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Gary Koop is Professor of Economics at the University of Strathclyde. Gary has published numerous articles econometrics in journals such as the Journal of Econometrics and Journal of Applied Econometrics. Gary has taught econometrics for many years and is the author of following textbooks, all published by John Wiley & Sons Ltd: Analysis of Economic Data 2ed, Analysis of Financial Data and Bayesian Econometrics

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Introduction to Econometrics has been written as a core textbook for a first course in econometrics taken by undergraduate or graduate students. It is intended for students taking a single course in econometrics with a view towards doing practical data work. It will also be highly useful for students interested in understanding the basics of econometric theory with a view towards future study of advanced econometrics. To achieve this end, it has a practical emphasis, showing how a wide variety of models can be used with the types of data sets commonly used by economists. However, it also has enough discussion of the underlying econometric theory to give the student a knowledge of the statistical tools used in advanced econometrics courses.

Key Features:

• A non-technical summary of the basic tools of econometrics is given in chapters 1 and 2, which allows the reader to quickly start empirical work.
• The foundation offered in the first two chapters makes the theoretical econometric material, which begins in chapter 3, more accessible.
• Provides a good balance between econometric theory and empirical applications.
• Discusses a wide range of models used by applied economists including many variants of the regression model (with extensions for panel data), time series models (including a discussion of unit roots and cointegration) and qualitative choice models (probit and logit).

An extensive collection of web-based supplementary materials is provided for this title, including: data sets, problem sheets with worked through answers, empirical projects, sample exercises with answers, and slides for lecturers.

URL: www.wileyeurope.com/college/koop

Fragmento. © Reproducción autorizada. Todos los derechos reservados.

Introduction to Econometrics

John Wiley & Sons

Chapter One

1.1 The importance of econometrics

The Duke of Wellington, a British commander of the Napoleonic Wars, once said: 'All the business of war, indeed all the business of life, is to endeavour to find out what you don't know by what you do; that's what I call ''guessing what is on the other side of the hill".' This is an apt description of what econometrics is all about.

Economics is full of unanswered questions such as: 'Will a change in interest rates affect the exchange rate?' 'Do the long-term unemployed have a more difficult time getting jobs than the short-term unemployed? 'What is the impact of gas prices on the choice of whether to drive or take the bus to work?'. These are examples of the 'what we don't know' of economics. The 'what we do know' of economics are data. All sorts of agencies (e.g. governments, newspapers, companies even individuals) collect facts that shed light on the 'what we don't know'. Look, for instance, in most newspapers and you will find lots of information about the prices of various assets (e.g. interest rates, exchange rates, stock prices, etc.). Most governments carry out surveys or censuses of many activities of their citizens, and these can, for example, be used to compare the experience of the long-term unemployed with that of the short-term unemployed. Economic researchers have carried out surveys of commuters, and some of the information provided can be used to investigate factors that influence the choice between the private car and public transport.

Wellington knew that one had to appeal to the facts to make a good military decision. The same applies in economics. Without an appeal to the facts (i.e. the data), economic debates can degenerate into a sterile repetition of fixed opinions. Or they can become informal storytelling sessions where economists support their views with their favorite anecdotes. When making military preparations, anyone can 'guess what is on the other side of this hill', but it takes a great commander to combine all the available information and draw the most sensible conclusions. To continue the analogy, the purpose of econometrics is to show the economist how to be a great commander, to use 'what we know' in the most effective manner in order to try and resolve 'what we don't know'. In other words, econometrics shows us how to use data in a sensible and systematic manner to shed light on economic questions.

The purpose of this chapter is to provide you with an understanding of the basic concepts and tools that are used by econometricians. Given the primary role of data in econometrics, it won't surprise you to learn that much of this chapter is about data. We discuss the types of data commonly used by economists and offer a brief discussion about where data are obtained. Following this, we discuss some simple ways of analyzing data (e.g. graphical methods and descriptive statistics) and offer an introduction to some of the basic theoretical tools used by the econometrician (e.g. expected values and variances). These basic concepts and tools are then used in all the remaining chapters of this book.

1.2 Types of economic data

This section introduces the types of data used by economists and defines the notation and terminology associated with them.

1.2.1 Time series data

Macroeconomists and financial economists are often interested in concepts such as gross domestic product (GDP), stock prices, interest rates, exchange rates, etc. Such data are collected at specific points in time. In all of these examples, the data are ordered by time and are referred to as time series data. The underlying phenomenon that we are measuring (e.g. GDP, stock prices, interest rates, etc.) is referred to as a variable. Time series data can be observed at many frequencies. Commonly used frequencies are: annual (i.e. a variable is observed every year), quarterly (i.e. 4 times a year), monthly, weekly or daily.

