How countries move between classes of a variable from one year to the next: the discrete Markov chain of Quah's distribution dynamics. Class 1 is the lowest.
Usage
transition_matrix(
data,
value,
n_classes = 5,
classes = c("quantile", "relative"),
step = 1
)Arguments
- data
A panel with
iso3c,yearand the value column.- value
The column to classify (unquoted), such as GDP per capita.
- n_classes
Number of classes (default
5).- classes
"quantile"(default) cuts each year at its own quantiles, so a class is a rank band;"relative"divides each value by its year's cross-country mean and cuts at the pooled quantiles of those ratios, so a class is a band of relative income that can fill or empty over time.- step
Years between the two observations of a transition (default
1); keyed on the year, so a gap in a country's series gives no transition rather than a longer one.
Value
A tibble of from, to, n (transitions observed) and p (the
probability of moving from from to to, NA for a class nothing left),
with attributes ergodic (the steady-state share of countries in each
class, if the chain ran on) and first_passage (the matrix of mean
first-passage times, in steps).
References
Quah, D. (1993). Empirical cross-section dynamics in economic growth. European Economic Review 37(2-3), 426-434. doi:10.1016/0014-2921(93)90031-5
Quah, D. T. (1996). Twin peaks: growth and convergence in models of distribution dynamics. The Economic Journal 106(437), 1045-1055. doi:10.2307/2235377
Examples
set.seed(1)
pan <- expand.grid(iso3c = c("FRA", "DEU", "BRA", "IND", "CHN", "NGA"),
year = 2000:2010, stringsAsFactors = FALSE)
pan$gdp <- exp(stats::rnorm(nrow(pan), 9, 1))
transition_matrix(pan, gdp, n_classes = 3)
#> # A tibble: 9 × 4
#> from to n p
#> <int> <int> <int> <dbl>
#> 1 1 1 6 0.3
#> 2 2 1 4 0.2
#> 3 3 1 10 0.5
#> 4 1 2 7 0.35
#> 5 2 2 10 0.5
#> 6 3 2 3 0.15
#> 7 1 3 7 0.35
#> 8 2 3 6 0.3
#> 9 3 3 7 0.35