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

influences can be controlled for when establishing a relationship between business ownership and
income movement. Moreover, the panel data that are available for this study are not only useful as
information on the movement of the same individuals over time, they help us address the effect of
unobserved factors. In the following we estimate conditional equations, dependent on statuses in
period t-1 and t, to assess the correlation between small business ownership, upward income mobility
and high income persistence, when other observable and unobservable effects are addressed.

Before presenting the multivariate approach, we should note the emphasis here on non-
causal interpretation of results. Owners of small businesses obviously self-select into the group, so that
interpreting the results in terms of causal effects require methods that control for group allocation
mechanisms. The main objective of the present study is to describe the achievements of owners of
small businesses during a period with a dual income tax system in place, and not for a randomly
selected person choosing business ownership. This is in accordance with assumptions implicitly or
explicitly made by other studies closely related to the present study; see the review of literature in
Section 2.

We address multivariate evidence through estimations of transition rates, which is a logical
extension of the mobility matrices approach seen in the previous section. In the following, the
approach is presented with reference to the relationship between business ownership and upward
movement, but the same type of approach may be used for the analysis of high-income persistence.

The latent probability for individual i belonging to state “non-rich” at time t-1, y_i^*_{t -1} , can be
seen as depending on a vector of explanatory variables, x_{it -1} , and individual effectα_i , and an error
term, τ_it-1,

(3) y^* = x^'  β+α +τ .

it-1        it-1           i       it-1

The observed outcome, y_it-1 , can be seen as taking values 0 or 1 dependent on the latent probability of
being non-rich, as defined by a cut-off point, λ. Let us reserve 1 for being rich. Then we have

1 if У* ≥ λ_it
it it

it ^0 else

Assuming that τ_it-1 : N (0,σ_u² ) , such a model can be estimated as

(4)       P[y_ιt-1 = 0]=φ(-x'_lt-ιβ- α_ι),

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