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Essays in the economics of education

Levin, J.D.

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Chapterr 4

Returnss to schooling in the Netherlands

4.11 Introductio n Forr a long time economists and scholars alike have thought of the participation in education as ann investment that increases the future earnings and well being of its recipient (termed later by Schultzz as an investment in "human capital"). However, it has been only recently that the benefitss and costs of making such an investment have been formally analyzed. Approximately fortyy years have passed since the pioneering work of Mincer (1958), Schultz (1961) and Beckerr (1964) on human capital first became published addressing the theoretical background off an investment in human capital and in particular, the rate of return such an investment fetches.. Since then a plethora of studies have been conducted attempting to calculate new and betterr estimates of the return to education for different time periods in different countries.

Invariably,, at the heart of these studies will be found the workhorse of educational investmentt rate-of-return analysis, the "Mincerian" earnings function estimated using ordinary leastt squares (OLS). With the widespread use of such a tool it was inevitable that theoretical argumentss would arise as to the validity of its estimates. Clearly, reliable estimates of the returnn to education are relevant to those that formulate educational policy as well as individualss making personal educational decisions. In response to the dismay of the academic communityy with the possibility of OLS producing inconsistent return estimates, certain techniquess have been utilized in hopes to yield corrected/consistent calculated returns. For a varietyy of reasons, different studies have cited both upward and downward biases in the rate of returnn to education when using OLS.

Thee focus of the current chapter is to explore the recent widespread use of instrumentall variables (IV) technique in order to obtain consistent educational return estimates andd apply the procedure using data from the Netherlands. The structure of the chapter will be ass follows: Section 4.2 will briefly present the human capital earnings function (Mincerian earningss function), its foundation in the human capital framework, and the theoretical argumentt in favor of IV estimation in order to obtain consistent rate-of-return estimates; 4.3 continuess with an exposition of the problems that may arise using this method; Section 4.4 providess a survey of contemporary studies that utilize IV technique to purge rate-of-return estimatess of inconsistency; Section 4.5 describes the data employed and results from IV estimationn procedures for the Netherlands; Section 4.6 summarizes and concludes.

90 0 ChapterChapter 4

4.22 Biases in the human capital earnings function and instrumental variables technique e

Pioneeredd by Jacob Mincer, the earnings function attempts to describe the relationship betweenn schooling and earnings as follows:

2 2 logvv// - a + fisi + yei + Se + £j (1)

wheree w, is wages; s, is years of schooling; e/ is a measure of experience; and, e, is an error termm (controls for personal and background characteristics have usually been included). Givenn this simple model, /?will be an estimate of the rate of return to schooling (the estimated percentagee increase in w resulting from an additional year of schooling). However, much attentionn has been drawn to the fact that this simple model assumes there is no correlation betweenn schooling and the error term (i.e. E(s„ £,) = 0). Ordinary least squares will estimate p consistentlyy if and only if schooling (si) is not correlated with the residual in the earnings equationn (e,). There are three reasons commonly cited as to why schooling might be correlatedd with the earnings error: endogeneity bias, ability bias and measurement error. The studiess by Grilliches (1977), Willi s and Rosen (1979) and more recently, Card (1999, 2000) presentt theoretical expositions of endogeneity bias arising from wealth (utility) maximization models.. The study by Grilliches also analyzes omitted ability bias while that of Card addressess both ability bias and measurement error in schooling.

Endogeneityy bias occurs due to individuals' optimal schooling decisions by which it is assumedd that persons behave as if they enroll in education up to the point where the cost of an additionall unit of schooling (marginal cost) just equals the benefit it provides (marginal benefit).. Under the plausible assumption that individuals with higher (lower) marginal benefitss (costs) invest in more (less) education on average, it is expected that using OLS will resultt in an upward bias in the estimated return to education. Card (1999, 2000) shows theoreticallyy this bias to be worse the larger is the variation in marginal benefits relative to marginall costs (discount rates) across individuals in the population. This will be exacerbated shouldd marginal benefits and marginal costs of education be negatively related.

Omittedd ability bias is thought to occur via a correlation between ability, the optimal amountt of schooling one chooses, and subsequent earnings. Ability bias can be viewed as a "gardenn variety" omitted variable bias whereby the influence of unobserved factors that are correlatedd with both earnings and schooling are unduly manifested in the rate of return estimatedd by OLS. However, in contrast to the case of endogeneity, the direction of the bias onn returns to schooling caused by the omission of ability in an OLS earnings equation is ambiguous.1 1

Finally,, there may be bias caused by classical measurement error in schooling due to misreporting,, faulty collection methods or other reasons. This mismeasurement puts downwardd pressure on the estimated schooling return coefficient.

11 The ambiguous effect of ability of optimal school length is illustrated in the study by Grilliches (1977) in which aa positive correlation between ability and earnings represents an increased marginal cost of attending school (in termss of foregone earnings) and hence, a lower optimal schooling level while a positive correlation between abilityy and the speed with which one can Finish a year of schooling will decrease the marginal cost having a positivee effect on school length.

ReturnsReturns to schooling in the Netherlands 91 1

Instrumentall variables estimation (IV) is a widely used technique in the attempt to obtainn consistent estimates of the return to schooling. As stated above, all three problems causee a correlation between the error in the earnings equation and the schooling variable. In orderr to obtain consistent rate-of-return estimates, it is necessary to find an estimation proceduree that alleviates this correlation. Suppose then, that we can create a new variable that onlyy contains the exogenous component of schooling (a part that is not correlated with unobservedd earnings). We could then consistently estimate schooling returns by regressing earningss on the new "improved" (exogenous) schooling variable. This is the idea behind IV estimation. .

Howw do we go about creating this "instrumented" variable? In practice, the technique boilss down to finding an exogenous variable or group of variables (henceforth referred to as "instrumental"" variables) that are correlated with the endogenous regressor in question (schooling),, but have no direct effect on the left-hand side variable (earnings). In other words, thee instrumental variable(s) must satisfy an exclusion condition (i.e. they can be legitimately excludedexcluded from the earnings equation). One can then perform a two stage least squares proceduree (2SLS) which employs the instrumental variable(s) in order to purge the endogeneityy from the system of equations. In the first stage, schooling is regressed upon all exogenouss variables in the system including the instrumental variable(s). Next, in the second stagee the predicted values of schooling are then used in the earnings equation, which excludes thee instrument(s). Given we have used valid instrument(s), the "instrumented" schooling variablee should no longer be correlated with the error in the earnings equation and consistent estimatess are obtainable. To see this econometrically, consider an IV estimator of the rate of returnn to schooling s,- in terms of wages w, using the instrument set z, (written in deviations form), ,

IVIV = ZlogWjZj = pLsjZj+YzjSj _ | £z,g,

ZSJZJZSJZJ 'LSJZI ^sizi

Iff we chose our instrument(s) correctly then, by construction of the estimator, the last term shouldd equal zero as the sample size gets large and we are left with a consistent estimate of thee rate of return to education.2

4.33 Issues and problems with instrumental variables Att first glance, the procedure seems fairly straightforward; simply find a set of (instrumental) variabless that are correlated with schooling and uncorrelated with earnings. However, as any researcherr applying the IV technique to estimating schooling returns can vouch, it is not as "cutt and dry" as it seems. First of all, one problem concerns the availability of variables that cann be considered usable instruments which is by in large dictated by the dataset at hand; a variablee that conforms to the aforementioned criteria might not be at the researcher's disposal therebyy making IV estimation impossible to implement.

Inn order to estimate the causal effect of a treatment in the natural sciences random experimentsexperiments are conducted in which treatment is randomly assigned to the sample of

22 For a full econometric exposition of instrumental variables estimation and the criterion of valid instruments see Pindyckk and Rubinfeld (1991, pp. 177-179).


observationn units. This is infrequently the case in social sciences. In our present context, we cannott randomly assign levels of education (treatment) to individuals within our sample. Instead,, the social scientist relies on the discovery of natural experiments. That is, we artificiallyy create a schooling variable with "natural" variation using instrumental variables thatt are thought to exert exogenous influence on the schooling decision (variables that have no directt effect on earnings), thereby purging the schooling variable of its endogenous component.. Indeed, as wil l be shown in the next section, there have been several ingenious attemptss justifying the use of various instruments to induce exogenous variation in the endogenouss regressor (treatment variable). However, even if one should be fortunate enough too find potentially suitable instruments, four issues that merit investigation have been put forth inn the literature concerning the use of IV techniques: quality, validity, sensitivity and imprecision. imprecision.

4.3.11 Instrument quality

Recentt claims concert that while most attention has been paid to the validity criterion, littl e hass gone towards quality when choosing instruments. The study by Hall et al (1996) emphasizess the consequences of using instruments that are weakly correlated with the "instrumented"" endogenous regressor. In addition, Bound et al (1995) and Shea (1997) make clearr the problems with using weakly correlated instruments and why they occur. It is shown that,, given a weak correlation between the instrument(s) and endogenous regressor, the inconsistencyy of the IV estimator relative to that of the OLS can turn out to be very great shouldd the instrument(s) be even slightly correlated with the error term of the structural (second-stage)) equation.3 Unless, the instrument is completely uncorrelated with the error termm of the structural equation, a weak correlation between the instrument(s) and endogenous regressorr can result in grossly inconsistent IV estimates. Recent literature has shown that the finitee sample distribution of the IV estimator can greatly differ from the asymptotic Normal distributionn in the presence of "weak" instrument(s). This has prompted several attempts to derivee the finite sample distribution of the IV estimator, all of which have found that the IV estimatorr exhibits bias in the same direction as that of OLS and becomes worse as the sample sizee gets small and/or instrument strength decreases.4 Bound et al, after reexamining the resultss of Angrist and Krueger (1991, discussed below), conclude:

"Ourr results imply that if the correlation between the instruments and the endogenouss variable is small, then even the enormous sample sizes available in the U.S.. Census do not guarantee that quantitatively important finite-sample biases will bee eliminated from IV estimates."

Itt follows then that measures are needed to gauge the effect of weakly correlated instruments onn the finite-sample bias of IV estimators. The partial R2 of the regression of the endogenous regressorr x on the instrument set z is one candidate to perform this task (see Appendix 4A). Inn addition, the F-statistic on a test of the excluded instruments from the first-stage equation is alsoo cited as a "rough" indicator as to the quality of IV estimates.5

ForFor proof of inconsistency under weakly correlated or invalid instruments, see Appendix 4A. 44 See for instance Bound et al (1995) and Staigerand Stock (1997).

Indeed,, Bound et a! (1995) suggests that empiricists routinely report these statistics.


