Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A human capital approach to occupational wage differentials Robb, Andrew Leslie 1967

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1967_A8 R62.pdf [ 3.66MB ]
Metadata
JSON: 831-1.0104676.json
JSON-LD: 831-1.0104676-ld.json
RDF/XML (Pretty): 831-1.0104676-rdf.xml
RDF/JSON: 831-1.0104676-rdf.json
Turtle: 831-1.0104676-turtle.txt
N-Triples: 831-1.0104676-rdf-ntriples.txt
Original Record: 831-1.0104676-source.json
Full Text
831-1.0104676-fulltext.txt
Citation
831-1.0104676.ris

Full Text

A HUMAN CAPITAL APPROACH TO OCCUPATIONAL WAGE DIFFERENTIALS by ANDREW LESLIE ROBB B;A., University of British Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1967 In p re sen t i ng t h i s t he s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r re ference and Study. I f u r t h e r agree that permiss ion fo r ex ten s i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h.i-s r ep r e s en t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l gain s h a l l not be a l lowed without my w r i t t e n pe rmi s s i on . Department of Economics  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date September 18, 1967 i ABSTRACT The occupational wage structure has been a subject of much interest in recent yearsI The interest, however, has concentrated primarily on the short-run aspects of the problem much to the neglect of the long-run. The recent interest in investment in education has prompted this theoretical and empirical study of the long-run occupational earnings structure from the point of view of investment in education. The paper begins by constructing a theoretical model of occupational earnings i n which the earnings of an occupa-tion are related to the investment in formal and informal (on the job training and learning by doing) education associated with that occupation. The relation between various occupational earnings streams i s established by equating the present values of the expected earnings streams of a l l occupations. From the theoretical relationship, i t can be predicted that the functional relationship between earnings and education should be non-linear with f i r s t and second derivatives positive. Moreover, i t can be predicted that the degree of non-linearity w i l l be related to the rate of discount that i s applied to investment in education. From this sec-tion of the paper arise two important conclusions for studies of long-run changes in the occupational wage structure; i i F i r s t l y , i n studying long-run changes in the occupational earnings structure, attention must be paid to the changing distribution of investment in education among the occupations. Secondly, a change in the shape of the functional relation between earnings and education could be related to long-run changes in the appropriate discount rate. The empirical section of the paper tests the predicted relation between earnings and education by means of regression analysis. The prediction that the relationship should be non-linear ( f i r s t and second derivatives positive) i s borne out by these tests. Moreover, the degree of non-linearity in the empirical relation appears to be approximately the same as predicted from the theoretical model. Finally, using only simple measures of schooling, over 80$ of the occupational earnings structure could be explained in the regression analysis. i i i TABLE OF CONTENTS Page ABSTRACT i TABLE OF CONTENTS.•.................»«.«•...«..iii LIST OF F I G U R E S . . . . . . . . . . ; . . . . . . . . . . . . . i v CHAPTER, I INTRODUCTION................................... 1 I I THE THEORETICAL MODEL. 5 I I I PRACTICAL SIGNIFICANCE AND EMPIRICAL SPECIFICATION OF THE MODEL. 26 I I I . A . The P r a c t i c a l S i g n i f i c a n c e of the model.27 I I I . B . The E m p i r i c a l S p e c i f i c a t i o n . . . . . . . . : . ; . . 3 5 IV EMPIRICAL TESTING .kk V CONCLUSION AND SUMMARY 50 BIBLIOGRAPHY. 55 APPENDIX I 5 8 iv LIST OF FIGURES Page' FIGURE I I - l . Earnings-Schooling Relation.......... 9 II-2. Alternate Life-Earnings Paths....;... 22 I I I - l . Graph of the Earnings-Schooling Relation............................. 29 CHAPTER I INTRODUCTION At l e a s t since the time of Adam Smith, economists have been interested i n the occupational choice of ind i v i d u a l s and s p e c i f i c a l l y i n the d i f f e r e n t i a l s In earnings among occupa-tio n s ; The c l a s s i c a l economists had a good deal to say about the determinants of the occupational choice and consequently about the r e l a t i v e earnings i n occupations, 1 In a recent paper, Melvin Reder 2 has distinguished between the long run and the short run aspects of occupational wage d i f f e r e n t i a l s ; I t i s h i s contention that "economic t h e o r i s t s have tended to explain occupational differences i n wages by differences i n costs of t r a i n i n g ; ; , ; , f o r long-run d i f f e r e n c e s , j n the short-run, demand i s held to play a much more important r o l e A very good summary of the c l a s s i c a l p o s i t i o n on t h i s point has been made by S; Rottenberg i n "On Choice i n Labour Markets, M I n d u s t r i a l and Labour Relations Review, IX, (Jan, 1956), p p ; 1 8 > 1 9 9 . — — — — 2 H; Reder, "Wage D i f f e r e n t i a l s : Theory and Measure-ment,"" i n Aspects of Labour Economics, A Conference of the U n i v e r s i t i e s — N a t i o n a l Bureau Committee f o r Economic Research (Princeton, N; J , : Princeton University Press, 1962) p;258, 3 I b i d . 2 i n t h e r determination of occupational d i f f e r e n t i a l s . I n keeping w i t h other f i e l d s of economics, the c l a s s i c i s t s were: more i n t e r e s t e d i n the long-run determinants, while work i n t h i s century (at l e a s t t h e o r e t i c a l work) has "been more con-1 cerned w i t h s h o r t - r u n problems; While economists have h e l d the long-run view o u t l i n e d above, a systematic long-run theory based on such premises has--not been worked out; I t w i l l be the aim of t h i s paper to provide a formal long-run theory of occupational wage d i f f e r e n -t i a l s ; The recent i n t e r e s t i n investment in. education has prompted t h i s study of the t h e o r e t i c a l and e m p i r i c a l aspects of o c c u p a t i o n a l wage d i f f e r e n t i a l s . More s p e c i f i c a l l y , Gary Becker's t h e o r e t i c a l a n a l y s i s of investment i n human c a p i t a l * ' i m which he makes, o c c a s i o n a l reference t o the i m p l i c a t i o n s of h i s a n a l y s i s f o r occupational earnings p a t t e r n s , 3 has shown need f o r more systematic and thorough research on t h i s p o i n t . In: a d d i t i o n t o Becker*s work, from the e m p i r i c a l s i d e , Weiss 1 h a r t i c l e hasp emphasized the importance of education and t r a i n i n g ss determinants of wage d i f f e r e n t i a l s . These works have served as a s t a r t i n g p o i n t f o r the present p r o j e c t ; . Isee: M. Reder, op. c l t . , f o r a review of recent work, 2G. S7. Becker, "Investment i n Human C a p i t a l j A Theo-r e t i c a l A n a l y s i s , M J o u r n a l of P o l i t i c a l Economy. LXX (Supple-ments Oct. 1962), pp. 9-50. 3 I b i d . , p. 39 f f . l*L. W, Weiss, "Concentration and Labour Earnings," American Economic Review, LVI (March 1966), pp. 96-117. I t i s a t h e s i s of the present work t h a t the d i s t i n -g u i s h i n g c h a r a c t e r i s t i c of an occupation i s that persons i n an occupation d i f f e r from those i n other occupations by 1 education, t r a i n i n g , and other learned c h a r a c t e r i s t i c s . That d i f f e r e n c e s i n occupational earnings would a r i s e does not f o l l o w d i r e c t l y from t h i s alone, however. I t i s the d i f f e r i n g amounts of time and e f f o r t — which must be compensated f o r by a s a t i s f a c t o r y r e t u r n — i n a c q u i r i n g the necessary s k i l l s f o r the various occupations that cause an occupational earnings s t r u c t u r e to emerge. D i f f e r e n c e s a r i s e "because earnings tend to be net of investment c o s t s and gross of 2 investment r e t u r n s . " In t h i s paper a model i s b u i l t which t r e a t s the d i f f e r e n t amounts of schooling i n the d i f f e r e n t occupations as a l t e r -n a t i v e investments which w i l l pay equal r a t e s of r e t u r n . The e q u i l i b r i u m earnings s t r u c t u r e i s determined by the e q u a l i -z a t i o n of present values of a l t e r n a t i v e earnings streams. By equating two earnings streams of d i f f e r e n t amounts of s c h o o l i n g , a r a t i o can be found which r e l a t e s the constant 3 annual earnings of two occupations which d i f f e r i n the In p r a c t i c e , t o d i s t i n g u i s h between occupations i s a task p a r a l l e l to t h a t of d e l i n e a t i n g a labour market. 2 G. S. Becker, o p . c l t . , p.43. "3 A constant annual earnings stream r e f e r s to an income which i s the same each year - constant over an i n d i v i d u a l s l i f e . amount of schooli n g r e q u i r e d by the members. At a l a t e r stage i n the a n a l y s i s , earnings streams which increase over a l i f e t i m e ( i n some systematic fashion) are equated and a s i m i l a r r e l a t i o n i s found between the average annual earnings i n the two occupations. By t h i s method, a s o l u t i o n can be found which r e l a t e s average earnings to the number of years 1 of education and t r a i n i n g r e q u i r e d . T h i s , i n b r i e f , i s the model which i s b u i l t i n Chapter I I of t h i s paper. Chapter I I I goes on t o d i s c u s s the shape of the r e l a t i o n s h i p and the e f f e c t s of changes i n the v a r i o u s parameters on t h a t shape. A l s o , In Chapter I I I , i s a d i s -c ussion of data t h a t can be used t o t e s t the model. Chapter IV d e s c r i b e s t e s t s t h a t were undertaken i n t h i s connection and the r e s u l t s of those t e s t s . The c o n c l u s i o n , Chapter V, discusses the a p p l i c a b i l i t y and importance of the model to st u d i e s of the occupational wage s t r u c t u r e . I t should be pointed out that since we are i n t e r e s t e d i n t r a i n i n g and education which reduces income i n the present and incre a s e s i t i n the f u t u r e , our i n t e r e s t i s w i t h 'general* as opposed to ' s p e c i f i c * t r a i n i n g . Becker makes t h i s d i s t i n c -t i o n In h i s a r t i c l e quoted above (p.12-13) which i s b r i e f l y : general t r a i n i n g i s marketable t o more than one f i r m w h i l e s p e c i f i c t r a i n i n g i s r e s t r i c t e d to one f i r m — consequently, the person r e c e i v i n g general t r a i n i n g tends to pay f o r i t hi m s e l f , w h i l e s p e c i f i c t r a i n i n g i s g e n e r a l l y p a i d f o r by the f i r m and recaptured l a t e r . There are some exceptions to t h i s which Becker p o i n t s out but which are not very important f o r t h i s work. CHAPTER II THE THEORETICAL MODEL In the Introduction, the theoretical relationship between occupations and earnings (through differences In Investment In education) was briefly outlined. In this chapter the basic model of occupational earnings structure w i l l be constructed. This model draws heavily on the work of J. Mincer* and G. Becker as a starting point. At the outset, a number of seemingly restrictive assumptions w i l l be made In order to establish the basis of the model. Later, some of these assumptions can be relaxed and. incorporated- into the model.. Let us begin with the following assumptions: (1) A l l persons spend the same number of years Involved in education and. working although the distribution of time 1Jacob Mincer, "Investment in Human Capital and Personal Income Distribution, " Journal of P o l i t i c a l Economy. LXX (Aug., 1958), pp. 281-3061 2G. S. Becker, "Investment in Human Capital: A Theo-re t i c a l Analysis," Journal of P o l i t i c a l Economy. LXX (Supplement: October^ i'9'S2')'i' pp. 9-50. 