I CHAPTER 5 The Process of Stratification Ratification systems may be characterized in various ways. Surely one i the most important has to do with the processes by which indi-lidds become located, or locate themselves, in positions in the ferarchy comprising the system. At one extreme we can imagine that it circumstances of a person's birth—including the person's sex and it perfectly predictable sequence of age levels through which he is destined to pass—suffice to assign him unequivocally to a ranted ntus in a hierarchical system. At the opposite extreme his prospective idaltstatus would be wholly problematic and contingent at the time afbirth. Such status would become entirely determinate only as adult-kod was reached, and solely as a consequence of his own actions lim freely—that is, in the absence of any constraint deriving from & circumstances of his birth or rearing. Such a pure achievement ■em is, of course, hypothetical, in much the same way that motion "torn friction is a purely hypothetical possibility in the physical •i Whenever the stratification system of any moderately large and *ptoi society is described, it is seen to involve both ascriptive and "wveraent principles. '»liberal democratic society we think of the more basic principle ""^ uiat of achievement. Some ascriptive features of the system * regarded as vestiges of an earlier epoch, to be extirpated as K possible. Public policy may emphasize measures designed to or to equalize opportunity—hopefully, to overcome asenp-- iuu cAcicise 01 ihe achievement principle. Wtion of how far a society may realistically aspire to go in ■°njs hotly debated, not only in the ideological arena but *t0^tTiC f°rUm aS Wel'' °Ur rontribucion> ^ anv' t0 tne debate r?e'y in submitting measurements and estimates of the 163 164 THE PROCESS OF STRATIFICATION strength of ascriptive forces and of the scope of opportunities in a large contemporary society. The problem of the relative importance of the two principles in a given system is ultimately a quantitative one. We have pushed our ingenuity to its limit in seeking to contrive relevant quantifications. The governing conceptual scheme in the analysis is quite a com. monplace one. We think of the individual's life cycle as a sequence in time that can be described, however partially and crudely, by j set of classificatory or quantitative measurements taken at successive stages. Ideally we should like to have under observation a cohort of births, following the individuals who make up the cohort as they pass through life. As a practical matter we resorted to retrospective que* tions put to a representative sample of several adjacent cohorts sou to ascertain those facts about their life histories that we assumed were both relevant to our problem and accessible by this means of obsem tion. Given this scheme, the questions we are continually raising in K: form or another are: how and to what degree do the circumstances of birth condition subsequent status? and, how does status attained (whether by ascription or achievement) at one stage of the life cwk affect the prospects for a subsequent stage? The questions are ueiths idle nor idiosyncratic ones. Current policy discussion and action come to a focus in a vaguely explicated notion of the "inheritanceof poverty." Thus a spokesman for the Social Security Administrate writes: It would be one thing if poverty hit at random and no one group wit singled out. It is another thing to realize that some seem destined to pow almost from birth—by their color or by the economic status or occupations their parents.1 Another officially sanctioned concept is that of the "dropout,' I person who fails to graduate from high school. Here the emj not so much on circumstances operative at birth but on the presunK effect of early achievement on subsequent opportunities. Thu> * "dropout" is seen as facing "a lifetime of uncertain emplovmtf" probable assignment to jobs of inferior status, reduced earningp°* and vulnerability to various forms of social pathology. 1 Mollie Orshansky, "Children of the Poor," Social Security BuUeW, *T 1963). 