Family Productivity, Labor Supply, and Welfare in a Low ... · No. 19 The Conceptual Basis of Measures of Household Welfare and Their Implied Survey Data Requirements No.20 Statistical

LSM-87LISIIIEIhIS SEPT. 1992

Living StandardsMeasurement StudyWorking Paper No. 87

Family Productivity, Labor Supply, and Welfarein a Low-Income Country

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LSMS Working Papers

No.18 Time Use Data and the Living Standards Measurement Study

No. 19 The Conceptual Basis of Measures of Household Welfare and Their Implied Survey Data Requirements

No.20 Statistical Experimentation for Household Surveys: Two Case Studies of Hong Kong

No.21 The Collection of Price Data for the Measurement of Living Standards

No.22 Household Expenditure Surveys: Some Methodological Issues

No.23 Collecting Panel Data in Developing Countries: Does It Make Sense?

No.24 Measuring and Analyzing Levels of Living in Developing Countries: An Annotated Questionnaire

No.25 The Demandfor Urban Housing in the Ivory Coast

No.26 The Cote d'Ivoire Living Standards Survey: Design and Implementation

No.27 The Role of Employment and Earnings in Analyzing Levels of Living: A General Methodology withApplications to Malaysia and Thailand

No.28 Analysis of Household Expenditures

No.29 The Distribution of Welfare in C6te d'Ivoire in 1985

No.30 Quality, Quantity, and Spatial Variation of Price: Estimating Price Elasticities from Cross-SectionalData

No.31 Financing the Health Sector in Peru

No.32 Informal Sector, Labor Markets, and Returns to Education in Peru

No.33 Wage Detenninants in Cote d'Ivoire

No.34 Guidelines for Adapting the LSMS Living Standards Questionnaires to Local Conditions

No.35 The Demandfor Medical Care in Developing Countries: Quantity Rationing in Rural Cote d'Ivoire

No.36 Labor Market Activity in COte d'Ivoire and Peru

No.37 Health Care Financing and the Demandfor Medical Care

No.38 Wage Detenninants and School Attainment among Men in Peru

No.39 The Allocation of Goods within the Household: Adults, Children, and Gender

No.40 The Effects of Household and Community Characteristics on the Nutrition of Preschool Children:Evidence from Rural Cdte d'Ivoire

No.41 Public-Private Sector Wage Differentials in Peru, 1985-86

No.42 The Distribution of Welfare in Peru in 1985-86

No.43 Profits from Self-Employment: A Case Study of C6te d'Ivoire

No.44 The Living Standards Survey and Price Policy Reform: A Study of Cocoa and Coffee Production inCote d'Ivoire

No.45 Measuring the Willingness to Payfor Social Services in Developing Countries

No.46 Nonagricultural Family Enterprises in C6te d'Ivoire: A Descriptive Analysis

No.47 The Poor during Adjustment: A Case Study of Cote d'Ivoire

No.48 Confronting Poverty in Developing Countries: Definitions, Information, and Policies

No.49 Sample Designs for the Living Standards Surveys in Ghana and Mauritania/Plans de sondagepour les enquetes sur le niveau de vie au Ghana et en Mauritanie

No.50 Food Subsidies: A Case Study of Price Reform in Morocco (also in French, 50F)

No.51 Child Anthropometry in C6te d'Ivoire: Estimatesfrom Two Surveys, 1985 and 1986

No.52 Public-Private Sector Wage Comparisons and Moonlighting in Developing Countries: Evidencefrom Cote d'Ivoire and Peru

No. 53 Socioeconomic Determinants of Fertility in C6te d'Ivoire

(List continues on the inside back cover)


The Living Standards Measurement Study

The Living Standards Measurement Study (LSMS) was established by theWorld Bank in 1980 to explore ways of improving the type and quality of house-hold data coUected by statistical offices in developing countries. Its goal is to fosterincreased use of household data as a basis for policy decisionmaldng. Specificaly,the LSMS is working to develop new methods to monitor progress in raising levelsof living, to identify the consequences for households of past and proposed gov-ernment policies, and to improve communications between survey statisticians, an-alysts, and policymakers.

The LSMS Working Paper series was started to disseminate intermediate prod-ucts from the TSMs. Publications in the series include critical surveys covering dif-ferent aspects of the LSMS data collection program and reports on improvedmethodologies for using Living Standards Survey (LSs) data. More recent publica-tions recommend specific survey, questionnaire, and data processing designs, anddemonstrate the breadth of policy analysis that can be carried out using Tis data.

ISMS Worlkng PaperNumber 87


John L. Newman and Paul J. Gertler

The World BankWashington, D.C.

Copyright © 1992The International Bank for Reconstructionand Development/THE WORLD BANK1818 H Street, N.W.Washington, D.C. 20433, U.S.A.

All rights reservedManufactured in the United States of AmericaFirst printing September 1992

j To present the results of the Living Standards Measurement Study with the least possible delay, thetypescript of this paper has not been prepared in accordance with the procedures appropriate to formalprinted texts, and the World Bank accepts no responsibility for errors.

The findings, interpretations, and conclusions expressed in this paper are entirely those of the author(s)and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to membersof its Board of Executive Directors or the countries they represent. The World Bank does not guarantee theaccuracy of the data induded in this publication and accepts no responsibility whatsoever for anyconsequence of their use. Any maps that accompany the text have been prepared solely for the convenienceof readers; the designations and presentation of material in them do not imply the expression of anyopinion whatsoever on the part of the World Bank, its affiliates, or its Board or member countriesconcerning the legal status of any country, territory, city, or area or of the authorities thereof or concerningthe delimitation of its boundaries or its national affiliation.

The material in this publication is copyrighted. Requests for permission to reproduce portions of it shouldbe sent to the Office of the Publisher at the address shown in the copyright notice above. The World Bankencourages dissemination of its work and will normally give permission promptly and, when thereproduction is for noncommercial purposes, without asking a fee. Permission to copy portions forclassroom use is granted through the Copyright Clearance Center, 27 Congress Street, Salem, M\assachusetts01970, U.S.A.

The complete backlist of publications from the World Bank is shown in the annual Index of Publications,which contains an alphabetical title list (with full ordering information) and indexes of subjects, authors,and countries and regions. The latest edition is available free of charge from the Distribution Unit, Office ofthe Publisher, Department F, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or fromPublications, The World Bank, 66, avenue d'1ena, 75116 Paris, France.

ISSN: 0253-4517

John L. Newman is economist in the World Bank's Welfare and Human Resources Division of thePopulation and Human Resources Department. Paul J. Gertler is senior economnist for the RAND Corporationand associate director of the Family and Economic Development Center.

Library of Congress Cataloging-in-Publication Data

Newman, John L., 1955-Family productivity, labor supply, and welfare in a low-income

country / John L Newman and Paul J. Gertler.p. cm. - (LSMS worldng paper, ISSN 02534517 ; no. 87)

Indudes bibliographical references.ISBN 0-8213-2253-21. Income-Peru. 2. Farm income-Peru. 3. Wages-Peru. 4. Labor

supply-Peru. 5. Family-Economic aspects-Peru. 6. Householdsurveys-Peru. 7. Welfare economics. I. Gertler, Paul J., 1955-. II. Title. mII. Series.HC230.15N48 1992331.1'0985-dc2O 92-27891

CIP

ABSTRACT

This paper develops an analytical approach to estimate family labor supply and

consumption decisions appropriate for developing countries. The approach allows for an

arbitrary number of family members, each of whom may or may not engage in multiple

activities. We identify the marginal returns to work in self-employment without directly

observing the marginal returns or estimating the enterprise's production function. The key

feature of the approach is to work with underlying structural marginal return and marginal rate

of substitution functions together with first order Kuhn-Tucker conditions.

We us this model to analyze family consumption and labor supply decisions of rural

landholding households in Peru. We estimate coefficients of the marginal rate of substitution

of family consumption for individual family member's leisure and marginal returns to two

activities - wage work and self-employed agriculture. Using the estimated coefficients of the

structural model together with the budget constraint, we simulate the effects of increasing returns

to wage work and self-employed agriculture on family consumption and hours of work in the

two activities. Estimating the structural parameters of the marginal rate of substitution allows

us to convert leisure to consumption units and to calculate the compensating and equivalent

variation of the changes in returns.

The results indicate that roughly 10 percent of the change in welfare following a pure

income transfer is accounted for by increases in leisure enjoyed by different family members.

A 20 percent increase in wage offers of prime-age males has roughly 2.3 times the effect on

family consumption than a similar 20 percent increase in wage offers of prime-age females,

conditional on there being an effect on the household at all. In order for there to be an effect,

at least one individual must either already be working in the wage sector or be induced to work

in the sector as a result of the change. On the other hand, a 20 percent increase in the marginal

returns to farm work of prime-age females and males has roughly the same effect on family

consumption. Taking into account the value of changes in leisure, the change in family welfare

due to a change in female returns is higher. This suggests that if the cost of achieving the gains

in productivity are comparable, then policies designed to enhance female productivity on the

farm would be an effective means of raising family welfare.

v

ACKNOWLEDGEMENTS

This paper has benefitted from comments by Arie Kapteyn, Mark Rosenzweig, Jacques

van der Gaag, and John Strauss and from excellent research assistance by Masako Ii and Menno

Pradhan. Paul Gertler gratefully acknowledges financial support from the NICHD Grant No.

P-50-12639.

- vi -

FOREWORD

What is the return to education in self-employed agriculture? Does raising the return to

females in self-employed agriculture have a larger effect on family welfare than raising that of

males? What is the effect of higher returns to off-farm work on labor supply in agriculture?

Answering these questions requires an analytical framework that reflects the multiple activities,

interrelations among family members, and importance of self-employment that characterizes

labor markets in developing countries. This paper attempts to provide that analytical framework.

The paper is part of a research program in the Population and Human Resources (PHR)

Department that examines the effect of government policies on household welfare. This research

program is located in the Poverty Analysis and Policy Division. The data used here are from

the Peru Living Standards Survey, one of the Living Standards Measurement Study (LSMS)

household surveys implemented in several developing countries with the assistance of the World

Bank. One of the objectives of this particular study and similar work using LSMS data is to

demonstrate the need for and usefulness of household data collection efforts in other developing

countries.

* Ann 0. HamiltonDirector

Population and Human Resources Department

- vii -

, , I . . . . . . .

