goedhart halberstadt kapteyn vanpraag

THE POVERTY LINE:CONCEPT AND MEASUREMENT*

THEO GOEDHARTVICTOR HALBERSTADT

ARIE KAPTEYNBERNARD VAN PRAAG

ABSTRACT

In this paper, a new approach to defining the poverty line is proposed inwhich family heads are asked what they consider a minimal income levelfor their own family. It was found that the respondents appeared tospecify higher amounts, the greater their actual income and family size,and that the relationship was loglinear. For each family size there is anincome level at which a respondent's stated minimum income is equal tohis actual income. This level is taken as a definition of the poverty line.The poverty line thus defined varies with family size.

/. INTRODUCTION

The primary aim of this paper is to propose a new way of defining the povertyline. As an illustration of our approach, quantitative estimates are developed fora particular case—The Netherlands, January 1975. Our method starts with asubjective approach; We ask a representative sample of people what they con-sider to be the minimum income at which they still could make ends meet. Therespondents' answers are positively related to their own income and to the sizeof their family. For each family size, there is an income level at which the typi-

Goedhart is with the {Central Bureau of Statistics, The Hague, The Netherlands. Halberstadt,Kapteyn, and van Praag are on the faculty of the Economic Institute, Leyden University,The Netherlands.* The research reported in this papei has been supported by grants from the Dutch

Ministry of Cujtural Affairs, Recreation, and Social Welfare and from the DutchMinistry of So4al ACfaiis. The authors are grateful to Robert H. Haveman, MalcolmLevitt, J. L. Nicholson, and anonymous referees for their very valuable comments onan earlier draft. The responsibility for the current text remains with the authors. Theauthors also thank Miss Bemelot Moens and Messrs. Verwey, Berkman, vanMaarseveen,Haimsen, and De Vet for their stimulating help in the preparatory stage of the surveyon which this report is based. [Manuscript received April 1976; accepted December1976.]

The Joumal of Human Resources • XII • 4

504 I THE JOURNAL OF HUMAN RESOURCES

cal respondent's stated minimum is equal to his actual income. This level is takenas a definition of the poverty line. The poverty line thus defined varies withfamily size.

In the following two sections, we review the principal current scientificapproaches to defining the poverty line. In order to determine what subjectivefeelings the respondents attach to various inv ome levels, the concept of tiieindividual welfare function of income is employed, and this concept is explainedin Section IV. In Section V we describe the sample and present some empiricalresults with respect to the individual welfare function of income and the mini-mum income stated by the respondents. In Section VI the poverty line is definedin the way described above. Estimates of the poverty line for Tl.ie .Netherlandsare presented in Section VII, jfn the eighth section we briefly discuss an alterna-tive method, and we present some conclusions in Section IX.

The quantitative outcomes can be refined by complicating tlie modelpresented in Sections V and V.I and by drawing larger ssmples. Therefore, weask the reader to look upon the empirical results priniarily as an illustration ofthe proposed methodology.

//. THE ECONOMIC DEFINITION OF POVERTY

In this paper, we are adopting the so-called economic definition of poverty aspresented in Watts [28]. He considers poverty to be "a property of the indi-vidual's situation, rather than a characteristic of the individual or of his patternof behavior" (p. 321). This viewpoint leads to a definition of poverty as a situ-ation in which the consumption set of the individual is severely constricted,while affluence is defined as a situation in which there is little constriction of theconsumption set. In simpler language, we may say tha: welfare is defined interms of command over real goods and services-conunand over resources, forshort. The less command one has over resources, the less welfare one enjoys; thatis, the poorer one is. Poverty is then defined as a situation where command overresources falls below a certain level, the poverty line.

The economic definition of poverty does .not attach welfare Jevels to aspecific commodity bundle. Because of different tastes, different individuals wE!choose different commodity bundles from a certain consumption set. Thus, thisdefinition does not impose any kind of standard behavior on individuals. Forexample, an individual A who prefers a situation, with a lev/ income and muchleisure is not poorer than individual B who has a high income and not muchleisure whenever the incorne-leisure combination of individual B is attainable forindividual A. Still, the economic definition of poverty involves an element ofinterpersonal welfare comparison since it is assumed that when these two indi-viduals, A and B, ate able to attain the same income-leisure combination, theywill be equally well off.

