Estimated earnings in an employment status model with banded data

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.