However,, it must be noted that arguments warning against the use of these indicators forr screening instruments have been put forth by Hall et al (1996). The main idea is that a highh correlation between the instruments and the endogenous regressor in the sample may be duee to the correlation between the instruments and the endogenous portion of the regressor in thee sample, regardless of the exogeneity of the instruments in the population. In turn, ex-ante screeningg or "weeding out" instruments that seem weak or irrelevant, as dictated by the F-test above,, may in fact increase the probability of obtaining inconsistent estimates. To this end, Sheaa (1997) concludes that the relevance measures, the partial R2 and F-test of excluded instruments,, should not be left by the wayside but rather used as ex-post indicators of instrumentt quality. The selection of instruments should be based on theory and reason rather thann pretests.

4.3.22 Instrument validit y Thee more commonly talked about criterion, that valid instruments must not be correlated with thee second-stage equation, must also be addressed. Sargan (1958) and Basmann (1960) independentlyy derived a test, later termed a "test of overidentifying restrictions", that addressess this criterion. The interpretation of this test is two-fold in that it checks the null hypothesiss that the instrument set is orthogonal to the second-stage residuals and that the modell is correctly specified. The test statistic is easily calculated by taking the R2 from a regressionn of the second-stage residuals on the instrument set and multiplying it by the numberr of observations.6 Davidson and MacKinnon (1993) advise:

"Testss of overidentifying restrictions should be calculated routinely whenever one computess IV estimates. If the test statistic is significantly larger than it should be by chancee under the null, one should be extremely cautious in interpreting the estimates, sincee it is likely either that the model is specified incorrectly or that some of the instrumentss are invalid."7

Onee shortcoming of the diagnostic is that the test is not defined when the system under scrutinyy is exactly identified (i.e. there exist the same number of instruments and endogenous regressors).. In this case the researcher is forced to use alternative measures to determine the validityy of instruments.8

4.3.33 Instrument sensitivity Ratherr than a problem dealing with the quality or validity of instruments, a third problem concernss the interpretation of IV estimates. The relevant question we have posed is "What is

66 The resulting statistic is yj distributed with (I-k) degrees of freedom, where / is the total number of exogenous variabless in the model and k is the number of exogenous right-hand side variables in the earnings equation. 77 For a more elaborate discussion of identification and overidentifying restrictions see Davidson and MacKinnon (1993,, pp. 232-237). 88 One such test is to simply include the instrument(s) in the baseline regression and determine significance via t-orr F-tests.


thee causal effect of an instrumented variable?" (education in our case). By definition, a causal effectt on a unit of observation is:

".. . . the comparison (e.g. difference) between the value of the outcome if the unit is treatedd and the value of the outcome if the unit is not treated."9

"Treatment"" refers to exposure to some stimulus described above by an endogenous regressor orr instrumented variable. Let us assume we have a dummy variable denoting treatment so that itss stimulus is binary (i.e. an individual is "treated" or "not treated"). Denote E(y,J and E(yc) ass the expected log earnings of the treated and control groups, respectively. Likewise, let E(S,)E(S,) and E(SC) be the expected levels of education for the two groups. If we use for the binary treatmentt variable the instrumented level of schooling in order to perform a regression of earningss on schooling, then the causal relationship of education on earnings is just the ratio of thee difference of earnings outcomes to the difference in schooling levels between the treatmentt and control groups,

phmphm^^== E(SE(Stt)-E(S)-E(Scc)) ( 3)

Iff the marginal return to education is equal for all individuals within the population then this wil ll be equal to the population average marginal return to schooling. However, in reality the marginall return to schooling is not the same for all individuals.10 Now suppose that there is somee intervention that only affects the schooling decisions of a subgroup of the population thatt contains a specific type of individual yet all other groups' schooling decisions are left unaffected.. The IV estimate in its probability limit for this subgroup then equals

plim/?? = i g s g (4) ZgASZgASggwwg g

wheree ASg equals the change in average schooling level for the subgroup g affected by the

treatment,, pg is the marginal return to education for the subgroup, and wg is the fraction of the totall population in the subgroup. Therefore, the IV estimate wil l describe the average marginall return for that subgroup of individuals that were affected by the intervention in terms off changing their treatment status (i.e. induced to alter their schooling decisions). Alternativelyy speaking, the estimated return wil l be sensitive to the instrument being used.

Ass an example, let us assume that the solely affected subgroup contains mostly individualss with high discount rates and hence, higher than average marginal returns. For instance,, assume there is some sort of intervention that marginally lowers the costs of educationn so that, as a result, only those who have high discount rates wil l enroll in more schoolingg (i.e. the intervention does not induce those with low discount rates to change their schoolingg decisions). Then the resulting estimated return from IV wil l be higher than that producedd by OLS because individuals in the "affected" group have higher then average discountt rates and hence, above average returns. Clearly, decision-makers should not formulatee general educational policies based on estimates that pertain to one group of

99 Quote taken from Angrist, Imbens and Rubin (1996). 100 For example, the theoretical framework of Card (1999, 2000) predicts individuals with higher discount rates and/orr lower ability will opt for less schooling and experience higher marginal returns.


individuals.. The example above shows that misinterpretation of these estimates as average causall effects across the whole of a population could lead to the implementation of inappropriatee policy measures.

4.3.44 Imprecision of estimates Thee last problem in using IV procedures is rather mechanical in nature stemming from the constructionn of the estimator. This is the well-known property of IV estimators to "blow up" thee standard errors of the estimated coefficients thereby causing imprecisely estimated coefficients.111 As will be seen in the next section, in the context of schooling returns, often IV estimatess are found to differ greatly from those obtained using OLS. However, because the IV pointt estimates are so imprecise rarely do the two estimates differ significantly.

4.44 Literatur e survey Sincee the early 1990's, several studies by economists have used IV to consistently estimate schoolingg returns. The table in Appendix 4C contains a detailed summary of ten rate-of-returnn studies that have made use of IV technique. What is of interest in the present context aree the strategies these studies use to address the three causes of bias in rate-of-return estimatess and, in particular, the ingenious instruments found to isolate exogenous variation in thee schooling variable. This section will briefly review the studies paying close attention to thee applied instruments and the justification behind their use.

Thee studies by Blackburn and Neumark (1993, 1995) use family background measures ass instruments for both ability and schooling in order to control for potential correlation betweenn these variables and the earnings equation error. It is thought that family background characteristicss should serve as valid instruments as one would expect them to be correlated withh an individual's ability and/or schooling while there is no reason to believe any correlationn exists between these characteristics and earnings. However, there is concern as to thee validity of the assumptions that underlie this proposition. Namely, it must be assumed that jobb "networking" by the parents for their children does not exist and therefore, better connectionss of parents with higher socio-economic status do not affect their children's earnings. .

Angristt and Krueger (1991) assess the effect of compulsory school attendance on durationn of schooling and hence, identify the causal effect of schooling on the earnings of individualss in the US. The study makes use of an individual's quarter of birth as an instrumentt for schooling. What makes this relationship operational is the interaction between individuall quarter of birth, the laws concerning timing of school entrance, and the ages for whichh schooling is compulsory. Because compulsory schooling laws in the US require individualss to complete education up to a specified age (historically 16 or 17 and as of late 18) andd admission to school is possible once a year in the autumn, those born in the early half of thee year will tend to enter school at a later age.12 It follows that individuals in this group will reachh their respective age at which schooling ceases to be compulsory with less education on

1'' An econometric proof of the imprecision associated with IV estimators can be found in Appendix 4B. 122 A common rule in U.S. school districts is that the enrolling student must be six years of age by January Is' of thee year they plan to enter school.


averagee than those born later in the year.13 Hence, there should be some correlation between quarterr of birth and amount of schooling due to the interaction of the laws concerning compulsoryy schooling and entry date on the one hand, and the arguably random quarter of birthh on the other.

Anotherr ingenious attempt at estimating the return to schooling in the presence of the biasess listed above is made by Angrist and Krueger (1992) using data from the Vietnam War draft.. Again, they find a natural experiment that makes it theoretically possible to obtain consistentt educational return estimates. The Selective Service Act of 1967 in the US allowed thee government to draft men born between 1944 and 1953 into military service. The selection mechanismm consisted of a lottery whereby numbers (1 through 365) were assigned to individualss based on their date of birth. Lower numbers corresponded to higher priority draft status.. The natural experiment comes in to play because individuals were allowed deferments iff they entered college or university. In turn, it is expected that those with high draft priority (loww lottery numbers) would be more likely to have enrolled in further education so that exogenouss variation is produced in the level of schooling (variation in schooling not related to earnings).. Therefore, the authors expect to find higher schooling on average for those with highh draft priority. In addition, because the lottery was a random draw, there is no reason to believee that the assigned lottery numbers have any direct affect on earnings and could thus be usedd to instrument schooling.

Cardd (1993) attempts to circumvent the biases due to endogeneity, omitted ability and/orr measurement error by simply considering the geographic proximity of individual residencee to a college when growing up as a viable instrument for schooling. Clearly, the distancee between one's home and college varies the cost of (higher) education in the population,, thus inducing exogenous variation in schooling:

"Studentss who grow up in an area without a college face a higher cost of college education,, since the option of living at home is precluded."

Hee expects the higher costs faced by those who grow up far away from a college to cause less investmentt in higher education for this group, particularly among individuals from low-incomee households.

Thee focus of the study by Butcher and Case (1994) is on the gender gap in educational participationn and subsequent earnings of men and women. The instruments used denote the numberr of siblings and gender composition of a sibship (i.e. number of brothers and sisters, indicatorr variables of brothers and sisters, and share of sibship that is female). There is no reasonn to believe that the gender composition of one's sibship should affect earnings later in life.. However, four reasons are postulated as to how size of sibship and gender composition mightt affect educational attainment. The models of parental preference show that, within a familyy facing borrowing constraints in order to maximize the sum of their children's incomes, parentss will allocate funds for education such that the child(ren) with the highest marginal

133 Indeed, for two birth cohorts (1930-1939 and 1940-1949) the authors find a small but significant difference in thee schooling levels for those individuals born in the first quarter compared to those born in the fourth quarter of aa given year. For instance, in the earlier cohort first quarter births had on average up to 12.5% less schooling thann their fourth quarter counterparts; this difference was 8.5% for the later cohort.


returnn to education will receive the most schooling.14 Therefore, when constraints on borrowingg are binding the size and composition of a sibship is not independent of the allocationn of educational funds. For example, if females have higher returns than males then a daughterr in a two-child family would receive relatively more schooling if her sibling were male.. Educational attainment could also be related to sibling sex composition should daughterss and sons have different effects on the household budget constraint. First, the costs off raising a son and daughter may differ due to different inputs needed for raising of each. Secondly,, they may have different earnings potential which affects the budget constraint. Two additionall reasons put forth as to why gender composition of siblings might affect educational attainmentt is found in the child development literature. Previous research shows that females whoo grow up with an older brother exhibit more "masculine" traits than those that grow up alonee or with a sister. If education is considered a "masculine" trait then females with an olderr brother will tend to have higher educational attainment. Also in the realm of child developmentt is the "reference group" theory that states that when a second sister is introduced too a sibship consisting of a daughter and son(s), the reference group of the first daughter changess in that the parents use new (lower) standards or expectations for their daughters' educationall attainment then was faced by the original sibship; whereas, the son faces the same expectationss as before.

