ECO 4412 ECONOMIC STATISTICS AND ECONOMETRICS

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ECO 4412ECONOMIC STATISTICS AND ECONOMETRICS

• Fall 2005
• 3 Credits
• 130-245 TR
• Prerequisites ECO 3401, ECO 3411

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Shelby Gerking

• CBAII 302M
• 407.823.4729
• Sgerking_at_bus.ucf.edu
• Office Hours 245-400 pm TR and by appointment

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Course Outline

• Text Stock and Watson, Introduction to
  Econometrics, 2004
• Goals Understanding how to use simple linear
  regression, multiple regression, dummy variables,
  hypothesis testing, panel data, and related
  issues and methods

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Schedule

• Chapter 4, 4 weeks
• Chapter 5, 3 weeks
• Chapter 6, 3 weeks
• Chapter 7, 3 weeks
• Chapter 8, 2 weeks
• Chapter 9, time permitting

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Grading

• Two mid-term exams (15 each)
• Final exam (15)
• Four papers
• Paper 1 (5)
• Papers 2,3,4 (10 each)
• Homework (20 altogether)
• Final letter grades based on curve as explained
  at first class meeting

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Papers

• Designed to help you learn about econometric
  software (LIMDEP)
• Require you to collect your own data
• Give you a chance to put econometric theory we
  study into practice
• Give you experience with making written
  presentations of regression analyses

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Late Work

• Homework and papers may not be turned in late
  except because of authorized university
  activities
• Exams (including the final) must be taken at the
  scheduled time set aside for this purpose except
  because of authorized university activities

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Academic Dishonesty

• Also known as cheating, academic dishonesty will
  not be tolerated in this class. This means that
  you must turn in only your own work on homework
  and paper assignments and on exams. Students
  attempting to enhance their grade by representing
  the work of others as their own will be subject
  to penalties prescribed by CBA and UCF policy.

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What Can We Learn?

• Dont be afraid of complex subjects
• Perform your analysis with complete objectivity
  and independence
• State your conclusions as truthfully as possible,
  even though they may be provocative and even
  though they may not be what people want to hear
• if it is not perfect, it is not good enough
• Respect for the data and the statistical methods
  of analysis

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Two-Variable Linear Model

• Consider the linear model
• Yi?0 ?1Xiui
• In this model, Y refers to the dependent
  variable, X refers to the independent variable
  and u is an error term representing the
  collective effect of all variables other than X
  on Y.
• General idea is that X is the cause and Y is
  the effect
• ?0 and ?1 are unknown population parameters to be
  estimated

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Known Variables and Unknown Parameters

• In our model,
• Yi?0 ?1Xiui
• We will have data on X and Y and will use those
  data to compute estimates of the unknown
  population values of the constant term and slope
  coefficient
• Estimates of these parameters made by ordinary
  least squares (OLS). This method described more
  fully later on.

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Examples

• Highway fatalities/stringency of drunk driving
  laws
• Elementary students standardized test
  scores/class size
• Annual earnings/years of schooling
• Sales/Advertising
• Quantity of a good demanded/Price
• Consumption/Income

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Numerical Example 1

• Regression of total annual attendance at major
  league baseball games in 1970 on population of
  city where team is located
• 23 (U.S.) teams in 1970, thus there are 23 pairs
  of observations (data points). Attendance and
  population measured in thousands of persons
• OLS yields
• Attendancei814.90.135x Populationiûi

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Scatter Diagram
0.135?ATT? ?POP
.
Attendance
.
.
.
.
Estimated Regression Line
.
.
.
.
.
.
814.9
.
Population
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Interpretation

• Estimated slope coefficient0.135 means that if
  city population rises by one unit (1000 persons),
  attendance rises by 0.135x1000 persons (or 135
  persons).
• Estimated constant term (814.9) determines the
  level of the regression line. Does not mean
  that attendance would be 814,900 if population
  were zero.
• Predicted attendance of a team in a city of 8
  million is 814.9(0.135x8,000)x10001,894,000

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Interpretation (continued)

• Regression line is an average relationship
  (e.g., slope coefficient is an average across all
  23 cities) for 1970? Would this relationship hold
  in other years? 2005?
• What variables are represented by ui in this
  regression?
• Won-loss record
• Average income of city residents
• Price of tickets
• Many other things

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Numerical Example 2

• How is attendance affected by won-loss record?
• Regress attendance on games behind (GB) in the
  standings at the end of the season
• The result is
• Attendancei1565.98-20.41xGBi ûi
• Note negative slope coefficient
• Does the constant term have a natural
  interpretation in this regression? What is it?

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Diagram of Regression
-20.41?Attendance/?Games Behind
Attendance
1565.98
Estimated Regression Line
Games Behind
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Ordinary Least Squares
0.135?ATT? ?POP
.
Attendance
.
.
.
.
Estimated Regression Line
.
.
.
.
.
.
814.9
.
Population
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OLS Residuals (Errors)
0.135?ATT/?POP
.
Attendance
Ûi0
.
.
.
.
Estimated Regression Line
.
.
.
.
.
.
814.9
.
ÛjPopulation
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Least Squares Method

• Minimize the sum of squared residuals (SSR)
• SSR?û12û22 ûn2
• We could think of minimizing SSR by successively
  choosing pairs of values for the constant term
  and slope coefficient until SSR is made as small
  as possible
• Or, we could use differential calculus (which
  turns out to be a lot easier)

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Estimated Parameters

• When using OLS
• Estimated slope coefficient equals the sample
  covariance between Y and X (Sxy) by the sample
  variance of X (Sx2)
• Estimated constant term equals the sample mean of
  Y minus the estimated slope times the sample mean
  of X