ECO 355 Introduction to Econometrics I Course Guide PDF

NATIONAL OPEN UNIVERSITY OF NIGERIA INTRODUCTION TO ECONOMETRICS I ECO 355 SCHOOL OF ARTS AND SOCIAL SCIENCES COURSE GUIDE Course Developer: Samuel Olumuyiwa Olusanya Economics Department, Nationa...

NATIONAL OPEN UNIVERSITY OF NIGERIA INTRODUCTION TO ECONOMETRICS I ECO 355 SCHOOL OF ARTS AND SOCIAL SCIENCES COURSE GUIDE Course Developer: Samuel Olumuyiwa Olusanya Economics Department, National Open University of Nigeria And Adegbola Benjamin Mufutau Part time Lecturer Lagos State University, Lagos State. 1 CONTENT Introduction Course Content Course Aims Course Objectives Working through This Course Course Materials Study Units Textbooks and References Assignment File Presentation Schedule Assessment Tutor-Marked Assignment (TMAs) Final Examination and Grading Course Marking Scheme Course Overview How to Get the Most from This Course Tutors and Tutorials Summary Introduction Welcome to ECO: 355 INTRODUCTION TO ECONOMETRICS I. ECO 355: Introduction to Econometrics I is a three-credit and one-semester undergraduate course for Economics student. The course is made up of nineteen units spread across fifteen lectures weeks. This course guide gives you an insight to introduction to econometrics and how it is applied in economics. It tells you about the course materials and how you can work your way through these materials. It suggests some general guidelines for the amount of time required of you on each unit in order to achieve the course aims and objectives successfully. Answers to your tutor marked assignments (TMAs) are therein already. Course Content This course is basically an introductory course on Econometrics. The topics covered include the econometrics analysis, single-equation (regression models), Normal linear regression model and practical aspects of statistics testing. Course Aims The aims of this course is to give you in-depth understanding of the macroeconomics as regards  Fundamental concept of econometrics  To familiarize students with single-equation of regression model 2   To stimulate student‘s knowledge on normal linear regression model  To make the students to understand some of the practical aspects of econometrics test.  To expose the students to rudimentary analysis of simple and multiple regression analysis. Course Objectives To achieve the aims of this course, there are overall objectives which the course is out to achieve though, there are set out objectives for each unit. The unit objectives are included at the beginning of a unit; you should read them before you start working through the unit. You may want to refer to them during your study of the unit to check on your progress. You should always look at the unit objectives after completing a unit. This is to assist the students in accomplishing the tasks entailed in this course. In this way, you can be sure you have done what was required of you by the unit. The objectives serves as study guides, such that student could know if he is able to grab the knowledge of each unit through the sets of objectives in each one. At the end of the course period, the students are expected to be able to:  to understand the basic fundamentals of Econometrics  distinguish between Econometrics and Statistics.  know how the econometrician proceed in the analysis of an economic problem.  know how the econometrician make use of both mathematical and statistical analysis in solving economic problems.  understand the role of computer in econometrics analysis  identify/explain the types of econometrics analysis.  understand the basic Econometrics models  differentiate between Econometrics theory and methods  know the meaning of Econometrics and why Econometrics is important within Economics.  know how to use Econometrics for Assessing Economic Model  understand what is Financial Econometrics.  examine the linear regression model  understand the classical linear regression model  be able to differentiate the dependant and independent variables.  prove some of the parameters of ordinary least estimate. 3   know the alternative expression for ̂  understand the assumptions of classical linear regression model.  know the properties that our estimators should have  know the proofing of the OLS estimators as the best linear unbiased estimators (BLUE).  examine the Goodness fit  understand and work through the calculation of coefficient of multiple determination  identify and know how to calculate the probability normality assumption for Ui  understand the normality assumption for Ui  understand why we have to conduct the normality assumption.  identify the properties of OLS estimators under the normality assumption  understand what is probability distribution  understand the meaning of Maximum Likelihood Estimation of two variable regression Model.  understand the meaning of Hypothesis  know how to calculate hypothesis using confidence interval  analyse and interpret hypothesis result.  understand the meaning of accepting and rejecting an hypothesis  identify a null and alternative hypothesis.  understand the meaning of Level of significance  understand the Choice between confidence-interval and test-of-significance Approaches to hypothesis testing  understand the meaning of regression analysis and variance  know how to calculate the regression analysis and analysis of variance Working Through The Course To successfully complete this course, you are required to read the study units, referenced books and other materials on the course. Each unit contains self-assessment exercises called Student Assessment Exercises (SAE). At some points in the course, you will be required to submit assignments for assessment purposes. At the end of the course there is a final examination. This course should take about 15weeks to complete and some components of the course are outlined under the course material subsection. 4 Course Material The major component of the course, What you have to do and how you should allocate your time to each unit in order to complete the course successfully on time are listed follows: 1. Course guide 2. Study unit 3. Textbook 4. Assignment file 5. Presentation schedule Study Unit There are 19 units in this course which should be studied carefully and diligently. MODULE ONE ECONOMETRICS ANALYSIS Unit 1 Meaning Of Econometrics Unit 2 Methodology of Econometrics Unit 3 Computer and Econometrics Unit 4 Basic Econometrics Models: Linear Regression Unit 5 Importance Of Econometrics MODULE TWO SINGLE- EQUATION (REGRESSION MODELS) Unit One: Regression Analysis Unit Two: The Ordinary Least Square (OLS) Method Estimation Unit Three: Calculation of Parameter and the Assumption of Classical Least Regression Method (CLRM) Unit Four: Properties of the Ordinary Least Square Estimators Unit Five: The Coefficient of Determination (R2): A measure of ―Goodness of fit‖ MODULE THREE NORMAL LINEAR REGRESSION MODEL (CNLRM) Unit One: Classical Normal Linear Regression Model Unit Two: OLS Estimators Under The Normality Assumption Unit Three: The Method Of Maximum Likelihood (ML) Unit Four: Confidence intervals for Regression Coefficients and Unit Five: Hypothesis Testing 5 MODULE FOUR PRACTICAL ASPECTS OF ECONOMETRICS TEST Unit One Accepting & Rejecting an Hypothesis Unit Two The Level of Significance Unit Three Regression Analysis and Analysis of Variance Unit Four Normality tests Each study unit will take at least two hours, and it include the introduction, objective, main content, self-assessment exercise, conclusion, summary and reference. Other areas border on the Tutor-Marked Assessment (TMA) questions. Some of the self-assessment exercise will necessitate discussion, brainstorming and argument with some of your colleges. You are advised to do so in order to understand and get acquainted with historical economic event as well as notable periods. There are also textbooks under the reference and other (on-line and off-line) resources for further reading. They are meant to give you additional information if only you can lay your hands on any of them. You are required to study the materials; practice the self- assessment exercise and tutor-marked assignment (TMA) questions for greater and in- depth understanding of the course. By doing so, the stated learning objectives of the course would have been achieved. Textbook and References For further reading and more detailed information about the course, the following materials are recommended: Adesanya, A.A., (2013). Introduction to Econometric, 2nd edition, Classic Publication limited, Lagos Nigeria. Adekanye, D. F., (2008). Introduction to Econometrics, 1st edition, Addart Publication limited, Lagos Nigeria. Begg, Iain and Henry, S. G. B. Applied Economics and Public Policy. Cambridge University Press, United Kingdom: 1998. Bello, W.L., (2015). Applied Econometrics in a large Dimension, Fall Publication, Benini, Nigeria. Cassidy, John. The Decline of Economics. Dimitrios, A & Stephen, G., (2011). Applied Econometrics, second edition 2011, first edition 2006 and revised edition 2007. Emmanuel, E.A., (2014). Introduction to Econometrics, 2nd edition, World gold Publication limited. Faraday, M.N., (2014) Applied Econometrics, 1st Edition, Pentagon Publication limited. 6 Friedland, Roger and Robertson, A. F., eds. Beyond the Marketplace: Rethinking Economy and Society. Walter de Gruyter, Inc. New York: 1990 Gordon, Robert Aaron. Rigor and Relevance in a Changing Institutional Setting. Kuhn, Thomas. The Structure of Scientific Revolutions. Gujarat, D. N. (2007) Basic Econometrics, 4th Edition, tata Mcgraw – Hill publishing company limited, New Delhi. Hall, S. G., & Asterion, D. (2011) Applied Econometrics, 2nd Edition, Palgrave Macmillian, New York city, USA Medunoye, G.K., (2013). Introduction to Econometrics, 1st edition, Mill Publication limited. Olusanjo, A.A. (2014). Introduction to Econometrics, a broader perspective, 1st edition, world press publication limited, Nigeria. Parker, J.J., (2016). Econometrics and Economic Policy, Journal vol 4, pg 43-73, Parking & Parking Publication limited. Warlking, F.G., (2014). Econometrics and Economic theory, 2nd edition, Dale Press limited. Assignment File Assignment files and marking scheme will be made available to you. This file presents you with details of the work you must submit to your tutor for marking. The marks you obtain from these assignments shall form part of your final mark for this course. Additional information on assignments will be found in the assignment file and later in this Course Guide in the section on assessment. There are four assignments in this course. The four course assignments will cover: Assignment 1 - All TMAs‘ question in Units 1 – 5 (Module 1) Assignment 2 - All TMAs' question in Units 6 – 10 (Module 2) Assignment 3 - All TMAs' question in Units 11 – 15 (Module 3) Assignment 4 - All TMAs' question in Unit 16 – 19 (Module 4). Presentation Schedule The presentation schedule included in your course materials gives you the important dates for this year for the completion of tutor-marking