Re: [Gretl-devel] cross-sectional mean, variance

Serendipitous fallout from adding lists to genr. It turns out that two of my students this semester are working on research papers dealing with convergence or non-convergence (of GDP per capita among ASEAN countries in one case, and of employment characteristics among US cities in the other). There are several ways of assessing convergence, but one nice simple way to start is to create a time-series plot of the cross-sectional variance (or coefficient of variation, perhaps) of the variable of interest. Sigma-convergence, it's called: does the variance show a declining trend, or what? You can compute this in gretl, but it's a bit fiddly because gretl is "column-oriented". Suppose you have a time-series data set with GDP for k countries or regions represented as k distinct variables. You can compute the desired time-series of cross-sectional variance by (a) transposing the data set or (b) stacking the data into a panel then looping across sub-samples restricted by year. Perfectly do-able but a bit daunting for a beginner. Lists to the rescue. I've extended the functions mean(), sd() and var() so that if you supply a list argument the result is a series each of whose values is the cross-sectional statistic for the listed variables in the given period. Here's an example illustrating strong sigma-convergence of per capita income across the regions of the US from the onset of the second world war till around 1980. (Run in the GUI when connected to the internet, and I hope you'll agree it's quite cool.) <script> # open US state/regional database on server open beapira --www setobs 1 1929 1973 # d/l regional income per capita data a91200 a92200 a93200 a94200 a95200 a96200 a97200 a98200 list L = a* # cross-sectional mean, std. dev., coeff of variation genr Lm = mean(L) genr Ls = sd(L) genr Lcv = Ls/Lm # print results print Lm Ls Lcv --byobs # time series plot of coeff of variation convplot <- gnuplot Lcv time --with-lines \ { set title "See the convergence?"; } convplot.show </script>