Education, Employment and Earnings of Secondary School-Leavers ...

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freedom for this test. In regard to the homoscedasticity test, the set of explanatoryvariables included in the earnings specifications provide the basis for the alternativeheteroscedastic relationship. The Q 1i to Q ki terms are constructed by interacting theσ_score i term with the x 1i to x ki explanatory variables from the regression model. Thereported degrees of freedom for this test are thus equal to the number of explanatoryvariables in the original specification. The normality test examines departures fromskewness and kurtosis and the Q 1i and Q 2i measures are constructed in this case byinteracting the pseudo-residuals with expressions for the third and fourth momentresiduals (see Chesher and Irish (1987) for more details). The number of degrees offreedom in this case is two.The resultant test statistics are all distributed as chi-squared with p = q – k degrees offreedom. The test represents the outer-product gradient (OPG) form of the score (orLagrange Multiplier) test. Orme (1990) has questioned the use of OPG-based testsand, using Monte Carlo simulations, demonstrated their poor finite sample propertiesin the context of the binary probit model. Orme’s findings suggest that efficient scoretests constructed using the OPG covariance matrix tended to reject the correct nullhypothesis far too frequently. Given the modest sample sizes we use here this may beviewed as something of a concern. Even if the simulation findings extend to theinterval regression models used here, though, the implication in using these tests isthat we are actually setting the estimated models a more stringent set of criteria topass. We take the view that it is more desirable to be transparent about the testfindings and report rather than ignore them. 20In circumstances where the homoscedasticity and/or normality assumptions areviolated, the variance-covariance matrix is corrected using the Huber (1967)‘sandwich’ estimator, which provides an appropriate asymptotic matrix for anestimator that is biased in an unknown direction. 21 This is defined as:Var-Cov( ∧ ) = [I( ∧ )] -1 ( x ' i ui 2 x i) [I( ∧ )] -1 [6]20 The estimation reported in this paper was undertaken using the LIMDEP 7.0 software package.21 However, see Greene (2000, pp.823-824) for some cautionary comments about its use and validity.15
where I( ∧ ) is the information matrix for the ∧ vector computed at the maximumlikelihood estimates.Given that we are interested in estimating an earnings equation within the establishedMincerian tradition, the thresholds used in the log-likelihood function [2] are based onthe natural logarithms of the reported thresholds. Thus, in the context of theemployee specification, a 1 = log e (50,000) and a 7 = log e (400,000), and so forth. 22Finally, there is potential for selection bias in the estimated earnings equations. Thesamples of employees and the self-employed may not represent a random drawingfrom the population of school-leavers. 23 As a consequence, the estimated coefficientsfor the returns to education and other characteristics may be potentially biased. Inorder to address this problem we use the procedure developed by Lee (1983), whichprovides a more general approach to the correction of selectivity bias than thatoriginally offered by Heckman (1979). The procedure is also two-step but exploitsestimates from a multinomial logit model (MNL) rather than a probit to construct theset of selection correction terms. We first estimate the reduced form MNL for thej=1,...,k categories and obtain the parameter estimates γ j . In our application k=4 withemployees, the self-employed, those in training and the unemployed providing thefour mutually exclusive categories. The predicted probabilities for each individuali=1,....,N for each category j are then computed and defined as P i1 ,P i2 ,....P i4 . The‘normits’ or standardized z values for each individual for each category j using theinverse standard normal operator are then computed. Thus: z i1 = Φ -1 (P i1 ), z i2 = Φ -1 (P i2 ),........ z i4 = Φ -1 (P i4 ) for all i=1,.....N. Finally, for each j category we construct thefollowing correction term:φ(z )Pijλ ij = for i=1,2,.......N and j=1,2,...k [7]ij22 See the notes to table 1 for the full set of intervals used in the case of the employees.23 In fact there is another potential source for selection bias in the estimation of our wage equationsgiven that our sample is conditioned on secondary school-leavers. It thus excludes those with primarylevelor no education. Given the positive relationship between earnings and education, the underlyingwage distribution may be truncated at the bottom end and there may be potential for an upward bias inour estimated educational returns as a consequence. In contrast to employment selection, there isnothing that can be feasibly done to address this selection problem given existing data constraints.16
Page 1 and 2: Education, Employment and Earnings
Page 3 and 4: The structure of the paper can now
Page 5 and 6: Despite large absolute increases in
Page 7 and 8: nine studies reviewed for sub-Sahar
Page 9 and 10: It should be noted, however, that e
Page 11 and 12: history, current activity and incom
Page 13 and 14: In order to understand how the mode
Page 18 and 19: where φ(·) denotes the probabilit
Page 20 and 21: 5.1 Earnings Equation - The Employe
Page 22 and 23: 4.8% per annum in the first three s
Page 24 and 25: confirm to some extent that unobser
Page 26 and 27: The ceteris paribus earnings for th
Page 28 and 29: [Table 7]The rate of return for a u
Page 30 and 31: 6. ConclusionsA key finding of our
Page 32 and 33: that the rates of return to educati
Page 34 and 35: Knight, J.B. and Sabot, R.H. (1981)
Page 36 and 37: Table 1: Highest level of education
Page 38 and 39: Table 4 (Cont’d)SelectionCorrecti
Page 40 and 41: Table 5 (cont’d)Selection Correct
Page 42 and 43: Table A1: Variable DescriptionVaria

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