Goedhart and Others \ 505

The operationalization of the concept "command over resources" causes anumber of problems. The commonly used proxy, animal income, is a very crudemeasure. At a minimum, one would like to consider after-tax rather than before-tax income. In addition, the researcher has to take into account the size of afamily that has to share a given income (compare, for example, Jackson [10],Seneca and Taussig [26], Fiegehen and Lansley [6], Nicholson [16]). Moreover,a family's income is also a reflection of the taste for leisure versus income(Garfinkel and Haveman |7]) . Another problem is that both the human andnonhuman capital: of a family should be taken into account, which necessitatesthe introduction of life-time aspects (see, for example, Weisbrod and Hansen[29] and Habib, .Kohn, and Lerman [8]). Taussig [27] and Plotnick [18] pro-vide a fuller discussion of these and related problems.

In the present paper, we will not consider all the problems mentioned sofar; rather, we will restrict ourselves to a definition of poverty in terms ofcurrent after-tax disposable family income. However, with respect to the prob-lem of properly accounting for family-size differences, our solution will emergefrom the analysis presented in the following sections.

///. DIFFERENT APPROACHES TO THE ASSESSMENTOF THE POVERTY LINE

Assume that for any two individuals in a given society, we are able to identifywhich individual's command over resources is the larger. Tims, we can rank allindividuals in society as to the degree of their "poorness." Do we then also knowwho is poor and who is not poor? Evidently the answer is negative. We still haveto define the level of the poverty line, that is, the level of command overresources below which an individual is poor.

The assessment of a poverty line involves some kind of political decision,for, from the perspective of social policy, the poverty line represents a criterionby which it can be decided which citizens need special benefits from the govern-ment to supplement their own incomes. Hence, we have to analyze under whatconditions and under what premises society is willing to devote special attentionto some of its poor citizens.

We shall look briefly at four different procedures for the assessment of apoverty line. For each, we point out some of the measurement problems in-volved, and we indicate to what extent there must be reliance on some kind ofinterpersonal welfare comparison.

The first approach is to leave the establishment of a poverty line entirelyto politicians. For example, according to Atkinson's definition [1], people arepoor when they are eligible for supplementary benefits from the government.This approach S( ems to involve no measurement problems whatever. Theamount of interpersonal welfare comparison is almost maximal. Politicians


simply decide, intuitively or on the basis of pressure from constituents, when anindividual's circumstances become unbearable.

The second approach is to inquire what a "representative citizen" con-siders to be the minimum level of command over resources. Here the analyses byKilpatrick [12] and Rainwater [23] are of interest. They analyze a number ofGallup polls in which respondents were asked "What is the smallest amount ofmoney a family of four (husband, wife, and two children) needs each week toget along in this community?" The average of the answers to this question canbe viewed as the respondents' perception of what the ievel of the poverty lineshould be. Tlie measurement problems here are of the usual type: possible mis-understanding by the respondent of the proper income concept, interaction be-tween interviewer and respondent, etc. Tlie amount of interpersonal welfarecomparison involved is considerable, as the respondents have to judge what acertain income means for others.

The third approach aims at an "objective" definition of the poverty line.We may call this the "subsistence-level" definition. Tne underlying idea is that ahuman being has certain basic needs which have to be satisfied—food, clothing,housing, etc. .Accordingly, the problem is conveyed to experts who have tomeasure these basic needs. The pioneering study using this approach is byRowntree [24], but perhaps the best-known recent study based on the sub-sistence-level definition is the one by Orshansky [17]. It appears that a numberof arbitrary steps must be taken in measuring basic needs, and it may be saidthat the whole procedure rests to a large extent on interpersonal welfare com-parisons by the experts v/ho have to define the needs. Detailed criticisms of thispiocedu:re .may be found in Rein [2.5] and Atkinson [2j.