TABLE OF CONTENTS

1. INTRODUCTION ........................................ 1

2. A FAMILY MODEL ...................................... 6

3. EMPIRICAL SPECIFICATION ............................... 10

SPECIFICATION ................................... 10

Wage function ...................................... 10Marginal return to farm work ............................ 11The marginal rate of substitution .......................... 13Observability ...................................... 15Logical consistency .................................. 16Identification ................................ 16

4. EMPIRCAL METHODS .................................... 19

ESTIMATON ..................................... 19

COMPARATIVE STATICS ............................. 22

5. FAMILY DECISIONS IN RURAL PERU ......................... 25

DATA AND SPECIFICATION ........................... 25

ESTIMATES OF STRUCTURAL COEFFICIENTS .... .......... 27

GOODNESS OF FIT ................................. 34

POLICY SIMULATIONS .............................. 36

6. CONCLUSIONS ........................................ 43

REFERENCES ........................................... 45

Appendix I. Residual Analysis ..................................... 47

- ix -

LIST OF TABLES AND FIGURES

Table 1. Means of Explanatory Variables .......................... 28

Table 2. Estimated Coefficients of Marginal Return and Marginal Rateof Substitution Functions (Females 18 - 64) ................... 29

Table 3. Estimated Coefficients of Marginal Return and Marginal Rateof Substitution Functions (Males 18 - 64) .......... ........... 30

Table 4. Estimated Coefficients of Marginal Return and Marginal Rateof Substitution Functions (Females 12 - 17) ....... ............ 31

Table 5. Estimated Coefficients of Marginal Return and Marginal Rateof Substitution Functions (Males 12 - 17) .32

Table 6. Actual and Predicted Values of Endogenous Variables .35

Table 7. Base Case - 10 Percent Random Sample of Households .38

Table 8. Policy Simulations . ................................... 39

Table Al. Kolmogorov-Smirnov Statistics for Hypothesis that Residualsare Normally Distributed ............................... 51

Figure Al. Plot of Quantiles of Simulated Residuals Against Quantiles ofNormal Distribution (Males/Females Aged 18-64) ............... 53

Figure A2. Plot of Quantiles of Simulated Residuals Against Quantiles ofNormal Distribution (Males/Females Aged 12-17) ..... .......... 54

-x -

1. INTRODUCTION

In developing countries the empirical investigation of standard issues such as the

returns to human capital, labor supply, and consumption decisions is complicated by

the structure of families. Small family enterprises, both agricultural and non-

agricultural, account for much of production, and many family members work only in

the enterprise. However, it is also common for some family members to work outside

for a wage, for some to do both, and for some not to work at all. For example, in a

1985 sample of 1390 households in rural Peru, 57 percent of prime age males worked

only in the family enterprise, 18 percent worked only for a wage, 11 percent did both,

and 14 percent did not work. Families in developing countries typically have a large

number of members and the young and the elderly often work. In our rural Peru

sample, the number of workers in a family ranged from one to ten with over 60 percent

of families having three or more workers.

Accounting for this reality within an empirical family model is difficult, even

assuming a single decision maker. Three problems present themselves: the jointness of

production and consumption decisions, the interdependence of family members

activities in the utility and enterprise production functions, and the difficulty in

measuring the marginaal returns to working in the enterprise.

Family consulmption decisions are linked to their decisions on enterprise

production, except under certain restrictions on nature of markets, on the enterprise

production technology, and on the family's preference structure.' Total production

depends on family labor supply to the enterprise. Family labor supply is based, in part,

1 See Singh, Squire, and Strauss (1986) and Benjamin (1992) for models of joint productionand consumption. They show that only when families are price takers in both consumption andproduction markets (including labor), when there are no nonparticipation corners, and hired labor andfamily labor are perfect substitutes can family consumption and production decisions be treatedseparately. These requirements are suspect in many developing countries. However, Pitt andRosenzweig (1986) and Benjamin (1992) cannot reject these restrictions for Indonesia.

on the family's relative marginal utilities of consumption and of leisure - i.e. time

spent in non-income producing activities, such as education, leisure, and home

production. Family labor supply to the enterprise also depends on the comparison of

individual members' marginal returns to working in the enterprise to what can be

earned in the wage sector.

The family cannot decide the time allocation of one family member

independently of another. Family members are linked through the utility and

enterprise production functions. The marginal return to one individual working in the

family enterprise depends on the labor supply of other family members. Moreover, the

family's marginal utility of one member's leisure depends on the amount of leisure

enjoyed by other family members as well as family consumption. We define leisure as

time spent in non-income producing activities.

Unlike wage work, the marginal return to working in a family enterprise - the

derivative of the enterprise net profit function - is unobservable. Only total

production and profits net of nonfamily labor expenses are, in principal, directly

observable. Even these data are extremely costly to collect and many times suffer from

substantial measurement error (Casley and Lury, 1990; Viverberg, 1991). While a

substantial number of farm production and net profit functions have been estimated,

most treat production and consumption decisions separately. Many treat labor as an

aggregate good and therefore can not examine individual returns to work. Many treat

factor inputs such as labor as exogenous.2 Because of these data problems little work

has been completed on the determinants of the marginal return to work in family

nonagricultural enterprises.

2 A recent paper that address this issues is Jacoby (1990) who estimates shadow wages inagricultural self-employment from the agricultural production function. However, Jacoby modelsproduction independently of consumption and off-farm labor supply.

-2 -

In this paper, we develop a unified framework to address many of problems that

make modelling family decisions in developing countries difficult. In the model, the

family jointly determines consumption and the labor supply of individual members.

The model allows for an arbitrary number of family members, each of whom may or

may not engage in multiple activities. We specify a structural model that identifies the

marginal returns to work in self-employment even though they are not directly

observed. Our approach does not require estimation of an enterprise production

function.

The model consists of two types of structural equations and an identity: marginal

return functions for each activity for each family member, the family's marginal rate of

substitution of family consumption for each family member's leisure, and the family

budget constraint. A family connection is maintained through several avenues. The

marginal return to self-employed work depends on own and other family members'

hours worked in that activity. In addition, the family's marginal rate of substitution of

an individual's leisure for family consumption depends on own leisure, the leisure of

other family members, and consumption. We treat this specification as a system of

simultaneous equations and use the first order Kuhn-Tucker conditions to model

possible nonparticipation of any family member in any and all activities.

An important advantage of working with the structural equations is the

opportunity to do welfare analysis. Estimating the structural parameters of the

marginal rate of substitution allows us to convert leisure to consumption units and

calculate the compensating and equivalent variations of the changes in exogenous

variables such as factors that influence the returns to work.

We apply this model to family consumption and labor supply decisions of rural

landholding households in Peru. We estimate coefficients of marginal returns to two

-3 -

activities, wage work and self-employed agriculture, and the marginal rate of

substitution of consumption for leisure. We then use the estimates to examine the

effects of poverty alleviation programs on labor supply, consumption and welfare of

families in rural Peru. The poverty alleviation policies include programs that increase

the returns to work in agriculture such as agricultural extension offices, increasing the

returns to wage work through for example training, targeting these programs to females

versus males, and direct transfer programs.

Many of the features that we incorporate into our unified framework have been

treated separately in previous literature. While structural models of individual labor

supply decisions date from Heckman (1974), structural models of family labor supply

are relatively rare.3 A larger literature deals with reduced form family models. One

strand of the literature focuses on the jointness of production and corLsumption

decisions4. A second looks at the interdependence of labor supply decisions of different

family members. However, the typical model of family labor supply usuallr consider

the case where the husband works full-time for a wage and the wife may or may not

work5 . A few papers look at labor supply to multiple activities6 . However, these

3 Kooreman and Kapteyn (1987) take an indirect utility function approach to estimatinghusband and wive's time allocation decisions among market work and multiple home productionactivities jointly with the demand for goods. However, they only consider the nonparticipation ofwives in market work. They are not able to estimate the marginal return to home productionactivities. Lopez (1986) estimates parameters of a household's consumption demand and productionfunction. However, because he uses aggregate data, he does not look at individual labor supply or atthe possibility of nonparticipation.

4 See Singh, Squire, and Strauss (1986) for a good review of the literature on joint productionand consumption decision making.

5 For example see Ashenfelter and Heckman, 1974; Hausman and Ruud, 1984. A notableexception is Pitt and Rosenzweig (1981), who look at the effect of children's illness on adults' laborsupply.

6 A few papers have looked at multiple activities. Rosenzwieg (1978 and 1980) considers off-farm labor supply of individuals living on farms, Huffman and Lange (1989) and Ransom (1987)consider family models where husbands work on the farm and wives may work on or off the farm.Graham and Green (1984) and Gronau (1977) examine individuals' time spent in wage work andhome production.

-4 -

models do not consider consumption decisions jointly with labor supply and do not yield

estimates of the welfare effects of changes in leisure7.

The paper is organized in the usual way: theory, empirical model, application,

and conclusions.

7 Only Ransom (1987) explicitly includes consumption as a determinant of labor supply, buttreats consumption as exogenous.

- 5-

2. A FAMILY MODEL

Consider a family with N members whose utility function8 is:

u U (C, 4el12, ... ) (1)

where: C is the value of total (aggregate) household consumption, Ii is theleisure of family member i.

The family faces a budget constraint and N time constraints, one for each

member. Each family member can engage in M possible activities. The family's budget

constraint is:

MV + E Qj(Hl,,...,HNj I Fj) = P C (2)

j=l

where: V is nonlabor income, Q, is the total value to the family of engagingin the jt activity, Hij is hours of work individual i spends in the jth activity,F. is a vector of semi-fixed enterprise inputs, and P is the price of theaggregate consumption good.

If activity j is wage work, then Qj is the wage income earned by the family (i.e.

Qj= wijH,j where w,j is individual i's wage). If activity j is a family enterprise, then

Qj(*) is the net profit function. The time constraints are:

ME Hj, + gi = T , i=1,...,N (3)j=1

where T is total time available for an individual and Hij > 0 for all i and j.

The optimization problem is to choose the hours that each member supplies to

8 This specification of the family utility function implicitly assumes that families use a two-stage decision making process. They first allocate resources among total family consumption and theleisure of each member and then allocate consumption among members.

-6 -

the various activities and the total value of family consumption so as to maximize

utility subject to budget, time and non-negativity constraints. The first order

conditions consist of the budget constraint in equation (2) and:

Him 2 0, Him ( U (C .. , (I,,...,HNI )0 V im (4)

1 Ou(C, e1'e2'---"N ) =_ S49 (l 12 .. 4N P (5)

where, via the time constraint, ii = T - E Hi,,,, . The term A is the Lagrange multiplierm=1

on the budget constraint and in equilibrium is equal to the family's marginal utility of

income.

