INTRODUCTION TO STATISTICS AND ECONOMETRICS

INTRODUCTION TO STATISTICS AND ECONOMETRICS

ECON 310.01
Tuesdays & Thursdays
6:00-7:50 p.m.
Appleby Center (AC) 232

Instructor: Bob Escudero
Office: Appleby Center 222D
Phone: (310) 506-4378
E-mail: Robert.Escudero@pepperdine.edu
Fax: (310) 506-7271
Website: http://arachnid.pepperdine.edu/socialscience/Faculty/Escudero/escudero.htm

Course Description

This course develops the basic concepts of statistical theory and their applications to statistical inference. Parameter estimation techniques involved in postulated economic relationships between variables and the methods of testing propositions will be developed. Topics that will be discussed include: descriptive vs. inferential statistics, probability distributions, sampling and estimation, hypothesis testing, analysis of variance, and regression and correlation. The multiple regression model will be covered, and students will be required to complete a course project involving the application of multiple regression.

Text

Kohler, Heinz and Ramanathan, Ramu. Statistics for Business and Economics and Applied Econometrics, 1^st edition. New York: South-Western/Thomson Learning Publishers, Inc., 2002. (The tables should accompany the shrink-wrapped text.)

Office Hours

My office hours will be scheduled on an individual basis. Please call me or speak to me during class to arrange for an appointment. I do not hold office hours on exam days.

Exams

There will be 4 unit exams and 1 cumulative statistics exam (optional) in this course. Each unit exam is worth 100 points, and the cumulative statistics exam is worth 200 points. If your score on the cumulative statistics exam is higher than the average of the first two unit exams, then the first two unit exam scores will be disregarded. However, if you are satisfied with your scores on the first two unit exams, then you do not have to take the cumulative statistics exam. You, nevertheless, must still take the fourth unit exam. If you miss either of the first 2 unit exams, you will have to take the cumulative statistics portion of the final because I do not give make-ups. The final exam will be given on Final Exam week. Therefore, do not make any other arrangements (i.e., travel plans) that will conflict with that date, because I do not give "Incompletes."

Multiple Regression Analysis Computer Project

Students are required to perform a multiple regression analysis on an instructor-approved, economic topic. The project is worth 100 points, and it must be turned in by 12 noon on the Friday of Dead Week (NO EXCEPTIONS!). Students are encouraged to refer to Chapter 14 of the Ramanathan text and to turn in "rough" drafts prior to the due date for initial feedback.

Introduction to Econometrics

In the field of Economics, more and more emphasis is being placed on developing and utilizing statistical techniques for analyzing economic problems. Econometrics is the systematic testing of theory against fact used by economists. Salvatore's definition of econometrics: "...the application of economic theory, mathematics, and statistical techniques for the purpose of testing hypotheses and estimating and forecasting economic phenomena." Theoretical relationships among variables are usually expressed in mathematical form, and economists use statistical analysis to test hypotheses about these relationships, to estimate actual magnitudes, and use these estimates to make quantitative predictions of economic events.

Kelejian and Oates state that "Econometrics is the branch of economics dealing with the quantitative analysis of economic behavior, and it serves two functions." First, it provides techniques for verifying or refuting theories, and, second, it provides quantitative estimates of the magnitudes of the relationships among variables. A set of definitions and assumptions that an economist can use to explain certain types of events is called an economic theory. This theory can aid the economist in determining how certain economic variables interact.

In order to evaluate the usefulness of theories, we need to determine their reliability in predicting economic events. Economic theories are, therefore, generally stated in a form that specifies some implied causal sequence of events. (These are typically based on the assumption that other relevant factors are held constant.) It will be expressed in a mathematical form by noting that one variable is a function of another variable and specifying the general character of the relationship involved. The problem that economists face is that most of their data come from daily experiences, and, therefore, in the real world other relevant factors are rarely unchanged.

