This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research

Volume Title: Education as an Industry

Volume Author/Editor: Joseph T. Froomkin, Dean T. Jamison and Roy Radner, eds.

Volume Publisher: NBER

Volume ISBN: 0-88410-476-1

Volume URL: http://www.nber.org/books/jami76-1

Publication Date: 1976

Chapter Title: Concepts of Economic Efficiency and Educational Production

Chapter Author: Henry M. Levin, Dean T. Jamison, Roy Radner

Chapter URL: http://www.nber.org/chapters/c4491

Chapter pages in book: (p. 149 - 198)

4HENRY M. Concepts of

LEVIN Economic EfficiencyStanford University

and EducationalProduction

L INTRODUCTIONThe education industry has two characteristics which make it a primecandidate for a study of efficiency: size and rising costs. Educationrepresents one of the largest industries in the nation with estimated totaldirect expenditures of about $108 billion in 1974—75, representing abouteight per cent of the gross national product (Bell 1974). During the sameperiod, estimated employment was over 3 million for student enroll-ments of about 59 million. Beyond its sheer magnitude, the educationindustry has experienced very steep increases in costs. For example,between 1961—62 and 1971—72 the current expenditure per pupil in realterms (1971—72 dollars) rose from $569 to $934 at the elementary-secondary level and from $1,676 to $2,367 at the college level (U.S.Department of Health, Education and Welfare 1972: 3). These representincreases in real costs over the decade of about 64 per cent and 41 percent respectively.

• Of course, one possible explanation for rising costs might be qualita-tive increases in educational output. Yet, there seems to be no evidenceof such a trend. Rather there appears to be increasing concern with thequality of schools as reflected in public opinion surveys (Gallup 1970),educational critiques (Silberman 1970; Greer 1972; Carnoy 1972), and

149

voter support. For example, in 1962 voters approved about 80 per centof school bond issues, while in 1969 the proportion of approvals haddeclined to only 44 per cent (Gallup 1970: p. 100).

The substantial increase in resource costs, coupled with growing dis-satisfaction with the schools, has surely raised important questions aboutthe performance of the educational sector. In response, economists haveincreasingly devoted their attentions to studying the internal efficiencyof the educational sector, and their early efforts suggest a natural bifur-cation into camps of optimism and pessimism.

The pessimists have suggested that the very nature of such activitiesas education must inevitably lead to higher real costs per unit of output.William Baumol has systematized this analysis by viewing education as a"technologically unprogressive" activity, where the latter term is appliedto those activities which cannot benefit from innovation, capital accumu-lation and economies of large scale (Baumol 1967). According to Baumol,the labor intensive nature of education is an end in itself, so that thepossibilities for capital-labor substitution are limited severely. Assumingthat money wages rise according to increases in labor productivity withinthe technologically progressive industries, these increases are passedalong to the nonprogressive sectors such as education in the form ofhigher real costs per unit of output. Baumol concludes that the real costsof even a constant level of output for nonprogressive industries such aseducation will increase indefinitely and without limit. Note that theBaumol model does not see costs rising because of inefficiency; ratherthey are rising because of inevitability. Accordingly, his palliative seemsto be: "Don't send advice, send

Nevertheless, since economists have a greater predilection for provid-ing advice than for fund raising, most economists who have concernedthemselves with the educational sector have tactitly assumed that pro-ductivity in education can be improved. They are the optimists, sincethey see their own approaches as ones which will lead to greater ef-ficiency in educational spending. While both Adam Smith and MiltonFriedman belong in this school, it is primarily the economists who haveattempted to estimate educational production functions that are includedin the present analysis.' Their studies have generally been addressed toestimating the pioduction set for education with the hope that themarginal products obtained can be compared with prices to obtain aleast-cost solution to eduèational production (Bowles 1970; Katzman1971; Per1 1973; Winkler 1972; Thomas 1971; Burkhead et al. 1967;Brown and 'Saks 1975; Kiesling 1967; Hanushek 1968, 1972; Levin1970a, 1970b; Michelson 1970; Murnane 1974). The tacit assumptionunderlying such investigations is that schools are allocatively inefficient,and that these studies can lead to the information necessary for better

resource allocatiobstacles to estiisome detailson 1970; Levinhave beenLevin, and StotLevin 1970b;et aI. 1972).

Yet, in my opiof these approac'The purpose ofwith regard to teducation. That iliterature is toeffectiveness of rwe examine thesolving it before

Educational Prodi'The general prodtional studies is i

(1) A11= g (FIt), S

The i subscript rc(t) refers to an ir

A = a vectorF,111=a vector'

lative to I.

Sj()) = a vectortime t;

P U) = a vector 0= a vector

the ith sti= a vector ol

We might view (1output in time pfrom somepoint in time forinfluenced not onas well. It is reaS(

150 Economic Efficiency and Educational Production ' 151 IHenry M.

ibout 80 per centof approvals had

vith growing dis-t questions abouteconomists have

efficiencyt a natural bifur-

of such activitiesunit of output.education as a

term is appliedcapital accumu-

to Baumol,tself, so that the

Assumingoductivity within

are passedin the form of

that the real coststidustries such asL Note that the

ratherpalliative seems

ection for provid-have concerned

that pro-optimists, since

to greater ef-and Milton

omists who have.1that are included

addressed toe hope that therices to obtain a

1970; Katzmanead et al. 1967;

1972; Levinassumptioninefficient,

essary for better

In

resource allocation in the educational sector. Some of the formidableobstacles to estimating these relationships have also been explored insome detail (Bowles 1970; Bowles and Levin 1968a and 1968b; Michel-son 1970; Levin 1970a and 1974). Moreover the findings of these studieshave been discussed in a public policy context (Guthrie, Kleindorfer,Levin, and Stout 1971; Kiesling. 1971; Hanushek 1972; Bowles 1970;Levin 1970b; Hanushek and Kain 1972; Cain and Watts 1970; and Jenckset al. 1972).

Yet, in my opinion, scant attention has been devoted to the relevanceof these approaches to questions of efficiency in educational production.The purpose of this paper is to explore several concepts of efficiencywith regard to their role in enabling us to evaluate the production ofeducation. That is, if the purpose of the educational production-functionliterature is to derive prescriptive decision rules for improving theeffectiveness of resource use in the educational sector, it is crucial thatwe examine the nature of the problem and the relevance of our tools forsolving it before applying them to the evaluative task.

Educational Production Functions.The general production function that appears common to most educa-tional studies is reflected in (1).

(1) A = g (F t>, S (I)' I It), 0 (ii, I )

The i subscript refers to the ith student; the t subscript in parentheses(t) refers to an input that is cumulative to time period t.

I

A it = a vector of educational outcomes for the ith student at time t;= a vector of individual and family background characteristics cumu-

lative to time t;S = a vector of school inputs relevant to the ith student cumulative to

time t;= a vector of peer or fellow-student characteristics cumulative to time t;= a vector of other external influences (community, etc.) relevant to

the ith student cumulative to time t; andlit = a vector of initial or innate endowments of the ith student at the time t.

We might view (1) as a capital-embodiment approach to education, sinceoutput in time period is mainly a function of inputs cumulative to tfrom some earlier time.2 That is, clearly the educational outcomes at apoint in time for an individual, a school, or a larger social collectivity areinfluenced not only by present observed circumstances but by past onesas well. It is reasonable to believe that from the time a child is conceived

151 Henry M. Levin

various environmental characteristics combine with his innate charac- specification biateristics to mold his behavior. In the context of (1) the educational number ofoutcome for the individual is determined by the cumulative amounts of the observed r"capital" embodied in him by his family, his school, his community, and student achieve:his peers as well as by his innate traits. The greater the amount and the the teacher's V(quality of investment from each of these sources, the higher will be the While teacheoutput. More specifically, the family provides a material, intellectual, achievement ornutritional, and emotional set of inputs which are embodied'in the child; rarely shown suand the schools, peer groups, media, and so on also provide flows of certification stalinputs over time which increase capital embodiment.3 show no appare

The operational formulation of (1) is subject to large errors in the studies have foequations and in the variables (Bowles 1970; Michelson 1970; Levin pupil performar1970a). Most studies have used only a single measure of output, scoreson standardized achievement tests, despite the fact that schools areexpected to produce a variety of attitudes and skills. Specification of theinput structure has been based in part upon what data are available, inpart upon the researcher's hunch, and only to a very small degree on II. SOME CONCtheories of development and learning.4

Family and background inputs generally include such measures of. Technical andsocial class as parental education, fatner s occupation, ramny possessions,

1 . . E ucationai Proifamily structure, race ana sex or stuaents. Scnooi cnaracteristrcs naveincluded such facilities as libraries, laboratories, age and nature of build- It is useful at tiings; personnel inputs (with special emphasis on class size) and such allocative. Techiteacher traits as experience, education, attitudes, and verbal aptitudes. such a way thatPeer influences include the social class and racial characteristics of fellow alternativestudents, and other influences include community variables and certain ficiency, or pricresidual variables. The difficulty of obtaining valid measures of innate that, given relatcharacteristics has meant that such variables have been omitted from the is obtained.econometric models. These omissions have probably resulted in an budgetary constupward bias in the estimated coefficients of family and background output (Farrellvariables.5 One of the m

In all of these studies, student background measures appear to be educational prodhighly related to educational achievement.6 Among school characteris- that is, that thetics, some facilities measures appear to show significant statistical rela- have selected.7tionships, but the most consistent relations are found between teacher production isoqivariables and academic achievement. Specifically, virtually all of the thought of as sdstudies that have measured teacher verbal aptitudes have found that constant educativariable to be significantly related to student achievement (Coleman tion frontier and1966; Hanushek 1972; Bowles and Levin 1968; Michelson 1970; Levin are to the north1970a). Indeed, the consistency of this finding is buttressed by the fact not technicallythat separate studies have been carried out at several grade levels and require higherfor samples of black, white, and Mexican-American students (Hanushek reasons for such1972). Of course, it is important to point out that in the light of inefficient schoo

152 Economic Efficiency and Educational Production 153 Henry M

innate charac-) the educationaldative amounts of

community, ande amount and the

will be theintellectual,

)died in the child;provide flows of

errors in thelson 1970; Levinof output, scoresthat schools are

pecification of theare available, insmall degree on

uch measures ofpossessions,

aracteristics haved nature of build-s size) and suchverbal aptitudes.

'cteristics of fellowand certain

of innateomitted from the

•y resulted in anand background

1res appear to becharacteris-

statistical rela-between teacher

rtually all of thehave found that

(Coleman1970; Levin

(essed by the factgrade levels and

jidents (Hanushekin the light of

specification biases, the teacher's verbal score may be a proxy for a largenumber of possible cognitive and personal traits of the teacher; so that

• the observed relationship between the teacher's verbal pattern andstudent achievement may derive from these associated traits rather thanthe teacher's verbal proficiencies per se (Griliches, 1957).

While teacher experience has also been found to be related to studentachievement on a fairly regular basis, the teacher's degree level hasrarely shown such an effect. Moreover, variables reflecting the teacher'scertification status on the basis of existing state requirements seem toshow no apparent association with student achievement. Finally, moststudies have found no statistical effect of differences in class-size onpupil performance.

II. SOME CONCEPTS OF EFFICIENCY

Technical and Allocative Efficiency inEducational Production

It is useful at the outset to define two types of efficiency, technical andallocative. Technical efficiency refers to organizing available resources insuch a way that the maximum feasible output is produced. That is, noalternative organization would yield a larger output. Allocative ef-ficiency, or price efficiency, refers to use of the budget in such a waythat, given relative prices, the most productive combination of resourcesis obtained. That is, no alternative combination of resources, given thebudgetary constraint, would enable the organization to produce a higheroutput (Farrell 1957; Leibenstein 1966).

One of the major assumptions that tacitly underlies the estimation ofeducational production functions is that schools are technically efficient,that is, that they are maximizing output given the input mix that theyhave selected.7 In Figure 1 the production frontier is depicted by theproduction isoquant AoAo', where the individual observations can bethought of as schools using various combinations of S1 and S2 to produceconstant educational output Ao. Schools a, b, and c are on the produc-tion frontier and are thus technically efficient. All of the other schoolsare to the northeast of the production frontier suggesting that they arenot technically efficient. That is, all schools other than a, b, and crequire higher levels of factor inputs to obtain the output Ao. Thereasons for such inefficiencies will be suggested below, but if technicallyinefficient schools are prevalent, then statistical estimates of the educa-

153 Henry M. Levin

efficiency aspIsomehow thewelfare. Sincecorrespondingderive a struciual welfare anLindblomway of commi.schools, it issimply to the(Williams

Figure 2 iii'sents a producand a2. andsuch that!1 rethat given thehighest level

Now supporepresented boutputs since ithe communilchoice of outpiyield a higheisubfrontier chfrontier excepinefficiently t}produce with

Efficiency and

Thus, weapplied to anallocative efficthat we shallgiven technicaoutputs for allintroduced if tsize variation cboth economiearea has beenthe enormousstructure andRiew 1966; Cc

Input S1

Ao'

..