2 Forrest A. Bogan, "Employment of High School Graduates and £j£ in 1964," Special Labor Force Report, No. 54 (U. S. Bureau of Labor » June 1965), p. 643. A BASIC MODEL 165 In this study we do not have measurements on all the factors implicit in a full-blown conception of the "cycle of poverty" nor all those variables conceivably responding unfavorably to the achievement of "dropout" status. For practical reasons, as explained in Chapter 1, W{ were severely limited in the amount of information to be collected, for theoretical reasons—also spelled out more fully in Chapter 1—and in conformity with the tradition of studies in social mobility, we chose to emphasize occupation as a measure both of origin status and of status achievement. The present chapter is even more strictly limited to variables we think can be treated meaningfully as quantitative and therefore are suited to analysis by the regression technique described in Chapter 4. This limitation, however, is not merely an analytical convenience. We think of the selected quantitative variables as being sufficient to describe the major outlines of status changes in the life ode of a cohort. Thus a study of the relationships among these variables leads to a formulation of a basic model of the process of stratification. In this chapter we consider also certain extensions of this model. Subsequent chapters provide, in effect, a number of additional detailed extensions, although these are secured only by giving up some of the elegance and convenience of the particular analytical procedures employed here. t BASIC MODEL To begin with, we examine only five variables. For expository (onvenience, when it is necessary to resort to symbols, we shall desig-r.aie them by arbitrary letters but try to remind the reader from time lotimeof what the letters stand for. These variables are: V: Father's educational attainment X: Father's occupational status U; Respondent's educational attainment W: Status of respondent's first job Y: Status of respondent's occupation in 1962 kdtof the three occupational statuses is scaled by the index described "Chapter 4, ranging from 0 to 96. The two education variables are ^on the following arbitrary scale of values ("rungs" on the "edu-"■w&l ladder") corresponding to specified numbers of years of for-Pooling completed: 0: No school k Elementary, one to four years Elementary, five to seven years 166 THE PROCESS OF STRATIFICATION 3: 4: 5: 6: 7: 8: Elementary, eight years High school, one to three years High school, four years College, one to three years College, four years College, five years or more (i.e., one or more years of postgraduate study) Actually, this scoring system hardly differs from a simple linear transformation, or "coding," of the exact number of years of school completed. In retrospect, for reasons given in Chapter 4, we feel that the score implies too great a distance between intervals at the lower end of the scale; but the resultant distortion is minor in view of tfe very small proportions scored 0 or 1. A basic assumption in our interpretation of regression statistics-though not in their calculation as such—has to do with the causal« temporal ordering of these variables. In terms of the father's career m should naturally assume precedence of V (education) with respect t-X (occupation when his son was 16 years old). We are not concerna with the father's career, however, but only with his statuses that cow prised a configuration of background circumstances or origin condi tions for the cohorts of sons who were respondents in the OCG studi Hence we generally make no assumption as to the priority of V wit" respect to X; in effect, we assume the measurements on these variaHJ to be contemporaneous from the son's viewpoint. The respondent! education, U, is supposed to follow in time—and thus to be suscea tible to causal influence from—the two measures of father's sum Because we ascertained X as of respondent's age 16, it is true that sob respondents may have completed school before the age to which I pertains. Such cases were doubtlessly a small minority and in onhi minor proportion of them could the father (or other family head) h« changed status radically in the two or three years before the resp» dent reached 16. The next step in the sequence is more problematic. We assume th> W (first job status) follows U (education). The assumption confa* to the wording of the questionnaire (see Appendix B), which stij lated "the first full-time job you had after you left school years since the OCG study was designed we have been made aware a fact that should have been considered more carefully in the * Many students leave school more or less definitively, only w r perhaps to a different school, some years later, whereupon die) A BASIC MODEL 167 finish a degree program.3 The OCG questionnaire contained information relevant to this problem, namely the item on age at first job. Through an oversight no tabulations of this item were made for the present study. Tables prepared for another study4 using the OCG data, however, suggest that approximately one-eighth