assignments and attending tutorials. Remember, you are required to submit all your assignments by due date. You should guide against falling behind in your work. 7 Assessment There are two types of the assessment of the course. First are the tutor-marked assignments; second, there is a written examination. In attempting the assignments, you are expected to apply information, knowledge and techniques gathered during the course. The assignments must be submitted to your tutor for formal Assessment in accordance with the deadlines stated in the Presentation Schedule and the Assignments File. The work you submit to your tutor for assessment will count for 30 % of your total course mark. At the end of the course, you will need to sit for a final written examination of three hours' duration. This examination will also count for 70% of your total course mark. Tutor-Marked Assignments (TMAs) There are four tutor-marked assignments in this course. You will submit all the assignments. You are encouraged to work all the questions thoroughly. The TMAs constitute 30% of the total score. Assignment questions for the units in this course are contained in the Assignment File. You will be able to complete your assignments from the information and materials contained in your set books, reading and study units. However, it is desirable that you demonstrate that you have read and researched more widely than the required minimum. You should use other references to have a broad viewpoint of the subject and also to give you a deeper understanding of the subject. When you have completed each assignment, send it, together with a TMA form, to your tutor. Make sure that each assignment reaches your tutor on or before the deadline given in the Presentation File. If for any reason, you cannot complete your work on time, contact your tutor before the assignment is due to discuss the possibility of an extension. Extensions will not be granted after the due date unless there are exceptional circumstances. Final Examination and Grading The final examination will be of three hours' duration and have a value of 70% of the total course grade. The examination will consist of questions which reflect the types of self-assessment practice exercises and tutor-marked problems you have previously encountered. All areas of the course will be assessed Revise the entire course material using the time between finishing the last unit in the module and that of sitting for the final examination to. You might find it useful to review your self-assessment exercises, tutor-marked assignments and comments on them before the examination. The final examination covers information from all parts of the course. 8 Course Marking Scheme The Table presented below indicates the total marks (100%) allocation. Assignment Marks Assignments (Best three assignments out of four that is 30% marked) Final Examination 70% Total 100% Course Overview The Table presented below indicates the units, number of weeks and assignments to be taken by you to successfully complete the course, Introduction to Econometrics (ECO 355). Units Title of Work Week’s Assessment Activities (end of unit) Course Guide Module 1 ECONOMETRICS ANALYSIS 1 Meaning Of Econometrics Week 1 Assignment 1 2 Methodology of Econometrics Week 1 Assignment 1 3 Computer and Econometrics Week 2 Assignment 1 4. Basic Econometrics Models: Linear Week 2 Assignment 1 Regression. 5. Importance Of Econometrics Module 2 SINGLE- EQUATION (REGRESSION MODELS) 1. Regression Analysis Week 3 Assignment 2 2. The Ordinary Least Square (OLS) Week 3 Assignment 2 Method Estimation 3. Calculation of Parameter and the Week 4 Assignment 2 Assumption of Classical Least Regression Method (CLRM) 4. Properties of the Ordinary Least Week 5 Assignment 2 Square Estimators 5. The Coefficient of Determination Week 6 Assignment 3 2 (R ): A measure of ―Goodness of fit‖ Module 3 NORMAL LINEAR REGRESSION MODEL (CNLRM) 1. Classical Normal Linear Regression Week 7 Assignment 3 Model 2. OLS Estimators Under The Week 8 Assignment 3 Normality Assumption 9 3. The Method Of Maximum Likelihood Week 9 Assignment 3 (ML) 4. Confidence intervals for Regression Week 10 Assignment 4 Coefficients and 5. Hypothesis Testing Week 11 Module 4 PRACTICAL ASPECTS OF ECONOMETRICS TEST 1. Accepting & Rejecting an Hypothesis Week 12 Assignment 4 2. The Level of Significance Week 13 Assignment 4 3. Regression Analysis and Analysis of Week 114 Assignment 4 Variance 4. Normality tests Week 15 Assignment 4 Total 15 Weeks How To Get The Most From This Course In distance learning the study units replace the university lecturer. This is one of the great advantages of distance learning; you can read and work through specially designed study materials at your own pace and at a time and place that suit you best. Think of it as reading the lecture instead of listening to a lecturer. In the same way that a lecturer might set you some reading to do, the study units tell you when to read your books or other material, and when to embark on discussion with your colleagues. Just as a lecturer might give you an in-class exercise, your study units provides exercises for you to do at appropriate points. Each of the study units follows a common format. The first item is an introduction to the subject matter of the unit and how a particular unit is integrated with the other units and the course as a whole. Next is a set of learning objectives. These objectives let you know what you should be able to do by the time you have completed the unit. You should use these objectives to guide your study. When you have finished the unit you must go back and check whether you have achieved the objectives. If you make a habit of doing this you will significantly improve your chances of passing the course and getting the best grade. The main body of the unit guides you through the required reading from other sources. This will usually be either from your set books or from a readings section. Some units require you to undertake practical overview of historical events. You will be directed when you need to embark on discussion and guided through the tasks you must do. The purpose of the practical overview of some certain historical economic issues are in twofold. First, it will enhance your understanding of the material in the unit. Second, it will give you practical experience and skills to evaluate economic arguments, and understand the roles of history in guiding current economic policies and debates outside your studies. In any event, most of the critical thinking skills you will develop during 10 studying are applicable in normal working practice, so it is important that you encounter them during your studies. Self-assessments are interspersed throughout the units, and answers are given at the ends of the units. Working through these tests will help you to achieve the objectives of the unit and prepare you for the assignments and the examination. You should do each self- assessment exercises as you come to it in the study unit. Also, ensure to master some major historical dates and events during the course of studying the material. The following is a practical strategy for working through the course. If you run into any trouble, consult your tutor. Remember that your tutor's job is to help you. When you need help, don't hesitate to call and ask your tutor to provide it. 1. Read this Course Guide thoroughly. 2. Organize a study schedule. Refer to the `Course overview' for more details. Note the time you are expected to spend on each unit and how the assignments relate to the units. Important information, e.g. details of your tutorials, and the date of the first day of the semester is available from study centre. You need to gather together all this information in one place, such as your dairy or a wall calendar. Whatever method you choose to use, you should decide on and write in your own dates for working breach unit. 3. Once you have created your own study schedule, do everything you can to stick to it. The major reason that students fail is that they get behind with their course work. If you get into difficulties with your schedule, please let your tutor know before it is too late for help. 4. Turn to Unit 1 and read the introduction and the objectives for the unit. 5. Assemble the study materials. Information about what you need for a unit is given in the `Overview' at the beginning of each unit. You will also need both the study unit you are working on and one of your set books on your desk at the same time. 6. Work through the unit. The content of the unit itself has been arranged to provide a sequence for you to follow. As you work through the unit you will be instructed to read sections from your set books or other articles. Use the unit to guide your reading. 7. Up-to-date course information will be continuously delivered to you at the study centre. 8. Work before the relevant due date (about 4 weeks before due dates), get the Assignment File for the next required assignment. Keep in mind that you will learn a lot by doing the assignments carefully. They have been designed to help you meet the objectives of the course and, therefore, will help you pass the exam. Submit all assignments no later than the due date. 9. Review the objectives for each study unit to confirm that you have achieved them. If you feel unsure about any of the objectives, review the study material or consult your tutor. 11  10. When you are confident that you have achieved a unit's objectives, you can then start on the next unit. Proceed unit by unit through the course and try to pace your study so that you keep yourself on schedule. 11. When you have submitted an assignment to your tutor for marking do not wait for it return `before starting on the next units. Keep to your schedule. When the assignment is returned, pay particular attention to your tutor's comments, both on the tutor-marked assignment form and also written on the assignment. Consult your tutor as soon as possible if you have any questions or problems. 