ConvergenceClubs: Finding Convergence Clubs

Description

Functions for clustering regions that form convergence clubs, according to the definition of Phillips and Sul (2009) doi:10.1002/jae.1080. A package description is available in Sichera and Pizzuto (2019).

Main functions

The package's main functions are findClubs and mergeClubs. The former finds clubs of convergence, given a dataset with units in rows and years in columns, returning an object of class convergence.clubs. The latter takes as argument an object of class convergence.clubs and applies the clustering procedure to the convergence clubs contained in the argument, according to either Phillips and Sul (2009) or von Lyncker and Thoennessen (2017) procedure.

Author(s)

Maintainer: Roberto Sichera rob.sichera@gmail.com [copyright holder]

Authors:

• Pietro Pizzuto pietro.pizzuto02@unipa.it

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.

von Lyncker, K.; Thoennessen, R., 2017. Regional club convergence in the EU: evidence from a panel data analysis. Empirical Economics 52 (2), 525-553

Sichera, R.; Pizzuto, P., 2019. ConvergenceClubs: A Package for Performing the Phillips and Sul's Club Convergence Clustering Procedure. The R Journal.

See Also

Useful links:

• https://CRAN.R-project.org/package=ConvergenceClubs

• Report bugs at https://github.com/rhobis/ConvergenceClubs/issues

Define the vector of tick marks for the axis of a plot

Description

Define the vector of tick marks for the axis of a plot

Usage

axis_marks(lx)

Arguments

Find a club

Description

Add units to core group according to step 3 of the clustering algorithm by Phillips and Sul (2007, 2009), in order to find the enlarged club.

Usage

club(
  X,
  dataCols,
  core,
  time_trim,
  HACmethod = c("FQSB", "AQSB"),
  cstar = 0,
  cstar_method = c("fixed", "incremental"),
  cstar_increment = 0.1,
  cstar_cap = 3
)

Arguments

Value

A list of three objects: id, a vector containing the row indices of club units in the original dataframe (input of function findClubs); rows, a vector of row indices of club units in the current dataset (input of function club); model, a list containing information about the model used to run the t-test on the units in the club.

References

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.

Compute H values

Description

Computes H values (cross-sectional variance) according to the clustering algorithm by Phillips and Sul (2007, 2009)

Usage

computeH(X, quantity = "H", id)

Arguments

Details

The cross sectional variation $H_{it}$ is computed as the quadratic distance measure for the panel from the common limit and under the hypothesis of the model should converge to zero as t tends towards infinity:

$H_t = N^{-1} \sum_{i=1}^N (h_{it}-1)^2 \rightarrow 0 , \quad t\rightarrow \infty$

where

$h_{it} = \frac{\log y_{it}}{( N^{-1} \sum_{i=1}^N log \, y_{it} )}$

Value

A numeric vector, a matrix or a list, depending on the value of quantity

References

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.

Examples

data("filteredGDP")

h <- computeH(filteredGDP[,-1], quantity="h")
H <- computeH(filteredGDP[,-1], quantity="H")
b <- computeH(filteredGDP[,-1], quantity="both")

Find core (primary) group

Description

Find the Core (primary) group according to step 2 of the clustering algorithm by Phillips and Sul (2007, 2009)

Usage

coreG(
  X,
  dataCols,
  time_trim,
  threshold = -1.65,
  HACmethod = c("FQSB", "AQSB"),
  type = c("max", "all")
)

Arguments

Details

According to the second step of the Phillips and Sul clustering algorithm (2007, 2009), the log t regression should be run for the first k units $2 < k < N$ maximizing k under the condition that $t-value > -1.65$. In other words, the core group size $k^*$ is chosen as follows:

$k^* = argmax_{k} \{t_k\}$

subject to

$\min{t_k} > -1.65$

Such behavior is obtained with type="max"; if type="all", all units that satisfy $t_k > -1.65$ are added to core group.

If the condition $t_k > -1.65$ does not hold for $k = 2$ (the first two units), the algorithm drops the first unit and repeats the same procedure for the next pair of units. If $t_k > -1.65$ does not hold for any couple of units, the whole panel diverges.

Value

A numeric vector containing the row indices of the units included in the core group; if a core group cannot be found, returns FALSE.