of the respondents report a combination of age at first job and education that would be very improbable unless (a) they violated instructions by reporting a part-time or school-vacation job as the first job, or (b) jiey did, in fact, interrupt their schooling to enter regular employment. (These "inconsistent" responses include men giving 19 as their age at first job and college graduation or more as their education; 17 or 18 with some college or more; 14, 15, or 16 with high-school graduation or more; and under 14 with some high school or more.) When ^ two variables are studied in combination with occupation of first job, a very clear effect is evident. Men with a given amount of education beginning their first jobs early held lower occupational statuses ihan those beginning at a normal or advanced age for the specified amount of education. Despite the strong probability that the U-W sequence is reversed jor an appreciable minority of respondents, we have hardly any alternative to the assumption made here. If the bulk of the men who interrupted schooling to take their first jobs were among those ultimately leaning relatively advanced education, then our variable W is downwardly biased, no doubt, as a measure of their occupational status immediately after they finally left school for good. In this sense, the correlations between U and W and between W and Y are probably attenuated. Thus, if we had really measured "job. after completing education" instead of "first job," the former would in all likelihood have loomed somewhat larger as a variable intervening between edu-ation and 1962 occupational status. We do not wish to argue that our respondents erred in their reports on first job. We are inclined to con-dude that their reports were realistic enough, and that it was our assumption about the meaning of the responses that proved to be fallible. The fundamental difficulty here is conceptual. If we insist on any "iilorrn sequence of the events involved in accomplishing the transi- ,'Bnict K Ecktend, College Dropouts Who Came Back," Harvard Educational S4|1964), 402-420. ^wverly Duncan, Family Factors and School Dropout: 1920-1960, U. S. Office ucation. Cooperative Research Project No. 2258, Ann Arbor: Univers. "*W'pn, 1965. of TION reality- Completion we doV1olence^^:niothelabor Parenial h°Tree crucial steps in this *<<^6 ^ m shon i to oi scl , °CCUT "Txed order. As won as we - are forced into A BASIC MODEL TABLE 5. 1. SIMPLE COBRELATIONS FOB FfVE STATUS VARIABLES 169 Variable Variable they within at r>° 6* data &>r aI\s Our assump on ^ q{ * C1*^^"^«Cii a ion -d subdue™ at0fVifraguniior«; 2'onal P^P* ^correct, we doubt E V to ^t 0n is not sncdy y: 1962 occ. Status W: First-job status U: Education X: Father's occ. status V: Father's education .596 .538 .405 .417 .438 .322 .332 .453 .516 *a ral te^Lo** ,ldDe limp ituting any itiiti; * ative o* "I al statu8 the ed by 5ubSlLine OCG questionnaire, d| waS entertained ;. dropPed f among others the reas ^ ^ mentioned reby-) rr.W transition ■ m ^ ththet/l20to24yearsol^ ' £ study, 20 to - T—r first jobs or ld wr Pr° ^en in * „r to take up «' , „ <** ^fiT^ir^ 8^/Q Unf rtunatel,. ^ong tbe finish thel in thlä Z inoendi* C). n( (h(ft n°e> 10 ^ tb£ Tse^ ^ AdST^ the inclusion oLtheJ bave 710 me°tl0 gitary sei , s resulted {or men aCC° Jecision . earlyde ^ith the old* results in only mjnor^ ined a, to 64 and to* to 64 1 a, oor jectio;JioSOtne tega „mrnat^ ^enc (P, XV ass umP >P ^To* data for «*» £ - n0 selioUS* l°?o^Ve" gavanet fthe ^ h«rdle *? y p,. '"ammaticai'y (W) - 00- . the very idealized assume ■actio" o£ *e mev,.hat >cie Q, ^ then, ^ order oi pr^,„nv » * rep^sefll. he stated diagr cessio rjt» be ovoPo^g this sequ ertce *e d „inc? that an eariy •■s meaning . , bul also«■ ^ eftects, 111 . „ variables uu ■ o i»-«fo "i*^ don matrix on which much of the subsequent analysis is based. In discussing causal interpretations of these correlations, we shall have to be dear about the distinction between two points of view. On the one band, the simple correlation—given our assumption as to direction of uusation—measures the gross magnitude of the effect of the ante-adent upon the consequent variable. Thus, if rYw = .541, we can say ilut an increment of one standard deviation in first job status pro-whether directly or indirectly) an increment of just over half oi one standard deviation in 1962 occupational status. From another point of view we are more concerned with net effects. If both first job ad 1962 status have a common antecedent cause—say, father's occupation—we may want to state what part of the effect