metadata: authors: 0: author: Dagsvik, John
1: author: Aaberge, Rolf
count: Peru
docna: 0: docna: Household production, time allocation, and
            welfare in Peru
docty: Policy Research Working Paper
subtopic: Labor Markets,Educational Sciences,Poverty Reduction Strategies,Employment and Unemployment,Rural Labor Markets
teratopic: Poverty Reduction
abstracts: cdata!: 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 relationship between variations in labor supply and
            income inequality.  It uses a decomposing method to analyze
            income inequality and utilizes 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.  Most of the available
            information on economic inequality in developing countries
            refers to the distribution of income among earners.
            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 household income or consumption.
            This paper uses this indicator in an analysis of economic
            inequality.  The methodological approach is based on a
            summary measure of inequality which is closely related to
            the Gini coefficient.  The essential difference is that the
            proposed measure of inequality gives more weight than the
            Gini coefficient to transfers related to the very poor.
geo_reg_key: 119228,517191
repnme: repnme: Household production, time allocation, and
            welfare in Peru
display_title: Household production, time
            allocation, and welfare in Peru
listing_relative_url: /research/1990/09/700172/household-production-time-allocation-welfare-peru
topicv3: Labor Markets m1326488 855,Education m1327048 470,Income Inequality m1503891 2668,Self-Employment m1504000 2698,Labor Supply m1504055 2751
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Poverty Reduction
origu: Policy, Research & Ect Affairs
no_of_pages: 51
model_extractions: **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 Living Standard Survey (PLSS) to analyze (1) inequality in the distribution of income, (2) men and women's participation in the labor market and variations in their work hours, and (3) the relationship between variations in the labor supply and income inequality.

Their purpose: to study the effect of changes in education and wage rates on production, consumption, and allocation of time. For example, how many men and women would participate in wage work if education were increased? How would policy changes affect the mean level and degree of inequality in the distribution of economic welfare?

# They conclude:

Entrepreneurial income is the most important source of income in rural and other urban areas. Male wage eamings contribute almost 40 percent of the household's consumption, which seems to reflect their share of total household hours of work. Women's eamings contribute about 17 percent of consumption.

But consumption and welfare are considerably less equally distributed than hours of work.

Proportional wage changes have only a small effect on behavior. Remarkably, wage increases also have little effect on the unequal distribution of per capita consumption. Even when wage rates are increased by the sane amount the indirect effect is small - but the increase does moderately reduce the inequality in distribution of per capita consumption.

Dagsvik and Aaberge use a decomposing method to analyze income inequality. They use a structural neoclassical model to analyze household production, consumption, welfare, and allocation of time. They use per capita (or per adult equivalent) household income or consumption as an indicator of welfare.

> 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.|Introd|uction<br>.........................................................|1|
|---|---|---|---|
|2.|Labor|market activty, income formation and welfare .....<br>...................<br>.|4|
||2.1|Measurement and decompositlon of inequaRty ..........................<br>.|4|
||2.2|Inequality In distributions of hours of work for||
|||females and males<br>.................................|7|
||2.3|Inequality In distributions of consumption for households ........<br>..|..........<br>10|
||2.4|Inequality In distributions of per-capita household consumption ......<br>..|........<br>14|
|3.|The e|conometric framework<br>..............................................|16|
||3.1|Theoretical model<br>.......................<br>........................|16|
||3.2|Model specification .................................<br>....|.....<br>19|
|4.|Summ|ary statistics and parameter estimates ...................................|22|
|5.|Policy|simulation results for Uma ..........................................|28|
||5.1|Wage effects<br>.........................<br>.........................|29|
||5.2|Education effects<br>.......................<br>........................|32|
|6.|Conc|lusion<br>.........................................|................<br>35|
|Refer|ences|.........................<br>I..............I........37||
|Appe|ndix 1.|Estimates of Inequality based on the Gini-coefficient.|38|
|Appe|ndix 2.|Deflnhtions of main variables<br>..|39|
|Appe|ndix3.|Figures relating to observed and simulated distributions of key||
|||variables<br>..|41|
# HOUSEHOLD PRODUCTION, TIME ALLOCAnlON, AND WELFARE IN PERU

# 1. **Introduction**

This paper uses the Peruvian Living Standard Survey (PLSS) data to analyze (a)<sup>inequality in the distribution</sup> of Income, (b) labor market participation of men and women and the variations<sup>in hours of work, and (c) the relation-</sup> ship between variations In labor supply and Income Inequality. We<sup>use a decomposing method to analyze income</sup> Inequality. Furthermore, we utilize a structural neo-classical model to analyze<sup>household production, consumption,</sup> time allocation and welfare. The purpose Is to study the effect on<sup>production, consumption, and time allocation of</sup> changes in education and wage rates. For example, how many men and women<sup>would participate in wage work</sup> if education were Increased? And how would policy changes affect the mean<sup>level and the degree of inequality in</sup> the distribution of economic weffare?

Most of the available information on economic Inequality in developing countries refers<sup>to the distribution</sup> of Income among eamers. Although this Information constitutes an important<sup>element for understanding the labor</sup> market and the related distribution of income, it is less helpful In the analysis of inequality<sup>as a welfare issue. A more</sup> relevant indicator of welfare is per capita (or per adult equivalent) household<sup>income or consumption. This paper</sup> uses this Indicator in an analysis of economic inequality. Our methodological<sup>approach is based on a summary</sup> measure of inequality which is closely related to the Gini coefficient.<sup>The essential difference is that our proposed</sup> measure of inequality gives more weight than the Gini coefficient to transfers related<sup>to the veiy poor.</sup> Based on the estimates of an econometric model of production, consumption<sup>and time allocation, we have</sup> examined the Impact of changes in wage rates and education on economic inequality.<sup>In particular we demonstrate</sup> how female labor and education affect economic inequality among households.

The structural econometric model we develop and estimate<sup>Is convenient for simulating certain types of</sup> policy experiments. It is of particular interest to apply empirically<sup>founded behavioral models to assess the labor</sup> supply response and the corresponding Impact on economic welfare from<sup>various policy measures. SpecHfically,</sup> given similar economic cond-tions in Peru as of 1985, our study suggests what we<sup>may be able to achieve, and how,</sup> for example, different measures would affect economic inequelity.

The theoretical model Is based on the neoclassical model for consumption and time<sup>allocation. Provided</sup> 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<sup>plays a</sup> 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 Interpre **t** he 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.<sup>11</sup> 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 selfemployment, 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-coefficien **t** hen 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 <!-- Start of picture text -->
-0  ye<br>(2-5)  G =  r r  (y-x)dF(x)dF(Y)  EX  r  y(2F(y)-1)dF(y)<br>0 0  0<br>and<br>e y e<br>(2-6) A=  1  rr  i  =Jx<br>EX  J A  F(y) dF(x)dF(y)  E  y  Y(1+lo9F(y))dF(y),<br>0 0  0<br><!-- End of picture text -->

