JEFFREY M WOOLDRIDGE Introductory Econometrics A MO D RN A P PRO ACH 2 E
c h a pt rone The nature of econometrics and Economic Data Ca hapter l discusses the scope of econometrics and raises general issues that result from the application of econometric methods Section 1.3 examines the kinds of data sets that are used in business economics. and other social sciences. Section 1. 4 provides an intuitive discussion of the difficulties associated with the inference of causality in the social sciences 1.1 WHAT ISECONOMETRICSH Imagine that you are hired by your state government to evaluate the effectiveness of a publicly funded job training program. Suppose this program teaches workers various ways to use computers in the manufacturing process. The twenty-week program offers courses during nonworking hours. Any hourly manufacturing worker may participate and enrollment in all or part of the program is voluntary. You are to determine what, if any, effect the training program has on each worker's subsequent hourly wage Now suppose you work for an investment bank. You are to study the returns on dif- ferent investment strategies involving short-term U.S. treasury bills to decide whether they comply with implied economic theories The task of answering such questions may seem daunting at first. At this point, you may only have a vague idea of the kind of data you would need to collect. By the end of this introductory econometrics course, you should know how to use econo- metric methods to formally evaluate a job training program or to test a simple eco- Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy. The most common application of econometrics is the forecasting of such important macroeconomic variables as interest rates, inflation rates, and gross domestic product. While forecasts of economic indicators are highly visible and are often widely published, econometric methods can be used in economic areas hat have nothing to do with macroeconomic forecasting. For example, we will study the effects of political campaign expenditures on voting outcomes. We will consider the effect of school spending on student performance in the field of education. In addition, we will learn how to use econometric methods for forecasting economic time series
Chapter 1 discusses the scope of econometrics and raises general issues that result from the application of econometric methods. Section 1.3 examines the kinds of data sets that are used in business, economics, and other social sciences. Section 1.4 provides an intuitive discussion of the difficulties associated with the inference of causality in the social sciences. 1.1 WHAT IS ECONOMETRICS? Imagine that you are hired by your state government to evaluate the effectiveness of a publicly funded job training program. Suppose this program teaches workers various ways to use computers in the manufacturing process. The twenty-week program offers courses during nonworking hours. Any hourly manufacturing worker may participate, and enrollment in all or part of the program is voluntary. You are to determine what, if any, effect the training program has on each worker’s subsequent hourly wage. Now suppose you work for an investment bank. You are to study the returns on different investment strategies involving short-term U.S. treasury bills to decide whether they comply with implied economic theories. The task of answering such questions may seem daunting at first. At this point, you may only have a vague idea of the kind of data you would need to collect. By the end of this introductory econometrics course, you should know how to use econometric methods to formally evaluate a job training program or to test a simple economic theory. Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy. The most common application of econometrics is the forecasting of such important macroeconomic variables as interest rates, inflation rates, and gross domestic product. While forecasts of economic indicators are highly visible and are often widely published, econometric methods can be used in economic areas that have nothing to do with macroeconomic forecasting. For example, we will study the effects of political campaign expenditures on voting outcomes. We will consider the effect of school spending on student performance in the field of education. In addition, we will learn how to use econometric methods for forecasting economic time series. 1 Chapter One The Nature of Econometrics and Economic Data d 7/14/99 4:34 PM Page 1
The Nature of econometrics and Economic data Econometrics has evolved as a separate discipline from mathematical statistics because the former focuses on the problems inherent in collecting and analyzing nonex perimental economic data. Nonexperimental data are not accumulated through con- trolled experiments on individuals, firms, or segments of the economy (Nonexperimental data are sometimes called observational data to emphasize the fact that the researcher is a passive collector of the data. )Experimental data are often collected in laboratory environments in the natural sciences, but they are much more difficult to obtain in the social sciences. While some social experiments can be devised, it is often impossible prohibitively expensive, or morally repugnant to conduct the kinds of controlled