[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>
--
Allin Cottrell
Department of Economics
Wake Forest University, NC