6 between the two varies widely. (2) The only costs of education to the i n d i v i d u a l are for e -gone earnings — t u i t i o n fees and inc i d e n t a l costs are assumed non-existent. (3) Education i s undertaken only when a •normal• return can 2 be earned on the Investment — there are no consumption aspects to education at the time of the investment or In the future. (4) There are no systematic occupational preferences; (5) Risk does not enter the occupational decision.-(6) The labour force i s composed of i n d i v i d u a l s of equal a b i l i t y — both as learners and producers; (7) The only method of improving the productivity df an i n d i v i d u a l i s by investment In education at a formal i n s t i -t u t i o n and there i s no depreciation on t h i s investment. In Later, t h i s i s taken to be between the ages of 12 and 65; A f t e r age 12 a l l education i s taken to be an investment and i n d i v i d u a l s stay i n the labour force u n t i l age 65. The term »labour force l i f e 1 w i l l be used to r e f e r to t h i s t o t a l of working and schooling years. 2 In t h i s system, the decision process can be envisioned to operate i n eit h e r or both of the following ways; Each i n d i v i d u a l at age 12 (the age at which investment begins) can make h i s occupational and educational choice; However, a decision (to stop or continue investing i n education) made at any time during the education process (which may be made on the basis of more information) t h e o r e t i c a l l y i s the same as making the decision at age 12; I f a person who has studied f o r N'years decides that i t would pay a normal return to study two a d d i t i o n a l years t h i s means that the present values of the two Income streams (with or without the addi t i o n a l schooling) w i l l be equated i n year N; Further discounting of the two streams back to year zero cannot ehange that equality; the f i r s t approximation, on the job training and learning by doing do not add to an individuals productivity. To the above assumptions i t i s necessary to add the basic economic behavioral statement —• individuals are maxi-mizers. An individual w i l l make the occupational choice ' that maximizes the present value of the net expected earnings stream than an occupation w i l l yield. Given assumptions 3 to 6 above, the demand forces are unimportant as determinants of the long-run occupational earnings structure, 1 and cbnse-quently, equilibrating forces w i l l tend to bring the occupa-tional earnings structure into a long-run equilibrium consis-tant with a normal return on the necessary investment i n education. What follows i n this chapter i s an analysis of the long-run equilibrium that follows from the above1 assump-tions. ' Given the above framework, i t i s possible to derive an equilibrium relationship between annual earnings and schooling for an individual; This relationship w i l l express the alternative earnings the individual could receive by investing in various amounts of education; Since (by assumption) this relationship i s the same for a l l persons, i t w i l l represent the relationship between schooling and earnings for society The assumptions made, imply a perfectly elastic long-run supply of workers to each occupation within the relevant range — leaving the occupational earnings structure to be established by supply considerations only. 8 as a whole. By the above assumptions and the definition of an occupation (see Chapter I) this relationship can be used to express the occupational earnings structure — an occupa-tion can be associated with a specific number of years of schooling and consequently with an earnings level. Since by assumption, an individual's annual earnings are the same in every year, the present value of lifetime earnings (before education commences) for an Individual can be expressed as follows; 1. where, p v n = PV n = An = L = n = r -t C - r t • _ , -m -rL. J e dt = (e -e ) the present value of an earnings stream for an individual with n years of schooling, the annual earnings for an individual with n years of schooling, the length of 'labour force l i f e * — defined in footnote 1 on page 6, the number of years of schooling, the discount rate, time in years, and the discounting process i s continuous. Similarly the present value of lifetime earnings for a 1 person with no investment in education can be written as; 2. PV0 = A o f e" r t dt = A Q (1.0 - e" r L) •0 F~ The form of these f i r s t two equations i s taken from J. Mincer, op.clt., p.285* Equating the present values of these two income streams ( i n accordance w i t h the long-run e q u i l i b r i u m c o n d i t i o n ) the * f o l l o w i n g r e l a t i o n s h i p i s found; 3. f ( n ) = A^ = A Q ( e r L - 1.0) / ( e r ( L " n ) - 1.0) I t i s then p o s s i b l e t o p l o t A^ against n to d i s c o v e r the 1 form of the r e l a t i o n s h i p between schooling and earnings. FIGURE I I - l Earnings - Schooling R e l a t i o n n Equating these streams of earnings assumes a maximizing s o r t of behavior on the part of workers. This d i s a l l o w s any income-leisure s u b s t i t u t i o n at higher income l e v e l s . Theo-r e t i c a l l y and p r a c t i c a l l y i t can be shown th a t some s u b s t i -t u t i o n occurs, but l t i s impossible to s p e c i f y the p r e c i s e nature of t h i s r e l a t i o n s h i p and consequently has been l e f t out of the formal a n a l y s i s of t h i s t h e s i s . 10 The relationship plotted in Figure II-1 i s concave from above, i.e., both f i r s t and second derivatives are positive (at least over the relevant range — with n between 0 and L). This non-linear relationship Is of some Interest to the economist studying occupational earnings structures. However, the importance attached to this finding w i l l be related to the degree of non-linearity of the relationship. This w i l l be discussed in Chapter III where simulated earnings-schooling functions are studied. Having formulated the earnings — education relationship under the restrictive assumptions spelled out at the beginning of this chapter i t i s advisable to relax some of these assumptions and study the effects of the others on the basic relationship. After this has been completed i t w i l l be possible to formulate hypotheses for testing. The assumptions w i l l be considered in the order they are l i s t e d at the beginning of this chapter. (1) The constant 'labour force l i f e . * The assumption that a l l persons are in the labour force (which i s taken to mean education plus working l i f e ) for a specific number of years can be relaxed without creating any problems for the above analysis. The 'labour force l i f e ' that i s considered here extends between 50 and 60 years. Any extension of this l i f e by a person in the labour force can be considered to yield income 50 to 60 years in the future. The addition to the present value of earnings 50 years in the future i s so small as to be negligible. For example, compound 11 discounting for 50 years at a rate of 10$ reduces a sum to less than one per cent of i t s face value. An alternative to the above assumption of equal "labour force l i v e s ' for a l l persons would be to assume Infinite working lives for those in the labour force. This lat t e r 1 assumption has been used by others and has been justified on the same grounds as the assumption made in this paper. Relaxing this assumption would not change the previously derived results perceptibly however, for mathematical f l e x i b i l i t y the assumption w i l l be kept as stated. (2 ) The lack of tuition fees The second assumption, that of opportunity costs being the only real costs of investment in human capital can be dealt with in much the same manner as the assumption above. Allowing tuition fees and other incidental costs of schooling to exist for the moment, suppose that the total costs of this type were constant for every year of schooling or in fact were Increasing. This would not change the shape of the basic relationship previously outlined although this change would tend to make the relationship more non-linear. On the other hand, i f tuition fees decreased with increased years of schooling, that i s , each additional year of schooling costs See, for example, G. Becker, op.cit.. p.36. 12 s l i g h t l y l e s s i n the way of t u i t i o n f e e s , t h i s would appear to have the e f f e c t of reducing the degree of n o n - l i n e a r i t y ' i n the o r i g i n a l r e l a t i o n s h i p . I t turns then t o an e m p i r i c a l q u e stion of the nature of t u i t i o n and I n c i d e n t a l c o s t s of sc h o o l i n g . These cost s ( t o the i n d i v i d u a l of course, not t o s o c i e t y ) appear t o "be low i n the e a r l y years of s c h o o l i n g , r i s i n g i n the e a r l y years of u n i v e r s i t y and f a l l i n g o f f or steady i n graduate schools (the fees of graduate school are hard t o a s c e r t a i n , f o r some they are higher, but f o r some they are almost non-existent, being oovered by l a r g e f e l l o w -s h i p s ) . To assume a s p e c i f i c shape f o r the cumulative cost curve of sc h o o l i n g i s an extremely d i f f i c u l t t a s k . Since these c o s t s comprise a small p a r t of t o t a l cost and are so d i f f i c u l t t o estimate, the author f e l t i t best t o assume a constant cost from year to year — that constant l e v e l being zero, ( 3 ) The l a c k of consumption b e n e f i t s t o education From d i s c u s s i o n s devoted t o the subject of education and from personal knowledge, I t i s obvious t h a t many persons f e e l t h a t there are consumption aspects i n v o l v e d i n the educa-t i o n . These b e n e f i t s apparently take the form of consumption b e n e f i t s d e r i v e d while the investment i n education i s being undertaken and/or consumption b e n e f i t s d e r i v e d l a t e r i n l i f e ! The consumption b e n e f i t s d e r i v e d a t school would tend t o narrow earnings d i f f e r e n t i a l s i n that persons would be w i l l i n g to undertake investment i n education at a lower apparent r a t e of 13 return than would otherwise be the case. However, i f these types of consumption benefits do not increase (as a propor-tion of schooling costs) with increasing years of schooling 2 they should not affect the previous results. By reason of ignorance on the part of social scientists, this assumption appears to be as valid as anyi About consumption benefits derived later in l i f e — these being of the nature of increased occupational status^ 3 the ""enjoyment of a f u l l e r , more complete l i f e , " etc., i t is d i f f i c u l t to formulate anything that can add to the theo-ret i c a l model. If in fact education i s undertaken with the idea that there w i l l be a non-monetary return to the invest-ment as well as a monetary one, by the equilibrium assumption, lower earnings would be observed than would otherwise be predicted in the occupations requiring large amounts of educa-tion;. It should be recognized that the fact that there are This i s not to say that investment i n education would yield a lower rate of return than other investments in the economy. It i s l i k e l y that students who are investing i n education are making no other investment because of lack of money. Por the most part, students are relatively poor and may therefore demand a high return to entice them to forego current consumption. That i s , because investment in education i s undertaken by a certain group of people, the return on that investment may not be equalized with other rates in the market. 2 That i s , consumption benefits may in some way be the •same*' in each year, so that only the rate of return Is affected, not the structure of earnings. 