We reformulate the first order conditions into expressions that will later prove

more empirically tractable. As specified above, the first order conditions depend upon

the marginal values of leisure and the marginal returns. The marginal value of leisure

functions depend upon the arguments of the utility function and the determinants of the

marginal utility of income (A). In equilibrium, the marginal utility of income depends

upon all endogenous and exogenous variables, which would render identification of a

specification based on the parameterization of the marginal value of leisure and

marginal returns impossible.

An alternative is to reformulate the first order conditions in terms of the

marginal rate of substitution of consumption for individual members' leisure. Using

equation (5) to substitute for (1/A) in equations (4) and dividing by P, the price of

-7 -

consumption, yields:

Hi > 0, Him (MRSj - H m V i, m (6)

a9 U (C, 9l,42, ...- N)

where: MRS = a e eU (C,914 2r--gN )

0C

The reformulated first order conditions consist of equations (2) and (6).

The conditions for participation and the determination of hours worked are

analyzed by comparing the real marginal returns with the marginal rate of substitution.

An individual i will not participate in activity j if the family's marginal rate of

substitution of consumption for i's leisure is greater than i's marginal return in activity

j, evaluated at zero hours of work in activity j. If, evaluated at zero hours, the

marginal return is greater, then the individual will work up to the point where the

marginal return is equated to the family's marginal rate of substitution.

An important issue for the empirical specification is that the margin functions

cannot have arbitrary properties. Specifically, if one of the marginal returns is constant

(i.e. wage work), then the marginal rate of substitution must increase with hours

worked (decrease with leisure) to assure the possibility of an interior solution for work

in the wage sector. In addition, for an individual to possibly be able to work in more

than one activity, at least one of the marginal return functions must depend negatively

on hours worked. Otherwise, if an individual worked at all, he or she would specialize

in the activity with the highest marginal return or wage. In general, to work in M

activities, M -1 marginal return functions must depend negatively on hours worked.

-8 -

Working with the marginal rate of substitution allows us to conduct welfare

analysis. Consider the effect of an increase in an individual i's market wages induced,

for example, by an exogenous increase in the demand for wage workers. Differentiating

the utility function with respect to the wage yields,

dU(C,el,..iN) a U DC +AU a +l dU 2 . U a8N

dwi =aCw awi +a, awi + s2 aWi *aN aWi

Dividing this by the marginal utility of consumption yields,

(du(CA-.9N) 8c+

dw; = 8C + MRS, al + MRS2 a .+ + MRSNagN (7)

In equilibrium a' the marginal utility of consumption, is cqual to AP, the

marginal utility of income. Thus, the left hand side of (7) is the change in utility

valued in real monetary units. The first term on the right hand side is the change in

consumption, where consumption is valued in real monetary units. The other terms on

the RHS are the changes in leisure for each individual in the family weighted by the

MRS1 . The MRSi converts individual i's leisure into consumption units. When the

MRSi is evaluated at the equilibrium values of consumption and leisure before the

change in wages, this expression measures the compensating variation. When it is

evaluated at the equilibrium values after the change, the expression is the equivalent

variation.

-9-

S. EMPIRICAL SPECIFICATION

In our empirical application we look at two activities - farm and off-farm work.

In this case, our family model consists of marginal return functions for both activities

for each family member, the family marginal rate of substitution of family consumption

for individual leisure for each family member, the Kuhn-Tucker equilibrium conditions,

and the family budget constraint. These equations are all that are needed to examine

the labor supply and consumption decisions, and to make welfare comparisons. It is not

necessary to recover either the underlying utility functions from the marginal rate of

substitution function or the underlying agricultural net profit function from the

marginal return functions.

Our approach is to parameterize and estimate the margin functions. The main

objectives in specifying the margin functions are to obtain parsimonious yet flexible

functional forms that are consistent with theory. In this section, we discuss

specification and identification of the marginal functions. In section 4, we present

estimation and comparative statics methods.

SPECIFICATION

Wage function

We define off-farm work as working for a wage, whether in agriculture or not.

The marginal return is therefore independent of hours worked. Following standard

practice in the literature, we specify family member i's real wage as a log-linear

function,

In Q p t In = Xii. + ei X i= 1, ... ,N (8)

- 10 -

where: Xi. is a vector of individual i's characteristics, such as age andeducation, that affect i's market wage and ei. is a zero mean randomdisturbance.

Specifying a common p across all individuals means that differences in the log

wages across individuals will arise only from differences in individual characteristics and

the random error terms. This restriction can be relaxed by allowing 6 to depend on

demographic characteristics of the individual. In our empirical specification we allow /

to depend on whether the individual is a young male, young female, prime-age male, or

prime-age female. This is equivalent to specifying separate log wage functions for each

of the four demographic groups. Within any given demographic group, the log wages

will vary with the characteristics and the random error terms.

Marginal return to farm work

In estimation, we exploit the Kuhn-Tucker conditions to model nonparticipation

corners and deal with the unobservability of the marginal return to farm work and the

marginal rate of substitution. This requires comparison of the marginal real return

functions with each other and with the marginal rate of substitution. These

comparisons are simpler if the marginal return to farm work and the marginal rate of

substitution are also specified as log-linear functions. Otherwise, the empirical model is

nonlinear in parameters and errors do not enter additively. Our specification the

natural log of the real marginal return to farm work of individual i is:

en p i 9Qf =n F= Xijf3if + yiHif + E i1 H,1 + (9)

where: H is i's hours of farm work; Hjf is other family member j's hours inagricultural production; X; is a set of personal, family, and communitycharacteristics, including other fixed factors of production such as land andfarm equipment; and eif is a random productivity shocks.

- 11 -

Note that we allow the coefficient of own hours to differ from that of other

family members' hours. Since the inputs into agricultural production enter the

marginal return separately, no second order restrictions are placed on the unlderlying

enterprise net profit function.9

The error term in the marginal return represents unobserved factors affecting

individual i's productivity in farm work. These unobservable productivity

characteristics in the marginal return to farm work may be the same as those

influencing the wage. Therefore, the error terms in (8) and (9) are likely to be

correlated.

As specified, individual i's characteristics such as age and sex only affect the

intercept, but do not affect the rate at which the marginal return declines with own

hours. In our empirical implementation, we allow not only the coefficient vector #if but

also the coefficient yj to differ for individuals across the four demographic groups. We

also allow zyj to depend on the specific demographic groups of individuals i and j.

Similar to the wage function, this is equivalent to specifying separate marginal return to

farm work equations for each of the four demographic groups. Within each group, the

marginal returns will differ according to the individual and family characteristics and

the hours worked by all family members.

The added flexibility introduced by allowing every other family member's hours

to have a separate impact on the marginal return would greatly increase the parameter

space. This is especially problematic because our sample contains some families with a

9 In general, other factors of production would affect the individual's marginal return to farmwork. If these factors reflect current period input choices of the household, then, assuming one hadinformation on the input use and relevant prices, one would want to estimate simultaneously otherinput demands, labor supply, family production, and consumption. With sufficient data, this wouldbe feasible. However, in this version, we have simplified the problem by imposing zero restrictions onthe cross partial effects of labor use and variable farm inputs (e.g. hired labor and fertilizer). Thisimplies that the variable farm inputs do not enter the marginal returns. We do allow for cross effectsof labor and fixed inputs - land and farm equipment.

- 12 -

large number of pot;ential workers. We make the model parsimonious by restricting the

effects of other family members' hours to be equal within a demographic group - that is,

zsj is restricted to be equal to Yik for individuals j and k in the same demographic group.

For example, the effect of the hours of work of a young male j on the marginal return of

a prime age male is restricted to be the same as the effect of the hours of work of

another young male on the marginal return of a prime-age male. If there is no other

family member in the demographic group, then the total number of hours worked in

that group is zero. The restriction implies that, in addition to own hours, the sums of

the hours worked by all members within each of the four demographic groups appears

on the right hand side of equation (9).

The effect of another individual j's hours of work on i's marginal return (yij),

will only be equal to the effect of i's hours on j's marginal return (7yj) if the two

individuals are in the same demographic group. However, the cross effects are not

restricted to be equal when they are in different demographic groups. For example, the

effect of a young male's hours of farm work on a prime-age male's marginal return need

not equal the effect; of a prime-age male's hours on a young male's marginal return.

The marginal rate of substitution

Recall that the marginal rate of substitution (MRS) is the slope of the

indifference curve. We enter all of the arguments of the utility function separately into

the log MRS, ensuring that there are no second-order restrictions on the shape of the

indifference curve and, therefore, on the underlying utility function.

NinMRS = Zia; + orjcC + bili + E jt + Uj , i= 1,...,N (10)

where: a's and 6's are parameters, and 1u are random taste shifters 'withzero mean.

- 13 -

The MRS1 changes with respect to family consumption, own leisure, and every

other family member's leisure. For a diminishing MRS,, the sign of 6i must be negative

and the sign of ai, be positive. That is, the MRS, decreases with own leisure and

increases with family consumption. The signs of the bj indicate how the MRS1 changes

with increases in j's leisure and defines whether the family views i and j's leisure to be

substitutes or complements.

The error term in the marginal rate of substitution represents unobserved

preferences and tastes. It is assumed to be uncorrelated with the unobserved

productivity shocks in the wage and marginal return functions, equations (8) and (9).

As specified, individual i's characteristics such as age and sex only affect the

intercept of MRS,. They do not affect the rate at which the MRSi varies with the

arguments of the utility function. To achieve greater flexibility, we allow all the

parameters of equation (9) to differ according to the demographic group of individual i.

As with the wage and marginal return to farm work functions, this is equivalent to

specifying a different function for each of the demographic groups.

Again, the flexibility introduced by allowing every other family members' leisure

to have a separate impact on the MRSi would greatly increase the parameter space.

We approach the problem in exactly the same way as we did before. Therefore, in

addition to own leisure and family consumption, the sums of leisure of all members

within each of the four demographic groups appears on the right hand side of equation

(9).

The effect of an individual j's leisure on the MRS; (6ij) will only be equal to the

effect of i's leisure on the MRSj (6j,) if the two individuals are in the same demographic

group. However, the cross effects are not restricted to be equal when the two

individuals are in different demographic groups.

