The Limits of Mathematics and NP Estimation in ... - Chichilnisky

84Advances in Econometrics - Theory and ApplicationsExp is the experience; X is a set of time-varying regressors, and Z is a set of time-invariantregressors. The β coefficient expresses the rate of return to education; 1 and 2 represent theearnings-experience profile, and and γ are the set of parameters accompanying theremaining regressors.Rather than using the education measure normally employed in the literature, years ofschooling, we consider the educational attainment of each worker, providing two clearadvantages. First, it does not impose the annual marginal effect of schooling as being thesame in each year of education, and second, the level of education is a more appropriatemeasure, since multiple education streams characterize European countries, and salaryprofiles used to be largely linked to the education category attained. In other words, theycapture the possibility that credentials matter more than years of schooling per se in thewage determination. This hypothesis is commonly known as the “sheepskin effect” andattempts to explain the discontinuous changes in earnings associated with completion ofelementary school, high school or college (Belman & Heywood, 1991; Hungeford & Solon,1987; Jaeger & Page, 1996).Educational attainment, which is considered time-invariant in our sample, represents thelast completed level of schooling, classified as primary, secondary, and high. Primaryincludes elementary and below elementary school, secondary includes vocational andmiddle school, and tertiary or high includes university studies (in either short or longcycles). Consequently, the fragment “β Edu i ” in equation (2) would be represented by “β 1EduS i + β 2 EduH i ”. The category of reference is EduP i , omitted in the estimation.ln w it = β 1 EduS i + β 2 EduH i + 1 Exp it + 2 Exp 2 it/100 + X' it + Z' i γ + u it , (3)The dependent variable is the natural log of net earnings, where these are defined as grossearnings less tax, expressed in per hour real terms. The earnings-experience profiles areanalyzed by considering the number of years that an individual has been working, and itssquared value divided by 100 to take care of the decreasing returns. Specifically, experienceis measured as the difference between the current age and the age of initiation at work,thereby expressing potential experience. The remaining independent variables, representedin equation (3) by X and Z, contain dummies for gender, marital status, training, occupation,sector, seniority, and a set of time fixed effects, as described in Section 4.3.2 Estimating the earnings equation: the Hausman-Taylor procedureThe general model in (3) assumes that the error term u it consists of the sum of twocomponents, i.e. u it = α i + v it , where α i represents the random individual-specific effect thatcharacterizes each worker and is constant through time, and v it is a random disturbancevarying over time and individuals. This latter stochastic term is assumed to be uncorrelatedwith all included variables. Similarly, it is also assumed that the random disturbance is asequence of i.i.d. random variables with mean zero and variance 2 v; that v it and i aremutually independent, and that i is i.i.d. over the panels with mean zero and variance 2 .Thus, the variance-covariance matrix of the system has the random effects structure that canbe represented as E(UU’) = 2 (i T i T ’ I N ) + 2 v (I T I N ), where i T is a Tx1 vector containing1s, I N (I T ) is the identity matrix of rank N (T), and U is an NTx1 vector of disturbances. Thus,random-effects or Generalised Leasts Squares (GLS) produce consistent estimators.However, the presence of measurement errors and unobserved variables, such as ability,motivation, etc., that may be correlated with schooling, bias GLS estimates. Specifically, it