3 ^See B. Weisbrod, "Education and Investment in Human Capital," Journal of P o l i t i c a l Economy. LXX (Oct. 1962) pp. 106-123,.for a more complete discussion of monetary and non-monetary returns to education. Ik post hoc consumption b e n e f i t s i s not i n I t s e l f s u f f i c i e n t to cause the r e d u c t i o n i n earnings d i f f e r e n t i a l s Just mentioned. I t i s necessary a l s o t h a t these b e n e f i t s be foreseen by those i n v e s t i n g i n education and that these b e n e f i t s be i n c l u d e d i n the c a l c u l a t i o n s of the r e t u r n on the investment,* To the degree t h a t t h i s i n i n f a c t the case, there w i l l be some e f f e c t on the basic r e l a t i o n s h i p . The degree of the e f f e c t , however, i s a q u a n t i t a t i v e , e m p i r i c a l q u e s t i o n t h a t cannot be p r e d i c t e d a p r i o r i , (k) No systematic .job preferences The assumption made about the l a c k of systematic job preference i s i n t i m a t e l y l i n k e d w i t h the previous assumption about the consumption aspects of education. The previous assumption r e f e r s t o b e n e f i t s d i r e c t l y l i n k e d w i t h the educa-t i o n a l process whereas the present assumption r e f e r s t o b e n e f i t s t h a t are job s p e c i f i c ( i t i s a matter of i n d i f f e r -ence whether these b e n e f i t s are termed consumption b e n e f i t s or non-monetary income). As w i t h consumption b e n e f i t s o f . education, systematic job preferences would tend t o d i s t o r t the p r e v i o u s l y discussed r e l a t i o n between education and e a r n i n g s i The d i s t o r t i o n would not tend to be systematic w i t h r e l a t i o n to education, however, since non-monetary •••This a l s o i s true f o r consumption b e n e f i t s of the f i r s t nature. I t i s not enough th a t s o c i a l s c i e n t i s t s look back on t h e i r school days w i t h s e n t i m e n t a l i t y , students must f e l l t h a t they are g a i n i n g consumption b e n e f i t s while they are i n v e s t i n g . 15 benefits could exist in occupations at any level of educa-1 tion. It i s true without question that some individuals derive large non-monetary benefits from specific occupa-tions. However, this fact alone i s not enough to require a change in the theory. It i s equally true that a l l persons do not prefer the same occupation or occupations (even though a few occupations are generally liked and a few gener-a l l y disliked). The basic economic force that enabled a: prediction in the f i r s t instance was the behavioral assump-tion of maximizing behavior on the part of Individuals. Under*this assumption, i t i s the marginal adjustment process that established the earnings structure. That some i n d i v i -dual s; in every occupation earn •rents" cannot alter this marginal process; Thus, while It Is clear that individuals do have job preferences, i t Is not clear (and cannot be predicted a priori) that this phenomenon i s significant ' enough to distort the previously deduced relationship between earnings and education i n anything but a random manner. (5) The lack of risk In the occupational choice There are at least three reasons why the assumption has been made that risk does not affect the occupational It i s generally thought that such benefits accrue In occupations requiring higher levels of education — in which case i t Is d i f f i c u l t to distinguish this assumption from the previous one — but this Is not necessarily the case. 16 d e c i s i o n . I n the f i r s t p l a c e , since i t i s occupations th a t are being considered, i t may be claimed that there i s l i t t l e reason to expect i n d i v i d u a l s to a t t a c h more or l e s s r i s k t o d i f f e r e n t occupations — that i s t o say, t h a t i n d i v i d u a l s would expect an equal chance of success i h vari o u s occupations (at l e a s t w i t h respect to the occupa-t i o n s which l i e i n h i s range of a b i l i t i e s ) . I n the second p l a c e , i t i s p o s s i b l e that i n d i v i d u a l s do not even con-s i d e r r i s k when making the occupational d e c i s i o n . This second p o i n t may overlap the f i r s t i n t h a t the reason that r i s k i s not even considered i s because i n d i v i d u a l s ' f e e l ' t h a t the va r i o u s occupations are 'equally r i s k y ' . There may, however, be other reasons that r i s k i s not considered i n the 1 occupational d e c i s i o n . In the t h i r d p l a c e i t may be that r i s k i s considered but that i t s e f f e c t s are of various types that tend to cancel out i n aggregate. For these 2 reasons, r i s k has been assumed n e u t r a l i n t h i s model. One of these p o s s i b l e reasons may be t h a t while an i n d i v i d u a l r a t i o n a l l y f e e l s that he should a l l o w f o r r i s k i n t h i s d e c i s i o n , he has no idea how t o estimate r i s k to b r i n g i t i n t o the decision." 2 M. Friedman and S. Kuznets i n Income from Independent  P r o f e s s i o n a l P r a c t i c e , (New York: N a t i o n a l Bureau of Economic Research, 195*0 > Chapter 3» hypothesize t h a t i n d i v i d u a l s w i l l act as r i s k takers because they g e n e r a l l y overestimate t h e i r own a b i l i t y . The author has he l d the opposite view w i t h some success — that persons w i l l act as r i s k a v e r t e r s , see "Occupational Wage D i f f e r e n t i a l s and Investment i n Human C a p i t a l " , unpublished paper, 1967. (This i s the more usual assumption — see f o r examples J . Tobln, " L i q u i d i t y Preference as Behavior towards R i s k " , Review of Economic S t u d i e s , XXV (Feb. 1958) pp.65-86). 17 (6) The a b i l i t y of I n d i v i d u a l s I f some s p e c i f i c d i s t r i b u t i o n of a b i l i t y i s allowed f o r i n the model ( r a t h e r than assuming i n d i v i d u a l s equal w i t h respect t o a b i l i t y as i n the o r i g i n a l assumption) there are a number of r a m i f i c a t i o n s f o r the s t r u c t u r e of earnings. The degree of adjustment to the previous model depends on the p r e c i s e d i s t r i b u t i o n of a b i l i t y among the v a r i o u s occupations. I t should be f i r s t recognized t h a t a b i l i t y cannot be i n t e r p r e t e d t o be a uni-dimensional concept. One i n d i v i d u a l may have an a b i l i t y , t o be a carpenter and another the a b i l i t y to be a medical doctor, but t o compare these a b i l i t i e s oh a unl-di m e n s i o n a l l y s c a l e i s not l o g i c a l l y p o s s i b l e . Each of these i n d i v i d u a l s may be s a i d t o be the best i n h i s f i e l d but f u r t h e r comparison ( w i t h respect t o a b i l i t y ) i s absurd. Secondly, l t should be pointed out th a t a b i l i t y i s not g e n e r a l l y a narrow or s p e c i f i c c h a r a c t e r i s t i c . A person w i t h high a b i l i t y I n one f i e l d , g e n e r a l l y has a s i m i l a r a b i l i t y i n c l o s e l y r e l a t e d f i e l d s . Thus, the h i g h l y able medical doctor r e f e r r e d t o above, may have chosen t o become a chemist or a d e n t i s t (and a l s o e x c e l l e d i n those f i e l d s ) had the r e t u r n t o the investment i n education i n those f i e l d s been higher (than the r e t u r n t o medical doctors) during the p e r i o d i n which he made h i s occupational choice. As a f i r s t s t e p , suppose there e x i s t e d a w e l l - d e f i n e d set of occupations, each of which contained a s i z e a b l e number of workers. Suppose moreover, that each i n d i v i d u a l has d i f f e r e n t a b i l i t i e s and the a b i l i t y of an i n d i v i d u a l can be 18 u t i l i z e d in more than one occupation; In fact, a b i l i t i e s in this labour force are distributed such that no occupation i s lacking workers of the required a b i l i t y to such a degree that i t i s necessary to pay a rent in that occupation — that Is, each occupation pays a normal return to the investment in human capital necessary to allow an Individual to enter that occupation. Moreover, i t can be added that the distribution of a b i l i t y to perform a specific occupation i s more or less normally distributed (within a specific occupation a uni-dimensional concept of a b i l i t y i s valid, that i s , the a b i l i t y to perform a specific task) within each occupation. Such a model of the distribution of a b i l i t y appears to the author as a not unreasonable position to hold;*iThis model does not require that each occupation pay a standard wage ; — there w i l l be some distribution (approximately nor-mal) within an occupation although obviously not as great a difference as between occupations. However, since the distribution of talent available to an expanding occupation i s the same as the distribution of already employed talent in that occupation, the long-run supply curve to an occupation can be considered as horizontal and the return on investment 1 This position could alternatively be expressed in Longfield's ideas of competition operating through a chain of intermediate professions. For an outline of this view, see E. Whittaker, A History of: Economic Ideas (Toronto: Longmans, Green and Co., 194-3) p.601, 1 9 i n eduoation f o r each occupation w i l l be kept at a 'normal* r a t e of r e t u r n . No d i s t o r t i o n i n the b a s i c model a r i s e s i f i t i s a l t e r e d i n t h i s f a s h i o n . While the above r e f o r m u l a t i o n i s not an e n t i r e l y r e a l i s t i c view of the labour market, i t i s much c l o s e r to r e a l i t y than the i n i t i a l r e s t r i c t i v e assumption. I t i s o b v i o u s l y t r u e a t the upper end of the occupational s c a l e (with respect t o the amount of Investment required) t h a t some I n d i v i d u a l s are p a i d r e n t s f o r a unique a b i l i t y but t h e r e i s a t l e a s t one reason to discount t h i s as a problem when the above (reformulated) model i s a p p l i e d to the r e a l world. The frequency of occurrence i s probably r a r e — note t h a t a d i s t r i b u t i o n of a b i l i t i e s i s already allowed f o r and i t i s the d e v i a t i o n s from t h i s d i s t r i b u t i o n and not d e v i a -t i o n s from the •norm' t h a t w i l l cause d i s t o r t i o n s i n the model. (7) On the Job T r a i n i n g and Learning by Doing. The f i n a l assumption that must be considered t h e o r e t i -c a l l y i s the assumption t h a t on the job t r a i n i n g and l e a r n i n g by doing do not add to the p r o d u c t i v i t y of an i n d i v i d u a l . This assumption must be r e l a x e d unless the previous r e s u l t s are to be rendered meaningless. I t i s w e l l known th a t on the job t r a i n i n g and l e a r n i n g by doing are very important aspects of an i n d i v i d u a l ' s investment i n education. U n t i l now, t h i s paper has considered only earnings' paths which are constant over an i n d i v i d u a l ' s l i f e because of the assumed non-20 existence of informal t r a i n i n g . Allowing f o r informal t r a i n i n g introduces a number of complexities into the analysis not the least of which i s the problem of specifying i n what manner informal t r a i n i n g should be introduced into the model. Since there i s no good measure of informal education 1 available, i t seemed of l i t t l e value to consider informal and formal education i n a general"way as inputs i n a process and l a t e r devise tests on t h i s basis. Moreover, from know-ledge of the educational process, the author f e l t t h i s method an u n r e a l i s t i c approach to the problem. Consequently, the method chosen here has been to postulate a s p e c i f i c r e l a t i o n between formal and informal education and incorporate t h i s into the model previously discussed. In considering the s p e c i f i c a t i o n of the relationship between formal and informal education, two possible alternative assump-tions suggested themselves; a) formal and informal education are substitutable inputs i n the production of a. worker, b) because of the nature of the two inputs — formal and informal education — the-inputs tend to be complementary. The author's view of the education process has caused him to opt f o r the second of these possible sp e c i f i c a t i o n s — 1 : B. W. Wilkinson, i n Studies i n the Economics of Education, Ottawa': Economics and Research Branch, Department of Labour, 1965,- -Chapter 2, converted an American measure of informal education requirements (by occupation) into Canadian measures but did not f i n d t h i s data r e l i a b l e . 