Introduction

This chapter describes the objective of the book, giving an overview and describing its structure. It also explains the advantages of the use of mathematical modeling.

Keywords

Book structure; mathematical modeling

Chapter Outline

Reports on international finance always make the headlines. Industries complain that exchange rates are too appreciated. The American government accuses the Chinese of maintaining their exchange rates artificially depreciated while the Chinese deny it is the result of an active government policy. The debt crisis of the 1980s took Latin American countries into a decade-long struggle against astronomical inflation rates and government fiscal difficulties. It is even known as the region’s lost decade. Now it is Europe that appears to be living its lost decade.

When is external debt excessive? How does one know if an exchange rate is overappreciated? What leads to an exchange rate crisis? Do variations in government spending affect the exchange rate? What is the relationship between fiscal deficit and current-account deficit? Which is better, a floating or fixed exchange rate regime? Should Greece abandon the Euro? This book intends to provide an analytical framework that allows the reader to understand how to deal with these and other important questions related to international economics from the macroeconomic point of view.

Macroeconomics and international finance are vast fields1 and covering all questions, models, and applications pertinent to these two fields would be a “mission impossible.” The objective for the choice of topics covered in this book is to provide a logical structure to aid in understanding and analyzing questions concerning exchange rates and balance of payments. Each chapter describes a facet of international finance, like pieces of a puzzle that, once put together, form a picture of international finance that allows one to appreciate the individual elements and their interactions. The idea is to help the reader in building their own conceptual framework, allowing them to form their own analysis and conclusions regarding issues related to macroeconomics and international finance. More important than understanding the crises in exchange rate that have already occurred, for example, is understanding how they function and what causes them, allowing one to analyze new international finance contexts that may come about in the future.

Each chapter presents economic situations that provide for the development of mathematical models to highlight the essence of the problem, understand how the economic variables interact, and illustrate the forces in play. These models are simple, presented in an intuitive manner, and have mathematical appendices that provide step-by-step explanations of how they work. Concrete examples show how the theory can be applied to real-world situations. The book presents graphs, using data easily found on the Internet, so that the reader can reproduce them for different countries or periods in order to perform their own analysis of situations of interest to them and which have not been covered in the book. The Annexes at the end of the book provide Internet addresses where the data used in the graphs can be found. The intent is to offer instruments for analysis and tools that can be used in concrete cases. Finally, exercises are given at the end of each chapter. Some are designed to consolidate the material presented while others propose questions that will require additional analysis.

1.1 Mathematical Modeling

Economic analysis is usually performed using mathematical models. It is important to emphasize that these are used as analytical instruments and not as an end in themselves. Mathematics can be considered a type of language where the mathematical model tells a story. But, why tell a story using mathematics and not English? Mathematics is a specific type of language with four characteristics that make it more attractive to use when dealing with economics.

First, each mathematical symbol, which corresponds to words, has a unique and precise definition. The same is not true for English. For example, the dictionary offers at least five different definitions for the word symbol.2 Second, mathematics is a concise language. Once a term has been precisely defined, it can be represented by a symbol. A mathematical expression can represent an idea that would take an entire page to explain were it transcribed into English. Given its due proportion, the expression “a picture is worth a thousand words” can be applied in this case. Third, mathematical grammar is also very precise. In mathematics, there are strict rules regarding the relationships that can be made, or rather, about what can be expressed based on the initial definitions. There is no room for reading between the lines or for metaphors. It is really less charming than a discourse in English (there are those who may disagree) but when one desires a precise understanding of a concrete element, mathematics is best. Finally, mathematics is a universal language. Not everyone speaks English, but anyone who has been to school has studied math.

Due to these characteristics, when one tells a story in mathematics, it is told in such a way that each of its elements is precisely defined and the logical structure is strictly obeyed. Mathematics obliges the author of the story to express all the hypotheses used and the grammar guarantees that there are no errors in logic. While it is true that the same story could be told in English, it is much more difficult to express with the same precision, and errors in logic are more easily made. Mathematics serves, therefore, as a tool to help mere mortals, such as myself, to make fewer mistakes.

Up to this point, I have only spoken regarding the advantages of using mathematics. After all, I must convince you that the analytical method presented in this book is the one best suited for its purpose: offer an analytical framework you can use to understand situations not covered in the book. I do not want to sell a pig in a poke: mathematics also has its limits. As is almost always true, its best quality is also is greatest liability. Given that it is very precise, mathematics does not capture all the nuances inherent to socioeconomic relations. Simplification is necessary to express the world in a mathematical model. This is where it becomes an art: how does one simplify in such a way as to make the model understandable while at the same time maintain the elements necessary to understand the problem?

If I throw a stone into the waters of Copacabana Beach in Rio de Janeiro, waves are created that, in principle, would reach Walvis Bay in Namibia. However, there is an ocean between Copacabana and Walvis Bay (both literally and figuratively) with currents and waves caused by other factors that make those waves created by my stone to be imperceptible in Africa (actually, well before reaching Africa). If, instead of my small stone, a large meteorite fell into the waters of Copacabana Beach, the impact would be felt in Walvis Bay. Just like waves in the ocean, markets and economies are interconnected. Buying grapes at the supermarket, in principle, could stimulate an increase in grape prices, which could lead people to eat more apples, given that grapes are more expensive. This could lead to greater apple imports, which could lead to a deficit in current account…and a crisis in balance of payments. Well, just as my small stone in the waters of Copacabana Beach will not cause a tsunami in Walvis Bay, I can buy grapes without worrying about causing an international crisis.

Of course, decisions in economic modeling are more subtle than the simple example given above. It is not always clear which variables are relevant. Actually, relevant variables can change over time, as will be seen in Chapter 9. Each new wave of exchange rate crises generates more literature, adding previously absent variables to the models. The first models developed in the 1980s did not consider foreign corporate debt, for example, which was essential to the development of the crises of the 1990s.

As George E.P. Box said, “essentially, all models are wrong, but some are useful.” If on the one hand simplifications to an economic model make it unrealistic, on the other, not simplifying makes it impossible to understand what is occurring. Useful models are those that are able to discard what is really unimportant, but keep those elements essential for comprehension. A good model should be like a good map: it shows the trajectory from one point to another, identifies obstructions, topography, vegetation, and any other element important in reaching the destination. I present models that are useful, pointing out their limitations. The notations are uniform throughout the book and, whenever possible, the same model structure is used.

1.2 Book Structure

The first part of the book defines the object of our analysis. Given that macroeconomics and international finance deal with economic relations between countries, Chapter 2 begins by describing the taxonomy of the international flow of goods and financial assets. The balance of payment registers the international transaction of goods, services, and financial assets between countries. In national accounts, we will see how the results of these transactions relate to the main macroeconomic aggregates. The main objective is to understand the relation between current-account...