REVIEW OF EMPIRICAL STUDY AND CLASSICAL LINEAR REGRESSION MODEL
1. Steps in an empirical study
a. Objective
b. Data
c. Get to know data
d. Statistical model
e. Estimation, hypothesis testing, goodness-of-fit
f. Conclusions
2. Objective
a. Explanation or prediction
b. Economic relationship(s)
c. Population of interest
d. Four questions
1. Do one or more variables have an effect?
2. What is the direction of the effect(s)?
3. What is the size of the effect(s)?
4. Which variables have the biggest and smallest effect?
3. Data
a. Sample
b. Population of interest
c. Population studied
4. Get to know data
a. Get to know variables
b. Organize, summarize, and describe the data
1. Univariate and bivariate descriptive statistics.
5. Statistical model
a. Equation
b. Variables
1. Variables of interest
2. Control variables
c. Functional Form
1. Linear in parameters
2. Often used functional forms
a. Linear in variables
b. Double-log
c. Log-linear
d. Quadratic
3. Interpretation of regression coefficients
d. Error term
1. Error term has mean zero
2. Error term has constant variance
3. Errors are uncorrelated
4. Error term has a normal distribution
5. Error term in not correlated with any explanatory variable
e. Statistical model in matrix format
6. Estimation
a. Choice of estimator
1. Least squares estimation procedure
2. Maximum likelihood estimation procedure
b. Least squares estimation procedure
1. OLS estimator
2. Properties of the OLS estimator
a. Mean
1. Error term has mean zero
2. Error term not correlated with explanatory variables
b. Variance and covariance
1. Error term has constant variance
2. Errors are uncorrelated
c. Variance-covariance matrix of estimates
d. Small sample properties
1. Unbiased
2. Efficient
e. Large sample properties
1. Consistent
c. Maximum likelihood estimation procedure
1. Maximum likelihood estimator
d. Estimator for error variance
e. Estimated variance-covariance matrix of estimates
7. Hypothesis tests
1. t-test
2. F-test
3. Likelihood ratio test
4. Wald test
5. Lagrange multiplier test
8. Goodness-of-fit
1. R-squared statistic
9. Conclusions
1. Do one or more variables have an effect?
a. Hypothesis test approach
b. Strength of evidence approach
2. What is the direction of the effect(s)?
a. Algebraic sign
3. What is the size of the effect(s)?
a. Marginal effect
b. Elasticity
4. Which variables have the biggest and smallest effect?
a. Elasticity
5. Validity of conclusions
a. Internal validity
1. Are the estimates of the effects unbiased?
a. Omitted confounding variables
b. Reverse causation
2. Are the estimates of the standard errors unbiased?
a. Heteroscedasticity
b. Autocorrelation
b. External validity