beta_conv {convergEU}

Beta-convergence statistic

Description

Given a dataframe of quantitative indicators along time, the unconditional beta convergence is a statistic capturing some important features. A time variable must be present and sorted. Missing values are not allowed. All other columns are indicator values in each considered country.

Usage

beta_conv(
  tavDes,
  time_0,
  time_t,
  all_within = FALSE,
  timeName = "time",
  useTau = TRUE,
  useCon = FALSE
)

Arguments

tavDes

the sorted dataframe time by countries on the original scale. No other variable besides time and countries' indicator must be present.

time_0

reference time.

time_t

target time strictly larger than time_0.

all_within

is FALSE if just two different years are considered (default); if more than two years are desired within the specified interval then it must be TRUE ; the reference time remains time_0.

timeName

the name of the variable that contains time information.

useTau

if TRUE the log ratio of indicator values is divided for the elapsed time (years).

useCon

if TRUE replaces 0 with a minimum constant value

Value

a list with the value of beta-conv, by OLS (least-squares), the transformed data and standard statistical tests.

References

https://www.eurofound.europa.eu/system/files/2022-04/introduction-to-the-convergeu-package-0.6.4-tutorial-v2-apr2022.pdf

Examples

# Example 1:
# Dataframe in the format years by countries:
require(tibble)
myTB1  <- tibble::tribble(
  ~years, ~UK, ~DE, ~IT,
  1990,   998,  1250, 332,
  1988,   1201, 868, 578,
  1989,   1150, 978, 682,
  1991,  1600,  1350, 802
)

# Sort the time variable:
newdata <- myTB1[order(myTB1$years),]

# Beta convergence statistic by considering just two times, e.g. 1989 and 1991:
myBC1 <- beta_conv(newdata,1989,1991,timeName="years")

# Visualize the summary of the results (estimated coefficients, standard errors, p-values):
myBC1$res$summary

# Visualize the adjusted R-squared:
myBC1$res$adj.r.squared

# Beta convergence statistic by considering more than two times:
myBC2 <- beta_conv(newdata,1988,1991,all_within=TRUE,timeName="years")

# Example 2:
# Dataframe in the format years by countries, time variable already sorted:
testTB <- tribble(
    ~time, ~countryA ,  ~countryB,  ~countryC,
    2000,     0.8,   2.7,    3.9,
    2001,     1.2,   3.2,    4.2,
    2002,     0.9,   2.9,    4.1,
    2003,     1.3,   2.9,    4.0,
    2004,     1.2,   3.1,    4.1,
    2005,     1.2,   3.0,    4.0
    )
myBC3 <- beta_conv(testTB, time_0 = 2000, time_t = 2005, timeName = "time")
myBC4 <- beta_conv(testTB, time_0 = 2000, time_t = 2005, all_within = TRUE, timeName = "time")

# Example 3
# Beta convergence for the emp_20_64_MS Eurofound dataset:
data(emp_20_64_MS)
empBC <- beta_conv(emp_20_64_MS, time_0 = 2002, time_t = 2006, timeName = "time")

# Summary of the model results:
empBC$res$summary

# Adjusted R-squared:
empBC$res$adj.r.squared