The Nature of Econometrics
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1 Lecture 1: The Nature of Econometrics and Economic Data (Ch 1) The Nature of Econometrics General speaking, econometrics is a discipline that develops statistical methods for analyzing economic relationships, testing economic theories and evaluating economic policies. (For example, Phillips Curve) What is the difference between statistics and econometrics? A: They have many techniques in common. But economists focus more on estimating parameters that are instructive to solving economic issues, while statistician lean more towards developing computational methods for different purposes. - Econometrics = use of statistical methods to analyze economic data - Econometricians typically analyze non-experimental data - Typical goals of econometric analysis 1) Estimating relationships between economic variables 2) Testing economic theories and hypotheses 3) Forecasting economic variables 4) Evaluating and implementing government and business policy Economic relationships we may be interested in: Sales & Advertising; Police enforcement & crime rate; Earnings & Education/gender/race; Changes in the tax law & distribution of income; Deductible payment on health insurance & demand for health
2 services; Square footage of a real estate property & its selling price; Rent control & housing price; CEO salary & return on firm equity; Mergers or leveraged buyout & returns of stockholders Economic theories we may want to test: Demand/Supply equations derived from utility/profit maximization; Structure-Conduct-Performance Theory; Positive relationship between money supply and inflation; Distortion due to externalities; Gains from trade Economic policies we may want to evaluate: Taxation policy; Interest rate cut; Bank rescue plan; Deregulation of electricity industry; Global warming treaty Methodology of Econometrics Econometric analyses normally take the following steps: 1.Statement of theory 2.Specification of the mathematical model of the theory 3.Specification of the econometric model 4.Data collection 5.Estimation of econometric model.
3 6.Hypothesis testing. 7.Forecasting/prediction, and study of policy impact Let us use an example in the textbook to illustrate this process: In a seminal article, Nobel Prize winner Gary Becker postulated a utility maximization framework to describe an individual s participation in crime (Step 1: Statement of theory). Certain crimes have clear economic rewards, but most criminal behaviors have costs. The opportunity costs of crime prevent criminal from participating in other activities such as legal employment. In addition if caught, the cost associated with detention. From Becker s perspective, the decision to undertake illegal activity is one of resource allocation, with benefits and costs of competing activities taken into account. Under general assumption we can derive an equation describing the amount of time spent in criminal activity as a function of various factors (Step 2: Specification of the mathematical model of the theory). It is an economic model as below: y= f(x 1,x 2,x 3,x 4,x 5,x 6,x 7 ) equation (1) y : hours spent in criminal activity x 1 : wage for an hour spent in criminal activity x 2 : hourly wage in legal activity x 3 : income other than from crime or employment x 4 : probability of getting caught x 5 : probability of being convicted if caught
4 x 6 : expected sentence if convicted x 7 : age The above variables are representative of the factors what may affect a person s decision to participate in crime, although other factors may also influence this decision. The functional form depends on an underlying utility function of the decision maker, which has to be specified. After we specify an economic model, we need to turn it into what we call an econometric model. We will be dealing with econometric models a lot in this course, and it is important to know how econometric model relates to an economic model. A second issue concerning the equation (1) above is how to deal with variables that can t be reasonably 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 it. Other variables such as the probability of being arrested cannot realistically be obtained. At most we can observe relevant arrest statistics or derive variables that approximate the probability of arrest such as relative number of policemen in the city or neighborhood. There are also many other factors affecting criminal behavior that we can t even list, let alone observe. To account for this ambiguity inherent in the economic model of crime, we specify an econometric model (Step 3) in the following way: crime = β 0 + β 1 wage m + β 2 othincome + β 3 numberofpolice + β 4 freqconv + β 5 avgsent + β 6 age + u Variables included are: crime: some measure of frequency of criminal activity
5 wage m: the wage that can be earned in legal employment othincome: the income from other sources (assets inheritance) numberofpolice: number of police officers in the city freqconv: the frequency of conviction avgsent: the average sentence length after conviction The choice of these variables is determined by economic theory as well as data considerations. The term u is an error term. It is a random variable that represents all portions of the data generating process that are not captured by the economic model. In our example, it contains unobserved factors, such as wage for criminal activity, moral character, family background, and errors in measuring things like criminal activity and the probability of arrest. Dealing with this error term or disturbance term is perhaps the most important component of any econometric analysis. β s are unknown parameters. A parameter of an econometric model is an unknown constant that describes the economic relationship the econometric model predicts. We do not know the values of these parameters, but if we are able to collect the data on the relevant variables (Step 4: Data collection), we can use appropriate econometric methods discussed in this course to estimate those values (Step 5: Estimation of econometric model). Once the econometric model has been specified and estimated, various hypothesis of interest in terms of the unknown parameters can be stated. For example, we might hypothesize that wage m has no effect on criminal behavior, or equivalently β 1 = 0. These hypotheses can be tested by using hypothesis-testing techniques. (Step 6: Hypothesis testing)
6 At last, we can use the estimated econometric model to make predictions such as by how much the crime rate will be reduced if the city increases the number of policemen by a certain amount. We can also evaluate the effectiveness of such government policies as raising the average sentence length (Step 7: Forecasting/prediction, and study of policy impact). The Structure of Economic Data There are three types of economic data we may encounter in our economic studies: Cross sectional A sample of individual observations taken at the same point in time The most widely used in economics and other social sciences E.g. Census 2000 tells us the annual income of each US household in 2000 Is the focus of our textbook and this course
7 Time-series A set of observations taken at different points in time Widely used in macroeconomics and finance E.g. daily price of a stock over the past month, US quarterly inflation rate over the past five years More difficult to analyze than cross-sections as economic observations can rarely, if ever, be assumed to be independent across time
8 Pooled data Combination of times series and cross-section Called pooled cross sections if different samples at different points in time, or panel/longitudinal data if times series for each cross-sectional member E.g. daily prices of a few stocks over a month, the inflation in different countries over the past ten years. Is not covered at the undergraduate level of this course
9 Causality and the Notion of Ceteris Paribus in Econometric Analysis In most tests of economic theory the economist s goal is to infer that one variable (such as education) has a casual effect on another variable (such was wages). Simply finding an association between two or more variables might be suggestive, but unless causality can be established, it is rarely compelling. The notion of ceteris paribus which means other relevant factors being equal plays an important role is causal analysis. For example, unless we know that income is held constant, we can t measure the impact of a price change. Also, if we are studying the impact of wages on education, we can t just look at the statistical relationship between wages and education because there are other factors that influence wages (e.g., the person s innate ability, experience, field of work). Therefore we need a way to hold these other factors constant and then look at the impact of education on wages (A problem of how do we control for ability something that may be unobservable). In most serious applications, a number of factors may influence the variables of interest. Isolating the impact of one particular variable is a hard task. But we will see that econometric methods, when carefully applied, can simulate a ceteris paribus experiment.
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