.S .

S .•S

Ac,

0

Production Frontier for SchoolsFIGURE 1

tional production will not be frontier ones even in the absence of errorsin the equations or variables.

If we assume that Z'Z is the relative price or iso-cost line facing allschools for the two factors, only school b is both technically efficient andprice or allocatively efficient. Firms a and c are technically efficient, butthey are clearly allocatively inefficient since they require a higherbudget to achieve output Ao' than would be required if they were atpoint b. Indeed, the underlying goal of the educational productionfunction studies is that of determining where point b lies on the produc-tion function.

Social Welfare Efficiency inEducational Production

Figure 1 assumes a single-valued output for the educational firm that issignified byA. Yet, schools are multi-product firms, soA =(a1, a2, a3a By assuming a value for A, the analysis overlooks another important

154 Economic Efficiency and Educational Production 155 Henry

IflPUt

of errors

ost line facing allDaily efficient andlally efficient, butrequire a higherIi if they were at

productionon the produc-

firm that isa2, a3,...,

tnother important

efficiency aspect which we might call overall social efficiency. That is,• somehow the A obtained for any given budget must maximize social

welfare. Since the various outputs comprising A probably have differentcorresponding values for different individuals, it may be impossible toderive a structure of outputs for any given input that maximizes individ-ual welftire and total social welfare (Arrow 1951; Little 1950; Dahl andLindblom 1953). Perhaps even more important, without having someway of communicating true "social" preferences among outcomes to theschools, it is possible that emphasis on productive efficiency may leadsimply to the efficient production of nonoptimal bundles of outputs(Williams 1970).

Figure 2 illustrates this situation for the two output case. AA' repre-sents a product transformation schedule between educational outputsand a2. and represent social indifference curves for the two outputssuch that represents a higher level of satisfaction than 10. It is obviousthat given the production possibilities and community preferences, thehighest level of welfare is represented by E1.

Now suppose that actual combination of outputs produced isrepresented by E0. E0 represents an efficiently produced bundle ofoutputs since it lies on the production frontier. It is evident that E0 givesthe community less satisfaction than E1, but more importantly anychoice of outputs within the shaded portion of the diagram (e.g., E 2) willyield a higher level of welfare than E0. That is, a large number ofsubfrontier choices make the community happier than any point on thefrontier except E1. Stated another way, it may be better to produceinefficiently that which is highly desirable to the community than toproduce with perfect efficiency that which is of low value.8

Efficiency and ScaleThus, we have identified three types of efficiency which might beapplied to an analysis of the educational sector: technical efficiency,allocative efficiency, and social welfare efficiency. A fourth type is onethat we shall not explore here in detail, that of size efficiency. Evengiven technical and allocative efficiency as well as the "correct" choice ofoutputs for all firms in the education industry, inefficiencies might beintroduced if the firms are too large or too small. Given the enormoussize variation of individual schools and school districts, it is possible thatboth economies and diseconomies of scale exist.9 Empirical work in thisarea has been carried out, but findings must be heavily qualified, giventhe enormous errors that are imposed by lack of a sound theoreticalstructure and measurement problems (Kiesling 1967; Kiesling 1968;Riew 1966; Cohn 1968).

155 Henry M. Levin

Output

Social Welfare and Choice of Output Combinations

III. BEHAVIORAL ASSUMPTIONS FOREDUCATIONAL FIRMSThe major reason for believing that private firms are efficient derivesfrom market theory. The incentive of profit maximization in combinationwith the pressure of competition can be reasonably expected to movefirms (and the industry) towards both technical and allocative efficiency,provided that certain other conditions exist. Moreover, the existence ofmarket prices for outputs enables the multi-product firms (and theindustry) to evaluate all outputs in terms of their contribution to reve-nue.'0

Let us list explicitly a few of the conditions which underlie ourexpectations of efficiency in the private sector." While these categoriesare not mutually exclusive, each emphasizes an aspect of competitivesupply that can be scrutinized for its applicability to educationalsuppliers in the public sector. The first two categories refer to technicalefficiency considerations; the next two refer to assumptions on market

structure andtence and vlsiof the firm. 'I

exist:1. manage2. substan3. a basic

tions (fi4. manage5. an obje

such as6. clear

of retuiOf course, toexpected to bregard to scalincreasingly thity that was ontion (Farrell 1and Chu 1968Lau and Yoto

The questiosuch public I

efficient beha'resounding Nschools appearsupplier in th

1. The edproduction setcess is so corinputs and ouor research. Srelate to prodphenomena; (1engineering le(Salter 1960, ieducational mMoreover, schare sophisticaltween changeLevin 1969).much insightset.

156 Economic Efficiency and Educational Production 157 Henry

'0

A

FIGURE 2

'efficient derivesi in combination

to moveative efficiency,

•.the existence offirms (and the

ibution to reve-

underlie ourthese categories

of competitiveto educational

to technicalions on market

structure and market information; and the final two refer to the exis-tence and visibility of managerial incentives that relate to the outcomesof the firm. Technical efficiency for an industry presumes that thereexist:

1. managerial knowledge of the technical production process;2. substantial managerial discretion over input mix;3. a basic competitive environment with all of its attendant assump-

tions (freedom of entry, many firms, perfect information);4. managerial knowledge of prices for both inputs and outputs;5. an objective function that is consistent with maximizing output

such as profit maximization; and6. clear signals of success or failure (profits, losses, sales, costs, rate

of return, share of market).Of course, to the degree that these do not hold, private firms can beexpected to be inefficient, both technically and allocatively and withregard to scale. Indeed, in recent years economists have recognizedincreasingly the possibilities of technical inefficiency for firms, a possibil-ity that was once assumed away by the textbook version of pure competi-tion (Farrell 1957; Leibenstein 1966; Nerlove 1965, Chapter 7; Aignerand Chu 1968; Timmer 1969 and 1971; Comanor and Leibenstein 1969;Lau and Yotopoulas 1971 and 1973).

The question that we wish to pose is: Do parallel conditions exist forsuch public firms as schools or school districts that would ensureefficient behavior in producing education? The answer seems to be aresounding No. For virtually every condition stipulated above, theschools appear to be at the opposite end of the spectrum from that of thesupplier in the competitive marketplace.

1. The educational managers at all levels lack knowledge of theproduction set for obtaining particular outcomes. The educational pro-cess is so complex and outputs are so diverse that relations betweeninputs and outputs are difficult to derive whether by casual observationor research. Salter defines three levels of technological knowledge thatrelate to production: (a) the basic principles of physical (or behavioral)phenomena; (b) the application of these principles to production, theengineering level; and (c) the level that relates to day-to-day operations(Salter 1960, p. 13). The sparsity of data at all three levels confronts theeducational manager, just as it confronts the educational researcher.Moreover, schools do not possess management information systems thatare sophisticated enough to obtain even approximate relationships be-tween changes in practices and educational outcomes (Hanushek andLevin 1969). The result is that neither science nor trial and error yieldsmuch insight to the educational manager on the nature of the productionset.

157 Henry M. Le'/in

-T2. Substantial management discretion does not exist over which in- laws promises

puts are obtained and how they are organized in educational production. performs. IndeSchool administrators make very few decisions regarding the purchase performance gc

and organization of school inputs. In part, this dereliction is due to since a captivedirect limitations on managerial discretion; in part it derives from the Of course, Ulack of knowledge of the production set; and in part it derives from an Thus, one muinbred reverence for existing practices. Each of these phenomena rein- individual famiforces the other, for when production relations are ambiguous and responsive. Th4organizations are governed by mandates, managers learn to avoid deci- little ability tosions and obey the rules. Any violation of the rules or the status quo is a lacks informatjorisk for which educational payoffs can rarely be demonstrated convinc- by extensive Puingly to all observers, many states ha

The "rules" for operating the schools derive from many sources, operations in afederal, state, local, and the vast legacy of traditional and, thus, sac- and the schoolsrosanct practices. At the federal level there exist particular guidelines for data on the edthe expenditure of federal educational funds for each category for which Levin 1969; Cfunds are available. More inhibiting is the fact that in many states the school boardslaws regulating the schools fill so many volumes that they require a mands, since thsubstantial bookshelf for nesting. These codes affect virtually every als than with tportion of school operations from the important to the minuwule. In themselves ladaddition, the state departments of education possess their own Cittell 1967; Ialabyrinths of operational minutiae which are imposed upon local school Perhapssystems. While matters of personnel licensing and personnel ratios are themselves totwo of the better known areas of control, most states can even dictate whether thesethe specific books that will be used in a particular class.'2 satory educatioi

Other factors that circumscribe the ability of managers to make sub- Indeed, they cstantial changes include local regulations and regional accreditation re- sclerosis," a mquirements. Moreover, negotiated contracts with educational personnel painful and unhave increasingly been used to stipulate in great detail the most uniform characterized bsystem of employment for a productive activity that lacks inherent community conuniformity. Finally, as we shall note below, the reward structure for thrown in themanagers discourages risk taking, since salaries and promotion are based in, the traditioiprimarily on seniority and docility rather than on any educationally 4. Prices ofmeaningful sense of leadership. All of these factors inhibit substantial educational mamanagerial discretion in operating educational institutions, information sys1

3. Little or no competition exists among schools. With the exception the markets forof nominal competition among school districts for families who can afford of the characteito migrate, there is no competition for students.'3 Usually the school productivity ha'that a child attends is determined simply by the attendance area in

, so on. Clearly, iwhich he lives. Rarely does he have a choice of schools to attend, even for purposes ofamong those within the school district. Thus, most schools possess one of these cmonopoly powers that would be the envy of any monopolistic industry, embodied in tiThe combination of assignment practices and compulsory attendance data on costs ai

158 Economic Efficiency and Educational Production 159 Henry I\

over which in-production.

the purchaseis due tofrom thefrom an

rein-ambiguous and

to avoid deci-status quo is a

trated convinc-

many sources,thus, sac-

guidelines forfor whichstates the

they require avirtually everyminuscule. In

their ownlocal school

ratios arekn even dictate

12

rs to make sub-ccreditation re-ional personnel

most uniformlacks inherent

structure foriotion are basedS' educationallyiibit substantial)ns.h the exceptionwho can afford

ially the schoolndance area in

attend, evenpossess

industry.ory attendance

laws promises a clientele for the school no matter how poorly the schoolperforms. Indeed, as we shall see below, these factors assure that goodperformance goes unrewarded and poor performance is uncensured,since a captive audience is always guaranteed.'4

Of course, the schools are not market institutions, but political ones.Thus, one must ask what system of political sanctions exists for anindividual family or group of citizens to ensure that schools will beresponsive. The answer to this must surely be that the public has verylittle ability to affect what is happening in the schools. First, the publiclacks information on both local schools and education itself as evidencedby extensive public opinion sampling (Gallup 1969, pp. 4—7). Moreover,many states have laws preventing citizens from "interfering" in schooloperations in any way including visiting of schools without permission,and the schools seem to be exceedingly deficient in providing desirabledata on the educational process (Gallup 1969, pp. 8—9; Hanushek andLevin 1969; Coleman and Karweit 1969; Wynne 1972). Second, theschool boards themselves seem to lack the ability to respond to de-mands, since they tend to identify more with the educational profession-als than with their citizens on matters of educational policy, and theythemselves lack the sanctions to change most outcomes (Lyke 1970;Gittell 1967; lannacone 1967).

Perhaps worst of all, the school bureaucracies have generally shownthemselves to be incapable of carrying out major changes in policy,whether these be school desegregation, curriculum reform, or compen-satory education (Rogers 1968; Schrag 1967; Gittell and Hollander 1968).Indeed, they can best be described as suffering from "organizationalsclerosis," a malady that makes a movement from the status quo bothpainful and unnatural (Jencks 1966; Rogers 1968). This frustration ischaracterized by demands for accountability, and even the pressures forcommunity control of schools are principally a reaction to the red tapethrown in the paths of citizens who seek information about, or changesin, the traditional school regimen (Levin 1970c).