Too deal with endogeneity bias Harmon and Walker (1995) use direct constraints on schoolingg decisions imposed by law as instruments. Related to the study by Angrist and Kruegerr who rely on the interaction between compulsory schooling laws and entrance age policyy to legitimize season of birth as an instrument, this work looks to changes in compulsory schoolingg laws as a cause for exogenous changes in the educational distribution in the UK. Thee UK imposed two changes in the minimum school leaving age (MSLA) since the 1944 Educationn Act was passed. In 1947, this minimum was raised from age 14 to 15 and, in 1971, wass raised again to 16. The authors show that the first increase in MSLA exerted much influencee on the schooling decisions of those who were "covered" by the change (individuals thatt were 14 in the period 1947 to 1971):

"Manyy of those who would otherwise have left at the old minimum stayed on beyond thee new minimum."

Inn addition, they show that the earnings differential between the two middle-aged (late career) cohortss that faced 14 and 15 year MSLA's is statistically insignificant. Therefore, because the directt constraint of minimum school age legislation seems to influence schooling decisions whilee exerting a negligible effect on earnings, it serves as a prime candidate to use as an instrumentt in an IV estimation of schooling returns.

Inn contrast to the other studies cited here, Kal wij (1996) utilizes an IV approach in a panell data model with random individual effects. Here both schooling and experience (squared)) are considered to be endogenous. Special attention is drawn to the fact that the IV estimationn is not based on one "unique" instrument. The author observes that older individualss in the panel have less education than those who are younger and uses this to

144 In the absence of borrowing constraints parents would invest in their children's schooling until the marginal returnn of each child just equals the marginal cost or market interest rate and therefore, (funds for) education wouldd be allocated optimally. However, this assumes that parents are not concerned with equitable split of allocatedd resources or expected outcomes.


constructt instruments that corrects for the assumed schooling endogeneity. In addition, birth-cohortt effects are taken into account by using per capita GNP at age 16 as an instrument.

Uusitaloo (1996) compiles data from various Finnish sources to provide a comprehensivee dataset that allows an IV estimation of schooling returns. In line with the two previouslyy mentioned studies by Blackburn and Neumark, Uusitalo starts his analysis addressingg the effect of ability bias on return estimates and later attempts to correct for the endogeneityy of schooling using family background variables such as indicators of father's educationn and job level as instruments.

Harmonn and Walker (1996) provide us with a study that has a broader focus than their previouss work. In this study they set out to address the cause of the downward bias found in virtuallyy all OLS versus IV return estimates. Three common causes are cited as the potential sourcess of the downward bias: neglected return heterogeneity (endogeneity), omitted motivationn or ability, and measurement error. If the first of these is the true cause of the downwardd bias then an IV procedure should relay the returns of those whose behavior is affectedd by the instrument; IV estimates should therefore be sensitive to the instruments being usedd (cf Section 4.3.3). However, should omitted motivation and/or measurement error be the culprit,, IV should not be affected by instruments that cause changes in the schooling decisions off particular groups of individuals. The authors maintain that it is important to discover whetherr population estimates are "instrument sensitive". If this is the case, IV estimates cannott be used to formulate general policy affecting the whole population. Therefore, the studyy proceeds by implementing different instruments thought to potentially affect different groupss of individuals (i.e. high- versus low-schooled) and to simply check whether the IV estimatess are sensitive to the different instruments.15 A set of policy related interventions stemmingg from the Robin's Report of 1963 are used that include: changes in the MSLA as in theirr 1995 study; changes in the supply of university places available (a proxy of this is the ratioratio of new and existing university students to the 18-20 year old population) ; changes in thee ratio of the number of student grants to university entrants; and, changes in the ratio of the numberr of student grants to the real value of the grants. In addition, the change in youth labor markett opportunities is considered as a potentially valid exclusion restriction, which is proxiedd as the ratio of earnings for individuals 16 to 20 to those over 20. This serves as a measuree of the opportunity cost 16 to 20 year olds incur should they enter university.

4.4.11 Literatur e survey conclusion Clearly,, a variety of instruments have been used in previous literature in order to

estimatee unbiased schooling returns. Let us briefly reflect on the conclusions of these studies. Thee literature presents us with two main questions: in which direction are OLS returns biased (andd by how much) and what is the cause of this bias?

155 Because the authors control for the endogeneity of a non-linear schooling choice, estimation is achieved throughh a two-stage Heekman method (using an ordered probit as the selection equation). Therefore, the authors doo not implement an IV technique per se and what they refer to as "instruments" should really be referred to as "exclusionn restrictions" (variables excluded from the earnings equation). 166 In order to fill vacant spaces, UK admissions standards (in the form of minimum entrance exam scores) were relaxedd causing a larger proportion of the 18 to 20 year old population to successfully enroll in university.


Regardlesss of theories that state otherwise, it is clear from the majority of the empiricall literature that, compared to alternative IV techniques, OLS understates the estimatedd rate of return to education. Moreover, most studies find that it is understated by a largee (though rarely statistically significant) amount. However, it is rather hard to believe that thee rate of return to education is really as high as 18% as the findings of Butcher and Case (1994)) and Harmon and Walker (1995) purport. Yet the evidence certainly suggests that for whateverr reason, there exists some mechanism(s) by which OLS estimates are subject to downwardd pressure and therefore should not be ignored. What is most amazing is the robustnesss of this finding across so many studies, which make use of data sets spanning throughh different time periods and that employ such a large variety of instruments.

Focusingg on the question of the cause of the downward bias found in OLS rate-of-returnn estimates, the answer still remains to be seen. Indeed, the last study by Harmon and Walkerr (1996) seems to rule out heterogeneous returns as the cause of the discrepancy betweenn OLS and IV estimates, but rather points to an omitted variable bias in which the effectt of an ignored variable termed "motivation", which is negatively (positively) correlated withh schooling (earnings), is manifested in the earnings error term. Yet, the study by Uusitalo (1996)) suggests that some sort of endogeneity bias where individual optimizing behavior is at play.. From studies such as Angrist and Krueger (1991) and Butcher and Case (1994), some consensuss has been reached in that it seems rather unlikely that solely measurement error couldd account for such a large discrepancy between the OLS and IV estimates.

Thee literature discussed above covers a number of attempts at obtaining consistent schoolingg return estimates using a broad range of instruments. However, only four of the ten studiess employ data from outside of the US. The question then remains, are the results of thesee studies robust across different countries? Do similar procedures run for different countriess yield similar results? The next section tries to provide part of the answer by extendingg the literature with another study using non-US data. To this end, we perform TV estimationss using two Dutch data sets in order to obtain consistent schooling return estimates forr the Netherlands.

4.55 Data and empirical results

4.5.11 Brabant Survey

Inn 1952, about one quarter of the sixth-grade pupils (approximately age 12) in the Dutch provincee of Noord-Brabant were sampled and surveyed, producing a "narrow" one-year cohort off individuals. Twenty-five years later, the observations (on schooling, intelligence and family background)) were still available. Consequently, in 1983 the same persons were interviewed for aa first follow-up. The data collection for this wave focused mainly on education, labor market positionn and earnings.1 Most recently, in 1993 the respondents were given a second follow-up, providingg updated information on labor market position and earnings.

Withh respect to our present context, the data set is rich in that it includes several variabless that can assist us in various IV procedures (i.e. potential instruments). Namely,

Thiss data has previously been analyzed in Hartog, Pfann and Ridder (1989) and Groot and Oosterbeek (1994).


individuall measures of ability and family background are both contained in the original 1952 survey.. Ability measures include scores from intelligence quotient (IQ) tests as well as final examss in history, physics, math, reading, and fill-in exercises. Note that all individuals had their IQQ tests at age 12 and therefore there is no problem of age effects on IQ found in other studies usingg scores from tests taken by individuals at different ages and/or amount of education (cf Blackburnn and Neumark, 1995). Family background variables include highest education of motherr and father, number of siblings, and individual order of birth. In addition, the 1983 surveyy contains father's occupation, teacher's evaluation of family's social status, labor market status,, average weekly hours worked, and wages received at the time of the survey. The 1983 respondentss were asked to carefully document their educational career. This allows for a precise calculationn of the actual number of years of schooling versus imputing specific values for each particularr level of education completed.

Wagess from the 1983 wave have been used in this analysis because individuals are at a moree interesting point in their labor market careers. In 1983 our cohort was approximately 43 yearss old which would put them in mid-career. Had we used individuals from the 1993 survey thatt reported themselves as employed wage earners we would be more likely to have based our analysiss on a non-random sample, due to the exit from employment due to unemployment, entry intoo disability schemes, or death.18'19 In the same vein, due to the timing of the base survey, it wass necessary to limit our analysis to males in the sample as the labor force participation of femaless in this cohort was rather uncommon (especially after giving birth) and would therefore confoundd our results.'

1,6133 of the original male respondents (1,879 individuals) answered the first follow up survey.. Of these individuals, 732 described themselves as employed working less than or equal too 60 hours per week, reported a wage, and provided sufficient schooling history to allow for a calculationn of education length. In addition to the calculation of logarithm of net weekly wages andd education length, IQ score and information on parental education, number of siblings and thee individuals rank in his sibship have been extracted to serve as an ability control and potential instruments,, respectively.21 Also, additional controls for potential experience and its square and averagee weekly hours worked are utilized in our analysis.

Beforee diving straight into the IV estimation, we should first pay attention to the previouslyy discussed question, "How valid are the potential instruments at our disposal?" The twoo conditions for instruments to be valid and of sufficient quality are: they cannot have any directt influence on the outcome (i.e. the dependent variable of the second-stage equation); and, theyy should not be too weakly correlated with the endogenous regressors that they are

1KK However, using the same data Plug (2000) shows there is littl e difference between the estimated rate of return too ability using the 1983 versus 1993 wages. 199 Additionally, using the 1993 wages would leave a ten-year window in which additional schooling would have to bee imputed and added to the more precisely calculated 1983 education measures. 200 Note that the bulk of previous research focussed on rates of return has also adopted this convention, thereby avoidingg the need to explicitly model the more variable labor force careers of women stemming from fertility decisions. . 211 Parental education is measured in five categories as follows: lower (reference group), lower secondary, upper secondary,, lower tertiary, and upper tertiary. 2222 Experience and its square are "potential" in that individuals were asked in which year they started working for pay. .