References

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.

dim method for S3 object convergence.clubs

Description

dim method for S3 object convergence.clubs

Usage

## S3 method for class 'convergence.clubs'
dim(x, ...)

Arguments

Value

an integer vector with two values: the first one indicates the number of clubs, the second one indicates the number of divergent units

Log-t test for convergence

Description

Estimates the log-t regression model proposed by Phillips and Sul (2007, 2009) in order to investigate the presence of convergence by adopting the Andrews estimator of long-run variance (fixed or adaptive bandwidth of the kernel).

Usage

estimateMod(H, time_trim = 1/3, HACmethod = c("FQSB", "AQSB"))

Arguments

Details

The following linear model is estimated:

$\log\frac{H_1}{H_t} - 2\log(\log{t}) = \alpha + \beta \log{t} + u_t$

Heteroskedasticity and autocorrelation consistent (HAC) standard errors are used with Quadratic Spectral kernel (Andrews, 1991), If HACmethod="FQSB", a fixed bandwidth parameter is applied, while with HACmethod="AQSB" an adaptive bandwidth parameter is employed.

Value

A named vector containing information about the model used to run the t-test on the units in the club: beta coefficient, standard deviation, t-statistics and p-value.

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.

Filtered per-capita GDP of 152 Countries from 1970 to 2003

Description

A dataset containing the per-capita GDP of 152 Countries over 34 years (Phillips and Sul, 2009). Data were filtered in order to remove business cycles.

Usage

data(filteredGDP)

Format

A data frame with 152 rows and 35 variables.

Details

ID

Country names (character);

Y1970, ..., Y2003

per-capita GDP from year 1970 to 2003 (filtered in order to remove business cycles).

References

Phillips, P. C.; Sul, D., 2009. Economic transition and growth. Journal of Applied Econometrics 24 (7), 1153-1185.

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

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)

Per-capita GDP of 152 Countries from 1970 to 2003

Description

A dataset containing the per-capita GDP of 152 Countries over 34 years (Phillips and Sul, 2009).

Usage

data(GDP)

Format

A data frame with 152 rows and 35 variables.

Details

ID

Country names (character);

Y1970, ..., Y2003

per-capita GDP from year 1970 to 2003.

References

Phillips, P. C.; Sul, D., 2009. Economic transition and growth. Journal of Applied Econometrics 24 (7), 1153-1185.

Merge convergence clubs

Description

Merges a list of clubs created with the function findClubs by either Phillips and Sul method or von Lyncker and Thoennessen procedure.

Usage

mergeClubs(
  clubs,
  time_trim,
  mergeMethod = c("PS", "vLT"),
  threshold = -1.65,
  mergeDivergent = FALSE,
  estar = -1.65
)

Arguments

Details

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:

1. 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;

2. Repeat the test adding the next group and continue until the basic condition (t-statistic > -1.65) holds;

3. 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:

1. 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 $m = 1, \dots, M$);

2. 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;

3. For the last element of vector M (the value of the last two clubs) the only condition required for merging is $t(m=M) > -1.65$.

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

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

See Also

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).

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, 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)

Merge divergent units

Description

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

Usage

mergeDivergent(clubs, time_trim, estar = -1.65)

Arguments

Details

von Lyncker and Thoennessen (2017) claim that units identified as divergent by the basic clustering procedure by Phillips and Sul might not necessarily still diverge in the case of new convergence clubs detected with the club merging algorithm. To test if divergent units may be included in one of the new convergence clubs, they propose the following algorithm:

1. Run a log t-test for all diverging units, and if $t_k > -1.65$ all these units form a convergence club (This step is implicitly included in Phillips and Sul basic algorithm);

2. Run a log t-test for each diverging units and each club, creating a matrix of t-values with dimensions $d \times p$, where each row d represents a divergent region and each column p a convergence club;

3. Take the highest $t > e^*$ and add the respective region to the respective club and restart from the step 1. the authors suggest to use $e^* = t = -1.65$;

4. The algorithm stops when no t-value > e* is found in step 3, and as a consequence all remaining units are considered divergent.

Value

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 it is present in the clubs object given in input).