4. Prices of both inputs and outputs are not readily available toeducational managers. In part, this is due to the inadequacy of schoolinformation systems, but in larger measure it is due to the complexity ofthe markets for educational inputs and outputs. On the input side, mostof the characteristics that have been associated with higher educationalproductivity have been such teacher traits as attitudes, verbal score, andso on. Clearly, it is difficult to disembody these particular characteristicsfor purposes of pricing, and it may also be difficult to obtain more of anyone of these characteristics per se without obtaining others that areembodied in the same person (Levin 1968, Chapters 6—8). Availabledata on costs are not related to homogeneous inputs. Rather, they are

159 Henry M. Levin

linked to line-item accounts or to objects that are not standardized withregard to quality, such as principals' salaries, materials, and so on (U.S.Department of Health, Education and Welfare 1957). Even the plan-ning, programming, and budgeting systems that have been designed forthe schools do not begin to make inroads into the quests for obtainingspecific prices or unit costs (Hartley 1968; Mushkin and Pollak 1970).

Prices for outputs are nonexistent in a market sense. Yet, the schoolsare expected to produce a large number of outcomes including jobpreparation, literacy, transmission of knowledge, and democratic val-ues.'5 In theory, referendums and representative governance of schoolsmight be used to reasonably reflect priorities among outputs in theabsence of prices. Unfortunately, the political realities suggest that thevalues of significant proportions of the population are not reflected in thedecision process because of imperfect information, inadequate politicalinstitutions, and communication gaps between those whose valuesshould be considered and those who actually implement the decisions(Lyke 1970; Jencks 1966; Gittell 1970; Rogers 1968).

5. The incentive or reward structures characteristic of schools seemto have little relation to the declared educational goals of those institu-tions. Financial rewards and promotions for school personnel are handedout primarily on the basis of seniority and accumulation of collegecredits rather than on demonstrated effectiveness. Individual schools,teachers, or administrators who are successful in achieving importanteducational goals are treated similarly to those who are unsuccessful,mediocre, or incompetent. In lockstep fashion, the schools rewardequally all personnel with the same nominal characteristics, regardless ofdifferences in performance (Kershaw and McKean 1962; Levin 1968).That is, success is not compensated or formally recognized, and thereward structure is divorced systematically from educational outcomes.'6

In contrast, commercial enterprises tend to compensate their person-nel on the basis of the contributions of employees to the effectiveness ofthe organization. Commissions for sales personnel, bonuses, promotions,profits, and salary increases all represent rewards for individual ororganizational proficiencies that do not seem to have their counterparts,in an output-oriented sense, in the schools.

6. Finally, there are no clear signals of success or failure for theschools that are comparable to sales, profits, losses, rates of return, orshares of market. Such standard measures as test scores and proportionof students graduating or gaining college entry are so heavily deter-mined by factors beyond the school's control, such as students' socialclass and cultural antecedents, that it is difficult to disentangle schoolinfluences from nonschool influences. Moreover, since education isessentially a dynamic process, the effects of present policy changes may

160 Economic Efficiency and Educational Production 161 Henry M.

only be discerndynamic effectsstructure thatsucceeded or faiof conciseobserve thebe removed. Tljof the schools isj

Standardized A

But if schools csuppliers, it is eoptimal mix offact becomes esof educationalare maximizingdents. Even thture of schools(Hanushek 197very little aboutson with our uYet the omissiproduction funccoefficients evestrict complem

The evidenceachievement sgoal. This is bElementary andone billion dollto schools educthe money local•design of theirresults of theirspecific goals uncan focus on th1programspresently beingtheir marginal

Since most ofto evaluate the €

withand soon (U.S.

the plan-en designed forts for obtainingd Pollak 1970).

the schoolss including jobdemocratic val-

of schoolsoutputs in the

suggest that thereflected in the

politicalwhose values

't the decisions

'of schools seetnpf those institu-hnel are handed

of collegeLividual schools,

importantFe unsuccessful,schools reward

cs, regardless of2; Levin 1968).

and theoutcomes.16

tte their person-effectiveness of

;es, promotions,ir individual or

counterparts,

failure for thees of return, orand proportionheavily deter-

students' socialfrntangle school

education ischanges may

only be discernible in the distant future. Furthermore, observation ofdynamic effects is obscured by mobility and dynamic changes in socialstructure that prevent observations on how well school policies havesucceeded or failed. Moreover, the multiplicity of outcomes and the lackof concise measures for most of them substantially limit the ability just toobserve the school's effects, even if the influence of other factors couldbe removed. Thus, informational feedback on operational performanceof the schools is neither visible nor easily obtainable from existing data.

Standardized Achievement as Educational OutputBut if schools cannot be appropriately viewed as acting like competitivesuppliers, it is erroneous to assume that they are maximizing the sociallyoptimal mix of educational outputs for any given set of resources. Thisfact becomes especially important when one considers that most studiesof educational production functions have simply assumed that schoolsare maximizing a single output, the achievement scores of their stu-dents. Even those analyses that do acknowledge the multi-product na-ture of schools generally limit their inquiry exclusively to test scores(Hanushek 1972, pp. 20—26). The usual presumption is that we knowvery little about the nature of measurement of other outputs in compari-son with our understanding of, and ability to measure, cognitive skills.Yet the omission of other outputs in the estimation of educationalproduction functions will lead to a biased set of estimated productioncoeflicients even for the achievement output if the other outputs are notstrict complements of achievement in the production process.

The evidence suggests that schools are not attempting to maximizeachievement scores even when their official rhetoric indicates this as agoal. This is best illustrated by the experience under Title I of theElementary and Secondary Education Act of 1965. Since 1965—66 overone billion dollars a year has been allocated by the federal governmentto schools educating children from low-income families. In applying forthe money local school districts were required to state the purposes anddesign of their Title I programs, and they were required to evaluate theresults of their efforts. Thus, we can take for granted that the school'sspecific goals under the program were the ones that they stated, and wecan focus on those outcomes. Moreover, the funds allocated to suchprograms represented approximately half again as much as what waspresently being spent on each eligible child, so one might have expectedtheir marginal impact to be substantial.

Since most of the programs concentrated on reading skills, it is usefulto evaluate the effect of Title I funds on that outcome. In evaluating the

161 Henry M. Levin

1966—67 and 1967—68 Title I funded reading programs, the U. S. Office (physical educof Education found that on the basis of reading test scores, "a child who incentives (n-iaparticipated in a Title I project had only a 19% chance of a significant pay and

a a significant achievement loss, and a analysis68% chance of no change at all [relative to the national norms]" outputs of sch(Picariello 1969, p. 1). Further, the projects included in the investiga- Yet, in ortion were "most likely to be representative of projects in which there achievement,was a higher than average investment in resources. Therefore more production frcsignificant achievement gains should be found here than in a more sent the maxjirepresentative sample of Title I projects." being utilized.

This inability to create even a nominal direct impact on specific cognitive achiobjectives appears to be endemic. Among many thousands of Title I since it isproject evaluations, the U.S. Office of Education selected the 1,000 reduces the a:most promising for purposes of further scrutiny by an independent case, it is obvresearch contractor. Of these, only 21 seemed to have shown sufficient consider onlyevidence of significant pupil achievement gains in language or numerical us estimatesskills (Hawkridge, Chalupsky, and Roberts 1968). A more recent analysis be obtained bhas shown a similar pattern of failure to improve test scores (Wargo et al. zero.1972). The obviou

Moreover, studies of school processes and organization suggest that product casethere are other agenda that dominate the educational production func- of the outputstion (Jackson 1968; Dreeben 1968). Gintis (1971) has found that grades conceptual ouand other social rewards of schooling are more consistently correlated relationships twith the personality attributes of students than with their cognitive nonachievemeachievement scores. It is not even apparent that the cognitive compo- that almost enent of schooling as reflected by student test scores has as large an production funeconomic impact as other outputs of the educational process. For exam- output.'8 In rple, studies of earnings functions suggest that the inclusion of a variable nored or themeasuring the cognitive performance of individuals (as reflected in test perfect jointscores) reduces by only a modest amount the observed earnings As we noted,coefficient for schooling (Taubman and Wales 1973; Griliches and Mason1972; and Gintis 1971). Presumably, the explanation for this phenome-non is that the other outputs of education that are quite independent oftest scores tend to be the ones that have the principal impact onearnings (Bowles and Ne son 1974; Bow es an Gintis 19 3). STUDENT

A more insightful analysis of the relationship between educational IMPLICATIproduction and labor market success seems to be reflected in the recentwork of Bowles (1972) and Cintis (1971) and Bowles and Gintis (1975). In the previcThese studies suggest that the principal purpose of schools is to repro- believing thatduce the social relations of production, and that achievement scores are ment andonly one component of the productive hierarchy. "The school is a counterpart fobureaucratic order with hierarchical authority, rule-orientation, strat- late the prodification of 'ability' (tracking) as well as by age, role differentiation by sex maximize ach

162 Economic Efficiency and Educational Production 163 Henry

the U.S. Office"a child who

of a significantloss, and a

national norms]"in the investiga-

in which thereTherefore morethan in a more

ipact on specificsands of Title 1ected the 1,000an independentshown sufficient

age or numericalre recent analysisres (Wargo et al.

ion suggest thatproduction func-und that gradesently correlatedtheir cognitive

compo-has as large an

ocess. For exam-sion of a variablereflected in test

served earningsiches and Mason

this phenome-e independent of

impact on1973).

'een educationalted in the recent

Cintjs (1975).tools is to repro-

scores areschool is a

frientation, strat-Irentiation by sex

(physical education, home economics, shop) and a system of externalincentives (marks, promise of promotion, and threat of failure) much likepay and status in the sphere of work" (S. Bowles, 1973, p. 353). Thisanalysis suggests that educational achievement is only one of the manyoutputs of schooling, and it is not necessarily the most important one.

Yet, in order to estimate a production function for educationalachievement, we must assume that all schools are operating on theproduction frontier for thi,s output, so that the observed relations repre-sent the maximum output that can be produced with the inputs that arebeing utilized. The fact that schools are producing other outputs besidescognitive achievement raises questions about this assumption,since it is reasonable to believe that the production of other outputsreduces the amount of cognitive learning that will be produced. In thiscase, it is obvious that statistical estimates among existing schools thatconsider only the achievement score outcomes of students will not giveus estimates of the production frontier, since more achievement couldbe obtained by reducing the levels of all noncomplementary outputs tozero.

The obvious answer to estimating production functions in the multi-product case is to specify a system of equations that takes into account allof the outputs of schooling. Unfortunately, our overall ignorance of theconceptual outputs of schools, their measurement, and their structuralrelationships to one another and to inputs, limits our ability to includenonachievement outputs in the analysis. The result of these limitations isthat almost every study that has attempted to estimate educationalproduction functions has considered only educational achievement as anoutput.'8 In most cases, the obvious problems involved are either ig-nored or the assumption is made that all other outputs are produced asperfect joint products in exact fixed proportion to achievement scores.As we noted, there is no empirical substantiation for this assumption.

IV. TECHNICAL INEFFICIENCY IN PRODUCINGSTUDENT ACHIEVEMENT AND ITSIMPLICATIONS FOR EVALUATIONIn the previous section we noted that there are many reasons forbelieving that schools are not technically efficient in producing achieve-ment and that the inefficiencies may be substantial.19 There is nocounterpart for the competitive environment of firms that would stimu-late the production of achievement. Even if the school attempted tomaximize achievement, the effort would be limited by the imperfect

163 Henry M. Levin

knowledge and limited discretion of school managers. Moreover, other Input S1outputs compete with achievement for school resources. Yet, attemptsto estimate educational production functions that use achievement as theoutput are based upon the tacit assumption that schools are producing asmuch achievement as can be obtained with their resources. That is, theyare producing on the "achievement" frontier. But given the high proba-bility of technical inefficiency, estimates of the production functions onthis output are likely to yield biased coefficients and misleading implica-tions.

This situation is shown in Figure 3, which represents a hypotheticalinput-input space where S1 and S2 represent two different school inputsinto the production of student achievement. Each observation repre-sents the combination of S1 and S2 that a particular school is using toproduce a given amount of achievement output, Ao. That is, each schoolin the sample is using a different input mix, even though the apparentoutput is the same.

Isoquant Ao1 represents the production frontier defined as the locus ofall observations that minimize the combinations of S1 and S2 required toproduce constant product Ao. Presumably, these schools are producingonly the socially minimal required levels of other school outputs.2° SinceAo1 is a mapping of the most efficient points for producing achievement

it is the production frontier. All observations to the northeast ofAo1are of schools that are using higher input levels to producethe same achievement.2' Now assume that we fit the observations statis-tically via normal regression procedures. We obtain the statistical equiv- FIGURE 3alent of Ao2 for all schools (both efficient and inefficient ones). Ofcourse, all points on Ao2 are farther from the origin than those on Ao1,showing that the average production relationship is a less efficient onethan the frontier relationship.