ReturnsReturns to schooling in the Netherlands 101

Tablee 1 - OLS Regressions of Male Wages on Instruments Using 1983 Brabant Survey

Father'ss education (inn five categories) Mother'ss education (inn five categories) Father'ss higher education n Mother'ss higher education n Father'ss education missing g Mother'ss education missing g Numberr of siblings

Siblingg rank

Numberr of siblings missing g Siblingg rank missing g Adjustedd R2

Observations s

Parentall Sibling All social Parental higher All social educationn composition background I education background II

0.0144 0.012 (0.014)) (0.014) 0.0577 0.057

(0.018)**** (0.018)*** 0.0466 0.039

(0.049)) (0.049) 0.1555 0.158

(0.058)**** (0.058)*** 0.0700 0.082 0.019 0.039

(0.065)) (0.066) (0.081) (0.082) -0.0377 -0.054 -0.198 -0.218 (0.065)) (0.066) (0.087)** (0.088)**

0.0055 0.004 0.005 (0.005)) (0.005) (0.005) -0.0099 -0.007 -0.008

(0.005)** (0.005) (0.005) -0.1577 -0.197 -0.185 (0.125)) (0.125) (0.126) 0.2199 0.253 0.244

(0.120)** (0.120)** (0.121)** 0.42666 0.4193 0.4311 0.4197 0.4248

7322 732 732 732 732

Dependentt variable is logarithm of net weekly wages. Al ll regressions include controls for the following: years of education and experience (squared), IQ, average weeklyy hours worked, and missing values for experience (squared). Standard errors in parentheses. Reference groupp for parental education is lower. Imputed values for parental education, number of siblings, sibling rank andd experience (squared) set at lower, four, first and 25.77 (663.94) years, respectively. ** significant at 10%; ** significant at 5%; ** * significant at 1%

instrumenting.. To address the first condition, five baseline OLS earnings equations have been runn with separate instrument combinations included as regressors.23 The results of this exercise aree listed in Table 1. In the first and third columns, mother's education has a strong significant influencee on earnings. In addition, columns 4 and 5 provide rather strong evidence that a mother'ss attendance of higher education has a direct influence on a child's earnings. In turn, it iss questionable that mother's higher education can be considered a valid instrument for schooling.. In this respect, the researcher's hands are "tied" in that the potential instruments are limitedd by the data set at his/her disposal. Because of this limitation in what follows we initially implementt all potential instruments and then investigate specifications that exclude mother's educationn as an instrument.

Thee baseline equation includes controls for the following: years of education and experience (squared), IQ, averagee weekly hours worked, and missing values for experience (squared). 244 A common explanation for this is the direct production of human capital in a child attributed to a mother or that theree is "networking" at play so that children of highly educated parents have access to better contacts and land higherr paying jobs.


Tablee 2a contains the results of OLS and IV regressions of net weekly wages using variouss instrument sets. In the first column, we find our baseline regression produces an estimatedd 3.1% return to schooling. The specification in column 2 attempts to control for ability biass by including IQ score. We find that adding the proxy for inherent ability causes the estimatedd return to fall by 0.5% to 2.6%.25

Next,, we consider the case in which schooling is considered to be potentially endogenouss and/or measured with error so that corrective action (i.e. an IV procedure) may be warranted.. The first IV procedure shows that father's education has a significantly positive impactt on a child's educational attainment. On average, each level of education attained by a fatherr raises the schooling of his child by over a third of a year.26 In addition, the sibling compositionn instruments both have a significant influence on individual schooling attainment." Onn average, an individual is expected to complete over tenth of a year more schooling for each additionall sibling. Conversely, the lower one's sibling rank (the later one is bom in their sibship),, the lower on average is his or her schooling attainment. The corresponding estimated schoolingg return is 9.7%, almost quadruple that of the baseline OLS estimate, while the effect of IQQ drops to 0.1% and becomes insignificant. Also, in spite of the inflated standard error resultingg from the IV procedure, the estimate is significantly different from that produced by OLS2X;; with a p-value of 0.0001 the Hausman test strongly rejects the null hypothesis that schoolingg is exogenous.

Complyingg with the suggestion made in Bound et al (1995) concerning the weakness of instruments,, for each IV specification an F-test of the joint significance of excluded instruments hass been performed. As is clear from the table, the F-tests corresponding to the first IV specificationn rejects the hypothesis that the coefficients of the excluded instruments jointly equal zero.299 Also, the test of overidentifying restrictions can not reject the null hypothesis that the variouss instrument combinations are orthogonal to the earnings equation error term and that the respectivee models are specified correctly. An alternative explanation, as put forth by Angrist andd Krueger (1991), is that the same estimates could not be obtained with a smaller subset of thee instruments used.

Itt should be noted that similar IV estimates have been performed treating parental educationn as non-linear by using dummies that equal one if the parent had attended higher

"" Average grade of final exams was also used as an ability proxy producing quite similar results. "66 Interestingly enough, mother's education does not seem to affect the schooling level of their children as is commonlyy seen in recent studies. However, considering the cohort we are analyzing it may be plausible (i.e. educationn level of Dutch mothers in Noord Brabant may have had littl e bearing on a child's education in the 1950's). . 277 However, for number of siblings is the effect is marginally significant (i.e. at the 10%-level). "KK This is determined via a Hausman specification test (1978) where a t-test based on the following t-statistic is

formulatedd to test the null hypothesis that the OLS and IV coefficients are equal: OLS TSLS . Jl'AR{OLS)-YAmTSLS) Jl'AR{OLS)-YAmTSLS)

Alternatively,, an equivalent test can be achieved by simply including the first-stage error(s) or instrumented endogenouss regressor(s) in the baseline OLS regression (including the original endogenous regressor) and evaluatee the significance of the corresponding estimated coefficient(s) using a t- or F-test. 299 In addition, the partial R" measures favorably against similar statistics reported in the literature.


Tablee 2a - OLS and IV Rate-of-Return Estimates for Males Assuming Schooling Endogeneity Using 1983 Brabantt Survey

Yearss of education

IQ Q

Fatherr education (fivee categories) Motherr education {fiv ee categories) Fatherr education Missing g Motherr education Missing g Numberr of Siblings s Siblingg rank

Numberr of siblings Missing g Siblingg rank missing g Constant t

Adjustedd R2

F-testt (p-value)

F-testt critical value Partiall R2

Sargann test (p-value) ) Sargann critical value e Hausmann test p-value e Observations s

Baselinee equations

Schooling g only y

0.031 1 (0.003)*** *

5.102 2 (0.187)*** *

0.3793 3

732 2

Schooling g andlQ Q

0.026 6 (0.003)*** *

0.005 5 (0.001)*** *

4.622 2 (0.196)*** *

0.4142 2

732 2

IVV using all social backgroundd instruments

Second--First-stage e

,, .. stage schoolingg r

earnings s 0.097 7

(0.025)*** * 0.0555 0.001

(0.009)**** (0.002) 0.356 6

(0.165)** * 0.322 2

(0.214) ) 0.249 9

(0.802) ) -0.195 5 (0.800) ) 0.104 4

(0.057)* * -0.127 7

(0.062)** * 0.900 0

(1.526) ) -0.793 3 (1.470) ) 4.4455 4.311

(2.412)** (0.280)*** 0.45711 N/A 2.49 9

(0.0115) ) F(X.7.8)=1.95 5

0.0341 1 7.88 8

(0.4454) (0.4454)

X\K,X\K, .951=15.51

0.0001 1

7322 732

IVV using all instruments exceptt mother's education _.. x x Second-First-stage e schoolingg .

°° earnings 0.082 2

(0.024)*** * 0.0566 0.001

(0.009)**** (0.002) 0.466 6

(0.147)*** *

0.050 0 (0.291) )

0.107 7 (0.057)* * -0.132 2

(0.062)** * 1.051 1

(1.513) ) -0.951 1 (1.453) ) 4.4622 4.376

(2.412)** (0.259)*** 0.45688 0.1409 2.92 2

(0.0081) ) F<6.. 7201=2.11

0.0311 1 6.12 2

(0.4100) (0.4100)

Z2,6..9S)=12.59 9

0.0040 0

7322 732

Dependentt variable is logarithm of net weekly wages. Alll regressions include controls for the following: experience (squared), average weekly hours worked, and imputedd missing values for experience (squared). Reference group for parental education is lower. Imputed valuess for parental education, number of siblings, sibling rank and experience (squared) set at lower, four, first andd 25.77 (663.94) years, respectively. Standard errors in parentheses. ** significant at 10%; ** significant at 5%; ** * significant at 1%


educationn and zero, otherwise. Here, only mother's attendance of higher education exhibited anyy effect on schooling. However, using these alternative measures of parental education we havee found there is little difference in the results other than a slightly better fit of the first-stage equationss when using the linear parental education variables. For this reason, in the following specificationss we only present the findings using this original measure of parental education.

Inn the second specification we consider the possibility that our model is misspecified due too the potential direct influence of mother's education on earnings. To this end, we create a "preferred"" specification by dropping mother's education so that only father's education and the twoo sibling composition variables are used as instruments. There is almost no change in the first-stagefirst-stage results except that the coefficients for the instruments have gotten slightly larger in magnitude.. With respect to the second-stage equation, the main difference from the first IV specificationn is that the estimated return to schooling drops by 1.5% measuring 8.2%, which againn proves to be significantly different from the baseline estimate. Turning to the F-tests, the hypothesiss of joint insignificance of the excluded instruments is strongly rejected and the test of overidentifyingg restrictions supports the null hypothesis that the earnings errors is orthogonal to thee instrument set.

Ass interesting as the previous results seem, it may be more realistic to consider both schooling andd ability as endogenous with respect to earnings and/or measured with error. Table 2b containss regressions that are specified to account for the dual endogeneity of both schooling and ability.. Columns 3 through 6 in the table contain results to the dual endogeneity specification wheree all family background variables are used as instruments. We find the common result thatt father's education strongly affects both the IQ and schooling length of a son while mother'ss education has a positive, yet only mildly significant effect on a son's schooling. On average,, for each category increase in father's education, his child is expected to score approximatelyy two points higher on his/her IQ exam and have almost one-half year more schooling.. In contrast, a mother's education has no discernible effect on a child's IQ, however, doess exert a marginally significant positive effect on schooling length (of a similar magnitude as father'ss education). Number of siblings no longer has a significant effect and sibling rank only exertss a marginally significant negative effect on schooling attainment. The point estimate of thee schooling return is less than 1% and insignificant. However, with this specification we obtainn a marginally significant return to ability of 2.5%. The Hausman test strongly rejects jointt exogeneity indicating that the IV procedure is appropriate. In addition, the instrument sett is shown to be of sufficient quality and validity according to our indicators (i.e. two F-tests onn the excluded instruments, partial R2 and Sargan test).

Thiss definition was decided on after treating parental education as non-linear by breaking each of the original variabless into six dummies representing education levels (primary through higher) and performing the above regressions.. Significant parental education effects were only found for individuals whose parents have attended higherr education.

