findClubs {ConvergenceClubs}R Documentation

Finds convergence clubs

Description

Find convergence clubs by means of Phillips and Sul clustering procedure.

Usage

findClubs(
  X,
  dataCols,
  unit_names = NULL,
  refCol,
  time_trim = 1/3,
  HACmethod = c("FQSB", "AQSB"),
  cstar = 0,
  cstar_method = c("fixed", "incremental"),
  cstar_increment = 0.1,
  cstar_cap = 3
)

Arguments

X

dataframe containing data (preferably filtered data in order to remove business cycles). Data must not contain any NA or NaN values, otherwise the clustering procedure will be stopped with an error. In order for the clustering procedure to work, data must be arranged such that each row represents a unit and each column represents a time period (year, month, ...)

dataCols

integer vector with the column indices of the data

unit_names

integer scalar indicating, if present, the index of a column with codes of the units

refCol

integer scalar indicating the index of the column to use for ordering data

time_trim

a numeric value between 0 and 1, representing the portion of time periods to trim when running log-t regression model. Phillips and Sul (2007, 2009) suggest to discard the first third of the period.

HACmethod

string indicating whether a Fixed Quadratic Spectral Bandwidth (HACmethod="FQSB") or an Adaptive Quadratic Spectral Bandwidth (HACmethod="AQSB") should be used for the truncation of the Quadratic Spectral kernel in estimating the log-t regression model with heteroskedasticity and autocorrelation consistent standard errors. The default method is "FQSB".

cstar

numeric scalar, indicating the threshold value of the sieve criterion (c^*) to include units in the detected core (primary) group (step 3 of Phillips and Sul (2007, 2009) clustering algorithm). The default value is 0.

cstar_method

a string specifying whether cstar should be mantained fixed (cstar_method="fixed") or increased iteratively until the whole club satisfies the condition tvalue>-1.65 (cstar_method="incremental"). Default is cstar_method="fixed" (see Details).

cstar_increment

a positive value specifying the increment to cstar, only valid if cstar_method="incremental" (see Details); the default value is 0.1.

cstar_cap

scalar indicating the maximum value up to which cstar can be increased; the default value is 3.

Details

In order to investigate the presence of convergence clubs according to the Phillips and Sul clustering procedure, the following steps are implemented:

  1. (Cross section last observation ordering): Sort units in descending order according to the last panel observation of the period;

  2. (Core group formation): Run the log-t regression for the first k units (2 < k < N) maximizing k under the condition that t-value is > -1.65. In other words, chose the core group size k* as follows:

    k^*= argmax_k \{t_k\}

    subject to

    min\{t_k \} > -1.65

    If the condition t_k >-1.65 does not hold for k = 2 (the first two units), drop the first unit and repeat the same procedure. If t_k >-1.65 does not hold for any units chosen, the whole panel diverges;

  3. (Sieve the data for club membership): After the core group is detected, run the log-t regression for the core group adding (one by one) each unit that does not belong to the latter. If t_k is greater than a critical value c^* add the new unit in the convergence club. All these units (those included in the core group k^* plus those added) form the first convergence club. Note that Phillips and Sul (2007) suggest to make sure t_k>-1.65 for the subconvergence group obtained. Otherwise, repeat the procedure by increasing the value of the c^* parameter until the condition t_k>-1.65 is satisfied for the subconvergence group;

  4. (Recursion and stopping rule): If there are units for which the previous condition fails (t_k <c^*), gather all these units in one group and run the log-t test to see if the condition t_k >-1.65 holds. If the condition is satisfied, conclude that there are two convergence clubs. Otherwise, step 1 to 3 should be repeated on the same group to determine whether there are other subgroups that constitute convergence clubs. If no k in step 2 satisfies the condition t_k >-1.65, the remaining units diverge.

Note that the clustering procedure may return groups with t_k <-1.65, which are not really convergence clubs. In this case, following step 3 of the clustering procedure there are two options: (i) allow an iterative increase of the cstar parameter until the subconvergence club satisfies the condition t_k >-1.65. In this case it should the argument cstar_method should be set to "incremental" and a positive argument for the cstar_increment argument should be chosen; (ii) increase the value of the cstar in order to increase the discriminatory power of the log-t test in the formation of each club.

Information about clubs, divergent units and the c^* used for each club can be easily displayed by means of the summary() function, for which the package provides a specific method for the convergence.clubs class.

Value

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)

References

Andrews, D. W., 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica: Journal of the Econometric Society, 817-858.

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.

See Also

mergeClubs, Merges a list of clubs created by findClubs;

mergeDivergent, Merges divergent units according to the algorithm proposed by von Lyncker and Thoennessen (2017)

Examples

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, HACmethod = "FQSB",
                   cstar = 0,
                   cstar_method = 'incremental',
                   cstar_increment = 0.1)



## Not run: 
# 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, HACmethod = "AQSB", cstar = 0)


## End(Not run)
[Package ConvergenceClubs version 2.2.5 Index]