Since virtually all estimates of educational production have been based oron the performance of both average and efficient schools rather than h 2

efficient ones only, the existing statistical studies of educational produc- =tion are not production function studies in the frontier sense. Moreover,their results may suggest erroneous conclusions about which combination Now considerof inputs (programs) maximizes achievement for a given budget con- h', = h '1 and fstraint. For example, assume the two-input production function can be defli

(2) A = h(S, S2)/1 — 'I —

In equilibrium, we would wish to satisfy the conditions set out in (3), ' "— — -

where P1 and P2 represent the prices of and S2 respectively. 2

aAIaS aA/as (4) reiterates(3) 1

P22

estimates and fo

164 Economic Efficiency and Educational Production 165 Henry M.

otherYet, attempts

as there producing as:s. That is, theythe high proba-5n functions oneading implica-

a hypotheticalschool inputs

repre-pool is using tois, each schoolLi the apparent

[as the locus ofS2 required toare producing

utputs.2° Sinceachievement

ortheast ofAojrels to produce'rvations statis-:atistical equiv-

,ient ones). Ofthose on Ao1,

ss efficient one

FIGURE 3 Frontier and Average Production Isoquants forStudent Achievement

been basedrather than

produc-nse. Moreover,jch combination

budget con-function

set out in (3),•ectively.

h'1 — 112

Pt P2

Input S1 1

I

. I

constant (average)

Ao1 = constant (frontier)

Input S2

or

Now consider two different values for h'1 and h'2. At the frontier,h'1, and for the average of all schools, h'1 = h'1. The symbols for

can be defined in the same way.

(4)Il'2 Il'2 P2

(4) reiterates the necessary conditions for a maximum, both for frontierestimates and for average estimates of the production function. In both

165 Henry M. Levin

cases, we wish to select the combination of inputs that equates the ratios Input

of marginal products (first derivatives) to the ratios of prices.

Cl

Efficiency Implications of the EstimatesIf we estimate only the average production function or only the frontierproduction function, can the optimal ratio of inputs derived from oneestimate also apply to the other? The answer to this question clearlydepends on whether there are differences in the structural parametersassociated with each input.

For example, it is possible that the inefficiencies of nonfrontier schoolsare neutral among inputs so that at every level of input and for everycombination of inputs the ratios of the marginal products are identical forboth frontier and average functions. That is, (5) holds.

h = yhi (i = 1,2)

'F

This can be represented by Figure 4, where Ao1 signifies the productionisoquant for Ao for all efficient schools and Ao2 represents the same levelof output for the entire set of schools, efficient and inefficient. B1B2 andC1C2 represent budget or iso-cost lines reflecting the various combina-tions of S1 and S2 obtainable for two given cost constraints, B1B2 andC1C2, where C1C2> The slope of the iso-cost lines is determinedby the ratio of the prices, P2/P1. Thus, E and F represent equilibrium FIGURE 4points which reflect (4). That is, the combination ofS1 and S2 that obtainsAo for budget constraint B1B2 is determined by the tangency of Ao1 toB1B2 at pointE for efficient or frontier schools and ofAo2 toC1C2 at point neutral amongF for schools on the average, such a way thr

It can be shown that the relative intensities of the two inputs will be greater than fiidentical for both groups of schools if a ray drawn from the origin evident in Flintersects both points of tangency. 0 M satisfies that condition, so the appears to besame ratio of S1/S2 is optimal for both groups of schools. Whether we physical schocuse the estimates of frontier schools or of all schools, the findings on the that the. organoptimal combinations of S1 and S2 will be binding for both. In such a more harmfulcase it does not matter which group we use to estimate the production achievement I

function, although the absolute product will be higher for the set of through the otschools at the frontier for any input level, sect both poir

The situation depicted in Figure 4 and defined by (5) is a kind of frontier schoolhappy state of affairs which would be desirable indeed for purposes of sect point F; r'evaluation. Yet, there is no evident reason that such a fortuitous case schools at polshould hold (Bowles 1970, pp. 16—17). Given technical inefficiencies in that representthe production of education, it is likely that such inefficiencies are not schools will be

166 Economic Efficiency and Educational Production 167i

Henry

bnly the frontiererived from one

clearlytural parameters

Infrontier schoolsut and for everyare identical for

the productionthe same level

B1B2 andcombina-B1B2 and

les is determinedequilibrium

S2 that obtainsngency of Ao1 totoC1C2 at point

inputs will bethe origin

condition, so thebls. Whether wee findings on theboth. In such a

e the productionfor the set of

(5) is a kind ofI for purposes ofa fortuitous caseI inefficiencies inciencies are not

167 Henry M. Levin

the ratiosprices.

Input Sj

Cl

M

constant (average)

0 82 C2 Input

FIGURE 4 Technical Inefficiency that is Neutralbetween Inputs

neutral among inputs. That is, the inefficient school may be organized insuch a way that the relative inefficiency in the use of one input may begreater than for another.22 This can be shown in Figure 5, and it is alsoevident in Figure 3. Here the relative inefficiency in the use of S1appears to be greater than that for S2. For example, if representsphysical school facilities and S2 represents teachers, Figure 5 suggests.that the. organizational arrangements in inefficient schools are relativelymore harmful to the productivity of the facilities in increasing studentachievement than to that of the teachers. In this case, a ray drawnthrough the origin representing a constant ratio of inputs will not inter-sect both points of tangency. That is, the optimal ratio of S1/S2 forfrontier schools represented by 0 M intersecting point E will not inter-sect point F; rather it intersects the production isoquant for the averageschools at point G, which is a more costly combination of inputs thanthat represented at F. In short, the optimal ratio of S1/S2 for frontierschools will be different from that for nonfrontier ones, and if we impose

-t

Input

Cl

Si

0 C2 Input

FIGURE 5 Technical Inefficiency that Is Biasedbetween Inputs

that input ratio (represented by 0 M) on the nonfrontier production set,we shall recommend an allocatively inefficient set of inputs for thenonfrontier firms.

Of course, the obverse is also true. If we were to base our estimates ofthe production set on the entire group of schools, and we derived anoptimal input ratio based upon 0 N which intersects tangency point F,we would impose an allocatively inefficient decision on frontier firms.That is, in either case, the results that we obtain for one group of schoolscannot be applied to the other group. Rather each set of schools willhave its own optimal combination of S1/S2 depending on the relativeefficiencies with which these inputs are used. The point to be em-phasized is that even with estimates based upon perfectly specifiedsystems of equations for educational achievement, the input combina-tions that might be considered optimal for the industry will actually leadto a reduction in allocative efficiency for some educational firms. Morespecifically, those schools on Ao2 using any combination of inputs within

168 Economic Efficiency and Educational Production

C C' would oing the advici

Now it becoof economistsfunctions canallocat ice efficprices, if evermarginal ratesprescriptive dtional sectorallocative effic

This prospethree firms, Zits own "prothisoquants for elevel of achievnations differ.primarily frompetition, meetproduction fro

Further, assthe industry.approximationcase every fin.condition shou.isoquants of sotthis will not bdescribed in F

Figure 7 shthis three-firmiso-cost line faThat is, at poioptimal combitassume that eaindustry evaluaing its allocativpoint b to indiindustry. Inbination R; firrrcombination Q.

By coinciderfirm Z2, and ththe same pointZ2. Following t

169 Henry

N

constant (average)

= constant (frontier)

G C' would operate with greater price or allocative efficiency by ignor-ing the advice of economic studies of "frontier" firms.

Now it becomes obvious that under reasonable conditions, the adviceof economists using econometric approaches to estimating productionfunctions can actually lead to recommendations that would decrease theallocative efficiency of the educational sector. Even with the same set ofprices, if every firm has a different set of marginal products such that themarginal rates of substitution of factors differ from firm to firm, then anyprescriptive decision rule on optimal input combinations for the educa-tional sector would have a high probability of producing a decrease inallocative efficiency.

This prospect becomes clearer if we depict an industry composed ofthree firms, Z1, Z2, and Z3. If we assume that each firm is operating onits own "production frmnction," we can depict the individual unit productisoquants for each firm as in Figure 6. Each firm is producing the samelevel of achievement output, but the mappings of feasible factor combi-nations differ. The assertion of this kind of idiosyncratic behavior derivesprimarily from our contention that educational managers lack the com-.petition, incentives, information, and discretion to move toward theproduction frontier for achievement in any consistent way.

Further, assume that we wish to obtain a unit production isoquant forthe industry. Fitting a convex hull to points a, b, and c, we obtain anapproximation to the industry production frontier, ac.23 Though in thiscase every firm's production surface is on the industry frontier, thiscondition should not be assumed ordinarily. Rather the unit productionisoquants of some firms will be tangent to the frontier, while for othersthis will not be true. Such a situation is perfectly consistent with thatdescribed in Figure 1.

Figure 7 shows the conditions for maximizing allocative efficiency inthis three-firm case. If we assume that B1 B2 is the relative price oriso-cost line facing the industry, then tangency with ac is at point b.That is, at point b it would appear that we would be obtaining theoptimal combination of S1/S2 for maximizing allocative efficiency. Nowassume that each educational firm accepts the recommendation of thisindustry evaluation with regard to the optimal ratio of s 1/S2 for maximiz-ing its allocative efficiency. Line 0 M is drawn from the origin throughpoint b to indicate the constant ratio of S1/S2 that was derived for theindustry. In following this recommendation, firm Z1 would select com-bination R; firm Z2 would select combination b; and firm Z3 would selectcombination Q. What is the effect on allocative efficiency for each firm?

By coincidence, the iso-cost line B1 B 2, the production isoquant forfirm Z2, and the estimated frontier for the industry ac are all tangent atthe same point. Therefore the choice of b is allocatively efficient for firmZ2. Following the evaluation recommendations, firm Z selected point R

169 Henry M. Levin

I

(average)

ant (frontier)

Input

production set,for the

estimates of'we derived angency point F,frontier firms.roup of schoolsof schools will

the relativemt to be em-

specifiedinput combina-ill actually lead

• al firms. Moreinputs within

Input Si Input S1

0 Input

FIGURE 6 Approximating the Industry Production Surface forThree Firms FIGURE 7 M

on iso-cost line aR. Yet it is obvious that Z1 would be more efficient byproducing at R1 which is tangent to iso-cost line C1 C2. Indeed, even iffirm Z1 were not at point R1, the choice of combination R coulddecrease its efficiency; for any selection of input combinations betweenpoint a and point R would be superior to R.

A similar situation exists for firm Z3. The manager of Z3 believes fullyin using the findings of "scientific" research and evaluation activity inmaking his choices. Accordingly, he selects input combination Q withthe expectation that his firm will be allocatively efficient. Yet, factorcombination Qi is tangent to a lower iso-cost line D1D2, and any inputcombination between c and W would be superior to Q.

Introducing Further Inefficiencies inEducational Production

In summary, by believing and implementing the results of the industryevaluation, the industry became less efficient rather than more efficient.

170 Economic Etficiency and Educational Production S 171 M.

z3

z'

C

0

In

Yet, the techniuseful tools of msingle estimatewill solve this pifirm to firm,allocative effickthere will be nosame relative prthese assumptio.ficiency recommstudent achievezbe more harmfu

Bear in mindmost educationaspecification andthe lion's share

Input

Surface for

ore efficient bykndeed, even if

R couldbetween

believes fullyactivity in

Q withYet, factor

and any input

Input S1

0

FIGURE 7 Maximizing Allocative Efficiency for the Three-FirmIndustry

Yet, the techniques of evaluation were based upon the enormouslyuseful tools of microeconomic analysis. Further, as Figure 7 suggests, nosingle estimate of the industry's production function for achievementwill solve this problem. That is, optimal factor proportions will vary fromfirm to firm, and a uniform adoption for the industry will reduce overallallocative efficiency. Moreover, even this analysis has assumed thatthere will be no errors in the estimation of the relationships and that thesame relative prices are applicable to each firm. The fact that neither ofthese assumptions are valid buttresses further the argument that ef-ficiency recommendations based upon statistical production functions ofstudent achievement for the education industry (or a segment of it) canbe more harmful than beneficial to sectoral efficiency.