In this book, we will use the notation [Y.sub.t] to indicate an observation on variable Y (e.g. an exchange rate) at time t. A series of data runs from period t = 1 to t = T. Here, T is used to indicate the total number of time periods covered in a dataset. To give an example, if we were to use monthly time series data from January 1947 to October 1996 on the UK pound/US dollar exchange rate - a period of 598 months - then t = 1 would indicate January 1947, t = 598 would indicate October 1996 and T = 598 would be the total number of months. Hence, [Y.sub.1] would be the pound/dollar exchange rate in January 1947, [Y.sub.2] would be this exchange rate in February 1947, etc. Time series data are presented in chronological order.

Working with time series data often requires some special tools, which are discussed in Chapters 6 and 7.

1.2.2 Cross-sectional data

In contrast to the above, researchers often work with data that are characterized by individual units. These units might refer to companies, people, or countries. For instance, a financial economist investigating theories relating to portfolio allocation might collect data on the return earned on the stocks of many different companies. With such cross-sectional data, the ordering of the data typically does not matter (unlike time series data).

In this book, we use the notation [Y.sub.i] to indicate an observation on variable Y for individual i. Observations in a cross-sectional dataset run from unit i = 1 to N. By convention, N indicates the number of cross-sectional units (e.g. the number of companies surveyed). For instance, a researcher might collect data on the share price of N = 100 companies at a certain point in time. In this case, [Y.sub.1] will be equal to the share price of the first company, [Y.sub.2] will be equal to the share price of the second company, and so on.

It is worthwhile stressing another important distinction between types of data. In the preceding example, the researcher collecting data on share prices will have a number corresponding to each company (e.g. the price of a share of company 1 is $25).This is referred to as quantitative data.

However, there are many cases where data do not come in the form of single numbers. For instance, the labour economist, when asking whether or not each surveyed employee belongs to a union, receives either a Yes or a No answer. These answers are referred to as qualitative data. Such data arise often in economics when choices are involved (e.g. the choice to buy or not to buy a product, to take public transport or a private car). Econo-metricians usually convert these qualitative answers into numeric data. For instance, the labor economist might set Yes = 1 and No = 0. Hence, [Y.sub.1] = 1 means that the first individual surveyed does belong to a union, and [Y.sub.2] = 0 means that the second individual does not. When variables can take on only the values 0 or 1, they are referred to as dummy (or binary) variables.

1.2.3 Panel data

Some datasets will have both a time series and a cross-sectional component. Such data are referred to as panel data. Economists working on issues related to economic growth often make use of panel data. They might work, for instance, with data for 90 countries for the years 1950-2000 for the variable Y = GDP. Such a dataset would contain the value of GDP for each country in 1950 (N = 90 observations), followed by GDP for each country in 1951 (another N = 90 observations), and so on. Over a period of T years, there would be TN observations on Y. We will use the notation [Y.sub.it] to indicate an observation on variable Y for country i at time t. Panel datasets are often used by labour economists. For instance, the government often carries out surveys of many people asking them questions about their employment, income, education, etc. From such a survey the labour economist might work with the variable Y = the wage of N = 1 000 individuals for T = 5 years.

1.2.4 Obtaining data

All of the data you need in order to understand the basic concepts and to carry out the analyses covered in this book can be downloaded from the website associated with this book. However, in the future you may need to gather your own data for an essay, dissertation, or report. Economic data come from many different sources, and it is hard to offer general comments on the collection of data. Below are a few key points that you should note about common datasets and where to find them.

It is becoming increasingly common for economists to obtain their data over the internet, and many relevant websites now exist from which data can be downloaded. You should be forewarned that the web is a rapidly growing and changing place, so that the information and addresses provided here might soon be outdated. Accordingly, this section is provided only to give an indication of what can be obtained over the internet, and as such is far from complete.

Some of the datasets available on the web are free, but many are not. Most university libraries or computer centres subscribe to various databases that the student can use. You are advised to check with your own university library or computer centre to see what datasets you have access to. Most universities will at a minimum have access to the major datasets collected by the government. For instance, in the UK the Office of National Statistics (ONS) collects all sorts of data, and these are usually available through UK university libraries. The UK Data Archive (http://www.data-archive.ac.uk/) is another useful source. An extremely useful American site is 'Resources for Economists on the Internet' (http://rfe.org). This site contains all sorts of interesting material on a wide range of economic topics and provides links to many different data sources. On this site you can also find links to journal data archives. Many journals encourage their authors to make their data publicly available, and hence, in many cases, you can get data from published academic papers through journal data archives. A good example is the Journal of Applied Econometrics Data Archive (http://www.econ.queensu.ca/jae/).

