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ZİPF YASASININ PATENT VERİSİ İLE TEST EDİLMESİ: TÜRKİYE ÖRNEĞİ

Year 2023, Volume: 18 Issue: 2, 85 - 93, 31.12.2023

Eren Yıldırım , Yasemin Asu Çırpıcı

https://doi.org/10.54860/beyder.1393258

Abstract

Ölçekleme kanunları, sıklığa dayanan veriler için birçok farklı disiplinde başvurulan değerlendirme biçimlerinden biridir. Farklı veri türleri için ölçekleme yapmak üzere çeşitli istatistiksel yöntemler geliştirilmiş ve bu yöntemler edebiyat, fizik, biyoloji, ekonomi gibi alanlarda uygulanmıştır. Zipf yasası da bir ölçekleme kanunu olarak birçok farklı verinin dağılımının yapısını ortaya koymak üzere uygulanmıştır. Farklı veri türleri ve istatistiki yöntemlerle ile test edildiğinde Zipf yasasının geçerliliği de değişiklik göstermektedir. Bu çalışmada, Zipf yasasının geçerliliği Türkiye şehirleri için patent verisi ile test edilmiştir. Bu bağlamda patent dağılımının yapısının bölgesel olarak gösterdiği farklılıkların bir ölçekleme yasasını takip edip etmediğini ortaya koymak hedeflenmiştir. 1995-2022 yılları arasını kapsayan veri seti kullanılmış ve her bir il için yayımlanan patent verisi coğrafi olarak sınıflanmıştır. Daha sonra patent verisi için ölçekleme Zipf yasası bağlamında yapılmıştır. Elde edilen sonuçlara göre Zipf yasası Türkiye şehirlerindeki patent dağılımı açısından kabul edilememiştir. Bununla birlikte Türkiye şehirleri için ölçekleme değeri, patentin coğrafi dağılımının üstel bir yasa izlediğini ortaya koymuştur.

Keywords

Zipf Yasası İnovasyon Patent Mekansal İktisat

References

  • Adamic, L.A., Huberman, B. (2002). Zipf’s law and the Internet, Glottometrics. 3, 143-150.
  • Aurélie, L., & Martin, Z. (2020). From Gibrat’s law to Zipf’s law through cointegration? Economics Letters, 192, 109211. https://doi.org/10.1016/j.econlet.2020.109211
  • Axtell, R. L. (2001). Zipf Distribution of U.S. Firm Sizes. Science, 293(5536), 1818–1820. https://doi.org/10.1126/science.1062081
  • C. Barry Pfitzner, T. M. T. (2017). Are Cities in Vietnam Distributed According to Zipf? Journal of Economics and Development Studies, 5(1). https://doi.org/10.15640/jeds.v5n1a1
  • Corominas-Murtra, B., Seoane, L. F., & Solé, R. (2018). Zipf’s Law, unbounded complexity and open-ended evolution. Journal of the Royal Society Interface, 15(149), 20180395. https://doi.org/10.1098/rsif.2018.0395
  • Denisov, S. (1997). Fractal binary sequences: Tsallis thermodynamics and the Zipf law. Physics Letters A, 235(5), 447–451. https://doi.org/10.1016/s0375-9601(97)00688-9
  • Duranton, G. (2006). Some foundations for Zipf’s law: Product proliferation and local spillovers. Regional Science and Urban Economics, 36(4), 542–563. https://doi.org/10.1016/j.regsciurbeco.2006.03.008
  • Fernholz, R. T., & Fernholz, R. (2020). Zipf’s law for atlas models. Journal of Applied Probability, 57(4), 1276–1297. https://doi.org/10.1017/jpr.2020.64
  • Gabaix, X. (1999). Zipf’s Law and the Growth of Cities. The American Economic Review, 89(2), 129–132. https://doi.org/10.1257/aer.89.2.129
  • Gabaix, X., Ioannides, Y. (2004). The evolution of city size distributions, ch. 53, p. 2341-2378 in Henderson, J. V. and Thisse, J. F. eds., Handbook of Regional and Urban Economics, vol. 4, Elsevier.
  • Giller, G. L. (2013). Further Beyond Zipf’s Law: An Empirically Useful Augmentation of the Zipf-Mandelbrot Law. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2227003
  • Harremoës, P., & Topsoe, F. (2005). Zipf’s law, hyperbolic distributions and entropy loss. Electronic Notes in Discrete Mathematics, 21, 315–318. https://doi.org/10.1016/j.endm.2005.07.075
  • Hinloopen, J., & van Marrewijk, C. (2006). Comparative Advantage, the Rank-Size Rule, and Zipf’s Law. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.943370
  • Ioannides, Y. M., & Overman, H. G. (2003). Zipf’s law for cities: an empirical examination. Regional Science and Urban Economics, 33(2), 127–137. https://doi.org/10.1016/s0166-0462(02)00006-6
  • Kirby, G. (1985). Zipf’s Law. UK Journal of Naval Science. 10(3), 180-185.
  • Kleiber, M. (1932). Body size and metabolism. Hilgardia, 6(11), 315–353. https://doi.org/10.3733/hilg.v06n11p315
  • Manaeva, I. (2019). Distribution of Cities in Federal Districts of Russia: Testing of the Zipf Law. Economy of Region, 15(1), 84–98. https://doi.org/10.17059/2019-1-7
  • Moura, N. J., & Ribeiro, M. B. (2006). Zipf law for Brazilian cities. Physica A: Statistical Mechanics and Its Applications, 367, 441–448. https://doi.org/10.1016/j.physa.2005.11.038
  • Ribeiro, H. V., Oehlers, M., Moreno-Monroy, A. I., Kropp, J. P., & Rybski, D. (2021). Association between population distribution and urban GDP scaling. PLOS ONE, 16(1), e0245771. https://doi.org/10.1371/journal.pone.0245771
  • Rozenfeld, H. D., Rybski, D., Gabaix, X., & Makse, H. A. (2011). The Area and Population of Cities: New Insights from a Different Perspective on Cities. American Economic Review, 101(5), 2205–2225. https://doi.org/10.1257/aer.101.5.2205
  • Soo, K. T. (2007). Zipf’s Law and Urban Growth in Malaysia. Urban Studies, 44(1), 1–14. https://doi.org/10.1080/00420980601023869
  • Stanley, M. H., Buldyrev, S. V., Havlin, S., Mantegna, R. N., Salinger, M. A., & Eugene Stanley, H. (1995). Zipf plots and the size distribution of firms. Economics Letters, 49(4), 453–457. https://doi.org/10.1016/0165-1765(95)00696-d
  • Türk Patent ve Marka Kurumu. (2023). Patent Yıllık İstatistikler. https://www.turkpatent.gov.tr/patent-istatistik Urzúa, C. M. (2000). A simple and efficient test for Zipf’s law. Economics Letters, 66(3), 257–260. https://doi.org/10.1016/s0165-1765(99)00215-3
  • Zipf, G. K. (1942). The Unity of Nature, Least-Action, and Natural Social Science. Sociometry, 5(1), 48. https://doi.org/10.2307/2784953

