Teaching is hard work (and also quite time consuming)! A quick update on my research, with more to follow later today...
For the last two weeks, I have been teaching myself how to program in Python. I have now done a quick pass through tutorials for all of the major modules that I suspect I will be using:
I now plan to double back and do more detailed work with each of the packages goals in mind. The first thing I plan to do is implement the Clauset et al (2009) procedure to detect power laws in empirical data using Python and then systematically apply the procedure to major economic variables. The Clauset et al procedure relies on MLE and an iterative application of the Kolmogorov-Smirnov (KS) test to determine the threshold value above which the power law is a good model. The authors are heavily critical of least-square approaches to fitting power laws to data and detail the issues with using such procedures. Interestingly most empirical studies of power laws in economics (that I have seen) seem to use ad hoc least-squares approaches.
Whether the results of this study will be publishable or not I have no idea, but I think it would be very useful to have an understanding of which economic variables exhibit power law behavior, and which are simply heavy-tailed (i.e., log-normal or something else)...if nothing else I will add a new tool to my arsenal that has significant practical applications...
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To play devil's advocate:
ReplyDeleteWhy do you think it would be useful to know which variables exhibit power-law behavior?
I would argue that there are both practical and theoretical reasons why...
ReplyDeleteFrom the practical perspective, being able to have a better understanding of the "true" distribution of the extreme values of important economic variables will help researchers to use the correct statistical techniques in their empirical models. Along these lines, I think it is important to be able to "bin" variables as to whether or not they have heavy tails, and for those that do have heavy tails are they log-normal? or heavier (such as a power law)?
On the theory side, I think that there should be some "deep" reason why some economic variables have heavy tails. I think this is an example of how good empirical work could help drive theory...first we need to determine which variables have heavy tails, then we need to determine which variables have log-normal tails and which have heavier than log-normal tails, and then we can start to think why this should be the case theoretically...
At least this is my current justification...thanks for keeping me honest!