21 that i s , t h a t formal and informal education are complemen-t a r y Inputs and the more formal education t h a t i s a t t a i n e d , the more i n f o r m a l education t h a t w i l l f o l l o w . The author > views formal education as a process whereby the' student absorbs the c a p a c i t y to l e a r n . This education i s not d i r e c t e d towards f i t t i n g the student to perform a s p e c i f i c t a s k , but to f i t the student to l e a r n more complex tasks i n the f u t u r e through i n f o r m a l t r a i n i n g . . Thus, the more formal education t h a t i s a t t a i n e d by a student, the more p r o f i t a b l e i t w i l l be to pursue extended i n f o r m a l t r a i n i n g on the job. A student who makes an occupational choice, a t the same time makes a choice as to the amount of formal education t h a t w i l l be necessary to s u i t him f o r l e a r n i n g , i n the i n f o r m a l 1 manner, the s p e c i f i c t a s k s a s s o c i a t e d w i t h the occupation. The assumption made above i s the major change i n the t h e o r e t i c a l framework i n t h i s s e c t i o n . However, i n order to i n c o r p o r a t e t h i s assumption i n t o the model, an a d d i t i o n a l minor assumption (of a more mechanical nature) must a l s o be made. The p a t t e r n of i n f o r m a l t r a i n i n g , w i t h respect to t i m i n g , must a l s o be s p e c i f i e d . I t i s t h e r e f o r e assumed, that on the job t r a i n i n g and l e a r n i n g by doing increase the i n d i v i d u a l ' s p r o d u c t i v i t y (andconsequently h i s earnings) i n a l i n e a r f a s h i o n . That i s , an i n d i v i d u a l ' s p r o d u c t i v i t y Knowledg gained from observation of age-earnings p r o f i l e s a l s o tends to support the case f o r complementarity. See G. Becker, o p . c l t . . p.43 and J . Mincer, o p . c l t . , p.292. 22 i n c r e a s e s by the same amount each year u n t i l some c u t - o f f p o i n t i s reached a f t e r which h i s earnings are i n v a r i a n t . * Thus an i n d i v i d u a l ' s l i f e earnings path has the shape shown below by G n as opposed to the path which d e p i c t s the l i f e earnings path of an i n d i v i d u a l w i t h n years of sc h o o l i n g 2 and no i n f o r m a l t r a i n i n g . FIGURE I I - 2 A l t e r n a t e L i f e - Earnings Paths j t ( y e a r s ) *The choice of a r e a l i s t i c c u t - o f f p o i n t was not simple because of the l a c k of adequate data from which to make a d e c i s i o n . The f o l l o w i n g a l t e r n a t i v e s were studied(and are discussed l a t e r ) although i t turned out that the choice made l i t t l e d i f f e r e n c e t o the f i n a l r e s u l t s ? i ) t h a t the increases continue over a c e r t a i n f r a c t i o n of the working l i f e , i i ) that the increases continue a c e r t a i n number of years a f t e r formal education ceases, i i i ) t h a t the increases continue u n t i l a c e r t a i n number of years before r e t i r e m e n t . 2These three paths are not meant to represent a l t e r n a t i v e s , An i s a path w i t h no investment i n education. A~ i s a path w i t h n years investment but not a l l o w i n g f o r on the job t r a i n i n g . Gn i s a v a r i a t i o n on An, a l l o w i n g f o r on the job t r a i n i n g . 23 The p o i n t ,D» i n the above diagram represents the age at which i n f o r m a l t r a i n i n g (and consequently increases i n earnings) ceases. The equation of the l i n e G Q can then be w r i t t e n : 4 . G n = B n + S n (t-n) f o r n £ t s D and 5. G n = B n + S n (D-n) f o r D*§ t "sL where; S n represents the slope of the l i n e (and S i s an i n c r e a s i n g f u n c t i o n of n by assumption (B) above) and B n represents the s t a r t i n g s a l a r y a f t e r h years of scho o l i n g — B i s some f r a c t i o n of A , The present value of the earnings path G n w i l l of course be equal t o the present value of the earnings path A N i n e q u i l i b r i u m and both w i l l be equal t o the present value of the earnings path AQ which represents the earnings path of an i n d i v i d u a l w i t h no formal or in f o r m a l t r a i n i n g . Given t h i s s t a r t i n g p o i n t , i t i s d e s i r a b l e t o f i n d the average l i f e t i m e earnings of an i n d i v i d u a l w i t h n years of sc h o o l i n g . The model can be summarized i n the f o l l o w i n g equations: 6. •'- A 0 / o L e - « d t = A n / L o - " d t which f o l l o w s from equations 1 and 2 above — equating the present values of two earnings streams f o r persons w i t h This i s d e s i r a b l e because i t i s one measure that can be estimated from the a v a i l a b l e data. 2k different amounts of education (and no Informal training). J,L — r t — r t (f^* — r t 1 e dt = B n J e dt + j (t-n) e + S (D-n) f e "L" dt dt n i r»L - r t D which equates an earnings stream with n years of schooling and no on the job training to a stream with n years of schooling plus on the job training in accordance with the two assumptions just made. That i s , equating the streams and G n i n figure II-2. 8. ST = B + ( (S /2) (D-n) 2 + S (L-D) (D-n) ) / (L-n) n n n n where A~ i s the average of the earnings stream G . n n The above equations (6, 7 and 8) can be solved to yield: 9. XT = A (Bl + B2) - S (B-? - nBk + DB? - nBg) n 0 B 2 n B 2 + ( (D-n)2/2 +' (L-D) (D-n) ) * S n/ (L-n) where; Bl = 1 e' r t dt B2 = f e • dt n B3 = • t e " r t dt mJ> - r t Bk = J e dt B5 = f n L - r t dt = B2 - Bk The solution of the system (given in equation 9 above) specifies a relationship between average earnings and years of schooling when on the job training and learning by doing 25 are allowed to occur i n the above-specified manner. I t turns out that t h i s r e l a t i o n s h i p — complicated as i t appears to be — has the same general shape as the more simple r e l a t i o n -ship given by equation 3 (that i s , without the on the job . 1 t r a i n i n g ) . This chapter has attempted to b u i l d a t h e o r e t i c a l model of the occupational wage structure. A model has now been constructed but i s as yet i n a very general form. I t w i l l be the task of the next chapter to examine the model more clo s e l y by specifying the parameters of the model, and to turn the t h e o r e t i c a l model into a form which can be subsequently tested. *The f i r s t and second derivatives of the expression A with respect to n are both p o s i t i v e . The equation would n not submit e a s i l y to mathematical d i f f e r e n t i a t i o n so r e a l i s t i c values of the parameters were used and the equation was put into a computer to f i n d t h i s r e s u l t . CHAPTER III PRACTICAL SIGNIFICANCE AND EMPIRICAL SPECIFICATION OF THE MODEL The aim of Chapter II was to build a theoretical model of the occupational wage structure that could be subjected to s t a t i s t i c a l tests; It i s nothing new to suggest that earnings of an occupation are somehow related to the s k i l l and training required for the occupation of an individual. References to this idea date back at least to Adam Smith. 1 However, the relationship has been of an intuitive nature and has not been made formally theoretical; A formal model has been constructed in the previous chapter, but before any testing can be undertaken there are two aspects of the model that must be discussed; (A) At various stages in the last chapter, conclusions were made about the shape of the relationship between earnings and investment in education and about the Importance of that shape in empirical analysis. It i s necessary therefore to begin this chapter by a more precise examination of the suggested Adam Smith, The Wealth of the Nations. (Homewood, 111.: R. D. Irwin, 1963) B o o k 1» Chapter 107 Part 1. 27 r e l a t i o n s h i p . To do t h i s , i t was necessary to employ the technique o f computer s i m u l a t i o n due to the complexity o f the r e l a t i o n (see e q u a t i o n 9 o f the l a s t c h a p t e r ) . In so d o i n g , another problem a r i s e s . To use the computer simu-l a t i o n method, v a l u e s must be a s s i g n e d to the v a r i o u s p a r a -meters i n the model. I f v a r i a t i o n o f the parameters causes marked v a r i a t i o n i n the o r i g i n a l r e l a t i o n s h i p , then g r e a t care must be employed i n choosing the parameter v a l u e s . T h u s ' i t w i l l be necessary i n t h i s s e c t i o n t o a l s o d i s c u s s the c h o i c e (and the importance o f the choice) of the p a r a -meters pf the model. (B) A l s o , b e f o r e any t e s t i n g can be undertaken, i t w i l l be necessary to r e l a t e the t h e o r e t i c a l n o t i o n s a l r e a d y d i s c u s s e d to the a v a i l a b l e d a t a . Prom the p u b l i s h e d data"'', v a r i a b l e s must be drawn t h a t correspond to the t h e o r e t i c a l v a r i a b l e s i n the model. T h i s w i l l I nvolve comparison of the t h e o r e t i -c a l concept o f o c c u p a t i o n s and s c h o o l i n g and t h e i r p r a c t i c a l c o u n t e r p a r t s . C o r r e c t i o n s w i l l have t o be employed t o b r i n g the two i n t o correspondence. P a r t A — The P r a c t i c a l S i g n i f i c a n c e of the Model. In o r d e r to d i s c u s s the s i m u l a t i o n of t h e model a t a l l , i t I s n e c e s s a r y to inform the reader o f the range o f v a l u e s t h a t the main independent v a r i a b l e (years o f s c h o o l i n g o r 1 I n t h i s case the 1961 Census o f Canada served as the source o f d a t a . 28 investment i n education) was allowed t o take on. The author f e l t i t necessary to the t h e o r e t i c a l framework to not begin counting s c h o o l i n g as an investment i n education u n t i l the age (or l e v e l ) at which a c h i l d c o uld make the d e c i s i o n to remain i n school or t o leave. I t was f e l t t hat age 12 and 1 grade 6 were most appropriate f o r t h i s purpose. Having chosen t h i s p o i n t as a base, the number of years of schooling i n an occupation w i l l f a l l between zero and t h i r t e e n years ( a c t u a l s c h o o l i n g minus 6 y e a r s ) . The maximum schooling allowed f o r ( t h i r t e e n years) represents twelve years i n grade school and seven i n U n i v e r s i t y -- t h i s e a s i l y accounts f o r .the e d u c a t i o n a l attainment i n any of the occupations s t u d i e d . Having discussed the choice of the independent v a r i a b l e , i t i s u s e f u l to graph immediately some earnings-education r e l a t i o n s f o r p a r t i c u l a r sets of parameter values. This w i l l be u s e f u l to f a m i l i a r i z e the reader with the form of the r e l a t i o n which w i l l be discussed i n the next few pages and a l s o as a reference point that can be used i n d i s c u s s i o n s of the parameters. 