experi- ments that would be needed to address economic issues. We give some specific exam- ples of the differences between experimental and nonexperimental data in Section 1.4 Naturally, econometricians have borrowed from mathematical statisticians when ever possible. The method of multiple regression analysis is the mainstay in both fields, but its focus and interpretation can differ markedly. In addition, economists hay devised new techniques to deal with the complexities of economic data and to test the 1.2 STEPS IN EMPIRICAL ECONOMIC ANALYSIS Econometric methods are relevant in virtually every branch of applied economics. They come into play either when we have an economic theory to test or when we have a rela- tionship in mind that has some importance for business decisions or policy analysis. An empirical analysis uses data to test a theory or to estimate a relationship. How does one go about structuring an empirical economic analysis? It may seer obvious, but it is worth emphasizing that the first step in any empirical analysis is the careful formulation of the question of interest. The question might deal with testing a certain aspect of an economic theory, or it might pertain to testing the effects of a gov ernment policy. In principle, econometric methods can be used to answer a wide range In some case olve the mal economic model is constructed. An economic model consists of mathematical building of models to describe a vast array of behaviors. For example, in intermediate microeconomics, individual consumption decisions, subject to a budget constraint, are described by mathematical models. The basic premise underlying these models is util- ity maximization. The assumption that individuals make choices to maximize their well ng, subject to resource constraints, gives us a very powerful framework for creating tractable economic models and making clear predictions. In the context of consumption decisions, utility maximization leads to a set of demand equations. In a demand equa tion, the quantity demanded of each commodity depends on the price of the goods, the price of substitute and complementary goods, the consumer's income, and the individ- Is characteristics that affect taste. These equations can form the basis of an econo- etric analysis of consumer demand. Economists have used basic economic tools, such as the utility maximization frame- work, to explain behaviors that at first glance may appear to be noneconomic in nature A classic example is Becker's(1968)economic model of criminal beha
Econometrics has evolved as a separate discipline from mathematical statistics because the former focuses on the problems inherent in collecting and analyzing nonexperimental economic data. Nonexperimental data are not accumulated through controlled experiments on individuals, firms, or segments of the economy. (Nonexperimental data are sometimes called observational data to emphasize the fact that the researcher is a passive collector of the data.) Experimental data are often collected in laboratory environments in the natural sciences, but they are much more difficult to obtain in the social sciences. While some social experiments can be devised, it is often impossible, prohibitively expensive, or morally repugnant to conduct the kinds of controlled experiments that would be needed to address economic issues. We give some specific examples of the differences between experimental and nonexperimental data in Section 1.4. Naturally, econometricians have borrowed from mathematical statisticians whenever possible. The method of multiple regression analysis is the mainstay in both fields, but its focus and interpretation can differ markedly. In addition, economists have devised new techniques to deal with the complexities of economic data and to test the predictions of economic theories. 1.2 STEPS IN EMPIRICAL ECONOMIC ANALYSIS Econometric methods are relevant in virtually every branch of applied economics. They come into play either when we have an economic theory to test or when we have a relationship in mind that has some importance for business decisions or policy analysis. An empirical analysis uses data to test a theory or to estimate a relationship. How does one go about structuring an empirical economic analysis? It may seem obvious, but it is worth emphasizing that the first step in any empirical analysis is the careful formulation of the question of interest. The question might deal with testing a certain aspect of an economic theory, or it might pertain to testing the effects of a government policy. In principle, econometric methods can be used to answer a wide range of questions. In some cases, especially those that involve the testing of economic theories, a formal economic model is constructed. An economic model consists of mathematical equations that describe various relationships. Economists are well-known for their building of models to describe a vast array of behaviors. For example, in intermediate microeconomics, individual consumption decisions, subject to a budget constraint, are described by mathematical models. The basic premise underlying these models is utility maximization. The assumption that individuals make choices to maximize their wellbeing, subject to resource constraints, gives us a very