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 R 2, 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 R 2 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?
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 Test Use where n 2 > k (1) Run the regression on the first set of data (i = 1, 2, 3, … n 1 ) & let its RSS be RSS n1 (2) Run the regression on the second set of data (i = n 1 +1, n 1 +2, …, end of data) & let its RSS be RSS n2 (3) Run the regression on the two sets of data combined (i = 1, …, end of data) & let its RSS be RSS n1 + n2
14 (4) Compute RSS U, RSS R, r and df U : –RSS U = RSS n1 + RSS n2 –RSS R = RSS n1 + n2 –r = k = total no. of coeffts including the constant –df U = n 1 + n 2 -2k (5) Use RSS U, RSS R, r and df U to calculate F using the general formula for F and find the sig. Level:
15 (b) Chow’s Second Test Use where n 2 < k (I.e. when you have insufficient observations on 2 nd subsample to do Chow’s 1 st test) (1) Run the regression on the first set of data (i = 1, 2, 3, … n 1 ) & let its RSS be RSS n1 (2) Run the regression on the two sets of data combined (i = 1, …, end of data) & let its RSS be RSS n1 + n2
16 (3) Compute RSS U, RSS R, r and df U : –RSS U = RSS n1 –RSS R = RSS n1 + n2 –r = n 2 –df U = n 1 - k (4) Use RSS U, RSS R, r and df U to calculate F using the general formula for F and find the sig.:
17 Example of Chow’s 1 st Test: n 1 : before 1986: n 2 : 1986 and after
20 Ramsey’s Regression Specification Error Test (RESET) for omitted variables: Ramsey (1969) suggested using y hat2, y hat3 and y hat4 as proxies for the omitted and unknown variable z:
21 RESET test procedure: –1. Regress y on the known explanatory variable(s) x: y = b1 + b2x and obtain the predicted values, y hat –2. Regress y on x, y hat2, y hat3 and y hat4: y = g 1 + g 2 x + g 3 y hat2 + g 4 y hat3 + g 5 y hat4
22 –3. Do an F-test on whether the coefficients on y hat2, y hat3 and y hat4 are all equal to zero. Restricted Model: y = b 1 + b 2 x –No y hat2, y hat3 and y hat4 on the RHS –I.e. coefficients on y hat2, y hat3 and y hat4 are restricted to = 0 Unrestricted Model: y = b 1 + b 2 x + b 3 y hat2 + b 4 y hat3 + b 5 y hat4 –I.e. coefficients on y hat2, y hat3 and y hat4 are not restricted to = 0 Null and alternative hypotheses: H 0 : b 3 = b 4 = b 5 = 0 => no omitted variables in y = b 1 + b 2 x H 1 : there are omitted variables in y = b 1 + b 2 x If the significance level is low and you can reject the null that b 3 = b 4 = b 5 = 0, then there is evidence of an omitted variable(s)
23 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