Introduction to Numerical Simulation for Trade Theory and Policy

John Gilbert, Edward Tower

• Publisher: WSPC
• Year: 2012
• ISBN:
  9789814401623
• Topic: Politics & International Relations
• Subtopic: Trade & Tariffs
• Index: Politics & International Relations

This volume provides a practical guide to building and using simulation models for international trade theory and policy. Through a sequence of carefully constructed and fully documented programs, the volume illustrates how numerical simulation can be used to analyze a wide array of problems. Modern computable general equilibrium (CGE) models for trade policy are challenging in their complexity, but can be thought of as constructions of much simpler building blocks. By developing the building blocks in a consistent manner, and gradually putting them together in more complex and interesting ways, the volume makes CGE accessible to anyone with a background in microeconomics/trade theory. The volume will be useful to graduate students and researchers in international trade looking for a detailed guide to building simulation models and to developing the skill set necessary to enter into the world of CGE modeling.

Contents:

• • Introduction
  • Getting Started With GAMS
• Theory of Consumption, Production and Trade:
  • Utility Maximization
  • Cost Minimization
  • Long-Run Production
  • Short-Run Production
  • Dual Approach
  • Transition
  • Higher Dimensions
  • Autarky
  • Small Country Trading Equilibrium
  • Non-traded Goods
  • Large Country Trading Equilibrium
  • Two Country Trading Equilibrium
  • Higher Dimensions and Trade
  • Reciprocal Dumping
  • Monopolistic Competition
• Commercial Policy and Distortions:
• • Tariffs and Other Trade Interventions
  • Domestic Taxes and Subsidies
  • Factor Market Distortions
• Computable General Equilibrium:
• • Multiple Households and Other Sources of Demand
  • Armington Preferences
  • Joint Production
  • Social Accounting Matrices
  • Closure
  • Single Country Competitive CGE
  • Concluding Comments

Readership: Graduate students and researchers in international trade theory and policy.

Chapter 1

Introduction

The traditional approach to learning the theory of international trade uses a variety of geometric devices to examine comparative statics. In advanced classes, this is usually supplemented by algebraic derivation of key results. A complementary technique that is less widely used is simulation with numerical models.

Using numerical simulation techniques can be beneficial in a number of ways. Working with numerical examples is often a useful aid to understanding abstract material, and is a hands-on activity where the user is free to experiment with the underlying data, parameters and model structure. It thereby helps to develop economic intuition, a feel for how key parameters affect results, and insights into the effect of model structures on outcomes. Numerical programming also encourages us to think about the models of international trade theory in terms of complete systems, and it can allow us to see more advanced results as being extensions of a common trade theoretic framework, a point that can sometimes be lost in trade theory’s myriad of algebra and geometry.

Perhaps even more importantly, numerical programming is a skill that forms an increasingly crucial part of the international economist’s toolbox. In addition to helping us to gain a better understanding of existing theory, the techniques of numerical simulation can be used as an aid to the development and testing of new economic ideas. Moreover, large scale numerical simulation models, in particular computable general equilibrium or CGE models, have become an integral part of modern trade policy analysis. These models have found widespread use in the assessment of a diverse range of real world trade policy problems and beyond. Well-known CGE models include the Michigan Model of World Production and Trade (Deardorff and Stern, 1986 and 1990), the ORANI model of the Australian economy (Dixon et al., 1982), GTAP (Hertel, 1997), and the World Bank’s LINKAGE model (van der Mensbrugghe, 2005).

Unfortunately, computable general equilibrium modeling is sometimes regarded as a difficult area of study for the beginner to enter. It requires a diverse set of skills, including a solid foundation in trade theory, programming capability, and the ability to work with sets of complex data. Many computable general equilibrium models are large and complicated. Moreover, their structure and inner workings can sometimes be opaque, leaving them open to the “black box” criticism.

We argue, however, that learning numerical simulation methods and CGE modeling techniques is not as difficult as it may appear to the uninitiated. While CGE models are indeed often large and complex, their component parts are relatively straightforward, and are not so difficult to learn when approached systematically.