Bear in mind that at the present time we cannot identify or measuremost educational outputs, and we are woefully ignorant of the properspecification and measurement of the input structures. Further, sincethe lion's share of the school budget is spent on personnel, one must

171 Henry M. Levin

a

Al

of the industrymore efficient.

raise the question whether teacher "prices" are the same for everystimuli much cschool or school district. Among labor markets this is not likely to be so, than the pagesbut even within a school district a set of teachers with given characteris-foolish for any Itics are not indifferent about the schools in which they teach. For thesuch studiessame salary level, teachers prefer to work in schools attended by The situatjomiddle-class youngsters, and in suburban areas, rather than those at- enterprises. iitended by lower-class and minority youngsters in rural or highly ur- tion, educationbanized areas (H. Becker 1952; Herriott and St. John 1966, Chapter 5). form decision oAs one might expect, the relative preferences of teachers for specific This penchant.school sites is reflected in the salaries required to obtain teachers for of many of theparticular schools.24 teachers, andFor the very reasons stated above, it is not possible to test adequately reflected in tlthe hypothesis that the production set differs among educational firms. Moreover, theSuch a test would require a better specified model than the present state go unquestioneof the art will support. Nevertheless, for those who like the feel of areas just intennumbers (even unreliable ones), I have used the appendix to compare the "emperor'sestimates of educational production functions at the "frontier" with those

. attire preferablfor a large sample of sixth graders, in toto. Such an empirical operation indistinguishablis relegated to the appendix because it is meant to be provocative ratherthan definitive. Indeed, no numerical result derived from this exerciseshould be taken seriously.25

Of course, it is possible that parallel and serious problems arise in ananalysis of private sector industries, leaving those studies open to er- V. SUMMARYroneous conclusions. Yet, there is a quantum difference in the possible Rising costs ofimpact of erroneous findings in those cases in comparison with such quality have rafindings in an evaluation of the education industry. The main difference sector. One apris that private firms will tend to decide their input combinations on the education is tobasis of the peculiar circumstances facing them rather than on average output; to relate"results" for the industry.26 Further, the higher the level of aggregation make policy reof firms, the more inapplicable the results would appear to any rea- raise the allocalsonably proficient manager. Since most studies of the industry produc- cent years a lation function use state averages as units of observation, it would be production funcunlikely that any particular firm would identify with such results.27 made to compa]For example, Griliches carried out a set of studies on agricultural But, in orderproduction functions (Griliches 1963, 1964). Using 39 states as "firms" outputs toand an unrestricted Cobb-Douglas equation, he found a ratio of marginal with the resourcrevenue product to marginal cost of about 3 to 5 for fertilizer (Griliches production1964). At the time, he notes that fertilizer use was growing at a tre- functions, it is amendous rate in reaction to the disequilibrium (p. 968). What is conjunction withnoteworthy here is that Griliches saw natural market forces moving that firms operatagriculture toward allocative efficiency in a dynamic setting. He did not and allocativelyintend his study to be used by individual farmers to make decisions. environment norRather he tacitly viewed their managerial behavior as being a function of ascribe to compe

172J

Economic Efficiency and Educational Production173 Henry M.

jsame for everylikely to be so,

characteristeach. For the

us attended bythan those at-or highly ur-

Chapter 5).tiers for specific}ain teachers for

test adequatelytucational firms.he present statelike the feel ofLdIx to comparetier" with those)irical operationovocatiVe rather

this exercise

stimuli much closer to their productive operations and more influentialthan the pages of economic journals. Indeed, it would be exceedinglyfoolish for any farmer to base his factor hiring decisions on the results ofsuch studies.

The situation is entirely different for the schools and other publicenterprises. The U.S. Office of Education, state departments of educa-tion, educational researchers, and school managers search out the uni-form decision or recommendation with the hope of applying it generally.This penchant for standardizing input proportions is reflected in the lawsof many of the states that require very specific ratios of administrators toteachers, and of teachers and other professional staff to students. It isreflected in the policy prescriptions of most educational reports.28Moreover, the fact that results derived from modern analytic tools oftengo unquestioned because many decision makers lack training in theseareas just intensifies the problem. There is an increasing desire to try onthe "emperor's new clothes" by educational managers who find thisattire preferable to the dull and monotonous garb which makes themindistinguishable from other bureaucratic chieftains.

lems arise in anlies open to er-

in the possibleprison with such

main differenceon

on averageof aggregation

pear to any rea-produc-

ton, it would beresults.27

on agriculturalstates as "firms"ratio of marginal

rtilizer (Grilichesat a tre-

968). What isforces moving

:ting. He did notmake decisions.

eing a function of

V. SUMMARY

I

Rising costs of education in conjunction with persistent concerns aboutquality have raised questions about the efficiency of the educationalsector. One approach to improving the effectiveness of resource use ineducation is to estimate the technical production set for educationaloutput; to relate the technical coefficients to prices of the inputs; and tomake policy recommendations on the basis of these analyses that willraise the allocative efficiency of the educational enterprise. Within re-cent years a large number of studies have estimated an educationalproduction function for student achievement, and an attempt has beenmade to compare marginal products with prices.

But, in order for observed statistical relations between inputs andoutputs to reflect the maximum amount of input that can be obtainedwith the resources being utilized, all firms in the sample must be on theproduction frontier. In conventional analyses of industry productionfunctions, it is assumed that the nature of a competitive environment inconjunction with the goal of profit maximization would tend to ensurethat firms operating in competitive industries would be both technicallyand allocatively efficient. But, schools neither operate in a competitiveenvironment nor do they have most of the other characteristics that weascribe to competitive firms. Accordingly, it is not reasonable to believe

173 Henry M. Levin

that schools are operating on the production frontiers for the particular this directionoutputs that we believe that they should be producing. production of:

Virtually all attempts to estimate educational production have spec- production selified educational achievement as reflected in test scores as the appropri- function studiate output of the educational process. We have shown that there is they may alscabundant evidence in conflict with the view that schools are attemptingto maximize achievement scores. Accordingly, it does not seem reason-able that educational firms are operating on the production frontier forstudent achievement, and estimates of production functions among APPENDIXschools will not be likely to yield the appropriate technical coefficientsthat show the maximum amount of educational achievement that can beobtained with a given set of resource inputs. Moreover, it is likely that A Temerarioususing the results of such studies for policy could decrease the economicefficiency of the educational industry with respect to the production of The major difiachievement rather than improving it. of the foregoi

It would seem that a more productive approach to future research in easier to obtaithis area would be to attempt to ascertain a behavioral theory of schools cally, The parthat describes what schools are producing and how they are doing it.29 tions have beSuch studies would investigate the internal processes of educational (Bowles 1970;enterprises as well as the various types of outcomes that they produce. it is useful to rThey would also study the interface between schools and their external in the equattoenvironment in order to determine the types of political sanctions and the proper speother characteristics that create the existing operations of the schools structure of th(Bowles and Gintis, 1975; Carnoy and Levin, 1976). This type of study relationship tomight also begin to explain what aspects of schooling in addition to are manycognitive achievement affect adult income and other social outcomes. At variables usedthe present time, our understanding of these relations is so inadequate ment error.that we are applying concepts derived from the competitive theory of Thus, no Stthe firm to bureaucratic, nonmarket institutions, and such an application ranted. Ratheiseems unjustified. generating nev

An important start in this direction is reflected in the work of Cintis results that we(1971) and Bowles (1972 and 1973). According to their analyses, schools analysis beforeserve to reproduce the social relations of production required bycapitalist enterprise. They trace the evolution of the American schools The Samplethrough two periods of great change in the capitalist order (1830—90 and1890—1930), and they assert that the changes in characteristics of school- The data set using tended to mirror the changes in the demands of capitalist enterprises Survey on Equ(Bowles and Gintis 1975). They have also related the internal activities of tion for the schschooling, including school organization and grading practices, to worker white sixthcharacteristics that have been linked to productivity and earnings in were enrolledhierarchical work settings. At the very least, their findings suggest that and recoded exthe function of schools is considerably more complex than the maximiza- ships, so theytion of student achievement. It would seem that research endeavors in utilized inform:

174 Economic Efficiency and Educational Production 175 Henry I

Tir the particular

have spec-as the apprOpri-n that there isare attempting

ot seem reason-lion frontier foriinctiOflS amongheal coefficientsent that can beit is likely thate the economic

production of

jture research inof schools

are doing it.29of educational

U they produce.their externalsanctions and

rof the schools

pis type of studyin addition to

tial outcomes. Atis so inadequate

theory ofan application

le work of Gintisanalyses, schoolspn required by

schools(1830—90 and

of school-enterprises

ernal activities ofLctices, to workerand earnings in

suggest thatthe maximiza-

ch endeavors in

In

this direction would yield much more information about efficiency in theproduction of schooling than the present naive approach to "estimating"production sets. The most that can be said about the present productionfunction studies is that they are interesting and harmless; unfortunately,they may also be misleading.

APPENDIX

j

A Temerarious Empirical ApplicationThe major difficulty in demonstrating some of the empirical implicationsof the foregoing analysis is that the necessary relationships are mucheasier to obtain mathematically and geometrically than they are statisti-cally. The particular problems in deriving educational production func-tions have been described elsewhere, so they will not be detailed here(Bowles 1970; Michelson 1970; Cain and Watts 1970; Levin 1970a). Yetit is useful to note that the statistical work in this area is subject to errorsin the equations as well as errors in the variables. In the former case,the proper specification of the model is still in the exploratory stage. Thestructure of the model, the specific variables to be included, and theirrelationship to one another have not been well established, and thereare many gaps in our knowledge. Moreover, most of the operationalvariables used in the models are subject to varying degrees of measure-ment error.

Thus, no strict application of our findings to public policy is war-ranted. Rather, the empirical aspects are meant to be provocative ingenerating new directions and thought on the process of evaluation. Theresults that we derive must surely be subject to replication and furtheranalysis before they can be considered acceptable for policy evaluation.

The SampleThe data set used in this analysis represent a subsample drawn from theSurvey on Equal Educational Opportunity of the U.S. Office of Educa-tion for the school year 1965—66. Specifically, it is composed of some 597white sixth graders who had attended only the school in which theywere enrolled at the time of the survey.30 These data were reanalyzedand recoded extensively for purposes of estimating the present relation-ships, so they differ in important ways from other studies that haveutilized information from the same survey. There are some 29 schools

175 Henry M. Levin

represented in the sample, and teacher characteristics represent theaverages for each school for all teachers who were assigned to grades 3through 5. These averages were intended to reflect the teacher charac-teristics that had influenced student behavior up to the time of thesurvey. Moreover, it was assumed that the observed measures of familybackground and other educational influences were related systematicallyto the cumulative impacts of each of these variables.

The equation that we will use to explore differences between frontierand average estimates will be a linear equation based on (1). Lineaiitynot only violates our assumptions about the second derivative, but it alsoruns counter to our intuition about the real world. Yet, the difficulties ofestimating particular nonlinear functions and the risk of greater spec-ification biases in the coefficients by imposing another arbitrary func-tional form suggest that the linear equation might yield reasonable firstapproximations to the estimates that we seek. Of course, this limits ourcomparison of the frontier and average estimates to that of the linearmarginal products and price ratios.

The variables in the equation are shown in Table A-i. These variablesare taken from the reduced-form equation for verbal achievement de-rived from a four-equation system encompassing three simultaneousequations and one that represents a recursive relationship. Once thatsystem is estimated one can solve for the reduced-form equation for anyof the three endogenous variables. Since the estimation of that system isdiscussed elsewhere, we shall concern ourselves only with the reducedform of the verbal equation.31 This equation was fitted to the entiresample of observations. Consequently, it represents the average produc-tion relation for the sample of schools. Results are shown for thisestimate in the right column of Table A-2.

Obtaining Frontier EstimatesUsing the same set of data and variables, we wish to obtain estimates ofthe equation for only the most efficient observations, those on thefrontier. While there are several ways of doing this, we have chosen theprogramming approach in input-output space suggested by Aigner andChu (1968). Since our individual observations are students rather thanschools, we wish to seek those students who show a particular outcome i...

with the lowest application of resources. Using the general notation from(1), the problem is to minimize (1-a).

(1-a)

where is the parameter for the ith input, is the mean of X1, and104E-

176J

Economic Efficiency and Educational Production

L

-—

--—

-—--

--—

r0 0 kI

— •

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=linordertoII

minimize(1-a)wl(3-a).I I

(2-a) Mi +

subject to:

I

— (3-a)

C CC

I I I I

&o + &i X1,,, +.0

Since this is ec..J as many "efficien

o C')C

• • function (assumirI I some of these fir

represent measuris impossible forefficient or spurobservations in o

Imer 1969). This i

C C CC • •

very few observaTable A-2 cont

function. Each olginal product ofused to obtain fro2 discarded the n

C vations; and Runcent of the samifrontier functionshall examinenitudes of the C(efficiency.

VRecall that in c

to yield the samC

—frontier schools,constant relation'C

4"o ratios of marginao

C S school variables.C>

4relationship betw

E teacher's verbala o

Iii the frontier, suchJ >' ,- C.a-Q ,

C4 a a a C

z

181 Henry M.

j 1 in order to obtain a constant term. More specifically, we wish tominimize (1-a) which can be rewritten as (2-a) subject to the constraints(3-a).

