Evaluation of the Australian Wage Subsidy Special Youth ...

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(6) a i * = d ‘ R i + ε i
where d ‘ = (π ‘,δ ‘) ; R i = (x i2 , w i ) ; ε i = γ v i2 + ε i *
If the v it are assumed to be normally distributed and the variance of ε i is one, and Φ(.) is
the standard normal distribution then the probability of no attrition is
(7) Prob (a i = 1) = Φ(a ‘ R i )
When using the balanced panel of complete observations, Hsaio (1986) p199 shows that
the conditional expectation of y i2 is
(8) E (y i2 | x i2 , a i =1 ) = β ‘ x i2 + σ 2 ε [φ (a ‘ R i ) / Φ (d ‘ R i )]
Where σ 2 ε is the covariance between v i2 + ε i and φ (.) is the standard normal
distribution. It is clear that this derivation is the same as the bivariate probit model
presented earlier in Chapter 3, but applied to the case of attrition.
In the Australian Longitudinal Survey, attrition is a strong issue for the analysis of
employment in 1986, as the employment in 1986 can never be known for those who are
not interviewed in 1986 because they are lost through attrition. This introduces the
problem of selection by virtue of survival, where the modelling of employment in 1986
can only take place for the sample surviving from 1984 to 1986 (Hoem (1985): 260). The
bias introduced by attrition is shown in equation 8. Unless σ 2 ε = 0 , then estimates of β
using the balanced panel of complete observations are biased and inconsistent.
The first formal econometric model of attrition and labour market behaviour is usually
attributed to Hausman and Wise (1979). There was a high attrition from the Gary Income
Maintenance experiment and they were concerned this would bias the experimental
estimates because the attrition was likely related to income, which was their outcome of
interest. They found evidence of attrition bias in modelling attrition alongside the income
equations, but concluded it had little effect on the experimental effect estimated. Ridder