Palgrave Handbook of Econometrics: Applied Econometrics

Sergio J. Rey and Julie Le Gallo 1267

Table 27.1 Markov transitions: US state incomes 1929–2000

t+ 1

t 0.661 0.884 1.031 1.309 1.934

0.661 0.893 0.107 0.000 0.000 0.000

0.884 0.013 0.913 0.073 0.001 0.000

1.031 0.000 0.054 0.872 0.074 0.000

1.309 0.000 0.001 0.065 0.913 0.021

1.934 0.000 0.000 0.000 0.112 0.888

Note:The row (column) headings are the upper bounds for the quintiles

of relative incomes normalized by the national average. The values in

the body of the table are the empirical transition probabilities of moving

from classiin periodtto classjin periodt+ 1.

Table 27.2 Ergodic US state income distribution

x 0.661 0.884 1.031 1.309 1.934

P(x) 0.029 0.233 0.314 0.358 0.067

Note:Column headings are the upper bounds for the quintiles

of relative incomes normalized by the national average.

the national average, the probability of moving up into the next higher income
class during one year was 0.107. At the other end of the distribution, states with
incomes greater than 193% of the national level moved down one income class
with a probability of 0.112.
Based on an estimate of the transition probability matrix, one can in turn gen-
erate an estimate of the ergodic distribution for the regional incomes. For the US
case, the long-run distribution implied by these transitional dynamics is reported
in Table 27.2. The tendency towards convergence is clearly evident in this distribu-
tion, as the extreme classes lose mass over what they had in the quintile distribution
at the beginning of the period (1929).
While the Markov chain is an innovative approach to the exploration of dis-
tributional dynamics, the estimates of the transition probabilities rest on several
assumptions, such as order, time-homogeneity and independent transitions. Inde-
pendent transitions mean that the spatial context facing a given economy is
not taken into account when estimating the probability of movement out of a
particular income class.

27.3.1.3 Spatial Markov

Rey (2001) extends the discrete Markov approach to consider this context by esti-
mating transition matrices subject to the spatial lag of the income values for an
economy. This is done for the US example in Table 27.3, where the same five income