References

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

See Also

mergeClubs, Merges a list of clubs created by findClubs;

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, cstar = 0, HACmethod = "FQSB")
summary(clubs)

# Merge clusters and divergent units
mclubs <- mergeClubs(clubs, mergeDivergent=TRUE)
summary(mclubs)

Plot method for S3 class convergence.clubs

Description

Plot the transition paths of units in the convergence clubs and the average transition paths of those clubs.

Usage

## S3 method for class 'convergence.clubs'
plot(
  x,
  y = NULL,
  nrows = NULL,
  ncols = NULL,
  clubs,
  avgTP = TRUE,
  avgTP_clubs,
  y_fixed = FALSE,
  legend = FALSE,
  save = FALSE,
  filename,
  path,
  width = 20,
  height = 15,
  device = c("pdf", "png", "jpeg"),
  res,
  plot_args,
  legend_args,
  breaks,
  ...
)

Arguments

Details

nrows and ncols are optional parameters used to define the row and column number for the plot layout. Both or just one of them may be specified. If none of them is specified, the layout dimension is chosen automatically.

If legend=TRUE and a column with units' names is available in the x object, those names are truncated to fit the plot's legend. The graphical parameter cex may be used to modify the size of the legend's labels, default is 0.8

Note that, when using RStudio, one may incur in an error if the plot window is too small. Enlarging the plot window usually solves the problem.

List of argument that could be included in plot_args as a list:

• lty numeric scalar or vector indicating the line type (values available range from 1 to 6)

• type a string indicating whether the points (markers) should be displayed. If 'l' no markers are displayed; if 'o' markers are displayed;

• pch numeric scalar or vector to specify symbols to use when plotting points (markers). If omitted, customized markers are used for each line. If fixed (e.g. pch=1) the same marker is used for each line. (Values available range from 0 to 25)

• cex number indicating the amount by which plotting text and symbols should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, and so on. Default is 1.

• lwd number indicating the line width. Default is 1.

• xlab string indicating x-axis label. If omitted, 'Time', is displayed

• ylab string indicating y-axis label. If omitted, 'Relative transition path', is displayed

• cex.lab number indicating the amount by which plotting x and y labels should be scaled relative to cex. Default is 1.

• col option to specify colors for each line. Colors could be specified by index, name, hexadecimal, or RGB. For example col=1, col="white", and col="#FFFFFF" are equivalent. If omitted, colors are chosen randomly.

• col_hline color of the horizontal line for h=1. Default is 'black'.

• xmarks vector with tic marks to be displayed in the x axis.

• xlabs vector with labels of marks to be displayed in the x axis.

• xlabs_dir number indicating the direction of x-axis labels. For horizontal labels xlabs_dir=0; for vertical labels xlabs_dir=2.

List of argument that could be included in legend_args as a list:

• cex number indicating the amount by which plotting text and symbols should be scaled relative to the default. Default is 0.9

• lwd Number indicating the line width. Default is 1.

• y.intersp number indicating the space between each legend entry. Default is 1.

• max_length_labels maximum length of the labels displayed for each legend entry.

Note that, when using RStudio, one may incur in an error if the plot window is too small. Enlarging the plot window usually solves the problem. We suggest to export plots in the available formats ("pdf", "png" or "jpeg") using adequate values of width and height.

Examples

data("filteredGDP")

clubs <- findClubs(filteredGDP, dataCols=2:35, unit_names = 1, refCol=35, time_trim = 1/3,
                   cstar = 0, HACmethod = "FQSB")



### Plot transition paths for all clubs
plot(clubs)
plot(clubs, y_fixed=TRUE)
plot(clubs, nrows=2,ncols=4)

plot(clubs, ncols=3, lty='dotdash', lwd=3, col="blue")
plot(clubs, ncols=3, y_fixed=TRUE, lty='dotdash', lwd=3, col="blue")

### Plot transition paths only for some clubs
plot(clubs, clubs=c(2,4,5))
plot(clubs, nrows=1, ncols=3, clubs=c(2,4,5), avgTP = FALSE)
plot(clubs, nrows=1, ncols=3, clubs=c(2,4,5), avgTP = FALSE, legend=TRUE)
plot(clubs, clubs=c(2,4,5), avgTP_clubs = c(1,3))
plot(clubs, clubs=c(2,4,5), avgTP_clubs = c(1,3), legend=TRUE)


