|
||||||
Applied
Econometrics
Econ 508 - Fall 2007 e-Tutorial 14: Measures of Inequality |
||||||
![]() |
||||||
Welcome
to the fourteenth issue of e-Tutorial. This time we focus on measures of
inequality. We will suggest some basic methods to calculate the Hill estimator,
the Lorenz curve, and the Gini coefficient. The data set to be used is
the same from the problem set 4. You can use the instructions to download
the data provided in e-Tutorial 13.
Hill Estimator I suggest a STATA do-file to compute the Hill estimator mentioned in Prof. Koenker's "Appendix A - Concentration of Productivity in Phuzics Scholarship". You can download this do-file here, or see below the code. The idea is to calculate the index of concentration "alpha" for the years between 1970 and 1990, and check if there is any unbiased trend. As mentioned in the note, if there is an unbiased positive trend, you can infer that phuzics productivity is becoming less concentrated, and the field is becoming less scientific (according to Parzen's definition of the term). An unbiased negative trend would mean the reverse. The code below can calculate the alpha-coefficient of concentration for a given year (say, 1970). You are expected to adjust the code such that you can reproduce the experiment for the other periods: **Start
here**
Using the data set phuzics01.dta, the results are as follows: .
use "C:\phuzics01.dta", clear
Hence, the alpha-coefficient
of concentration is about 3.2. You need to go ahead and calculate similar
coefficients for the remaining years, and then plot the coefficients along
time.
Bootstrap Bias-Correction for the Hill Estimator: In STATA, you can implement the bootstrap bias correction for the Hill estimator, suggested in Prof. Koenker's "Appendix A - Concentration of Productivity in Phuzics Scholarship", by using the command bsample. I will do that for one year, say, 1970, and then you can replicate the experiment for other years. The strategy is as folows: Numerator: The first step is to calculate the numerator of the formula on page 2 of the note "Appendix A - Concentration of Productivity in Phuzics Scholarship", called alpha_N. This is done as follows. 1) Open the original data
set;
Here is the code for that: **Start
here**
The final result is
going to be used as the Hill estimator for the pooled sample for all years
of interest. This corresponds to Appendix A's "alpha_N".
Denominator: 1) Open the original data
set;
For example, here is a sequence
of these preliminary commands and results:
**Start
here**
This routine will give you one bootstrapped alpha for the year 1970. You need to repeat the experiment "B" times (say, 20 times), and get "B" (say, 20) different bootstrapped alphas for 1970. After that, take the average of those "B" (say, 20) alphas and use this number as the denominator of the formula on page 2 of Prof. Koenker's "Appendix A - Concentration of Productivity in Phuzics Scholarship". Finally, you need to apply the formula: multiply the original Hill estimator of 1970 by the pooled Hill estimator (here called "numerator") and divide it by the average bootstrapped estimator for 1970 (here called "denominator"), so that you find a bias-corrected Hill estimator for the year 1970. This procedure is required
for every year in the period 1970-1990. Each year will have its respective
corrected alpha. The final step is to plot those corrected alphas along
time, and check if there is any trend.
Lorenz Curves and Gini Coefficient STATA provides add-ins to
calculate these statistics. You can type
This will provide a menu of add-in programs related to the topic. You need to install the selected package and the help files. I will let you free to decide whether to use add-ins or to write your own code. The most important thing, though, is to understand the theoretical background of such measures, which we will discuss in class.
|
||||||
![]() |
Last update: November 13, 2007 |