A fourtli approach consists of asking people v/hat they consider a rrdnimallevel of income for themselves. The measurement problems are similar to thoseof the second approach, and, in addition, one has 1.o assume that people do notdeliberately misrepresent their preferences. On the other hand, there is less needfor interpersonal welfare comparisons. We will not go into detail here since thisfourth approach will be elaborated in Sections V and VL

Each of the approaches discussed so m involves interpersonal welfarecomparisons. In all of tliem, powrty is defined by a low value of a particularwelfare measure, the main difference being die type of welfare measure used tocompare xhs situation of different individuals, .fa the next section we discussmore explictly the welfare comparisons inherent in rhe definition of the povertyHue.,

IV. THE INDIVIDUAL WELFARE FUNCTION OF INCOME

As a welfare measure, we use the so-called individual welfare Junction of income,introduced and elaborated upon by van Praag [20, 211 and van Praag and

Goedhart and Others | 507

Kapteyn [22] .* This function descrihes the welfare evaluation of income levelsby an individual and is measured by asking him the following question:

In answering the following question it is advisable to start with theunderlined words. Try at any rate to fill in all amounts asked for to thebest of your judgment.

Taking into account my (our) present living circumstances, I wouldregard a net weekly/monthly/yearly (encircle the period) family incomeas:excellent if it were abovegood if it were between andamply sufficient if it were between andsufficient if it were between andbarely sufficient if it were between andinsufficient if it were between andvery insufficient if it were between andbad if it were between _____ andvery bad if it were below

We call this the income-evaluation question.The verbal evaluations (good, sufficient, bad, etc.) are transformed into

numbers on a zero-one scale by identifying these evaluations with equalquantiles. In this way one obtains points on a graph of the individual's welfarefunction. According to the theory outlined in van Praag [20], the answers to theincome-evaluation question will foEow a definite pattern. More precisely, theevaluation of U{z) (on a zero-one scale) of an income z is fairly well approxi-mated by:

(1) U{z) = (l/0^y2i)/MlA) exp|-l/2[ln(r) -M)/a

where A(.;/X,CT) is the lognorriial distribution function with parameters ix and aand N(.,tx,a) is the normal distribution function with mean /i and variance CT^.^The parameters ii and a are estimated from the income-evaluation question foreach respondent separately.^

1 We shall often refer to this measure as the welfare function. When we refer to income,in aU cases we niean disposable family income.

2 In the sequel we use the following properties of the normal and lognormal distributionfunction: N(x;n,a) = N(.x - ii;0,o) = NKx - ix)la;O,l]. So,ifr = exp(;c)(i.e.,x = hi(r)),we have

Denoting the aniount in the left-hand column in the ifh row of the income evaluationquestion by Zf and the corresponding evaluation by U(2f), we obtain a sequence[Z;,t/(z,-)] 5_ . Note that the amount in the ninth row may be discarded since it will beequal to the aniount in the eighth row. According to an information-maximizationargument, the qualification "excellent" is identified with f(z,) = 0.888, the quaUfi-


U(z)

1.00

0.90

0.80

0.70

0.60

0.5Q

0.40

0.30

0.20

0.10

0

/ 0 - 0.40/ R = 8.80

/

I /

/

/

5 10 15

y^ a = 0.40/ % - 9.75

/ «xp{;() =17,180

/ /

/JF

/

/

\

20 25 30 35

Income z

/ ^• xp(jt)

,

4 0

(Dfl.x

= 0.40

= 29,730

45 SO

1,000)

FIGURE 1THE INDIVIDUAL WELFARE FUNCTION OF INCOME FOR SOME VALUES OF ju

(In the present sample the mean value of M is equal to 9.75with a sample standard deviation of 0.33.)

In the present nonstochastic context, the parameters \i and a of the log-normal distribution function have a psychological rather than a statisticalmeaning. These so-called welfare parameters differ between individuals. In theaforementioned papers, a rather extensive interpretation of [i and a is given.

The quantity expOu) is the income level which is evaluated by 0.5 (seeFigure 1). It is the median value of the lognormal distribution function. Jf indi-vidual A has a higher /x (and consequently a higher exp(M)) than individual B,then A needs more income to reach a certain evaluation level than does B. Thequantity exp(/u) has been called the natural unit of income (for a motivation ofthe term, see van Praag [20, p. 37]). It may be viewed as a want parameter.

The parameter a determines the slope of the welfare function around themedian value expOu) (see Figure 2). The smaller an individual's a, the steeper hiswelfare function will be. The parameter a has been called the welfare sensitivity(van Praag [20, p. 38]).*

cation "good" is identified with t^(zj) s 0.777, etc. In general, f/(z,-) = (9 - 0/9 0 = 1 ,. . . , 8). Since f/{z,-) = A'[ln(rj-) - n)la;O,l ], the parameters ti and a can be estimatedfrom the eight points [z,-,t/(ZjO] /s^j.

