Thailand Law Journal 2009 Spring Issue 1 Volume 12

We implement the exogeneity test by regressing years of education in 2001 on the vector Z and by computing the (first step) residuals. Appendix Table A1 reports the key estimated coefficients from this regression, as well as the Bound test statistic. We find that both the mother's age at birth and the individual's birth order had statistically significant effects on education. The sign of the former effect is positive, but turns negative when the individual is the oldest son or daughter. The sign of the latter effect depends crucially on the mother's age: it is positive when mothers are younger than 26, and negative when mothers are older. Finally, a higher number of siblings in the households was associated with a statistically significant reduction in educational attainment.

Since the Bound test is equal to 5.47 (p-value: 0.001), we reject the null hypothesis of no (joint) statistical significance of the additional instruments at the 1% level of confidence. Next, we run the bi-probit model for training incidence and the tobit model for training intensity after adding the first step residuals to each model and test whether this variable is statistically significant. [FN15] A positive result would reject the hypothesis that education is exogenous for training. It turns out that the estimated coefficients of the first step residuals are never statistically significant at the 0.05 level of confidence. Therefore, we cannot reject the null hypothesis of exogeneity of education in the training equations. [FN16]

Table 5 focuses on training incidence and shows that individuals with higher education were less likely than others to receive OJT and more likely to receive OFFJT. We also find that the probability of receiving training increased with age. The effects of tenure and experience varied with the type of training, and were negative for OJT and positive for OFFJT. Finally, women were statistically significantly more likely than men to receive OJT.

Table 6 looks at training intensity and confirms the relationship between education, OJT, and OFFJT. The estimates in Tables 5 and 6 refer to the overall effect of education on training, which includes both the direct effect and the effect mediated by the allocation of individuals to jobs and positions. One would like to know, however, whether an individual endowed with higher formal education who filled a given position was likely to receive more or less OJT or OFFJT. To answer this question we need to hold constant the type of position, for clearly different positions require different degrees of training, in both extent and type.

We control for the position held by restricting our sample to production workers, and by excluding team leaders, foremen, and other positions. The results reported in Tables 7 and 8 confirm the qualitative findings of Tables 5 and 6, with the sole exception that the positive effect of education on OFFJT is not statistically significant in the case of training incidence.

 Table 7. Bivariate Probit Estimates of Training Incidence, Production Workers

    Only, 1998-2001. (dependent variables: OJT and OFFJT incidence; robust    

                        standard errors in parentheses)                        

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                  Years of Education Treated as    Testing for Exogeneity of  

                            Exogenous                      Education          

                  -----------------------------  ------------------------------
Variable               OJT            OFFJT            OJT            OFFJT    

-------------------------------------------------------------------------------
Sex                   -0.028         -0.026           0.090          -0.147    

                      (.075)         (.075)          (.151)          (.152)    

                                                                              
Age                   0.189*         0.270**         0.266*           0.158    

                      (.114)         (.116)          (.155)          (.154)    

                                                                              
Age2               -0.007*        -0.008**         -0.008*         -0.005    

                      (.003)         (.003)          (.004)          (.004)    

                                                                              
Age3 * 10           0.007*         0.007**         0.001**          0.000    

                      (.003)         (.003)          (.000)          (.000)    

                                                                              
Tenure in 1998       -0.019*          0.011         -0.022**          0.010    

                      (.010)         (.010)          (.011)          (.011)    

                                                                              
Previous             -0.013*         0.015*          -0.012           0.013    

Experience in                                                                

  1998                                                                        

                      (.008)         (.008)          (.008)          (.008)    

                                                                              
Education           -0.064***         0.014          -0.143*          0.095    

                      (.011)         (.011)          (.086)          (.085)    

                                                                              
First Step              --             --             0.079          -0.083    

  Residuals                                                                    

                                                     (.086)          (.085)    

                                                                              
<<rho>>              0.320***                       0.307***                  

                      (.031)                         (.028)                    

                                                                              
Observations          3,523           3,523           3,487           3,487    

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   Notes: See notes to Table 5.                                                

[FN15]. With panel data, one might expect the error term to be correlated across individuals. With Stata, robust standard errors are easily computed for the bi-probit model. Since this option is not available for the tobit model, we bootstrap standard errors, using 50 replications of the estimates. Bootstrapping uses Monte Carlo simulation to compute adjusted standard errors. See Wooldridge (2001).

[FN16]. Under the null hypothesis that residuals are not statistically different from zero, we do not have to adjust standard errors for the presence of generated regressors. See Blundell and Smith (1986).

This article is published with the kind permission of Kenn Ariga and Giorgio Brunello. The article originally appeared in Volume 59, Issue 4, July 2006, of the Industrial and Labor Relations Review. Copyright Cornell University.