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

||||||Femal|es|||||
|---|---|---|---|---|---|---|---|---|---|---|
|||Males||All||Married|||Unmar|ried|
||Em-<br>ploy-<br>ment<br>rates|An-<br>nual<br>mean<br>hours|Em-<br>ploy-<br>A-<br>ment<br>inequality rates|An-<br>nual<br>mean A-<br>hours Inequality|Em-<br>ploy-<br>ment<br>rates|An-<br>nual<br>mean<br>hours|A-<br>Inequality|Em-<br>ploy-<br>ment<br>rates|An-<br>nual<br>mean<br>hours|A-<br>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<br>urban|<br>.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 selemployment, (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 behaviora **l** abor 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<sup>Distributions of Hours of Work for Females and Males, With Respect</sup> to (1) Wage Work, (2) Nonagricultural Sel-Employment,<sup>(3) Agricultural Self-Employment and (4) Unpaid Family</sup> VWork, by Region

|Region (level of<br>Inequality for<br>|Employment<br>|Sectoral f<br>of overal<br>litv (2erc|raction<br>l lnequa.<br>ent)|Sectoral ft<br>of total ho<br>work (per|ractlon<br>urs of<br>cent)|Interacti<br>coefflcie|on<br>nt|
|---|---|---|---|---|---|---|---|
|females and malss)|sector|||||||
|||Female|Male|Fem-;a|Male|Female|Male|
||1<br>|21.9<br>|39.9<br>|22.0<br>|42.9<br>|0.518<br>1|0.368<br>0531|
|Peru<br>|2<br>|28.5<br>|27.2<br>|24.1<br>|20.3<br>|0.68<br>|.<br>|
|(0.521)<br>|3<br>|7.5<br>|17.7<br>|7.8<br>|16.1<br>|0.501<br>|0.435<br>|
|(0.396)|4|42.1|15.2|46.1|20.7|0.476|0.292|
||1<br>|53.2<br>|58.3<br>|52.8<br>|66.6<br>|0.573<br>|0.348<br>|
|Uma<br>|2+3<br>|37.8<br>|40.4<br>|33.0<br>|29.8<br>|0.653<br>|0.539<br>|
|(0.569)<br>(0.398)|4|9.0|1.3|14.2|3.6|0.360|0.144|
||1<br>|25.4<br>|44.7<br>|26.1<br>|50.4<br>|0.547<br>1|0.385<br>0558|
|Other urban<br>|2+3<br>|53.8<br>|50.7<br>|45.8<br>|39.4<br>|0.66<br>|.<br>|
|(0.563)<br>(0.434)|4|20.8|4.6|28.1|10.2|0.417|0.195|
||1<br>|8.6<br>|26.8<br>|7.5<br>|24.4<br>|0.536<br>|0.403<br>|
|Rural<br>|2<br>|13.1<br>|8.3<br>|11.2<br>|6.8<br>|0.543<br>|0.451<br>0409|
|(0.467)<br>|3<br>|13.2<br>|35.2<br>|13.6<br>|31.9<br>|0.455<br>|.<br>2|
|(0.370)|4|65.1|29.7|67.7|36.9|0.449|0.98|

Note: Fraction of overall Inequality<sup>=</sup> Fraction of total hours of work) x (I:lteraction<sup>coefficient)</sup> Overall inequalIty Example: Wage sectors fraction of overall inequality<sup>for females in Peru</sup> 22.0 x 0.518

- ____ = 21.9 0.521

According to table 2, wage work plays a<sup>predominant role for males and females In Uma and for males</sup> In other urban areas. In rural areas males<sup>and females work mainly in the agricultural sector, but the wage work</sup> accounts for almost 25 percent of the total<sup>hours of work for rural men.</sup> The large Interaction coefficients In table<sup>2 suggest that females with long total hours work more hours In</sup> each sector than females with short total hours<sup>of work. Toacertain extent thIs conclusion Is also valid for males.</sup> For males, however, there is a weak Interactin<sup>between the hours worked as an unpaid family worker and total</sup> hours of work. Tnis means that males with<sup>short total hours of work do neai</sup> 1<sup>y as much unpaid family work as males</sup> with long total hours of work. Note that the<sup>sel-employment sectors have the largest Interaction coefficients, which</sup>
- 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:

|Peru|Uma|Other<br>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

||Peru|Lima|Other<br>urban areas|Rural areas|
|---|---|---|---|---|
|Number of observations<br>....|.<br>4,622|1,287|1,316|2,019|
|Mean**.**<br>**.............**|**.**<br>42,500<br>(10,066)|40,120<br>(2,250)|71,104<br>(32,912)|25,373<br>(8,273)|
|Median ................|11,433|22,344|15,660|4,423|
|A-inequality ......<br>......|0.864<br>(0.033)|0.680<br>(0.016)|0.892<br>(0.049)|0.895<br>(0.034)|

Note: In intis (Peruvian Currency) at june 1985 prices. Standard deviations In parenthesis.
. 12Table 4. Mean Consumption for Households Uving In Peru by Deciles Decomposed with respec **t** o Females, Males and Chilcrens Wage Eamings and with respect to the Households Net Entrepreneurial Income and Other Income

|Decile|Mean<br>|Dec<br>wa<br>|ile specfic<br>ge eamin<br>|mean<br>as for<br>|Decile<br>specific<br>mean net<br>entrepreneuria<br>|Decile<br>specfic<br>mean of<br>l other|
|---|---|---|---|---|---|---|
||household<br>consumption|Female<br>(15-70)|s Males<br>(15-70)|Children<br>(7-14)|income<br>for househ|Income<br>olds|
|I .................<br>|397<br>|13<br>|40<br>|2<br>|324|18|
|2 .................<br>|1,700<br>|80<br>|222<br>|15<br>|1,296<br>|87|
|3 .................<br>|3,443<br>|192<br>|793<br>|27<br>|2,268<br>|163|
|4 .................<br>|6,077<br>|387<br>|1,964<br>|42|3,270|394|
|5 .................<br>|9,478<br>|884<br>|3,634<br>|29<br>|4,203<br>|718<br>|
|6 .................<br>|13,643<br>|1,367<br>|6,086<br>|63<br>|5,244|883|
|7 .................<br>|19,082<br> <br>|1,741<br>|8,220<br>|35<br>|7,630<br>|1,456<br>|
|8 ..........<br>|.......<br>27,073<br>|4,665<br>|10,902<br>|214<br>|10,723<br>|1,924<br>|
|9 .................<br>|41,140<br>|4,718<br>|15,592<br>|53<br>|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 coefficien **t** akes 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<sup>of Consumption by Males, Females, and Children's</sup> Wage Income, and by Net Entrepreneurial Household Income Plus Other Income, by Region.

|Region<br>(Level of<br>inequality)|Income<br>(consumption)<br>factor|Fraction of<br>overall In-<br>equality<br>(percent)|Fraction of<br>consump-<br>tlon<br>(percent)|Interaction<br>coefficient|
|---|---|---|---|---|
||Females (15-70) wage eamings<br>|7.6<br>|7.8<br>|0.842<br>|
||Males (15-70) wage eamings .<br>|16.0<br>|18.7<br>|0.742<br>|
|PERU (0.864)|Childrens (7-14) wage eamings<br>Households net entrepreneurial<br>|0.1|0.2<br>|0.635<br>|
||income .72.7<br>||69.3<br>|0.906<br>|
||Other Income .3.6||4.0|0.767|
||Females (15-70) wage eamings .<br>|18.5<br>|17.0<br>|0.741<br>|
||Males (15-70) wage earnings . .<br>|35.9<br>|39.5<br>|0.618<br>|
|UMA (0.680)|Childrens (7-14) wage eamings<br>Households net entrepreneurial<br>|0|0.1<br>|-0.076<br>|
||income .38.2<br>||34.9<br>|0.744<br>|
||Other income .7.4||8.5|0.596|
||Females (15-70) wage earnings .<br>|5.1<br>|5.6<br>|0.805<br>|
|OTHER<br>|Males (15-70) wage earnings<br>|8.1<br>|11.5<br>|0.629<br>|
|URBAN (0.892)|Childrens (7-14) wage eamings<br>Households net entrepreneurial<br>|0.1|0.1<br>|0.741<br>|
||Income .84.8<br>||80.2<br>|0.943<br>|
||Other Income .1.9||2.6|0.665|
||Females (15-70) wage eamings .<br>|2.2<br>|2.4<br>|0.829<br>|
||Males (15-70) wage earnings . .<br>|9.7<br>|10.9<br>|0.795<br>|
|RURAL (0.895)|Childrens (7-14) wage earnings<br>Households net entrepreneurial<br>|0.3|0.4<br>|0.774<br>|
||Income .85.7||84.1<br>|0.911<br>|
||Other income .2.1||2.2|0.866|