1 At the present the compulsory attendance age v a r i e s between 12 and lk (across Canada) or between grade 6 and 8. As t h i s c u t - o f f p o i n t was lower i n the past r e v i s i o n of t h i s choice may be necessary; 29 • $ i 5 9 o o o A n (r=12#) An (T=lk%) n(years) With the a i d of the above diagram i t i s now p o s s i b l e t o di s c u s s the choice of the parameters i n the model as to t h e i r s i g n i f i c a n c e . For each of the parameters, a number of a l t e r -n a t i v e values have been s t u d i e d to d i s c o v e r i f an i n c o r r e c t The f o l l o w i n g parameter values are used i n the above diagram; the discount r a t e at 12 and lk% f o r the lower and upper curves r e s p e c t i v e l y ; retirement age = 65 ( i . e . L, the labour f o r c e l i f e = 53); A©, the base wage =.-12000; the age at which s a l a r y increments cease = L-15 (15 years before r e t i r e m e n t ) ; and the slope — S — i s chosen a t = JOn. The X a x i s measures years of investment i n education, and the Y a x i s measures the unweighted average earnings of an occupation ( i n d o l l a r s ) . These are the. same paths that are t a b u l a t e d i n Appendix I , Tables I and I I . 30 choice would g r e a t l y b i a s the r e s u l t s that f o l l o w . Of the parameters, i t appeared t h a t only the choice of the discount 1 r a t e was important. Some of the other parameters were of s l i g h t importance and others of no apparent importance.. The fo l l o w i n g paragraphs d i s c u s s these r e s u l t s . The choice of an appropriate discount r a t e has been based on p r i v a t e r a t e s of r e t u r n to Investment In education 2 3 c a l c u l a t e d by Becker and others. Although no consensus of 4 opi n i o n on the appropriate r a t e of r e t u r n p r e v a i l s the author has chosen r a t e s of 10, 12, and 14 per cent to study.^ The discount r a t e has a very important i n f l u e n c e on the shape of the p l o t t e d f u n c t i o n . A small change i n the discount r a t e (a v a r i a t i o n of 2% or so) has a marked p o s i t i v e e f f e c t Important from the po i n t of view that s l i g h t v a r i a t i o n s i n the parameter value would r e s u l t i n l a r g e changes i n the curvature of the ba s i c education-earnings r e l a t i o n . Generally i t was c l e a r what range the parameter values should take but not the.exact value. G. S. Becker, Human C a p i t a l , (New York and London: Na t i o n a l Bureau of Economic Research, 1964). 3see W. G. Bowen, "Assessing the Economic C o n t r i b u t i o n of Education", An A p p r a i s a l of A l t e r n a t i v e Approaches," i n h i s book, Economic Aspects of Education ( P r i n c e t o n , N. J . : Pr i n c e t o n U n i v e r s i t y P r e s s , 1964)"or B. W. Wil k i n s o n , Studies l n ^ t h e Economics of Education (Ottawa: Economics and Research Branch, Department of Labour, 1965), Chapter 1, f o r d i s c u s s i o n s of the var i o u s r e s u l t s t h a t have been found i n c a l c u l a t i n g r e t u r n s to education. 4 •^W. G. Bowen. o p . c i t . . p.27 f f . •''Since s t a t i s t i c a l work has been completed, i t has been pointed out that a study on Canadian data suggests the r a t e to be 15 to 20$ — see footnote i n G. Bertram, The C o n t r i -bution of Education to Economic Growth, (Ottawa: Economic Council of Canada, 196677 " 31 on the second d e r i v a t i v e — that i s , an increase i n the i n t e r e s t r a t e increases the degree of n o n - l i n e a r i t y of the f u n c t i o n 1 (Tables I and I I of Appendix I show the e f f e c t of va r y i n g the discount r a t e o n l y ) . Two r a t h e r important i m p l i c a t i o n s f o l l o w from t h i s f i n d i n g ; i ) i f the t h e o r e t i -c a l r e l a t i o n i s to be used t o approximate the e m p i r i c a l r e l a -t i o n , a very c a r e f u l choice of the discount r a t e must be made, i i ) i f , as some contend, there has been a s e c u l a r d e c l i n e i n i n t e r e s t r a t e s , and i n p a r t i c u l a r i n the r a t e of r e t u r n on investment i n education, d e f i n i t e changes i n the occupa-2 t i o n a l earnings s t r u c t u r e , a r e i m p l i e d , Por a retirement age, ages of 65, 70 and 75 were s t u d i e s . •••Some change i n the f i r s t d e r i v a t i v e i s a l s o noted but i s of l i t t l e s i g n i f i c a n c e as v a r i a t i o n of the slope parameter w i l l b r i n g t h i s back i n t o l i n e . 2That i s , i f the d e c l i n e i n the discount r a t e represents a s e r i e s of long-run e q u i l i b r i u m r a t e s of r e t u r n . I f the d e c l i n e represents only a movement towards an e q u i l i b r i u m , the i m p l i c a t i o n i s not at a l l c l e a r from t h i s model. H i s t o r i -c a l comparisons of the wage s t r u c t u r e which d i s c u s s the com-pr e s s i o n of the wage s t r u c t u r e over time would do w e l l to consider the long-run d e c l i n e i n i n t e r e s t r a t e s as an explana-t o r y f a c t o r i n t h i s connection. -'This a l l o w s comparison of the e f f e c t of postponed retirement of a l l members of the lab o u r f o r c e . One p o s s i b i l i t y not allowed f o r by t h i s v a r i a t i o n i s that d i f f e r e n t occupa-t i o n s (or persons w i t h d i f f e r e n t l e v e l s of formal education) r e t i r e a t d i f f e r e n t ages. I t was shown i n Chapter I I however, tha t due to the d i s c o u n t i n g of earnings so f a r i n the f u t u r e , the e f f e c t s of such behavior should be minimal. Moreover, to have any e f f e c t on the r e l a t i o n s h i p whatever, i t would be necessary that a d e c i s i o n on retirement age be made a t the time of educational and occupational choice. To hypothesize that i n d i v i d u a l s would expect any retirement age other than the average f o r the labour f o r c e as a whole would be r i s k y . 32 R e c a l l i n g t h a t L represents the 'labour f o r c e l i f e ' — the number of years of investment i n education p l u s the number of years working ~ then f o r these three retirement ages, L 1 w i l l take on the values of 53, 58, and 63. V a r i a t i o n i n the retirement age r e s u l t s i n only s l i g h t e f f e c t s to the earnings-education r e l a t i o n . A f i v e year increase i n the retirement age r e s u l t s i n Increases i n both the f i r s t and second d e r i v a t i v e s but the changes are i n s i g n i f i c a n t (the change i n the f i r s t d e r i v a t i v e i s the l a r g e r but of l i t t l e i n t e r e s t h e r e ) . The reader may judge f o r h i m s e l f by con s u l -t i n g Tables I and I I I of Appendix I which reproduce two education-earnings r e l a t i o n s h i p s — the only d i f f e r e n c e i n which i s the v a r i a t i o n i n the retirement age. In studying the base l e v e l of earnings AQ (the earnings l e v e l f o r an i n d i v i d u a l w i t h no educational investment — ' :* 2 formal or Informal) a range of |1600 to $2000 was considered. V a r i a t i o n s i n t h i s parameter tended to s h i f t the earnings-3 education r e l a t i o n , of course, but a l s o very minor v a r i a t i o n s This r e s u l t s from s e t t i n g age 12 as the s t a r t i n g p o i n t f o r investment i n education. T h i s l a r g e a range was not necessary as i t was c l e a r that the obvious choice of t h i s parameter would l i e c l o s e to $2000, however, a wider choice was considered i n case s t u d i e s were to be undertaken of e a r l i e r or l a t e r data. 3 Minor, as used here, r e f e r s to a change of the order of t h a t between the earnings' paths i n Tables I and I I I of Appendix I . 33 1 i n the f i r s t and second d e r i v a t i v e s were n o t i c e d . The v a r i a t i o n of the c u t - o f f p o i n t and the slope should be considered simultaneously because they are chosen i n t h a t manner — once a c u t - o f f p o i n t i s s e l e c t e d , a slope can be 2 chosen which leads t o a r e a l i s t i c range of a l t e r n a t i v e s . V a r i a t i o n i n the c u t - o f f p o i n t , with appropriate v a r i a t i o n i n the slope to maintain r e a l i s t i c values of earnings, 3 r e s u l t e d i n only small changes i n the shape of the earnings-education r e l a t i o n and f u r t h e r c o n s i d e r a t i o n of t h i s choice i s unnecessary a t t h i s time. I n the past few pages, a d i s c u s s i o n of the importance of v a r i o u s changes i n the parameters i n the model has been presented; a l l t h a t remains to be accomplished i n the present s e c t i o n of t h i s paper i s a d i s c u s s i o n of the degree of non-l i n e a r i t y of the education-earnings r e l a t i o n s h i p . In order to t e s t the relevance of the n o n - l i n e a r shape of the curve to the ' r e a l world' a simple t e s t has been employed. That t h i s should occur i s not a t a l l c l e a r i n t u i t i v e l y , i t a r i s e s because i n equation 9 there are three terms added together on the r i g h t hand side of the equation. The f i r s t term i s by f a r the l a r g e s t term and has f i r s t and second d e r i v a t i v e s p o s i t i v e . The other two terms taken together (added) have f i r s t d e r i v a t i v e p o s i t i v e and second d e r i v a t i v e negative. A change i n AQ a f f e c t s only the f i r s t term — by a f r a c t i o n a l i n c rease i n earnings a t each l e v e l of education. Adding a term w i t h a negative second d e r i v a t i v e tends to reduce the second d e r i v a t i v e i n the f i r s t term. However, a f t e r AQ i s i n c r e a s e d , the added term (combined second and t h i r d terms) has l e s s e f f e c t on the t o t a l r e l a t i o n . 2 C u t - o f f p o i n t such as; n +. 25, L - lf>, and (L - n)/2, were t y p i c a l of those s t u d i e s . Slopes t o correspond to these c u t - o f f p o i n t s were of the type; 30n, 35n, and 40n. • ^ i . e . , of the order noted when the retirement age i s v a r i e d (see Tables I and I I I i n Appendix I ) . 34 L i n e a r r e g r e s s i o n s have been performed u s i n g as the dependent v a r i a b l e the average earnings f i g u r e s c a l c u l a t e d from the t h e o r e t i c a l r e l a t i o n s h i p (equation 9) and as the independent v a r i a b l e , the appropriate number of years of s c h o o l i n g ( i n v e s t -ment i n education) i n a simple and i n a squared form. This procedure was c a r r i e d out f o r a number of a l t e r n a t i v e combina-t i o n s of values of the parameters. The r e s u l t s were n e a r l y 1 i d e n t i c a l r e g a r d l e s s of the parameter valu e s . The f o l l o w i n g •• 2 two equations are t y p i c a l of the r e s u l t s of the r e g r e s s i o n s . 2 1. iL, = 900.0 + 1137.3 n R = .976 ^ (51.7) — • 2 2 2. A^ = 2182.8 + 495.9 n + 49.3 n R = .999 These r e s u l t s i n d i c a t e that the percentage of the dependent v a r i a b l e explained can not be increased g r e a t l y by the a d d i t i o n of the n o n - l i n e a r form of the schooling- term. The r e l a t i o n s h i p which has been d e r i v e d t h e o r e t i c a l l y — the n o n - l i n e a r form, t h a t i s — does not seem p a r t i c u l a r l y impor-tant i n p r a c t i c a l work. While the n o n - l i n e a r r e s u l t i s 1 I t should be pointed out, however, t h a t the discount r a t e , as p r e v i o u s l y shown, does e x h i b i t a p o s i t i v e r e l a t i o n w i t h the second d e r i v a t i v e of the education-earnings r e l a t i o n . Hence, the f o l l o w i n g two r e g r e s s i o n equations which employ the l a r g e s t discount r a t e considered, 14$, w i l l show the maximum s i g n i f i c a n c e of the S z term. Even when the n term i s maximized, the importance of i t i s very minor. o The values of the parameters f o r t h i s p a r t i c u l a r set of regr e s s i o n s are as f o l l o w s ; r (discount r a t e ) = 14$, Ag ( s t a r -t i n g wage f o r those w i t h no educational investment) = #2000, D (the c u t - o f f p o i n t or age a f t e r which no person i n v e s t e d f u r t h e r i n i n f o r m a l t r a i n i n g = retirement age l e s s 15 years, L (the labour f o r c e l i f e — p r e v i o u s l y defined) = 53 years, and the slope of the age-earnings p r o f i l e was chosen as pr e v i o u s l y o u t l i n e d . 