Review Lecture: Guide to the SSSII Assignment

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Review Lecture Guide to the SSSII Assignment

• Gwilym Pryce
• 5th March 2006

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Plan

• Overview of Modelling Strategy
• Style issues
• technical report
• Presenting and Analysing output
• Themes to pull out of the results
• Specific Topics
• Chow tests
• Ramsey RESET test

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Overview of Modelling Strategy
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Style Issues

• Technical report
• As opposed to a policy/non-technical report
• Very little explanation of methods
• As opposed to a journal article
• Particular tests not described in detail
• Simply give reference e.g. White 1980
• Technical report will
• explain the rationale and practical steps
  involved in each test
• Details of the modelling strategy

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Presenting and Analysing output

• Condensing output
• SPSS output is very inefficient in its use of
  space
• E.g. SPSS Output from 10 regressions could take
  up 20 pages, but could easily be condensed to a
  single table that takes up one page.
• Rather than showing the workings of each time you
  run a test, show the workings for each type of
  test only once
• Condense subsequent output from repetitions of
  the same test into a table or graph.
• E.g. if carrying out Ramsey RESET test on each
  regression, simply list the Ramsey test statistic
  with R2, n etc in regression output table.

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• Explaining output
• Condensing the presentation of output gives you
  more space to spend on describing and explaining
  your tables
• One table of 10 regressions might only take up
  one page, but explanation may take up five pages.
• Explain each coefficient
• Is the sign as anticipated?
• What does the coefficient mean?
• Does the coefficient change in value across your
  various model specifications/sub-samples?
• Explain the diagnostics
• Why does the sample size change?
• Explain and justify your modelling decisions

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What does the coefficient mean?

• E.g. Coefficient on age of dwelling
• Older dwellings seem to be worth more
• Does this mean that properties appreciate in
  value as they get older?
• I.e. negative depreciation? Contradictions basic
  accounting theory!
• Does the coefficient mean what you think it means?

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Themes that should run through your explanations

• (i) What is the real world meaning of you model?
  What are its implications? How useful is it?
• The reason why we dont recommend an automated
  approach to regression model building is that the
  outcome can be meaningless
• I.e. can have good R2 etc but impossible to
  interpret
• Can the model be used to simulate policy
  scenarios?
• Difference between size of effect and
  significance of effect
• May be highly significant but a small effect.

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• (ii) How do you know that your model is correctly
  specified?
• The robustness of the coefficients you have
  estimated rest on how well you have specified the
  model.
• Checked for omitted variable bias, structural
  breaks, multicolinearity, heterskedasticity etc.

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• (iii) How generalisable is your model?
• How random is the sample?
• E.g. missing values can mean that you end up with
  a model that is run on a very non-random sample
• How random are the missing values?
• Structural breaks?
• Can one model really be used to represent all
  observations?
• Inference?
• Can you infer from your sample to the population?
• How narrow are the confidence intervals?

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Specific Topics

• Chow Test
• Ramsey RESET test

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Chow TestTesting for Structural Breaks

• Sometimes we want to test whether the estimated
  coefficients change significantly if we split the
  sample in two at a given point
• These tests are sometimes called Chow Tests
  after one of its proponents.
• There are actually two versions of the test
• Chows first test
• Chows second test

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(a) Chows First TestUse where n2 gt k

• (1) Run the regression on the first set of data
  (i 1, 2, 3, n1) let its RSS be RSSn1
• (2) Run the regression on the second set of data
  (i n11, n12, , end of data) let its RSS be
  RSSn2
• (3) Run the regression on the two sets of data
  combined (i 1, , end of data) let its RSS be
  RSSn1 n2

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• (4) Compute RSSU, RSSR, r and dfU
• RSSU RSSn1 RSSn2
• RSSR RSSn1 n2
• r k total no. of coeffts including
  the constant
• dfU n1 n2 -2k
• (5) Use RSSU, RSSR, r and dfU to calculate F
  using the general formula for F and find the sig.
  Level

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(b) Chows Second TestUse where n2 lt k (I.e.
when you have insufficient observations on 2nd
subsample to do Chows 1st test)

• (1) Run the regression on the first set of data
  (i 1, 2, 3, n1) let its RSS be RSSn1
• (2) Run the regression on the two sets of data
  combined (i 1, , end of data) let its RSS be
  RSSn1 n2

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• (3) Compute RSSU, RSSR, r and dfU
• RSSU RSSn1
• RSSR RSSn1 n2
• r n2
• dfU n1 - k
• (4) Use RSSU, RSSR, r and dfU to calculate F
  using the general formula for F and find the sig.

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Example of Chows 1st Test

• n1 before 1986 n2 1986 and after

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Ramseys Regression Specification Error Test
(RESET) for omitted variables

• Ramsey (1969) suggested using yhat2, yhat3 and
  yhat4 as proxies for the omitted and unknown
  variable z

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RESET test procedure

• 1. Regress y on the known explanatory variable(s)
  x
• y b1 b2x
• and obtain the predicted values, yhat
• 2. Regress y on x, yhat2, yhat3 and yhat4
• y g1 g2 x g3 yhat2 g4 yhat3
  g5yhat4

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• 3. Do an F-test on whether the coefficients on
  yhat2, yhat3 and yhat4 are all equal to zero.
• Restricted Model
• y b1 b2x
• No yhat2, yhat3 and yhat4 on the RHS
• I.e. coefficients on yhat2, yhat3 and yhat4 are
  restricted to 0
• Unrestricted Model
• y b1 b2x b3 yhat2 b4 yhat3 b5 yhat4
• I.e. coefficients on yhat2, yhat3 and yhat4 are
  not restricted to 0
• Null and alternative hypotheses
• H0 b3 b4 b5 0 gt no omitted variables
  in y b1 b2x
• H1 there are omitted variables in y b1 b2x
• If the significance level is low and you can
  reject the null that b3 b4 b5 0, then there
  is evidence of an omitted variable(s)

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Summary

• Overview of Modelling Strategy
• Style issues
• technical report
• Presenting and Analysing output
• Themes to pull out of the results
• Specific Topics
• Chow tests
• Ramsey RESET test