The aim of this volume then, is to help readers to develop the skills necessary to design, implement, and use numerical simulation models useful for trade and trade policy analysis. We start with simple “toy” models that are familiar from the pure theory of international trade, and gradually add complexity until we have systems that are representative of the current “standard” CGE models. The volume grew out of a series of GAMS programs developed by Tower for teaching trade theory at the University of Auckland, and extended by Gilbert for classes taught at Utah State University. The programs have also been used at Duke University and Chulalongkorn University.

The volume has several unique features. First, the model development emphasizes the underlying optimization problems which define the various economic models and their component parts. We have tried to be very consistent in the way that the models are presented. Readers coming to the volume with a limited background in trade theory or computable general equilibrium will still find the approach accessible.

Second, we emphasize using “toy” models to develop programming skill and economic intuition. Readers coming to the volume with a strong background in trade theory will find the models and their properties to be very familiar, and can concentrate on learning how to translate the models into a numerical simulation form. Readers with less background in trade theory will develop skill in programming numerical models at the same time as learning more about the structure and behavior of the basic models of international trade.

We have tried to provide a very clear link between the simulation models and the pure theory of international trade. Indeed, the majority of the topics covered in a typical advanced course in international trade theory are covered here, and the volume also provides a guide to important results in the trade theory literature, and references for further reading. While the volume is not intended to be a textbook on international trade theory, but rather to complement existing treatments, the model and topic development does follow typical textbook approaches such as Bhagwati et al. (1998). By integrating a treatment of trade theory with a treatment of computational models, we hope to provide a set of knowledge and skills that will ultimately make the reader a better numerical modeler.

Third, the volume features a gradual development of the models, introducing new features in small, easily digestible parts. Many of the more difficult models can be thought of as constructions of much simpler building blocks. Hence, the approach is to develop the building blocks sequentially, gradually putting them together in more complex and interesting ways. In doing so, the volume facilitates a stronger understanding of how each of these parts work, and avoids overwhelming the reader by presenting a complex CGE system in full at the outset.

Finally, we make all of the codes and models that are developed in the volume fully available to the reader. The programs described in each chapter can be downloaded through the RePEc database at http://econpapers.repec.org/software/uthsfware/, or through any of the other RePEc services. A search for “GAMS Models for Trade Theory” will bring up the site. The reader is free to use the provided models as a base, and to modify them to suit their own purposes.

All of the programs that we present in the volume are built with the General Algebraic Modeling System (GAMS). This is a high-level programming environment that is particularly well suited to building large-scale numerical simulation models. GAMS is in widespread use, and learning how to program in GAMS is a useful skill in its own right.

We assume no prior knowledge about GAMS or programming in this volume, although some familiarity with programming languages in general is probably useful. The volume is not intended to be a stand-alone guide to GAMS programming, a purpose for which the GAMS User’s Guide is more than satisfactory, but we provide considerable detail on the mechanics of programming in GAMS, as well as advice for dealing with the inevitable problems that arise when building numerical models.

Of course, GAMS is not the only environment suitable for constructing the types of models that we discuss in this volume. Computable general equilibrium models are also commonly built in other languages, including GEMPACK and Matlab. It is even possible to construct quite sophisticated models in common programs like Excel (see Gilbert and Oladi, 2011, for example). The basic principles of model building that we set out in this volume are applicable to readers working in those environments also, although the mechanics will of course differ.

As the title suggests, the volume is introductory in nature. We have tried to make the material and approach amenable to researchers looking for a good way to get started in numerical modeling/CGE, and to make the volume accessible for advanced undergraduate or beginning graduate students. Hence, the volume’s background requirements are relatively modest. Familiarity with the tools of microeconomics at the intermediate level is a prerequisite, as is basic algebra and calculus, although we have tried to be no more formal than is necessary. Varian (1992) or (2009), or Perloff (2011) provide sufficient background for the former. Dixit (1990) emphasizes the constrained optimization approach that we adopt here, and is another useful reference. For mathematics, Chiang and Wainwright (2005) covers all the necessary material.