### Export customized plots
#Only plot average transition paths
plot(clubs, clubs=NULL, avgTP = TRUE, legend=TRUE)

#only lines, without markers and legend
plot(clubs, save = TRUE, filename ="name.pdf" , path = tempdir(), width = 15, height = 10)

#markers and legend (up to the fourth characther is shown)
plot(clubs, legend=TRUE, plot_args=list(type='o'),
    legend_args=list(max_length_labels=4, y.intersp=1),
    save = TRUE, filename ="name.pdf", path = tempdir(), width = 15, height = 10)

#for large samples the legend could be better displayed by plotting each club
#in turn and by increasing the plot dimension (through width and height)
plot(clubs, clubs=1, avgTP=FALSE, legend=TRUE, plot_args=list(type='o'),
    legend_args=list(max_length_labels=8, y.intersp=1),
    save = TRUE, filename ="name.pdf", path = tempdir(), width = 20, height = 15)

#customize x-labels - 1
plot(clubs, legend=TRUE, plot_args=list(type='o', xmarks=seq(1,34),xlabs=seq(1970,2003),
    xlabs_dir=0), legend_args=list(max_length_labels=4, y.intersp=1),
    save = TRUE, filename ="name.pdf" , path = tempdir(), width = 15, height = 10)

#customize x-labels - 2
plot(clubs, legend=TRUE, plot_args=list(type='o', xmarks=seq(1,34,1), xlabs=seq(1970,2003,1),
    xlabs_dir=2), legend_args=list(max_length_labels=4, y.intersp=1),
    save = TRUE, filename ="name.pdf" , path = tempdir(), width = 15, height = 10)

#show only the plot with the average transition paths of each club
plot(clubs, clubs=NULL, avgTP=TRUE, legend=TRUE,
    plot_args=list(type='o', xmarks=seq(1,34), xlabs=seq(1970,2003), xlabs_dir=0),
    save = TRUE, filename ="name.pdf" , path = tempdir(), width = 15, height = 10)

#markers and legend - png format
plot(clubs, legend=TRUE, plot_args=list(type='o'),
    legend_args=list(max_length_labels=4, y.intersp=1),
    save = TRUE, filename ="name.png" , path = tempdir(), width = 15, height = 10,
    device= "png", res=100)

Print method for S3 object summary.convergence.clubs

Description

Print method for S3 object summary.convergence.clubs

Usage

print_table(x, ...)

Arguments

Print method for S3 object convergence.clubs

Description

Print method for S3 object convergence.clubs

Usage

## S3 method for class 'convergence.clubs'
print(x, ...)

Arguments

Long run variance of errors

Description

Estimate long run variance of errors through Andrews' method

Usage

ps_andrews_hac(x)

Arguments

Details

This function computes the long run variance of residuals of an lm model by means of Andrews' with Quadratic Spectral kernel and fixed bandwidth. The code is an adaptation of Phillips and Sul (2007)'s code, which was written in GAUSS.

Value

a numeric value representing the long run variance of errors

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.

Summary method for S3 object convergence.clubs

Description

Summary method for S3 object convergence.clubs

Usage

## S3 method for class 'convergence.clubs'
summary(object, ...)

Arguments

Extract transition paths from a convergence.clubs object

Description

Given a convergence.clubs object (created by either findClubs or mergeClubs function), returns a list with transition paths for each club.

Usage

transition_paths(
  clubs,
  include_unit_names = TRUE,
  output_type = c("list", "data.frame")
)

Arguments

Value

If output_type=="list", a list of data frames, one for each club; each data frame will contain transition paths for the units in the correspondent club. If output_type=="data.frame", a data.frame.

References

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

findClubs, Finds Convergence Clubs; mergeClubs, Merges a list of clubs created by findClubs; plot.convergence.clubs, Plots transition paths from a convergence.clubs object.

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, cstar = 0, HACmethod = "FQSB")

# Extract Transition Paths
tp <- transition_paths(clubs)
tp <- transition_paths(clubs, output_type = 'data.frame')