of W on Y con-BG in a transmission of the prior influence of X. Or, thinking of X k the initial cause, we may focus on the extent to which its influence «V ii transmitted by way of its prior influence on W. We may, then, devote a few remarks to the pattern of gross effects Wore presenting the apparatus that yields estimates of net direct and indirect effects. Since we do not require a causal ordering of father's ion with respect to his occupation, we may be content simply to we that r.vr = .516 is somewhat lower than the corresponding correction. ru-— .596, observed for the respondents themselves. The Htrence suggests a heightening of the effect of education on occu-piional status between the fathers' and the sons' generations. Before ct»ing this interpretation, however, we must remember that the twirements of V and X do not pertain to some actual cohort of here designated "fathers." Each "father" is represented in the affect d in t-^r Lu„d: Structure* ihe< .he »"- •„ the se°.u able* ^%laine' first varial C\VK Ad1 eflt, as 195». P' ■Iss«1' Socio1 Mob»'1? and Class ""proportion to the number of his sons who were 20 to 64 years * "i March 1962. BK recorded status of the son himself is education (U). We *w is just slightly greater than rvx. Apparently both mea-the father represent factors that may influence the son's edu- ^'ms of gr°ss effects there is a clear ordering of influences on hus rwu > rwx > rwv. Education is most strongly corre- PATH COEFFICIENTS 171 THE PHOCESS OF STRA^ CATION 0\ Respo^f auses piitures 9tiatificatw- and then* 1962 ^'t;^l0^ laced with hrst job, followed by fatherS father's education. _^ noarently >s in"uen' Occupational status in stron ' u" Plication than by first)' first-jv,- between rvw and rV£f is rather occuP ced W oft (Y) aPj, job'. by education than, earlier discussion measure suggests we should not overemphasize the Men* -d ri Each, however, is substantially greater more impress^ than rrr. nan of the system of reJatrowfcp o« our basic model I of Ox- * as • „t such as pyW, carries a double subscript. The first subscript is the fiable at the head of the path, or the effect; the second is the causal jable. (This resembles the convention for regression coefficients, the first subscript refers to the "dependent" variable, the second {j,e "independent" variable.) "finally- we see lines with no source indicated carrying arrows to ^ch of the effect variables. These represent the residual paths, stand-f0r all other influences on the variable in question, including not recognized or measured, errors of measurement, and de-of the true relationships from additivity and linearity, prop-its that are assumed throughout the analysis (as explained in the etion on regression in Chapter 4). An important feature of this kind of causal scheme is that variables cognized as effects of certain antecedent factors may, in turn, serve as auses for subsequent variables. For example, U is caused by V and X, jutitin turn influences W and Y. The algebraic representation of the nheme is a system of equations, rather than the single equation more often employed in multiple regression analysis. This feature permits iBexible conceptualization of the modus operandi of the causal net-wrt. Note that Y is shown here as being influenced directly by W, U, «1X, but not by V (an assumption that will be justified shortly). But isdoesnot imply ihat V has no influence on Y. V affects U, which ta affect Y both directly and indirectly (via W). Moreover, V is corre-htdwith X, and thus shares in the gross effect of X on Y, which is wtlv direct and partly indirect. Hence the gross effect of V on Y, (miously described in terms of the correlation rYVl is here interpreted • being entirely indirect, in consequence of f"s effect on intervening Its and its correlation with another cause of Y. coefficients, the estimation we must become iamiliar with the <."■• ^ (, ing this kind of diagram. The link bet* Thjj js [0 a curved line mth an arrowhead at b°tn be paths of inflw" horn the other lines, which are taken running ft, the case of V and X we may s^ped 3 . , for ,he respa '->^r. But if ^dt^mlai0[ lhe<*^b it to serses i {ormer to the MH COEFFICIENTS Whether a path diagram, or the causal scheme it represents, is *S«ate depends on both theoretical and empirical considerations, 'minimum, before constructing the diagram we must know, or be to assume, a causal ordering of the observed variables (hence ) discussion of this matter earlier in this chapter). This ■ation is external or a prion with respect to the data, which \ describe associations or correlations. Moreover, the