1.1 CGE Models

So what exactly is a CGE model and why is it useful to learn how to build one? Computable general equilibrium models are a particular type of numerical simulation model based on general equilibrium theory. In essence, this just means that a (symbolic) model from economic theory is built using specific functional forms instead of abstract ones, implemented as a computer program and fitted to real world data. The model is then perturbed, or shocked, in a way that represents a policy or structural change, and the numerical results are evaluated to provide insights into the possible economic implications of the shock. Whereas general equilibrium theory is often concerned with issues such as the existence and uniqueness of equilibrium, the basic objective of CGE modeling is to turn the abstract models of general equilibrium theory into a practical tool for policy analysis.

A number of features distinguish CGE models from other quantitative methods used in international economics, such as partial equilibrium modeling or gravity models. They are multi-sectoral, and in many cases multi-regional, and the behavior of economic agents is modeled explicitly through utility and profit maximizing assumptions. In addition, economywide constraints are rigorously enforced within the models. In other words, the markets in a computable general equilibrium model are all linked together. Distortions in an economic system will often have repercussions far beyond the sector in which they occur, and by linking markets, CGE techniques are effective at capturing the relevant feedback and flow-through effects.

Computable general equilibrium models have a number of advantages as a tool of policy analysis. First, they are theoretically consistent, with a solid foundation in microeconomic theory. Moreover, the theoretical choices that must be made in any modeling exercise are tackled front-on and are made explicit when programming a CGE model (although, regrettably, not always when reporting the results).

Second, CGE models are able to incorporate many unique features of an economic system. While the basic structure of most CGE models is recognizably Walrasian, many other types of economic features can and have been incorporated into CGE models, including imperfect competition and numerous other distortions. Hence, CGE models can adapt well to the analysis of a wide range of problems and economic circumstances.

Finally, CGE models can be used to predict values for many economic variables in an economic system. Unlike gravity models, for example, which are designed to help us understand and predict trade flows, the CGE approach models a complete economic system. Hence, we can use CGE models to evaluate the potential effect of a policy change on production, employment, trade, government revenue, and so on, or on all of these economic variables and more. The models also highlight the linkages between those economic variables.

On the other hand, CGE models have a number of limitations too.¹ The data requirements of CGE models are substantial (although they might be considered modest relative to the number of economic variables being considered). There is often uncertainty over parameters, specification, and experimental design. Because they cover all sectors in an economy, a CGE model may miss key features of critical sectors. It can also sometimes be difficult to know what is driving the results of CGE simulations. Finally, the human capital investment required for building/using these models can be high.

There is no doubt that CGE analysis is not suitable for all types of problems. As a broad guide, CGE will be an appropriate methodological choice if (1) the policy question of interest involves large changes that are well outside of historical experiences; (2) there is the potential for significant general equilibrium effects; and (3) the policy question requires information on the economic system and not broad economic aggregates.

The first requirement is obvious enough, and it suggests the need to use simulation techniques of some kind. The second is less obvious. What do we mean by “significant general equilibrium effects”? Basically, we mean that the policy question of interest involves multiple sectors. For example, a typical free trade agreement involves at least two countries simultaneously liberalizing many different sectors of the economy. This suggests that we need general equilibrium rather than partial equilibrium techniques to capture the full effect of the shock. Alternatively, the policy question may involve only one sector directly, but that sector is large enough to have an impact on the overall economy. For example, for many least developed economies the textile industry is so large relative to the overall economy that general equilibrium may be justified even if the policy scenario involves only that sector.

The last condition simply recognizes that a trade-off must be made for the sectoral detail that a CGE model provides. Hence, for example, if trade flows are the only variable of interest, extrapolation from a gravity model may be preferred to CGE analysis. If, however, we need to know how sectoral employment patterns will change when a trade policy is implemented, computable general equilibrium makes more sense.

We argue that to a large degree the weaknesses of CGE models are often more weaknesses of CGE modeling practice than limitations of the models themselves. Uncertainty over parameters and specification can be addressed by careful model construction and through the use of sensitivity analysis, and advances are being made in parameter estimation techniques (see Jansson and Heckelei, 2010, for example). Moreover, we hope that readers who work through this volume, will find the experience dramatically diminishes the problems of building CGE models and knowing what is driving their simulation results.