powerful framework for creating tractable economic models and making clear predictions. In the context of consumption decisions, utility maximization leads to a set of demand equations. In a demand equation, the quantity demanded of each commodity depends on the price of the goods, the price of substitute and complementary goods, the consumer’s income, and the individual’s characteristics that affect taste. These equations can form the basis of an econometric analysis of consumer demand. Economists have used basic economic tools, such as the utility maximization framework, to explain behaviors that at first glance may appear to be noneconomic in nature. A classic example is Becker’s (1968) economic model of criminal behavior. Chapter 1 The Nature of Econometrics and Economic Data 2 14/99 4:34 PM Page 2
The Nature of econometrics and Economic data EXAMPLE1.1 (Economic Model of crime In a seminal article, Nobel prize winner Gary Becker postulated a utility maximization frame- work to describe an individuals participation in crime. Certain crimes have clear economic rewards, but most criminal behaviors have costs. The opportunity costs of crime prevent the criminal from participating in other activities such as legal employment. In addition, there are costs associated with the possibility of being caught and then, if convicted, the costs associated with incarceration. From Becker's perspective, the decision to undertake illegal activity is one of resource allocation, with the benefits and costs of competing activities aken into account Under general assumptions, we can derive an equation describing the amount of time spent in criminal activity as a function of various factors. We might represent such a fund =f(x1,x2x3,x4,xs,x6,x), y= hours spent in criminal activities x1="wage"for an hour spent in criminal activity in legal employ x3=income other than from crime or employment x4= probability of getting caught x6= expected sentence if convicted is representative of what might result from a formal economic analysis. As is common in economic theory, we have not been specific about the function f(- )in(1. 1). This function depends on an underlying utility function, which is rarely known. Nevertheless, we can use economic theory-or introspection -to predict the effect that each variable would have criminal activity. This is the basis for an econometric analysis of individual criminal activity Formal economic modeling is sometimes the starting point for empirical analysis, on to use economic theory less formally, or even to rely entirely intuition. You may agree that the determinants of criminal behavior appearing in equa tion(1. 1)are reasonable based on common sense; we might arrive at such an equation directly, without starting from utility maximization. This view has some merit, although there are cases where formal derivations provide insights that intuition can
EXAMPLE 1.1 (Economic Model of Crime) In a seminal article, Nobel prize winner Gary Becker postulated a utility maximization framework to describe an individual’s participation in crime. Certain crimes have clear economic rewards, but most criminal behaviors have costs. The opportunity costs of crime prevent the criminal from participating in other activities such as legal employment. In addition, there are costs associated with the possibility of being caught and then, if convicted, the costs associated with incarceration. From Becker’s perspective, the decision to undertake illegal activity is one of resource allocation, with the benefits and costs of competing activities taken into account. Under general assumptions, we can derive an equation describing the amount of time spent in criminal activity as a function of various factors. We might represent such a function as y f(x1,x2,x3,x4,x5,x6,x7), (1.1) where y hours spent in criminal activities x1 “wage” for an hour spent in criminal activity x2 hourly wage in legal employment x3 income other than from crime or employment x4 probability of getting caught x5 probability of being convicted if caught x6 expected sentence if convicted x7 age Other factors generally affect a person’s decision to participate in crime, but the list above is representative of what might result from a formal economic analysis. As is common in economic theory, we have not been specific about the function f() in (1.1). This function depends on an underlying utility function, which is rarely known. Nevertheless, we can use economic theory—or introspection—to predict the effect that each variable would have on criminal activity. This is the basis for an econometric analysis of individual criminal activity. Formal economic modeling is sometimes the starting point for empirical analysis, but it is more common to use economic theory less formally, or even to rely entirely on intuition. You may agree that the determinants of criminal behavior appearing in equation (1.1) are reasonable based on common sense; we might arrive at such an equation directly, without starting from utility maximization. This view has some merit, although there are cases where formal derivations provide insights that intuition can overlook. Chapter 1 The Nature of Econometrics and Economic Data 3 d 7/14/99 4:34 PM Page 3
