Evaluation of the Australian Wage Subsidy Special Youth ...

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Φ = cumulative distribution function for the standard bivariate normal
This approach has been applied in several evaluation problems for solving the issue of
selection bias, where programme participants are not randomly selected, as discussed in
the brief review of Maddala (1983). It allows for selection into participation in the wage
subsidy on the basis of variables that are unobservable, or more usually variables that are
unobserved in the data. The model is made operational by assuming a bivariate normal
distribution for the errors in the participation and employment equations. This assumption
makes the unobservable characteristics that jointly influence participation and
employment follow the bivariate normal distribution. The participation equation is
explicitly modelled to provide a variable that is then used to control for the part of
unobserved variation of the employment equation that is correlated with the unobserved
variation in the participation decision. With full information maximum likelihood
methods, the selection and employment equations are estimated jointly, in which case the
correlation between the unobservables is estimated directly.
The sets of exogenous variables x i , z i can be overlapping, in which case only the
functional form assumption provides identification. However, in practice this is not
recommended as identification based solely on functional form is likely to be empirically
fragile. The model is more appropriately identified if at least one variable in the set z i is
not in the set x i , as the exclusion restriction improves the identification of the parameters
of interest. Thus, practical implementation usually requires a variable included in the
participation equation estimated that is excluded from the employment equation. 60 This
exogenous variable should be suitable in that it influences selection but not employability.
An important aspect of this estimation approach is the identification of a credible
instrument for the exclusion restriction. Also, the results of estimation rest upon the
60 Wilde (2000) points out that earlier references presented contradictory opinions on this matter, so that
Maddala (1983) held that a model with overlapping sets of exogenous variables x i , z i was only identified if
at least one variable in the set z i is not in the set x i , while Heckman (1978) maintained that the functional
form sufficed for identification. However Wilde (2000) clarifies that Maddala’s argument is only valid for
his particular example, and is not the case generally due to the nonlinear relationships between z and the
probability P(d=1 | z), and further concluded it could be avoided by assuming each equation contains at
least one varying exogenous regressor. Wilde (2000) points out that this is a rather weak assumption in
economic applications. Hence, Maddala’s argument commonly holds in econometric practice.