- 14 -

Obseruability

A major stumbling block is that the marginal rate of substitution and the

marginal return to farm work cannot be observed directly. Utility functions and their

margins are never directly observable. An individual's marginal return - the

derivative of the net profit function - is only directly observable when the enterprise

uses a single input. However, because we observe the wage, we can use the Kuhn-

Tucker conditions to infer equilibrium values of the MRS and the marginal return to

farm work depending on participation in the two activities. In some regimes the

equilibrium values of the MRS, and the marginal return are equal to the wage rate. In

the other regimes in which we cannot observe the equilibrium values, the Kuhn-Tucker

conditions provide bounds on the equilibrium values. This will be exploited later in the

specification of the likelihood function. Below we summarize the information contained

in the Kuhn-Tucker conditions.

Observability of Dependent Variables

WVorking on Farm Not Working on Farm

w_ _Working - -MRS (H., Hf) W= MRS (H., Hf=O)for wage P

w = MRF(Hf) w MRF(Hf=O)p= P P P

Not Working MRS(HW=O, Hf) > w MRS(HW=O, Hf=O) > pfor wage

MRFp(Hf) = MRS(HW=O,Hf) MRS(HW=O, Hf=O MRF(H=)

- 15 -

What can be observed depends upon the work regime of the individual. If the

individual is working both on and off the farm, then his or her wage is equal to the

marginal return to farm work and the MRS. If the individual is working only for a

wage, then the wage is equal to the MRS and is greater than the marginal return to

farm work evaluated at zero hours of farm work. If the individual is working only on

the farm, the marginal return is equal to the MRS and greater than the wage. If the

individual is not working at all, the MRS evaluated at zero hours of wage work and

farm work is greater than the marginal return and the wage.

Logical consistency

The specification of the margin functions must satisfy logical consistency

conditions of multiple regime models (Amemiya, 1974; Waldman, 1981; Maddala, 1983).

The above discussion points out that there are multiple regimes in our empirical model.

This arises because there are multiple activities with the possibility of nonparticipation.

Since the regimes are mutually exclusive, if an individual satisfies the conditions for

being in one regime, he or she must not simultaneously satisfy the conditions for being

in another (i.e a unique solution). In addition, the specification must allow for the

possibility of interior solutions. In our case, the logical consistency conditions are

satisfied if the marginal return to farm work decreases with own hours and the MRS

decreases (increases) with own leisure (work). We do not impose the logical consistency

conditions in the specification. Rather, we check the estimated coefficients to see

whether they are satisfied and find that they are.

Identification

To simplify the exposition, we discuss identification and, later, estimation of the

- 16 -

model for a two person household. The results can be readily extended to an n-person

household. The model for the two person case consists of the marginal return and

marginal rate of substitution functions of each individual, the Kuhn-Tucker conditions

applying to each individual, and the family budget constraint. Thus, the system of

equations is:

gn MRS, = Zlaor + alcC + bl(T-H1 .-Hlf) + b 1 2 (T-H2 .- H2 f) + ul (11)

Pn pl = Xljw, + Elw (12)

in MRl = X1 .01f + yl Hlf + 7 12 H2f + Elf (13)P

in MRS2 = 2c]2 + a 2cC + 62 (T-H2 w-H2 f) + 62l(T-Hlw-Hlf) + u2 (14)

ip = X2wf2 2w + E2w (15)

n MRF2 = X 2 #2f + 7Y2H 2 f + 721 Hlf + e2f (16)p

Hl. (Wl- MRS,) = 0 , Hl w > 0 (17)

Hlf* (Ml_ MRS 1 ) = 0, Hlf 2 0 (18)

H 2 . (2 p- MRS 2 ) = H 2W > 0 (19)

H2 f * (M2_ MRS2 ) = 0, H2 f > 0 (20)

P C = V + exp(Wl w ) Hlw + exp(W 2 ) .H 2 w +

Hlf H2f

fexp(MRF,(hl, h2)) dhl + f exp( MRF2 (h1 , h2 )) dh2 (21)

0 0

-17 -

Note that the marginal returns to farm work depend on the farm hours of both

individuals. Similarly, the marginal rates of substitution depend on the leisure of both

individuals. Following our discussion of the previous section, if the two individuals are

from the same demographic group the coefficients in their margin functions will be the

same. If the two individuals are from different groups, these coefficients will be

different.

We estimate the coefficients in equations (11-16). The wage equations are

identified as there are no right hand side endogenous variables. However, identification

is an issue in the marginal return to farm work and the MRS equations. Identification

is achieved through natural exclusionary restrictions.

The marginal return to farm work depends on own and the other individual's

hours of work. Excluded from this equation are individual, family, and community

variables that affect own wage, own MRS, and the other individual's wage, MRS, and

marginal return to farm work. Candidate variables include wage experience,

community-levei demand for wage workers, taste shifters, and the other individual's

education and farm experience.

The marginal rate of substitution depends on family consumption, own total

hours of work, and other's total hours work. Excluded from this equation are unearned

income and individual, family, and community variables that affect the wage and the

marginal returns to farm work. Candidate variables include own and other's work

experience, fixed factors affecting agricultural production (such as land), producer

prices, and community-level demand for wage workers. As long as there are personal

characteristics that affect the return to one activity that do not affect the return to

another, exclusionary restrictions also identify households with more than two members.

- 18 -

4. EMPIRICAL METHODS

ESTIMATION

We assume that the error terms in the (log) wage, marginal return to farm work,

and MRS equations are from a multivariate normal distribution and estimate the model

using maximum li]kelihood10 . With no restrictions on the covariances, the likelihood

function for a two-person household involves quadruple integration. The likelihood

function for an N-person household involves 2 N integration. Because our sample

includes householdls with up to ten members, allowing a completely unrestricted

covariance structure is computationally burdensome.

We restrict error terms to be uncorrelated across family members. Given the

assumption that the error terms across individuals are uncorrelated, the multivariate

normal distribution of the errors factors into independent components involving only

errors of a single individual. The likelihood function involves no dimension higher than

a bivariate density. In addition to simplifying the computation, these covariance

restrictions across individuals provide overidentifying information.

Even though the likelihood function factors into separate terms for each

individual, full information estimation of the model must still use the family as the unit

of observation. This is because family consumption appears in the MRS of each family

member. A full information approach requires us to substitute in the budget constraint

for consumption to account for endogeneity. This introduces nonlinearities in

parameters and error terms, which increases the complexity of estimation.

We follow an alternative, limited information approach, and do not impose the

10 In our empirical application we examine the validity of the normality assumption.Appendix 1 presents 1ilots of estimated residuals and normality tests based on the estimated residuals.

- 19 -

budget constraint in the estimation. First, we predict family consumption using

nonlabor income and the presence of other relatives living away from home as

identifying variables. As family consumption is a continuous variable, this

instrumenting can be done by OLS.'1 In the second step, we replace actual family

consumption with its predicted value from the first stage.

Together with the assumption of uncorrelated errors across individuals,

conditioning on consumption results in a family likelihood function that is separable

across the individual members. This allows us to estimate the structural coefficients of

the model in the second stage using individuals as the units of observation. Because we

allow the coefficients to differ for each one of four demographic groups, we estimate the

second stage separately for individuals in each group.

While the error terms are assumed uncorrelated across individuals, we allow the

error terms in the wage and marginal return to farm work equations for an individual to

be correlated. These error terms represent unobserved productivity factors. The error

terms in the marginal rate of substitution represent taste shifters, which we assume are

uncorrelated with the unobserved productivity factors.

11 This assumes that family consumption is a continuous function of the underlying latentvariables (the wage and marginal return to farm work). See Blundell and Smith, 1990.

- 20 -

The likelihood function in the second stage for individual 1 in our two-person

household is:

= Y * 61 * f( W1-Xl.)1w , Wl-Xpljf-7Hlf- 712 H2f, W1- Z1cl- acC -

6i(T-H1 .- Hj1) - 612(T-H2 u,-H2f) , Pwf Pwu ,Pfu

UB2

I6 I f (W,-Xlwt6lw I Y }

W1- Zial- acC - bl(T-HI.) - 612(T-H2.- H2f) Pwf, p , pu)fu d y

UB1f I -7- 61 f ( x, Zlal + atcG + 61(T-Hlf) + 612(T-H2w-H2 f)

-00

=Xl,8f-yjHlf Sy12H2f7 pi ) dxz

UBI1 UB2

f f f(xz,y, p') dxzdy

where: W1 = In WP

UB1 = Zlal + acC + 6l(T-Hlw) + 612(T-H2w-H2j) - X1p61 - yl2H2f

UB2 = - X6f

p, = Pwf Uw O, - PW;WvO' - Pfuafu + OIUp ol~~~~~w u * OJf-u

Estimating the structural coefficients in this likelihood function is a

computationally tractable problem. However, it still requires a considerable amount of

time for the estimation to converge. For example, estimating the model with 39

- 21 -

parameters for a sample of 2352 individuals takes overnight to converge using GAUSS

on a 25 Mhz 80486 machine.

It is possible to relax the covariance restrictions since the model is identified

through exclusionary restrictions. However, the added computational burden makes

these extensions impractical for the moment. The simplest way of relaxing the

covariance restrictions across individuals would be to include family specific error terms

in the marginal return to farm work and MRS equations. These terms could be treated

as random effects. Conditional on the common family effects, the error terms of the

individual family members would be independent and the common factors could be

integrated out. Even this step adds considerably to the computational complexity, for

it requires using the family, rather than the individual, as the unit of observation. It

also increases the order of integration in the family likelihood function by two.

Similarly, it is possible to impose the budget constraint at the cost of additional

computational complexity.12

COMPARATIVE STATICS

The estimated structural coefficients provide information on the effects of

explanatory variables on the wage, marginal return to farm work, and the MRS. This is

of interest in and of itself. For example, we can estimate directly the rate of return to

education in self-employed farm work. We can also learn how families value leisure of

family members in different demographic groups. However, knowledge of the structural

coefficients alone does not provide information on the effects of exogenous explanatory

variables on family choices and welfare.

To obtain the family choices and welfare, we use the estimated structural

12 We are investigating the feasibility of these extensions using recently developed simulatedintegration methods.

- 22 -

coefficients and the Kuhn-Tucker conditions to solve for the utility maximizing values

of labor supply and family consumption. The structural coefficients were obtained using

individuals as the units of observation. However, due to the interdependence of the

margin functions and the binding family budget constraint, solving for the equilibrium

choice values requires using the family as the unit of analysis.

