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Review Lecture: Guide to the SSSII Assignment

Review Lecture: Guide to the SSSII Assignment. Gwilym Pryce 5 th March 2006. 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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Review Lecture: Guide to the SSSII Assignment

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  1. Review Lecture: Guide to the SSSII Assignment Gwilym Pryce 5th March 2006

  2. 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

  3. Overview of Modelling Strategy

  4. 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

  5. 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.

  6. 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

  7. * 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?

  8. Themes that should run through your explanations: • (i) What is the real world meaning of you model? What are it’s implications? How useful is it? • The reason why we don’t 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.

  9. (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.

  10. (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?

  11. Specific Topics • Chow Test • Ramsey RESET test

  12. Chow Test:Testing 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: • Chow’s first test • Chow’s second test

  13. (a) Chow’s First TestUse where n2 > 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 = n1+1, n1+2, …, 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

  14. (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:

  15. (b) Chow’s Second TestUse where n2 < k(I.e. when you have insufficient observations on 2nd subsample to do Chow’s 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

  16. (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.:

  17. Example of Chow’s 1st Test: n1: before 1986: n2: 1986 and after

  18. Ramsey’s 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:

  19. 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 + g2x + g3yhat2 + g4 yhat3 + g5yhat4

  20. 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 + b3yhat2 + 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 => 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)

  21. 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

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