Income Mobility of Owners of Small Businesses when Boundaries between Occupations are Vague

of explanatory variables for the two equations (identical z-vectors). Estimations of conditional
probabilities or transition rates have, for example, recently been seen in the literature focusing on the
low end of the income distribution, explaining low pay dynamics, low income dynamics and poverty
dynamics; see for instance Stewart and Swaffield (1999) and Cappellari and Jenkins (2002; 2004).

As seen in Equation (7), the empirical approach allows us to take an individual specific time
invariant effect into account when describing the transitions, represented by αi. We will treat this as a
random effect and estimate equation (7) by the random effects probit model. This means, see e.g.,
Wooldridge (2002), there is no correlation between observed explanatory variables and the individual
effect, E (α_i∖z_i)=0, where z_i ≡ (z_i1993,z_i1994,...,z_i2003). However, note how the estimation of Equation
(7) in effect turns the panel into an unbalanced panel, which implies that random effects estimations
are only carried out for individuals observed more than one time. This selection may be non-innocent,
and is the main reason for also referring to pooled probit estimates (in the Appendix).

4.2 Descriptive statistics

Table 9 presents descriptive statistics for the two estimated equations: one for becoming rich and one
for staying rich. All figures are averages across the 10 waves that we have information
for: {1993/94,1994/95,...,2002/2003}. Estimations are carried out both for quintile and decile
specifications.

There is a large degree of permanence at the high end on the income distribution; on average
approximately 80 percent of the people at the upper quintile at year t were there in year t-1, whereas as
the corresponding figure for the decile specification is 76 percent, see the “Stay rich” columns.
Correspondingly, people do not move as frequently into the upper quintile and upper decile, see the
“Upward mobility” columns, only 4.9 percent and 2.6 percent on average.

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