However, econometricians have devised statistical techniques in order to artificially hold the other influences constant on the variable in question. In this way, they can determine the effect of one variable on another variable. While knowledge of the general character of these relationships is valuable, it is usually not adequate in order to make decisions. Therefore, quantitative techniques must be capable of generating estimates of magnitude in addition to providing an assessment of the more general propositions typically suggested by economic theory.

The Two Variable Regression Model

In many instances, the value of one variable that is associated with the value of another variable in some systematic way is very important to economists. The awareness of linkages between variables can be of great use to researchers and decision makers because it enables them to predict, from a knowledge of the value of one variable, the value of the other variable. Regression and correlation analysis can help in this way by establishing what types of linkages between variables exist and how strong these linkages are. WORD OF CAUTION: these techniques are used to determine the existence and strength of associations between variables, but they unable to prove anything about the possible cause-and-effect relationships.

Regression analysis is a statistical method that focuses on the establishment of an equation that allows the unknown value of one variable to be estimated from the known value of one or more other variables. When a single variable is used to estimate the value of an unknown variable, the method is referred to as simple regression analysis. Don't confuse the term "simple" with "easy." On the other hand, when several variables are used to estimate the value of an unknown variable, the method is referred to as multiple regression analysis.

Simple correlation analysis is a statistical method that focuses on the establishment of an index that provides, in a single number, an instant measure of the strength of association between two variables. Depending on the size of this quantitative measure, one can tell how closely two variables move together and, therefore, how reliably one can estimate one with the help of the other.

Basic Concepts

In regression analysis, the variable the value of which is assumed known (and that is being used to explain or predict the value of the other variable) is symbolized by X and is referred to as the "independent," "explanatory," or "predictor" variable and, on occasion the "regressor." In contrast, the variable the value of which is assumed unknown (and that is being explained or predicted on the basis of its relationship with the other variable) is symbolized by Y and is referred to as the "dependent," "explained," or "predicted" variable and, on occasion the "regressand."

The relationship between any two variables, X and Y, can be one of two types. It can be a "precise," "exact," or "deterministic" relationship, such that the value of Y is uniquely determined when ever the value of X is specified. It can, in contrast, be an "imprecise," "inexact," or "stochastic" relationship, such that many possible values of Y can be associated with any one value of X.

If the values of the dependent variable, Y, increase with larger values of the independent variable, X, theirs is said to be a "direct" relationship, and the slope of the regression line will be positive. If instead the values of the dependent variable, Y, decrease with larger values of the independent variable, X, theirs is an "inverse" relationship, and the slope of the regression line will be negative.

Estimated Regression Equation: Y_x = β₀ + β₁X₁ + β₂X₂where:

Y_x = dependent variable based on given values of X₁ and X₂

β₀ = constant or intercept term

β₁ = slope coefficient that explains how Y changes for a 1-unit increase in X₁, holding X₂ constant

β₂ = slope coefficient that explains how Y changes for a 1-unit increase in X₂, holding X₁ constant

X₁ = first independent variable

X₂ = second independent variable

ECONOMETRICS AND ITS USES

Econometrics has three major uses:

(1) the description of economic reality
(2) the testing of hypotheses about economic theory
(3) the forecasting of future economic activity

Description

The simplest use of econometrics is description. For example, consumer demand for a particular commodity often can be thought of as a relationship between the quantity demanded 8) and the commodity's price (P), the price of a substitute good (Ps), and disposable income (Yd). For most goods, the relationship between consumption and disposable income is expected to be positive, because an increase in disposable income will be associated with an increase in the consumption of the good. Econometrics actually allows us to estimate that relationship based upon past consumption, income, and prices. In other words, a general and purely theoretical functional relationship like C = f (P, Ps, Yd) can become explicit: C = -60.5 - 0.45P + 0.12Ps + 12.2Yd

This technique gives a much more specific and descriptive picture of the function.

