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"Under Construction" scheduled to be complete late June 2013
Textbook: Introductory Econometrics (Any Edition) by Jeffrey Wooldridge
Review out of class notes (Week 1)
Chapter 1 The Nature of Econometrics and Economic Data (Week 1)
Chapter 2 The Simple Regression Model (Week 1 & Week 2)
Chapter 3 Multiple Regression Analysis: Estimation (Week 2)
Chapter 4 Multiple Regression Analysis: Inference (Week 2 & Week 3)
Chapter 5 Multiple Regression Analysis: OLS Asymptotics (Week 3 & Week 4)
Chapter 6 Multiple Regression Analysis: Further Issues (Week 4)
Chapter 7 Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables (Week 5)
Chapter 8 Heteroskedasticity (Week 5)
"The Basics" - Section Week 1 - April 4th 2012
Topics: Estimating the Mean, When is an estimate of mean unbiased? Unbiased estimator. Variance of a random variable,
- Week 1 Section Notes (gDoc pdf) by Jacopo
Installing and loading data with R software. Basic summary stats and histogram.
- How to Load a File into R Software (VIDEO)
- Sign-Up: receive updates about my sections, notes, etc.
Section Week 2 - April 11th 2012
Topics: Population Variance, Sample Variance, Standard deviation, Estimating the variance. Adjusting for using the sample mean. Variance of estimate of mean (mu-hat). T-distribution. Inference using t-distribution
- gDoc pdf: Week 2 Section Notes by Kun
Central limit theorem, t-test (small samples), test-statistics (larger samples). Hypothesis testing. T-distribution table.
- Curtis' Section Supplement (pdf, R-Code).
Homework 1 - due April 11th 2012
Expectations, mean, variance, and effect in non-systematic reporting error. R-softtware: basics, summary statistics, subsetting.
Section Week 3 - April 18th 2012
Topics: Inference about the location of the sample mean. T-statistic. Asymptotic results - the law of large numbers. The Central Limit Theorem
- gDoc pdf: Week 3 Section Notes by Curtis
large sample test-statistics, hypothesis testing in R software.
Homework 2 - Due April 18th 2012
Standard error of the mean, determining bias of an estimate, small and large sample hypothesis testing, t-distribution and z-distribution, central limit theorem in action,
In R-software: taking a sample of data, small and large sample hypothesis testing, taking multiple samples.
- .r file: solutions (by Curtis)
- pdf: #6 Solution. Effect on Variance of Measurement error independent of X (by Curtis)
Mid-Term One Review - April 18th 2012
Review of all material leading up to mid-term one.
There will be errors, so be vigilant!
- pdf: Econ113 Mid-Term One Review {S2012 Dobkin}
Section Week 4 - April 26th 2012
Topics: Derivation of beta-hat-1 and beta-hat-nought. Simple regression model example.
- .csv: section and class attendance and exam scores data.
- .R: R code from today's section.
- .pdf: Section Notes (by Jean Paul) (classdata.csv)
P-values. Regression, Ordinary Least Squares (OLS)
in R software.
Section Week 5 - May 2nd 2012
Topics: Conditions under which OLS gives an unbiased estimate. "Proof" that OLS is unbiased under Simple Regression (SR) Assumptions. Assessing the assumptions.
- pdf: Section Notes (by David) (Rcode, data_journals.csv, cigars.csv)
Regression, Ordinary Least Squares (OLS) in R software. Pretty useful notes.
Homework 3 - due May 4th
- pdf: questions (attendance.csv data needed for #4)
Calculate a P-Value. "Prove" Ordinary Least Squares (OLS) regression coefficients (beta-hat-nought and beta-hat-one) minimize the squared distance between the dependent variable and the regression line. Plot, calculate OLS coefficients by hand, and interpret. Plot, calculate OLS coefficients in R, and interpret.
- pdf solutions (by Curtis) (R Code)
Section Week 6 - May 10nd 2012
Topics: Calculating the bias. Variance of beta-hat-one. Variance of beta-hat-1 and inference.