12. After completing the last unit, review the course and prepare yourself for the final examination. Check that you have achieved the unit objectives (listed at the beginning of each unit) and the course objectives (listed in this Course Guide). Tutors and Tutorials There are some hours of tutorials (2-hours sessions) provided in support of this course. You will be notified of the dates, times and location of these tutorials. Together with the name and phone number of your tutor, as soon as you are allocated a tutorial group. Your tutor will mark and comment on your assignments, keep a close watch on your progress and on any difficulties you might encounter, and provide assistance to you during the course. You must mail your tutor-marked assignments to your tutor well before the due date (at least two working days are required). They will be marked by your tutor and returned to you as soon as possible. Do not hesitate to contact your tutor by telephone, e-mail, or discussion board if you need help. The following might be circumstances in which you would find help necessary. Contact your tutor if. You do not understand any part of the study units or the assigned readings You have difficulty with the self-assessment exercises You have a question or problem with an assignment, with your tutor's comments on an assignment or with the grading of an assignment. You should try your best to attend the tutorials. This is the only chance to have face to face contact with your tutor and to ask questions which are answered instantly. You can raise any problem encountered in the course of your study. To gain the maximum benefit from course tutorials, prepare a question list before attending them. You will learn a lot from participating in discussions actively. Summary The course, Introduction to Econometrics II (ECO 355), expose you to the field of Econometrics analysis such as Meaning of Econometrics, Methodology of Econometrics, Computer and Econometrics, and Basic Econometrics Models: Linear Regression, 12 Importance of Econometrics etc. This course also gives you insight into Single- Equation (Regression Models) such as; Regression Analysis, the Ordinary Least Square (OLS) Method Estimation, Calculation of Parameter and the Assumption of Classical Least Regression Method (CLRM), Properties of the Ordinary Least Square Estimators and the Coefficient of Determination (R2): A measure of ―Goodness of fit‖. The course shield more light on the Normal Linear Regression Model (CNLRM) such as Classical Normal Linear Regression Model, OLS Estimators Under The Normality Assumption, the Method Of Maximum Likelihood (ML). However, Confidence intervals for Regression Coefficients and and Hypothesis Testing were also examined. Furthermore the course shall enlighten you about the Practical Aspects of Econometrics Test such accepting & Rejecting an Hypotheses, the Level of Significance, regression Analysis and Analysis of Variance and Normality tests. On successful completion of the course, you would have developed critical thinking skills with the material necessary for efficient and effective discussion on Econometrics Analysis, Single- Equation (Regression Models), Normal Linear Regression Model (CNLRM) and Practical Aspects of Econometrics. However, to gain a lot from the course please try to apply anything you learn in the course to term papers writing in other economic development courses. We wish you success with the course and hope that you will find it fascinating and handy. 13 MODULE ONE: ECONOMETRICS ANALYSIS Unit One: Meaning of Econometrics Unit Two: Methodology of Econometrics Unit Three: Computer and Econometrics Unit Four: Basic Econometrics Models: Linear Regression Unit Five: Importance of Econometrics Unit One: Meaning of Econometrics CONTENTS 1.0 Introduction 2.0 Objectives 3.0 Main content 3.1 Definition/Meaning of Econometrics 3.2 Why is Econometrics a Separate Discipline 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 1.0 INTRODUCION The study of econometrics has become an essential part of every undergraduate course in economics, and it is not an exaggeration to say that it is also an essential part of every economist‘s training. This is because the importance of applied economics is constantly increasing and the ability to quantity and evaluates economic theories and hypotheses constitutes now, more than ever, a bare necessity. Theoretical economies may suggest that there is a relationship between two or more variables, but applied economics demands both evidence that this relationship is a real one, observed in everyday life and quantification of the relationship, between the variable relationship using actual data is known as econometrics. 2.0 OBJECTIVES At the end of this unit, you should be able to:  understand the basic fundamentals of Econometrics  distinguish between Econometrics and Statistics. 14 3.0 MAIN CONTENT 3.1 Definition/Meaning of Economics Literally econometrics means measurement (the meaning of the Greek word metrics) in economic. However econometrics includes all those statistical and mathematical techniques that are utilized in the analysis of economic data. The main aim of using those tools is to prove or disprove particular economic propositions and models. Econometrics, the result of a certain outlook on the role of economics consists of the application of mathematical statistics to economic data to tend empirical support to the models constructed by mathematical economics and to obtain numerical results. Econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inferences. Econometrics may also be defined as the social sciences in which the tools of economic theory, mathematics and statistical inference are applied to the analysis of economic phenomena. Econometrics is concerned with the empirical determination of economic laws. 3.2 Why Is Econometrics A Separate Discipline? Based on the definition above, econometrics is an amalgam of economic theory, mathematical economics, economic statistics and mathematical statistics. However, the course (Econometrics) deserves to be studied in its own right for the following reasons: 1. Economic theory makes statements or hypotheses that are mostly qualitative in nature. For example, microeconomics they states that, other thing remaining the same, a reduction in the price of a commodity is expected to increase the quantity demanded of that commodity. Thus, economic theory postulates a negative or inverse relationship between the price and quantity demanded of a commodity. But the theory itself does not provide any numerical measure of the relationship between the two\; that is it does not tell by how much the quantity will go up or down as a result of a certain change in the price of the commodity. It is the job of econometrician to provide such numerical estimates. Stated differently, econometrics gives empirical content to most economic theory. 2. The main concern of mathematical economics is to express economic theory in mathematical form (equation) without regard to measurability or mainly interested in the empirical verification of the theory. Econometrics, as noted in our discussion above, is mainly interested in the empirical verification of economic theory. As we shall see in this course later on, the econometrician often uses the mathematical equations proposed by the mathematical economist but puts these equations in such a form that they lend themselves to empirical testing and this conversion of mathematical and practical skill. 15 3. Economic statistics is mainly concerned with collecting, processing and presenting economic data in the form of charts and tables. These are the jobs of the economic statistician. It is he or she who is primarily responsible for collecting data on gross national product (GNP) employment, unemployment, price etc. the data on thus collected constitute the raw data for econometric work, but the economic statistician does not go any further, not being concerned with using the collected data to test economic theories and one who does that becomes an econometrician. 4. Although mathematical statistics provides many tools used in the trade, the econometrician often needs special methods in view of the unique nature of the most economic data, namely, that the data are not generated as the result of a controlled experiment. The econometrician, like the meteorologist, generally depends on data that cannot be controlled directly. 4.0 CONCLUSION In econometrics, the modeler is often faced with observational as opposed to experimental data. This has two important implications for empirical modeling in econometrics. The modeler is required to master very different skills than those needed for analyzing experimental data and the separation of the data collector and the data analyst requires the modeler familiarize himself/herself thoroughly with the nature and structure of data in question. 5.0 SUMMARY The units vividly look at the meaning of econometrics which is different from the modern day to day calculation or statistical analysis we are all familiar with. However, the units also discuss the reasons why econometrics is studied differently from other disciplines in economics and how it is so important in formulating and forecasting the present to the future. 6.0 TUTOR MARKED ASSIGNMENT 1. Differentiate between mathematical equation and models. 2. Explain the term ‗Econometrics‘. 7.0 REFERENCES/FURTHER READINGS Gujarat, D. N. (2007) Basic Econometrics, 4th Edition, tata Mcgraw – Hill publishing company limited, New Delhi. Hall, S. G., & Asterion, D. (2011) Applied Econometrics, 2nd Edition, Palgrave Macmillian, New York city, USA. 16 UNIT 2 METHODOLOGY OF ECONOMETRICS CONTENTS 1.0 Introduction 2.0 Objectives 3.0 Main content 3.1. Traditional Econometrics Methodology 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 1.0 INTRODUCTION One may ask question that how economists justifies their argument with the use of statistical, mathematic and economic models to achieve prediction and policy recommendation to economic problems. However, econometrics may also come inform of applied situation, which is called applied econometrics. Applied econometrics works always takes (or, at least, should take) as its starting point a model or an economic theory. From this theory, the first task of the applied econometrician is to formulate an econometric model that can be tested empirically and the next task is to collect data that can be used to perform the test and after that, to proceed with the estimation of the model. After this estimation, an econometrician performs specification tests to ensure that the model used was appropriate and to check the performance and accuracy of the estimation procedure. So these process keep on going until you are satisfied that you have a good result that can be used for policy recommendation. 2.0 OBJECTIVES At the end of this unit, you should be able to:  know how the econometrician proceed in the analysis of an economic problem.  know how the econometrician make use of both mathematical and statistical analysis in solving economic problems. 17 3.0 MAIN CONTENT 3.1 Traditional Econometrics Methodology The traditional Econometrics methodology proceeds along the following lines: 1. Statement of theory or hypothesis. 2. Specification of the mathematical model of the theory. 3. Specification of statistical, or econometric, model. 4. Obtaining the data. 5. Estimation of parameters of the econometric model. 6. Hypothesis testing. 7. Forecasting or prediction. 8. Using the model for control or policy purposes. However, to illustrate the proceeding steps, let us consider the well-known Keynesian theory of consumption. 1. Statement of the theory Hypothesis Keynes stated: The fundamental psychological law is that Men (Women) are disposed as a rule and on average, to increase their consumption as their income increases, but not as much as the increase in their income. In short, Keynes postulated that the marginal propensity to consume (MPC), the rate of change of consumption for a unit change income is greater than zero but less than 1. 