Hypothesis Testing

The second and perhaps the most common use of econometrics is hypothesis testing, the testing of alternative theories with quantitative evidence. For example, you could test the hypothesis that the product from the first equation above is what economists call a normal good (one for which the quantity demanded increases when disposable income increases). You could do this by applying various statistical tests to the estimated coefficient (12.2) of disposable income (Yd) in the above equation. Unfortunately, statistical tests of such hypotheses are not always easy, and there are times when two researchers can look at the same set of data and come to different conclusions. Even given this possibility, the use of econometrics in testing hypotheses is probably its most important function.

Forecasting

The third and most difficult use of econometrics is to forecast or predict what is likely to happen next quarter, next year, or further into the future. For example, economists use econometric models to make forecasts of variables like sales, profits, Gross National Product (GNP), and the inflation rate. The accuracy of such forecasts depends in large measure on the degree to which the past is a good guide to the future. For example, if the president of a company that sold the product modeled in the first equation above wanted to decide whether to increase prices, forecasts of sales with and without the price increase could be calculated and compared to help make such a decision. In this way, econometrics can be used not only for forecasting but also for policy analysis.

What is Regression Analysis?

Econometricians use regression analysis to make quantitative estimates of economic relationships that previously have been completely theoretical in nature. After all, anybody can claim that the quantity of compact discs demanded will increase if the price of those discs decreases (holding everything else constant), but not many people can actually put numbers into an equation and estimate by how many compact discs the quantity demanded will increase for each dollar that price decreases. To predict the direction of the change, you need a knowledge of economic theory and the general characteristics of the product in question. To predict the amount of the change, though, you need a sample of data, and you need a way to estimate the relationship. The most frequently used method to estimate such a relationship in econometrics is regression analysis.

Possible Topics

Demand/consumption for any good
Crime and Punishment
Health Care/Health and Education
Religion
GDP and Income
Poverty and Income
Housing/Homeless
Immigration
Interest Rates
Production of anything
Labor Force/Employment/Unemployment
Prices and Inflation/CPI/PPI
Money and Banking
Transportation
Agriculture
International Trade and Finance/Imports/Exports
Stock Market/DJIA/S&P 500 index
Motor Vehicles/Registrations/Production/Accidents/Fatalities
Professional Sports Salaries
U.S. Trade deficit
Real Estate market/Housing/Mortgage interest rates
Students' grades/Study habits
Company's market share

Instructions

1. The report must be typed, 12 pt. font, double-spaced with 1 inch margins!! NO EXCEPTIONS!!

2. There is no page limit; it will be as long as it takes to cover all the material.

3. In your report and on your print-outs, make sure that you have correctly labeled your Xs and Y.

4. Make sure that you include the following results with your report and incorporate them into the text; don't just attached the print-outs to the end of the report.

a. summary measures for all variables (means, variances, correlations)

b. scatter diagrams of all combinations of variables

c. output, including OLS, first-order autocorrelation (GLS), Park Test, residual plots, time plots

5. Include your estimated multiple regression equation (in the correct form) in the report.

6. In your report, make sure that you:

a. explain your βs for your problem and the relationship they have with respect to your Y.

b. discuss how r, R², and adjusted R² were computed and interpret them.

c. discuss the relationship between the obtained t-values and standard errors for all estimated βs.

d. discuss the purpose of the t-test, adjusted R², and F-statistic.

e. hypothesize and explain your expected signs (using theory) and explain the results of your Hos.

f. calculate the average elasticity coefficients of your Y with respect to all your Xs and interpret them.

g. explain whether or not the 7 classical assumptions of OLS hold, and if not, list the one(s) you would question and why.

h. if you have time-series data, run a test for serial correlation and explain the results.

i. run a test for multicollinearity and explain the results.

j. if you have cross-sectional data, run a test for heteroskedasticity and explain the results.

WRITING THE PAPER

The purpose of this paper is to demonstrate that you can design, perform, and report an econometric study. The final paper, then, should be much more than a stack of printouts. It should include a discussion of the theory behind your model and any implications of your research. The results per se are less important than your interpretation of them. Also remember that I will grade the writing style as well as your research methods.

I. Introduction

A. State the problem you are studying.
B. Identify your independent and dependent variables.

II. The Model

A. Why did you construct the model as you did? Why did you select your particular functional form?
B. What signs do you expect on the individual parameter estimates?