To obtain comparative statics, we calculate the equilibrium values before and

after a change in an exogenous variable. Operationally, this involves computing the

solution for each of the possible regimes and checking which one satisfies the Kuhn-

Tucker conditions. :Since the logical consistency conditions are satisfied in estimation,

we are assured that only one solution satisfies the Kuhn-Tucker conditions.

For the two-person household, we use equations (11-16) replacing the coefficients

with their estimated values. These equations include unobserved errors. We could

replace them with their mean values. However, due to the nonparticipation corners,

there are multiple regimes. Conditional on being in a particular regime, the mean of

the error terms are means of truncated trivariate normals and are nonzero. The means

need to be calculated separately for each regime. With two household members there

are 16 possible regimes. With four family members, there are 256 possible reduced

forms. The means are different for each family because they depend on the

characteristics of the family and therefore must be calculated separately for each family.

Rather than using conventional numerical integration, we simulate the error

distributions. We work with each family separately. Given the estimated variance-

covariance matrix of the error terms in the wage, marginal return to farm work, and

marginal rate of substitution equations for the particular age and sex group, take a draw

of the error terms. Given the draw, all terms on the right hand side of the margin

equations are known. We evaluate each of the possible regimes to determine in which

- 23 -

regime the Kuhn-Tucker conditions are satisfied. We then repeated the procedure for

100 draws. The average values of the solutions provides a measure of the unconditional

expected values of the endogenous variables. The percentage of solutions which fall in a

particular regime provide an estimate of the probability of being in that regime.

- 24 -

5. FAMILY DECISIONS IN RURAL PERU

DATA AND SPECIFICATION

Data used in this study are drawn from the Peruvian Living Standards Survey

(PLSS), conducted between July 1985 and July 1986 as a collaborative effort between

the Instituto Nacional de Estadistica in Peru and The World Bank. A random sample

of 5,120 households was chosen to reflect the distribution of the population in urban and

rural areas and in four natural regions. The households were chosen with an equal

probability of being selected in any given month to minimize the impact of seasonal

variation. This multipurpose survey collected information on family background and

resources available to the households. Thus, it gathered data on health, education and

training, migration, housing, fertility, income, expenditures, assets, labor force, and

faxm and business activities. In rural areas, the household level information was

complemented by a community questionnaire which gathered information on public

services, transportation, communication, and prices.13 Our sample includes all

households outside of Lima with land holdings greater than 0.01 hectares.

We estimate structural coefficients for the wage, marginal return to farm work,

and marginal rate of substitution functions for all family members aged 12 to 64.

Following the discussion in section 3, we classify all family members into four age and

sex groups - males aged 12 to 17, females aged 12 to 17, males aged 18 to 64, and

females aged 18 to 64 - and estimate separate structural coefficients for each group.

We estimate two models. The unrestricted model allows the total hours of farm

work of other family members within each age and sex group to affect one's own

13 For more information on the Peruvian survey, see The World Bank (1986). The Peruviansurvey is part of a series of Living Standards surveys conducted in an increasing number of developingcountries by The World Bank and the central statistical agencies. Surveys have been conducted or arecurrently in operation in C6te d'Ivoire, Mauritania, Ghana, Jamaica, Bolivia, Morocco, and Pakistan.

- 25 -

marginal return to farm work. It also allows the marginal rate of substitution to depend

upon the total hours of leisure of other family members within each age and sex group.

The restricted model allows only the effect of one's own hours of farm work to affect

one's own marginal return to farm work. Similarly, the marginal rate of substitution is

restricted to depend only on one's own leisure.

As discussed earlier, we follow a two-step estimation procedure. In the first step

we predict family consumption using nonlabor income and the characteristics of

relatives living outside the household as the principal instrument.14 It is measured as

the sum of retirement and pension benefits, medical or life insurance, interest on savings

accounts or other forms of savings, dividends on bonds and profit shares, rentals for

buildings, machinery, and vehicles, and inheritances. The measure of total family

consumption includes imputed returns from consumer durables and a valuation for the

auto-consumption of agricultural crops.'" It is deflated to reflect June 1985 values by a

temporal price index specific to one of thirteen regions.

The variables in the marginal rate of substitution equation are family

consumption, own leisure of the prime age male and female and a set of taste shifters.

The total hours of leisure for an individual are calculated as the total hours in the week

minus the hours spent in farm work and the hours spent in off-farm work. Leisure

includes hours spent working at home, taking care of children, and attending school. In

subsequent analysis we plan to analyze home production and hours of schooling jointly

with market work. The number of potential workers in the family and the individual's

age and age squared make up the set of taste shifters.

The marginal return to work on the farm is assumed to depend on the hours the

14 The instrumenting equation for real monthly household consumption had an adjusted R2 of0.38. The coefficient on other income was positive with a t statistic of 3.7.

5 For further details on the construction of this variable, see Glewwe (1987).- 26 -

individual works on the farm, the family's farm assets, the log of land, seasonal

dummies, agricultural producer prices, and vector of individual characteristics. The

omitted season is that of June, July, and August. The family's farm assets are

measured as the total value of equipment and the value of livestock. The producer

price index is calculated from the median price of the 16 most important agricultural

crops in Peru, which account for 80 percent of the value of all production. With fixed

weights, variation in the producer prices arises from price variation over 13 regions of

the country. Ideally, it would be desirable to calculate the index only from the price of

cash crops so as to avoid correlation between producer and consumer price indices. The

personal characteristics are age, education, and the years of experience in agricultural

work.

The wage is assumed to depend on the provincial per capita GDP, the

population density in the province, the distance from the individual's residence to a

permanent market, a dummy variable equal to one if the family's community is served

by public transportation two or more times a day, and the individual's age, age squared,

education, and the years of experience working for others.

Following the discussion in sections 3A and 3B, we allow all coefficients, sigmas,

and correlation coefficients to differ for males and females. The means of the

explanatory variables for each of the age and sex groups are presented in Table 1.

ESTIMATES OF STRUCTURAL COEFFICIENTS

Tables 2 through 5 present the estimated coefficients for females aged 18 to 64,

males aged 18-64, females aged 12-17, and males aged 12-17. The first column presents

estimates for the restricted models and the third for the unrestricted models.

Likelihood ratio tests reject the restricted in favor of the unrestricted model. In both

- 27 -

Table 1. Means of Explanatory Variables

M 12-17 F 12-17 M 18-64 F 18-64

Variables in wage function

GDP per capita/1000 0.13 0.13 0.13 0.13Population density/1000 0.03 0.03 0.03 0.03Km. to permanent market/100 0.94 0.95 0.92 0.85Availability of Public Transport 0.52 0.53 0.54 0.55Wage experience/100 0.003 0.001 0.06Age/100 0.14 0.14 0.37 0.37Years of schooling/10 0.43 0.39 0.44 0.27

Additional variables in marginal return to farm work equation

Farm assets/100 0.07 0.07 0.07 0.07Log of land 0.67 0.67 0.67 0.54Producer price 0.99 0.99 0.99 0.99Seasonal dummy 1 0.25 0.27 0.26 0.27Seasonal dummy 2 0.24 0.22 0.26 0.25Seasonal dummy 3 0.30 0.30 0.28 0.27Farm experience/100 0.039 0.036 0.17 0.16Total male 12-17 farm hours/100 0.09 0.08 0.09 0.08Total female 12-17 farm hours/100 0.07 0.08 0.08 0.07Total male 18-64 farm hours/100 0.40 0.42 0.22 0.40Total female 18-64 farm hours/100 0.32 0.32 0.30 0.14Own farm hours/100 0.18 0.17 0.30 0.23

Additional variables in marginal rate of substitution equation

Number of potential workers/10 0.47 0.47 0.41 0.40Predicted consumption/10000 0.1448 0.1426 0.1433 0.1415Total male 12-17 farm leisure/100 0.70 0.68 0.70 0.69Total female 12-17 farm leisure/100 0.70 0.74 0.75 0.69Total male 18-64 farm leisure/100 1.77 1.82 0.99 1.75Total female 18-64 farm leisure/100 1.92 1.91 1.97 1.04Own leisure 1.47 1.50 1.28 1.38

- 28 -

Table 2. Estimated Coefficients of Marginal Returnand Marginal Rate of Substitution Functions

(Females 18 - 64)

Coef. Std. Error Coef. Std. Error

Wage

Constant -4.58' 0.89 -4.69* 0.89GDP per capita (/1000) 1.01 0.86 1.00 0.84Population density (/1000) -0.67' 1.44 -0.92 1.38Km. to permanent market (/100) -0.24' 0.07 -0.25* 0.07Availability of public transport 0.42* 0.16 0.40 0.16Experience in Wage work (/100) 12.34' 1.27 12.28* 1.23Age (/100) 9.35' 4.14 9.93' 4.14Age Squared (/10000) -13.71' 5.00 -14.24' 5.00Years of schooling (/10) 1.82' 0.28 1.81 0.281/Sigma wage 0.50' 0.03 0.50 0.03


Constant 0.41 1.00 -0.42 0.94Farm assets (/100) 15.23' 2.91 10.72- 2.51Log of land 0.05 0.04 0.04 0.04Producer Price -0.94" 0.50 0.81 0.46Seasonal dummy 1 0.32" 0.20 0.36 0.18Seasonal dummy 2 -0.01 0.20 0.02 0.18Seasonal dummy 3 0.16 0.20 0.17 0.18Experience in farm work (/100) 14.47- 1.44 12.49- 1.13Age (/100) 1.15 4.52 3.62 4.34Age Squared (/10000) -12.51' 5.73 -13.35 5.44Years of schooling (/10) 0.07 0.28 0.28 0.26Male 12-17 farm hours (/100) --.-- --.-- 0.23 0.37Female 12-17 farm hours (/100) --.- .-- 0.52 0.34Male 18-64 farm hours (/100) --.-- --.-- 0.09 0.17Female 18-64 farm hours (/100) --.- .- 0.57* 0.23Own farm hours (/100) -6.99' 0.87 -5.88' 0.641/Sigma MRF 0.38' 0.04 0.44' 0.04

