555

8.618

5.163

524

143.994

0.373

1938

334

8.656

19.937

6.111

681

355.502

0.428

1951

336

10.666

39.638

6.379

785

715.250

0.500

1964

345

15.937

92.455

7.396

965

1.697.311

0.615

1973

383

19.140

147.547

7.029

833

2.861.913

0.691

1985

384

25.672

217.821

7.767

797

4.236.490

0.743

1993

391

28.064

252.483

6.982

270

4.945.448

0.786

2005

396

36.264

346.825

7.503

885

6.840.116

0.822

(d) Pacific region

1835

98

2.067

1.546

1.675

156

8.173

0.389

1843

94

2.782

1.832

2.320

179

10.376

0.335

1851

103

2.948

2.080

2.377

199

11.848

0.359

1870

130

3.059

2.423

2.176

480

12.743

0.391

1905

107

6.481

5.888

4.656

325

30.835

0.414

1912

118

6.669

4.893

5.272

938

27.760

0.351

1918

127

7.247

6.128

5.634

261

45.525

0.379

1938

131

11.804

11.393

9.209

1.109

101.883

0.391

1951

136

16.388

26.951

10.184

954

284.186

0.485

1964

141

22.892

55.991

13.374

2.149

637.929

0.544

1973

153

27.733

82.912

13.040

1.938

991.549

0.593

1985

153

34.534

119.513

14.119

3.661

1.429.026

0.643

1993

163

36.422

134.530

15.329

2.063

1.666.468

0.648

2005

177

41.955

165.143

15.696

3.481

2.119.843

0.672

  1. Note: Regions are defined as follows: Caribbean (La Guajira, Magdalena, Atlántico, Bolívar, Cesar, Córdoba, and Sucre); Central (Antioquia, Caldas, Caquetá, Huila, Quindío, Risaralda, and Tolima); Eastern (Boyacá, Cundinamarca, Meta, Norte de Santander, and Santander); Pacific (Cauca, Chocó, Nariño, and Valle); New Departments (Amazonas, Arauca, Casanare, Guainía, Guaviare, Putumayo, Vaupés, and Vichada)
  2. Source: Authors’ calculations based on Census data

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Pérez-Valbuena, G.J., Meisel-Roca, A. (2020). City Size Distribution in Colombia and Its Regions, 1835–2005. In: Poot, J., Roskruge, M. (eds) Population Change and Impacts in Asia and the Pacific. New Frontiers in Regional Science: Asian Perspectives, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-0230-4_3

Download citation

Publish with us

Policies and ethics

Search

Navigation