Male wage eamings in Uma provide almost 40 percent<sup>of household consumption which is attained at the</sup> expense of about 43 percent of the households total<sup>hours of work In wage employment by male members of the</sup> household. For females, the corresponding figure is<sup>about 17 percent, whichi reflects 17 percent of the households</sup> hours of work. However, despite the fact that this<sup>particular structure In the distribution of hours of work among</sup> households is maintained in the distribution of consumption<sup>among households, consumption Is cons'rderably more</sup> unequal than hours of work. The explanation<sup>is that the Interaction coefficlents referring to the consumption</sup> distribution for Uma, given In table 5, are considerably<sup>larger than the corresponding interaction coefficients related</sup> to the distribution of hours of work reported in Aaberge<sup>and Dagsvik (1990). This resuit Is due to skew distributed</sup> wage rates and a positive correlation between wage<sup>rates and hours of work. By applying a particular non-linear</sup> decomposifton method (not reported here) we also found<sup>that the wage rates contributed more strongly to Inequality</sup> in the distribution of household consumption than<sup>hours of work in the wage sector. These effects are stronger for</sup> females than for males.
- 14 -

Note that the Interaction coefficient for children's wage earnings in<sup>Lima Is weakly negative, which moans</sup> that children's wage earnings have a modest equalizing effect on the distribution of consumption<sup>among households.</sup> This effect Is In contrast with the effect of children's wage work on the inequality<sup>of tne corresponding distribution</sup> of hours of work and is mainly due to nonworking children of rich households<sup>with low or medium total hours of</sup> work. In both cases the children's contribution to overall inequality<sup>is of minor importance, as shown In the first</sup> column of table 5.

In contrast to the results for Lima, wage eamings in other<sup>urban areas yield a modest contribution to total</sup> household consumption, compared to the contribution of the household's<sup>hours In wage work to the households</sup> total hours of work. The fractions are, respectively, 17 and 40 percent.<sup>For the same reason as for Lima the</sup> Interaction coefficients related to the distribution of consumption<sup>are considerably larger than the corresponding</sup> interaction coefficients for the distribution of hours of work. Similar results<sup>hold for the rural areas, although the</sup> distribution of household consumption seems to a greater extent to reflect<sup>the distribution of household hours of</sup> work.

2.4. Inequality in Distributions of Per-Capita Household Consumption The information in section 2.3 about the economic structure<sup>of the labor market must be Interpreted</sup> cautiously when analyzing welfare because of the variations In household<sup>composition and size. To allow for the</sup> fact that some households have several persons while others have just<sup>one, we need an aternative to household</sup> consumption as an indicator of welfare. Clearly, an Index of welfare using<sup>the information on household size and</sup> composition is required. In the PLSS data an equivalence scale accounts<sup>for this heterogeneity. Specifically, the</sup> costs of children are specified in terms of fractions of one aduft. The weights<sup>are 0.2 for a child under 7 years old,</sup> 0.3 for a child aged 7 to 12, 0.5 for a child 13 to 17, and 1 for a person over<sup>17. The sum of these weights for each</sup> household is used as the scale. Consumption per capita is defined as<sup>household consumption relative to the</sup> equivalence scale and it is used as an indicator of household welfare.<sup>Note that these weights are consistent with</sup> the weights estimated for Sri Lanka and Indonesia by Deaton and Mullbauer<sup>(1986) and have been applied by</sup> Glewwe (1987X in analyzing the distribution of welfare in Peru In 1985.86. Glewwe's<sup>analysis is based on expenditure</sup> data rather than on income data.

The lack of sufficient data makes it impossible to distinguish<sup>consumption levels among members of the</sup> household. Therefore we have to assume that the welfare level of an<sup>individual is equal to the per capita</sup> consumption of the household. It is particularly interesting to examine<sup>the relationship between the distribution of</sup> per capita household consumption among households and the distribution<sup>of per capita household consumption</sup> 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 Ginicoefficient **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

|Popula-<br>|Pe<br>|ru<br>|Li<br>|ma<br>|Oth<br>urban<br>|er<br>areas<br>|Rura<br>|l areas<br>|
|---|---|---|---|---|---|---|---|---|
|tion|Mean|Median|Mean|Median|Mean|Median|Mean|Median|
|All**...........**|**....**<br>11,692<br>(24,|3,332<br>126)|10,668<br>(6,|5,983<br>541)|19,139<br>(6,9|4,190<br>52)|7,454<br>(10,|1,404<br>633)|
|Females ...........|13,282<br>(7,|3,508<br>376)|10,406<br>(2,|6,036<br>256)|25,154<br>(2,1|4,143<br>85)|6,654<br>(2,|1,332<br>935)|
|Malee .............|12,207<br>(7,|3,820<br>004)|11,529<br>(2,|6,418<br>090)|20,013<br>(2,0|4,423<br>54)|7,097<br>(2.|1,516<br>860)|
|Children4'**..........**|10,118<br>(9,|2,965<br>746)|10,1V8<br>(2,|<br>5,404<br>195)|13,630<br>(2,7|3,945<br>13)|8,150<br>(4,|1,380<br>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

||Peru|Lima|Other urban<br>areas|Rural|
|---|---|---|---|---|
|Households ........|.857<br>(.029)|.676<br>(.017)|.881<br>(.048)|.895<br>(.032)|
|Persons ..........|.856<br>(.014)|.662<br>(.008)|.883<br>(.021)|.888<br>(.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<sup>that the set of feasible positlons, B, (choice set)</sup> is finite (relative to the individual. The individual's maximization<sup>problem can be described as follows. The budget</sup> 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<sup>a given posifton J, hours of work are given. The third</sup> equation states that B is the set of feasible positions. Equation<sup>(3.2) is the standard economic budget constraint.</sup> Let U(h,C,j = v(h,C) + ei be the individual's utility of hours of work, h, consumption, C, and position,<sup>j. We assume that this utility can be</sup> decomposed in a structural term, v(h,C), (common to observationally<sup>Identical Individuals) and a random term, ej,</sup> that reflects individual preferences for positions wnh the same<sup>level of hours and consumption. Thus ej takes into</sup> account heterogeneity In tastes across Individuals with respect<sup>to posiions as well as the unobserved attributes of</sup> the positions.

The random term e is assumed independent of the<sup>choice set of feasible positions. Thus our approach</sup> Is In fact a type of disequilibrium model In which the choice<sup>opportunities are considered fixed. The Individual's</sup> 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<sup>=w.</sup><sup>**_JeB_**and let n(h,w) be the number of positions in</sup> B(h,w).