35 I n t e r e s t i n g t h e o r e t i c a l l y , i t may not be important i n a c t u a l t e s t s made on incomes of occupations, which are i n f l u e n c e d by many omitted f a c t o r s . Some of the. more important of the omitted f a c t o r s were discussed i n Chapter I I and, from the arguments put f o r t h t h e r e , were f e l t t o be of minor importance. From the argu-ments of Chapter I I and t h i s part of Chapter I I I , t h e r e f o r e , the p r e d i c t i o n emerges t h a t a s u b s t a n t i a l p a r t of the d i f f e r -ences i n occupational earnings should be explained by the 2 v a r i a b l e s n and n (rep r e s e n t i n g schooling) although i t remains 2 to be seen whether or not the n term w i l l be important i n such work. Part B — The E m p i r i c a l S p e c i f i c a t i o n In Chapter I I and the f i r s t p a r t of t h i s Chapter, a t h e o r e t i c a l r e l a t i o n s h i p between sc h o o l i n g i n occupations and average earnings i n the occupations has been constructed and d i s c u s s e d . Without t h i s r e l a t i o n s h i p i t would have been p o s s i b l e t o have simply hypothesized a r e l a t i o n s h i p and t e s t e d i t by means of r e g r e s s i o n a n a l y s i s . However, having developed the t h e o r e t i c a l r e l a t i o n s h i p , i t i s nowclearer how the v a r i a b l e s should be entered i n a r e g r e s s i o n a n a l y s i s . In the r e g r e s s i o n a n a l y s i s i t i s obvious that some form of average earnings should be used as the dependent v a r i a b l e and some measure of education as the independent v a r i a b l e . However, there are some problems a s s o c i a t e d w i t h the e m p i r i c a l t e s t i n g that must be given c o n s i d e r a t i o n at t h i s time. The f o l l o w i n g are the problems which w i l l be given c o n s i d e r a t i o n 36 at t h i s time; 1) the discrepancy between the t h e o r e t i c a l n o t i o n of an occupation and the n o t i o n used i n the a v a i l a b l e data, 2) the discrepancy between the t h e o r e t i c a l measure of earnings (unweighted average earnings i n an occupation) and the measure a v a i l a b l e (weighted average e a r n i n g s ) , 3) the problems a s s o c i a t e d w i t h f i n d i n g an adequate v a r i a b l e to measure sc h o o l i n g from the data a v a i l a b l e . (1) In the t h e o r e t i c a l treatment we have t r e a t e d a l l occu-p a t i o n s s i m i l a r l y i n the sense that an i n d i v i d u a l would enter a chosen occupation and remain there f o r l i f e . In the ' r e a l w orld*, however, there are many occupational t r a n s f e r s t h a t occur over a person's l i f e . . The model would depend on occu-p a t i o n a l t r a n s f e r s i n a d i s e q u i l i b r i u m (short-run) s i t u a t i o n i n which t r a n s f e r s would be made t o e f f e c t e q u i l i b r i u m . I t i s occupational t r a n s f e r s of another type that create a prob-lem i n t h i s model. In many cases i n the * r e a l world* an occupation, so d e f i n e d , i s not an occupation i n the sense that i t i s a l i f e t i m e v o c a t i o n , but i s only a * stepping stone* to another occupation. An obvious example of t h i s i s the occu-p a t i o n d e f i n e d (according to the Occupational C l a s s i f i c a t i o n Manual, Census of Canada, 196l) as ' N u r s e s - i n - t r a i n i n g * . Obviously t h i s i s not an occupation i n the t h e o r e t i c a l sense i n which the term was used i n Chapter I I . I t i s an ed u c a t i o n a l -t r a i n i n g stage t o the occupation of 'Nursing*. There are many examples of occupations l i k e t h i s — although the t r a i n i n g stage i s not so obvious. Managers of var i o u s types, f o r example, o f t e n go through a t r a i n i n g program duri n g which 37 time they are c l a s s i f i e d as salesmen, accountants, c l e r k s , or any of a number of other occupations. Since occupations are not d e f i n e d i n the * r e a l w o r l d 8 i n the way i t was necessary 1 to d e f i n e them i n the t h e o r e t i c a l model, i t w i l l be necessary i n the e m p i r i c a l a n a l y s i s to take account of t h i s f a c t o r . Persons who f o l l o w e d such a c i r c u i t o u s route as the above one would tend to have more in f o r m a l education than would be p r e d i c t e d by the model and the incomes i n • f i n a l * occupations of t h i s type would tend to be higher.than otherwise expected. Although i t i s very d i f f i c u l t to measure t h i s f a c t o r , a proxy v a r i a b l e which would tend to measure such i n f l u e n c e s suggests i t s e l f . I t was f e l t by the author t h a t the age a t which persons t y p i c a l l y entered an occupation would r e v e a l any tendency f o r one occupation to r e l y on another f o r t r a i n i n g . " U n f o r t u n a t e l y , the only source from which such a measure could be drawn was the e x i s t i n g age d i s t r i b u t i o n s of occupations. I t was f e l t that a measure th a t would be r e l a -t i v e l y f r e e of demand i n f l u e n c e s and would s u i t t h i s purpose, was the age belowwhich 10$ of the persons employed i n an occupation f a l l — t h i s w i l l toe r e f e r r e d to as the 'lower d e c i l e age*. Mot a l l demand i n f l u e n c e s can be avoided In any such measure, but t h i s choice i s aimed at m i n i m i z i n g the *In order t o correspond to the t h e o r e t i c a l model, one would want to c l a s s i f y an i n d i v i d u a l as a manager as soon as h i s formal education was f i n i s h e d — t h i s of course i s impossible i n r e a l i t y . 38 1 i n f l u e n c e . (2) The average earnings concept u t i l i z e d i n the t h e o r e t i -c a l model i s what i s g e n e r a l l y c a l l e d an unweighted average earnings f i g u r e — that i s , the average i s not weighted by the numbers a t the var i o u s age groups i n the occupation. Published data always give (when averages are c a l c u l a t e d and published) the average earnings of persons a c t u a l l y engaged i n a s p e c i f i c occupation — which i s a weighted average earnings f i g u r e . I f data were a v a i l a b l e that gave average earnings by age and occupation an unweighted average of the type discussed above could be computed. U n f o r t u n a t e l y , how-ever, such data are not a v a i l a b l e . Consequently, the weighted average earnings of the occupations have been used i n the f o l l o w i n g a n a l y s i s . I t was p o s s i b l e , f o r t u n a t e l y , to conduct a rough t e s t . of the v a l i d i t y of using the weighted average as opposed to the unweighted average. From the po p u l a t i o n sample of the 1' Demand would i n f l u e n c e t h i s measure i n the f o l l o w i n g manner. Suppose that an occupation was dying out — f o r example, due to improved technology, very few persons would enter t h i s occupation and the members of t h i s occupation would tend to be o l d e r than i n most occupations — t h i s f o l l o w s from the theory of investment i n r e t r a i n i n g — the o l d e r persons i n the occupation would be the l e a s t l i k e l y to move out as they would not expect to be able to recapture the investment i n m o b i l i t y (and p o s s i b l y t r a i n i n g ) t h a t would be r e q u i r e d . A measure at the lower end of the age d i s t r i -b u t i o n , however, minimizes t h i s d i f f i c u l t y . 39 1961 Census of Canada data have been published g i v i n g average 1 earnings by age groups f o r s e l e c t e d occupations. In co-2 . . o r d i n a t i o n w i t h previous work done by the author a t e s t was 3 conducted on a sample of 20 occupations to f i n d i f any s i g n i f i c a n t d i f f e r e n c e e x i s t e d between the occupational weighted average earnings and an unweighted average computed 4 from the above mentioned data. A c o r r e l a t i o n between these two sets of earnings f i g u r e s y i e l d e d a c o r r e l a t i o n c o e f f i c i e n t of .998, r e v e a l i n g t h a t the weighted average approximated the unweighted average extremely w e l l . Moreover, i f the unweighted average i s regressed on the weighted average as f o l l o w s ; Yw = K + B*Yu where Yw = weighted average Canada. Dominion Bureau of S t a t i s t i c s . Census of Canada: 1961. P o p u l a t i o n Sample. #98-502, Table-!"©' — "T o t a l income from employment by s i z e f o r the non-farm male popula-t i o n 25-64 years of age, i n the current labour f o r c e , by occupation, schooling,and age, f o r Canada, f o r the year ended May 31, 1961." 2"Occupational Wage D i f f e r e n t i a l s and Investment i n Human C a p i t a l , " unpublished paper, 1967. ^These 20 occupations are chosen from the same occupa-t i o n a l c l a s s i f i c a t i o n as used l a t e r , but since data was given f o r o n l y s e l e c t e d occupations the choice could not be random. ^The unweighted average used does not correspond e x a c t l y w i t h the t h e o r e t i c a l model because r a t h e r than averaging the (average) earnings a t each age, only the average of the (average) earnings f o r , the age groups 25-34, 35-44, 45-54, and 55-64 could be found. For the above mentioned purposes i t was f e l t t hat t h i s was a reasonable approximation. 40 Yu - unweighted average K = r e g r e s s i o n constant the r e g r e s s i o n c o e f f i c i e n t B = 1.04. The weighted average earnings f i g u r e s are j u s t s l i g h t l y lower than the unweighted f i g u r e s t h a t would be the more d e s i r a b l e measure. The d i f f e r e n c e s between these two v a r i a b l e s are so small as to warrant the use of the weighted average. (3) The t h i r d problem t h a t i s encountered when an attempt i s made to devise a t e s t of the p r e v i o u s l y o u t l i n e d theory i s the l a c k of good data on investment i n education. The census provides i n f o r m a t i o n on school attendance — p u b l i s h i n g data on the highest grade attended according to the f o l l o w i n g breakdown; Elementary l e s s than grade 5» Elementary grade 5 and over, Secondary 1 - 2 years, Secondary 3 years, Secondary 4 - 5 years, Some U n i v e r s i t y , U n i v e r s i t y degree. For the purposes of a t e s t on investment i n education t h i s data i s i n s u f f i c i e n t i n the f o l l o w i n g r e s p e c t s ; ( i ) the data on scho o l i n g i n the census do not i n c l u d e s c h o o l i n g undertaken at v o c a t i o n a l schools, i n s t i t u t e s of technology, and other such i n s t i t u t i o n s . These i n s t i t u t i o n s c e r t a i n l y account f o r a great deal of investment i n education that i s missed i n the 1 a v a i l a b l e data. Tbe v a r i a b l e discussed i n s e c t i o n (1) above — One important instance i s that i n some provinces (and abroad), engineers are t r a i n e d . i n t e c h n o l o g i c a l i n s t i t u t e s and not i n u n i v e r s i t i e s . 