III. The Data

A. Where did the data come from? Document your sources.
B. Are you comfortable with the data? That is, do you believe they are reliable?

IV. Reporting Results

A. Interpret and use your results. Simply stating that the t-ratios are significant is of little use. For example, if the model uses time series data, make a one-step forecast. Is the forecast reasonable?

B. Remember, "negative" results--results that are inconsistent with your initial hypothesis--are results nevertheless. If your hypothesis is not verified by the data, do not try to hide it. Do try to explain what happened.

V. Summary and Conclusions

A. Don't even pretend that your study is the final word. If your hypothesis appears to be verified and your summary statistics are good, fine, but more sophisticated methods might shed doubt on your study.

B. Econometric analysis is never finished. Even practicing econometricians invariably call their studies "preliminary" and mention that research is continuing.

C. Conclude your paper with a section discussing further work.

MULTIPLE REGRESSION ANALYSIS COMPUTER PROJECT

Topic/Rationale/Variables (Due: Week 12)
Hypotheses/Functional Form/Rationale/Data Source(s) (Due: Week 13)

Student's Name: _____________________________________________________________________________________________

Economic Topic: _____________________________________________________________________________________________

Rationale: __________________________________________________________________________________________________

Dependent Variable: __________________________________________________________________________________________

Independent Variables: (You can use more than 4.)

a. _________________________________________________________________________________________________________

b. _________________________________________________________________________________________________________

c. _________________________________________________________________________________________________________

d. _________________________________________________________________________________________________________

Hypotheses: ________________________________________________________________________________________________

___________________________________________________________________________________________________________

Functional Form: _____________________________________________________________________________________________

Rationale: __________________________________________________________________________________________________

___________________________________________________________________________________________________________

Data Source(s): _____________________________________________________________________________________________

___________________________________________________________________________________________________________

G Approved G Disapproved Reason: ____________________________________________________________

Signature: _____________________________________________________ Date: _______________________________________

Grading System

The final course grade is based on 500 total points, and the distribution is as follows:

PERCENTAGES POINTS GRADES

92.5 -100.0 463 - 500 A
89.5 - 92.4 448 - 462 A-
86.5 - 89.4 433 - 447 B+
82.5 - 86.4 413 - 432 B
79.5 - 82.4 398 - 412 B-
76.5 - 79.4 383 - 397 C+
72.5 - 76.4 363 - 382 C
69.5 - 72.4 348 - 362 C-
66.5 - 69.4 333 - 347 D+
62.5 - 66.4 313 - 332 D
59.5 - 62.4 298 - 312 D-
below 59.5 below 298 F

Attendance Policy

If you have more than 2 unexcused absences, your course grade will be lowered by one letter grade. If you have more than 4 unexcused absences, you will be given a failing grade in the course. 3 tardies to class will result in 1 unexcused absence. Special needs must be discussed with me in advance of the absence. If you participate in official University activities (athletics, debate, etc.), you need to provide a schedule of events that will require you to miss class. When you miss class, you are responsible for obtaining all class notes, information, etc. from another class member.

Ethics and Academic Honesty

Academic dishonesty is inexcusable in the university setting. By far, almost every student realizes this, and most students behave ethically in the classroom. Students and faculty alike are distressed by students who cheat on exams or in the writing of papers. It is every student's responsibility to avoid giving the impression that he/she is cheating. I will assume that every student is honest and will abide by the Seaver College Code of Academic Ethics, detailed in your student handbook. I will not tolerate dishonest behavior, and reserve the right to respond by giving the student(s) a grade of 0 for the exam/project, giving the student(s) a course grade of "F," and/or reporting the incident to the Academic Ethics Committee. Therefore, students should refrain from copying answers during tests. Also, students should avoid leaving the room during exams. Please use the restroom before exams. Students should arrive on time to every class meeting. In the last few years, there has been a trend of papers that utilize the Internet. Students have often gone to web sites, downloaded text from selected reference sources, and simply submitted the material as their paper. Such papers will be given no credit. Please make sure that you reference your sources (data and text) whether they be from the Internet or from printed sources.