TESTING THE ZIPF’S LAW USING PATENT DATA: THE EXAMPLE OF TURKIYE

Year 2023, Volume: 18 Issue: 2, 85 - 93, 31.12.2023

Eren Yıldırım , Yasemin Asu Çırpıcı

https://doi.org/10.54860/beyder.1393258

Abstract

Scaling laws are an evaluation method used in many disciplines for frequency-based data. Various statistical methods have been developed to scale for different data types and applied in fields such as literature, physics, biology and economics. Zipf's law has also been used as a scaling law to reveal the distribution structure of many different datasets. The validity of Zipf's law also varies when tested with different data types and statistical methods. With this study, we test the validity of Zipf's law with patent data for Turkish cities. In this context, it is aimed to reveal whether the regional differences in the structure of patent distribution follow a scaling law. A data set covering 1995-2022 is used, and each province's patent data is classified geographically. Then, scaling for the patent data is measured in the context of Zipf's law. According to our results, Zipf's law regarding patent distribution in Turkish cities could not be accepted. On the other hand, the measured scaling coefficient for Turkish cities revealed that the geographical distribution of patents follows a power law.

Keywords

Zipf's Law Innovation Patent Spatial Economics

References

  • Adamic, L.A., Huberman, B. (2002). Zipf’s law and the Internet, Glottometrics. 3, 143-150.
  • Aurélie, L., & Martin, Z. (2020). From Gibrat’s law to Zipf’s law through cointegration? Economics Letters, 192, 109211. https://doi.org/10.1016/j.econlet.2020.109211
  • Axtell, R. L. (2001). Zipf Distribution of U.S. Firm Sizes. Science, 293(5536), 1818–1820. https://doi.org/10.1126/science.1062081
  • C. Barry Pfitzner, T. M. T. (2017). Are Cities in Vietnam Distributed According to Zipf? Journal of Economics and Development Studies, 5(1). https://doi.org/10.15640/jeds.v5n1a1
  • Corominas-Murtra, B., Seoane, L. F., & Solé, R. (2018). Zipf’s Law, unbounded complexity and open-ended evolution. Journal of the Royal Society Interface, 15(149), 20180395. https://doi.org/10.1098/rsif.2018.0395
  • Denisov, S. (1997). Fractal binary sequences: Tsallis thermodynamics and the Zipf law. Physics Letters A, 235(5), 447–451. https://doi.org/10.1016/s0375-9601(97)00688-9
  • Duranton, G. (2006). Some foundations for Zipf’s law: Product proliferation and local spillovers. Regional Science and Urban Economics, 36(4), 542–563. https://doi.org/10.1016/j.regsciurbeco.2006.03.008
  • Fernholz, R. T., & Fernholz, R. (2020). Zipf’s law for atlas models. Journal of Applied Probability, 57(4), 1276–1297. https://doi.org/10.1017/jpr.2020.64
  • Gabaix, X. (1999). Zipf’s Law and the Growth of Cities. The American Economic Review, 89(2), 129–132. https://doi.org/10.1257/aer.89.2.129
  • Gabaix, X., Ioannides, Y. (2004). The evolution of city size distributions, ch. 53, p. 2341-2378 in Henderson, J. V. and Thisse, J. F. eds., Handbook of Regional and Urban Economics, vol. 4, Elsevier.