Marlinal Rate of Substitution

Constant 11.51' 1.29 13.44' 1.37No. of potential workers (/10) 0.83" 0.43 -13.43' 2.21Predicted family cons. (/10000) 4.47' 1.10 3.40 1.13Age (/100) -8.16" 4.20 -7.41" 4.32Age squared (/10000) 9.61" 5.25 8.67 5.36Male 12-17 leisure (/100) --.-- --.-- 0.88' 0.16Female 12-17 leisure (/100) --.-- --.-- 0.95 0.15Male 18-64 leisure (/100) --.-- --.-- 1.23' 0.17Female 18-64 leisure (/100) --.-- --.-- 1.00 0.16Own leisure (/100) -7.34' 0.61 -7.85- 0.631/Sigma MRS 0.43' 0.03 0.41' 0.03

Corr. of marginal returns 0.36' 0.05 0.42 0.05- Log likelihood 2078.53 2032.74

N 2352 2352

:Significant at 5% level"Significant at 10% level

- 29 -


(Males 18 - 64)


Wage

Constant -2.18' 0.37 -2.29' 0.37GDP per capita (/1000) 0.28 0.30 0.34 0.34Population density (/1000) -0.95' 0.46 -0.88s* 0.51Km. to permanent market (/100) -0.06* 0.02 -0.06- 0.02Availability of public transport 0.08* 0.05 0.10"- 0.05Experience in Wage work (/100) 3.32 0.50 3.71' 0.50Age (/100) 12.65' 1.93 12.70' 1.94Age Squared (/10000) -17.17 2.48 -17.42' 2.48Years of schooling (/10) 0.82' 0.13 0.85* 0.13I/Sigma Wage 0.91* 0.03 0.89' 0.03


Constant -1.92* 0.41 -2.35' 0.43Farm assets (/100) 2.64* 0.86 2.02- 0.96Log of land 0.09' 0.02 0.09 0.02Producer Price 0.32' 0.16 0.41* 0.18Seasonal dummy 1 0.09 0.06 0.09 0.07Seasonal dummy 2 0.19' 0.07 0.19' 0.07Seasonal dummy 3 0.08 0.06 0.08 0.07Experience in farm work (/100) 2.66* 0.43 3.08* 0.45Age (/100) 10.99' 2.06 12.14* 2.08Age Squared (/10000) -15.30' 2.62 -16.85' 2.65Years of schooling (/10) 0.60^ 0.13 0.62- 0.13Male 12-17 farm hours (/100) . . 0.26' 0.11Female 12-17 farm hours (/100) . . -0.10 0.14Male 18-64 farm hours (/100) --.-- . 0.29^ 0.08Female 18-64 farm hours (/100) . . 0.18' (.08Own farm hours -0.85' 0.14 -1.01' 0.151/Sigma MRF 0.89' 0.04 0.87* 0.04

Marginal rate of substitution

Constant 16.18' 1.47 16.75* 1.36No of potential workers 0.90* 0.39 -10.08' 1.86Predicted family cons. (/10000) 5.42' 1.00 4.29' 0.96Age (100) -3.58' 0.63 -3.47' 0.59Male 12-17 leisure (/100) . . 0.82 0.14Female 12-17 leisure (/100) . . 0.75 0.13Male 18-64 leisure (/100) . 0.88* 0.15Female 18-64 leisure (/100) --.-- . 0.67' 0.13Own leisure (/100) -11.63' 1.05 -11.03' 0.87l/Sigma MRS 0.37' 0.04 0.40' 0.03

Corr. of marginal returns 0.81* 0.05 0.76* 0.05

- Log Likelihood 2409.14 2367.97N 2281 2281

:Significant at 5% level"Significant at 10% level

- 30 -


(Females 12 - 17)


Waae

Constant -10.19- 3.79 -11.86 4.59GDP per capita (/1000) -1.14 3.93 -0.98 4.54Population density (/1000) 11.60'* 6.05 11.49 7.14Km. to permanent market (/100) -0.45 0.44 -0.53 0.53Availability of public transport -0.14 0.74 -0.20 0.80Experience in Wage work (/100) 121.82* 0.31 138.90 50.74Age (/100) 36.67 21.69 43.26 24.80Years of schooling (/10) -1.19 1.67 -1.25 1.83l/Sigma wage 0.39* 0.12 0.35 0.13

Marcinal return to farm work

Constant 1.47 3.51 -0.79 2.89Farm assets (/100) 24.46' 11.13 13.38" 7.06Log of land -0.12 0.12 -0.08 0.09Producer Price -1.40 1.34 -0.90 1.02Seasonal dummy 1 -0.39 0.46 -0.37 0.37Seasonal dummy 2 0.60 0.53 0.42 0.38Seasonal dummy 3 0.72 0.54 0.48 0.37Experience in farm work (/100) 74.56' 28.44 53.49* 13.68Age (/100) -22.59 20.19 -8.19 17.23Years of schooling (/10) -1.82 1.13 -1.11 0.71Male 12-17 farm hours (/100) --.-- --.-- 0.70 0.76Female 12-17 farm hours (/100) --.-- --.-- 1.78 0.88Male 18-64 farm hours (/100) --.-- --.-- - 0.67 0.43Female 18-64 farm hours (/100) --.-- --.-- 1.19" 0.63own farm hours (/100) -11.25 6.45 -7.43' 3.471/Sigma MRF 0.28' 0.13 0.39' 0.13


Constant 6.31' 2.84 9.14 - 3.50No of potential workers (/10) 1.29 1.13 -14.56' 5.88Predicted family cons. (/10000) 10.05' 3.81 7.68' 3.12Age (/100) -3.94 16.52 -1.29' 16.63Male 12-17 leisure (/100) --.-- --.-- 1.12' 0.39Female 12-17 leisure (/100) --.-- --.-- 1.20* 0.42Male 18-64 leisure (/100) --.-- --.-- 0.93 0.39Female 18-64 leisure (/100) --.-- --.-- 1.44 0.44Own leisure (/100) -4.96- 1.69 -6.17' 1.801/Sigma_ul 0.62' 0.12 0.58' 0.14

Corr. of marginal returns 0.08 0.17 0.14 0.18

- Log likelihood 354.03 318.98N 843 843.00

'Significant at 5% level"Significant at 10% level

- 31 -


(Males 12 - 17)


Wace

Constant -4.30' 1.88 -4.43' 1.99GDP per capita (/1000) 0.92 1.57 1.32 1.74Population density (/1000) 3.15 2.46 3.09 2.66Km. to permanent market (/100) -0.21" 0.11 -0.22" 0.12Availability of public transport -0.63" 0.35 -0.73" 0.38Experience in Wage work (/100) 43.30* 11.35 46.81* 11.74Age (/100) 18.13 11.23 16.63 11.80Years of schooling (/10) 1.36 0.65 1.51 0.69I/Sigma wage -0.76 0.16 -0.68' 0.14


Constant -1.33 1.79 -0.83 1.84Farm assets (/100) 15.39* 5.07 9.19 4.57Log of land 0.09 0.06 0.03 0.07Producer Price 1.09 0.75 0.96 0.78Seasonal dummy 1 -0.81' 0.38 -0.60 0.35Seasonal dummy 2 0.77' 0.33 0.75 0.31Seasonal dummy 3 0.21 0.28 0.18 0.30Experience in farm work (/100) 36.68' 9.20 35.19* 6.87Age (/100) -2.44 11.34 -9.21 11.20Years of schooling (/10) -0.40 0.56 0.00 0.06Male 12-17 farm hours (100) . . 4.35 0.91Female 12-17 farm hours (/100 . . 1.20** 0.63Male 18-64 farm hours (/100) . . 1.15' 0.38Female 18-64 farm hours (/100) . . 0.14 0.33Own farm hours (/100) -5.51' 2.18 -5.92* 1.571/Sigma MRF 0.46' 0.13 0.46 0.08


Constant 9.83' 2.93 12.64' 3.16No of potential workers (/10) 0.07 0.73 -6.08" 3.34Predicted family cons. (/10000) 6.05' 2.03 4.74' 2.16Age (/100) -10.22 10.81 -18.81 11.04Male 12-17 leisure (/100) --.-- --.-- 0.80 0.23Female 12-17 leisure (/100) . . 0.47 0.23Male 18-64 leisure (/100) --.-- --.-- 0.61 0.25Female 18-64 leisure (/100) . . 0.47 0.23Own leisure (/100) -5.21' 1.10 -6.10' 1.221/Sigma MRS 0.63' 0.13 0.57' 0.11

Corr. of marginal returns 0.28' 0.12 0.30' 0.12

- Log likelihood 510.20 458.04N 842 842.00

Significant at 5% level"Significant at 10% level

- 32 -

the marginal return to farm work and the marginal rate of substitution, family

interactions matter.

These structural estimates are consistent with the theoretical model. In all

cases, the marginal rate of substitution is decreasing with additional leisure (increasing

with hours worked). Again, in all cases, the marginal return to farm hours is decreasing

with own hours worked. These two results are sufficient to satisfy the logical

consistency conditions, thereby ensuring a unique solution and allowing for the

possibility of an interior solution.

The marginal rate of substitution functions exhibit conventional economic

relations. The coefficients on family consumption and own leisure indicate diminishing

marginal rate of substitution. The coefficients on the leisure of other family members

are always positive, indicating complementarity in leisure. By comparing the

coefficients on consumption and own leisure across the four age and sex groups, we can

rank the value families place on the leisure of its members. Families are willing to give

up larger amounts of consumption for an additional hour of leisure, the larger the

coefficient on consumption and the smaller (in absolute value) the coefficient on own

leisure. The coefficients indicate that families value the leisure of children more than

adults, and the leisure of young girls more than young boys. Thus, we expect children

to have lower labor supply responses than adults and young girls smaller than young

boys.

The estimated coefficients in the wage functions are consistent in signs and

magnitudes with other results in developing countries. The rate of return to schooling

in the wage sector for prime age females is 18 percent, roughly double that for males.

However, this pattern is reversed at young ages. The rate of return to education in the

wage sector is 13 percent for males 12 to 17 and insignificant for females.

- 33 -

The structural coefficients in the marginal return to farm work are estimated

exploiting the information from the first order conditions. No information on

agricultural income is used. Nonetheless, the estimated returns to land, farm assets,

and farm experience appear reasonable in comparison to other studies in developing

countries. For example, farm assets significantly improve the marginal productivity for

all age and sex groups, especially for females and the young. Land significantly

increases the productivity of prime age males, but not other groups. The rate of return

to education in farm work is 6 percent for males 18-64, typically the heads of

households, and close to zero for everyone else. Jacoby (1990) finds a rate of return of

4.7 percent for male heads of household in his production function estimates.