causal ■ must be complete, in the sense that all causes are accounted P> as in most problems involving analysis of observational achieve a formal completeness of the scheme by representing , |o IrA ^""'eo r c^l ^ the rerr inc u„— eQ. een 1 oDlei« 41' (iablt 1 -causes as a residual factor, presumed to be uncorrelated have »ot correlauo» 0[ the P ^ ^ p I remaining factors lying behind the variable in question. If explanation there ^ The straight W ltlflue represent direct {or o^^mbo^ THE PROCESS OF STRATIFICATION 172 THE PROCESS ur u, any factor is known or presumed to operate in some other way it muj be represented in the diagram in accordance v/hh its causal role, eve» though it is not measured. Sometimes it is possible to deduce interest ing implications from the inclusion of such a variable and to seem, useful estimates of certain paths in the absence of measurements ^ it, but this is not always so. A partial exception to the rule that jfl causes must be explicitly represented in the diagram is the uj. measured variable that can be assumed to operate strictly as an intp vening variable. Its inclusion would enrich our understanding 0f causal system without invalidating the causal scheme that omiti Sociologists have only recently begun to appreciate how stringent ^ the logical requirements that must be met if discussion of cauoi processes is to go beyond mere impressionism and vague verbi formulations.8 We are a long way from being able to make caual inferences with confidence, and schemes of the kind presented ha had best be regarded as crude first approximations to adequate cam* models. On the empirical side, a minimum test of the adequacy of a cans diagram is whether it satisfactorily accounts for the observed con* tions among the measured variables. In making such a test we era* the fundamental theorem in path analysis, which shows how toobta the correlation between any two variables in the system, given i path coefficients and correlations entered on the diagram.7 Witldj stating this theorem in general form we may illustrate its appJiaa here. For example, *rx = pyx + pyvrvx + Pywtwx; and ?wx = pwx + pwvrvx-We make use of each path leading to a given variable (such as first example) and the correlations of each of its causes with ... variables in the system. The latter correlations, in turn, mat alyzed; for example, rwx, -which appeared as such in the firsttj^H is broken down into two parts in the second. A complete e.xpa"l along these lines is required to trace out all the indirect C" between variables; thus, rYX — pyx -f PyvPux + pvupcvrvx + pvwpwx + Pw?< pYWp\VUpUVrvx- 6 H. M. Blalock, Jr., Causal Inferences in Nonexperimenlal Ro^ Hill: Univer. of North Carolina Press, 1964. TSewall Wright, "Path Coefficients and Path Regressions."*' (1960), 189-202; Otis Dudley Duncan, "Path Analysis," America* Sociology, 72(1966), 1-16. PATH COEFFICIENTS 173 flow, if the path coefficients are properly estimated, and if there is inconsistency in the diagram, the correlations calculated by a formula like 'he foregoing must equal the observed correlations. Let us winpare the values computed from such a formula with the corresponding observed correlations: fwv — pwxrxr + pwvrvv = (.224)(.516) -f (.440)(.453) = .116 -f- .199 = .315 which compares with the observed value of .332; and I fyy = pYvH'v + pYXrXV + pYW?WV - (.394)(.453) + (.115)(,516) + (.281)(.315) = .326 using here the calculated rather than the observed value of rwv), resembles the actual value, .322. Other such comparisons—for ryI, for example—reveal, at most, trivial discrepancies (no larger than 001). W'e arrive, by this roundabout journey, at the problem of getting tonerical values for the path coefficients in the first place. This in-ralves using equations of the foregoing type inversely. We have illus-•jited how to obtain correlations if the path coefficients are known, hit in the typical empirical problem we know the correlations (or at lost some of them) and have to estimate the paths. For a diagram of lit type of Figure 5.1 the solution involves equations of the same form ■ those of linear multiple regression, except that we work with a wursive system of regression equations8 rather than a single regres-uxi equation. Table 5,2 records the results of the regression calculations. It can be urn that some alternative combinations of independent variables studied. It turned out that the net regressions of both W and Y • I'were so small as to be negligible. Hence V could be disregarded • i direct influence on these variables without loss of information, net regression of Y on