Some Words of Advice

Some students experience a degree of fear ranging from mild apprehension to an extreme mental block whenever they see a number or mathematical equation. If you happen to belong to this category, you should especially try to set aside any notion you may have to the effect that "statistics is something I know I'll never be able to understand." The level of mathematics required in this text is such that 2-3 years of high school algebra, MATH 214, plus a quick review of a few elementary algebraic operations (from handouts) should be ample preparation. It must be remembered, however, that mathematics and statistics texts cannot be expected to read like novels. Material is usually presented in a highly condensed form. Therefore, careful re-reading and an active rather than passive orientation to the material presented will be required. For this reason, there is no substitute for daily preparation, reading the material before class, and the working of practice problems. I will not formally assign homework problems to be turned in and graded. It is up to each of you to do that. It has been my experience that those students who read the assigned material before class and work the problems in the text do significantly better in the course than those who do not. I do not expect you to have understood all that you have read, however, some of the questions that might arise while reading will probably be answered during the class lectures. Also, the class lectures will make a lot more sense if you have already read the material.

How to Succeed in the Course

Read the material prior to the day that it will be covered.
Don�t fall behind; you won�t have enough time to catch up.
Come to class prepared to discuss and/or do board work.
Don�t hesitate to ask questions; there is no such thing as a stupid question (unless it can be answered by reading this syllabus)!
Bring your text, notebook, and calculator every day.

Tentative Course Schedule

UNIT 1

Introduction to course, expectations, prerequisites, Math review
Nature of Statistics (K-1)
Generating New Data: Census Taking and Sampling (K-4)
Presenting Data: Tables and Graphs (K-6)
Presenting Data: Summary Measures (K-7)
Unit 1 Exam (Kohler, Chapters 1, 4, 6, 7)

UNIT 2

The Theory of Probability (K-8)
Discrete Probability Distributions (K-9)
Continuous Probability Distributions (K-10)
Sampling Distributions (K-11)
Estimation (K-12)
Hypothesis Testing: The Classical Technique (K-13)
Analysis of Variance (K-15)
Unit 2 Exam (Kohler, Chapters 8-13, 15)

UNIT 3

Introduction to Econometrics (R-1)
The Simple Linear Regression Model, Ordinary Least Squares, and the Classical Model (R-3)
Learning to Use Regression Analysis
Multiple Regression Models (R-4)
Unit 3 Exam (Ramanathan, Chapters 1, 3, 4)

UNIT 4

Specification: Choosing the Independent Variables (R-7) and a Functional Form (R-6)
Multicollinearity (R-5)
Serial Correlation (R-9)
Heteroskedasticity (R-8)
Review for Cumulative Statistics Exam/Unit 4 Exam
Cumulative Statistics Exam (optional re-take)
Computer Project Due by 12 noon
Unit 4 Exam (Ramanathan, Chapters 5-9) [7:30-10:00 p.m.]
Graduation

ECON 310
STUDENT INFORMATION SHEET

Name__________________________________________________________________________

Student ID#____________________________________________________________________

Preferred first name______________________________________________________________

Campus Mailing Address___________________________________________________________

______________________________________________________________________________

Campus Phone Number____________________________________________________________

Permanent Address_______________________________________________________________

______________________________________________________________________________

Permanent Phone Number__________________________________________________________

Previous classes relevant to this course_______________________________________________

______________________________________________________________________________

_______________________________________________________________________________

______________________________________________________________________________

Previous experiences relevant to this course____________________________________________

______________________________________________________________________________

Intended career__________________________________________________________________

_______________________________________________________________________________

______________________________________________________________________________

By signing below, I agree to abide by the policies in this ECON 310 course syllabus and the Seaver College Code of Academic Ethics as outlined in the Student Handbook.

_________________________________________________________________________________

Signature Date

_________________________________________________________________________________

Printed Name CWID