The theoretical discussion highlighted the importance of having at least one of

the marginal returns vary with hours worked. The empirical results strongly indicate

that the marginal return to farm work decreases with own farm hours. In addition,

other family members' hours of farm work affect the own marginal return to farm work.

The effects differ by age and sex group. Roughly speaking, other male hours worked

increase male marginal returns and other female hours worked increase female marginal

returns. This suggests that males and females are doing different tasks on the farm.

GOODNESS OF FIT

To assess how well we predict participation and hours of work, we solve for mean

values conditional on predicted family consumption and hours of work of other family

members. This is solved separately for each individual. Table 6 presents the actual

and predicted participation rates and hours supplied to each sector for each

demographic group. The table reveals that model does a good job of predicting mean

values within the sample. The model with family interactions does better.

- 34 -

Table 6. Actual and Predicted Values of Endogenous Variables

Females 18 64

Actual No Interactions Family Interactions

Prob. both 8.97. 8.1% 8.1%Prob. wage 8.5 9.2 9.8Prob. farm 59.6 60.8 60.6Prob. none 22.9 21.8 21.4

Hours farm 23.5 20.4 20.3Hours wage 5.7 5.6 5.8

Males 18-64Actual No Interactions Family Interactions

Prob. both 11.17 8.7% 9.47.Prob. wage 17.3 29.2 28.6Prob. farm 57.3 55.9 54.8Prob. none 14.3 6.2 7.2


Females 12-17Actual No Interactions Family Interactions

Prob. both 1.44% 1.3% 1.2%Prob. wage 2.7 2.0 2.5Prob. farm 58.4 54.9 55.2Prob. none 37.5 41.8 41.1


Males 12-17Actual No Interactions Family Interactions

Prob. both 3.6% 3.3% 3.4%Prob. wage 4.3 3.8 4.1Prob. farm 59.4 57.5 58.0Prob. none 32.8 35.4 34.4


- 35 -

We next considered how well the model predicts family behavior. We followed

the simulation procedure described in the estimation section to solve for the equilibrium

values of family consumption and the hours of work of all family members jointly. To

reduce the computational burden, we took a 10 percent random sample of households

and limited the calculations to those with no more than four potential workers. In

addition, we simulated the model only once for each household. The value of the

random error term assigned was calculated as the mean of 100 draws from the

distribution given by the estimated variance-covariance matrix."6

The mean actual consumption of the sample of 139 households was 1316.4 Intis

per month. The predicted mean value of consumption was 1337.5 Intis per month. The

model does a remarkably good job of predicting mean consumption given our limited

information approach. The structural coefficients were estimated to fit labor supply

behavior conditional on consumption. They were not estimated to fit family

consumption well.

POLICY SIMULA TIONS

Simulating the family model allows us to address important policy questions.

For example, should governments try to raise welfare by increasing returns to self-

employed agricultural activities or by expanding wage opportunities? What is the

extent to which they should target investments? Some investments, such as those in

infrastructure, are targeted towards communities and families and will influence the

returns of all family members. Other policies, such as education, can be targeted to

individuals within a household. The government may promote female education or

16 Even with these simplifications, solving for the four person household involves calculating256 solutions of a nonlinear simultaneous system of equations. This takes 3 hours on a 25Mhz 80486PC. The number of solutions that must be obtained for each family increases by a factor of four foreach additional potential worker. The calculation time doubles with each additional draw.

- 36 -

direct agricultural extension efforts towards the type of activities typically done by

women on the farm.

In this section, we use the model to evaluate the labor supply and welfare effects

of three poverty alleviation policies - increasing returns to wage work, increasing returns

to farm work, and direct monetary transfers. We calculate effects due to increases in

returns separately for males and females to investigate the merits of targeting. In this

exercise, we do not analyze the mechanisms and the costs of implementing these

policies, but focus on the benefits. However, the changes in returns that are feasible to

achieve. For example, we consider the effects of a 20 percent increase in female wages.

Our structural estimates suggest that such an increase could be achieved by raising

mean education levels by one year. Based on our structural coefficients, a 20 percent

increase in marginal return to farm work for prime age males could be achieved with

approximately a one standard deviation increase in the log of land. A 20 percent

increase in the- marginal return to farm work for prime age females and children could

be achieved by a one standard deviation increase in farm assets.

The base case is presented in Table 7. Table 8.a presents the results of the first

simulation - increasing the wage offers to prime age males (18-64) by 20 percent. The

top row reports the weekly unconditional changes to own hours worked in the wage and

farm sectors for prime age males 18-64 and the changes in leisure for young males 12-17,

young females 12-17, prime age males, and prime age females 18-64. On average over

the whole sample, prime age males work 3.17 hours more in the wage sector and 2.72

hours less in the farm sector in response to the 20 percent increase in wage offers. Ona

net, prime age males work 0.46 more hours. Young males receive 0.19 hours more of

- 37 -

Table 7. Base Case - 10 Percent Random Sample of HouseholdsNumber of potential workers < 4

Individual Data

Pc-t Both Pct E Pct. Farm Pct. None Ha Ifa His axm

Males 12-17

Base caseSimulation 0 3.0 81.8 3.0 0.2 10.5

Number in sample: 33

Females 12-17

Base CaseSimulation 0 0 62.1 37.9 0 6.8


Males 18-64

Base CaseSimulation 15.9 18.6 65.5 0 10.9 27.5


Females 18-64

Base CaseSimulation 4.5 6.2 83.9 5.8 2.0 21.6


Family data

Distribution of family size

One person households 10.8Two person households 39.6Three person households 28.1Four person households 21.5Total number of households 139

Mean actual consumption 1316.4Std. dev. actual consumption (1214.9)Mean base case consumption 1337.5Std. dev. base case consumption (1031.8)

- 38 -

Ta-bl SPOUCY SIMULATIONS

.a 20S INCREASE IN MALE WAGE

Changin Cho a iWeek Cage in inahWeek HowN Hew of Leiswoe C _em,pei Weim

Wae Farm Mal" P w I M F_l Jwork Work 12-18 12-18 19.65 19-65

Meom 3.17 -2.72 0.19 0.01 0.46 0.10 44.9 413

Sid. 6ev. (6.61) (6.12) (0.50) (0.30) (0.71) (0.3) (93.2) (974)

Man 7.34 4.27 0.43 0.03 -1.07 0.33 128.0 123.0

Sid. dnv. (8.41) (8.08) (0.71) (057) (IJ (0.55) (119.4) (135.8)

S.b 20% INCREASE IN FEWALE WAGE

Chop in Cbnp ln WeekbJ Cln ine Cluz in

Weekly Hows HOUl of Leise C _mrip WedSi&

Wap I Fam M Feamas Ma | F

Work Work 12-1S 12-18 1945 19-65

mank 1 0.49 -0.20 0C0 4.01 0.00 4.29 6J S.l

Sid. dev. | (I.SX) (0.76) | ) (0.02) 10.0.3 0.75) (300) 0.7243)

Mean 3.19 -1.30 0.00 0.01 0.01 -1 89 55.9 53.5

Sid. 6ev. (1.92) (3.78) (0.00) (0.02) (0.20) (0.8" (68.9) (6272)

8.e 20% INCREASE IN MARGINAL RETtlRN TO FARM WORK FOR MALES

CIim In ClahiCl In Weekly Cago i C la ia

Weokly Heus Hours of L1 se C mmytim Wela

! | Iw | Fasm Mls Fe_ru l Males Faeules

il|Work |Wsork 12-18 | 12-1 | 19-65 1965 |

mean -2.74 3.44 0.18 0.37 -0.10 0.21 107.3 104.0

S!d. dev. (6.21) (5.8n (0.77) (0.56) (0.60 (.28) (96.2) (98.5)

Mean -3.0S 3.87 0.21 0.52 -0.79 0.27 142.8 138.3

WS. d6v. (6.53) (6.12) (0.8) (0.6) (0.58) (0.29) (88.1) (90.3)

S.d 20% INCREASE IN MARGINAL RETURN TO FARM WORK FOR FEMALES

Cunp in Cu in 3nWeekly ( uwnp in Cump il

Weekly lm HeWS of Isure Comnption WelSre

|Wage Farm | Maes Fen |le Male FerrulesWotk | Work | 12-1 12- 19.65 19.65

mean -04.21 1.10 0.48 0.31 030 4-S8m 12D.7 123.8

Std. dev. ( @.n (0.76) (0-55) (0.56) /0.5S) (0.60 (l54,4) (1653)

mum"X 40.21 1.14 0.53 0.34 0.36 40.94 139.0 143.7

Std.dev. (0.87 (0.72) (0j55) (0.59) (0.59) (060) (157.8) (170.0)

8.e 20% INCREASE IN UNEARNED INCOME

Cee in C_| e l Weekly | Cu In Clun In|

| Weekly Nom Heuws of Lekwo C-u tion Welhre

| Waer Farm Mals F _ma e Mals Ferru

I! I_______ _ wj IWork t j 12-lB 12-18 19.65 19.65 j __11

jj mean 0.96 0.97 0.99 0.78 T 250.7 1 274.4 1S

1d.dev. ( I ( (0.87) (0.10) (0.28) j (27.6) (11.0)

- 39 -

leisure and prime age females 0.10 additional hours of leisure. There is no effect on

young females.

In order for the increase in wage offers to affect the family at all, a prime age

male must either already be working in the wage sector or be induced to work in the

sector as a result of the change. Otherwise, the increase in wage offers is irrelevant.

The second row presents estimates of the changes in hours worked and leisure

conditional on a male already working in the wage sector. As expected, the conditional

effects are substantially larger.

The last two columns of Table 8.a report the effects of the increase in prime age

male wages on family consumption and welfare. The unconditional mean effect is an

increase of 44.9, approximately 3 percent of mean family consumption. Again, this

unconditional effect is averaged over some households for which the change is irrelevant.

If one conditions on there being an a male already employed in the wage sector, the

mean change in consumption is 3 times large, or 9.6 percent of meau family

consumption. The 20 percent increase in male wages does not lead to a 20 percent

increase in family consumption because other family members are contributing to

consumption.

The welfare effects takes into account the family's change in leisure as well as

the change in consumption. They were calculated using predicted marginal] rates of

substitution at base case values of consumption and leisure. While prime age males

work more in response to the wage increase, other family members enjoy more leisure.

However, the net effect of the changes in leisure on family welfare is negative. This is

evident from the fact that the change in welfare is less than the change in consumption.

In this case, the difference between the consumption and welfare effect is roughly 4

percent.