4 Since a plays only a minor role in the subsequent analysis, we abstain from a furtherinterpretation. We refer to van Praag and Kapteyn [22] for more details.

Goedhart and Others 509

U(z)

10 15 20 25 30Income z

35 40 45 50(Dfl. X 1,000)

FIGURE 2THE INDIVIDUAL WELFARE FUNCTION OF INCOME FOR SOME VALUES OF o

(In the present sample the mean value of a is equal to 0.40with a sample standard deviation of 0.17.)

Over a five-year period, the individual welfare functions of about 13,000indi\dduals were measured from written and oral questionnaires, and a numberof attempts were made to explain the individual welfare parameters [i and afrom the individual's personal and social circumstances. We will discuss theresults of these attempts briefly and only as far as they are relevant to the sub-ject of this papeij In van Praag [21] and van Praag and Kapteyn [22], it wasreported that the following regression equation yielded statistically significantresults:

where/s is the size ofthe family, measured by the number of family mernbersjjis net family incc^me; e is a random disturbance term with zero expectation,distributed identically for each family; and |8o, (3i, 2 are parameters.*'*

5 Henceforth we issume that any measured individual welfare function of income be-longs to the head of the family. Therefore, when we speak of individuals or persons orpeople, we mean family heads, and we assume that the family head's welfare function:represents the family's welfare function.

6 In Kapteyn and van Praag [11], the family-size concept h^s been complicated byweighting family members according to age and rank in the family. In Kapteyn, vanPraag, and van Herwaarden [12], the additional explanation of n by reference-group


The main factors that influence a are an individual's "income history" andthe income distribution in his social reference group. That is, the more an indi-vidual's income has varied over time or the larger the dispersion of incomes in hissocial reference group, the larger his a will be. However, the proportion of vari-ance of a over individuals, which is explained by these factors, is rather small(about 5 percent; see Kapteyn et al. [12] and van Herwaarden et al. [9]). Sincea does not reveal a significant relationship with the variables of interest in thisstudy, y and fs (see Sections V and VI), in the remainder of this paper we shalltreat a as an exogenous variable, fixed at the average sample value 0.40.

V. DESCRIPTION OF THE SAMPLE, MEASUREMENT OF THEINDIVIDUAL WELFARE FUNCTION OF INCOME,EXPLANA TION OF fx

In January 1975 a written survey was conducted among a random sample of2885 Dutch families. The questionnaire contained, among others, the income-evaluation question quoted in the previous section, questions with respect to thecomposition and size of net family income, and the following question:

We would like to know which net family income would, in your cir-cumstances, be the absolute minimum for you. That is to say, that youwould not be able to make both ends meet if you earned less.

In my (our) circumstances I consider the following net familyincome the absolute minimum: per week/per month/ peryear (encircle the period).

The answer to this question wiU be referred to as the respondent's minimumincome (y^mV

After sending reminders and ultimately visiting the families who did notrespond, we obtained a total of 2489 questionnaires (86.3 percent) that were atleast partially completed. Of the 2489 individuals who fiUed in the question-naire, 1748 (61 percent) answered the questions on income evaluation,minimum income, and composition and size of the net family income. In thesubsequent analysis we are concerned only with these 1748 respondents.*

effects has been considered by taking into account a number of social characteristics ofthe individual (such as age, job, education, etc.). As the data to be used in this paper donot allow for the estimation of the parameters that play a role in the complicatedfamily-size concept or the reference-group model, we shall not consider these compli-cations in the present paper, but will confine ourselves to specification (2).

7 Or "minimum income" for short. This tetm should not be confused with the term"statutcMry minimum income" which is the income level guaranteed to almost allpeople in The Netherlands by the Dutch Social Security system.

8 In fact, the sample of 2885 was obtained from respondents to an oral interview withwhom the questionnaire was left behind. Hence some social characteristics, such aseducation and income, of the respondents in the sample of 2885 are knowft. A compar-


TABLE 1STATISTICS CONCERNING THE MEASUREMENT OF THE INDIVIDUALWELFARE FUNCTIONS AND THE RESPONDENTS' MINIMUM INCOMES^

Average exp(/i)Average value of >'^jnAverage incomeAverage evaluation of own current

income, A(y;jx,a)Average aNumber of observations

Dfl. 18,081Dfl. 16,257Dfl. 20,815

0.580.40

Standard Deviation

(6,238)(6,412)(9,225)

(0.22)(0.17)

1748

a AU statistics are averages over all individual estimates. .At the time of the sturvey, aDutch guilder was equivalent to 0.407 U.S. dollars.