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Thee second "preferred" specification uses only father's higher education and the two siblingg composition variables as instruments. The first-stage equation shows the common positivee effect of father's education and negative effect of sibling rank on both IQ and schoolingg attainment. The number of siblings one has does not seem to have any effect on the twoo potentially endogenous regressors. A resulting schooling return point estimate has a perversee sign at -2.4% but is highly insignificant. On the other hand, the model produces an abilityy return of 2.9% that is significant at the 10%-level. Again, with this specification joint exogeneityy of ability and schooling is strongly rejected and our gauges of quality and validity supportt the use of the instrument set.

4.5.22 OSA Panel Thee panel survey conducted by the Organization for Strategic Labor Market Research (Organisatiee voor Strategisch Arbeidsmarkt Onderzoek or OSA) was originally established to identifyy characteristics and mobility of the Dutch labor supply. The first wave was conducted inn 1985 and followed by successive waves every two years from 1986 onward. The survey is administeredd to individuals aged 16 to 64 and includes a broad range of questions pertaining too educational background as well as labor market status and conditions. The current study employss the 1994 wave in which 4,538 individuals were questioned. Out of this total sample, 1,3300 males reported themselves as either employed or self-employed, reported a net weekly wage,, and provided sufficient information to calculate their length of schooling.

Similarr to the 1983 Brabant Survey, the OSA allows the respondent to report up to eightt different educational episodes allowing for an accurate calculation of the actual length of schoolingg one has taken. Unfortunately, unlike the Brabant Survey, the OSA does not have informationn pertaining to ability making it impossible to directly investigate potential omitted abilityy bias with this data set. Turning to remedies for endogeneity bias and/or measurement errorr in the schooling variable, family background instruments can be measured using the job levell of and highest education attained by the "bread-winning" parent when the respondent wass 12. In addition, the following variables have been extracted or constructed to instrument schooling:: quarter of birth dummies a la Angrist and Krueger (1991), tuition of higher educationn faced by respondent at age 18 (representing direct costs of tertiary schooling), a three-yearr average of tuition faced by the respondent "around" this age (i.e. average tuition of higherr education at 17, 18 and 19) and dummies of the compulsory minimum school leaving agee (MSLA) as well as indicators of the different MSLA regimes a la Harmon and Walker (1995).. Additional controls are employed for experience and its square, average regular and overtimee hours worked per week, marital status, and geographic region of residence at time of survey. .

Again,, let us start by roughly evaluating the validity of our instruments by checking whetherr they exhibit any direct influence on earnings. Table 3 includes OLS regressions of nett weekly wages on education length, the control variables mentioned above, and each of our potentiall instruments in turn. As is clear from the table, only the indicators for missing parentall education and the 1947 and 1950 changes in MSLA have any discernable direct effect onn the logarithm of net weekly earnings. However, implementation of two-stage least squares iss necessary to obtain formal tests of instrument validity and quality.

ReturnsReturns to schooling in the Netherlands

Tablee 3 - OLS Regressions of Male Wages on Instruments Using 1994 Wave of OS A Panel

Parentt secondary vocationall education Parentt secondary Generall education Parentt intermediate vocationall education Parentt higher vocational andd general education Parentt education Missing g Parentt job level medium

Parentt job level high

Parentt job level missing

Firstt quarter of birth

Secondd quarter of birth

Thirdd quarter of birth

Tuitionn faced at age 18

Three-yearr average tuitionn faced at age 18 Minimumm school Leavingg age 14 Minimumm school Leavingg age 15 19422 change in school Leavingg age (13 to 14) 19477 change in school Leavingg age (14 to 13) 19500 change in school Leavingg age (13 to 15) Adjustedd R2

Observations s

Baselinee earnings equations Tuitionn of Average M g L A M S L A

Parentall Parental Quarter of higher of tuition regime educationn job level birth education of higher ^ ^ . ^ ^

att age 18 education -0.022 2 (0.030) ) -0.025 5 (0.033) ) -0.006 6 (0.037) ) -0.046 6 (0.048) ) -0.044 4

(0.026)* * 0.021 1

(0.024) ) 0.017 7

(0.030) ) 0.030 0

(0.019) ) -0.000 0 (0.026) ) -0.029 9 (0.024) ) -0.029 9 (0.029) )

0.000 0 (0.000) )

0.000 0 (0.000) )

-0.006 6 (0.041) ) -0.005 5 (0.037) )

-0.095 5 (0.062) ) -0.129 9

(0.067)* * -0.118 8

(0.069)* * 0.46800 0.4683 0.4672 0.3502 0.3367 0.3462 0.3477 13300 1330 1330 1209 1182 1188 1188

Dependentt variable is logarithm of net weekly wages. Alll regressions include controls for the following: years of education and experience (squared), average weekly regular and overtimee hours worked, five indicators of residential location, marriage status, and missing values of regular/overtime hours and experiencee (squared). Standard errors in parentheses. Reference groups for parental education and parental job level are lower educationn and job level medium, respectively. Reference groups for MSLA and change in MSLA are age 13 and the period 1928-1942,, respectively. Imputed values for parental education and job levels set at upper secondary general and medium, respectively. ** significant at 10%; ** significant at 5%; *** significant at 1%


Tablee 4a contains the results of a "baseline" OLS regression and three separate IV procedures.. The baseline estimate is highly significant and equals 3.8%. The next two columnss contain an IV specification where parent's highest education serves as the instrument.. The first-stage equation shows that parental education has a highly significant positivee effect on a child's schooling length. All levels above lower secondary education are associatedd with a significant monotonie increase in the average child's schooling length from 0.88 to 3.7 years. The resulting schooling return drops by more than one-fifth (from 3.8 to 3%) andd proves to be highly significant. Looking at our test statistics related to instrument quality andd validity, we find that the instruments are jointly significant in the first-stage equation and theirr orthogonality with respect to the earnings equation error is supported. However, the Hausmann test supports exogeneity of the schooling variable indicating that the IV point estimatee does not significantly differ from that of the baseline equation. Therefore, the model ass specified gives evidence that endogeneity and/or measurement error of schooling does not posee a problem.

Thee second specification in the table employs job level indicators of the household's breadwinningg parent as instruments for schooling.32 We find that relative to children whose parentss had lower level jobs, those with parents in medium and high level occupations are expectedd to have about two-thirds of year and two and a third years more schooling. The indicatorss are both individually and jointly different from zero at the conventional 5%-level andd prove to be valid. The IV schooling return for this specification increases slightly (0.4%) overr that estimated by the baseline OLS equation, but the two do not significantly differ.

Tablee 4b contains five additional instrumentation strategies that are associated with directt constraints. The first IV specification in the table follows the work of Angrist and Kruegerr (1991) by implementing quarter of birth dummies as instruments. Children in the Netherlandss are required to enroll in their first year of schooling by the first day of the month followingg their fifth birthday.33 In addition, students are required to finish out their last year off education. Therefore, in the context of Dutch educational regulation we might expect quarterr of birth instruments to affect average school length in a similar fashion. Individuals bornn before the school year ends (i.e. in the first two quarters) are able to finish their first year off schooling in a shorter period of time, complete the statutory level of schooling more quickly,, and thus have shorter average schooling careers.34 However, there are two possible reasonss why quarter of birth may not behave as well in the Dutch context. First, as opposed to youngerr individuals, older cohorts were required to start a new school year in September

Parent'ss highest education is for the "breadwinner" of the family and can assume the following five values: lowerr education (reference group), lower secondary general and vocational, upper secondary general, intermediatee vocational and higher education whether it be vocational or general. '~~ The indicators are "high", "medium" and "low" (reference group) job levels and derived from International Standardd Classification of Occupations (ISCO) codes produced by the International Labor Organization (ILO). 333 In practice, the majority of individuals (over 90%) are enrolled by the age of 4. 344 Note, although the expected effect of quarter of birth on schooling career is similar in the two countries, the mechanismm in the Netherlands with variable enrollment and fixed exit dates is the "mirror" image of that in the USS where there are fixed enrollment and variable exit dates (cf Angrist and Krueger (1991)).


Tablee 4a - OLS and IV Rate-of-Return Estimates for Males Using Social Background Instruments from 1994 Wave of OSAA Panel

Yearss of education

Parentall education (inn 5 categories) Parentt lower secondary general/vocationall education Parentt secondary generall education Parentt intermediate vocationall education Parentt higher vocational/ generall education Parentt education missing

Parentt job level medium



Constant t

Adjustedd R2

F-testt (p-value) F-testt critical value Partiall R2

Sargann test (p-value) Sargann critical value Hausmann test p-value Observations s

Baseline e earnings s 0.038 8

(0.002)*** *

4.853 3 (0.077)*** *

0.4672 2

1330 0

First-stagee Second-stage schoolingg earnings

0.030 0 (0.010)*** *

-0.002 2 (0.331) ) 0.800 0

(0.359)** * 1.196 6

(0.399)*** * 3.666 6

(0.514)*** * -0.032 2 (0.284) )

9.8611 4.934 (0.841)**** (0.134)***

0.23800 0.4636 16.29(0.0000) ) F<5.. i3ii)~ 2.22

0.0550 0 6.422 (0.2675)

r,5.. .95» =11-07 0.4568 8

13300 1330

First-stagee Second-stage schoolingschooling earnings

0.042 2 (0.012)*** *

0.646 6 (0.259)** *

2.334 4 (0.322)*** *

0.121 1 (0.214) ) 30.0055 4.811

(0.825)**** (0.154)*** 0.22433 0.4662

18.28(0.0000) ) F|3.. 1313) = 2.61

0.0379 9 5.63(0.1310) ) X2

(3.,9MM = 7 .81 0.7552 2

13300 1330

Dependentt variable is logarithm of net weekly wages. Alll regressions include controls for: years of experience (squared), average weekly regular and overtime hours worked, five indicatorss of residential location, marriage status, and missing values of regular/overtime hours and experience (squared). Standard errorss in parentheses. Reference groups for parental education and parental job level are lower education and job level medium, respectively.. Imputed values for parental education and job levels set at upper secondary general and low, respectively. ** significant at 10%; ** significant at 5%; *** significant at 1%

followingg their 6 birthday. In addition, through 1957 half of the country started school in Aprill rather than September.

Relativee to individuals born in the fourth quarter (the reference category), being born inn the second quarter has a marginally significant negative effect on the length of schooling; onn average individuals born in the second quarter receive about a half-year less schooling than thosee born in the last quarter. The second-stage earnings equation yields a larger point estimatee of the return to schooling on the order of 9.1% (significant at the 10.5%-level) but failss to significantly differ from the baseline OLS estimate. Although the Sargan test shows

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thatt the instrument set is orthogonal to the second-stage earnings residual, inspection of the F-testt shows that our criterion of instrument quality is not met; joint significance of the quarter off birth coefficients in the first-stage equation is not supported.