Formally, the probability that the optimal position<sup>has hour-wage combination (h,w) Is expressed as</sup> o(h,w) = P ( max (v(Hj,HjWj+l)+ee) = max(v(Hj,HjW,+I)<sup>+ e)}.</sup> Moreover, if we assume that the random preference<sup>terms ei are independent, extreme value distrlbuted across</sup> positions, we get Immediately from the formal<sup>theory of discrete choice as developed by McFadden (1973) (see</sup> 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<sup>are feasible. By inserting In (3.4) we get</sup> 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<sup>et al. (1985). The function * expresses the</sup> labor supply density. Its observable counterpart is the<sup>fraction of individuals who work h hours at wage rate w.</sup> Instead of the usual specifications where the labor supply density<sup>Is expressed as a function of the parameters of</sup> the labor supply function we realize from (3.5) that In<sup>our model the density Is expressed as a function of the</sup> structural part of the utility function.

Moreover, this model allows the notion of rationing.<sup>SpecIfically, (3.5) expresses the aggregate labor supply</sup> as a simple function of the mean utility, v, and the opportunity density,<sup>g(h,w).</sup> Let us consider a particular extension to the case where the<sup>individual has the choice of participating in two</sup> sectors - wage work and informal self-employment. In<sup>this case the set of feasible positions consists of</sup> combinations of market activities and type of production.<sup>Thus a specific position defines the type of wage work,</sup> type of production, and so on. To a position j there<sup>correspond attributes</sup> _ (H J. H;, WJ, Tj * where H and H J are hours of work in wage work and<sup>self-employment,W3 isthe wage rate, Ti is a variable</sup> characterizing technology (unobservable) associated with position<sup>j.</sup> 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<sup>hours and Yj is the profi. (For analytical convenience we</sup> assume the structure to be of the multiplicative form.) The essential postulate that ensures identification<sup>is that the opportunity density with respec</sup><sup>**t**o offered hours</sup> is assumed to be uniform. We assume no constraints<sup>on hours of work (given that work in the respective sectors</sup> is available). The offered distribution of wages<sup>across positions (conditional on education) is assumed to be log</sup> normal with mean dependent on experience<sup>and level of schooling (splines). The opportunity density of the profit</sup> (conditional on hours) is assumed log normal with<sup>mean that is log linear with an interaction term in hours. Unlike</sup> Jacoby (1988) our approach accounts for possible<sup>simuttaneous equation bias, and does not distinguish between</sup>
- 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:

## **a1**

where Ljr is defined by 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 ° otherwise. **L**
- 20-

Except fOr the term 1 3S h JF fj, utility is assumed additively separable In consumption and leisure. Note that apart from the peak at full-time (2475,2525) the utility of consumption Is concave and Increasing when a, < 1, *3 C 11 a7 < 1 1

> 4 + a 5 logAJH + a 6 ( logAm )2 > 0

and

**a8** + aglogAjF + alo (lOgAjr )2 > 0.

The dummy varlable, D M. allows males to have a particular preference for total hours of work In the interval (2575, 2525). The motivation for introducing this dummy is that the data shows a marked concentration of hours in this interval both for males that are engaged In wage work as well as In farm and nonfarm self-employment. This can only cccur

- (1) If males have a particular preference for full-time work,

- (2) If there are constraints on hours (there are more full-time work positions relative to other positions),

- (3) if ths data are corrupted by measurement errors.

The estimated model is consistent with all these explanations but we are not able to identify which is the true one.

The conditional profit function for the rural area given Inputs is specified as
21

- (3.9) log Y **=0** +<sup>13</sup> 10g(l+hm) + 32109g(1+hF) + 833109(1+h,) + **B4Iog(1 +h,)iog(1 +ht)** + B13 5<sup>og(1+TOTWET)</sup> + B61og(1+TOTDRIED) + B7MAXED + T

where Y = profit of household from self-employment (both farm and nonfarm) h* = total male hours of work in self-employment hF **=** total female hours of work in seHf-employment he = total child hours of work in self-employment TOTWET = total area of watered land TOTDRIED = total area of dry land MAXED = length of schooling of most educated member of the household T = rancom error term - normally distributed.

T Is supposed to account for unobserved choice variables that affect the production technology. The distribution of the technology attribute, T, is assumed to be normal N(O,t), and it Is assumed to be independent of other Input factors. Note that the land variables appear only in agricultural production, not in nonfarm production. The conditlonal profit function for Uma Is specified as

- (3.10) logY **=** + ,log(l +hM) + 0 2109(l+hF) + P3log(l+hM) log (1+hF) + **014** MAXED + T,

Let g. be the fraction of all self-employment positions that are feasible for the household. Let g9 be the fraction of feasibe positions for an individual of sex r, r=F,M, that are nonfarm self-employment positions. Let g **r** and 9r be defined analogously as the corresponding opportunity probabiiitles for farm self-employment and wage work, respectively.

We have parameterized g, as B (3.11) 1 -gy = - . a+8(1-a) where B = [(-9 r )(1-g r AMr r=F,M
. 22 and mF, mm are the numbers of females and males In the household and I<sup>>a>0 Is a parameter. The case a=1</sup> corresponds to the case In which all self-emp!oyment opportunity sets are Independent across household members. The particular parametrization (3.11) has been cr,osen for computational<sup>convenience. Finally, we have Introduced</sup> g, which Is the fraction of feasible self-employment positions that<sup>yields positive profit during a period (one year).</sup> The rationale behind g9 is that In addition to a llmited set of feasible<sup>self-employment positions Is the fact that a</sup> successful businesa does not necessarily yield positive profRt through every period. In fact the data demonstrates that profit is negative for some households during the period of<sup>the data collection. We may interpret alternatively</sup> as the (average) traction of the year the business Is likely to operate wnh<sup>positive profit. A rigorous treatment of the</sup> choice of self-employment activity would of course require a model<sup>for decision under uncertainty.</sup> The offered wage densities are assumed log normal where the means<sup>depend on experience, SPLYRSC1,</sup> SPLYRSC2, SPLYRSC3 where experience Is defined as age minus length of<sup>schooling minus 6 and</sup> r (X,O,O) if x t 5 (SPLYRSC1, SPLYRSC2, SPLYRSC3) = . (5,x-5,0) if 5 < x 5 _10_ ! (5,5,x-10) if x > 10. **L**

# 4. Summar statcs and p eter esimates

The summary statistics of the variables generated from the household survey data are presented<sup>in Table</sup> 8 for Lima and rural areas. There are differences In observed household behavior<sup>In production and consumption,</sup> and in inovidual and household attributes. For example, consumption (income)<sup>per capita is much higher In Uma</sup> than in rural areas. Women in Uma spend more hours In wage work than<sup>women in rural areas; women In rural</sup> areas spend more hours in self-employment. However rural households<sup>record higher profits from seit-employment</sup> than do households In Uma. This is not surprising given that nontarrn<sup>production is dominant in Uma while</sup> agricultural production is the leading activity in the self-employment category.<sup>Interestingly, female wage workers</sup> earn more In rura: areas than male wage workers. For more details see section<sup>2 and Aaberge and Dagsvik (1990).</sup> The parameters of the opportunity density and of the utility function are estimated<sup>simultaneously by a</sup> modified maximum likelihood procedure. The estimates of the utility<sup>function are presented in Table 9, while the</sup> estimates of the opportunity density are given in Table 12. The estimates<sup>of the wage and profit functions are shown</sup> in Tables 10 and 11 respectively. We have also estimated the wage equations<sup>and the profit function by ordinary</sup> least squares. This procedure may lead to biased estimates since it does<sup>not account for the fact that households</sup> do not maximize profit but the utility of consumption and leisure. Consequently,<sup>the conditional expectation of the</sup> error term in the profit firnction given the hours is in general a function of<sup>these hours because they enter the utility</sup> function through consumption and leisure. The results are reported here only<sup>for Lima and rural areas.</sup>
- **23 -**