X was likewise small but, as it appears, not ""fly negligible. Curiously, this net regression is of the same order u»nitude as the proportion of occupational inheritance in this ion—about 10 per cent, as discussed in Chapter 4. We might * that the direct effect of father's occupation on the occupa-aUis of a mature man consists of this modest amount of strict nal inheritance. The remainder of the effect of X on Y is 'nasmuch as X has previously influenced U and W, the son's " and the occupational level at which he got his start. For "wed in Chapter 3 we do not assume that the full impact of ^ "P- pp. 54ff. PATH COEFFICIENTS 175 lTl5lCATI°N a COEFFICIENTS] 174 1962 »0W to take «P the taken i , estimate* efficients f°* HgmU is registered, in tit occupation mind we may tun. father ■ soi»e latg cables 3f the e stent vetlient£ail t°a' the va^tlon in the effect rmination; if stei» -ef&Cieoft0V ol the"three independ. ölrdation o SociologU»* **** - rW.r^:i^; sidual, undei «4 .nPd from the c A«\*obt « ^ c0ir' re*idU uared t* study^^ sUCh a soaetyfrofli birth by th cllri words oi affiuence*' "destined to ^ ^ by educa In sU' ü°n ___,erty a lmostfrom (in the no, "? "I too1 alter ilUea' thin1 '?i:^ö>»"'irr»io«p-wuge<' of an e»! though' an eX! 0 a causal interpretation is almost certainly wrong. The fact is that ^ size of the residual (or, if one prefers, the proportion of variation .^plained") is no guide whatever to the validity of a causal interpre-gtion. The best-known cases of "spurious correlation"—a correlation leading to an egregiously wrong interpretation—are those in which ^coefficient of determination is quite high. The relevant question about the residual is not really its size at all, lut whether the unobserved factors it stands for are properly repre-jtnted as being uncorrelated with the measured antecedent variables. tfe shall entertain subsequently some conjectures about unmeasured variables that clearly are not uncorrelated with the causes depicted in figure 5.1- It turns out that these require us to acknowledge certain ble modifications of the diagram, whereas other features of it 'amain more or less intact. A delicate question in this regard is that jlthe burden of proof. It is all too easy to make a formidable list of ^measured variables that someone has alleged to be crucial to the process under study. But the mere existence of such variables is al-iady acknowledged by the very presence of the residual. It would Km to be part of the task of the critic to show, if only hypothetically, M specifically, how the modification of the causal scheme to include inew variable would disrupt or alter the relationships in the original faram. His argument to this effect could then be examined for plausibility and his evidence, if any, studied in terms of the empirical possibilities it suggests. Our supposition is that the scheme in Figure 5.1 is most easily Bbject to modification by introducing additional measures of the «nt kind as those used here. If indexes relating to socioeconomic idground other than V and X are inserted we will almost certainly oimate differently the direct effects of these particular variables. If Kupational statuses of the respondent intervening between W and known we should have to modify more or less radically the •^ihand portion of the diagram, as will be shown in the next sec-ton. Vet we should argue that such modifications may amount to an *ichment or extension of the basic model rather than an invalida-of it. The same may be said of other variables that function as ■tnening causes. In theory, it should be possible to specify these '■orae detail, and a major part of the research worker's task is *5*dy defined as an attempt at such specification. In the course of *ork, to be sure, there is always the possibility of a discovery Id require a fundamental reformulation, making the present solete. Discarding the model would be a cost gladly paid for °f such a discovery. *uUiP! or nearly so. cortex01 whereas 176 THE PROCESS OF STRATIFICATION Postponing the confrontation with an altered model, the one at hand is not lacking in interest. An instructive exercise is to compa^ the magnitudes of gross and net relationships. Here we make use of the fact that the correlation coefficient and the path coefficient have the same dimensionality. The correlation rYX — -405 (Table 5.1) means that a unit change (one standard deviation) in X produces a changf of 0.4 unit in Y, in gross terms. The path coefficient, pYx=.