« August 2006 | Main | October 2006 »

September 28, 2006

Left-Out Variables

We considered the consequences of mistakenly leaving out a regressor.

Set up for the two-variable regression model:

P9280004a.jpg

Consider two possibilities:

P9280006a.jpg

If the truth is I and we pick I, we are in good shape:

P9280010a.jpg

An important proposition:

P9280012a.jpg

If the truth is II and we pick I, we have a left-out variable, which effectively becomes part of the error term.

P9280008A.jpg

We can derive an expression for the resulting left-out variable bias.

P9280018a.jpg

P9280020a.jpg


Posted by bparke at 09:29 PM | Comments (0)

September 26, 2006

Functional Form

Somebody forgot his camera today, but the material we discussed resembled a Fall 2005 lecture and a Spring 2005 lecture.

Posted by bparke at 08:24 PM | Comments (0)

September 21, 2006

The F Test

We can use an F test to test a hypothesis involving more than one restriction.

P9210002a.jpg

We created rvm2 = rvm*rvm to show that an F test for one linear restriction is equivalent to a t test.

P9210004a.jpg

Posted by bparke at 10:52 PM | Comments (0)

September 19, 2006

Multiple Regression

P9190054a.jpg

P9190056a.jpg

P9190058a.jpg

Posted by bparke at 10:29 PM | Comments (0)

September 14, 2006

Ordinary Least Squares

P9140021a.jpg

P9140023a.jpg

P9140029a.jpg

P9140031a.jpg

What is better, large n or small n? What is better, big V(x) or small V(x)?

P9140030a.jpg

Supplement -- a way to think about the model:

P9140033a.jpg

Posted by bparke at 10:32 PM | Comments (0)

September 12, 2006

Random Numbers

Stata generates random numbers uniformly distributed between 0 and 1 if you use "gen x = uniform()". To generate standard normal random variables use "gen e = invnorm(uniform())".

P9120003a.jpg

Posted by bparke at 10:23 PM | Comments (0)

Ordinary Least Squares

Posted by bparke at 09:52 PM | Comments (0)

Monte Carlo "do" File

The following "do" file will probably be used in today's lecture.
mc1.do

Posted by bparke at 12:13 AM | Comments (0)

September 07, 2006

Hypothesis Testing

The basic strategy

P9070087a.jpg

One-tail test

P9070078a.jpg
P9070081a.jpg

Two-tail test

P9070085a.jpg

P9070091a.jpg

Posted by bparke at 05:49 PM | Comments (0)

September 05, 2006

Bayesian vs. Classical Statistics, including Confidence Intervals

A fairly innovative approach via Bayesian statistics reviewed confidence intervals (of classical statistics).

P1010053a.jpg

P1010055b.jpg

P1010055a.jpg

P1010057a.jpg

P1010056b.jpg

P1010058a.jpg

P1010060a.jpg

If you were in class, you know that the last diagram illustrates a point of profound importance.

Posted by bparke at 09:27 PM | Comments (0)