Table 8. Household and Individual Sample Statistics

|Variables|Lima, Mean<br>(Standard<br>devlation)||Rural Areas<br>(Standard<br>deviation)|, Mean|
|---|---|---|---|---|
|Household Statistics<br>|||||
|Number**of**households 898|||||
|Consumption per capita (intis) .....<br>..........<br>|**6,900**<br>|(150)<br>|2578<br>|(86)<br>|
|Female hours of work in wage work (yearly)<br>.....<br>|832<br>|(44)<br>|101<br>|(13)<br>|
|Female hours**of**work In self-employment (yearly)<br>|638<br>|(44)<br>|2232<br>|(49)<br>|
|Male hours**of**work in wage work (yea**_,)_.......**<br>|2.171<br>|(61)<br>|594|(29)|
|Male hours**of**work in self-employrnent (yearly) . ..<br>|907<br>|(50)<br>|2724<br>|(51)<br>|
|Childrens hours**of**work In self-employment (yearly)<br>|**53**<br>|(10)<br>|4<br>|(0.1)<br>|
|Total gross revenue from self-employment (Intis) . .<br>|10,700<br>|(600)<br>|9056<br>|(385)<br>|
|Total profit from self-employment (Intis) ....<br>.....<br>|6,300<br>|(400)<br>|7183<br>|(311)<br>|
|Number of children below 7**.....**<br>**...........**<br>|0.84<br>|(0.03)<br>|1.34<br>|(0.03)<br>|
|Number of children below 14**.....**<br>**..........**<br>|1.08<br>|(0.04)<br>|1.39|(0.03)|
|Number of females 1S-70 .... .<br>............<br>|1.79<br>|(0.04)<br>|1.f2 9<br>|O.02)|
|Number of people above 70**.....**<br>**...........**<br>|0.09<br>|(0.01)<br>|0.08<br>|(0.01)<br>|
|Equivalence scale .......<br>................|4|(0.10)|3.7|(0.04)|
|Individual Statistics<br>|||||
|Number**of**females 15-70, 1,611<br>|||||
|Number of males 15-70, 1.539|||||
|Participation rates in<br>|||||
|wage work for females ......<br>.............<br>|0.32<br>|(0.01)<br>|0.07<br>|(0.01)|
|self-employment for females .....<br>...........<br>|0.35<br>|(0.01)<br>|0.85<br>|(0.01)<br>|
|wage work for males ......<br>..............<br>|0.63<br>|(0.01)<br>|0.34<br>|(0.01)<br>|
|self-employment for males .....<br>............|0.35|(0.01)|0.89|**(0.01)**|
|Hours**of**work in<br>|||||
|wage work for females (yearly) .....<br>.........<br> <br>|463<br>|(21)<br>|67|(7|
|seHf-employment<br>**for**females (yearly) ....<br>......<br>|**356**<br>|(20)<br>|**1477**|(25)|
|wage work for males (yearly) .....<br>..........<br>|**1,267**<br>|(32)<br>|387<br>|(17)<br>|
|self-employment for males (yearly) ....<br>.......|529|(27)|**1777**|(25)|
|Wage rate, females (intis per day) ....<br>.........<br>|5.25<br>|(0.40)<br>|7.38|(2.45)|
|Wage rate, males (intis per day) ..............|6.41|(0.20)|2.98|(0-30)|
- 24 -

Table 9. Parametqr Estimates for the Utilty Function

|||Lima|Rural Areas|
|---|---|---|---|
|Variables|Coefficients|Estimates<br>(t.values)|Estimates<br>(t-values)|
|Consumption<br>.........|r 1<br>I|-0.776<br>(7.9)|-12.941<br>(4.0)|
||1*2<br>L|4.832<br>(7.3)|35.891<br>(2.0)|
||r<br>3<br>I|-3.605<br>(9.5)|-7.680<br>(14.9)|
|Leisure males .....|I<br>4<br>I<br>..<br>i|43.258<br>(5.4)|3.189<br>(3.3)|
|,|<br><br>15<br>I|-23.194<br>(5.3)|-1.704<br>(3.3)|
||Ia6<br>L|3.134<br>(4.1)|0.231<br>(3.3)|
||ra7<br>I|-1.454<br>(5.7)|-5.380<br>(12.6)|
|Leisure, females .......|Iaa<br>I<br>|86.655<br>(5.5)|5.057<br>(2.8)|
||<br>**a9**<br>I|46.354<br>(5.3)|-2.475<br>(2.5)|
||a<br>**@10**<br>L|6.369<br>(3.2)|0.320<br>(2.3)|
|10-3 zfi .f~|**@**<br>oi|-0.149<br>(2.3)|-0.152<br>(2.2)|
|z DjM .......<br>...|<br>**a12**|2.234<br>(18.8)|2.231<br>(19.7)|

Note: t-values in parenthesis.
-25 -

Table 10. Wage Equations for LUma. Simultaneous ML Estimation Procedure Versus Ordinary Least Squares

|||L<br>|IMA<br>|||RURAL|AREAS||
|---|---|---|---|---|---|---|---|---|
|||Males<br>|F|emales<br>||Males<br>||Females<br>|
||OLS|Simul-<br>taneous ML|OLS|Simul-<br>taneous ML|OLS|Simul-<br>taneous ML|OLS|Simul-<br>taneous ML|
|Intercept|0.049<br>(0.4)|-0.105<br>(0.8)|-0.596<br>(3.5)|<br>*0.674<br>(3.8)|0.352<br>(6.2)|0.395<br>(5.4)|0.473<br>(4.0)|0.451<br>(3.2)|
|SPLYRSC1+<br>SPLYRSC2|0.092<br>(8.4)|0.100<br>(8.2)|0.126<br>(8.2)|0.125<br>(7.9)|0.040<br>(3.5)|0.034<br>(2.3)|||
|SPLYRSC3|0.117<br>(10.1)|0.136<br>(9-9)|0.126<br>(6.2)|0.150<br>(6.5)|0.284<br>(6.1)|0.306<br>(4.8)|0.303<br>(3.0)|0.540<br>(3.4)|
|Experience|0.050<br>(~ 3)|0.038<br>(5.7)|0.056<br>(5.7)|0.050<br>(5.0)|||||
|(Experience)<br>2/100|-0.060<br>(5.3)|<br>-0.039<br>(3.1)|-0.073<br>(3.5)|<br>-0.063<br>(3.1)|||||
|Standard error|0.659|0.660<br>(40.4)|0.780|0.753<br>(32.9)|0.888|0.933<br>(34.4)|1.856|1.316<br>(17.7)|
|R<sup>2</sup>|0.27||0.25||0.09||0.06||

Note: t-values In parenthesis.