2. Specification of the mathematical model of consumption Although Keynes postulated a positive relationship between consumption and income, he did not specify the precise form of the functional relationship between the two. However, a mathematical economist might suggest the following form of the Keynesian consumption function: where. Where Y = consumption expenditure and X = income and where , known as the parameters of the model, are respectively, the intercept and slope coefficients. The slope coefficient measures the MPC. In equation (1) above, which states that consumption is linearly related to income, is an example of a mathematical model of the relationship between consumption and income that is called consumption function in economics. A model is simply a set of mathematical equations, if the model had only one equation, as in the proceeding example, it is called a single equation model, whereas if it has more than one equation, it is known as a multiple-equation model. In equation (1), the variable appearing on the left side of the equality sign is called the ‗dependent variable‘ 18 and the variable(s) on the right side are called the independent or explanatory variables. Moreover, in the Keynesian consumption function in equation (1), consumption (expenditure) is the dependent variable and income is the explanatory variable. 3. Specification of the Econometric Model of Consumption The purely mathematical model of the consumption function given in equation (1) is of limited interest to econometrician, for it assures that there is an exact or deterministic relationship between consumption and income. But relationships between economic variables are generally inexact. Thus, if we were to obtain data on consumption expenditure and disposable (that is after tax) income of a sample of, say, 500 Nigerians families and plot these data on a graph paper with consumption expenditure on the vertical axis And disposable income on the horizontal axis we would not expect all 500 observations to lie exactly on the straight line of equation (1) above, because, in addition to income other variables affect consumption expenditure. For example size of family, ages of the members in the family, family religion etc are likely to exert some influence on consumption. To allow for the inexact relationships between economic variables, the econometrician would modify the deterministic consumption function in equation (1) as follows: Where u, known as the disturbance, or error term, is a random (Stochastic) variable that has well-defined probabilistic properties. The disturbance term ‗u‘ may well represent all those factors that affect consumption but are not taken into account explicitly. Equation (2) is an example of an econometric model. More technically, it is an example of a linear regression model, which is the major concern in this course. 4. Obtaining Data To estimate the econometric model in equation (2), that is to obtain the numerical values of , we need data. Although will have more to say about the crucial importance of data for economic analysis. The data collection is used to analysis the equation (2) and give policy recommendation. 5. Estimation of the Econometric Model Since from ‗obtaining the data‘ we have the data we needed, our next point of action is to estimate the parameters of the say consumption function. The numerical estimates of the parameters give empirical content to the consumption function. The actual mechanics of estimating the parameters will be discussed later in this course. However, note that the statistical technique of regression analysis is the main tool used to obtain the estimates. For example assuming the data collected was subjected to calculation and we obtain the following estimates of , namely Thus, the estimated consumption function is: ̂ 19 The hat on the y indicated that it is an estimate. The estimated consumption function (that is regression line) is shown below. 5000 4500 4000 PCE (y) 3500 3000 4000 5000 6000 7000 GDP (x) Figure 1: Showing personal consumption expenditure (y) in relation to GDP (x) from 1682 – 1996. Moreover, the regression line fits the data quite well in that the data points are very close to the regression line. 6. Hypothesis Testing Assuming that the fitted model is a reasonably good approximation of reality, we have to develop suitable criteria to find out whether the estimates obtained in equation (3) are in accord with the expectations of the theory that is being tested. According to ―positive‖ economists like Milton Freedman, a theory or hypothesis that is not verifiable by appeal to empirical evidence may not be admissible as a part of scientific enquiry. As noted by Keynes that marginal propensity to consume (MPC) to be positive but less than 1. In equation (3) the MPC is 083. But before we accept this finding as confirmation of Keynesian consumption theory, we must enquire whether this estimate is sufficiently below unity to convince us that this is not a chance occurrence or peculiarity of the particular data we have used. In conclusion, 0.83 is statistically less than 1. If it is, it may support Keynes theory. This type of confirmation or refutation of the economic theories on the basis of sample evidence is based on a branch of statistical theory known as statistical inference (hypothesis testing). 7. Forecasting or Prediction If the model we choose does not refute the hypothesis or theory under consideration, we may use it to predict the future value(s) of the dependent, or forecast variable y on the basis of known or expected future value(s) of the explanatory or predictor variable x. Let us make use of equation (3) as an example. Suppose we want to predict the main consumption expenditure for 1997. The GDP value for 1997 (for example say is) 20 6158.7billion dollars. Putting this GDP figure on the right-hand side of equation (3), we obtain ̂ Therefore ̂ ̂ or about 4944 billion naira. Thus given the value of the GDP, the mean or average, forecast consumption expenditure is about 4944 billion naira. The actual value of the consumption expenditure reported in 1997 was 4913.5 billion naira. The estimated model (in equation 3) thus over predicted the actual consumption expenditure by about 30.76 billion naira. We could say that forecast error is about 30.76 billion naira, which is about 0.74 percent of the actual GDP value for 1997. 8. Use of the Model for Control or Policy Purpose Let us assume that we have already estimated a consumption function given in equation (3). Suppose further the government believes that consumer expenditure of about say 4900 (billion of 1992 naira) will keep the unemployment rate at its current level of about 4.2 percent (early 2000). What level of income will guarantee the target amount of consumption expenditure? If the regression result given in equation (3) seem reasonable, sample arithmetic will show that 4900 = – 144.06 + 0.8262x ______________ (5). Which gives x = 6105, approximately. That is, an income levels of about 6105 (billion) naira, given an MPC of about 0.83, will produce (10) an expenditure of about 4900 billion naira. From the analysis above, an estimated model may be used for control or policy purposes. By appropriate fiscal and monetary policy mix, the government can manipulate the control variable x to produce the desired level of the target variable y. 4.0 CONCLUSION Stages of econometrics analysis are the process of getting on economic theory, subject it to empirical model, and then make use of data, estimation, and hypothesis and policy recommendation. 5.0 SUMMARY The unit has discussed attentively the stages econometrics analysis from the economic theory, mathematical model of theory, econometric model of theory, collecting the data, estimation of econometric model, hypothesis testing, forecasting or prediction and using the model for control or policy purposes. Therefore at this end I belief you must have understand the stages of econometrics analysis. 6.0 TUTOR MARKED ASSIGNMENT Discuss the stages of econometrics analysis 21 7.0 REFERENCES/FURTHER READINGS Adekanye, D. F., (2008). Introduction to Econometrics, 1st edition, Addart Publication limited, Lagos Nigeria. Dimitrios, A & Stephen, G., (2011). Applied Econometrics, second edition 2011, first edition 2006 and revised edition 2007. 22 UNIT 3 COMPUTER AND ECONOMETRICS CONTENTS 1.0 Introduction 2.0 Objectives 3.0 Main content 3.1. Definition of Macroeconomics 3.2. Types of Econometrics Basic 3.3. Theoretical versus Applied Economics 3.4. The Differences between Econometrics Modeling and Machine Learning 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 1.0 INTRODUCTION In this unit, we are going to know briefly the role computer application in econometrics analysis and to be able to convinced people that are not economists that computer help in bringing the beauty of economic model to reality and prediction. The computer application are peculiar to social sciences techniques/analysis and economics in particular. 2.0 OBJECTIVES At the end of this unit, you should be able to:  understand the role of computer in econometrics analysis  identify/explain the types of econometrics analysis. 3.0 MAIN CONTENT 3.1 The Role of Computer Regression analysis, the bread-and-better tool of econometrics, these days is unthinkable without the computer and some access to statistical software. However, several excellent regression packages are commercially available, both for the mainframe and the microcomputer and the lot is growing by the day. Regression software packages such as SPSS, EVIENS, SAS, STATA etc. are few of the economic software packages use in conducting estimation analysis on economic- equations and models. 