(2-a) Mi + + . . . +

subject to:&o + &IXII +. . . + � 1'1

(3-a)

&,, + X1m +... + Xnm � Ym

al � 0Since this is essentially a linear programming problem, there will be

as many "efficient" observations as there are inputs into the productionfunction (assuming that no two observations are identical). Yet, clearlysome of these firms will appear to be efficient when in fact the figuresrepresent measurement errors.32 Accordingly, a problem arises in that itis impossible for us to know a priori whether a particular observation isefficient or spurious. Following Tim mer we have discarded extremeobservations in order to eliminate what might be spurious points (Tim-mer 1969). This is particularly important for the frontier estimates, sincevery few observations determine the structural coefficients.

Table A-2 ëontrasts the frontier estimates with those for the averagefunction. Each of the coefficients represents the first derivative or mar-ginal product of the function.33 Four linear programming runs wereused to obtain frontier estimates. Run 1 eliminated no observations; Run2 discarded the nine most "efficient" points; Run 3 eliminated 23 obser-vations; and Run 4 discarded the 38 most extreme points (or about 6 percent of the sample). We shall focus on the comparisons between thefrontier function from Run 4 and the average function. In doing this weshall examine two properties of the estimates: (1) the relative mag-nitudes of the coefficients; and (2) implications for allocative or priceefficiency.

Recall that in order for evaluation findings of optimal input intensitiesto yield the same relative applications of inputs for both average andfrontier schools, the marginal products for both functions must bear aconstant relation to each other as reflected in (5). Table A-3 shows theratios of marginal products for the two sets of estimates for all of theschool variables. According to this table, there is no obvious systematicrelationship between the two sets, and some of the coefficients, such asteacher's verbal score, are different at statistically significant levels. Atthe frontier, such inputs as the teacher's verbal facility and the propor-

181 Henry M. LevinI.

Kindergarten .888Teacher's verbal ability 3.164Teacher's parents' income .001Teacher's undergraduate institution 1.273Teacher experience .783Teacher satisfaction 1.841% white students 3.787Library volumes per student .276Teacher turnover .347Constant .513

tion of white students show marginal products that are more than threetimes their counterparts derived for the sample as a whole. On the otherhand, such variables as teacher turnover, teacher experience, and li-brary volumes per student show much smaller coefficients for the frontierfunction.

If these estimates are truly unbiased, the implications are that so-called frontier schools are more efficient in the use of some inputs andless efficient in the use of others. Thus any optimal combination ofinputs for any set of schools or any individual school is likely to benonoptimal for any other set of schools or individual ones. In otherwords, for any given array of prices (P1, P2 the optimal set offactor or input proportions may vary significantly from school to school.

For purposes of generalization, this is the worst of all possible worlds.That is, while we might be able to derive the optimal input structure forfrontier schools or for schools on the average as represented by equilib-rium conditions stated in (4), it is likely that the desirable combination ofinput intensities will differ between the two sets of schools (and in allprobability will differ significantly frOm school to school).

An illustration of this is found in Table A-4, which shows the esti-mated ratios of prices of two inputs as well as the two sets of marginalproducts for those inputs. The prices reflect the increments to annualteacher salaries for each of the characteristics as derived from an equa-tion relating teacher attributes to earnings in the Eastmet teacher mar-ket.34 The marginal products associated with a unit change in teacherverbal score and teacher experience are taken from Table A-2. Inequilibrium the ratios of the marginal products of the inputs should be

182 Economic Efficiency and Educational Production 183 Henry M.

TABLE A-3 Ratio of Marginal Products at "Frontier" toMarginal Products for Entire

MP (frontier)School Variables MP (averagëj

TABLE A-4

PriceMarginal productMarginal product

equal to the ralestimates thestefficiency is unbe based upon

On the otheproducts four tsuggests that titimes as muchexperience. If Itotal output by:while reducing

The significaicombination ofences persist aning general rulschools seems t(production techaverage nor froIndeed, in the etion function, mapplicable to in

NOTES1. Both Smith anc

run schools hay737; Friedman

2. The rudiments3. For a more lite

taly value of popportunity cos

• tier" to

MP (frontier)MW(averaqe)

.8883.164

.001

I 1.273.783

1.8413.787

.276

more than threeNe. On the otherk,erience, and ii-ts for the frontier

ons are that so-some inputs and

combination of1 is likely to be

ones. In otherthe optimal set of

to school.jl possible worlds.

structure forby equilib-

(le combination of(and in all

p0!).h shows the esti-o sets of marginal

to annualfrom an equa-

met teacher mar-in teacher

n Table A-2. Ininputs should be

TABLE A-4 Relative Prices and Marginal Products forTeacher Experience and Teacher Verbal Score

Teacher VerbalScore

(1)

TeacherExperience

(2)

Ratio(1)÷(2)

(3)

Price $24.00 $79.00 0.303Marginal product atMarginal product on

frontieraverage

0.7910.250

0.6160.787

1.2840.317

equal to the ratios of their respective prices. For the average productionestimates these ratios are almost identical, so that allocative or priceefficiency is implied even though the average estimates are assumed tobe based upon technically inefficient (nonfrontier) schools.

On the other hand, the frontier estimates show a ratio of marginalproducts four times as great as the price ratio for the two inputs. Thissuggests that the utilization of more verbally able teachers yields fourtimes as much output per dollar as the utilization of additional teacherexperience. If this is correct, the schools on the frontier could increasetotal output by reallocating their budgets in favor of teacher verbal scorewhile reducing teacher experience.35

The significant aspect of this analysis is that the output maximizingcombination of inputs differs between the two estimates. If these differ-ences persist among schools of different efficiencies, the hope of obtain-ing general rules for decision making which can be applied acrossschools seems to be frustrated. That is, the lack of similarities among theproduction techniques used by different schools may mean that neitheraverage nor frontier findings can be applied to any particular school.Indeed, in the extreme case each individual school is on its own produc-tion function, and evaluation results for any group of schools will not beapplicable to individual schools in the sample.

NOTES1. Both Smith and Friedman are concerned about inefficiencies that result when state-

run schools have little or no incentive to fulfill their stated objectives. (Smith 1937, p.737; Friedman 1955 and 1962).

2. The rudiments of this specification were first suggested by Hanushek 1968.3. For a more literal interpretation see Dugan (1969). Dugan has calculated the mone-

tary value of parents educational investment in their offspring by calculating theopportunity cost or market value of such services. The values of educational

183 Henry M. Levin

-n

investment, mother's educational investment, and school investment (all measured indollars) seem to have high combined predictive value in explaining achievement levels, earlier work

Also see Leibowitz, 1974. yin (1968a

4. These "theories" are essentially "black-box" hypotheses, based upon correlational 18. Exceptions tofindings or upon man-machine analogies. They do not specify general input-output (1970), as westructures or the physical, psychological, biological, and physiological processes Un- 19. Of course, mdenying them. Indeed, there is no engineering knowledge of the educational process that the corn]that is remotely analogous to those in agriculture and manufacturing. See for exam- variety of ex;pie, Bloom (1964). efficiency" of

5. The reasons for this assertion are found in Levin (1970a, pp. 65—66). it would appe6. For general reviews of findings see Bowles (1970); Guthrie et a!. (1971, Chapter 3); would promo

Kiesling (1971); and Averch et al (1974). (1968); Tirnm7. This assumption has been questioned by Michelson (1970, pp. 134—149); Bowles 20. In theory, sc

(1970, pp. 16—17); and Levin (1970a, pp. 57—59). Outputs. That8. Certainly this can be related to the criticisms of the schools made by many commen- of

tators who see the schools focusing on the wrong outputs. For a more sophisticated, minimal levelbut related, social welfare argument see Gintis (1969 and 1971) and Levin (1974a). schools produ

9. School districts in the United States vary in enrollments from a handful of students to frontier are oithe over 1 million enrollees in New York City. Individual schools show enrollments outputs. Thatvarying from a few children into the 10,000 student range. There were some 19,000 schools thatoperating school systems and 44.5 million public-school students in 1969. Of these 21. Inefficiency issystems, only 1 per cent of them had 25,000 or more pupils. Yet, almost one-third of which more 0the students were in the 25,000 and over category while less than 2 per cent were in from other ouschool systems with less than 300 pupils (Sietsema and Mongello, 1970, p. 6). or "x-inefficiei

10. For an analysis of the production decisions faced by the multi-product firm generally inefficiency, I

and the joint product firm specifically, see Sune Carlson (1956, Chapter V); and inputs. But, aPfouts (1961). of production

11. The conventional "theory of the firm" has come increasingly under attack by those and energy, siwho charge that it is a theory of an environment rather than a theory of behavior. See production froCyert and Hedrick (1972) for a review of this controversy, process. Whe

12. In California, the state department of education even prints many of the books another mill, irequired at the elementary level. The cumbersomeness of this arrangement has just happensresulted in a perennial ritual by which several hundred thousand youngsters have analyst is steelacked their reading and arithmetic books for periods of up to two or three months inefficiency cafollowing the opening of school. For greater detail on the degree of external control is a function csee Levin (1974a). the concept of

13. While Tiebout has suggested that such a public market exists, its efficiency must be (1966). In ourquestioned. Costs of migration are high, preventing frequent movement in response outlined moreto disequilibria. Moreover, zoning and other impediments limit the usefulness of the 22. There is an ohousing market as a vehicle for educational choice. (See Tiebout 1956.) Of course, technologicalprivate alternatives exist for those willing and able to make substantial financial 23. For discussionsacrifices. (1968).

14. For some approaches to implementing competition among the public schools see 24. For evidenceDowns (1970). Data on the voucher-inspired federal experiment in San Jose, Califor- types of schoonia, are found in Weiler et ai. (1974). 25. These results

15. For an extensive taxononiy of educational objectives see Bloom (1956); and 26. See Hall and'Krathwohl, Bloom, and Masia (1964). differences in

16. For a more general analysis of the relation between institutional performance and 27. See the commincentive structures see Schultze (1968) and Riviin (1971). Educational applications 28. See for exampiare found in Pincus (1974). C' 'I Ri ht 1

17. Muiticoilinearity among such inputs is a major basis of criticism for some of the IV1 gand Cain and

184 Economic Efficiency and Educational Production 185 Henry hI

(all measured inachievement levels.

upon correlatiOnaleneral input-output

processes un-'educational process

See for exam-

I. (1971, Chapter 3);

134—149); Bowles

by many commen-more sophisticated,and Levin (1974a).ndful of students to

is show enrollmentse were some 19,000s in 1969. Of thesealmost one-third of2 per cent were in

ho, 1970, p. 6).duct firm generally

Chapter V); and

der attack by thosetory of behavior. See

many of the booksis arrangement has

knd youngsters haveor three months

of external control

efficiency must bein response

the usefulness of the)ut 1956.) Of course,substantial financial

:e public schools seein San Jose, Califor-

Bloom (1956); and

nal performance andapplications

ksm for some of the

earlier work done in the area of estimating educational production. See Bowles andLevin (1968a and 1968b).

18. Exceptions to this are the multi-product estimations of Levin (1970a) and Michelson(1970), as well as the work of Boardman et al. (1973).

19. Of course, many private firms are likely to be technically inefficient to the degreethat the competitive assumptions do not hold for them. See Leibenstein (1966) for avariety of examples illustrating substantial differences in technical efficiency orefficiency" of firms. Nevertheless, while the inefficiency club is not an exclusive one,it would appear a priori that public schools have even fewer of the characteristics thatwould promote efficient production than do private firms. See Aigner and Chu(1968); Timmer (1971); and Farrell (1957).

20. In theory, schools on the frontier for student achievement are producing no otheroutputs. That is, the production of other outputs is assumed to detract from theproduction of student achievement. But, in fact, it is likely that there is a sociallyminimal level of other outputs (such as citizenship, work attitudes, and so on) that allschools produce. In this case, the schools that appear to be on the achievementfrontier are on a 'modified frontier," which assumes a socially minimal level of otheroutputs. That is, short of an experiment, we are unable to obtain production data onschools that are producing only student achievement.

