Beta convergence (growth regression)

Do poor countries grow faster than rich ones? The classic unconditional beta-convergence test: each country's average log growth rate is regressed on its log initial level. A significantly negative beta is convergence; the implied convergence speed and half_life (years to close half the gap) are derived from it.

Usage

beta_convergence(data, value)

Arguments

data

A panel with iso3c and year.

value

The value column (unquoted); must be positive (log scale).

Value

A one-row tibble: beta, se, t_value, p_value, r_squared, n (countries), speed (annual convergence rate, NA when beta >= 0) and half_life (years). The fitted lm object is attached as the "model" attribute.

See also

sigma_convergence() for the dispersion-over-time counterpart.

Examples

set.seed(1)
start <- runif(20, 6, 11)                              # log initial level
growth <- 0.05 - 0.004 * start + rnorm(20, 0, 0.002)   # poorer grow faster
panel <- data.frame(
  iso3c = rep(sprintf("C%02d", 1:20), each = 2),
  year  = rep(c(2000L, 2020L), 20),
  gdp   = as.vector(rbind(exp(start), exp(start + growth * 20)))
)
beta_convergence(panel, gdp)
#> # A tibble: 1 × 8
#>       beta       se t_value  p_value r_squared     n   speed half_life
#>      <dbl>    <dbl>   <dbl>    <dbl>     <dbl> <int>   <dbl>     <dbl>
#> 1 -0.00464 0.000296   -15.7 6.14e-12     0.932    20 0.00487      142.