23 3.2 TYPES OF ECONOMETRICS Econometrics Theoretical Applied Classical Bayesian Classical Bayesian Figure 2: Showing categories of Econometrics. As the classificatory scheme in figure 2 suggests, econometrics may be divided into two broad categories: THEORETICAL ECONOMETRICS and APPLIED ECONOMETRICS. In each category, one can approach the subject in the classical or Bayesian tradition. Furthermore, theoretical econometrics is concerned with the development of appropriate methods for measuring economic relationships specified by econometrics models. In this aspect, econometrics leans heavily on mathematical statistics. Theoretical econometrics must spell out the assumptions of this method, its properties and what happens to these properties when one or more of the assumptions of the method are not fulfilled. In applied econometrics we use the tools of theoretical econometrics to study some special field (s) of economics and business, such as the production function, investment function, demand and supply functions, portfolio theory etc. 3.3. Theoretical versus Applied Economics The study of economics has taken place within a Kuhnian paradigm of perfect competition for years. Within this paradigm, the models of perfect competition, rational expectations, supply and demand, and the other economic theories have been described. In recent years, there has been a strong movement towards mathematics and econometrics as a way to expound upon already established theories. This movement has come under some criticism, both from within the profession and without, as not being applicable to real world situations. There has been a push to move away from the econometric methods that lead to further theory explanation and to focus on applying economics to practical situations. While the theories are innately important to the study of any economic activity, the application of those theories in policy is also important. There are many areas of applied economics, including environmental, agricultural, and transitional. However, the recent trends towards mathematical models has caused some to question whether or not expounding on the theories will help in the policy decisions of taxation, inflation, interest rates, etc. Solutions to these problems have been largely theoretical, as economics is a social science and laboratory experiments cannot be done. 24 However, there are some concerns with traditional theoretical economics that are worth mentioning. First, Ben Ward describes "stylized facts," or false assumptions, such as the econometric assumption that "strange observations do not count." While it is vital that anomalies are overlooked for the purpose of deriving and formulating a clear theory, when it comes to applying the theory, the anomalies could distort what should happen. These stylized facts are very important in theoretical economics, but can become very dangerous when dealing with applied economics. A good example is the failure of economic models to account for shifts due to deregulation or unexpected shocks. These can be viewed as anomalies that are unable to be accounted for in a model, yet is very real in the world today. Another concern with traditional theory is that of market breakdowns. Economists assume things such as perfect competition and utility maximization. However, it is easily seen that these assumptions do not always hold. One example is the idea of stable preferences among consumers and that they act efficiently in their pursuit. However, people's preferences change over time and they do not always act rational nor efficient. Health care, for another example, chops down many of the assumptions that are crucial to theoretical economics. With the advent of insurance, perfect competition is no longer a valid assumption. Physicians and hospitals are paid by insurance companies, which assures them of high salaries, but which prevents them from being competitive in the free market. Perfect information is another market breakdown in health economics. The consumer (patient) cannot possibly know everything the doctor knows about their condition, so the doctor is placed in an economically advantaged position. Since the traditional assumptions fail to hold here, a manipulated form of the traditional theory needs to be applied. The assumption that consumers and producers (physicians, hospitals) will simply come into equilibrium together will not become a reality because the market breakdowns lead to distortions. Traditional theorists would argue that the breakdown has to be fixed and then the theory can applied as it should be. They stick to their guns even when there is conflicting evidence otherwise, and they propose that the problem lies with the actors, not the theory. The third concern to be discussed here ties in with the Kuhnian idea of normal science. The idea that all research is done within a paradigm and that revolutions in science only occur during a time of crisis. However, this concerns a "hard" science, and economics is a social science. This implies that economics is going to have an effect on issues, therefore, economists are going to have an effect on issues. Value-neutrality is not likely to be present in economics, because economists not only explain what is happening, predict what will happen, but they prescribe the solutions to arrive at the desired solution. Economics is one of the main issues in every political campaign and 25 there are both liberal and conservative economists. The inference is that economists use the same theories and apply them to the same situations and recommend completely different solutions. In this vein, politics and values drive what solutions economists recommend. Even though theories are strictly adhered to, can a reasonably economic solution be put forth that is not influenced by values? Unfortunately, the answer is no. Theoretical economics cannot hold all the answers to every problem faced in the "real world" because false assumptions, market breakdowns, and the influence of values prevent the theories from being applied as they should. Yet, the Formalist Revolution or move towards mathematics and econometrics continues to focus their efforts on theories. Economists continue to adjust reality to theory, instead of theory to reality. This is Gordon's "Rigor over Relevance." The concept that mathematical models and the need to further explain a theory often overrides the sense of urgency that a problem creates. There is much literature about theories that have been developed using econometric models, but Gordon's concern is that relevance to what is happening in the world is being overshadowed. This is where the push for applied economics has come from over the past 20 years or so. Issues such as taxes, movement to a free market from a socialist system, inflation, and lowering health care costs are tangible problems to many people. The notion that theoretical economics is going to be able to develop solutions to these problems seems unrealistic, especially in the face of stylized facts and market breakdowns. Even if a practical theoretical solution to the problem of health care costs could be derived, it would certainly get debated by economists from the left and the right who are sure that this solution will either be detrimental or a saving grace. Does this mean that theoretical economics should be replaced by applied economics? Certainly not. Theoretical economics is the basis from which economics has grown and has landed us today. The problem is that we do not live in a perfect, ideal world in which economic theory is based. Theories do not allow for sudden shocks nor behavioral changes. This is important as it undercuts the stable preferences assumption, as mentioned before. When the basic assumptions of a theory are no longer valid, it makes very difficult to apply that theory to a complex situation. For instance, if utility maximization is designed as maximizing my income, then it should follow that income become the measuring stick for utility. However, if money is not an important issue to someone, then it may appear as if they are not maximizing their utility nor acting rationally. They may be perfectly happy giving up income to spend time with their family, but to an economist they are not maximizing their utility. This is a good example of how theory and reality come into conflict. 26 The focus in theoretical economics has been to make reality fit the theory and not vice- versa. The concern here is that this version of problem-solving will not actually solve any problems. Rather, more problems may be created in the process. There has been some refocusing among theoreticians to make their theories more applicable, but the focus of graduate studies remains on econometrics and mathematical models. The business world is beginning to take notice of this and is often requiring years away from the academic community before they will hire someone. They are looking for economists who know how to apply their knowledge to solve real problems, not simply to expound upon an established theory. It is the application of the science that makes it important and useful, not just the theoretical knowledge. This is not to say that theoretical economics is not important. It certainly is, just as research in chemistry and physics is important to further understand the world we live in. However, the difference is that economics is a social science with a public policy aspect. This means that millions of people are affected by the decisions of policy-makers, who get their input from economists, among others. Legislators cannot understand the technical mathematical models, nor would they most likely care to, but they are interested in policy prescriptions. Should health care be nationalized? Is this the best solution economically? These are the practical problems that face individuals and the nation every day. The theoreticians provide a sturdy basis to start from, but theory alone is not enough. The theory needs to be joined with practicality that will lead to reasonable practical solutions of difficult economic problems. Economics cannot thrive without theory, and thus stylized facts and other assumptions. However, this theory has to explain the way the world actually is, not the way economists say it should be. Pure economic theory is a great way to understand the basics of how the market works and how the actors should act within the market. False assumptions and market breakdowns present conflict between theory and reality. From here, many economists simply assume is not the fault of the theory, but rather the economic agents in play. However, it is impossible to make reality fit within the strict guidelines of a theory; the theory needs to be altered to fit reality. This is where applied economics becomes important. Application of theories needs to be made practical to fit each situation. To rely simply on theory and models is not to take into account the dynamic nature of human beings. What is needed is a strong theoretical field of economics, as well as a strong applied field. This should lead to practical solutions with a strong theoretical basis. 