Table 11. Parameter Estimates of the Conditional Profit Function

|||LIM|A<br>Simulta|neous||RURA|L AREAS<br>Simultan|eous|
|---|---|---|---|---|---|---|---|---|
|Variable|OLS||ML estim|ate|OLS||ML estim|ate|
|Intercept ...........<br>|2.681<br>|(5.9)<br>|3.078<br>|(7.1)<br>|4.246<br>|(7.1)<br>|2.181<br>|(2.5)<br>|
|Male labor ..........<br>|0.756<br>|(13.3)<br>|0.572<br>|(10.5)<br>|0.329<br>|(4.3)<br>|0.543<br>|(4.9)<br>|
|Female labor ........<br>Interaction, female-male<br>|0.756<br>|(11.0)<br>|0.487<br>|(8.7)<br>|0.222<br>|(2.7)<br>|0.393<br>|(3.4)<br>|
|labor ..............<br>|-0.085|(9.8)|-0.061|(7.6)|-0.031<br>|(3.0)<br>|-0.063<br>|(3.5)<br>|
|Child labor<br>|||||-0.0004<br>|(0.4)<br>|-0.010<br>|(0.7)<br>|
|Watered land<br>|||||0.419<br>|(7.5)<br>|0.443<br>|(5.2)<br>|
|Dry land<br>|||||0.264<br>|(7.6)<br>|0.249<br>|(4.8)<br>|
|Maxed ............<br>|0.047<br>|(2.4)|0.072<br>|(4.0)<br>|0.578<br>|(9.7)|0.734<br>|(7.3)<br>|
|Standttrd error .......<br>R2 .................|1.356<br>0.33||1.257|(31.9)|1.303<br>0.18||1.445|(31.3)|

Note: t-values in parenthesis.
-26 -

Table 12. Estimates of the Opportunity Probabilities

|SECTOR|Opportunity<br>Probability<br>Function|UMA|RURAL AREAS|
|---|---|---|---|
|Agricuttural sel-employment<br>males .........|**<br>g 1M<br>l......<br>og<br>_ **<br>1-g1M|-2.804|1.932<br>(19.3)(24.0)|
|Nonagricuitural self-employment<br>males ...............|91M<br>log -<br>*<br>1-9 1M|-0.197<br>(2.5)|-1.501 + 0.027S<br>(13.0)<br>(1.5)|
|Wage work, males .......|log -<br>_1_1M|-0.488 + 0.103S<br>(2.6)<br>(5.4)|-0.545 + 0.042S<br>(5.5)<br>(1-9)|
|Agricultural self-employment,<br>i<br>females..............|<br>9 F<br>log-*<br>1-9IF|-1.198<br>(12.5)|1.656<br>(24.0)|
|Nonagricultural self-employment<br>females ..............|91F<br>log<br>-<br>-<br>-91F|0.007<br>(0-1)|-0.516<br>(9.4)|
|Wage work, females ......|91F<br>log-<br>1 - 1 F|-1.236 + 0.152S<br>(7-0)<br>(8-1)|-2.656+0.162S<br>(15.2)<br>(4.7)|
|Household profit from<br>self-employment ........|a|-0.577<br>(8.0)||
|Positive profit from<br>self-employment|93<br>log<br>1-g,|1.884<br>(12.2)||

S = Length of schooling.

Note: t-values in parenthesis.
27 The estimates of Table 9 Imply that the systematic term (3.8) of the utility function Is strictly concave and Increasing In consumption and leisure. The estimates also show that the utility of leisure is U-shaped as a function of age with a minimum at 40.6 years for males and 37.4 for females In Lima. In rural areas the corresponding ages are 40.3 and 47.8. Moreover, the Impact of small children seems to be the same in Lima as In rural areas.

The functional form (3.8) implies that the corresponding labor supply functlons are highly non-linear and cannot be expressed In closed form. As a consequence the parameters of Table 9 do not have a simple interpretation In terms of elasticities. Table 10 shows that education and experience are very important determinants for the wage rate in the wage work sector of Lima. It also shows that the selectivity bias is negligible for Uma but for rural areas OLS seems to underestimate the effect of education for females. The bias is however not significantly different from zero. Due to few observations experience has been excluded from the wage equations for the rural areas. In addition SPLYRSC1 and SPLYRSC2 have been excluded for females in rural areas for the same reason. The justification for Imposing the same coefficient of SPLYRSC1 as of SPLYRDSC2 is that preliminary estimation runs produced estimates that were quite close. For the rural areas the model is estimated conditional on farms with positive proft from self-employment. The reason for this is that there are few obse.vations with zero or negative profit for households with self-employment activity. More important, preliminary estimation resufts suggest that the type of farms with reported zero or negative self-employment are essentially different from the rest of the sample.

Although the difference between the OLS and the ML estimates in Table 11 is not statistically significant the results seem to Indicate that in the rural areas OLS seems to underestimate the Impact of male and female labor, and the education variable MAXED (the length of schooling of the highest educated member of the family). In Uma OLS seems to underestimate the Impact of male and female labor and overestimate the Impact of MAXED. Recall that the OLS estimates may be biased (i.e., simultaneous equation bias) while the ML estimates are obtained by a procedure that take into account that the input factors are endogenous.

The profit-function estimates also Impty that the Cobb-Douglas structure Is rejected since there Is a strong negative Interaction between male and female hours of work. In contrast to the result for the rural areas MAXED - seems to be of little importance for the level of the profit I Lima Thus the return to education in self-employment Is much higher in rural areas (0.7) than In Uma (0.1). The est.mates of the opportunity probabilities in Table 12 show that length of schooling has a substantial effect on the opportunities for wage work, particularly for females in Lima and In rural areas. Recall that the parameter a accounts for possible dependence In self-employment opportunities across family members where a = I corresponds to independence. Since a is estimated to be 0.577, Independence Is ruled out. The last line of Table 12 Implies that g, is estimated to be 0.87. Thus, on average, the seif-employment businesses in Lima will produce posiiive prorit a fraction of 0.87 per year (given that labor Input take place).
**-28** -

# **5. Poiy Simlatin** Resunts for **LUma**

Using the econometric framework above we can perform complex simulation experiments that take Into account the household budget constraint, differences In age, schooling, and household size and compositlon. In addition we are able to account for unobserved heterogeneity, represented in the model by random error terms associated with the wage, conditlonal profit, and utility functilon. After the model has been estimated it is possible to perform simulations since we then 'know the parameters of the structural part of the utility, the wage, and the proft function, and the probability distributions of the related random terms.

in practical policy simulation experiments we proceed as follows. For each household the respective random terms are drawn from the corresponding probability distributions. The maximizatlon of the utility function Is a pure numerical problem given the observed household characteristics. The resuhting hours that maximize utility are the female and male labor supply In each sector. This procedure Is performed for each household In the sample to obtain participation rates, distribution of labor In each sector, and consumption and profits from self-employment. Note that this procedure implies exact aggregation. Unfortunately, since the model Is so rich it Is quite costly to perform precise simulations. We have therefore only carried out approximate simulations In which the approximation error Is of moderate size. Figures 1-6 In Appendix 3 show the observed and simulated distribution of male and female hours of work and per capita consumption. These figures demonstrate that the model Is capable of reproducing the survey data fairly well.

We confine the analysis to households with at least one female and one male aduit, where per capita household consumptlon does not exceed 20,000 Intis. Note that this selectlon was not made In Section 2.

The simulation experiments relate to the effect of changes In wages and education on labor supply, wage earnings, profit from self-employment, and distribution of economic welfare.

# 5.1. Wage effects

Table 13 reports the effect of wage changes on participation probabilitles and on mean hours worked In each sector. The table shows that a 20 percent Increase has only a small effect on labor supply. For the females, mean hours of work and participation In the wage sector Increase by 5.8 and 3.2 percent respectively. The effect on mean hours and participation In self-employment Is almost negligible. The cross effect on male participation rates and mean hours of work In each sector is negligible.