41 what had been l a b e l l e d the 'lower d e c i l e age' v a r i a b l e — w i l l tend to catch t h i s investment i n education i n the r e g r e s s i o n a n a l y s i s . To some extent, t h e r e f o r e , t h i s e r r o r i n the data i s not as damaging as i t f i r s t sounds, ( i i ) the task of transforming the above-mentioned school achievement groupings i n t o a random v a r i a b l e i s somewhat d i f f i c u l t . To a s s i g n numerical values to the v a r i o u s groups i s a more or l e s s a r b i t r a r y d e c i s i o n t h a t i s based on the author's ( l i m i t e d ) knowledge of schooling i n Canada. The f o l l o w i n g weights have been chosen; Elementary, l e s s than grade 5 = 4 , Elementary grade 5 and over = 6, Secondary 1 - 2 years = 8, Secondary 3 years = 10, Secondary 4 - 5 years = 12, Some U n i v e r s i t y = 14, and U n i v e r s i t y degree = 16. ( i i i ) the t h i r d problem w i t h the a v a i l a b l e data i s c l o s e l y r e l a t e d to the. second. The values used above, although admittedly a r b i t r a r y are acceptable as f a r as they go. However, i n the groupings a v a i l a b l e from the census, there i s no d i f f e r e n t i a t i o n between v a r i o u s u n i v e r s i t y degrees. While the weight of 16 i s a p p r o p r i a t e f o r a bachelor degree l t I s not a t a l l a p p r o p r i a t e f o r higher degrees. I t i s not acceptable, more-over, simply t o upgrade the weighting used i n the l a s t category f o r a l l occupations. I t i s obvious t h a t some occupations c a l l f o r (almost as a matter of n e c e s s i t y ) more u n i v e r s i t y education than a bachelor's degree. For t h i s reason the author has made an attempt to vary the weighting attached to the highest educational grouping according to 42 the occupations i n v o l v e d . For example, i t i s w e l l known that an M. D. degree comprises more than 16 years of scho o l i n g — the education r e q u i r e d f o r t h i s degree v a r i e s 1 T (across Canada) between 18 and 19 years of s c h o o l i n g . i n the census data, persons are c l a s s i f i e d as doctors w i t h l e s s 2 than t h i s amount of education and f o r t h i s reason the author decided t h a t the best weighting f o r t h i s group would be 18 years of s c h o o l i n g . S i m i l a r c o r r e c t i o n s (not always the same 3 weighting) have been c a r r i e d out f o r other occupations. By t h i s technique, I t i s f e l t t hat a more accurate measure of scho o l i n g has been achieved. From the above d i s c u s s i o n , i t should be apparent t h a t the theory can be t e s t e d i n a r a t h e r .simple form. I n the next s e c t i o n r e g r e s s i o n and c o r r e l a t i o n a n a l y s i s w i l l be used to t e s t the data a g a i n s t the t h e o r e t i c a l model. Regres-sions have been undertaken w i t h weighted average earnings as the dependent v a r i a b l e and measures of investment i n education as the independent v a r i a b l e s . V a r i a b l e s have been incorporated u s i n g years of sc h o o l i n g , years of schooli n g squared, and a l s o p r e v i o u s l y discussed proxy v a r i a b l e •"•The same i s true of d e n t i s t s . 2 Some even who have not completed high s c h o o l . -"The f o l l o w i n g occupations have been given weightings higher than 16 f o r the highest educational grouping; P h y s i c i a n s and Surgeons, D e n t i s t s , P h a r m i c i s t s , V e t e r i n a r i a n s , Engineers, S c i e n t i s t s , Lawyers, and a few other s i m i l a r p r o f e s s i o n s . 43 which has been termed the 'lower d e c i l e age* v a r i a b l e . A separate r e g r e s s i o n was c a r r i e d out u s i n g a t h e o r e t i c a l l y -d e r i v e d v a r i a b l e .-- the average earnings that would be p r e d i c t e d by the t h e o r e t i c a l model, given the number of 1 years of schooling a s s o c i a t e d w i t h each occupation. The p r e c i s e form of the v a r i a b l e s , the manner i n which they were entered i n t o the r e g r e s s i o n s , and the r e s u l t s of the a n a l y s i s w i l l be presented i n the next chapter. The same parameters were, used i n the d e r i v a t i o n of the t h e o r e t i c a l v a r i a b l e as were used i n the diagram sketched i n the Pa r t A of t h i s Chapter — Figure I I I - l . CHAPTER IV EMPIRICAL TESTING In Chapter II of this paper, a theoretical framework in which to study occupational wage differentials was out-lined. In Chapter III, special problems associated with choosing values for the parameters of the model and with selecting data to conform to the theoretical variables i n the model were discussed. Having completed these sections of the work, i t i s now possible to turn to the empirical testing of the model. The estimated regression equations w i l l f i r s t be written down and then discussed in turn. 1) A n 988:0 + 582.On (22;8) R' 2 1719 2) 962.6 + 293.8n + 28.6n' (78.7) (7.5) .734 2 3) A n 811.5 + 515.6n + 164.9P (19.7) (14.5) R 2 .811 45 4) A = -681.0 + 276.2n+ 23.9n2 + 161.1P n (64.6) (6.2) (14.5) R 2 = .822 1 2 The following are the variables used in the above equations: A~ i s the weighted average earnings of an occupation, n calculated from the 1961 Census.3 n i s a variable representing the number of years of investment In education also calculated from the 1961 Census. P i s the proxy variable representing the "lower decile age" also from the 1961 Census.-* These four equations are regressions of the observed variables representing Investment in education on the weighted average earnings of the occupations calculated from the census. These regressions reveal that a large proportion of occupational earnings can be explained by these simple measures of investment in education. 1 2 R i s the coefficient of determination and the bracketed numbers below the regression coefficients refer to the standard error of the estimator. 2256 observations were employed in these equations. 3 •'Canada. Dominion Bureau of Statistics, Census of Canada: 1961. Labour Force. Series 3.3. "^Canada. Dominion Bureau of Statistics. Census of  Canada: 1961. Labour Force. Series 3.1. 5 I b i d . An i n t e r e s t i n g comparison can be made between these regressions and the regressions on the t h e o r e t i c a l variables presented at the end of Part A i n Chapter I I I . While the present empirical variables explain l e s s than d i d the 1 corresponding t h e o r e t i c a l variables, the additional amount explained by the Inclusion of the schooling i n I t s squared form i s very nearly the same i n the two cases — the • a d d i t i o n a l amount explained i s i n the order of 2% and the size of the c o e f f i c i e n t of the squared term Is about 10$ of the c o e f f i c i e n t of the l i n e a r term i n both instances. The degree of non-linearity i n the •real world 1 r e l a t i o n s h i p of education and earnings appears to bear out the t h e o r e t i c a l predictions very w e l l . In a l l cases, the regression c o e f f i c i e n t s show to be s t a t i s t i c a l l y s i g n i f i c a n t (with an P-test at the 5$ l e v e l ) . The fourth equation i s the best estimator of average earnings with over 80$ of the v a r i a t i o n i n occupational earnings being explained — note that the addition of the age of entry proxy variable adds considerably (9 percentage points) to the amount explained of the dependent vari a b l e . This The o r i g i n a l p r e d i c t i o n was that the long-run occupa-t i o n a l wage structure i n equilibrium would be explained by these v a r i a b l e s . However* the cross section data used here w i l l measure the state of the wage structure at a point i n time only — i.e. ?not l i k e l y an equilibrium s i t u a t i o n . A reasonably good B would be predicted nevertheless since the e q u i l i b r a t i n g forces would keep the wage structure i n the •neighbourhood of equilibrium*. 47 appears to be a very good r e s u l t i n terms of the model and i n terms of the data used f o r t e s t i n g . I t was f e l t by the author, t h a t a second way of t e s t i n g the theory t h a t was developed e a r l i e r i n t h i s paper (and a t the same time t e s t i n g the choice of parameters made) would be to attempt to p r e d i c t the earnings i n an occupation (given the number of years of schooling i n the occupation) from equation 9 of Chapter I I . various sets of parameters were s e l e c t e d and the t h e o r e t i c a l average earnings were c a l c u l a t e d f o r the observed years of schooli n g i n the occupations. These t h e o r e t i c a l average earnings were then regressed a g a i n s t the observed average earnings. The f o l l o w i n g f o u r r e g r e s s i o n equations t y p i f y the r e s u l t s . 1277.1 + .692T1 (.027) .729 -2236.8 + .6l4Ti+ 162.7P (.023) (14.5) ;819 1270.1 + .648T2 (.024) .736 -2205.3 + .575T« +161.OP " • (021 r (14.4) .824 , 5) = R 2 = 6) 17 = 7) V = R 2 = 8) S ; -R 2 = The f o l l o w i n g new symbols are introduced i n the above equa-48 t i o n s (the other v a r i a b l e s are as p r e v i o u s l y d e f i n e d i n connection w i t h equations 1 t o 4)s T- t h i s v a r i a b l e i s c a l c u l a t e d from equation 9 of Chapter I I given the number of years of sch o o l i n g i n an occupation and the f o l l o w i n g parameters? r e d i s c o u n t r a t e ) = 12$, L (the "labour f o r c e l i f e " as p r e v i o u s l y defined) = 53, An (the base wage l e v e l a l s o p r e v i o u s l y defined) 1 = $2000, D (the c u t - o f f p o i n t ) = L =• 15 y e a r s , and the slope was chosen as 35n» T ? i s a t h e o r e t i c a l v a r i a b l e c a l c u l a t e d as above w i t h parameters? r = 12$, L = 53, A 0 = #2400, D = n + 25, and n the slope was chosen as before as 35^9 The above f o u r equations are r e p r e s e n t a t i v e of the type of r e s u l t t h a t can be obtained i n t h i s manner 9 They are not to be considered the best r e s u l t s that could be obtained,, Time d i d not a l l o w f o r a study of many of the p o s s i b l e parameter choices ( s i n c e most of the parameters are of l i t t l e importance one would mainly wish to explore r e s u l t s f o r v a r i o u s discount r a t e s ) . The explanatory power of the above equations would be expected to be no g r e a t e r than i n equations 1 through 4 of t h i s chapter (and as good as i n the f i r s t f o u r equations only i f the model and the s p e c i f i c a t i o n of parameters are c o r r e c t ) . This f o l l o w s f o r two reasons? f i r s t l y , the reg r e s s i o n s here are u s i n g the same independent v a r i a b l e s as i n the f i r s t f o u r equations (schooling) only i n a transformed form, secondly, i t would not have been expected t h a t a tran s f o r m a t i o n of the s c h o o l i n g v a r i a b l e would 2 e x p l a i n more than n and n together could e x p l a i n — t h i s 49 f o l l o w s from the t h e o r e t i c a l r e g r e s s i o n s presented a t the 2 end of P a r t A I n Chapter I I I . i n which n and n explained •999 of the t o t a l v a r i a t i o n In the dependent v a r i a b l e . A comparison of the above four equations w i t h the f i r s t f o u r equations i n t h i s chapter confirms these expectations. As mentioned before, however, the above reg r e s s i o n s on t h e o r e t i c a l v a r i a b l e s are only to be considered represen-t a t i v e since the p o s s i b i l i t i e s open i n the choice of para-meters were not exhausted owing to the pa u c i t y of time a v a i l a b l e . Reconsideration of the choice of parameters since the r e g r e s s i o n work was completed suggests t h a t a lower value f o r the 'base wage l e v e l " , A n ( i n the neighbourhood of |1500) combined w i t h a lower discount r a t e and a l e s s steep slope (S n) would r e s u l t I n a t h e o r e t i c a l v a r i a b l e t h a t would be more n e a r l y i d e n t i c a l to the occupational earnings v a r i a b l e (An") o m i t t i n g random e r r o r s . That I s , the constant term i n an equation such as 5 would be c l o s e r to zero and the c o e f f i c i e n t of T c l o s e r to one. CHAPTER V CONCLUSION AND SUMMARY Starting with a simple concept of an occupation and a specific hypothesis about the behavior of individuals with respect to occupational choice, this paper has proceeded to build a theoretical model of the occupational earnings structure amenable to s t a t i s t i c a l testing. The underlying thesis of the