27 3.4. THE DIFFERENCE BETWEEN ECONOMETRICS MODELING AND MACHINE LEARNING Econometric models are statistical models used in econometrics. An econometric model specifies the statistical relationship that is believed to be held between the various economic quantities pertaining to a particular economic phenomenon under study. On the other hand- Machine learning is a scientific discipline that explores the construction and study of algorithms that can learn from data. So that makes a clear distinction right? If it learns on its own from data it is machine learning. If it is used for economic phenomenon it is an econometric model. However the confusion arises in the way these two paradigms are championed. The computer science major will always say machine learning and the statistical major will always emphasize modeling. Since computer science majors now rule at face book, Google and almost every technology company, you would think that machine learning is dominating the field and beating poor old econometric modeling. But what if you can make econometric models learn from data? Lets dig more into these algorithms. The way machine learning works is to optimize some particular quantity, say cost. A loss function or cost function is a function that maps a value(s) of one or more variables intuitively representing some ―cost‖ associated with the event. An optimization problem seeks to minimize a loss function. Machine learning frequently seek optimization to get the best of many alternatives. Now, cost or loss holds different meanings in econometric modeling. In econometric modeling we are trying to minimize the error (or root mean squared error). Root mean squared error means root of the sum of squares of errors. An error is defined as the difference between actual and predicted value by the model for previous data. The difference in the jargon is solely in the way statisticians and computer scientists are trained. Computer scientists try to compensate for both actual error as well as computational cost – that is the time taken to run a particular algorithm. On the other hand statisticians are trained primarily to think in terms of confidence levels or error in terms or predicted and actual without caring for the time taken to run for the model. That is why data science is defined often as an intersection between hacking skills (in computer science) and statistical knowledge (and math). Something like K Means clustering can be taught in two different ways just like regression can be based on these two approaches. I wrote back to my colleague in Marketing – we have data scientists. They are trained in both econometric modeling and machine learning. I looked back and had a beer. If university professors don‘t shed their departmental attitudes towards data 28 science, we will have a very confused set of students very shortly arguing without knowing how close they actually are. 4.0 CONCLUSION Computer and Econometrics have a long history in econometrics analysis. The use of software to calculate data in economics analysis is very important in econometrics analysis and it has shown and gives the way forward in forecasting and policy recommendations to the stakeholders, private companies and government. 5.0 SUMMARY The unit discussed extensively on the role of computer in econometrics. When equations in economics are turn to mathematical equations and becomes a model in economics, the computer software or what are ‗economists‘ called econometrics packages to solve/run the analysis for forecast and policy recommendation. 6.0 TUTOR MARKED ASSIGNMENT Discuss the role of computer in econometrics analysis 7.0 REFERENCES/FURTHER READINGS Begg, Iain and Henry, S. G. B. Applied Economics and Public Policy. Cambridge University Press, United Kingdom: 1998. Cassidy, John. The Decline of Economics. Dimitrios, A & Stephen, G., (2011). Applied Econometrics, second edition 2011, first edition 2006 and revised edition 2007. Friedland, Roger and Robertson, A. F., eds. Beyond the Marketplace: Rethinking Economy and Society. Walter de Gruyter, Inc. New York: 1990 Gordon, Robert Aaron. Rigor and Relevance in a Changing Institutional Setting. Kuhn, Thomas. The Structure of Scientific Revolutions. 29 UNIT 4: BASIC ECONOMETRICS MODELS: LINEAR REGRESSION CONTENTS 1.0. Introduction 2.0. Objectives 3.0. Main content 3.1. Econometrics Theory 3.2. Econometrics Methods 3.3. Examples of a Relationship in Econometrics 3.4. Limitations and Criticism 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 1.0 INTRODUCTION The basic tool for econometrics is the linear regression model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis. Estimating a linear regression on two variables can be visualized as fitting a line through data points representing paired values of the independent and dependent variables. Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis. For example, consider Okun's law, which relates GDP growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate ( ) is a function of an intercept ( ), a given value of GDP growth multiplied by a slope coefficient and an error term, : The unknown parameters and can be estimated. Here is estimated to be −1.77 and is estimated to be 0.83. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77 points. The model could then be tested for statistical significance as to whether an increase in growth is associated with a decrease in the unemployment, as hypothesized. If the estimate of were not significantly different from 0, the test would fail to find evidence that changes in the growth rate and unemployment rate were related. The variance in a prediction of the 30 dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares. 2.0. OBJECTIVES At the end of this unit, you should be able to: 1. To understand the basic Econometrics models 2. To be able to differentiate between Econometrics theory and methods 3.1. Econometric Theory Econometric theory uses statistical theory to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. An estimator is unbiased if its expected value is the true value of the parameter; it is consistent if it converges to the true value as sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size. Ordinary least squares (OLS) is often used for estimation since it provides the BLUE or "best linear unbiased estimator" (where "best" means most efficient, unbiased estimator) given the Gauss-Markov assumptions. When these assumptions are violated or other statistical properties are desired, other estimation techniques such as maximum likelihood estimation, generalized method of moments, or generalized least squares are used. Estimators that incorporate prior beliefs are advocated by those who favor Bayesian statistics over traditional, classical or "frequents" approaches. 3.2. Econometrics Methods Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analyzing economic history, and forecasting. Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled experiments. In this, the design of observational studies in econometrics is similar to the design of studies in other observational disciplines, such as astronomy, epidemiology, sociology and political science. Analysis of data from an observational study is guided by the study protocol, although exploratory data analysis may be useful for generating new hypotheses. Economics often analyzes systems of equations and inequalities, such as supply and demand hypothesized to be in equilibrium. Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous-equation models. These methods are analogous to methods used in other areas of science, such as the field 31 of system identification in systems analysis and control theory. Such methods may allow researchers to estimate models and investigate their empirical consequences, without directly manipulating the system. One of the fundamental statistical methods used by econometricians is regression analysis. Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous-equation models. 3.3. Examples of a Relationship in Econometrics A simple example of a relationship in econometrics from the field of labor economics is: This example assumes that the natural logarithm of a person's wage is a linear function of the number of years of education that person has acquired. The parameter measures the increase in the natural log of the wage attributable to one more year of education. The term is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, under specific assumptions about the random variable. For example, if is uncorrelated with years of education, then the equation can be estimated with ordinary least squares. If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages. The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that is uncorrelated with education produces a misspecified model. Another technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render identifiable. An overview of econometric methods used to study this problem was provided by Card (1999). 32 3.4. LIMITATIONS AND CRITICISMS Like other forms of statistical analysis, badly specified econometric models may show a spurious relationship where two variables are correlated but causally unrelated. In a study of the use of econometrics in major economics journals, McCloskey concluded that some economists report p values (following the Fisherian tradition of tests of significance of point null-hypotheses) and neglect concerns of type II errors; some economists fail to report estimates of the size of effects (apart from statistical significance) and to discuss their economic importance. Some economists also fail to use economic reasoning for model selection, especially for deciding which variables to include in a regression. It is important in many branches of statistical modeling that statistical associations make some sort of theoretical sense to filter out spurious associations (e.g., the collinearity of the number of Nicolas Cage movies made for a given year and the number of people who died falling into a pool for that year). In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects. In such cases, economists rely on observational studies, often using data sets with many strongly associated covariates, resulting in enormous numbers of models with similar explanatory ability but different covariates and regression estimates. Regarding the plurality of models compatible with observational data-sets, Edward Leamer urged that "professionals... properly withhold belief until an inference can be shown to be adequately insensitive to the choice of assumptions" 4.0 CONCLUSION The unit critically conclude that basic econometrics models is the basis of econometrics and from the simple straight line graph we can see that a simple/linear regression equation is derived from the graph and from there, the model of econometrics started to emanate to becomes higher level of econometrics model which is called multiple regression analysis. 5.0 SUMMARY The unit discussed extensively on basic Econometrics models of linear regression analysis such as Econometrics theory, Econometrics Methods, Examples of econometrics modeling and the limitations and criticism of the models. 6.0 TUTOR MARKED ASSIGNMENT Discuss the theory and methods of Econometrics modeling 33 7.0. REFERENCES/FURTHER READINGS Olusanjo, A.A. (2014). Introduction to Econometrics, a broader perspective, 1st edition, world press publication limited, Nigeria. Warlking, F.G., (2014). Econometrics and Economic theory, 2nd edition, Dale Press limited. 34 UNIT FIVE: IMPORTANCE OF ECONOMETRICS CONTENTS 1.0. Introduction 2.0. Objectives 3.0. Main content 3.1. Why is Econometrics important within economics 3.2. Meaning of Modern Econometrics 3.3. Using Econometrics for Assessing Economic Model 3.4. Financial Economics 3.4.1. Relationship with the capital Asset pricing model 3.4.2. Co integration 3.4.3. Event Study 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 1.0. INTRODUCTION Econometrics contains statistical tools to help you defend or test assertions in economic theory. For example, you think that the production in an economy is in Cobb-Douglas form. But do data support your hypothesis? Econometrics can help you in this case. To be able to learn econometrics by yourself, you need to have a good mathematics/statistics background. Otherwise it will be hard. Econometrics is the application of mathematics, statistical methods, and computer science to economic data and is described as the branch of economics that aims to give empirical content to economic relations. 