Problem Set 2:
Inflation and Central Bank Independence
Due Friday October 14, 2011
DASL, the Data and Story Library at Carnegie Mellon, has data on the inflation rate, two measures of central bank independence (of which we will focus on one, the questionnaire-based index), and a binary indicator of development, for 23 countries; see http://lib.stat.cmu.edu/DASL/Stories/inflation.html for details.
A copy of the data in Stata format is available in the datasets section of the course website, and can be read into net-aware Stata using
use http://data.princeton.edu/wws509/datasets/inflation
Note that the measure of inflation is missing for Lebanon. Stata will automatically exclude it from all regressions using inflation as outcome.
[1] The Inflation Rate
(a) Plot the inflation rate versus the questionnaire-based measure of central bank independence, using different symbols for developed and developing countries. Make sure you identify the point on the lower left as Ethiopia. (In part d you will add to this plot; turn in only the final result.)
For simplicity, exclude Ethiopia from the analyses in parts 1.b, 1.c and 1.d
(b) Regress the inflation rate on the indicator variable for developed countries and interpret the coefficients. Test the significance of the coefficient of developed countries.
(c) Add the measure of central bank independence to the model and comment on the results. What happens to the difference between developed and developing countries once you adjust for central bank independence?
(d) Test whether the slope of inflation by central bank independence is the same in developed and developing countries by adding an interaction effect. Superimpose the fitted lines from this model on the plot of part a.
(e) Comment briefly on how the conclusions of the analysis in part 1.d would be altered if we included Ethiopia.
[2] Working with Log(Inflation)
(a) Plot the log of the inflation rate versus the measure of central bank independence. (In part d you will add to this plot. Turn in only the final result.)
For simplicity, exclude Ethiopia from the analyses in parts 2.b, 2.c and 2.d
(b) Regress the log of the inflation rate on the indicator variable for developed countries and interpret the coefficient of developed countries. (Be careful if your interpretation relies on a common approximation; you should make sure it is reasonable in this case.)
(c) Add the measure of central bank independence to the model and interpret the estimated slope.
(d) Test for an interaction between central bank independence and the indicator of development. Superimpose the fitted lines from this model on the plot of part 2.a. Do we have evidence that these lines are not parallel?
(e) Comment briefly on how including Ethiopia would alter your conclusions in part 2.d.
[3] Regression Diagnostics
Calculate the following diagnostics for the additive model of part 2.c including Ethiopia, so we can see what the different measures would say about this country.
(a) Compute leverages and comment briefly on the four countries with the most leverage. Why do you think Costa Rica comes at the top of the list?
(b) Calculate the jack-knifed residuals and list any countries with values in excess of 2. Do we have evidence of any outliers, after making allowance for the fact that we are making multiple tests?
(c) Compute the Cook distances. Any indication of an influential observation? Why is Ethiopia, at the low end of the scale of central bank independence, a lot more influential than Germany, at the high end?
[4] Box-Cox Transformations
(a) Did we need to transform the data? Was the natural logarithm a good transformation? Explore these two questions in a Box-Cox framework by formally testing for the log and identity transformations using an additive model excluding Ethiopia.
(b) Plot the Box-Cox profile log-likelihood as a function of the transformation parameter. The Stata logs section of the website shows how to do this in a simple loop.Posted Tuesday, October 4, 2011