- pdf: Section Notes (by Jae) (data, Rcode)
Multivariate Regression in R. Normality assumption. R's linear model regression summary. Hypothesis testing with regression results. Finding and interpreting a regression's P-Value.
Homework 4 - due May 11th
- pdf: questions (attendance.csv data)
Derive variance of OLS intercept estimate. Regression, hypothesis testing and interpretation. Examination of regression assumptions required for inference.
Section Week 7 - May 17nd 2012
Topics: TSS: total sum of squares. ESS: explained sum of squared. RSS: sum of squared residuals. R-squared, goodness of fit. Motivation for multivariate regression. Estimation and interpretation.
- pdf: Section Notes (by Curtis)
Homework 5 - due May 18th
- pdf: questions (attendance.csv data)
Derive multivariate coefficients. Multivariate regression in R. P-Values, R-squared. Derive effect of mean zero measurement error (attenuation bias). Measurement error in Data, example.
- solutions (by Curtis)
Problem 2 (R Code)
Homework 6 - due June 8th
- pdf: questions (NLSY Extract.csv data)
Multiple-variable regression. Level-level vs log-level regression. Interpretation, logging variables. Joint significance test, the F-test, plus interpretation. Normalizing variables and interpretation.
- solutions (pdf by Curtis)
Tip: F-Test critical value in R:
qf(ConfLevel,dof_Numerator,dof_Denominator)
CritVal <- qf(0.95,2,4852)
The Basics and Review
The Basics and Review
Table of Contents
1.0 Introduction
What is econometrics
Types of data
1.1 Definitions
Random variable:
Sample vs population:
Probability distribution:
Expected value of probability distribution:
Variance of probability distribution:
Expected value: (expected value theory)
Sample statistics and measures:
Unbiased:
Consistent:
1.2 Intuitive characterization of a distribution:
1.3 Measures of Center
Population mean
Sample mean:
Estimate of population mean.
Unbiased?
Median
Mode
Histogram - visualizing a center of a distribution
Assumptions
1A The sample is random
2A No systematic error
Proof of unbiased sample mean
Effect of adding systematic measurement error
Effect of adding unsystematic measurement error
1.4 Measures of dispersion
Range:
Variance
Population variance:
Discrete vs. continuous
Sample variance
Sample variance when population mean is known
Sample variance when population mean is unknown
Bias in estimates of variance
(bigger the sample, the lower the bias in the estimate for variance)
What determines the level of precision?
Effect of measurement error on variance
Effect of systematic measurement error on variance estimate
Effect of unsystematic measurement error on variance estimate
Standard deviation:
Histogram - visualizing the dispersion of a distribution
1.5 Describing the relatedness of two variables.
Covariance
Correlation
Scatterplot - visualizing the relatedness of two variables.
Examples of correlations via scatterplot
1.6 Odds and ends
Normal distribution.
Continuous random variable
Distribution of sample mean
Standard error of sample mean
Visualization
Histogram:
Frequency table:
Scatter plot:
R Software for Statistical Analysis
...link to overview website....
Regression Analysis
Ordinary Least Squares (OLS)
Derive the simple regression model
Simple Regression Analysis
Regressing one variable on one other variable.
Assumptions needed for ...particular interpretations
Assumption SR1:
Assumption SR2:
Assumption SR3:
Assumption SR4:
Assumption SR5:
Unbiased Estimate - "Proof" that if ASR1 thru ASR5 hold, then we have a causal estimate, E[\beta\hat_1 | x] = \beta_1 (plus lots of intuition)
Measurement Error:
Goodness of Fit - how well does the regression fit?
Total Sum of Squares (SST)
Residual Sum of Squares (SSR)
Explained Sum of Squares (SSE)
R-Squared (1):
Changing Units of Measurement (e.g. switching from thousands to millions....)
Nonlinear Effect (e.g. log-level, level-log, log-log, etc. Exponential growth)
Proof of OLS unbiasedness.