2.0. OBJECTIVES At the end of this unit, you should be able to:  know the meaning of Econometrics and why Econometrics is important within Economics.  know how to use Econometrics for Assessing Economic Model  understand what is Financial Econometrics. 3.0. MAIN CONTENT 35 3.1. WHY IS ECONOMETRICS IMPORTANT WITHIN ECONOMICS? So Econometrics is important for a couple of reasons though I would strongly urge you to be very wary of econometric conclusions and I will explain why in a minute. 1. It provides an easy way to test statistical significance so in theory, if we specify our econometric models properly and avoid common problems (i.e. heteroskedasticity or strongly correlated independent variables etc.), then it can let us know if we can say either, no there is no statistical significance or yes there is. That just means that for the data set we have at hand, we can or cannot rule out significance. Problems with this: Correlation does not prove causality. It is theory which we use to demonstrate causality but we most definitely cannot use it to "discover" new relationships (only theory can be used to tell us what causes what, for example, we may find a strong statistical significance between someone declaring red is their favorite color and income, but this obviously not an important relationship just chance) Another problem is that many times people run many regressions until they find one that "fits" their idea. So think about it this way, you use confidence intervals in economics, so if you are testing for a 95% confidence interval run 10 different regressions and you have a 40% chance of having a regression model tell you there is statistical significance when there isn't. Drop this number to 90% and you have a 65% chance. Alot of shady researchers do exactly this, play around with data series and specifications until they get something that says their theory is right then publish it. So remember, be wary of regression analysis and really only use it to refute your hypotheses and never to "prove" something. Regression analysis is your friend and you will see how people love to use it. If you don't understand econometrics very well, particularly how to be able to sift through the different specifications so that you rule out any poorly specified models, and so that you understand what all these crazy numbers they are throwing at you mean. If you don't know econometrics yet try reading some papers using regression analysis and notice how you don't know what any of the regression analysis means. This should give you an idea of why you need to learn it. However, many people use it, and believe me many people get undergraduate degrees in economics without knowing econometrics and this makes you less capable then those peers of yours who did learn it. 3.2. MEANING OF MODERN ECONOMETRICS Modern econometrics is the use of mathematics and statistics as a way to analyze economic phenomena and predict future outcomes. This is often done through the use of complex econometric models that portray the cause and effect of past or current 36 economic stimuli. Econometric analysts can plug new data into these models as a means of predicting future results. One of the distinguishing features of modern econometrics is the use of complex computer algorithms that can crunch tremendous amounts of raw data and create a concise and coherent overview of some aspect of the economy. For a long period of time in the past, economists could make hypotheses and guesses about the economy but couldn‘t prove their theories without some sort of obvious sea change in the economy as an indicator. As a result, many started to use mathematics and statistics to give proof about their different ideas. Some began to realize that these same tools could actually give accurate assessments about future economic events, which is how the field of modern econometrics first came into being. Although it can be defined in many different ways, modern econometrics essentially boils down to plugging statistical information about an economy into mathematical formulas. When that happens, the results can show cause and effect about certain economic characteristics. For example, when interest rates rise, it might affect employment levels, inflation, economic growth, and so on. Using econometrics, an analyst might be able to pinpoint exactly how and to what extent this occurs. Economic models are a huge part of the field of modern econometrics. This is where the leaps and bounds made by computer technology in the modern era come into play. Sophisticated programs devised by analysts can take all of the information that is entered, analyze the relationships between the numerical data, and come up with specific information about how certain economic stimuli affect the overall picture. It is an effective way for those practicing econometrics to use the past to predict the future. Proponents of modern econometrics should factor in those unforeseen circumstances that can trigger huge negative changes in an economy. One way to do this is to simulate worst-case scenarios for an economy. By doing this, analysts can see what the potential damage done by hypothetical economic catastrophes might be. In addition, models can be used to show the ways out of such dire occurrences. The boundaries for econometrics are practically limitless, but using them can be fruitless without sound economic theories as their basis. 3.3. USING ECONOMETRICS FOR ASSESSING ECONOMIC MODELS Econometrics is often used passively to provide the economist with some parameter estimates in a model which from the outset is assumed to be empirically relevant. In this sense, econometrics is used to illustrate what we believe is true rather than to find out whether our chosen model needs to be modified or changed altogether. The econometric analyses of this special issue should take its departure from the latter more critical approach. We would like to encourage submissions of papers addressing questions like whether a specific economic model is empirically relevant in general or, more 37 specifically, in a more specific context, such as in open, closed, deregulated, underdeveloped, mature economies, etc. For example, are models which were useful in the seventies still relevant in the more globalized world of today? If not, can we use the econometric analysis to find out why this is the case and to suggest modifications of the theory model? We encourage papers that make a significant contribution to the discussion of macroeconomics and reality, for example, by assessing the empirical relevance of influential papers, or the robustness of policy conclusions to econometric misspecification and the ceteris paribus clause, or by comparing different expectation‘s schemes, such as the relevance of forward versus backward expectations and of model consistent rational expectations versus imperfect/incomplete knowledge expectations, etc. 3.4. FINANCIAL ECONOMETRICS Financial econometrics is the subject of research that has been defined as the application of statistical methods to financial market data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include capital markets , financial institutions, corporate finance and corporate governance. Topics often revolve around asset valuation of individual stocks, bonds, derivatives, currencies and other financial instruments. Financial econometrics is different from other forms of econometrics because the emphasis is usually on analyzing the prices of financial assets traded at competitive, liquid markets. People working in the finance industry or researching the finance sector often use econometric techniques in a range of activities – for example, in support of portfolio management and in the valuation of securities. Financial econometrics is essential for risk management when it is important to know how often 'bad' investment outcomes are expected to occur over future days, weeks, months and years. The sort of topics that financial econometricians are typically familiar with include: 1. Arbitrage pricing theory In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. The theory was proposed by the economist Stephen Ross in 1976. The Model; 38 Risky asset returns are said to follow a factor intensity structure if they can be expressed as: where  is a constant for asset  is a systematic factor  is the sensitivity of the th asset to factor , also called factor loading,  and is the risky asset's idiosyncratic random shock with mean zero. Idiosyncratic shocks are assumed to be uncorrelated across assets and uncorrelated with the factors. The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities: where  is the risk premium of the factor,  is the risk-free rate, That is, the expected return of an asset j is a linear function of the asset's sensitivities to the n factors. Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of factors may never surpass the total number of assets (in order to avoid the problem of matrix singularity). Arbitrage is the practice of taking positive expected return from overvalued or undervalued securities in the inefficient market without any incremental risk and zero additional investments. In the APT context, arbitrage consists of trading in two assets – with at least one being mispriced. The arbitrageur sells the asset which is relatively too expensive and uses the proceeds to buy one which is relatively too cheap. Under the APT, an asset is mispriced if its current price diverges from the price predicted by the model. The asset price today should equal the sum of all future cash flows discounted at the APT rate, where the expected return of the asset is a linear function of 39 various factors, and sensitivity to changes in each factor is represented by a factor- specific beta coefficient. A correctly priced asset here may be in fact a synthetic asset - a portfolio consisting of other correctly priced assets. This portfolio has the same exposure to each of the macroeconomic factors as the mispriced asset. The arbitrageur creates the portfolio by identifying x correctly priced assets (one per factor plus one) and then weighting the assets such that portfolio beta per factor is the same as for the mispriced asset. When the investor is long the asset and short the portfolio (or vice versa) he has created a position which has a positive expected return (the difference between asset return and portfolio return) and which has a net-zero exposure to any macroeconomic factor and is therefore risk free (other than for firm specific risk). The arbitrageur is thus in a position to make a risk-free profit: Where today's price is too low: The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate. The arbitrageur could therefore: Today: 1 short sell the portfolio 2 buy the mispriced asset with the proceeds. At the end of the period: 1 sell the mispriced asset 2 use the proceeds to buy back the portfolio 3 pocket the difference. Where today's price is too high: The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at less than this rate. The arbitrageur could therefore: Today: 1 short sell the mispriced asset 2 buy the portfolio with the proceeds. At the end of the period: 1 sell the portfolio 2 use the proceeds to buy back the mispriced asset 3 pocket the difference. 