21. Inefficiency is used here in a very narrow way. Specifically, it refers to the case inwhich more of a particular output could be obtained by reallocating existing resourcesfrom other outcomes to the one under scrutiny. The case of "technical inefficiency"or 'x-inefficiency" is just a misnomer for this condition. Under conditions of technicalinefficiency, it appears that more output could be obtained with the same level ofinputs. But, as we have shown elsewhere (Levin and Muller, 1973), the physical lawsof production must surely behave according to the principles of conservation of massand energy, so that nothing is "lost" in the production process. One is always on theproduction frontier in that there is a mapping of outputs on inputs for any productionprocess. When a steel mill is producing less steel for a given set of inputs thananother mill, it is producing more heat energy or worker leisure or other outputs. Itjust happens that the most-valued or preferred output from the perspective of theanalyst is steel rather than heat energy or worker leisure. Thus, so-called technicalinefficiency can always be shown to reduce to allocative or price inefficiency, since itis a function of values rather than energy losses in a physical sense. For reference tothe concept of technical efficiency or x-efficieney, see Farrell (1957) and Leibenstein(1966). In our view, the conception is erroneous for reasons mentioned above andoutlined more systematically in Levin and Muller (1973). Also see Knight (1923).

22. There is an obvious similarity between this issue and the question of neutrality oftechnological progress. See Salter (1960); Brown (1966).

23. For discussion of techniques for deriving such a convex hull, see Aigner and Chu(1968).

24. For evidence of price differences attributable to teacher preferences for particulartypes of schools and teaching environments, see Toder (1972) and Levin (1968).

25. These results are also reported in Levin (1974).26. See Hall and Winsten (1959) for a discussion of complications arising from interfirm

differences in environmental conditions.27. See the comments by Walters (1963, pp. 5—11).28. See for example James S. Coleman et al. (1966, Chapter 1); and U.S. Commission on

Civil Rights (1967). For criticism of such policy uses see Bowles and Levin (1968a),and Cain and Watts (1970).

185 Henry M. Levin

29. There is an obvious parallel with the behavioral theory of the firm. See Cyert and Bowles, Samuel, aj

March (1963) and Cyert and Hedrick (1972). (Nov/Dec30. See Levm (1970a) for details. Bowles, Samuel, au

31. Ibid. Books, Inc.,32. Unfortunately each observation is a student rather than a firm. The proper approach Bowles, Samuel, au

is to seek efficient firms (schools) rather than students. The reason that students are Critical Ap1used rather than firms is due to the limited sample size of schools, 29. Since it would (Winter 196require 18 of these firms to fit the frontier—given 18 parameters—one could hardly . "More onmaintain that the frontier coefficients were based only on efficient firms. Resources 3

33. Since a1 � 0, those variables that showed coefficients for the average Bowles, Samuel, aifunction represented problems for the programming estimates. The array for each Reproductiosuch variable was multiplied by (—1) for the programming estimates, and the signs 1974): 39—5'were reversed in turn when reporting the results in Table A-2. The author is Brown, Byron, amindebted to Richard C. Carison for computing the programming estimates. See his Within Schpaper "Educational Efficiency and Effectiveness," May 1970, prepared for the Brown, Murray. 0Seminar in Economics of Education, Stanford. Cambridge

34. These are taken from Levin (1968). For a similar application of these prices see Levin Burkhead et al. I(1970c). University 1

35. For a similar finding, see Levin (1970c). Cain, Glen C., anColeman Re

Carlson, Richard CSeminar in

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to 1981-82. National Center for Educational Statistics, Office of Education. Wash- In his taxono

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31 (Jan/Apr., 1963): 1—66. inefficiency), an

Wargo, Michael J.; Tailmadge, C. Kasten; Michaels, Debbra D.; Lipe, Dewey; and inefficiency). ThMorris, Sarah J. "ESEA Title I: A Reanalysis and Synthesis of Evaluation Data concerning techi

lic policy. That i

190 Economic Efficiency and Educational Production 191I

Comme'

fl. L. Johns et al., From Fiscal Year 1965 Through 1970." Palo Alto, Calif.: American Institutes for101, 2. Gainesville, Research, March 1972.

Weiler, Daniel, et al. A Public School Voucher Demonstration: The First Year at Alum'liwtion Functions. Rock. Santa Monica, Calif.: Rand Corporation, June 1974.

Williams, Andrew T. "Education and the Joint Product Production Function." Paperhi-Product Firm." prepared for the Seminar in Economics of Education, Stanford University, 1970,

processed.bifice of Program, Winlder, Donald R. The Production of Human Capital: A Study of Minority Achievement.• Ph.D. diss., Department of Economics, University of California at Berkeley, 1972.ew of Educational Wynne, Edward. The Politics of School Accountability. Berkeley, Calif.: McCutchan

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4 COMMENTSD.C.:

jB—70 Public School Eric A. HanushekNational Center for Yale Universityi1970.

1970.lew York: Random It always helps to take stock periodically of what we are doing and where we

are going. Educational research is certainly no exception. It is simply tooAbility and Screen- easy to continue doing what we know best. However, after being forced by

Levin into a reappraisal of the directions of educational research, I remainI Sons, 1971. unpersuaded that drastic modification is called for. I have some seriousfPolitical Economy reservations about the conclusions and implications both for research and

s Department of public policy drawn from Levin's analysis, particularly as it pertains totechnical inefficiency in the schools.

Technical Ef- In many ways, Levin's viewpoint does not diverge significantly from myown. We start from the same data; there is no disagreement about the

A Possible Source constraints on the system or about the amount of knowledge and information54 (Nov. 1972): available to the participants in the educational process. We also agree on

many of the results that develop from constraints on information and possi-ducation. Financial ble actions. Our major points of disagreement arise from nomenclature ofitional Records and observed output differences and the subsequent implications for future re-GPO, 1957. ,

, search and public policy.ducatwnal Statistics . .

In his taxonomy of types of inefficiency, Levin argues that there aref Education. Wash- .

reasons to believe that schools are not operating on the production frontier

Econometrica (technical inefficiency), are not operating with the best input mix (allocativeI inefficiency), and are not providing the desired output mix (social welfareLipe. Dewey; and inefficiency). The heart of his analysis is directed toward the evidenceof Evaluation Data concerning technical inefficiency and its implications for research and pub-

lic policy. That is also the central issue in my discussion.

191 Comments by Hanushek

Before entering that debate, however, I wish to make two points relating toallocative and social welfare efficiency. These are not points of disagree- They are j:

ment with Levin; they are simply added to emphasize certain aspects of the terms, defininc

discussion. First, allocate inefficiency has not only been the central concern analysis of ted

of economists but is also almost a necessary condition for analysis. In the the base moth

absence of large differences in the relative prices of inputs, allocative inefficiency the

inefficiency is needed to analyze educational production functions. 0th- chosen

erwise we would observe one point on the production function, and our the frame of

statistical techniques are noticeably weak at drawing multidimensional veloped from a

planes through one point. Second, the whole issue of social welfare ef- amount of me

ficiency, or producing the best mixture of outputs, has the same elusive becoming avai

character as choosing the right quantity and mixture of general public goods. A different

The optimum marginal conditions on the social welfare function are easy well-specified

enough to derive, but the operational questions have generally been beyond differences in

the economist's ability to answer. Nevertheless, in my subjective evaluation, function that p

this is probably the most important area of concern in education today. The man-hours with

question of whether or not schools are producing the outputs desired and view of the lab

needed in society remains important but unresolved. We are not sure what are represente

the outputs of schools are, how to measure the outputs, how to produce correlated with

each, or what tradeoffs exist among outputs. Not only space limitations on stein's internati

this discussion but also the difficulty of the issue preclude my going into a distorted vie

more detail on this. why the analys

The main message delivered by Levin is that there are compelling reasonsgo into produc

to believe that what have paraded under the banner of educational produc- seen in a micr

tion functions are not really production functions in the economist's usage ofIn point of fa

the term, because they do not describe the frontier of possible production.day in educati

Instead they are a weighted average of the practices of efficient, or 'fron-decade have n

tier," schools and inefficient, or "nonfrontier," schools. With these averageneous teachers

relationships, blind application of well-known optimization rules could evenpurchased

degrade the production by a school system which is almost universally citedthey have look

as inefficient,verbal ability. -

A crucial facet of the debate is how one should define technical inef-other attributes

ficiency. Past discussions, for example, Leibenstein's development ofHowever, to th

X-efficiency [2] and Levin's presentation, rest heavily upon a micro- proportion of th

economic textbook treatment of production, where output is a function of aimportance of

quantity of homogeneous capital and homogeneous labor. Then, noting thatminished.

these inputs are really not homogeneous, firms with poorer "homogeneous" If we map a

inputs are observed to produce less output than firms with identical quan- chased by sch

tities but better quality "homogeneous" inputs. The availability of better or education), we

worse "homogeneous" inputs can be related to incomplete labor contracts, This will happeil

lack of knowledge of the production function, motivational differences, or tors have a smi

simply general managerial ability. Differences in output for equal" inputs characteristics

are used as a measure of technical inefficiency, factors are not1

A real problem remains in specifically defining technical inefficiency. In schools with

a measure of the strength of Yet, within the

variables omitted from a model of the production process. These omitted is: Do schools

variables may take the form of education, motivation, laziness, or what haveheld

It is

192 Economic Efficiency and Educational Production193 Comma

pointS relating toints of disagree-in aspects of thecentral concern

- analysis. In theiputs, allocative

functions. 0th-jnctiofl, and ourmultidimensionalocial welfare ef-he same elusivecal public goods.dnction are easy

been beyondactive evaluation,bation today. The)uts desired and

not sure whathow to produce

1ce limitations onmy going into

jmpelling reasonsucational produc-nomist's usage of

production.or "fron-

Ith these averagerules could evenuniversally cited

ie technical inef-development ofupon a micro-

is a function of aThen, noting that

r homogeneous'Lh identical quan-ibility of better ore labor contracts,al differences, orfor equal" inputs

inefficiency. Inof the strength of

These omittedess, or what have

L

you. They are just the explanations given for efficiency differences. In theseterms, defining technical inefficiency becomes very difficult. Before anyanalysis of technical inefficiency can be developed, one must define whatthe base model of the production process should look like. Amounts ofinefficiency then become difficult to measure, since they are a function of thechosen degree of misspecification in the base model. A common way to setthe frame of reference appears to be using the model which can be de-veloped from available data. This, of course, creates problems, because theamount of inefficiency can change over time simply due to better databecoming available.

A different way of looking at this 'inefficiency," however, is to use awell-specified model as the standard and to view observed productiondifferences in terms of model misspecification. The traditional productionfunction that pictures output as a function of the quantity of man-hours orman-hours within given human capital classifications provides an incompleteview of the labor input to production. There are more attributes to labor thanare represented in these functions. These omitted attributes often tend to becorrelated with management ability or firm size or nationality in Leiben-stein's international examples. Estimated production functions can then givea distorted view of the production potential. There is, however, no reasonwhy the analyst cannot specify or attempt to specify all of the attributes thatgo into production. He need not be bound to specifying just those inputs asseen in a microeconomic text or those explicitly purchased by the firm.

In point of fact, this extension of the list of inputs has been the order of theday in educational research. Educational production functions of the pastdecade have not looked at schools as providing a given number of homoge-neous teachers; nor have they looked at schools as providing only the set ofpurchased inputs (class size, experience, and graduate education). Insteadthey have looked at schools as providing a set of attributes, such as teacherverbal ability. The attributes explicitly measured may well be proxies forother attributes which have direct causal relationships with achievement.However, to the extent that a set of stable proxies which represent a fairproportion of the real teacher inputs to education have been analyzed, theimportance of the technical inefficiency argument is considerably di-minished.

If we map achievement outputs against only those inputs explicitly pur-chased by schools (class size, teacher experience, and teacher graduateeducation), we will certainly find the picture indicated by Levin's Figure 1.This will happen because, according to past analyses, the purchased fac-tors have a small or nonexistent effect on output, but other nonpurchasedcharacteristics of teachers do have an important effect. Since these otherfactors are not randomly distributed by schools—as shown in Levin [31,

schools with apparently the same input levels will show different outputs.Yet, within the context of educational production functions, the real questionis: Do schools have different outputs after the relevant teacher inputs areheld constant?

It is reasonable that past discussions in fields other than education have

193 Comments by Hanushek

centered upon technical inefficiency in production. This arises largely fromhaving poorer data sources for, say, aggregate manufacturing firms than foreducational firms. Research in education has been aided by having detailedmeasures of relevant inputs. Further, the emphasis within educational re-search has been on refining the measures of inputs. This is not to say that wenow have perfectly specified models of educational production. We have along way to go in that regard. It does imply that attention has been placedwhere I think it properly should be—on model specification and, to a certainextent, on experimental design.

The case by Levin for technical inefficiency derives chiefly from theobservations that school managers do not know what the production functionfor education looks like and that these managers are severely constrained intheir operating and hiring practices. Other factors relating to technical in-efficiencies are the general lack of competition in education and lack of bothincentives and clear-cut signals of success or failure.