Recall that the sum of the participation rates across sectors may be greater than one because many Individuals work In both sectors. When male wages are Increased by 20 percent, their participation and mean hours of work in the wage sector Increase by 1.6 and 2.7 percent, respectively. In the self-employment sector, male
-29 -

partcipatIon and mean hours of work fall by 1.2 and 2 percent respeclvely, while female participation and mean hours of work fall by 2 and 2.4 percent The drop In female labor supply reflects the Income effect that stems from the Increase In mate wages. When both male and female wages Increase by 20 percent, the Impact Is similar but weaker.

The largest effect Is obtained when the female wages go up by 20 percent of the mean wage. Then paricipation and mean hours In wage work rlse 3.8 and 8 percent, respectively. Table 13 shows that mean hours In the wage sector Increase by 4 percent The drop In participation and mean hours recorded In sel-employment sector, however, ls small. So Is also the change In male labor supply.
- 30 -

Table 13. Changes in Participation Rates, Annual Hours of Work, Earnings, and Consumption as a Result of Wage Increments (Percentage Changes From Base Case)

|Percentage<br>increase||Sector<br>partici|specifi<br>pation|c<br>|Sect<br>cific<br>nual<br>of wo<br>cond<br>naD*|or spe-<br>an-<br>hours<br>rk (un-<br>itio-<br>)|Wa<br>ear<br>(un<br>tion<br>(inti|ge<br>nings<br>condi-<br>a)<br>s)|W<br>ear<br>(int|age<br>nings<br>is)|Con<br>tio<br>(int|sump-<br>n<br>is)|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||Wa|ge wor|k SeHf<br>me|emplo<br>nt|<br>y- Wa|<br>ge work|Selfe<br>m|mp,oy-<br>ent|||||
||F|M|**F**|**M**|F|M|F|M|F|M|F|M|
|Base case ..........|0.32|0.62|0.34|0.35|414|1165|414|492|2300|8100|1790|0 27800|
|20 percent Increase<br>In female wages .3.2<br>20 percent increase||-0.6|-0.9|-1.2|5.8|-0.7|-0.5|-0.4|30.0|-1.2|6.3|5.0|
|<br>In males wages<br>20 percent increase in both|-1.9|1.6|-2.0|-1.2|-2.2|2.7|-2.4|-2.0|-4.6|22.3|17.1|11.9|
|<br>females and males wages|0.6|0.6|-1.8|-1.4|1.9|1.9|-1.5|-2.4|19.8|20.5|21.2|11.5|
|Female wage rates increased|||||||||||||
|by 20 percent of the<br>mean wage<br>.<br>Male wage rates Increased<br>by 20 percent of the<br>mean wage<br>.<br>Female and male wage rates<br>increased by 20 percent of<br>the mean wage|........<br>8.8<br>.....**.**..<br>9 9<br>1.6..|.<br>-1.4<br>.<br>2.1<br>....**.**<br>1 0|-0.9<br>-0.9<br>-2.3|0<br>-2.3<br>-2.9|8.0<br>-3.6<br>3.4|-1.4<br>3.8<br>2.0|-1.5<br>-0.5<br>-2.7|0<br>-3.5<br>-4.3|25.0<br>-4.5<br>19.7|-0.8<br>17.6<br>15.1|5.0<br>14.0<br>16.2|4.7<br>7.0<br>8.6|

*) Recall that conditional hours in the respective sectors can be obtained by dividing the unconditional hours by the corresponding participation rates.

Table 14. Changes in Mean Level and Inequality in the Distribution of Per Capita Household Consumption as a Result of Wage Increments (percentage change)

||Mean level|A-coefficient|Gini-coefficient|
|---|---|---|---|
|Base case .........<br>.............|7,600 (in intis)|0.566|0.438|
|20 percent increase in female wages<br>....|5.3|2.1|3.2|
|20 percent increase in male wages<br>.....|11.9|0.6|0.7|
|20 percent Increase in both female and<br>male wages .........<br>............|11.6|-1.3|-1.6|
|Female wage rates increased by 20||||
|<br>percent of the mean wage .....<br>......|4.9|0|0.7|
|Male wage rates Increased by 20 percent||||
|<br>of the mean wage ......<br>...........|6.4|-3.0|-3.4|
|Male and female wage rates Increased||||
|by 20 percent of the mean wage ......|8.6|-3.0|-3.4|
- 31 -

When males wages increase by 20 percent of the mean level, their participation and hours of work In the wage sector increase by 2.1 and 3.8 percent respectively. In the sel-employment sector, their participation and mean hours decrease 2.3 and 3.5 percent. The corresponding Income effect implies that female participation and mean hours in the wage sector decrease 2.9 and 3.6 percent respectively, while there is almost no change in female participation and mean hours In the self-employment sector.

Table 14 demonstrates that wage changes have a modest effect on inequality In the distribution of per capia consumption among households. A 20 percent Increase has very little distributional Impact, reducing Inequality by 3 percent (A-coefficient). This reduction corresponds to Introducing a proportional tax of 3 percent and then Increasing each household's per capita consumption by an equal share of the total tax revenue. In other words the transfer to each household is equal to 3 percent of the mean consumption per capita (before taxes). A similar increase In female wages increases the mean level of the household's per capita consumption by 4.9 percent, while the level of inequality is not influenced. This result corresponds to Increasing each household's per capita consumption by 4.9 percent. Note that the relative changes in inequality are larger when inequality is measured by the Gini coefficient than by the A coefficient, particularly when female wages are increased by 20 percent. This means that the central part of the distribution of per capita consumption Is more strongly Influenced by wage changes than the lower part of the distribution.

Note that we only repon aggregate effects here. We have also done wage change simulations for a twoperson family for the particular case in which all the random terms are equal to zero and wihout any choice constraints. The results are not reported here. (See Dagsvik and Aaberge, 1989). These simulations demonstrate that the elasticities of hours are highly dependent on the level of the wage rates. The reason the corresponding aggregate effects are much smaller may be due to the large heterogeneity In wage rates and the fact that In many families one or several persons are 'stuck, in corner solutions, that is, they participate at most In one sector. Such families are therefore less responsive to wage changes than families where all members work in both sectors. In addition, restrictions on opportunities prompt a large number of corner solutions.
-32 -

# 5.2. Education effects

Table 15 shows the impact of education through the opportunity probabilHies. Here the wage rates and the education variable (MAXED) in the conditional profit function are kept unchanged. Thus we study the pure *opportunity effect. Contrary to the wage simulations above, e obtain a large effect from Increased education. If female education Is Increased by one year, female participation in the wage sector Increases by 9.2 percent. The change In the participatlon rate in self-employment, however, Is wlthin the simulatlon error margin. If male education is Increased by one year, participation In wage work Increases by 3.4 percent, and remains unchanged for the selfemployed. If the minimum education for females Is Increased to nine years, female participation in the wage sector Increases by 19 percent. When males' level of schooling is Increased analogously, male participatlon In the wage sector Increases by 3.9 percent. The cross effects appear to be negligible.