In Table 1 we present some statistics on the measurement of the parame-ters of the individual welfare functions and the respondents' minimumincomes.*

According to equation (2), the regression yields:

(3) M = 4.41 + 0.131n(/s) + 0.531nO) R^ = 0.60 N = 1748(0.13) (0.01) (0.01)

The numbers in parentheses are the estimated standard errors of the regressioncoef:Ficients. °

VI. THE DEFINITION OF THE POVERTY LINE

It was argued in Section III that any definition of poverty rests on the notionthat an individual is poor when he experiences a low level of welfare." In terms

ison between the distribution of social characteristics in the sample of 2885 and thesample of 1748 does not reveal significant differences between the samples.

9 There appeared to be some problems with the definition of the income concept in thequestionnaire. In an appendix we describe the problems and present the solution weadopted. This appendix is available from the authors on request: Economic Institute,Groenhovenstrait 5, Leyden, The Netherlands.

10 The estimates are similar to earlier outcomes. For example, the corresponding regres-sion on the sample used by van Praag and Kapteyn [22] yieldsM = 3.S3 + p.l4In(/i) + 0.60In(>') i J ' = 0.63 N = 2952

(0.10) (0.01) (0.01)Van Herwaarden, Kapteyn, and van Praag [9] provide a discussion of the differencesbetween this result and (3).

11 This idea is also advanced by others. For example, Leveson [14] defines poverty as"the existence of a low level of utility."


of the individual welfare function of income, a low level of welfare means thatU(y) = A{}';iJi,d) falls below some prescribed minimum value A°. In other words,

(4) PnO) - ju ] / a<7 i

where 7i follows from

(5) A[exp('yi);O,l]=A<'

The reader will note that according to (4) individuals may not only become poorif their incomes decrease, but also if there is a change in their welfare parametersIX and o. Since o is treated as exogenous, we abstract from differences in oamong individuals. In the following analysis we assign to all individuals identicalas equal to the average a in the sample {a = 0.40).

Taking the value of o for granted, equation (4) suggests that the respond-ent's minimum income (y^jfi), stated in the questionnaire, would follow from

(6) ln(ymrn)-M = To

In other words we conjecture that ln(}>min) will be equal to the respondent'sH plus a constant jo -'

A combining of (6) with (2) suggests that hypothesis (6) might be testedto see whether cti and aa in regression equation

(7) lnO^ ,.„ ) = ao+at ln(fs) + % ln |» + T?

are equal to jSj and ^2 in (2).^^Least-squares estimation of the parameters of ao, a i , and aj in (7) yields

(8) ln0'^,-^) = 3.60 + 0.121n(fs) + 0.601n(j;) .R^=0.57 N=1748(0.15) (0.01) (0.02)

where the estimated standard errors of the parameters have been added inparentheses.'* We see that )3i (see equation (3)) and ai are only one standarddeviation apart. But since P2 and Oj are significantly different, we have toreject (6). That is, the welfare level associated with a respondent's minimumincome is not independent of his actual income.

Subtracting (3) from (8) we obtain'^

(9) lnOmi«) - i" = -0.81 + 0.

12 If poverty is represented by a welfare level under 0.5,7, is negative.13 The variable TJ in (7) represents a random disturbance term, with expectation equal to

zero.14 In order to test whether specification (8) is correct, we have also estimated specifi-

cations where higher order terms in ln(y) were added to the right-hand side of (8).However, the fit did not improve and the regression coefficients of the added termswere insignificant.

15 We have ignored the small insignificant difference between the values of Oj aiid Pj.When regressing [ln(y^i^) - it] directly on lnCv) we obtain

Goedhart and Others I 513

In

In

. r (2)1 , r (1)7I n j y I I n j y | ln(y)

FIGURE 3THE RELATIONSHIP BETWEEN LOG-MINIMUM INCOME

AND LOG-INCOME FOR A GIVEN FAMILY SIZE

In Other words, equations (8) and (9) imply that when the individual's actualincome rises, his minimum income rises as well. The latter quantity increases at afaster rate than the; natural unit, exp(ju).