Thee following two specifications use tuition of higher education when the individual is 188 and the three-year average of tuition at this time. Referring back to the framework of Harmonn and Walker (1996) and Card (1999), if individuals are indeed heterogeneous with respectt to schooling returns, an IV estimator will convey the marginal return of only that subpopulationn whose schooling decision is influenced by the intervention (defined by the instrumentt being used). Therefore, the use of higher education tuition (at or near the time of possiblee entry into this level of schooling) as an instrument might be thought to affect the schoolingg decisions of those in the upper part of the schooling distribution and result in an IV estimatedd return that is lower than average. Both specifications show that tuition at and aroundd the time of potential entrance in higher education have a highly significant negative effectt on schooling attainment. When tuition faced at age 18 is used the resulting point estimatee is over 1% lower than that of OLS but not significantly different. When using tuition "around"" age 18 as an instrument the rate-of-return estimate becomes perverse at -0.001 and is insignificant.. Because these equations are exactly identified (there is one instrument and one endogenouss regressor) the t-test on the instrument coefficient from the first-stage regressions andd the F-test of excluded instruments are equivalent tests and both support the relevance of thee respective instruments.35 Yet, despite the quality of our instruments, Hausman tests for bothh specifications accept the null hypothesis that schooling is exogenous with respect to earningss suggesting that IV procedures are not necessary.

Thee last two specifications follow from the studies by Harmon and Walker (1995, 1996)) that make use of changes in the minimum school leaving age (MSLA) as instruments. Inn contrast to changes in university tuition, changes in the MSLA are thought to influence the schoolingg decisions of individuals in the lower portion of the schooling distribution, those that wouldd otherwise drop out before the minimum age was reached. Hence, if our estimates were "instrumentt sensitive" we would expect the estimated returns from an IV procedure using MSLAA as instruments to exceed those of OLS.

Sincee the beginning of the century the Netherlands experienced the following nine changess in the level of compulsory schooling and hence the minimum school leaving age:

Changess in Years of Compulsory Schooling MSLA in the Netherlands from 1900 to the Present

Period d 19000 to 1921 19211 to 1924 19244 to 1928 19288 to 1942 19422 to 1947 19477 to 1950 19500 to 1975 19755 to 1985

19855 to Present

Yearss of compulsory schooling 6 6 7 7 6 6 7 7 8 8 7 7 9 9 10 0 12 2

Minimumm school leaving age 12 2 13 3 12 2 13 3 14 4 13 3 15 5 16 6 17 7

Inn addition, exact identification makes a Sargan test impossible.


Duee to the timing of the survey (1994) many individuals covered by the most recent change in MSLAA (from 16 to 17 years) did not have a chance to complete their education and are thereforee omitted from the analysis. Additionally, those affected by the second most recent changee are omitted because the portion that continued in post-compulsory education (particularlyy towards the end of the covered period) were most likely still students (not in the laborr market) which would provide us with a non-random sample of observations. Finally, theree are no individuals in the sample that were affected by the first three changes in MSLA. Thiss leaves us four MSLA instrumental dummies with which to perform our analysis: a changee in MSLA from 12 to 13 in 1928, 13 to 14 in 1942, from 14 back down to 13 in 1947, andd from 13 up to 15 in 1950 (the earliest of these changes serves as the reference group).

Thee first-stage equation in column 8 only uses dummy indicators for individuals subjectt to MSLA's of 13 (the reference group), 14 and 15. Relative to students required to stayy in school until age 13, those that were forced to participate until age 15 are expected to havee over two years less schooling. However, the resulting rate of return is just 0.002 less thann that produced by OLS. When indicators for the actual MSLA reform regimes are used ratherr than just indicators for number of mandatory schooling years the results are also rather counter-intuitive.. Relative to the 1928 change in MSLA from 12 to 13 years, the effect of the changee in MSLA from 13 to 14 years in 1942 is significantly negative. In other words, there wass a decreasing trend in the average schooling attainment despite an increase in the MSLA. Thee 1947 decrease in MSLA back down to 13 years of schooling makes a bit more sense in thatt the negative value is bigger than that associated with the previous MSLA increase.36

However,, the more recent change in MSLA (1950) from 13 to 15 years is estimated to have thee same ominous result exhibited by the change in 1942, a large negative effect on the averagee schooling attainment of those it covered!37 Clearly, these effects also include time-specificc factors that also influenced the schooling decisions of the individuals in these periods. Too counter any possible age and/or cohort effects manifested in the MSLA indicator coefficientss two additional specifications were run, one that simply replaced experience (squared)) with age (squared), and one that added both the age and experience variables. Althoughh in the latter specification the instrument coefficients all became positive (but insignificant),, in both specifications the instrument set could not sufficiently explain schoolingg (i.e. pass the instrument quality criteria). The resulting "corrected" rates of return aree 3.6 and 4.9%, both significant at the conventional 5%-level. For both specifications Hausmann tests clearly accept exogeneity of the schooling variable with respect to earnings at thee conventional 5%-level. Checking the validity of the three MSLA dummies as instruments wee find that they are jointly significant and the partial R2 is quite large compared to similar statisticss reported in the literature. Finally, Sargan tests show that the MSLA instrument sets aree both orthogonal to the second-stage earnings residual.

Finall specifications have been run using the social background and direct constraint instrumentt sets pooled for each of these categories separately and all together (our "preferred"

Yet,, there is littl e reason to believe that the 1947 change to an MSLA from 14 to 13 would be associated with lesss schooling than the change in MSLA marked by the reference group (the 1928 change from an MSLA of 12 too 13). 377 However, it should be mentioned that this finding is similar to that of Harmon and Walker (1995) in which a changee in MSLA from 15 to 16 years has a negative effect on the average schooi ing attainment in the UK.


specification)) with the results reported in Table 4c. Compared to the previous specifications thee results of the pooled instrument first-stage equations show some differences. The first specificationn shows that medium parental job level no longer has an effect on educational attainmentt while in the pooled direct constraint equation second quarter of birth and tuition at agee 18 become insignificant. The "corrected" rates of return of 3.7 and 3.3% are slightly smallerr than that produced by the baseline equation. When all instruments are pooled together wee find that first and second quarter of birth become marginally significant. The relative robustnesss of the coefficients to the pooled instrument specification indicates that, in general, eachh instrument has its own distinct influence on schooling attainment (i.e. no instrument is undulyy "picking up" the influence of another). Instrument quality is supported by an F-test stronglyy rejecting the null hypothesis of joint insignificance whereas we can only marginally confirmm instrument-earnings error orthogonality per the Sargan test. The point estimate of this mostt elaborate specification (3.2%) is also smaller than that of the baseline OLS. In all specificationss on the table the respective Hausman tests accept the null hypothesis that schoolingg is exogenous with respect to earnings.

AA comparison of IV procedures using the two datasets shows that all specifications usingg the OS A Panel indicate that schooling is not endogenous with respect to earnings whereass those using the Brabant Survey generally support the endogeneity of schooling. Therefore,, the question is brought forth, "Is schooling endogenous with respect to the earnings off Dutch males?" However, the answer may not be so "black-and-white". Clearly an obvious possiblee explanation for this contradiction lies in the different compositions of the two samples.. More precisely, the Brabant Survey includes individuals who were approximately 43 att the time of survey whereas the OS A is a cross-section aged 16 to 64. This leads us to the hypothesiss that the endogeneity of schooling (for Dutch males) may have diminished over time.. In order to test the validity of this hypothesis the OSA sample has been split into two sub-sampless of individuals above and below (or equal) to 42 years of age and the IV proceduress applied to each.

Tablee 4d contains the results of the IV procedures run on the subsample of Dutch maless over 42 using the pooled social background, direct constraints and both sets as instruments.399 The baseline rate of return has now dropped to 3.1% and is highly significant. Thee first stage of the social background specification produces the common result that parentall education has a positive monotonie effect on a son's education attainment. Similarly,

Onlyy the actual age indicators (MSLA of age 14 and 15) are included in the pooled specifications because they performm slightly better in the first stage than the MSLA regime change indicators (of 1942, 1947 and 1950) and, moree importantly, both sets could not be included as there is a perfect correlation between the MSLA's of 14 and 155 and the 1942 and 1950 regime changes. 399 AH individual specifications found in Tables 4a and 4b have also been performed for both the older and youngerr subsamples but are not reported here for sake of brevity.

1144 Chapter 4

Tablee 4c - OLS and IV Rate-of-Return Estimates for Males Using Al l Available Instruments from 1994 Wave of OSA Panel

Yearss of education

Parentt lower secondaryy education

Parentt upper secondary Generall education Parentt intermediate vocationall education Parentt higher education

Parentt education missing








Three-yearr average off age 18 tuition

Minimumm school Leavingg age 14 Minimumm school Leavingg age 15 Constant t

Adjustedd R"

F-testt (p-value)

F-testt critical value

Partiall R2

Sargann test (p-value)

Sargann critical value

Hausmann test p-value

Observations s

Baseline e earnings s

0.038 8 (0.002)*** *

4.853 3 (0.077)*** *

0.4672 2

1330 0

Second--VV irst-stage schooling g

earnings s 0.037 7

(0.009)*** *

0.315 5 (0.334) )

1.041 1 (0.361)*** *

1.404 4 (0.401)*** *

3.281 1 (0.521)*** *

-0.162 2 (0.282) )

0.348 8 (0.262) )

1.720 0 (0.335)*** *

0.347 7 (0.215) )

8.9277 4.867 (0.869)**** (0.121)***

0.25333 0.4671

14.11 1 (0.0000) )

F(S.. 13(W) =

1.95 5

0.0739 9 12.47 7

(0.1316) )

X"(K ,, 451 =

15.51 1 0.8778 8

13300 1330

„„ Second-First-stage e fcfc stage schooling g


(0.012)*** *

-0.393 3 (0.297) )

-0.445 5 (0.274) ) -0.320 0 (0.330) )

0.000 0 (0.001) )

-0.003 3 (0.001)*** *

-0.029 9 (0.459) ) -2.321 1

(0.406)*** * 18.1988 5.090

(1.118)**** (0.184)*** 0.28433 0.3360

8.09 9 (0.0000) )

F(7.. 1161) =

2.02 2 0.0408 8

8.16 6 (0.3188) )

14.07 7

0.9696 6

11822 1182

Second--First-stage e

,, ,.° stage schooling g

earnings s

0.032 2 (0.008)*** *

0.054 4 (0.354) )

0.746 6 (0.385)* *

1.195 5 (0.418)*** *

2.716 6 (0.538)*** *

-0.240 0 (0.295) ) 0.185 5

(0.272) ) 1.454 4

(0.342)*** *

0.365 5 (0.224) ) -0.522 2

(0.288)* * -0.517 7

(0.266)* *

-0.310 0 (0.320) )

