### Abstract

Introduction:
In this paper we consider the estimation of earnings equations for individuals
who are either self employed or are in paid employment, and who are assumed
to have freely chosen their employment status. The key aspect of the available
data is that we do not observe an individual's earnings. Instead we only
know in which of several bands an individual's earnings are located. This
has implications for the choice of econometric technique and implies that
the ordered probit, or the ordered probit with selectivity, are the statistical
models that appear most appropriate. Commonly used estimation techniques
such as the two-step estimator due to Heckman (1979) are inappropriate.
However, there is an important difference between the ordered probit model
as defined in this paper and as defined in, for example, Greene (1997). The
Greene definition of the ordered probit assumes that the band separations
are unknowns to be estimated, whereas they are known in our data set. This
situation is not uncharacteristic of survey data where individuals, or firms, are
reluctant to disclose their precise income. Knowledge of the band separations
implies that the parameters in the earnings equation are identified and can
therefore be estimated1. Parameter estimation is discussed in detail in section
2. The data and the economic framework are discussed in section 3. The
estimation results are presented and discussed in section 4. Our conclusions
are presented in section 5.

Original language | English |
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Place of Publication | Glasgow |

Publisher | University of Strathclyde |

Number of pages | 31 |

Publication status | Published - 2007 |

### Keywords

- estimation of earnings equations
- self employed/ paid employment
- econometric technique
- statisticalmodels
- two-step estimator
- ordered probit
- band separations
- economic framework

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## Cite this

Ashcroft, B. K., Holden, D. R., Low, K., The research was funded by the Economic and Social Research Council (Funder), & also supported by Scottish Enterprise (Funder) (2007).

*Estimated earnings in an employment status model with banded data*. University of Strathclyde.