The welfare evaluation of the minimum income is obtained by inserting(9) in the individual welfare function (1). We obtain

(10) N[lnO>^in) - M;O,a] = iV[-0.81 + 0.071n(y);0,ff]

The average value of (10) in the sample is equal to 0.39 (with sample standarddeviation 0.19). From the positive coefficient of lnCy) on the right-hand side of(10), it follows that the welfare evaluation of the minimum income rises withincome, that is, richer people are more demanding with respect to their mini-

itaO'mm) -" ] = -0.77 + O.O7hiO;) R^ = 0.02(0.12) (0.01)

irhe addition of p. number of socioeconomic characteristics as dummy variables on theright-hand side of this equation does not yield a significant increase in i? ' .


mum income than are poor people, not only in money terms but also in welfareterms.'*

Let us now turn to the problem of how to define a poverty line for thesociety as a whole. Relation (8) shows that individuals' minimum income levelsvary with current income and family size. Can we extract from this diversity ofindividual minimum incomes one poverty line for the entire society? To answerthis question we look at Figure 3 where relation (8) is depicted for a certainfamily size.

Consider an individual with income y^^h His minimum income will beymin ^^^ Figure 3). Suppose he evaluates y^^^ by 0.8 and>'^/„ by 0.45. Nowlet his income fall fromy^^^ t o /W^. Immediately his new income j ^ ^ ^ ^ ^ will beconsidered to be absolutely minimal. However, as time passes he will becomeaccustomed to the new situation and he will realize that he is actually in situa-tion y^'^\ which is quite tolerable. He then will evaluate j'(2) ^y Q g for in-stance, and according to (8) he will begin to consider y^j^ to be the absoluteminimum for him. If his income should fall ftom y^^^ toy^j^,an adaptationprocess would start, similar to the adaptation process that took place when hisincome fell from j<^l) ^^ymin > ^ ' ^ '^^ process stops when 7 =y^in-

Apparently a respondent's perception of the poverty line is distorted bythe fact tJiat his actual income is not equal to his minimum income level. Thereis only one income level,.)/;*;•„, where this misperception does not obtain. There-fore, we take ;-•*,,•„ as our definition of the poverty line.

According to this argument, it seems as if we only honor the opinion ofpeople wlio can just make ends meet, and one may wonder why we included theothers in the sample. It is ob\'ious that we do not know a priori which peoplehave an income equal to y^jn- Therefore we use ail observations to obtainequation (8) and consequently the value of J'^jn in Figure 3. Wlien we excludethose with higher incomes froin the sample, tlie estimation of (8), and conse-quently of jj^j.j^, becomes less reliable. In other words, we need all observationsin order to find out which people's opinion, on minimum income we shouldhonor.

VII. RESULTS

The value of y*J{„ for different family sizes is easily computed from theequation

(11) inCv^ in) = tto + «! (ln(

16 A possible explanation is that individuals with high incomes have relatively largeproportions of comniitted expenditures. For example, they have to pay mortages,whereas lower-income individuals pay relatively low rents (in The Netherlands).


TABLE 2POVERTY LINE FOR A NUMBER OF DIFFERENT FAMILY SIZES

(Standard errors in parentheses)

Evaluation Statutory EvaluationEstimated of Minimum Income^ of Dutch

Level of the Estimated The Netherlands Statutory U.S. PovertyFam:ily Poverty Line Poverty Januaiy 1, 1975 Miaimum Line 1974Size (guilders/year) Line (guilders/year) Income (guilders/year)"

1

2

3

4

5

6

7

7,700(310)

9,510(270)

10,770(290)

11,760(330)

12,580(390)

13,310(450)

13,950(510)

0.33

0.34

0.35

0.35

0.35

0.35

0.35

8,080

11,500

12,340

13,430

14,660

15,960

17,290

0.35

0.42

0.41

0.41

0.42

0.44

0.45

6,130

7,889

9,670

12,378

14,618

16,459

20,278

a These minimums are based on the provisions of the so-called Social Assistance Act (asper Januaiy 1975).

b 1 Dfl. = 0.407 UlS. dollars.

which yields

(12)