Another site with useful links is the National Bureau of Economic Research (http:// www.nber.org/). One good data source available through this site is the Penn World Table (PWT), which gives macroeconomic data for over 100 countries for many years. We will refer to the PWT below. Most countries also have large panel datasets where large groups of individuals are surveyed every year. In America, the Panel Study of Income Dynamics (http://psidonline.isr.umich.edu/) is a valuable resource for researchers in many fields. In the UK, the comparable panel dataset is the British Household Panel Survey (http://www.iser.essex.ac.uk/ulsc/bhps/).

With regard to financial data, there are many excellent databases of stock prices and accounting information for all sorts of companies for many years. Unfortunately, these tend to be very expensive and, hence, you should see whether your university has a subscription to a financial database. Two of the more popular ones are DataStream by Thompson Financial (http://www.datastream.com/) and Wharton Research Data Services (http://wrds.wharton.upenn.edu/). For free data, a more limited choice of financial data is available through popular internet ports such as Yahoo (http://yahoo.finance.com). The Federal Reserve Bank of St Louis also maintains a free database with a wide variety of data, including some financial time series (http://research.stlouisfed.org/fred2/). The Financial Data Finder (http://www.cob.ohio-state.edu/fin/osudata.htm), provided by the Fisher College of Business at the Ohio State University, is also a useful resource. Many academics also make the datasets they have used available on their websites. For instance, Robert Shiller at Yale University has a website that provides links to many different interesting financial datasets (http://aida.econ.yale.edu/%7Eshiller/index.html). A general point worth stressing is that spending some time searching the web can often be very fruitful.

1.2.5 Data transformations: levels and growth rates

In this book, we will mainly assume that the data of interest, Y, are directly available. However, in practice, it is common to take raw data from one source and then transform it into a different form for empirical analysis. For instance, the financial economist may take raw time series data on the variables X = company earnings and W = number of shares and create a new variable: Y = earnings per share. Here, the transformation would be

Y = X/W.

The exact nature of the transformation required depends on the problem at hand, so it is hard to offer any general recommendations on data transformation. Some special cases are considered in later chapters. Here, it is useful to introduce some transformations that often arise with time series data.

To motivate this transformation, note that in many cases macroeconomists and financial economists are not interested directly in a variable (e.g. GDP), but rather how it is changing over time. To make things concrete, consider financial economists. In many cases they would not be interested in the price of an asset, but rather in the return that an investor would make from purchase of the asset. This depends on how much the price of the asset will change over time. Suppose, for instance, that the financial economist has annual data on the price of a share in a particular company for 1950^1998 (i.e. 49 years of data), denoted by [Y.sub.t] for t = 1 - 49. In some cases this might be the variable of primary interest. Such a variable is referred to as a level (i.e. we refer to the 'level of the share price'). However, people are often more interested in the growth of the share price. A simple way to measure growth is to take the share price series and calculate a percentage change for each year. The percentage change in the share price between period t - 1 and t is calculated according to the formula % change = [[Y.sub.t] - [Y.sub.t]-1] / [Y.sub.t]-1]] x 100.

It is worth stressing that a percentage change always has a timescale associated with it (e.g. the percentage change between period t - 1 and t). For instance, with annual data this formula would produce an annual percentage change, with monthly data the formula would produce a monthly percentage change, etc. As will be discussed in later chapters, it is sometimes convenient to take the natural logarithm of variables. The definition and properties of logarithms can be found in Appendix A: Mathematical Basics at the end of this book. Using the properties of logarithms, it can be shown that the percentage change in a variable is approximately

% change [approximately equal to] [ln([Y.sub.t]) - ln ([Y.sub.t-1]) x 100.

In practice, the 'x 100' is often dropped, so that, say, 5% would be 0.05. The percentage change in an asset's price is often referred to as the growth of the price or the change in the price. Changes in variables are often used with macroeconomic variables. For instance, macroeconomists sometimes study GDP growth (instead of the level of GDP) or inflation (which is the change in the price level). Chapters 6 and 7 cover time series econometrics, and in these chapters it is often important to distinguish between the level of a variable and its growth rate.

1.3 Working with data: graphical methods

Once you have your data, it is important for you to summarize it. After all, anybody who reads your work will not be interested in the dozens or, more likely, hundreds or more observations contained in the original raw dataset. Indeed, you can think of the whole field of econometrics as one devoted to the development and dissemination of methods whereby information in datasets is summarized in informative ways. Charts and tables are very useful ways of presenting your data. There are many different types (e.g. bar chart, pie chart, etc.). In this section, we will illustrate a few of the commonly used types of chart. Since most economic data are either in time series or cross-sectional form, we will briefly introduce simple techniques for graphing both types of data.

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