Table 15. Effects of Education on Sector-Specific Participation Rates When Wages Are Fixed (percentage change)

||Se|ctor-soecifi|c particiDation ra|tes|
|---|---|---|---|---|
||<br>Wac|<br>e work|<br>Self emp|<br>lovment|
||F|M|<br>F|<br>M|
|Base case ..........<br>..............|0.32|0.62|0.34|0.35|
|One year of additional schooling<br>for females .........<br>..............|9.2|-1.4|0|0|
|One year of additional schooling<br>for males ...........<br>..............|.1.3|3.4|0|-0.6|
|One year of additional schooling<br>for both males and females .....<br>.......|<br>7.6|2.4|0|-0.9|
|Nine years of schooling as a lower<br>limit for females .......<br>.............|19.0|-1.0|0|-0.3|
|Nine years of schooling as a lower<br>limit for males ........<br>.............|-1.3|3.9|0|-0.9|
|Nine years of schooling as a lower<br>limit for both males and females ....<br>....|.<br>18.0|3.5|0|-1.2|
-33 -

Table 16 reports the impact of increased educatlon on labor supply. Here only MAXED Is kept unchanged. In other words the increase In schooling affects both wages and the choice set of work posiions. The first line demonstrates that the wage effect seenis to be small compared to the Impact through the opportunity probabilItles. In Table 15 we found that the corresponding female participation rate Increased 18 percent, or only 3.5 percentage points less than we obtained by Increasing minimum schooling to nine years without keeping the wage rate fixed. The subsequent effect on mean hours of work In the wage sector is a 25.6 percent increase for females and a 2.7 percent decrease for males. The corresponding Increase In the conditional mean hours given participation In the wage work sector for females Is 3.3 percent The other Income and cross effects on hours are small. The mean wage earnings for females Increases dramatically to 42.6 percent.

If the minimun i level of schooling for males Is increased to nine years the Impact on labor supply Is much less. In this case participation In wage work rises 5.6 percent for males and falls 3.5 percent for females. Mean hours of wage work increase 6.7 percent for males and decline 4.4 percent for females. Other income and cross effects on labor supply are small. Wages Increase by 14.8 percent for males and fall by 5 percent for females. But the total effect on household Income is larger than it was when the minimum education for females was raised to nine years.

When both males and females have at least nine years of education, female participation and mean hours In wage work Increase by almost the same amount as In the marginal, case reported In the first line of Table 16. Male participatlon and mean hours In wage work Increase by 3.7 and 3 percent respectively, which Is much less than the response In the 'marginal' case (second line).

We have also carrded out simulations In which MAXED Is Increased. The results (not reponed here) show a very small Impact on profits.
- 34 **-**

Table 16. Changes In Participation Rates, Annual Hours of Work, Earnings and Consumption as a Result of Additional Schooling and Subsequent Increase In Wage Rates. (percentage changes from base case)

|Percentage increase||Secto<br>partic|r spe<br>ipatio|cific<br>n|Secto<br>citic<br>nual<br>of wo<br>condi<br>nan*l|r spe-<br>an-<br>hours<br>rk (un<br>tio-<br>|Wag<br>earni<br>-(unco<br>tional<br>(intis|e<br>ngs<br>ndi-<br>)<br>)|Wage<br>earnin<br>(intis)|<br>gs<br>|Consum<br>tion<br>(intis)|p-|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||Wag|e work|<br>S<br>emDl|elf-<br>ovment|Wag<br>|e work|<br>**Se**<br>emplo|**lf-**<br>vment|||||
||F|M|F|M|F|M|F|M|F|M|F|M|
|Base case**.....**<br>**.......**|0.32|0.62|0.34|0.35|414|1,165|414|492|2,300|8,100|17,900|27,800|
|Nine years of schooling as<br>lower limit for females ...<br>.|21.5|-1.8|1.2|**_-0.6_**|25.6|-2.7|-1.5|0|42.6|-2.0|8.4|6.5|
|Nine years of schooling as<br>lower limit for males .....|-3.5|5.6|0|-1.7|-4.4|6.7|0|-3.5|-5.0|14.8|11.2|7.6|
|Nine years of schooling as<br>lower limit for both males<br>and females ...........|19.0|3.7|0.9|-1.4|20.5|3.0|-1.2|-2.4|33.9|11.1|17.3|11.2|

Table 17. Effect of Education on Mean Level and Inequality in the Distribution of Per Capita Consumption among Households with a Subsequent Increase in Wage Rates. (percentage changes from base case)

||Mean level|A-coefficient|Gini-coefficienit|
|---|---|---|---|
|Base case.|7600|0.566|0.438|
|Nine years of schooling as lower<br>limit for females .5.3||0|0|
|Nine years of schooling as lower||||
|<br>limit for males .6.6||-1.8|-1.8|
|Nine years of schooling as lower||||
|<br>limit for both males and females|10.5|-3.0|-3.2|
Earlier we concluded that the Impact of wage changes on Inequality in the distribuilon of per capita consumption Is modest. Table 17 demonstrates that this Is also the case when schooling Is increased. In spite of a considerable Increase in mean per capita consumption, the reduction of Inequality in the distribution of per capta consumption Is surprisingly small. Since the changes In inequality are the same whether t Is measured by the C-in-coefficient or the A-coefficient, we can conclude that changes In schooling have the same impact on the lower part of the distribution of per capita consumption as on the central part of this distribution.

# 6. CONCLUSION

The data show that male wages play a dominant role In household consumptlon In Lima, while entrepreneurial Income is the most important income source in rural and In other urban areas. In Lima males wage earnings contribute by almost 40 percent of the household's consumption, which seems to reflect their share of total household hoprs of work. For females the corresponding shares are both about 17 percent. The same relationship holds for rural areas. Despite the similarity, consumption Is considerably less equally distributed than hours of work. This is also the case when we examine the distribution of welfaie. As an indicator of welfare we apply household consumption relative to an equivalence scale. This indicator accounts for some of the heterogeneity In household demographic composition.

The estimated structural model departs from the assumption that the members of a household behave so as to maximize a household utility function, given available work resources and production opportunnites. The corresponding econometric approach dfffers from the traditional labor supply models in the literature. Our particular approach has the advantage of being well-suited for taking Into account latent opportunity constraints, the interdependence between each persons activities in different sectors, and the Interdependence between household members. Since many households have more than two adults, this Is a major challenge.

It may not be obvious that the neoclassical type model used in this analysis Is appropriate for examining Peru's labor market. The analysis rests on the assumption that the data reflects the heterogeneity of preferences and opportunities to a 'large' extent. For example, **t** may be questionable if essential background information about the heterogeneity In customs and value systems across social classes, ethnic groups, and "professlons' is reflected in the data. It Is also essential that the data on hours, participation and economic variables are not corrupted by measurement errors. Such errors in economic variables may occur if, for instance, household members are engaged in black-market activities, or if a substantial part of the goods and labor markets operates by trading services and goods without explicit prices. This is particularly relevant in countries where inflation Is high, as in Peru. Also we assume that the average number of feasible wage positions with low (offered) hours is the same as the number of
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feasible wage posRtions wRh high offerec hours. Under the assumption that there are no restrictions on hours of work In the self-employment sector, It is possible to test this assumption.

It we are willing to accept the neoclassical point of departure as well as the assumptions about the data and the choice environment, the estimation results reported here demonstrate that the parameters are determined with remarkable precision and have the expected signs according to economic theory. The model also reproduces the aggregate distributions of hours and consumption fairly well.

The simulation results for Lima demonstrate that proportional wage changes have only a small effect on behavior It is also remarkable that the wage increases have very little effect on the Inequality In the distribution of per capita consumption. Even when wage rates are increased by the same amount the indirect effect is small. This increase does, however, moderately reduce the inequality In the distribution of per capita consumption.

These simulation exercises show that it is very difficult to reduce inequality in per capita consumption by changing wage and education policies.