Household production, time allocation, and welfare in Peru

Policy, Research, and External Affairs WORKING PAPERS Women In Development Population and Human Resources Department The World Bank September 1990 WPS 503 Household Production, Time Allocation, and Welfare in Peru John Dagsvik and Rolf Aaberge Simulation exercises suggest that it is difficult to reduce in- equalities in per capita consumption by changing wage and education policies. -.9A The Policy, Research, and External Affairs Complex distributes PRE Working Papers todiss5cninate the findings of work in progress and to encourage the exchange of ideas among Bank staff and all others interested in developmcnt issues These pap 5s cary the names of the authors, re:lect only their views, and should be used and cited accordingly. The findings, interpretations, and conclusions are the authors' own. They should not be attributed to the World Bank. its Board of Directors, it. management, or any of its member countries.  Policy, Fesearch, and External Affairs Women In Development WPS 503 This paper - a product of the Women in Development Division, Population and Human Resources Department - is part of a larger effort in PRE to determine if and how women's productivity (and thus family welfare) are improved when women are given more access to education, extension, training, credit, healthcare, and otherpublic resources. Copiesare available free from the World Bank, 1818 H StreetNW, Washington, DC 20433. Please contact Maria Abundo, room S9-125, extension 36820 (46 pages with figures and tables). Dagsvik and Aaberge use data from the Peruvian work. Women's eamings contribute about 17 Living Standard Survey (PLSS) to analyze (1) percent of consumption. inequality in the distribution of income, (2) men and women's participation in the labor market But consumption and welfare are consider- and variations in their work hours, and (3) the ably less equally distributed than hours of work. relationship between variations in the labor supply and income inequality. Proportional wage changes have only a small effect on behavior. Remarkably, wage increases Their purpose: to study the effect of changes also have little effect on the unequal distribution in education and wage rates on production, of per capita consumption. Even when wage consumption, and allocation of time. For rates are increased by the sane amount the example, how many men and women would indirect effect is small - but the increase does participate in wage work if education were moderately reduce the inequality in distribution increased? How would policy changes affect the of per capita consumption. mean level and degree of inequality in the distribution of economic welfare? Dagsvik and Aaberge use a decomposing method to analyze income inequality. They use They conclude: a structural neoclassical model to analyze household production, consumption, welfare, Entrepreneurial income is the most important and allocation of time. They use per capita (or source of income in rural and other urban areas. per adult equivalent) household income or Male wage eamings contribute almost 40 percent consumption as an indicator of welfare. of the household's consumption, which seems to reflect their share of total household hours of The PRE Working Paper Scries disseminatcs thc findings of work undcr .-ay in the Bank's Policy, Research, and Extemal I AffairsComplex. An objectiveofthcseries is to getthese findings outquickly, even ifpresentations are less than fully polished. i The findings, interprctations, and conclusions in these papers do not necessarily reprecrnt official Bank policy. Produced by the PRE Dissemination Center  CONTENTS Page 1. Introduction ......................................................... 1 2. Labor market activty, income formation and welfare ..... ................... . 4 2.1 Measurement and decompositlon of inequaRty .......................... . 4 2.2 Inequality In distributions of hours of work for females and males ................................. 7 2.3 Inequality In distributions of consumption for households ........ .. .......... 10 2.4 Inequality In distributions of per-capita household consumption ...... .. ........ 14 3. The econometric framework .............................................. 16 3.1 Theoretical model ....................... ........................ 16 3.2 Model specification ................................. ......... 19 4. Summary statistics and parameter estimates ................................... 22 5. Policy simulation results for Uma .......................................... 28 5.1 Wage effects ......................... ......................... 29 5.2 Education effects ....................... ........................ 32 6. Conclusion ......................................................... 35 References .........................I..............I........37 Appendix 1. Estimates of Inequality based on the Gini-coefficient. 38 Appendix 2. Deflnhtions of main variables ..39 Appendix 3. Figures relating to observed and simulated distributions of key variables ..41  HOUSEHOLD PRODUCTION, TIME ALLOCAnlON, AND WELFARE IN PERU 1. Introduction This paper uses the Peruvian Living Standard Survey (PLSS) data to analyze (a) inequality in the distribution of Income, (b) labor market participation of men and women and the variations in hours of work, and (c) the relation- ship between variations In labor supply and Income Inequality. We use a decomposing method to analyze income Inequality. Furthermore, we utilize a structural neo-classical model to analyze household production, consumption, time allocation and welfare. The purpose Is to study the effect on production, consumption, and time allocation of changes in education and wage rates. For example, how many men and women would participate in wage work if education were