Variance of OLS Estimator
Variance of Beta\hat_0
Varaince of Beta\hat_1
Hypothesis Testing (Part 1)
Inference
Key Concepts: (all links to the subpage location)
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Problems and Applications
Key Concepts: (all links to the subpage location)
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Problems and Applications
Key Concepts: (all links to the subpage location)
Outline and example of problem (hypothesis about mean height)
Is our guess of a mean correct? compare estimate mean to ....
Central Limit Theorem
Law of large numbers
Assume x is distributed normally
Significance level:
Critical value:
Test-statistic: (t-stat)
Student's t distribution.
Large vs. small sample
Looking up critical value
degrees of freedom.
P-Value for a t-test
Computing P-Value for a t-test.
Interpreting P-value.
Multiple Regression Analysis
Multiple Regression Analysis
Introduction
Example with two independent variables
With k independent variable.
Interpreting multivariate repression results.
Comparing simple vs. multivariate regression estimates. (leads to omitted variable bias... )
R-Squared (Part 2) with multiple variables:
Regression with extraneous variables.
Mistake 1: including an irrelevant variable.
Omitted Variable Bias.
Mistake 2: failing to including a relevant variable.
Positive bias example:
Negative bias example:
Zero bias example:
Simple Regression Assumption 6 (SR6): Homoskedasticity
Homoskedasticity and inference.
Variance of multivariate regression parameter estimates.
Standard Error, se(\beta\hat)
Components of variance of parameter estimates
~ Error variance sigma^squared
~ Total Sample Variation
~ R-squared from regression x_j on all other independent variables.
Multicollinearity.
Variance of miss-specified model.
Problems and Applications
Key Concepts: (all links to the subpage location)
Key Concepts: (all links to the subpage location)
Problems and Applications
topic 1
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Gauss-Markov Theorem.
Simple Regression Assumption 7 (SR7): Normality.
Theorem Normal Sampling Distributions.
Seven Assumptions
Distribution of parameters if the errors are normal.
Normal sampling distribution.
Hypothesis Testing (Part 2)
Hypothesis Testing (Part 2)
t-distribution and hypothesis testing with regression estimates.
statistical significance.
One-sided test
Two-sided test
Other hypotheses: (not testing if beta is zero)
Interpreting regression output:
Examples
P-Value for a t-test
Computing P-Value for a t-test.
Interpreting P-value.
Practical significance. i.e. vs. statistical significance.
Confidence Intervals
Key Concepts: (all links to the subpage location)
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F-Test
Testing linear restrictions on parameters.
Example: Compare the return of a year of JC to the return on a year of univeristy education.
Testing multiple linear restrictions.
F-Test. Overall significance of a regression.
Testing general linear restrictions.
Adjusted R-Squared: (R-squared 3)
Limitation of R-squared
Key Concepts: (all links to the subpage location)
topic 1
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More "Types" of Regression Models
Effects of Scaling on Regression estimates
Simple example
Standardizing coefficients -
Models with logs
Level level regression
Log level regression
Exponential
Log log regression
Level log regression
Models with quadratics. (diminishing returns)
Models with interaction terms
Models with dummy variables.
More on Multiple Regression Models.
More on Multiple Regression Models.
Predictions and their standard errors
Prediction of value of a regression at at particular point.
What is our confidence at this point? i.e. what is our prediction and what is our standard error for this prediction?
Residual analysis
Heteroskedasticity and robust standard errors.
Testing for Heteroskedasticity.
Breusch-Pagan test for Heteroskedasticity
White test for Heteroskedasticity
~ potential issues
Adjusting for Heteroskedasticity
Weighted least squares.
Robust standard errors
Measurement Error revisited.
Measurement error in independent/explanatory variable
Classical error in variables
Effect on estimate
Effect on variance
Measurement error in dependent variable
Effect on estimate
Effect on variance
Key Concepts: (all links to the subpage location)
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Key Concepts: (all links to the subpage location)
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