In Table 2 we present the y^jn for various values of (fs), with the standarderrors in parentheses below." For comparison, the levels ofthe statutory mini-mum income (also called the legal minimum) in The Netherlands in January

17 Since the parameters Oo > ''i > and cij in (12) contain errors of measurement, 7,^,.^ con-itains errors of measurement as well. Assuming that the vector of estimators of theparameters is distributed according to a multivariate normal distribution, with avariance-covariance matrix which can be estimated from the data, we simulated aiample of 3000 values of the vector (a,,, a,, CKJ ). For each vector value the corre-sponding value was computed according to (1). The standard deviation ofthesample distribution of the simulated values of J'jJ,,- is taken as an estimate of thestandard enor of the estimate of y^fn. The more traditional approach of approximat-ing the standard error ofy^in by expanding the right-hand side of (12), according to aTaylor series (see Cramer [4, p. 96]), yields almost identical results.

516 1 THE JOURNAL OF HUMAN RESOURCES

1975 are listed in the fourth column, and the levels of the U.S. poverty line for1974 (converted to guilders according to the January 1975 exchange rate) in thesixth column. To both the estimated levels of the poverty line and the statutoryminimums, we have added a column of numbers that represent the welfareevaluations of these amounts, according to equations (1) and (2).

It is seen from Table 2 that the Dutch legal mininiurns are well above theestimated values of the poverty line. The standard errors of the latter are smallenough so that the differences between the Dutch legal minimums and the esti-mated values of the poverty line are statistically significant except for a one-person family. The U.S. 1974 poverty line appears to increase far more withfamily size than do the Dutch legal minimums or our estimated poverty lines.

Readers familiar with the literature on family equivalence scales may findthe increase in the estimated poverty line with fajmily size very small. .Apart fromthe fact that the definition of family size as the number of persons in the familyis rathei primitive (we have improved upon tiiis procedure in Kapteyn E-OG vanPraag [II]) , we believe that the moderate increase in>'*;•„ vvith family size is abetter approximation of a constant welfare family equivalence sca;e thsji thevalues usually obtained. Although we recognize that: the life-style and prefer-ences change drastically when, a family size changes from one to two or fionitwo to three, oi..:r smalj estimates of the increase in needs reflect tht fac; dtat thepreferences within the family shift in such a way diat material needs do notincrease very much. For example, a two-person family [husband and wife) maybe accustomed to a life-s:yle which includes relatively high .holiday sxperiditures.When tbe first child is born, the parents decide to spend tlieir holidaj's ai home,thus saving money which may be used to compensate for the additionaJ expendi-tures caused by the increase in family size.

In ou: opinion, substitution possibilities of this kir,<d are net fully takeninto account in rMU&xiX titerature on die family equivalence scale.

VIII. AN ALTERNATIVE METHOD

The values of the poverty line given in the second column of Table 2 followfrom the application of the methodology proposed in Section VI to the data inour sample. Politicians may find the corresponding welfare evaluations in thethird column of the table unacceptable. For example, they may feel that a wel-fare evaluation of 0.35 is too low and that it should be at least 0.40, or 0.45.Obviously, the concept of the individual welfare function in connection withrelation (3) makes it easy to compute the corresponding income levels for anywelfare evaluation specified.

By way of examples, in Table 3 we present the income levels correspondingto the welfare evaluation levels 0.40,0.45, and 0.50.


TABLE 3INCOME LEVELS (GUILDERS/YEAR)

CORRESPONDING TO DIFFERENT WELFARE EVALUATIONS

Family Size

I234567

0.40

9,04010,91012,19013,18014,00014,71015,340

Welfare Evaluation Level

0.45

10,09012,18013,60014,70015,62016,42017,120

0.50

11,24013,57015,15016,38017,40018,29019,070

IXi CONCLUSIONS

We do not present our methodology as a perfect substitute for the otherapproaches to determining a poverty line, as described in Section III, but ratheras a complement to them—a method that could be employed in conjunctionwith one or another of them. The results summarized in Sections VI and VIIshed some light on the measurement problems in these approaches, so let usbriefly respond to all three along with our own.

