**We covered the following topics in the course:**

1. Assumptions required for estimates to be BLUE

2. Hypothesis testing:

a. t- tests (both one-sided and two-sided)

b. Joint hypotheses (F-Tests, Chi-square tests, etc.)i. Exclusion restrictions

ii. Linear combinations of parameters

3. Heteroskedasticity

a. What is heteroskedasticity?

b. How heteroskedasticity occur?

c. The consequences of estimating a heteroskedastic model with OLS

d. Testsi. LaGrange Multiplier Tests (Models 1, 2, and 3)

Model 1:

Model 2:

Model 3:ii. Goldfeld-Quandt test

iii. White's teste. Corrections/Estimation procedures

i. Feasible GLS

Model 1:

Model 2:

Model 3:iii. White’s correction

8. Autocorrelation

a. What is it and why might it occur?

b. Consequences of ignoring serial correlation and estimating with OLSi. Model with serially correlated errors (model 1 in class)

ii. Model including a lagged dependent variable (model 2 in class)

iii. Model with both a lagged dependent variable and serial correlated errors (model 3 in class)c. Tests for serial correlation

i. The Durbin-Watson test.

ii. Durbin's h-test.

iii. The Breusch-Godfrey test for higher order serial correlation.d. Corrections

i. Non-linear estimation

9. Testing for ARCH errors

10. Stochastic Regressors and Measurement Errors

a. Assessing the bias and consistency of an estimator

b. Errors in variablesi. Consequences of estimating with OLS when there are errors in measuring the right-hand side variables (i.e. errors in measuring the independent variables, the X's).

ii. Consequences of estimating with OLS when there are errors in measuring the dependent variable (i.e. in the measurement of Y).

iii. Application of errors in variables: Friedman's Permanent Income Hypothesis.c. Instrumental variable estimation

i. What is an instrument.

ii. How is IV performed?

iii. Show how IV estimation can solve the problem of correlation of the right-hand side variables with the error term.

11. Simultaneous equation models

a. Structural equations (behavioral, identities, equilibrium conditions, technical equations) and reduced form equations. Endogenous, exogenous, and predetermined variables.

b. Consequences of ignoring simultaneity, i.e. demonstrate simultaneity bias.

c. Underidentified models, exactly identified models, and overidentified models

d. Estimation by 2SLS

12. Multicollinearity

a. What is multicollinearity and how does it affect OLS estimates and standard errors?

b. Detection of multicollinearity

c. What to do for perfect and imperfect multicollinearity.

13. Specification tests

a. LM test for adding a variable to a model

b. LM test for adding a variable in a system of equations

c. LM test for serial correlation in a system of equations

d. AIC and SIC criterion

14. Qualitative and limited dependent variables

a. Linear probability model

i. description of model, problems, and estimation

b. Probit model

i. description of model and estimation

c. Logit model

i. description of model, attractive properties, and estimation

d. Limited dependent variables

i. description of the model when the dependent variable is limited, problems with OLS, and estimation

15. Maximum likelihood

a. Brief description of what maximum likelihood estimation does.

b. properties of maximum likelihood estimators.

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