Increased? And how would policy changes affect the mean level and the degree of inequality in the distribution of economic weffare? Most of the available information on economic Inequality in developing countries refers to the distribution of Income among eamers. Although this Information constitutes an important element for understanding the labor market and the related distribution of income, it is less helpful In the analysis of inequality as a welfare issue. A more relevant indicator of welfare is per capita (or per adult equivalent) household income or consumption. This paper uses this Indicator in an analysis of economic inequality. Our methodological approach is based on a summary measure of inequality which is closely related to the Gini coefficient. The essential difference is that our proposed measure of inequality gives more weight than the Gini coefficient to transfers related to the veiy poor. Based on the estimates of an econometric model of production, consumption and time allocation, we have examined the Impact of changes in wage rates and education on economic inequality. In particular we demonstrate how female labor and education affect economic inequality among households. The structural econometric model we develop and estimate Is convenient for simulating certain types of policy experiments. It is of particular interest to apply empirically founded behavioral models to assess the labor supply response and the corresponding Impact on economic welfare from various policy measures. SpecHfically, given similar economic cond-tions in Peru as of 1985, our study suggests what we may be able to achieve, and how, for example, different measures would affect economic inequelity. The theoretical model Is based on the neoclassical model for consumption and time allocation. Provided the data are not corrupted by measurement error, this framework is useful since: * No one can spend more than his or her income. (In other words the budget constraint plays a role.) * There is also a time constraint of 24 hours a day.  -2 - it is reasonable to assume that people are not indifferent with respect to different levels of lelsure and consumption. Thus we introduce the notion of preferences and represent them by utility indexes. In standard models of labor supply the decision-maker Is assumed to maximize utility with respect to leisure and consumption (subject to the budget constraint). One objection to this framework, however, Is that individuals and households in developing countries can hardly be viewed as having full freedom of choice. On the contrary their job and production opportunities are often severely constrained. An Individual's opportunities are influenced by education and experience, by the sinicture of the economy, and by govemment and sector-speclffc policies. Thus It Is crucial that a realistic economic model of household behavior accommodate variations in opportunities across households. The econometric model used in this study differs somewhat from the standard models in that the undertying decision variable Is latent and Is denoted position. By position we mean a particular combination of market and nonmarket activities, such as agricultural production combined with work In a wage-eaming job. A position is characterized by specific attributes, like type and level of output and input factors, hours of work, wage rates, and so on. These attributes are assumed fixed, given the positon. The choice problem Is viewed as one In which the household selects the best package, of attributes from a set. This choice set Is known to the household but Is unobservable to econometriclans. The set of household-specHifc feasible posiions Is represented In the model by a distribution functlon called the oPoortunitv distribution (density). The opportunity density represents an aggregate measure of choice opportunities and it Is defined as the fraction of positions with specffied levels of attributes that are feasible to the household. For example, if the attributes are job-specific hours, wages, and profits In own-farm production, the opportunity density measures the amount of positions with a specific level of wages, hours, and profts that Is feasible. Due to unobserved heterogeneity in opportunities across households, it is natural to Interpret the opportunRty density as a grobabillty density. Specifically, it is the pr ~bability that a particular posiion-specific combination of attributes is feasible to a (randomly selected) household.11 The econometric model Is simultaneous in consumption, hours of work, wage rates, and proft condRitonal on family size and schooling. By conditional we mean that we have specified a conditional density for chosen hours of work, consumption, wage rates, and output given the chosen family size and schooling. Thus the model Is consistent with the notion of simultaneous choice In all the attributes including schooling and family size. 1 This approach was developed and applied by Dagsvik (1988) and Dagsvik and Strom (1989), and it is related to the models developed by McFadden (1973) and Ben-Akiva and others (1985).  -3 - While the Introduction of the opportunity ciistribution In addition to the specification of a household utility function Is appealing, It raises problems of functional form and the identffication of parameters of the opportunity density and utility function. Even if these parameters cannot be fully identified without strong assumptions, tl a formulation has the advantage in that It suggests a natural and convenient way of taking into account unobserved heterogeneity In opportunities and introduces variables for Individual qualifications as well as variables that characterize the community and the environment. At this stage the opportunity density Is specified as a function of the indMidual's education. Specifically, the fraction of feasible wage work positions is specified as a function of years of schooling. Similarly the fraction of nonagricultural self-ernpi-yment postlions Is specified as a function of level of schooling. This enables us to simulate the effect of Increased education on the allocation of time in different sectors while keeping wage rates and preferences tfxed. We can also study the effect of schooling through Increased wages while keeping the opportunity density fixed. The labor supply functions that correspond to the util:ty function are not linear In the parameters But our assumptions imply convenient expression for the probability distribution of (observed) consumption and labor supply. This distribution is a function of the parameters of the utility function and it is used in a maximum likelihood estimation procedure. Once the parameters of the utility function have been estimated, we can simulate individual household response. This paper Is organized In the following way. Section two presents a brief discussion on the methodology of measuring economic Inequditv and then applies the methodology on observed distributions . rs of work, household Income, and per capita income as a measure of welfare. Section three outlines the structural econometric model. Section four reports the estimation resufts for the econometric model. Section five discussas the policy simulation results. The resuits are summarized and policy implications discussed In the concluding section of the paper. 2. Labor Market Activitv. Incomne Formation, and Welfare This section supplements the information on labor market activity and distribution of weltfare reported In Newman (1987) and Glewwe (1987). One objective Is to examine the relative differences in hours of work among employed males and females by estimating the inequality in the actual distribution of hours of work. For this purpose we employ a Gini-related measure of inequality, which also represents our basis for studying the distribution of income and welfare. Second, we identify the contribution from wage work, agricultural self-employment, nonagricultural self- employment, and unpaid fe- v work to the distribution of hours of work by employed males and females. More  4.- precisely we decompose the Inequality In the actual distribution of hours of work. We use a similar approach to assess the contribution of wage eaming- of males, females, and children to the level of inequalky in the distribution of household consumption. In this way we obtain Important Information about economic structure and the functioning of the labor market. This information Is, however, less nelp .i the ana.ysis of economic inequality from a welfare perspectve. A more relevant Indicator of welfare Is per capita household Income, which also constitutes the basic variable In our study on welfare. 2.1. Measurement and Decomoositlon of Ineaualitv A common approach for measurlng Inequality In distributions of Income Is to employ the Gini coefficient, which satisfes the principles of scale invariance and transfers. The principle of scale invariance states that inequality should remain unaffected n each Income is altered by the same proportion and t requires, therefore, the Inequality measure to be independent of the scale of measurement. The principle of transfers implies that If a transfer of Income takes place from a richer to a poorer person without changes in the relative posAions, the level of inR-ualiky diminishes. The reader is referred to Sen (1972) for a more comprehensive discussion of the normative implications of different measures of Inequwlity.  -5- Th.e Gini coefficient (G) is related to the Lorenz curve (L) In the following way 1 (2.1) G = 1 t1-2L(u)Jdu. 0 The Gini coefficient offers a method for ranking distributions and quantifying the dffferences In inequality between distributions. This strategy, however, suffers from certain Inconveniences. Evidently no single measure can reflect all aspects of inequality of a distribution, H can only summarize it to a certain extent. Consequently, It is Important to have aitematives to the Gini coefficient. As pointed out by Atkinson (1970), the Gini-coefficient assigns more weight to transfers In the centre of an unimodal distribution than at the tai s. As an altemative to the Gini coefficient, we will employ an Inequality measure - the A-coefficient - that assigns more weight to transfers at the lower tall than at the centre and the upper tall. The A-coefficient (see Aaberge 1986) has a similar geometric Interpretation and relation to the Inequality curve M defined by (2.2) M(u) =E iXX s Fu.l, o u s 1, EX as the Gini-coefficient has to the Lorenz curve. Here X has distribution function F. The A-coefficient Is defined by 1 (2.3) A = 1 [1-M(u)]du. 0 If X is an income variable, then M(u) for a fixed u expresses the ratio of the mean income of the poorest 100u percent of the population to the mean income of the population. The egaiitarian line of the Lorenz curve is the straight line joining the points (0,0) and (1,1). The egaiitarian line of the M-curve Is the hlorizontal line joining the points (0,1) and (1,1). Thus the universe of M- curves Is bounded by a unit square, while the universe of Lorenz curves is bounded by a triangle. Therefore, there is a sharper visual distinction between two dtfferent M-curves than between the two corresponding Lorenz curves. Note that the M- curve will be equal to the diagonal line (M(u)=u) i and only n the underlying distribution is uniform (0,a) for an arbritary chosen a. The A-coefficient then takes the value 0.5, while the maximum attainable value is 1 and the minimum attainable value Is 0. Note that M(u) = L(u)/u, which implies 1 (2.4) A = 1-_L(u du . u 0  -6- Alternative expressions for G and A are given by -0 ye (2-5) G = r r (y-x)dF(x)dF(Y) EX r y(2F(y)-1)dF(y) 0 0 0 and