\li (Figure 5.1), tells us that about one-fourth of this gross effect is a result of the direct influence of X on Y. (We speculated above on the role of occupational inheritance in this connection.) The remainder (.405.. .115 = .29) is indirect, via U and W. The sum of all indirect effects, therefore, is given by the difference between the simple correlation and the path coefficient connecting two variables. We note that lit indirect effects on Y are generally substantial, relative to the direct Even the variable temporally closest (we assume) to Y has "indirta effects"—actually, common antecedent causes—nearly as large as ri direct, Thus ryw = .541 and pYW = so that the aggregate a "indirect effects" is .26, which in this case are common determinant of Y and W that spuriously inflate the correlation between them. To ascertain the indirect effects along a given chain of causatice we must multiply the path coefficients along the chain. The procedim is to locate on the diagram the dependent variable of interest, arc then trace back along the paths linking it to its immediate and remit causes. In such a tracing we may reverse direction once but « once, following the rule "first back, then forward." Any bidirectioni correlation may be traced in either direction. If the diagram conns more than one such correlation, however, only one may be used i a given compound path. In tracing the indirect connections» variable may be intersected more than once in one compound paii Having traced all such possible compound paths, we obtain & entirety of indirect effects as their sum. Let us consider the example of effects of education on first job, t on W. The gross or total effect is rwv = .538. The direct piii» pwu = '440. There are two indirect connections or compound pi* from W back to X then forward to U; and from W back to A',* back to V, and then forward to U. Hence we have: *wv — Pwv + Pwxpux + PwxrxvPvv -v-"* (poss) (direct) (indirect) nUffl"k m = .440 + (.^(.279) + (.224X.M6H.Si») _ .440 + .062 + .036 — .440 + .098. AGE CROUPS 177 In this case all the indirect effect of U on W derives from the fact that ^(h U and W have X (plus V) as a common cause. In other instances, ^en more than one common cause is involved and these causes are foemselves interrelated, the complexity is too great to permit a suc-jjfict verbal summary. A final stipulation about the scheme had best be stated, though it is implicit in all the previous discussion. The form of the model itself, bat most particularly the numerical estimates accompanying it, are submitted as valid only for the population under study. No claim is made that an equally cogent account of the process of stratification y. another society could be rendered in terms of this scheme. For other populations, or even for subpopulations within the United States, die magnitudes would almost certainly be different, although we have jome basis for supposing them to have been fairly constant over the to few decades in this country. The technique of path analysis is not i method for discovering causal laws but a procedure for giving a quantitative interpretation to the manifestations of a known or issumed causal system as it operates in a particular population. When •it same interpretive structure is appropriate for two or more popu-iitions there is something to be learned by comparing their respective Mth coefficients and correlation patterns. We have not yet reached the suge at which such comparative study of stratification systems is feasible. iCt GROUPS: THE LIFE CYCLE OF A SYNTHETIC COHORT For simplicity, the preceding analysis has ignored differences among ipgroups. Our present task is to venture some interpretation of such iilerences. The raw material for the analysis is presented in Table 5.3 form of simple correlations between pairs of the five status variables under study. For the reasons mentioned in Chapter 3, this is is confined to men with nonfarm background, must consider immediately what kinds of inferences or interpre-wions are allowed by comparisons among the four cohorts. Three of variables are specified as of a more or less uniform stage of the ■"pendent's life cycle: father's occupation (X), respondent's educa-and first job (W). Father's education (V), on the other hand, "»presumably determinate in the father's youth; the time interval ^ftn V and any of the former variables would be determined in Vpart by father's age at respondent's birth. This interval is vari->n length. We might, however, assume that the time interval from "X. though highly variable within each cohort of respondents, has ^ w average and dispersion from one cohort to another. If lather's Ih°n is taken as a fixed status once the father has completed his