With respect to the first approach, we observe that the politicians who arecalled upon to determine the level of the poverty line usually earn incomes farabove the J ^ w ™i Fig' ' ® 3. Consequently, following the argument put forwardin Section VI, their perception of what a poverty line really means may beseverely biased. Thus, because they are not poor themselves, politicians may notbe qualified to make any diirect intuitive assessment ofthe poverty line.'^ How-ever, the analysis in the previous section yields a possible alternative for them;although their intuitive perception pf a minimum income in "income space"may be biased, this need not be the case with their perception in "welfarespace." That is, politicians can stipulate a certain minimum welfare evaluationbelow which citizens should not fall. The computation of the correspondingincome levels is then straightforward.

With respect to the second approach, which leaves the decision on the levelof tlie poverty line to a representative citizen, the same objection can be made aswith the first approach. The income of the representative citizen is not equal to

^; hence, his perception also would be biased. Here our analysis prowdes an

18 They may be a^le to make better assessments, however, interacting with their con-stituents, especially those with relatively low incomes.


alternative since, for example, we could ask citizens: "What is the minimal wel-fare evaluation (on a zero-one scale) below which no family in this communityshould fall?" Translating the average of the answers to this question into moneyamounts via the procedure sketched in the previous section is again simple.

The mininium-subsistence-level definition of the poverty line (the thirdapproach) presumably suffers from the same kind of bias as the first two ap-proaches, as the incomes of the experts are usually well above the poverty lineand their judgment as to what is minimally required may well reflect their ownsocial backgrounds. In this connection, we may mention sorne evidence sum-marized by Kilpatrick [13, pp. 331-32]. He observes that the judg.menr.s ofexperts on minimum subsistence rise significantly with average ir!com.e insociety, a finding that highlights a considerable sociocultural component inexperts' judgments. Given this observation, it seems unlikely that, experts couldcompletely divorce themselves from their own circumstances.

The fourth approach is the one that underlies the definition of v,* ,•„ inSection VI, The only value judgment involved seems to be that people them-selves are best qualified to judge what their m.inimal requirements are. Once oneaccepts that value judgment and the analysis presented in Section VI, the level ofthe poveity line readily follows.

Although we want to stress the methodological advantages of iJie approachadopted in this paper, we do not believe that this analysis should be \'iewed asfinal. Our aim was to investigate whether ic is possible to define the concept ofthe poverty line in a simple and operational way. .k. number of aspects-forinstance, wealth and differences between annual and permanent income-werenot considered here, but these and other factors relevant for the definition ofpoverty can easily be built into the model in a manner similar to the way thefamily-size variable was used in our example." Thus many other factors thatinfluence .j ^ j (and therefore y'^in), such as psychological factors (socia) refer-ence group effects, for example), health status, and/or environmental factors(urban o: rural residence) also could be taken into accoiirtt. In fact, any quanti-fiable factor that has a measurable effect on the individuai's welfare parameter n(and tluu; presumably ony^m ^'^ *' ') might be incorporated into the definitionof the poverty line..

REFERENCES

1. A. B. Atkinson. Poverty in Britain and the Reform of Social Security.Cambridge, England: Cambridge University Press, 1969.

2. . The Economics of Inequality. Oxford: Clarenddn Press, 1975.3. Kenneth E. Boulding, M. Pfaff, and A. Pfaff, eds. Transfers in Urbanized

19 Of course, the relevance of famUy composition has been studied earlier (see, e.g.,Fiegehen and Lanslay [6]), but in a different manner.


Economy. Belmont, Calif.: Wadsworth Publishing Co., 1973.4. J. S. Cramer. Empirical Econometrics. Amsterdam: North Holland Pub-

lishing Co., 1969.5. Louis A. Feiman, Joyce L. Kombluh, and Alan Haber, eds. Poverty in

America. Ann Arbor: University of Michigan Press, 1968.6. G. C. Fiegehen and P. C. Lansley. A Note on Household Size and Income

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9. F. G. van Herwaarden, A. Kapteyn, and B. M. S. van Praag. "TwelveThousand Individual 'Welfare Functions of Income: A Comparison of SixSamples in Belgium and The Netherlands." European Economic Review(forthcoming).

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14. Irving LevesOn. "Strategies Against Urban Poverty." In Transfers inUrbanized Economy, eds. K. Boulding et al. Belmont, Calif.: 'WadsworthPublishing Co., 1973. Pp. 131-59.

15. Daniel P. Moynihan. On Understanding Poverty. New York: Basic Books,1968.

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goedhart halberstadt kapteyn vanpraag

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