Countries do not all converge to one steady state; they converge in groups. This implements the Phillips-Sul (2007) log-t procedure: a regression test for whether a set of countries is converging, applied iteratively to peel off clubs that converge internally even when the whole sample does not.
Arguments
- data
A panel with
iso3c,yearand the value column.- value
The value column (unquoted); usually income per head.
- min_size
Smallest club to report (default
2). Countries left over are returned as clubNA.- alpha
Significance level for the one-sided log-t test (default
0.05; the critical value is \(-1.65\)).
Value
A tibble: iso3c, club (an integer, 1 = highest-level club, NA =
not classified), and the club's log_t statistic. The per-club test results
are attached as the "countryatlas_clubs" attribute.
The test
For each country form the relative transition path \(h_{it} = y_{it} / \bar{y}_t\), then regress \(\log(H_1/H_t) - 2\log(\log t)\) on \(\log t\) over the last part of the sample, where \(H_t\) is the cross-sectional mean of \((h_{it}-1)^2\). The one-sided t statistic on \(\log t\) is the log-t statistic: above \(-1.65\) the group is converging. Clubs are then formed by sorting countries on their final-period value and growing a core group while the test still passes.
A panel needs a reasonable number of periods for this to mean anything – below roughly fifteen the test has very little power, and the function warns.
References
Phillips, P. C. B. & Sul, D. (2007). Transition modeling and econometric convergence tests. Econometrica 75(6), 1771-1855. doi:10.1111/j.1468-0262.2007.00811.x
Examples
set.seed(1)
# two groups converging to different levels
panel <- expand.grid(iso3c = c(paste0("A", 1:5), paste0("B", 1:5)),
year = 2000:2024)
panel$y <- ifelse(startsWith(as.character(panel$iso3c), "A"), 100, 30) +
rnorm(nrow(panel), 0, 2)
convergence_club(panel, y)
#> # A tibble: 10 × 3
#> iso3c club log_t
#> <chr> <int> <dbl>
#> 1 A1 1 -1.21
#> 2 A2 1 -1.21
#> 3 A3 1 -1.21
#> 4 A5 1 -1.21
#> 5 B4 2 -0.140
#> 6 B5 2 -0.140
#> 7 B2 3 -0.880
#> 8 B3 3 -0.880
#> 9 A4 NA NA
#> 10 B1 NA NA