From a specification point of view, the implications to be drawn fromLevin's observations of current school operations change considerably. First,I am uncertain how the school principal, whether he knows the productionfunction or not, affects technical efficiency. If, as past research would sug-gest, the main school inputs to education under the current technology areattributes of the teacher, it is hard to see how the principal affects therelationship between these attributes and achievement by very much. interms of managing teachers, the principal may assign his best readingteacher to teach physical education; this is an allocatively poor decision thatwould reduce total achievement in a school for his expenditures, but notnecessarily one that falls off the production frontier for education. It indicatesthat the analyst must be careful to separate the characteristics of thephysical education teacher and the reading teacher, But, given this, thereseems to be no reason to require the principal to know that he is making amistake.

The fact that there are constraints on the manager's actions does not seemto destroy the usefulness of estimated production functions either. Con-straints imply that he can only operate on a limited portion of possible inputmixes. For example, a principal probably does not have the option to installa Computer-Assisted Instruction (CAl) program on his own. Nevertheless, hecan attempt to suboptimize within the portion of the production frontieravailable to him. There is no reason to suspect that any such suboptimiza-tion attempts lead to. technical inefficiency.

The other conceptual reasons for concluding that technical inefficiency isprobably large produce a similar discussion. Such reasons seem to implythat schools could be allocatively very inefficient but not technically in-efficient.

There is an empirical question about the importance of variables relatingto facilities, curriculum, and management which may be systematically re-lated to achievement and not generally included in production models. I

have made a modest attempt to answer this question with a sample of 515students from blue-collar families within one school system. The data sam-

pie and estimastandardizingthere were charaffected output.was allowed toperformed to a;intercept dummfects, regardlesquately specificmeasure of tect

Within thisper cent of thedizircg for teachexistence of rn

finding that thecent with no desuperior experiexperience andachievement. (Iiof 22 per cent

Finally, we kwith individualor better informsample, whetheicontext of viewinreason to believito make decisiocschools, we are.In other words,

CONCLUSIONSIt is not evidenproblem, unlessWithin the contwithin the pastranted. I do noteducational procinefficiency seec

The differenccsemantics. First,free lunch, thatabout significantwhen viewed inbringing "ineffic

194 Economic Efficiency and Educational Production 195I

Comme

largely fromhg firms than forhaving detailededucational re-

1ot to say that we1tion. We have a

been placedto a certain

phiefly from the'duction functiony constrained into technical in-and lack of both

be drawn fromsiderably. First,the productionrch would sug-technology are

ipal affects thevery much. In

'is best readingor decision thatditures, but nottion. It indicatesteristics of the

this, therehe is making a

Ls does not seemeither. Con-

pf possible inputoption to install

Nevertheless, hebduction frontier

suboptimiza-

inefficiency isIS seem to implyIt technically in-

relatingystematically re-uction models. I

a sample of 515The data sam-

pie and estimated educational models are reported elsewhere [11. Afterstandardizing for different teacher inputs, I attempted to find out whetherthere were characteristics of schools and principals which systematicallyaffected output. For this analysis, each of twenty-three schools in the samplewas allowed to have its own intercept value, and statistical tests wereperformed to ascertain whether these intercepts differed by school. Theintercept dummy variables provide estimates of the systematic school ef-fects, regardless of whether the components of these effects can be ade-quately specified or measured. These effects would be equivalent to ameasure of technical efficiency.

Within this sample, only one school out of twenty-three (comprising twoper cent of the students) produced significantly higher outputs after standar-dizing for teacher inputs.' This appears to be very weak evidence for theexistence of important technical inefficiencies. Matched against this is thefinding that the total wage bill could be reduced by approximately 22 percent with no decrease in achievement by not hiring individuals possessingsuperior experience or graduate education, or by not paying for suchexperience and graduate education, which were shown to have no impact onachievement. (In other words, by improving allocative efficiency, a savingsof 22 per cent could be realized.)

Finally, we know that there is a large random component associatedwith individual achievement. There is no reason to suspect that we get moreor better information about educational production by looking at a smallersample, whether by linear programming or least squares. Also, even in thecontext of viewing "efficient" production with linear programming, there is noreason to believe that specification problems are any less severe, If we wishto make decisions about educational production from considering "efficient"schools, we are still left with trying to decide why such schools are efficient.In other words, we are left with the same specification problems.

CONCLUSIONSIt is not evident to me that technical inefficiency is a particularly largeproblem, unless we use obviously misspecified models as the standard.Within the context of well-specified models, similar to those developedwithin the past few years, emphasis upon allocative efficiency appears war-ranted. I do not wish to indicate that we know all there is to know abouteducational production. Yet, both conceptually and empirically, allocativeinefficiency seems more important than technical inefficiency.

The difference in my approach and Levin's is more than a question ofsemantics. First, use of the term inefficiency tends to imply that there is afree lunch, that some organizational changes within the school will bringabout significant changes in outputs at little or no cost. On the other hand,when viewed in terms of omitted variables, it is immediately obvious thatbringing "inefficient" schools up to the level of "efficient" schools may not

195I

Comments by Hanushek

be free. Second, the term technical inefficiency seems to imply that theobserved differences in outputs are related almost exclusively to manage-ment differences. However, my work has led me to suspect that the realefforts should be directed toward better specifying teachers and their inputsto education. Third, the concept of technical efficiency appears vacuousfrom a public policy viewpoint. Even if some consensus could be arrived atas to how this inefficiency should be measured, we are at best led to tryingto explain these differences in order to reduce the differentials involved.

If the problem is looked upon as one of specification problems, it leads tointensifying data collection efforts and broadening the scope of our mea-surement of teacher attributes, It also calls for experimentation in order toobserve other parts of the production frontier. If instead, one concludes thatschool management in terms of approaching the production frontier is thekey issue, a different course of action is called for, In this case, much moreeffort should be directed toward analyzing organizational behavior and therelationship between management, teachers, and facilities. In my judgment,the former course of action will have much higher payoffs.

On the other hand, Levin's observations about the definition and measure-ment of educational outputs cannot be disregarded. Even though cognitiveability, as measured by test scores, is undoubtedly an important aspect ofelementary and secondary schools, this is not the sole output of schools.While the joint product problem is not completely developed by Levin, it

represents a very important issue for future research. Unfortunately, themethodology for handling joint production when there are no prices (orweights) to combine the different dimensions of output is an underdevelopedarea of economics.

NOTE1. Another significant aspect of this estimation was the finding that the dummy variable for this

school had a very low correlation with each of the included school variables. (The simplecorrelation was always less than .1.) This implies that even if we were to believe that thedummy variable represented some omitted management aspects for this school, its effect onthe included coefficient estimates is small: that is, the amount of specification bias would besmall.

REFERENCES1. Hanushek Eric A. Education and Race, Lexington, Mass.: D.C. Heath, 1972.2. Leibenstein, Harvey. "Allocative Efficiency vs. 'X-Efficiency'," American Economic Review 56

(June 1966): 392—415.

3. Levin. Henry M. "Recruiting Teachers for Large-City Schools." washington, D.C.: BrookingsInstitution, 1968. processed.

Harold W. \iUniversity of Wisconsin

The primary Cotions for improwhich takes p1mated producticated than thethat naive atterbe counter-prowarnings orat the end of s

Levin opens Iing the risingquality of schocthat improvemesome of the incBut the existencrising Costs orsome steady rafalling quality,ficiency. In no rtive to the "petsuffer cost ncrsequent wage i

But there isI

educational sysuse productionkinds of inefficiification can foone principaltechniques willestimation of ameasurements isions) and thatas a conseque,

The next secsupport of the pseems to be thcritical respectsno basis for aceducation "induthe perfect propof the real worlttions to invalidacriticizes for edpublic schools

196 Economic Efficiency and Educational Production 197 ICommt

The primary conclusion Levin arrives at in this paper is that valid prescrip-tions for improving efficiency of the educational process (or that partS of itwhich takes place in public schools) cannot be derived from existing esti-mated production functions. He argues that the world is much more compli-cated than the available econometric models of educational production andthat naive attempts to draw normative conclusions from such models couldbe counter-productive. These conclusions seem appropriate enough aswarnings or expressions of humility, but they also seem quite anticlimacticat the end of so many pages of analytic threshing about.

Levin opens by attempting to motivate our interest in efficiency by observ-ing the rising costs of education combined with dissatisfaction over thequality of schools and loss of voter support for bond issues. It is quite clearthat improvements in efficiency, if any are available, would offset for a whilesome of the increase in costs and might produce a more popular product.But the existence of inefficiency, in any of its varieties, does not imply eitherrising costs or consumer dissatisfaction. If inefficiency were getting worse atsome steady rate, we might expect the consequences of rising costs and/orfalling quality, but Levin does not provide evidence of progressive inef-ficiency. In no sense does the hypothesis of inefficiency provide an alterna-tive to the 'pessimistic" view of Baumol that 'unprogressive" sectors willsuffer cost increases as other sectors enjoy productivity gains and con-sequent wage increases.

But there is probably plenty of interest in efficiency as a property of theeducational system and further motivation is unnecessary. Levin proceeds touse production isoquartts and output transformation loci to illustrate variouskinds of inefficiency and also to introduce various ways that model misspec-ification can foul up econometric estimates of production functions. Hereone principal point is that productive units that are not using efficienttechniques will not lie on the production frontier and will result in theestimation of a subfrontier production function. A second one is that outputmeasurements may be incorrectly specified (either in one or many dimen-sions) and that spurious inefficiencies or 'second bests" may be perceivedas a consequence of that misspecification.

The next section of Levin's paper presents a long a priori argument insupport of the proposition that schools must be inefficientl The main premiseseems to be that they are unlike private competitive firms in a number ofcritical respects, and without those characteristics educational "firms" haveno basis for achieving efficiency. I find myself quite convinced that theeducation "industry" is poles apart from the straw-man industry which has allthe perfect properties of the competitive model. However, it seems that mostof the real world of productive enterprises share enough of those imperfec-tions to invalidate for them the simpleminded empirical analysis that Levincriticizes for education. Again, I can easily accept the argument that ourpublic schools leave something to be desired in terms of efficiency, but I

197I

Comments by Watts

Harold W. WattsUniversity of Wisconsin

imply that theto manage-

that the realand their inputsppears vacuous

be arrived atbest led to trying

involved.it leads to

bpe of our mea-in order to

b concludes thatn frontier is thease, much moreehavior and theIn my judgment,

n and measure-hough cognitiveortant aspect oftput of schools.ped by Levin, itnfortunately, thee no prices (orunderdeveloped

variable for thisJariables. (The simplere to believe that thes school, its effect onication bias would be

1972.

Economic Review 56

D.C.: Brookings

-J

cannot agree that the contrast other private or public production isparticularly unfavorable.

The other part of the section spells out the limitations of standardizedachievement tests as measures of school output. I fully share all Levin'sreservations here and would welcome any progress toward satisfactorymeasures of neglected aspects, but again, this is a problem of measuringthe outputs of a human-service industry and that is an unsolved problemeverywhere.

The next section explores the GIGO1 production function as applied toeconometric research and derived policy prescriptions in education. Levinis quite persuasive about the various kinds of mischief that can result from azealous application of intermediate theory to the estimated production func-tions for education which have appeared in respectable journals. He ismotivated in this analysis by a belief that there is a real danger of thesehalf-baked conclusions being promulgated by ukasé, and even worse, thatthey will affect school practice.

My own appreciation of how hard it is to get any real change in the wayschools and teachers behave, combined with Levin's own sense about howvaried schools are, both on and off the efficiency frontier, make the threat oflockstep imitation of the latest econometric optimality formula pretty remote.Consequently, I can accept his analysis of what-if-everyone-acted-silly with-out agreeing on the likelihood of the premise.

In the end, Levin pleads for better models—always a popular plea—andsuggests that a "behavioral theory of schools" may be under construction byBowles and Gintis. Clearly one can begin to be relevant once a reasonablycomprehensive concept of the objectives or outputs of schools has beenspecified; and maximum standardized achievement test scores do not fillthe bill. Better models also include more attention to how observations aregenerated and to the implications for econometric estimation. The use ofprogramming techniques to form "envelope" estimates is one possible im-provement and Levin's numerical example shows that it may be of someimportance. Clearly our economic and econometric analyses of the educa-tion industry in general and its production function in particular are verycrude and are not strong enough to support policy recommendations. I ammore optimistic than Levin that the work to date has been harmless and mayeven have been helpful in moving toward more useful models. I am quitepessimistic about the chance of an estimated second derivative ever becom-ing the basis of a universally followed command which will halt or reversethe upward trend of educational costs.

NOTE1. Garbage In Garbage Out.

198 Economic Efficiency and Educational Production