e y e (2-6) A= 1 rr i =Jx EX J A F(y) dF(x)dF(y) y E Y(1+lo9F(y))dF(y), 0 0 0 respectively. Given the inequality In the distribution function F measured by A or G, the next step Is to Iderify the sources tilat make substantial contributions to the Inequality. Assume that the mair variable X is the sum of s dffferent factor components, (2.7) X = z X 1=1 According to Aaberge (1986), A and G satisfy the following decomposition rules (2.8) A = A _ 1=1 IL where L /it is the ratio between the means of X. and X, respectively, and ai iS, loosely spoken, the conditional A- inequality of factor I given the units rank order in X. Analogously, s iL (2.9) G = z _ Y i=1 I where YL related to G has a similar interpretatio' aS aL related to A. Notice that a, and YL are measures of Interaction between factor 1, X., and the sum X. Assume for example that ii > 0. Then, a negative value of al cr Y. expresses negative Interaction and means that factcr I has an equalizing effect on the inequality in the distribution F of X. A positive value expresses a disequalizing effect on the inequality In F. For t, < 0, then positive values of a, and YL express an equalking effect on the inequality in F. For ILL < 0, then positive valr es of a. and Y. express an equalizing effect on the inequality in F. 2.2. lnep liitv in Distributions of Hours of Work for Males and Females  -7 - In this section we focus on the distribution of hours of work among employed persons. The objective is to estimate inequality In distributlons of hours of work, I.e., elative dffferences in hours of work among employed persons. A similar study for children and households is reported in Aaberge and Dagsvik (1990). Table 1. Employment Rates, Annual Mean Hours of Work and A-inequality In Distributions of Hours of Work for Males and Married and Unmarrieri .emales, by Region Females Males All Married Unmarried Em- An- Em- An- Em- An- Em- An- ploy- nual ploy- nual ploy- nual ploy- nual ment mean A- ment mean A- ment mean A- ment mean A- rates hours inequality rates hours Inequality rates hours Inequality rates hours inequality Peru .82 2,351 .396(.004) .64 1.746 .b21(.004) .69 1,728 .521(.005) .57 1,775 .521(.006) Lima .77 2,356 .398(.008) .51 1,594 .569(.008) .55 1,580 .586(.011) .47 1,611 .547(.012) Other urban .76 2,286 .434(.008) .56 1,656 .563(.007) .62 1,613 .573(.009) .49 1,717 .546(.011) Rural .91 2,388 .370(.006) .79 1,8S8 .467(.005) .81 1,344 .455(.066) .75 1,912 .483(.008) Note: Numbers In parenthesis are standard deviations. 1 able 1 examines regional employment and regional distributions of hoirs of work for employed rr ales and females aged 15-702'. The participation rates for males and females are considerably higher in rural than in urban areas. Rates for married females are higher than those for unmarried females, perhaps due to an income effect. Females In rural areas work consL.erably longer than females in urban areas. Males also work longer in rural areas, but the differencr is less significant. The figures In table 1 may cover large Individual differences in hours of work. We now employ the A-coefficient as a measure of the relative differences in hours of work (see section 2.1); corresponding results based on the Gini coefficient are given In Appendix 1. The estimates of the A-coefficient are displayed in table 1. The inequaliy estimates show large Individual variations in hours of work, particularly among females. Except for rural women, the inequality in the distribution of hours of work is significantly higher than i the Individual hours of work were generated randomly, I.e. trom a uniform (O,a) diLtribution for an arbftrary a. There are not, however, significant discrepancies In inequality between the distribution of hours of work for married and unmarried females. Inequality is lowest in the rural area for both males and females. 2/ Individuals are classified as employed i they worked one hour or more during the seven days or 12 months prior to the survey. The definition and measurement of annual hours of work are reported in Appendix 2.  8 - The observed distribution of hours of work Is the resut of a process where the ir,dividuals make decisions on hours of work In each sector simultaneously. The sectors are dafned as (1) wage work, (2) nonagricultural sel- employment, (3) agricultural self-employment, and (4) unpaid family work. By decomposing the overall Inequalky In the dstrIbutlon of hours of work wih respect to these sectors, we obtaln information about ths contribution of each sector to the overall Inequality. (it Is understood that the behavioral labor market adjustments are given). By applying the decompsition method for the A-zoefficient, we obtain the results In table 2. For females the first and third column (second and fourth for males) give the relative contribution from each sectoi to overall Inequality and to total hours of work, respectively. The ffth and sixth column give the Interaction ;oefficients. The positive ir, :atction coefficlents demonstrate that each sector has a disequalizing Influence oii the distribution of hours of work h. each region. Note that the sectoral contriiution to overall Inequality for females Is equal to the prod-cts of the figures In columns three and five divided by 100. Consequently, the sum of the first four sectoral Inequality contributions fc: females In table 2 Is equal to the overall inequalIty (0.521) in the distribution of hours of work for females In Peru.  .9.