Analysis of Czech Trade Structure Using the Zipf’s Law

• Název práce v češtině: Analýza struktury českého obchodního trhu pomocí Zipfova zákona
• Název v anglickém jazyce: Analysis of Czech Trade Structure Using the Zipf’s Law
• Akademický rok vypsání: 2020/2021
• Typ práce: bakalářská práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: RNDr. Michal Červinka, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 14.09.2021
• Datum zadání: 21.03.2022
• Datum a čas obhajoby: 08.06.2022 09:00
• Místo konání obhajoby: Opletalova - Opletalova 26, O314, Opletalova - místn. č. 314
• Datum odevzdání elektronické podoby: 29.04.2022
• Datum proběhlé obhajoby: 08.06.2022
• Oponenti: Mgr. Lenka Nechvátalová

Zásady pro vypracování

Research question and motivation
In my thesis, I am going to analyze structure of trade flows of the Czech Republic by using the Zipf’s Law.

For several decades, Zeta function has possessed a central place in Mathematics and dozens of mathematicians have performed their utmost in order to deal with the world-famous Riemann Hypothesis – Hilbert’s 8th problem. The same Zeta function, as a versatile empirical law, gradually gave a rise to newer implications in not only Mathematics, but also Physics and Social Sciences. This thesis focuses on a specific yet indirect application of Zeta function in Economics: Zipf’s Law.

Also called the Zipfian distribution, the Zipf’s Law was first proposed by a Harvard scholar George Kingsley Zipf, who claimed that rank-frequency distribution is an inverse relation such that frequency of usage of words (e.g., in a book) is inversely related to their ranks in the frequency table. Although this phenomenon occurs in Linguistics, research that has been done later on reveals that the relationship between countries and their populations follow up a fit which is strikingly similar to the Zipfian distribution (Gabaix, 1999). The slope of this fit is revealed to be -1 approximately, which is also the power law exponent. Unbiased estimations for the power law have been developed by Gabaix and Ibragimov (2011) with a basic yet elegant OLS model.

A study conducted by Hinloopen and van Marrewijk (2006) showed that theory of comparative advantage, developed by Ricardo (1817), associates with the rank-size rule in the same fashion. To clarify, comparative advantage, acting as a cornerstone in International Trade theory, is a fundamental concept that emphasizes a country’s ability to produce goods and services at lower (higher) costs in contrast to other trade partners. To quantify this tenet, Balassa (1965) proposed a gambit which is referred as Revealed Comparative Advantage (RCA) index. In this thesis, Balassa RCA indices will be used as a relevant tool for analyzing in which export and import sectors the Czech Republic is stronger/weaker than its counterparties.
In connection with the Zipf’s Law, RCA indices will be examined to find out whether their distribution follows a similar log-linear relationship just like in Zipf’s rank-size rule; and if there are certain linkages, how their interdependence with some well-known macroeconomic indicators can be explained.

Contribution
There are numerous studies focusing on the role of the Czech Republic in international trade from several perspectives, including the analysis of RCA indices too. However, to the best of my knowledge, no attempt has been made in practice so far in adressing the same exact issue by using rank-size rule. Therefore, this thesis might shed light on possible implications in International Trade theory from a more specific and narrower viewpoint, and fill the gap in the existing literature as well.

What my study can reveal is how the Czech trade is structured with respect to category of traded items and partner countries. In fact, the acquired results will priorly unearth which trade sectors the Czech Republic performs well in and which policies have been embraced by the government to improve its position in trade with other countries. Moreover, once the findings from the study encounter the reality, readers can have a more extensive understanding of the financial system of the Czech Republic as well. For instance, since there is a complex relationship amoung currencies of countries, their trade balances can explain why a currency appreciates (depreciates) and how central banks take precautionary measures to prevent wild fluctuations.

Methodology
In my thesis, I am going to re-check viability of the Zipf’s law in accordance with the Czech trade data collected from the United Nations (UN) Comtrade database. The analysis will be based on panel data estimations spanning a period between 1998 and 2020; results will be utilized to better comprehend what power law exponent looks like under the data for the Czech Republic. Moreover, estimations for the exponent will be subject to further examination using vector autoregression (VAR) model. To exemplify, it will stress the relationship between explanatory variables, such as GDP, population, exports, imports, etc. – collected from The World Bank’s World Development Indicator (WDI) – and estimated power law coefficient. As is known, the VAR model will take variables from previous years that act as lagged values.

Seznam odborné literatury

Balassa, B. (1965) Trade Liberalization and Revealed Comparative Advantage. The Manchester School of Economic and Social Studies, 33, 99-123. https://doi.org/10.1111/j.1467-9957.1965.tb00050.x

Gabaix, X. (1999). Zipf's Law for Cities: An Explanation. The Quarterly Journal of Economics, 114(3), 739-767. Retrieved June 14, 2021, from http://www.jstor.org/stable/2586883

Gabaix, X., & Ibragimov, R. (2011). Rank — 1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents. Journal of Business & Economic Statistics, 29(1), 24-39. Retrieved June 14, 2021, from http://www.jstor.org/stable/25800776

Hinloopen, J., van Marrewijk, C. Comparative advantage, the rank-size rule, and Zipf’s law. Tinbergen Institute Discussion Paper. November 2006. https://papers.tinbergen.nl/06100.pdf

Ricardo, David, (1817), On the Principles of Political Economy and Taxation, 3 ed., McMaster University Archive for the History of Economic Thought, https://EconPapers.repec.org/RePEc:hay:hetboo:ricardo1821.

Předběžná náplň práce

Outline

1. Introduction
2. Literature Review
3. Theoretical Background
3.1. Ricardian Model of Trade and RCA indices
3.2. Mathematics of the Zipf’s Law
4. Data & Methodology
5. Results
6. Conclusion

Předběžná náplň práce v anglickém jazyce

Outline

1. Introduction
2. Literature Review
3. Theoretical Background
3.1. Ricardian Model of Trade and RCA indices
3.2. Mathematics of the Zipf’s Law
4. Data & Methodology
5. Results
6. Conclusion