1.2 Volume Organization

As noted above, the main objective of this volume is to illustrate how numerical simulation methods can be used to construct an array of useful models of international trade theory and the theory of commercial policy, and to help readers develop the skills necessary to build models for themselves. GAMS is used as the programming platform.

Because we assume many readers will be unfamiliar with GAMS, we begin the volume with a quick primer on obtaining, installing and using GAMS to solve simple problems. More details are provided in subsequent chapters, and Appendix B sets out some advanced topics in GAMS programming, including sensitivity analysis, data interface and reporting options, and debugging.

The remainder of the volume is divided into three parts. In the first we cover modeling the theory of consumption, production and trade. In the second we move on to modeling the theory of commercial policy and other distortions. The final part of the volume deals with extensions to the basic models of trade theory that are commonly incorporated into modern computable general equilibrium models.

In Part 1 of the volume, we begin with the familiar problems of utility maximization and cost minimization, then move on to models of short and long-run production, and extensions including higher dimensions and intermediate goods. Next, we bring the demand and supply components together in a series of models dealing with autarky, small and large open economies, a complete global economy, and extensions including non-traded goods. Finally, we consider the international trade implications of imperfectly competitive markets.

Part 2 consists of three chapters. The first deals with the implications of trade interventions (tariffs, export subsidies, quotas, and so on) in various contexts (small and large economy, and a two country world). The second deals with domestic taxes and subsidies to production, consumption and factor use. The third deals with modeling the implications of various distortions to factor markets, including wage differentials, minimum wages, and imperfect factor mobility.

The final part of the volume contains chapters dealing with incorporating multiple households and other sources of demand into the models, dealing with intra-industry trade using Armington preferences, and dealing with joint production. We also have chapters on organizing the data for a CGE model, and on choosing a closure rule. The last major chapter brings the material together in a description of what might be called the “standard” CGE model. We finish up with some notes on where the reader can go to learn more.

In each of the model-oriented chapters in the volume, we begin with an underlying optimization problem or problems, show how we can solve the problem generally, and then how we can form a version of the model using specific functional forms. Next we outline the process of translating the model to GAMS. The GAMS programs are presented in full in the early chapters. As we progress, only incremental changes are discussed in most cases. The models outlined in each chapter are all available for download in full.

Each chapter concludes with a series of exercises. Many of the exercises can be completed by perturbing the model developed in the chapter by altering data or parameters. The objective is help develop an intuition for the model’s behavior. Other exercises involve extending the models in various ways, relaxing restrictions, changing functional forms, integrating new elements or elements from previous chapters, and so on. The aim here is to help develop independent programming skill. Most chapters conclude with a set of recommended readings on the topics covered.

The developmental sequence is important, and later chapters refer back frequen...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Preface
• Acknowledgment
• Contents
• List of Figures
• List of Tables
• 1. Introduction
• 2. Getting Started With Gams
• Theory of Consumption, Production and Trade
• 3. Utility Maximization
• 4. Cost Minimization
• 5. Long-Run Production
• 6. Short-Run Production
• 7. Dual Approach
• 8. Transition
• 9. Higher Dimensions
• 10. Intermediate Inputs
• 11. Autarky
• 12. Small Country Trading Equilibrium
• 13. Non-traded Goods
• 14. Large Country Trading Equilibrium
• 15. Two Country Trading Equilibrium
• 16. Higher Dimensions and Trade
• 17. Reciprocal Dumping
• 18. Monopolistic Competition
• Commercial Policy and Distortions
• 19. Tariffs and Other Trade Interventions
• 20. Domestic Taxes and Subsidies
• 21. Factor Market Distortions
• Computable General Equilibrium
• 22. Multiple Households and Other Sources of Demand
• 23. Armington Preferences
• 24. Joint Production
• 25. Social Accounting Matrices
• 26. Closure
• 27. Single Country Competitive Cge
• 28. Concluding Comments
• Appendix A. Lagrangian Multipliers, Shadow Prices and Marginal Social Values
• Appendix B. Gams Tips and Tricks
• Bibliography
• Index