- Table 2. Decomposition of the Ainequallty In Distributions of Hours of Work for Females and Males, With Respect to (1) Wage Work, (2) Nonagricultural Sel-Employment, (3) Agricultural Self-Employment and (4) Unpaid Family VWork, by Region Sectoral fraction Sectoral ftractlon Region (level of of overall lnequa. of total hours of Interaction Inequality for Employment litv (2ercent) work (percent) coefflcient females and malss) sector Female Male Fem-;a Male Female Male 1 21.9 39.9 22.0 42.9 0.518 0.368 Peru 2 28.5 27.2 24.1 20.3 0.618 0.531 (0.521) 3 7.5 17.7 7.8 16.1 0.501 0.435 (0.396) 4 42.1 15.2 46.1 20.7 0.476 0.292 1 53.2 58.3 52.8 66.6 0.573 0.348 Uma 2+3 37.8 40.4 33.0 29.8 0.653 0.539 (0.569) 4 9.0 1.3 14.2 3.6 0.360 0.144 (0.398) 1 25.4 44.7 26.1 50.4 0.547 0.385 Other urban 2+3 53.8 50.7 45.8 39.4 0.661 0.558 (0.563) 4 20.8 4.6 28.1 10.2 0.417 0.195 (0.434) 1 8.6 26.8 7.5 24.4 0.536 0.403 Rural 2 13.1 8.3 11.2 6.8 0.543 0.451 (0.467) 3 13.2 35.2 13.6 31.9 0.455 0.409 (0.370) 4 65.1 29.7 67.7 36.9 0.449 0.298 Note: Fraction of overall Inequality = Fraction of total hours of work) x (I:lteraction coefficient) Overall inequalIty Example: Wage sectors fraction of overall inequality for females in Peru 22.0 x 0.518 - ____ = 21.9 0.521 According to table 2, wage work plays a predominant role for males and females In Uma and for males In other urban areas. In rural areas males and females work mainly in the agricultural sector, but the wage work accounts for almost 25 percent of the total hours of work for rural men. The large Interaction coefficients In table 2 suggest that females with long total hours work more hours In each sector than females with short total hours of work. To a certain extent thIs conclusion Is also valid for males. For males, however, there is a weak Interactin between the hours worked as an unpaid family worker and total hours of work. Tnis means that males with short total hours of work do neai1y as much unpaid family work as males with long total hours of work. Note that the sel-employment sectors have the largest Interaction coefficients, which  - 10 - implies that these sectors make the largest contributions to the observed differences in hours of work among males and females. 2.3. Inequality In distribution of household consumotion This section deals with measurements of economic inequality. Such studies depend on the definition of Income, the unit of observation, the period of time over which the chosen Income variable Is measured, and a summary measure of inequality. We define the basic Income variable as consumption defined as: 31 consumption =z wage eamings + z net entrepreneurial Income + z other income. In this definition savings are included in consumption. Note that consumption of home-grown food and other In-kind Income Is given a monetary value so that net entrepreneurial Income include consumption of these iems. The basic unit of observation is the household and the reference period is one year. The Z' in the definition of consumption means sum over all persons who lived In the household during the year in question. As a supplement to the Information on individual variations in hours of work given in section 2.2 we give estimates of the A-coefficient for the regional distributions of hours of work among households: Other Peru Uma urban areas Rural areas 0.487 0.497 0.492 0.458 (0.004) (0.009) (0.008) (0.006) (Standard deviations In parenthesis) The figures for Lima and other urban areas are approximately equal to the inequality in a uniform (O,a) distribution. When we plot the respective underlying inequality curves, however, we find that households In the lower and upper tails of the observed distribution have longer hours of work than In the uniform (O,a) distribution. As for the distribution of hours of work among individuals (see table 1) the Inequality in the corresponding distribution among households is lowest in rural areas. In spite of large inequality In the household distribution of hours of work, we cannot automatically ascertain the immediate implication for the Inequality In the corresponding distribution of household consumption. The distribution of consumption is the resuft o' preferred hours and offered wages and prices, and will therefore depend 3/ See appendix 2 for details.  - 11 - on the wage rate, the returns to self-employment activities, the hours of wage work and self-employment, and nonlabor Income as well as the Interdependence among these variables. For example, i households with high retums to self-employment activities work longer hours than households with low returns to their self-employment activities, and if In additlon there exists a positive relationship between wage rates and the household's hours of work in the wage sector, then we must expect more Inequality in consumption than In the distribution of hours of work. Table 3 shows mean and median household consumption and inequality In the distribution of consumption among households. Note that these estimates are based on fewer observations than the estimates used in tables I and 2 because we have excluded households with observed negative net entrepreneurial Income. The large figures of the A-coefficient In table 3 reveal extreme Income inequality. The mean consumption of the richest 5 percent of the households is 128 times the mean consumption of the poorest 50 percent of the households, and 1,355 times the mean consumption of the poorest 10 percent. Table 3. Mean and Median DistributLIon of Household Consumption (in intis), and A-Inequality Among Households, by Region Other Peru Lima urban areas Rural areas Number of observations ..... 4,622 1,287 1,316 2,019 Mean . .............. 42,500 40,120 71,104 25,373 (10,066) (2,250) (32,912) (8,273) Median ................ 11,433 22,344 15,660 4,423 A-inequality ...... ...... 0.864 0.680 0.892 0.895 (0.033) (0.016) (0.049) (0.034) Note: In intis (Peruvian Currency) at june 1985 prices. Standard deviations In parenthesis.  . 12- Table 4. Mean Consumption for Households Uving In Peru by Deciles Decomposed with respect to Females, Males and Chilcrens Wage Eamings and with respect to the Households Net Entrepreneurial Income and Other Income Decile Decile specific specfic Decile specfic mean mean net mean of Decile Mean wage eaminas for entrepreneurial other household Females Males Children income Income consumption (15-70) (15-70) (7-14) for households I ................. 