40 3.4.1. Relationship with the capital asset pricing model The APT along with the capital asset pricing model (CAPM) is one of two influential theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in its assumptions. It allows for an explanatory (as opposed to statistical) model of asset returns. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM can be considered a "special case" of the APT in that the securities market line represents a single-factor model of the asset price, where beta is exposed to changes in value of the market. Additionally, the APT can be seen as a "supply-side" model, since its beta coefficients reflect the sensitivity of the underlying asset to economic factors. Thus, factor shocks would cause structural changes in assets' expected returns, or in the case of stocks, in firms' profitabilities. On the other side, the capital asset pricing model is considered a "demand side" model. Its results, although similar to those of the APT, arise from a maximization problem of each investor's utility function, and from the resulting market equilibrium (investors are considered to be the "consumers" of the assets). 3.4.2. Co integration Co integration is a statistical property of a collection (X1,X2,...,Xk) of time series variables. First, all of the series must be integrated of order 1 (see Order of Integration). Next, if a linear combination of this collection is integrated of order zero, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order 1, and there exist coefficients a,b,c such that aX+bY+cZ is integrated of order 0, then X,Y, and Z are co integrated. Co integration has become an important property in contemporary time series analysis. Time series often have trends — either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends — these are also called unit root processes, or processes integrated of order 1 — I(1). They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them. If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (I(1)) but some (co integrating) vector of coefficients exists to form a stationary linear combination of them. For instance, a stock market index and the price of its associated futures contract move through time, each roughly following a random walk. Testing the 41 hypothesis that there is a statistically significant connection between the futures price and the spot price could now be done by testing for the existence of a co integrated combination of the two series. 3.4.3. Event study An Event study is a statistical method to assess the impact of an event on the value of a firm. For example, the announcement of a merger between two business entities can be analyzed to see whether investors believe the merger will create or destroy value. The basic idea is to find the abnormal return attributable to the event being studied by adjusting for the return that stems from the price fluctuation of the market as a whole. As the event methodology can be used to elicit the effects of any type of event on the direction and magnitude of stock price changes, it is very versatile. Event studies are thus common to various research areas, such as accounting and finance, management, economics, marketing, information technology, law, and political science. One aspect often used to structure the overall body of event studies is the breadth of the studied event types. On the one hand, there is research investigating the stock market responses to economy-wide events (i.e., market shocks, such as regulatory changes, or catastrophic events). On the other hand, event studies are used to investigate the stock market responses to corporate events, such as mergers and acquisitions, earnings announcements, debt or equity issues, corporate reorganisations, investment decisions and corporate social responsibility (MacKinlay 1997; McWilliams & Siegel, 1997 4.0 CONCLUSION The unit critically concludes that Econometrics is very important in Economics and financial analysis. Econometrics is the basis of using economics theories to justify a real life situation in the micro and macro economy of any nation. 5.0 SUMMARY The unit discussed extensively on the importance of Econometrics and why econometrics is very useful in our day to day activities and how the financial analyst also makes use of it to financial forecast and analysis. 6.0 TUTOR MARKED ASSIGNMENT Differentiate between Modern and Financial Econometrics 42 7.0. REFERENCES/FURTHER READINGS Medunoye, G.K., (2013). Introduction to Econometrics, 1st edition, Mill Publication limited. Parker, J.J., (2016). Econometrics and Economic Policy, Journal vol 4, pg 43-73, Parking & Parking Publication limited. 43 MODULE TWO – SINGLE- EQUATION (REGRESSION MODELS) Unit One: Regression Analysis Unit Two: The Ordinary Least Square (OLS) Method Estimation Unit Three: Calculation of Parameter and the Assumption of Classical Least Regression Method (CLRM) Unit Four: Properties of the Ordinary Least Square Estimators Unit Five: The Coefficient of Determination (R2): A measure of “Goodness of fit” Unit One: Regression Analysis CONTENTS 1.0. Introduction 2.0. Objectives 3.0. Main content 3.1. The Linear Regression Model 3.2. The Classical Linear Regression Model 3.3. Regression Vs Causation 3.4. Regression Vs Correlation 4.0 Conclusion 5.0 Summary 6.0 Tutor-Marked Assignment 7.0 References/Further Readings 44 1.0 INTRODUCTION The term regression was introduced by Francis Galton. In a famous paper, Galton found that, although there was a tendency for tall parents to have tall children and for short parents to have short children, the average height of children born of parents of a given height tended to move to ―regress‖ toward the average height in the population as a whole. In other words, the height of the children of unusually tall or unusually short parents tends to move toward the average height of the population. Galton‘s law of universal regression was confirmed by his friend Karl Pearson who collected more than a thousand records of heights of members of family groups. He found that the average height of sons of a group of tall fathers was less than their father‘s height and the average height of sons of a group of short fathers was greater than their fathers‘ height, thus ―regressing‖‖ tall and short sons alike toward the average height of all men. In the word of Galton, this was ―regression to mediocrity‖. 2.0. OBJECTIVES At the end of this unit, you should be able to:  examine the linear regression model  understand the classical linear regression model 3.0 MAIN CONTENT 3.1 The Linear Regression Model We can ask ourselves a question that why do we regress? Econometric methods such as regression can help to overcome the problem of complete uncertainty and guide planning and decision-making. Of course, building a model is not an easy task. Models should meet certain criteria (for example a model should not suffer from serial correlation) in order to be valid and a lot of work is usually needed before we achieve a good model. Furthermore, much decision making is required regarding which variables to include in the model. Too many may cause problems (unneeded variables misspecification), while too few may cause other problems (omitted variables misspecification or incorrect functional form). 3.2 The classical linear regression model The classical linear regression is a way of examining the nature and form of the relationships among two or more variables. In this aspect we will consider the case of only two variables. One important issue in the regression analysis is the direction of causation between the two variables; in other words, we want to know which variable is affecting the other. Alternatively, this can be stated as which variable depends on the other. Therefore, we refer to the two variables as the dependent variable (usually denoted by Y) and the independent or explanatory variable (usually denoted by X). We want to 45 explain /predict the value of Y for different values of the explanatory variable X. Let us assume that X and Y are linked by a simple linear relationship: Where denotes that average value of for given and unknown population parameters ‗a‘ and (the subscript t indicates that we have time series data). Equation (1) is called the population regression equation. The actual value of will not always equal its expected value There are various factors that can ‗disturb‘ its actual behaviour and therefore we can write actual as: or Where is a disturbance. There are several reasons why a disturbance exiaists: 1. Omission of explanatory variables: There might be other factors (other than ) affecting that have been left out of equation (III). This may be because we do not know. These factors, or even if we know them we might be unable to meaure them in order to use them in a regression analysis. 2. Aggregation of variables: In some cases it is desirable to avoid having too many variables and therefore we attempt to summarize in aggregate a number of relationships in only one variable. Therefore, eventually we have only a good approximation of with discrepanceis that are captured by the disturbance term. 3. Model misspecification: We might have a smisspecified model in terms of its structure. For example, it might be that is not affected by , but it is affected by the valaue of X in the previous period (that is ). In this case, if and are closely related, the estimation of equation (III) will lead to discrepancies that are again captured by the error term. 4. Functional Misspecification: The relationship between X and Y might be non- linear. 5. Measurement Errors: If the measurement of one or more variables is not correct then errors appear in the relationship and these contribute to the disturbance term. 3.3 Regression Vs Causation Although regression analysis deals with the dependence of one variable on other variables, it does not necessarily imply causation. In other words of Kendall and Stuart, ―A statistical relationship, however strong and however suggestive, we can never establish cuasal connection: our ideas of causation must come from outside statistics, ultimately from some theory or other. In the crop-yield, there is not statistical reason to 46 assume that rainfall does not depend on crop yeild. The fact that we treat crop yeeld as dependent on rainfall (among other things) is due to nonstatistical considerations: common sense suggests that the relationship cannot be reversed for we cannot control rainfall by barying crop yield. 3.4 Regression Vs Correlation