0.000 0 (0.001) ) -0.003 3

(0.001)*** *

-0.171 1 (0.446) )

-2.049 9 (0.395)*** *

16.1388 5.098 (1.170)**** (0.134)***

0.32877 0.3359

9.68 8 (0.0000) )

F(15.. 11531 =

1.68 8

0.1004 4 23.09 9

(0.0822) )

X"<15.. .95) =

25.00 0 0.8880 0

11822 1182

Dependentt variable is logarithm of net weekly wages. Al ll regressions include controls for: years of experience (squared), average weekly regular and overtime hours worked, five indicators of residentiall location, marriage status, and missing values of regular/overtime hours and experience (squared). Standard errors in parentheses. Referencee groups for parental education, parental job level and MSLA are lower education, job level medium and age 13, respectively. Imputedd values for parental education and job levels set at upper secondary general and medium, respectively. ** significant at 10%; ** significant at 5%; ** * significant at 1%


Tablee 4d - OLS and IV Rate-Of-Return Estimates for Males Over 42 Using All Available Instruments from 1994 OSA Panel

Yearss of education

Parentt lower secondaryy education Parentt upper secondary Generall education Parentt intermediate vocationall education Parentt higher education









Three-yearr average off age 18 tuition Minimumm school Leavingg age 14 Minimumm school Leavingg age 15 Constant t

Adjustedd R2

F-testt (p-value)


Partiall R2



Hausmann test p-value Observations s


0.031 1 (0.004)*** *

5.180 0 (0.277)*** *

0.2495 5

601 1

rr . . Second-rr irst-stage schoolingg .

earnings s -0.003 3 (0.020) )

0.647 7 (0.513) ) 1.015 5

(0.570)* * 1.466 6

(0.626)** * 3.330 0

(0.909)*** * -0.054 4 (0.473) ) 0.419 9

(0.423) ) 1.553 3

(0.549)*** * -0.008 8 (0.333) )

23.1588 6.093 (2.620)**** (0.578)***

0.33966 0.1602 3.91 1

(0.0002) (0.0002) F(8,, 579) =

1.95 5 0.0385 5

8.82 2 (0.3574) (0.3574)

X~(S,, .95) =

15.51 1 0.0516 6

6011 601

_.. . t Second-First-stage e schoolingg .

earnings earnings 0.061 1

(0.010)*** *

-0.191 1 (0.404) ) -0.597 7 (0.371) ) -0.307 7 (0.451) ) 0.017 7

(0.002)*** * -0.004 4

(0.002)** * 2.027 7

(0.469)*** * -0.552 2 (0.430) ) 18.6288 4.403

(2.628)**** (0.358)*** 0.45144 0.1779 20.20 0

(0.0000) ) F(7.574)) =

2.03 3 0.1881 1

8.91 1 (0.2591) (0.2591) X'n.X'n. .95) =

14.07 7 0.0002 2

5955 595

„ .. Second-First-stage e schoolingg .


(0.009)*** * 0.205 5

(0.467) ) 0.683 3

(0.519) ) 0.905 5

(0.569) ) 1.915 5

(0.837)** * -0.285 5 (0.431) ) -0.047 7 (0.386) ) 0.766 6

(0.503) ) 0.039 9

(0.303) ) -0.257 7 (0.403) ) -0.653 3

(0.371)* * -0.295 5 (0.450) ) 0.017 7

(0.002)*** * -0.004 4

(0.002)*** * 1.796 6

(0.473)*** * -0.460 0 (0.430) ) 17.9288 4.677

(2.702)**** (0.341)*** 0.45755 0.2190 10.50 0

(0.0000) ) F(15,566)) =

1.68 8 0.1974 4

31.55 5 (0.0074) )

X~tt 15. .95) =

25.00 0 0.0095 5

5955 595

Dependentt variable is logarithm of net weekly wages. Alll regressions include controls for: years of experience (squared), average weekly regular and overtime hours worked, five indicators of residentiall location, marriage status, and missing values of regular/overtime hours and experience (squared). Standard errors in parentheses. Referencee groups for parental education, parental job level and MSLA are lower education, job level medium and age 13, respectively. Imputedd values for parental education and job levels set at upper secondary general and medium, respectively. ** significant at 10%; ** significant at 5%; *** significant at 1%


onlyy parents with high job levels are associated with longer educational attainment. In contrastt to the corresponding IV rate of return using the whole sample, here we find the estimatee has dropped to -0.003 and is highly insignificant. The Hausman test rejects the equalityy of the baseline OLS and IV estimates at the 5.2%-level and the instrument set passes bothh tests of quality and validity.

Thee results of the direct constraint specifications for the older subsample can be found inn columns 4 and 5 of the table. Compared to the specifications using the whole sample, limitingg the sample to individuals over 42 again produces quite different results. While tuitionn at age 18 played no role on educational attainment for the whole sample, for the older subsamplee it is expected to have a positive effect on amount of schooling. However, the three-yearr average of this variable still exerts a significant negative influence on schooling and hass increased in magnitude. With respect to mandatory education we now find that an MSLA off 14 causes the average individual in the older subsample to enroll in over two years more schoolingg than those that were subject to laws requiring only 13 years, whereas the MSLA of 155 increases substantially and becomes insignificant. The corrected rate of return is almost doublee that produced by the baseline OLS estimate (and by the corresponding specification usingg the full sample). In addition, the Hausman test strongly rejects schooling exogeneity so thatt the OLS and IV estimates can be considered truly different from one another and again diagnosticc tests support both the quality and validity of ourr instrument set.

Thee fully saturated model shows that the only significant social background variable remainingg is parent's higher education. Interestingly, the negative effect of second quarter birthh becomes marginally significant. The only other notable difference in the direct constraintt effects from the previous specification is a slight drop in the MSLA 14 coefficient. Again,, we find the IV rate of return of 5.1% to be larger and significantly different from the baselinee estimate. However, the Sargan test now strongly rejects the null hypothesis that there iss negligible correlation between the full instrument set and the earnings equation error so that thee estimated schooling coefficient cannot be trusted.

Tablee 4e reports the results of the same pooled specifications using the subsample of maless under 43. The baseline rate of return for the younger subsample is 4.4% marking a 0.6%% increase on that of the whole sample. We find now that only parental higher education andd a high job level have a significant impact on schooling attainment.4 The corrected rate of returnn is approximately 1% higher than the corresponding estimate for the whole sample. The pooledd social background IV estimate for the younger subsample exceeds that of the older groupp by over 5%. Turning to the second specification, t- and F-tests show that the direct constraintss both individually and jointly have no significant effect on schooling attainment. In contrastt to the older subsample, the evidence suggests that direct constraints do not play a significantt role in the schooling decisions of the younger group. As a result, the corrected returnn of 0.7% clearly seems more biased than the baseline estimate.

400 Yet, the latter result is marred by the fact that the indicator for missing values of parental job level is significant. .


Tablee 4e - OLS and IV Rate-Of-Return Estimates for Males Under 43 Using All Available Instruments from 1994 OSA Panel

Yearss of education

Parentt lower secondaryy education Parentt upper secondary generall education Parentt intermediate vocationall education Parentt higher education









Three-yearr average off age 18 tuition Constant t

Adjustedd R2

F-testt (p-value)


Partiall R2



Hausmann test p-value Observations s


0.044 4 (0.003)*** *

4.570 0 (0.139)*** *

0.5177 7

729 9

rr.. t t Second-First-stage e

,, ..° stage schoolingg r


(0.010)*** * -0.218 8 (0.404) ) 0.466 6

(0.427) ) 0.583 3

(0.476) ) 2.953 3

(0.580)*** * -0.289 9 (0.313) ) 0.125 5

(0.300) ) 1.538 8

(0.383)*** * 0.556 6

(0.253)** *

9.6588 4.515 (1.510)**** (0.176)***

0.31099 0.5162 11.08 8

(0.0000) (0.0000) F(8,, 707) =

1.95 5 0.1015 5

8.47 7 (0.3890) ) XX (8..95) ~

15.51 1 0.6032 2

7299 729

„ .. Second-First-stage e schoolingg .


(0.048) )

-0.574 4 (0.360) ) -0.149 9 (0.333) ) -0.136 6 (0.396) ) -0.000 0 (0.001) ) 0.001 1

(0.001) ) 14.0711 5.200

(1.730)**** (0.698)*** 0.35500 0.2674 0.74 4

(0.5956) ) F(S,568)) =

2.23 3 -0.0021 1

0.53 3 (0.9975) (0.9975) v2 2

X.. (6. .95) _

12.59 9 0.5352 2

5877 587

rr.. , t Second-First-stage e schoolingg .

earnings s 0.044 4

(0.011)*** * -0.683 3 (0.467) ) 0.047 7

(0.495) ) 0.107 7

(0.530) ) 2.227 7

(0.629)*** * -0.337 7 (0.340) ) -0.072 2 (0.323) ) 1.134 4

(0.400)*** * 0.475 5

(0.277)* * -0.701 1

(0.345)** * -0.277 7 (0.320) ) -0.172 2 (0.379) ) -0.000 0 (0.001) ) 0.000 0

(0.001) ) 13.2788 4.668

(1.744)**** (0.212)*** 0.41222 0.3291 5.18 8

(0.0000) ) F(I3,, 560) =

1.74 4 0.0871 1

11.65 5 (0.6343) ) Z"(13.-95)) =

23.68 8 0.3881 1

5877 587

Dependentt variable is logarithm of net weekly wages. Alll regressions include controls for: years of experience (squared), average weekly regular and overtime hours worked, five indicators of residentiall location, marriage status, and missing values of regular/overtime hours and experience (squared). Standard errors in parentheses. Referencee groups for parental education, parental job level and MSLA are lower education, job level medium and age 15, respectively. Imputedd values for parental education and job levels set at upper secondary general and medium, respectively, ** significant at 10%; ** significant at 5%; *** significant at 1%


Whenn all instruments are implemented the coefficients on parental higher education andd high job level decrease in magnitude, the missing value indicator for parental job level becomess only marginally significant, and the first quarter of birth effect of -0.7 becomes significantt at the 5%-level. The fully instrumented rate of return is equal to the baseline estimatee of 4.4%. Unsurprisingly, for all three cases the IV estimates do not significantly differr from the OLS baseline.

Turningg to the question of differences in schooling endogeneity over time, Table 4f consolidatess the results of Hausman tests of (schooling) exogeneity for the above-mentioned IVV specifications using the whole sample and broken out by the younger and older subsamples,, respectively. The second column of the table reiterates the motivation behind thiss exercise. That is, although the results from the Brabant Survey seem to indicate significantt schooling endogeneity, using the full sample from the OSA Panel we find no specificationn that supports this finding. However, focussing on the results for the older subsamplee (column 2) we find that in half of the ten specifications there is evidence of significantt endogeneity bias in the schooling variable that cannot be attributed to weakly correlatedd or invalid instruments. In comparison, the results for the younger subsample providee no instances in which the Hausman test rejects the exogeneity of schooling.