397 13 40 2 324 18 2 ................. 1,700 80 222 15 1,296 87 3 ................. 3,443 192 793 27 2,268 163 4 ................. 6,077 387 1,964 42 3,270 394 5 ................. 9,478 884 3,634 29 4,203 718 6 ................. 13,643 1,367 6,086 63 5,244 883 7 ................. 19,082 1,741 8,220 35 7,630 1,456 8 ................. 27,073 4,665 10,902 214 10,723 1,924 9 ................. 41,140 4,718 15,592 53 16,970 3,807 10 ................. 302,982 20,460 31,874 326 242,670 7,651 All ................. 42,500 3,315 7,948 85 29,461 1,691 Note: Intis at June 1985 prices. The results In Table 3 show that the Inequality In the distribution of consumption Is considerably higher In rural areas than In Uma, even though hours of work were more equally distributed In rural areas. To obtain Information on why inequality varies across distributions, we will examine the Impact of different income sources on overall Inequality. By dacomposing the inequaliy in the actual distribution of consumption by males, females, and children's wage earnings, and by households' net entrepreneurial Income, we may see why the consumption distributions differs across regions. By applying the decomposHion method for the A-coefficient, we obtain the results In table 5. The Interpretation Is analogous to the Interpretation of table 2. To give an Impression of the variations behind the coefficients for Peru In table 5, table 4 displays mean household consumption by deciles, corresponding meani earnings for males, females, and children, mean entrepreneurial household Income and mean other income for each decile. Since the decile-specffc mean wage earnings for females Increases wHth Increasing deciles, the corresponding Interaction coefficient takes a large posHitve value, which Is In accordance wHh the estimate (0.842) In table 5. But If the decile-specHfic means are equal, then the corresponding Interaction coefficient would become zero or approximately zero.  - 13 - Table 5. Decompositlon of the A-inequality in the Dlstribution of Consumption by Males, Females, and Children's Wage Income, and by Net Entrepreneurial Household Income Plus Other Income, by Region. Fraction of Fraction of Region Income overall In- consump- (Level of (consumption) equality tlon Interaction inequality) factor (percent) (percent) coefficient Females (15-70) wage eamings 7.6 7.8 0.842 Males (15-70) wage eamings . 16.0 18.7 0.742 PERU (0.864) Childrens (7-14) wage eamings 0.1 0.2 0.635 Households net entrepreneurial income .72.7 69.3 0.906 Other Income .3.6 4.0 0.767 Females (15-70) wage eamings . 18.5 17.0 0.741 Males (15-70) wage earnings . . 35.9 39.5 0.618 UMA (0.680) Childrens (7-14) wage eamings 0 0.1 -0.076 Households net entrepreneurial income .38.2 34.9 0.744 Other income .7.4 8.5 0.596 Females (15-70) wage earnings . 5.1 5.6 0.805 OTHER Males (15-70) wage earnings 8.1 11.5 0.629 URBAN (0.892) Childrens (7-14) wage eamings 0.1 0.1 0.741 Households net entrepreneurial Income .84.8 80.2 0.943 Other Income .1.9 2.6 0.665 Females (15-70) wage eamings . 2.2 2.4 0.829 Males (15-70) wage earnings . . 9.7 10.9 0.795 RURAL (0.895) Childrens (7-14) wage earnings 0.3 0.4 0.774 Households net entrepreneurial Income .85.7 84.1 0.911 Other income .2.1 2.2 0.866 Male wage eamings in Uma provide almost 40 percent of household consumption which is attained at the expense of about 43 percent of the households total hours of work In wage employment by male members of the household. For females, the corresponding figure is about 17 percent, whichi reflects 17 percent of the households hours of work. However, despite the fact that this particular structure In the distribution of hours of work among households is maintained in the distribution of consumption among households, consumption Is cons'rderably more unequal than hours of work. The explanation is that the Interaction coefficlents referring to the consumption distribution for Uma, given In table 5, are considerably larger than the corresponding interaction coefficients related to the distribution of hours of work reported in Aaberge and Dagsvik (1990). This resuit Is due to skew distributed wage rates and a positive correlation between wage rates and hours of work. By applying a particular non-linear decomposifton method (not reported here) we also found that the wage rates contributed more strongly to Inequality in the distribution of household consumption than hours of work in the wage sector. These effects are stronger for females than for males.  - 14 - Note that the Interaction coefficient for children's wage earnings in Lima Is weakly negative, which moans that children's wage earnings have a modest equalizing effect on the distribution of consumption among households. This effect Is In contrast with the effect of children's wage work on the inequality of tne corresponding distribution of hours of work and is mainly due to nonworking children of rich households with low or medium total hours of work. In both cases the children's contribution to overall inequality is of minor importance, as shown In the first column of table 5. In contrast to the results for Lima, wage eamings in other urban areas yield a modest contribution to total household consumption, compared to the contribution of the household's hours In wage work to the households total hours of work. The fractions are, respectively, 17 and 40 percent. For the same reason as for Lima the Interaction coefficients related to the distribution of consumption are considerably larger than the corresponding interaction coefficients for the distribution of hours of work. Similar results hold for the rural areas, although the