The Nature of Econometrics and Economic data Here is an example of an equation that was derived through reasoning. E M PLE.2 (Job Training and worker productivity) Consider the problem posed at the beginning of Section 1. 1. a labor economist would like to examine the effects of job training on worker productivity. In this case, there is little need for formal economic theory. Basic economic understanding is sufficient for realizing that factors such as education, experience, and training affect worker productivity. Also, econ omits are well aware that workers are paid commensurate with their productivity This sim- le reasoning leads to a model such as where wage is hourly wage, educ is years of formal education, exper is years of workforce experience, and training is weeks spent in job training. Again, other factors generally affect he wage rate, but (1. 2) captures the essence of the problem After we specify an economic model, we need to turn it into what we call an econo- metric model. Since we will deal with econometric models throughout this text, it is important to know how an econometric model relates to an economic model. Take equa- tion(1. 1)as an example. The form of the function f( )must be specified before we car ndertake an econometric analysis. A second issue concerning(1. 1)is how to deal with variables that cannot reasonably be observed. For example, consider the wage that a person can earn in criminal activity. In principle, such a quantity is well-defined, but it yould be difficult if not impossible to observe this wage for a given individual. Even ariables such as the probability of being arrested cannot realistically be obtained for iven individual. but at least we can observe relevant arrest statistics and derive a var- able that approximates the probability of arrest. Many other factors affect criminal behavior that we cannot even list let alone observe but we must somehow account for them The ambiguities inherent in the economic model of crime are resolved by specify g a particular econometric model: crime=Bo+ B, wage B2othinc B3freqarr Bafreqcomv 13) Bsavgsen bage +l where crime is some measure of the frequency of criminal activity, wage is the wage at can be earned in legal employment, othinc is the income from other sources(assets inheritance, etc. freqarr is the frequency of arrests for prior infractions(to approxi- mate the probability of arrest), fregcomm is the frequency of conviction, and avgsen is the average sentence length after conviction. The choice of these variables is deter mined by th theory as well as data considerations. The term u contains unob-
Here is an example of an equation that was derived through somewhat informal reasoning. EXAMPLE 1.2 (Job Training and Worker Productivity) Consider the problem posed at the beginning of Section 1.1. A labor economist would like to examine the effects of job training on worker productivity. In this case, there is little need for formal economic theory. Basic economic understanding is sufficient for realizing that factors such as education, experience, and training affect worker productivity. Also, economists are well aware that workers are paid commensurate with their productivity. This simple reasoning leads to a model such as wage f(educ,exper,training) (1.2) where wage is hourly wage, educ is years of formal education, exper is years of workforce experience, and training is weeks spent in job training. Again, other factors generally affect the wage rate, but (1.2) captures the essence of the problem. After we specify an economic model, we need to turn it into what we call an econometric model. Since we will deal with econometric models throughout this text, it is important to know how an econometric model relates to an economic model. Take equation (1.1) as an example. The form of the function f() must be specified before we can undertake an econometric analysis. A second issue concerning (1.1) is how to deal with variables that cannot reasonably be observed. For example, consider the wage that a person can earn in criminal activity. In principle, such a quantity is well-defined, but it would be difficult if not impossible to observe this wage for a given individual. Even variables such as the probability of being arrested cannot realistically be obtained for a given individual, but at least we can observe relevant arrest statistics and derive a variable that approximates the probability of arrest. Many other factors affect criminal behavior that we cannot even list, let alone observe, but we must somehow account for them. The ambiguities inherent in the economic model of crime are resolved by specifying a particular econometric model: crime 0 + 1wagem + 2othinc 3 freqarr 4 freqconv 5avgsen 6age u, (1.3) where crime is some measure of the frequency of criminal activity, wagem is the wage that can be earned in legal employment, othinc is the income from other sources (assets, inheritance, etc.), freqarr is the frequency of arrests for prior infractions (to approximate the probability of arrest), freqconv is the frequency of conviction, and avgsen is the average sentence length after conviction. The choice of these variables is determined by the economic theory as well as data considerations. The term u contains unobChapter 1 The Nature of Econometrics and Economic Data 4 14/99 4:34 PM Page 4