paper i s that the differences i n occupational earnings arise because earnings as measured are gross of the returns to the investment i n education which characterizes an occupation. In building the theoretical model the author became aware of the problem of the paucity of data that would allow testing of a very general model. This was especially true with respect to data on 'on the job training*. To avoid this problem, i t was necessary to specify a relation between formal and informal education. Hence, both formal and informal investment in education could be measured by the one variable —- years of schooling. It would be desireable to have a model i n which formal and informal education were treated s t r i c t l y as two inputs in a general way, but the data made this an impossibility. There are two types of conclusions which emerge from this type of a study. The f i r s t type of conclusion i s that which follows from the most general outline of the model — 51 n o t a t a l l d e p e n d e n t o n t h e s p e c i f i c f o r m u l a t i o n c h o s e n f o r t e s t i n g b u t d e p e n d e n t o n t h e b e h a v i o r a l h y p o t h e s e s f r o m w h i c h t h e m o d e l i s b u i l t . T h e s e c o n d t y p e o f c o n c l u s i o n i s o f a m o r e s p e c i f i c n a t u r e w h i c h f o l l o w s f r o m t h e a s s u m p t i o n s made i n o r d e r t o c h a n g e t h e g e n e r a l m o d e l i n t o a t e s t a b l e f o r m . T h e r e a r e t w o I m p o r t a n t c o n c l u s i o n s w h i c h f a l l i n t o t h e f i r s t c a t e g o r y m e n t i o n e d a b o v e ; 1) T h e l o n g - r u n d i s t r i b u t i o n o f e a r n i n g s among o c c u p a t i o n s w i l l b e c l o s e l y t i e d t o t h e d i s t r i b u t i o n o f i n v e s t m e n t i n human c a p i t a l i n t h e e c o n o m y . T h e d i s t r i b u t i o n o f i n v e s t -m e n t i n human c a p i t a l w i l l , o f c o u r s e , b e r e l a t e d t o t h e demands f o r s k i l l i n t h e l a b o u r m a r k e t w h i c h i n t u r n a r e l i n k e d t o c h a n g e s i n t e c h n o l o g y i n t h e e c o n o m y . I t f o l l o w s , t h e r e f o r e , t h a t s e c u l a r c h a n g e s i n t h e o c c u p a t i o n a l e a r n i n g s s t r u c t u r e w i l l b e r e l a t e d t o t h e o c c u p a t i o n a l c h a n g e s t h a t o c c u r i n t h e e c o n o m y — t h a t I s , t h e a d d i t i o n o f new o c c u -p a t i o n s a t v a r i o u s s k i l l l e v e l s a n d t h e v a r i a t i o n i n t r a i n i n g a n d s k i l l r e q u i r e m e n t s o f t h e o c c u p a t i o n s t h a t a l r e a d y e x i s t i n t h e e c o n o m y . T h i s s u g g e s t s , f o r e x a m p l e , t h a t s e c u l a r c o m p a r i s o n s o f t h e " s k i l l e d v e r s u s u n s k i l l e d * ' t y p e a r e i n c o m p l e t e w i t h o u t some r e f e r e n c e t o t h e c h a n g e s i n t h e r e l a t i v e d e g r e e o f s k i l l t h a t h a v e t a k e n p l a c e . 2) G i v e n t h a t a s t u d y c o n s i d e r s t h e c h a n g e s i n t h e s k i l l d i s t r i b u t i o n i n t h e e c o n o m y w h e n c h a n g e s i n t h e e a r n i n g s s t r u c t u r e a r e b e i n g c o n s i d e r e d , i t i s a l s o n e c e s s a r y t o 52 consider changes in,the discount rate or the return to investment in education. Changes in the discount rate with no changes in the s k i l l composition would result in changes in the structure of earnings. Since this rate could change secularly (due to overall changes in the rates of return in the capital market or due to changes in the degree of imper-fection in the market for funds for Investment in human capital) and probably has, to discuss secular changes in the earnings structure without some reference to the discount rate would also be faulty. With respect to the second type of conclusion — derived from the special assumptions made about the parameters of the model and the relation between formal and informal education — there i s the result (discussed in previous chapters) that the relation between years of schooling in an occupation and the average earnings of that occupation w i l l be a non-linear one. The prediction made in this paper was that the relation would be only slightly non-linear. This was confirmed i n the empirical testing reported in Chapter IV. The other specific conclusion that derives from this paper i s that over 80$ of the variation In average annual earnings among occupations can be explained by simple variables related to the time and effort invested in training for that occupation. While this i s a large and significant part of the variation i n occupational earnings, there s t i l l remains some 18$ of the variation that i s not explained by 53 the variables used. The immediate response i s to turn to the variables assumed unimportant in the above work — risk, occupational preference, and a b i l i t y ~ for an explanation of the unexplained variation. A second response i s to search for better data that would give more consistent measures of education and also that would give data for more than one year (to allow an averaging of the earnings over a few years to eliminate some of the short-run disturbances to the occupational earnings structure due to demand incluences. A third response Is to attempt to find a good measure of informal training requirements for the various occupations used in the analysis. Future work should concentrate on these three lines of attack, to eventually allow for construction of a model that w i l l explain a greater amount of the variation i n occupational incomes. BIBLIOGRAPHY 55 BIBLIOGRAPHY BOOKS Becker, G. S. Human Capital. New York and London: National Bureau of Economic Research, 1964. Bowen, W. G. Economic Aspects of Education. Princeton, N. J.: Princeton University Press, 1964. Cartter, Allan. Theory of Wages and Employment. Homewood, 111.: Irwin, 1959. Daniere, A. Higher Education in the American Economy. New York and Toronto: Random House, 1964. Friedman, M. and Kuznets, S. Income from Independent Professional Practice; New York: National Bureau of Economic Research, 1954. Ginzberg, E l i et a l . Occupational Choice. An Approach to a General Theory. New York and London: Columbia University Press, 1951• Hicks, J. R. The Theory of Wages. New York and London; St. Martin's Press, 1963. Reynolds, L. G. and Taft, C. H. The Evolution of Wage Structure. New Haven: Yale University Press, 1956. Schultz, T. W. The Economic Value of Education. New York: Columbia University Press, 196*37" Thomas, L. G. The Occupational Structure and Education. Englewood~Cllffs, N. J. : Prentice-Hall, Inc., 1966. Vaizey, John. The Costs of Education. London: George Allen and Unwin Ltd., 1958. Welsbrod, B. A. External Benefits of Public Education. An Eoonomlo Analysis. Princeton, N. J. : Princeton University Press, 1964. Whittaker, E. A History of Economic Ideas. New York, London, Toronto: Longman's, Green and Co;, 1943; 56 ARTICLES AMD PERIODICALS Becker, G. S. "Investment i n Human C a p i t a l : A Theoret i c a l , A n a l y s i s , " J o u r n a l of P o l i t i c a l Economy. LXX (Supplement, October 1962), pp. 9-50. . "Underinvestment In College Education," American Economic Review, L, No. 2 (Papers and Proceedings, May I960), pp. 375-378. Carnoy, M. "Earnings and Schooling i n Mexico," Economic Development and C u l t u r a l Change. V o l . 15, No"!'"4 ( J u l y . 1967), pp. 408^09. Garbarino, J . "A Theory of I n t e r - I n d u s t r y Wage St r u c t u r e V a r i a t i o n , " Q u a r t e r l y J o u r n a l of Economics. LXIV (May 1950), pp. 282-305. Mincer, Jacob. "Investment i n Human C a p i t a l and Income D i s t r i b u t i o n , " J o u r n a l of P o l i t i c a l Economy. LXVI (August 1958), pp. 281-300. ., "On the Job T r a i n i n g : Costs, Returns, and Some I m p l i c a t i o n s , " J o u r n a l of P o l i t i c a l Economy. LXX (Supplement, October 1962), pp. 50-8-. M i l l e r , H. P. "Annual and L i f e t i m e Income i n R e l a t i o n to Education: 1939-59»w American Economic Review. L (December I960), pp. 962-987. Reder, M. W. "The Theory of Occupational Wage D i f f e r e n t i a l s , " American Economic Review. XLV (December 1955), PP» 833-852. . "Wage D i f f e r e n t i a l s : Theory and Measurement," Aspects of Labour Economics. A Conference of the U n i v e r s i t i e s N a t i o n a l Bureau Committee For Economic Research. P r i n c e t o n , N. J . : P r i n c e t o n U n i v e r s i t y P r e s s , 1962. Ross, A. M. and Goldner, W. ""Forces A f f e c t i n g the I n t e r -i n d u s t r y Wage S t r u c t u r e , " Q u a r t e r l y J o u r n a l of Economics. LXIV (May 1950), pp. 254-281. Rottenberg, S. "On Choice i n Labour Markets," I n d u s t r i a l and Labour R e l a t i o n s Review. IX (January 1956), pp. 183-199. "~ ~ — Schultz., T. W. " C a p i t a l Formation by Education," Journal of P o l i t i c a l Economy. LXVIII (December i960), pp. 571-58*4. 57 . "Investment i n Human C a p i t a l , " American Economic Review. L I (March 1961), pp. 1-17. Weisbrod, B. A. "Education and Investment i n Human C a p i t a l , " J o u rn a l of P o l i t i c a l Economy. LXX (Supplement, October I962)7~pp. 10T-123. Weiss, L. W. "Concentration and Labour Earnings," American Economic Review. LVI (March 1966), pp. 96-117." W i l k i n s o n , B. W. "Present Values of L i f e t i m e Earnings f o r D i f f e r e n t Occupations," Journal of P o l i t i c a l Economy, LXXIV (December 1966), pp. GOVERNMENT PUBLICATIONS Bertram, G. W. The C o n t r i b u t i o n of Education to Economic  Growth. Ottawa: Economic Council of Canada, 1966. Canada. Dominion Bureau of S t a t i s t i c s . Census of Canada: 1961. Labour Force. Volume I I I . Canada. Dominion Bureau of S t a t i s t i c s . Occupational  C l a s s i f i c a t i o n Manual. Census of Canada, 196T7 Canada. Dominion Bureau of S t a t i s t i c s . Census of Canada: 196l. P o p u l a t i o n Sample. *~ Wil k i n s o n , B. W. Studies In the Economics of Education. Ottawa: Economics and Research Branch, Department of Labour, 1965. 58 APPENDIX I TABLE I --- EABNINGS-EDUCATION RELATION Years of Investment j First Second in Education Earnings Differences Differences 0 $ 2000 725 1 2725 727 2 2 3^ 52 732 5 3 4184 742 • 10 4 4926 757 15 5 . 5683 780 23 6 6463 28 808 7 7271 846 . 38 8 8117 890 44 9 9007 947 57 10 9954 1013 66 11 IO967 1094 81 12 12061 1189 95 13 13250 1 The average Earnings (given schooling) are calculated using the following parameters; discount rate (r) = 12$; Retirement age -65 (L = 53); Earnings with no education (A ) = $2000; slope = 30n; and cut-off point = L - 15 years. 59 TABLE I I EARNINGS-EDUCATION RELATION WITH A CHANGED DISCOUNT RATE (CHANGED FROM TABLE I) Years of Investment ^ F i r s t Second i n Education Earnings D i f f e r e n c e s D i f f e r e n c e s 0 $ 2000 887 1 2887 895 8 2 3782 909 14 3 4691 933 24 4 5624 963 30 5 6587 1006 43 6 7593 105? 53 7 8652 1127 68 8 9779 1211 84 9 10990 101 • 1312 124 10 12302 1436 11 13738 1583 147 12 15321 I76O 177 13 17081 The parameters used i n c a l c u l a t i n g t h i s e arnings 1 path are the same ones used i n Table I w i t h the exception o f the discount r a t e which has been increased t o 14$. 60 TABLE I I I EARNINGS-EDUCATION RELATION WITH A CHANGED RETIREMENT AGE (CHANGED FROM TABLE I) Years of Investment 1 F i r s t Second i n Education Earnings D i f f e r e n c e s D i f f e r e n c e s 0 | 2000 . 803 1 2803 805 2 2 3608 810 5 3 4418 821 11 4 5239 835 14 5 6074 857 22 6 6931 28 885 36 7 7816 921 8 8737 45 966 54 9 9703 1020 10 IO723 66 1086 11 11809 1164 78 12 12973 1256 ; 92 13 14229 The parameters used i n c a l c u l a t i n g t h i s earnings' path are the same ones used i n Table I w i t h the exception of the retirement age which has been increased t o 70 years. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0104676/manifest

Comment

Related Items