distribution of household consumption seems to a greater extent to reflect the distribution of household hours of work. 2.4. Inequality in Distributions of Per-Capita Household Consumption The information in section 2.3 about the economic structure of the labor market must be Interpreted cautiously when analyzing welfare because of the variations In household composition and size. To allow for the fact that some households have several persons while others have just one, we need an aternative to household consumption as an indicator of welfare. Clearly, an Index of welfare using the information on household size and composition is required. In the PLSS data an equivalence scale accounts for this heterogeneity. Specifically, the costs of children are specified in terms of fractions of one aduft. The weights are 0.2 for a child under 7 years old, 0.3 for a child aged 7 to 12, 0.5 for a child 13 to 17, and 1 for a person over 17. The sum of these weights for each household is used as the scale. Consumption per capita is defined as household consumption relative to the equivalence scale and it is used as an indicator of household welfare. Note that these weights are consistent with the weights estimated for Sri Lanka and Indonesia by Deaton and Mullbauer (1986) and have been applied by Glewwe (1987X in analyzing the distribution of welfare in Peru In 1985.86. Glewwe's analysis is based on expenditure data rather than on income data. The lack of sufficient data makes it impossible to distinguish consumption levels among members of the household. Therefore we have to assume that the welfare level of an individual is equal to the per capita consumption of the household. It is particularly interesting to examine the relationship between the distribution of per capita household consumption among households and the distribution of per capita household consumption among persons.  Table 6 shows average welfare levels for Lima, other urban areas, and rural areas. The figures show considerable differences in welfare between adults and children, and between urban and rural areas. The large differences between corresponding medians and means indicate extremely skewed distributions, which are confirmed by the estimates of the A-coefficient In table 7. Table 7 shows only insignificant differences In inequality across per capita household consumption among households and persons. This Is in line with the results reported by Berry (1988). More surprising Is the finding that the inequality in per-caplta household consumption dfffers little from Inequality in the corresponding distribution of total household consumption (compare tables 3 and 7). This result is due to an extremely unequal distribution of consumption (Income) In Peru In 1985-86. Glewwe (1987) reports that this was also the case in 1966, when the Gini- coefficient for per capita income inequality among persons was 0.666. We estimate the Gini-coefficient of the distribution of per capita household consumption among persons in 1985-86 to be 0.789 (see Appendix 1, table G3). Table 6. Mean and Median Per Capita Consumption Among Persons by Sex, Age, and Region Other Popula- Peru Lima urban areas Rural areas tion Mean Median Mean Median Mean Median Mean Median All ............... 11,692 3,332 10,668 5,983 19,139 4,190 7,454 1,404 (24,126) (6,541) (6,952) (10,633) Females ........... 13,282 3,508 10,406 6,036 25,154 4,143 6,654 1,332 (7,376) (2,256) (2,185) (2,935) Malee ............. 12,207 3,820 11,529 6,418 20,013 4,423 7,097 1,516 (7,004) (2,090) (2,054) (2.860) Children4' .......... 10,118 2,965 10,1V8 5,404 13,630 3,945 8,150 1,380 (9,746) (2,195) (2,713) (4,838) Note: Intis figures at June 1985 prices. Number of observations in parenthesis. 41 Less than 15 years old.  - 16 - Table 7. A-inequality In Distributions of Per Capita Consumption Among Households and Persons, by Region Other urban Peru Lima areas Rural Households ........ .857 .676 .881 .895 (.029) (.017) (.048) (.032) Persons .......... .856 .662 .883 .888 (.014) (.008) (.021) (.016) Note: Standard deviations in parenthesis. 3. The Econometric FramnwAork of a Structural Neoclassical Model 3.1. Theoretical Model This section focuses on the essential features of our framework and its relationship to the traditlonal approach in the empirical analyses of labor supply (see Klilingsworth 1983). For the sake of simplicity we take tha case of one individual. The traditional approach starts by postulating a direct (or indirect) utility function In leisure (nonmarket activities) and consumption from which the labor supply function is derived by maximizing utility subject to the budget constraint. (Aiternatively, the labor supply function is postulated directly so that it is consistent with a well-defined utility function). In this approach it is assumed that the Ir,dividual Is free to adjust his or her hours of work. The notion of rationing with respect to job offers or hours of work Is rarely taken into account. Another feature of most empirical models Is the assumption of linear labor supplv curves. Linear supply functions imply a particular and quite restrictive form of the utlity function that seems unjustified a priori. For example it Implies that the 'backward bending case is excluded a priorl. The altemative empirical approach we use here is consistent with neoclassical theory but it departs from the econometric specifications used by others. We assume that the essential choice variable is Job or positionr and that hours of work and wage ratas are determined once the position is given. By positon we understand a particular combination of market and nonmarket activities. For example, one position may be defined as specific farmwork tasks combined with a particular wage work job. Thus hours of work and wage rates are attributes that characterize the positions. Let (Hj, W) be the hour-wage combination of position. Here j Is an Indexation of the positon. For nonmarket postlions, Wi=0. The choice set Is assumed known to the individual but Is unobserved by the econometrician. Onty the hours of work and wage rates are observed. That Is, the hour-wage combination associated with the chosen positon is observed.  - 17 - To make the exposition as simple as possible, we assume that the set of feasible positlons, B, (choice set) is finite (relative to the individual. The individual's maximization problem can be described as follows. The budget constralnts are given by (3.1) h = Hi (3.2) C = HiWi + I (3.3) j * B where I Is nonlabor Income. Equation (3.1) states that for a given posifton J, hours of work are given. The third equation states that B is the set of feasible positions. Equation (3.2) is the standard economic budget constraint. Let U(h,C,j = v(h,C) + ei be the individual's utility of hours of work, h, consumption, C, and position, j. We assume that this utility can be decomposed in a structural term, v(h,C), (common to observationally Identical Individuals) and a random term, ej, that reflects individual preferences for positions wnh the same level of hours and consumption. Thus ej takes into account heterogeneity In tastes across Individuals with respect to posiions as well as the unobserved attributes of the positions. The random term e is assumed independent of the choice set of feasible positions. Thus our approach Is In fact a type of disequilibrium model In which the choice opportunities are considered fixed. The Individual's problem Is to find the position j i B that maximizes v(Hj, HjW +I) + e.l Now let B(h,w) be the set of positions for which Hi=h, W =w. JeB and let n(h,w) be the number of positions in B(h,w). Formally, the probability that the optimal position has hour-wage combination (h,w) Is expressed as o(h,w) = P ( max (v(Hj,HjWj+l)+ee) = max(v(Hj,HjW,+I) + e) }. Moreover, if we assume that the random preference terms ei are independent, extreme value distrlbuted across positions, we get Immediately from the formal theory of discrete choice as developed by McFadden (1973) (see Maddala, 1983) that n(h,w)exp(v(h,hw- 1)) (3.4) *(h,w) = z n(x,y)exp(v(x,xy+I)) x,y Let n(h,w) g(h,w) = - z n(x,y) x,y  18 - be the fraction of positions with hours and wages equal to (h,w) that are feasible. By inserting In (3.4) we get g(h,w)exp(v(h,hw+ I)) (3.5) *(h,w) = z g(x,y)exp(v(x,xy+l)) x,y This model is analogous to the one developed by Ben-Akiva et al. (1985). The function * expresses the labor supply density. Its observable counterpart is the fraction of individuals who work h hours at wage rate w. Instead of the usual specifications where the labor supply density Is expressed as a function of the parameters of the labor supply function we realize from (3.5) that In our model the density Is expressed as a function of the structural part of the utility function. Moreover, this model allows the notion of rationing. SpecIfically, (3.5) expresses the aggregate labor supply as a simple function of the mean utility, v, and the opportunity density, g(h,w). Let us consider a particular extension to the case where the individual has the choice of participating in two sectors - wage work and informal self-employment. In this case the set of feasible positions consists of combinations of market activities and type of production. Thus a specific position defines the type of wage work, type of production, and so on. To a position j there correspond attributes (H J. H;, WJ, Tj _ * where H and H J are hours of work in wage work and self-employment, W3 is the wage rate, Ti is a variable characterizing technology (unobservable) associated with position j. Now the budget constraints take the form (3.6) C = Ha Wj + Yi + I (3.7) YJ = F(Hj)Tj where F (H j) Tj is a profit function conditional on hours and Yj is the profi. (For analytical convenience we assume the structure to be of the multiplicative form.) The essential postulate that ensures identification is that the opportunity density with respect to offered hours is assumed to be uniform. We assume no constraints on hours of work (given that work in the respective sectors is available). The offered distribution of wages across positions (conditional on education) is assumed to be log normal with mean dependent on experience and level of schooling (splines). The opportunity density of the profit (conditional on hours) is assumed log normal with mean that is log linear with an interaction term in hours. Unlike Jacoby (1988) our approach accounts for possible simuttaneous equation bias, and does not distinguish between  - 19 - output from agricultural and nonagricultural self-employment. In the actual empirical application below a continuous analogue to the discrete model above has been estimated. For details we refer io Dagsvik and Aaberge (1989). 3.2. Model specification The preferences are represented in the model by a Box-Cox type utility function that is additively separable In consumptlon and in each of the individual's leisure. The leisure torms are p,.rameterized as a function of age and for females we hav, added the number of children below six yea,-s of age In interaction with hours of work In the wage sector. Thus tne systematic term, v, of the utility function Is assumed to have the form: ((1 + C )1 .1) (3.8) V(q., 17F' C,f _____2_low a1 + E (a4 + as log Ajm + a6(iog AJM)2) -1 j3 + Z (as + @tg log AF + a10(log AJF)2) J a7 + all z h fJ + E12 E D3M i i 12 j where Ljr is defined by L3r = 1 Jr, r = F,M 8760 C = per capita household consumption, fi = number of children less than six years, Ajr = age of household member j, gender r = F,M, hjr = total annual hours of work for household member j, gender r h JF = annual hours of wage work, female J, and r ' i male j has hours of work in (2475, 2525) I