Were interested in the probability distribution of regression coefficients. But lets start with something
simpler, the probability distribution of a sample mean. (The first question is easy, youve done m
Professor Richard Startz
Be able to understand, interpret, and implement multiple regression
and related statistical techniques
Know the limitations and pitfalls of regression methods
Be able write a focused e
I. Academic salaries and gender (on slightly dated data).
II. When is OLS Unbiased?
a. Handout on website
b. What happens if you omit a required variable?
c. What happens if you include an extraneous variable?
a. Tests of multiple restrictions
b. Joint confidence intervals
c. Chow tests
II. Categorical variables with more than one category
a. Make multiple dummies
b. Sometimes imposing linearity of response isnt a
I. Regression example: How does having children in the home affect wages?
II. Classical regression assumptions
a. yi xi ui is true model
b. x fixed, or at least exogenous
c. E ui 0
2 , i j
d. E uiu j
0, i j
I. Gauss-Markov proof for simple regression
a. OLS is BLUE
b. Use web handout
c. In multiple regression is holds for each coefficient.
a. Think cross-partials
III. Taylor Series Approximations
I. Type I and Type II errors
a. Size and power
Generalized Least Squares (GLS)
i. What happens if you run OLS?
ii. Transforming the equation and running GLS
iii. Huber-White Robust standard er
I. Special guest: Michael Dueker, Head U.S. Economist, Russell Investments
II. Serial correlation
a. Specifically, autoregressive model:
i. AR(1): ut ut 1 t
ii. AR(2): ut 1ut 1 2ut 2 t
III. Lagged Dependent Variables
a. Using exogenous variables
i. yT k xT k
b. Lagged endogenous variables
i. If yt yt 1 ut , yT 1 yT , yT 2 2 yT
c. Whats the goal? Coefficient or forecast accuracy?
II. Vector Autoregressions (VAR)
I. Limited dependent variables
a. Explain probability of outcome, rather than outcome
b. Probit model
II. Maximum likelihood estimation
Textbook Chapter 10
I. Generalized Least Squares (GLS)
i. Transforming the equation and running GLS
ii. Huber-White Robust standard errors.
II. Serial correlation (well see how far we get)
a. In general
I. ARIMA Models AutoRegressive-Integrated-Moving Average
III. AR(p) models
V. Integrated models
b. unit root, and tests for nonstationar
I. Go back over t-statistic versus z-score
II. Least squares as data fitting solving the equations to minimize the sum of
a. y x u
b. y x u
c. y 1x1 2 x2 u
d. yi 1xi1 2 xi 2
k xik ui
III. True DGP ve
I. More on regression specification
a. Dummy variables
b. What should you control for? Direct vs indirect effects
a. Tests of multiple restrictions
b. Joint confidence intervals (if time)
c. Chow tests (if t
Is education worth it a regression example.
a. Regression coefficient as marginal response.
b. Multiple regression to control for conflating variables
Global warming in Seattle.
a. Estimate model over sample period
1. This question introduces the idea of joint distribution. Consider two discrete random
variables X and Y, each of which can take four possible values. X is the weather of Seattle,
which can be sunny (X
1. Assume x and u both have expected value zero and that the variances and covariances are
given respectively by x , u , xu . Assume y is generated by y x u . Derive the
correlation coefficient b
In the questions that follow, suppose that xt has been zero for a long time and that xt then
changes to 1.0 and stays there.
1. If the equation for yt is yt xt , describe the time path for the change for
This is a group homework. Three is a good size for a group, but whatever size you pick is fine. Each
person needs to submit their answers to get a grade, but its fine if each person in the group submits
Read one or more term papers that are posted on the web site from previous years. Write
a paragraph that tells what question the author looked at, what the substantive answer
was, and identify where t
Consider the regression model
yi 1 xi1 2 xi 2 ui ,
The first step in deriving the least squares estimators of 1 and 2 is to write-out the two firstorder conditions for minimizing the sum of squared re
According to the Fisher hypothesis, an increase in expected inflation is passed one-for-one into
nominal interest rates.
Unfortunately, we observe actual rather than expected inflation. According to the
Part I - Excerpt from Yale Stat 102 Homework
In 1639, a "Court Holden 4th of December" decided how the colonists were to divide up the land
in the new settlement of New Haven. The "First Division" of lan
This is an exercise in conditional versus unconditional forecasting.
In the land of Krispie, the economy consists of three variables: SNAP, CRACKLE, and POP.
The data generating process for the ec
I. Example for the birds: interpreting regression
II. Estimator as random variable drawn from distribution over repeated
III. Review of math and statistical concepts
Example of throwing a die and finding di
I. Do a regression example relating unemployment and GDP
II. Derive tests on sample mean
c. Various p-values
d. two-sided versus one-sided tests
III. Confidence intervals
Maybe derive least squa
Use the data set UWLAW2000.wf1 for this homework. To be sure you have valid data set the
smpl if gpa<=4 and lsat>99 and lsat<200
The variable ADMIT is a dummy for whether an applicant was ad
I. Endogeneity X is correlated with u
a. If RHS variable is correlated with error term its bad news
b. IV (TSLS) can fix, but auxiliary information is needed.
c. Plim is (probability) limit of expectation