Lecture 1
Econometrics - definition
Flow chart
- econometric models
- estimation
- structural analysis and forecasting
Illustrations
- demand for gasoline (not done this year)
- forensic economics: Exxon Valdez
Lecture 2
Review of Univariate and Bivariate Statistics
Random Variables
Relative Frequency - Probability
Properties of Probabilities
Probability Functions and Probability Density Functions
- Pj = Mj/N
Bivariate Distributions
Marginal Probabilities
Conditional Distributions
Lecture 3
Characteristics of Distributions; Normal Distribution
"Moments" of Distributions
- Expected Value and Properties
- Variance and Properties
- Covariance and Joint Distributions
- Correlation
Normal Distribution
Standardization of Normal Distribution
Lecture 4
Review of Estimation and Inference (univariate case)
Central Limit Theorem and Distribution of x-bar
- x-bar is normally distributed with mean mu and s.e. sigma
squared/n
t Distribution
Point Estimates
Confidence Intervals (as sets of acceptable hypotheses)
Lecture 5
Properties of Estimators; Hypothesis Testing
- Linearity
- Unbiasedness
- Efficiency
- Consistency
Hypothesis Testing
Simple Regression
Digression on Linearity
Sample Regression Function
4 Maintained Hypotheses for OLS
- E(u given X i) = 0
- Cov(ui,uj) = 0, for i not equal to
j
- Var(ui given Xi) = sigma squared
(constant)
- Cov(ui given Xi) = 0
Rules of Summation Notation
Lecture 6
Sample Regression Function (SRF)
SRF Properties
- goes through (x-bar,y-bar)
- yi hat bar = yi bar
- mean ei = 0
- ei uncorrelated with Xi with
Yi hat
Variance b2
Variance b1
Gauss Markov Theorem: OLS is "BLUE"
Confidence Intervals for B1, B2
Lecture 7
Goodness of Fit
Variation in Y
TSS, ResSS, ExSS
R squared = ExSS/TSS
Using Regression for Prediction
Lecture 8
From Simple to Multiple Regression
Explanation of t-ratios on SHAZAM output
Multiple Regression Models
Omitted Variables Bias
- omitted variable is relevant to explaining Y
- omitted variable correlated with included variable
Lecture 9
Goodness of Fit
In Multiple Regression Models
- general model
- restricted model
R squared
Adjusted R squared
Hypothesis Testing in Multiple Regression
Confidence Ellipses
Lecture 10
Joint Hypotheses
Joint Confidence Ellipses
- F-tests
- ANOVA from means
Functional form
- Linear vs log-linear vs log-log models
- Use of /LOGLOG, /LOGLIN option on OLS
Lecture 11
More Flexible (General) Models
Interaction Terms
- non-constant derivatives
Dummy Variables
- intercept shifter(s)
- slope shifter(s)
Lecture 12
Categorical Explanatory Variables; Regime Changes
More on Dummy Variables
- m categories, m-1 dummies
- Changes in Regime
Class Survey
Lecture 13
Regression Pathologies: Multicollinearity
definition
evidence of Multicollinearity
- lousy t-ratios
- high R squared
- joint significance - "good" F-test results
- point estimates jump around as you add more regressors
What is the source of multicollinearity?
- look at pairwise correlations (STAT/PCOR)
- auxiliary regressions among RHS variables
- check R squared values
- high R squared - multicollinearity?
Remedies for Multicollinearity
- gather more data
- use information from prior studies
- drop an offending variable - CAUTION
- may just have to give up
Lecture 14
Regression Pathologies: Heteroscedasticity
definition - unequal error variances
consequences
- point estimates still unbiased
- standard error terms b1, b2
incorrect
- flawed hypothesis testing, t-ratios, P-values, CI's
Recourse
- use sigma i squared if known
- switch to weighted least squares (WLS)
- wi = 1/sigma i squared
Diagnosis: any relationship between error variances X variable(s)?
- OLS Y X/Resid=e
- GENR e2=e*e
- OLS e2 X
Try logs
Look diligently for any evidence of some relationship explaining error
variances
Goldfeld-Quandt Test
- rank Observations (SORT) by variable that appears to be
"culprit"
- omit "c" observations in middle (use SAMPLE command)
- examine (error variance 2)/(error variance 1)
Lecture 15
Heteroscedasticity, cont'd
- Weighted Least Squares
- Examples: assumptions about error variances
Lecture 16
Pathologies: Serially Correlated Errors
definition - autocorrelation in errors
Time Series
Detection
- run OLS, save residuals
- create lagged errors, assess correlation
Is correlation significant? - Durbin-Watson test statistics
FGLS Estimation
AUTO Y X gives desired b1, b2 purged of AR(1) error
problems
Lecture 17
Pathologies: Endogeneity of Regressors
Exogenous Regressors - flip coin to decide participation; X's beyond
observation's control
Endogenous Regressors - self selection into program; observation chooses own X
values
Examples: debate over capital punishment and fishing avidity
Remedies - Two Stage Least Squares (overview only)
Lecture 18
Discrete Dependent Variables
Maximum Likelihood Estimation (MLE) intuition
PROBIT (and LOGIT) discrete choice models (overview only)
Example
Lecture 19
Overflow; Recap