Merges a list of clubs created with the function findClubs by either Phillips and Sul method or von Lyncker and Thoennessen procedure.
mergeClubs(
clubs,
time_trim,
mergeMethod = c("PS", "vLT"),
threshold = -1.65,
mergeDivergent = FALSE,
estar = -1.65
)Ad object of class convergence.clubs, containing a list of
Convergence Clubs, for each club a list is return with the
following objects: id, a vector containing the row indices
of the units in the club; model, a list containing information
about the model used to run the t-test on the units in the club;
unit_names, a vector containing the names of the units of the club (optional,
only included if parameter unit_names is given)
an object of class convergence.clubs (created by findClubs function)
a numeric value between 0 and 1, representing the portion of
time periods to trim when running log t regression model; if omitted, the same
value used for clubs is used.
character string indicating the merging method to use. Methods
available are "PS" for Phillips and Sul (2009) and "vLT" for
von Lyncker and Thoennessen (2017).
a numeric value indicating the threshold to be used with the t-test.
logical, if TRUE, indicates that merging of divergent units should be tried.
a numeric value indicating the threshold \(e^*\) to test
if divergent units may be included in one of the new convergence clubs.
To be used only if mergeDivergent=TRUE
Phillips and Sul (2009) suggest a "club merging algorithm" to avoid over determination due to the selection of the parameter \(c^*\). This algorithm suggests to merge for adjacent groups. In particular, it works as follows:
Take the first two groups detected in the basic clustering mechanism and run the log-t test. If the t-statistic is larger than -1.65, these groups together form a new convergence club;
Repeat the test adding the next group and continue until the basic condition (t-statistic > -1.65) holds;
If convergence hypothesis is rejected, conclude that all previous groups converge, except the last one. Hence, start again the test merging algorithm beginning from the group for which the hypothesis of convergence did not hold.
On the other hand, von Lyncker and Thoennessen (2017), propose a modified version of the club merging algorithm that works as follows:
Take all the groups detected in the basic clustering mechanism (P) and run the t-test for adjacent groups, obtaining a (M × 1) vector of convergence test statistics t (where \(M = P - 1\) and \(m = 1, \dots, M\));
Merge for adjacent groups starting from the first, under the conditions \(t(m) > -1.65\) and \(t(m) > t(m+1)\). In particular, if both conditions hold, the two clubs determining \(t(m)\) are merged and the algorithm starts again from step 1, otherwise it continues for all following pairs;
For the last element of vector M (the value of the last two clubs) the only condition required for merging is \(t(m=M) > -1.65\).
Phillips, P. C.; Sul, D., 2007. Transition modeling and econometric convergence tests. Econometrica 75 (6), 1771-1855.
Phillips, P. C.; Sul, D., 2009. Economic transition and growth. Journal of Applied Econometrics 24 (7), 1153-1185.
von Lyncker, K.; Thoennessen, R., 2017. Regional club convergence in the EU: evidence from a panel data analysis. Empirical Economics 52 (2), 525-553
findClubs, finds convergence clubs by means of Phillips and Sul clustering procedure.
mergeDivergent, merges divergent units according to the algorithm proposed by von Lyncker and Thoennessen (2017).
data("filteredGDP")
# Cluster Countries using GDP from year 1970 to year 2003
clubs <- findClubs(filteredGDP, dataCols=2:35, unit_names = 1, refCol=35,
time_trim = 1/3, cstar = 0, HACmethod = "FQSB")
summary(clubs)
# Merge clusters
mclubs <- mergeClubs(clubs, mergeMethod='PS', mergeDivergent=FALSE)
summary(mclubs)
mclubs <- mergeClubs(clubs, mergeMethod='vLT', mergeDivergent=FALSE)
summary(mclubs)
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