  • Giller, G. L. (2013). Further Beyond Zipf’s Law: An Empirically Useful Augmentation of the Zipf-Mandelbrot Law. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2227003
  • Harremoës, P., & Topsoe, F. (2005). Zipf’s law, hyperbolic distributions and entropy loss. Electronic Notes in Discrete Mathematics, 21, 315–318. https://doi.org/10.1016/j.endm.2005.07.075
  • Hinloopen, J., & van Marrewijk, C. (2006). Comparative Advantage, the Rank-Size Rule, and Zipf’s Law. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.943370
  • Ioannides, Y. M., & Overman, H. G. (2003). Zipf’s law for cities: an empirical examination. Regional Science and Urban Economics, 33(2), 127–137. https://doi.org/10.1016/s0166-0462(02)00006-6
  • Kirby, G. (1985). Zipf’s Law. UK Journal of Naval Science. 10(3), 180-185.
  • Kleiber, M. (1932). Body size and metabolism. Hilgardia, 6(11), 315–353. https://doi.org/10.3733/hilg.v06n11p315
  • Manaeva, I. (2019). Distribution of Cities in Federal Districts of Russia: Testing of the Zipf Law. Economy of Region, 15(1), 84–98. https://doi.org/10.17059/2019-1-7
  • Moura, N. J., & Ribeiro, M. B. (2006). Zipf law for Brazilian cities. Physica A: Statistical Mechanics and Its Applications, 367, 441–448. https://doi.org/10.1016/j.physa.2005.11.038
  • Ribeiro, H. V., Oehlers, M., Moreno-Monroy, A. I., Kropp, J. P., & Rybski, D. (2021). Association between population distribution and urban GDP scaling. PLOS ONE, 16(1), e0245771. https://doi.org/10.1371/journal.pone.0245771
  • Rozenfeld, H. D., Rybski, D., Gabaix, X., & Makse, H. A. (2011). The Area and Population of Cities: New Insights from a Different Perspective on Cities. American Economic Review, 101(5), 2205–2225. https://doi.org/10.1257/aer.101.5.2205
  • Soo, K. T. (2007). Zipf’s Law and Urban Growth in Malaysia. Urban Studies, 44(1), 1–14. https://doi.org/10.1080/00420980601023869
  • Stanley, M. H., Buldyrev, S. V., Havlin, S., Mantegna, R. N., Salinger, M. A., & Eugene Stanley, H. (1995). Zipf plots and the size distribution of firms. Economics Letters, 49(4), 453–457. https://doi.org/10.1016/0165-1765(95)00696-d
  • Türk Patent ve Marka Kurumu. (2023). Patent Yıllık İstatistikler. https://www.turkpatent.gov.tr/patent-istatistik Urzúa, C. M. (2000). A simple and efficient test for Zipf’s law. Economics Letters, 66(3), 257–260. https://doi.org/10.1016/s0165-1765(99)00215-3
  • Zipf, G. K. (1942). The Unity of Nature, Least-Action, and Natural Social Science. Sociometry, 5(1), 48. https://doi.org/10.2307/2784953
There are 24 citations in total.

Details

Primary Language Turkish
Subjects Macroeconomics (Other)
Journal Section Articles
Authors

Eren Yıldırım 0000-0002-3705-2424

Yasemin Asu Çırpıcı 0000-0003-0483-2907

Early Pub Date December 9, 2023
Publication Date December 31, 2023
Submission Date November 20, 2023
Acceptance Date December 7, 2023
Published in Issue Year 2023 Volume: 18 Issue: 2

Cite

APA Yıldırım, E., & Çırpıcı, Y. A. (2023). ZİPF YASASININ PATENT VERİSİ İLE TEST EDİLMESİ: TÜRKİYE ÖRNEĞİ. Bilgi Ekonomisi Ve Yönetimi Dergisi, 18(2), 85-93. https://doi.org/10.54860/beyder.1393258
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