Furthermore,, consider the direction of the bias implied by the IV point estimates from thee pooled and fully saturated models for the younger and older groups. Table 4f classifies thesee outcomes in the context of instrument sensitivity. The low IV rate of return for the older generationn implies that the social background instruments affected the schooling decisions of individualss in this group with low discount rates and/or marginal returns.41 Conversely, the sett of direct constraint instruments generate a relatively high rate of return implying that this modell has identified the schooling decisions and subsequent earnings of those older individualss with relatively high discount rates and/or marginal returns. In contrast, the pooled andd saturated models for the younger generation show that direct constraints have a negligible effectt on the schooling decision while social background affects schooling decisions of those withh above-average discount rates/marginal returns. Therefore, the evidence suggests that rate-of-returnn estimates presented here are subject to significant instrument sensitivity, especiallyy using the older subgroup of individuals.

4.66 Concluding remarks

Implementationn of the IV technique to estimate schooling returns using the two Dutch surveys yieldss some of the common results found in the mainstream literature. More precisely, turningg to the Brabant Survey, it is found that the inclusion of an ability measure in the OLS estimatee gives evidence to a small omitted ability bias similar to that found in the studies by Blackburnn and Neumark (1993, 1995).

Notee this finding is corroborated by the final results of the Brabant Survey analysis (Table 2b, above).


Tablee 4f - Hausman Tests of Schooling Exogeneity from IV Procedures Using Various Subsamples of 1994 OSAA Panel (p-values)

Instrumentss used Parentall education Parentall job level Quarterr of birth Tuitionn at age 18 Three-yearr average of age 18 tuition MSLAA age indicators MSLAA reform year indicators Sociall background pooled Directt constraint pooled Alll instruments

Sample e

Wholee sample

0.4568 8

0.7552 2 0.2675 5 0.8383 3 0.1446 6 0.9218 8 0.2539 9 0.8778 8 0.9696 6 0.8880 0

Overr 42

0.0592* * 0.2243 3

0.0824* * 0.3190 0 0.0073* * 0.8345 5 0.5325 5 0.0516* * 0.0002* * 0.0095 5

Underr and equal to 42

0.7937 7 0.5710 0 0.1585 5 0.8061 1 0.9222 2 N/A A N/A A

0.6032 2 0.5352 2

0.3881 1

** denotes specification that rejects schooling exogeneity at 10%-level or better using instrument set that passes qualityy and validity tests (at the 90 and 10%-levels, respectively).

Whenn schooling alone is considered endogenous, the first-stage equations give evidence that: :

father's education has a significant positive effect on the expected educationall attainment of a child;

the number of siblings has a significant positive effect on an individual's expectedd length of schooling;

sibling rank or the order in which an individual is born has a significant effectt on the expected amount of education he receives; the larger the numberr of older siblings one has the lower will be his expected educational attainment. . Thee second-stage results of these specifications suggest that there exists some

mechanismm that causes OLS to inconsistently measure the rate of return to schooling thus necessitatingg the use of an alternative consistent estimator such as IV. The findings also conformm to those commonly reported in the literature suggesting that the direction of this inconsistencyy is downward. In most cases, the difference between the OLS and the "corrected"" IV estimate is statistically significant at conventional levels.

Yet,, when both ability and schooling are considered endogenous, the numbers tell a differentt story. Mother's education also takes a role in promoting the amount of education her sonn is expected to obtain. Also, the effect of number of siblings on an individual's schooling careerr tends to disappear. From the second-stage equations, it seems that there is a negligible ratee of return to education produced regardless of the specification used.42 Rather, in contrast too OLS estimates, those produced by IV procedures show that returns accrue only to ability andd vary from 2.5 to 2.9%. This should not be so alarming once the source of the data is takenn into account. By the time the 1983 survey was administered most of the sample had beenn working for approximately 20 years. Clearly, as time passes the effects of education on earningss should dissipate and earnings effects of ability ensue which could partially explain a

422 Of the literature reviewed above, similar findings can be seen in Card (1993) and the latter study by Blackburn andd Neumark (1995).


lowerr schooling return. Nevertheless, one would not expect the returns to education to be negligiblee (even after 20 years in the labor market). Additionally, common only to the latest studiess mentioned above, for almost all of the IV specifications run with the Brabant data, exogeneityy of schooling and/or ability is rejected (though in some cases only marginally).43

Turningg to the OSA Panel, the results conform less to those found in previous studies. Initially ,, the first-stage equations for the most part behave as one might expect and/or find in thee literature:

post-secondary parental education has a significantly positive effect on educationall attainment of a child;

birth in the second quarter decreases an individual's educational attainment; ;

tuition fees of higher education decrease the schooling length of an individual; ;

changes in the minimum school leaving age are associated with decreases inn individual schooling attainment.

Thee second-stage equations are less assuring than their first-stage counterparts. In eight of the tenn specifications the estimated IV return is significant. Yet in seven of these cases the correctedd return is less than the OLS baseline. Finally, common to several of the IV studies citedd above, in none of the IV specifications is the exogeneity of schooling with respect to earningss rejected. In light of the contradiction put forth by the strong support of schooling endogeneityy using the Brabant data and exogenous schooling by the OSA Panel an attempt at explanationn is made by analyzing two sub-samples of the latter, those over 42 (the same age or olderr than those in the Brabant Survey) and those 42 and under. The results give fairly strong evidencee as to instrument sensitivity affecting our results, especially for the older generation. Whereas,, the schooling decisions of the older subsample have been affected by both social backgroundd and direct constraints, the latter instrument set has no effect on the educational decisionss of the younger group.

433 These studies include Harmon and Walker (1996), Kalwij (1996) and Uusitalo (1996).


Appendixx 4A Inconsistency with weakly correlated and invalid instruments Lett us assume a simple two-equation model with one endogenous variable (for simplicity, we assumee that all random variables have mean 0 and have dropped their individual subscripts),

yy = J3x + e

xx = yz + v

wheree y is a Nxl vector of the observations on the dependent variable; x is a Nxl vector of observationss on the random endogenous variable; z is a Nxk vector of observations on the k instrumentall variables; /? and a are parameter vectors corresponding to x and z, respectively; and,, the parameters e and v are both Nx 1 vectors representing error terms. The OLS and IV estimatorss in their respective probability limits are:

plinV?0i55 =p +

pliimVV =j3 + ^£-<j<j -

X X

Indeed,, the OLS estimator will only be consistent if JC is uncorrelated with e (x is exogenous) andd the variance of x is non-zero. Similarly, the IV estimator will be consistent when the variancee of the predicted JC is non-zero (there exists some association between x and the z it is regressedd on) and the predicted x is uncorrelated with e (alternatively speaking, z is uncorrelatedd with e).

Too calculate the inconsistency of the IV estimator relative to that of the OLS we simplyy subtract /? from each side and divide through the second equation by the first yielding

plim/%% _

P'im/WW R2XZ

Wee see that the denominator equals the partial R2 of the first-stage regression of x on z (the R2

fromm the first-stage regression where the effects of all variables common to the second-stage aree partialled out). This provides us with a clear illustration of the inconsistency arising in the presencee of a weak correlation between the endogenous regressor x and instrument(s) z. Shouldd the partial R be low (representing a weak association between the instrument(s) and endogenouss regressor) then even a slightly invalid instrument (a tiny correlation between z andd the e via x) will cause an inconsistency larger than in the case of OLS. Also, as is clear fromm the equation, the IV estimator will exacerbate the inconsistency associated with OLS shouldd there be a significant direct influence of the instrument set on the dependent variable (manifestedd in a significant correlation between x and e).

X,£ X,£


Appendixx 4B Imprecision associated with instrumental variables Thee imprecision associated with instrumental variables technique can easily be seen by a simplee comparison of variances between the OLS and IV estimators. Let us proceed using a simplee univariate model where the right-hand side variable is standardized around a zero meann (in matrix notation)

yy - xfl + £

Thee well-known OLS estimator of /?is

POLSPOLS = (*'xylx'y

Takingg the variance of the OLS estimator yields the following:

Var(0Var(0OLSOLS)) = Var[{x'x)-lx'y]

== Var[(x'x)~] x'(xp + £)] = Var[(x'x)~] x's]

== (x'xyl{£'£) = N{x'xyx<jl

(x'x) (x'x)

Iff we consider x to be potentially endogenous then the IV estimator (using z as an instrument) is s

PlVPlV ={zx)~lz'y

andd taking its variance,

Var(PVar(PIVIV)) = Vaï{(z'x)-Xz<y}

== Var[{z'xylz\xP + £)\ = Var[(z' x)~l z' e]

== (z<xyl(z'z)(z'xy\£'£) = N(z'xy](z'z)(z'xylaï

(z'x)(z'x)2 2

Forr reasons that will become apparent very shortly, let us now multiply the numerator and denominatorr of the variance of the IV estimator by x'x which give us

Var(J3Var(J3IVIV)) = 2 N (z'x)(z'x)22 (x'x)

(z'z){x'x) (z'z){x'x)

(zx) (zx) Var(PVar(POLSOLS) )


Withh a littl e algebraic manipulation we find the ratio of the respective variances,

Varjfay)Varjfay) = jz'zXx'x)

Var{PVar{P0LS0LS)) (z'x)2

andd finally, the ratio of the standard errors,

J(z'z)(x'x)/ J(z'z)(x'x)/ SEjfiiv)SEjfiiv) = /N

SE(POLS)SE(POLS) VX)/N

1 1 {z'x)/ {z'x)/

/N/N _ ]

V(Z'Z)(JT'X)) pXyZ

N N Therefore,, we see that the ratio of standard error of the IV estimator to that of the OLS estimator iss equal to one divided by the correlation of our potentially endogenous regressor to the instrument.. Clearly, unless the two are perfectly correlated the standard error of the IV estimator wil ll always be larger than that of the OLS estimator. This can only occur if the instrument is a linearr transformation of the potentially endogenous regressor in which case it will certainly violatee the first criterion of valid instruments and cannot be legitimately used as an instrument. Onee interesting, albeit abstract, case of this is when the instrument is the endogenous regressor itselff in which we simply have an OLS regression. That is to say, OLS is in fact a special case of IVV where the instrument is the endogenous regressor. The reader should also note that the relationshipp proven above also illustrates how the magnitude of inflation of the IV standard errorss is dependent upon the relative weakness of the instruments being used. Clearly, the weakerr the instruments being used are (as determined by their correlation with the endogenous regressor),, the larger will be the IV estimator standard errors relative to those of OLS.

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