Topic 8: Testing & Structural change Flashcards Preview

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Flashcards in Topic 8: Testing & Structural change Deck (9)
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How do we test conditions, ie B1 = B2

We rearrange to get B^1 - B^2 = 0 then consider that any addition of normal variables are normally distributed



How do we test restictions

Using a t-test or f-test


How do we test a restriction, t-test style?

Say we test B1+B2=1, rearrange to B1+B2-1=0 t-test = (B1^+B2^-1)/SE(B1^+B2^-1)


How do we test a restriction, F-test style?

Using restricted least squares, eliminate as many estimates as restrictions. For B1+B2 = 1, you get Yi = B1 + Xi(1-B1). Then we get u^r, the residuals for our restricted regression. Our F-test is then shown below; where m = number of restrictions, n = observations k = parameters in unrestricted regression

note, missing divide by m in diagram



What is meant by a structural change in the data?

A change in the underlying PRF that occurs in the observations, present usually in time series


How is a chow test performed?

1. Obtain full RSS, then RSS1 & RSS2 for the two seperate groups.

Now RSS restricted = RSS1+RSS2.

2. Make Fstat


What does the chow test assume? Are there problems/ How do we diagnose?

-Constant variance in groups

-> can be tested by σ^2 / σ2 ~ F(n1-k,n2-k)

-identical & independent distributions



What is the Chow predictive failure test?

A test which considers the whole sample and one group within the sample, used when the other group has a small number of observations. B1^ & B2^ are used to predict observations for the second group. RSS for the first group is RSSur, RSS for the entire sample is RSSr. Test is


Name some tests for non-linear models. How do thse tests work?

- Likelyhood ratio, -Wald - Lagrange multiplier

With large sample sizes they are identical

1. Find log-likelyhood ratio without restrictions (ULLF)

\2. Find log-likelyhood ratio with restrictions (RLLF)

3. calculate LR = 2(ULLR-RLLR)

4. use R ~ chi(m) to run test