- 40 -

Table 8.b presents results for a 20 percent increase in female wage rates. Very

few females work in the wage sector in the base case or are induced to work by the

increase in wages. Thus, unconditional effects of the wage increase are small. However,

for those families where females already participate in the wage sector, prime age

females experience a larger reduction in leisure than was the case with the 20 percent

increase in male wages. Despite this, the conditional effect on family consumption was

smaller than that of the wage increase of males, reflecting, in part, lower wages earned

by females. There were essentially no effects on the leisure of other family members in

different age and sex groups.

Tables 8.c and 8.d present results for 20 percent increases in male and female

marginal returns to farm work. The same general pattern with respect to weekly

changes in hours of work and leisure is revealed as was the case for the change in wage

offers. However, the effect is larger for the change in female marginal farm returns.

The picture with respect to monthly changes in consumption and welfare is considerably

different than was the case for the change in wage offers. In the first place, more males

and females work in the farm sector and, thus, are more affected by changes in the

marginal returns to farm work than they were by the changes in wage offers. This is

revealed by the smaller difference in the unconditional and conditional consumption and

welfare effects than for the wage changes. The contrast with the results from changes in

wage offers is especially pronounced for females.

The most striking result from Tables 8.c and 8.d is the similarity in the

conditional consumption effects of increases to male and female returns. This is in

marked contrast to the relative conditional effects of changes in wages offers.

Conditional on having an effect, the 20 percent increase in male marginal returns to

farm work led to an increase of family consumption of 142.8 (roughly an 11 percent

- 41 -

increase), while that due to the same percentage increase in the marginal returns of

females led to an increase of 139.0.

The ranking of the relative effects on the family of increases in male versus

female marginal returns is reversed if changes in welfare rather than consumption are

considered. This reflects the family's differential valuation of leisure of the different

groups that reallocate labor in response to the two changes. With the increase in male

returns the increase in consumption is obtained at the expense of male leisure. In the

base case, prime-age males have the least amount of leisure of any group. With the

increase in female returns, prime age males and young males and females receive more

leisure, while prime-age females receive less. The end result is that the increase in male

returns leads to a smaller change in welfare than in consumption, while the increase in

female returns leads to a larger change in welfare than in consumption.

Although the relative benefits to family welfare are higher for increases in female

returns to farming, it is important to consider also the costs of achieving the

productivity gains. If the costs are not higher for increasing female returns, our results

imply that such policies would be a cost-effective way of raising rural family welfare.

Table 8.e presents the effect of an increase in nonlabor income of 280 intis, a

little over 20 percent of mean family consumption. Simulating the effects of this change

allows us to investigate how families value the leisure of different age and sex groups.

The first row indicates that prime age females receive the smallest increase in leisure.

Of course, those who are already not working cannot receive more leisure. With the

increase in nonlabor income, all families have a positive consumption effect. The mean

effect is lower than the 280 Intis that was given to each household because families have

chosen to enjoy more leisure. The change in welfare is 10 percent higher than the

change in consumption.

- 42 -

6. CONCLUSIONS

This paper has developed an analytical approach to estimating family labor

supply and consumption decisions appropriate for developing countries. The key feature

of the approach is to work with underlying structural marginal return and marginal rate

of substitution functions. This allows us to handle .the complexity of having multiple

corner solutions for families with a large and variable number of potential workers. To

reduce the computational burden, we estimated the model using a limited information

approach and restricted the error terms in the marginal functions to be uncorrelated

across family members. It is possible to relax the covariance restrictions since the

model is identified through exclusionary restrictions. It is also possible to impose the

budget constraint in estimation. Making these extensions greatly increases the

computational complexity. For this reason, we believe that the next step would be to

investigate the feasibility of these extensions using simulated integration methods.

The general model developed for farm and off-farm work in Peru is applicable to

other analyses of multiple activities and/or interdependent family time allocations.

Examples include analyses of the effect of the availability of child care on the mother's

work at home and in the market, of the effect of illness of one family member on

activities of another, and the effect of infrastructure investment of the family's decision

of allocating their children's time among market work, home work, and school

attendance.

- 43 -

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Barnum, H. and L. Squire (1978), "An Econometric Application of the Theory of theFirm Household", Journal of Development Economics, Vol. 6, pp. 79-102.

Benjamin, D. (1988), "Household Composition and Labor Demand: Testing for RuralLabor Market Efficiency", Industrial Relations Section Working Paper No. 244,Princeton University, Princeton, N. J.

Blundell, R. and R. Smith (1990), "Estimation in Simultaneous MicroeconometricModels with Censored or Qualitative Dependent Variables", mimeo, UniversityCollege London, January.

Casley, D. J. and D. A. Lury (1987) Data Collection in Developing Countries, 2nd. ed.,London: Oxford University Press.

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- 46 -

Appendix L Residual Analysis

The importance of analyzing residuals in limited dependent variables models is

now well established (see Pagan and Vella, 1989; Blundell, 1987; Gourieroux et al 1987a,

1987b). Because the dependent variable is not continuously observed, it is not possible

to construct estimates of the residuals simply by subtracting the predicted value from

the actual value. Our approach to this problem constructs estimated residuals under

the maintained hypothesis that the error terms in the marginal return equations follow

a bivariate normal distribution and are independent of the error term in the marginal

rate of substitution equation. The latter error term is assumed to follow a univariate

normal distribution. The construction of the estimated residuals must be done

separately for each of the four possible outcomes in the estimation procedure. We

illustrate the procedure with the model with no family interactions. The procedure is

exactly the same in the model with family interactions.

Case I - Individual Works Both On and Off the Farm

In this case the marginal returns are equal to each other and to the marginal rate

of substitution. Because the real wage offer is observable, it is possible to construct

estimates of the three error terms. Thus,

u = In W- Z& + &aO + 6 (T- H.- Hf)

fw= In -F ~w#I

- ff = en - Xf,Sf - 4-Hf

-47 -

Case II - Individual Works Only in the Wage Sector

The equations relevant for this case are given by eqs. (19-21) on page 16 in the

text and are reproduced below.

e W =Z +: c (T- H) + uP

In p = X.P. +e.

In W > Xpf + ef

When the individual works only in the wage sector, the real wage is observable

making it possible to obtain estimates u1 and u, exactly as before. However, all that is

known about ef is that it is less than en W XfAf . One alternative as an estimate

of ef is E( ef I ef < gn W Xf1 f). This is the idea of generalized residuals that

form the basis for diagnostic tests proposed by Chesher and Irish (1987) and Gourieroux

et al (1987a). However, replacing ef by its conditional mean over the sample places too

much mass of the density away from the low end of the distribution. The number of

observations in the tail of the distribution will be understated. Our approach is as

follows.

* Take 500 draws from the distribution of ef given C' and the estimated variances.-

. Identify all draws e2 such that e2 < Qn -

. Randomly select one e2 satisfying the above condition as an estimate of 2f.

- 48 -

Because there is more mass of the conditional density function close to the

conditional mean, it is more likely that the single draw that is randomly selected will be

close to the conditional mean. However, this procedure does allow for the possibility of

selecting a draw from the far tail of the distribution. This approach is similar to that of

simulated residuals developed by Gourieroux et al (1987b), without their second-stage

estimation. A monte-carlo simulation comparing this approach to the results from

generalized residuals is given in Newman (1991).

Case III - Individual Works Only on the Farm

The equations relevant for this case are given by eqs. (22-23) on page 16 in the

text and are reproduced below.

Za + &cC + 6 (T - Hf) + u > XP,ffl, + c.

Xf + Hf + ef = Za + aCC + 6 (T - Hf) + U

The procedure for estimating residuals in this case is as follows:

* Take 500 draws of u, given its estimated variance.

* Solve for ef using the second equation above. This yields 500 values of cf.

* Given the conditional density of C. given ef and estimated variances, take one

random draw of ew for each of the 500 values of cf. This yields 500 values of

the triplet (c,,,, eU u).

* Select all triplets that satisfy the condition given in the first equation above.

* Randomly select one triplet from the set satisfying the condition.

- 49 -

Case IV - Individual Does Not Work

The relevant equations are given by eqs. (24-25) on page 16 in the text and are

reproduced below.

Za + a'C + 6 T + u > X.#. + ew

Za + a6 + a T + u > Xpf + cf

The procedure for estimating residuals in this case is as follows:

- Take 500 draws of u, given its estimated variance.

* Randomly draw 500 values of (c., ef) given its joint distribution and estimated

variance-covariance matrix. This yields 500 values of the triplet ('w, c1, u).

e Select all triplets that satisfy the conditions given in above two equations.

e Randomly select one triplet from the set satisfying the conditions.

Plots of Estimated Residuals and Normality Tests

After estimating the residuals separately for each case, they are combined to

yield estimated residuals for the entire sample. Figure Al plots the quantiles of the

estimated residuals against quantiles of the normal distribution for prime age males and

females. Figure A2 plots the same relationships for the younger males and females.

These figures indicate a divergence from normality in the tails of the distribution,

principally for the prime age male. This is confirmed by the Kolmogorov-Smirnov test

statistics presented in Table Al.

- 50 -

Table Al. Kolmogorov-Smirnov Statistics for Hypothesis thatResiduals are Normally Distributed

Wage MRF MRS

Malea AZged 18-64

K-S Statistic 0.05 0.05 0.03P level 0.00 0.00 0.00

F emales 18-64


Males Aged 12-17


Females Aged 12-17


For some cases, it is not possible to reject the null hypothesis that the estimated

residuals are normally distributed. However, there is enough of a divergence to suggest

that in future work, one would want to consider alternative specifications of the

deterministic component of the model or the stochastic components. As there is

considerable scope for modifying the deterministic component, it may be more fruitful

to pursue this route before tackling the more complicated nonparametric estimation of

this model. For example, the effect of additional leisure of prime age males on the

marginal rate of substitution might be expected to depend on the age of the male. This

could be accommodated by allowing for interactions of age and leisure in the marginal

rate of substitution. Allowing for interactions of leisure and hours of farm work with

- 51 -

exogenous family or individual characteristics would be expected to improve the fit of

the model and, possibly, reduce the deviations from normality. Similarly, additional

data that could better identify the marnal returns to fam and off-farm work

(particularly for prime-age males) would be expected to improve the fit of the model

and affect the estimated residuals.

-52-

Fia. Al Plot of Guantiles of Simulated Residuals AgainstQuantiles of Normal Distribution

-6.11 7.31 -7.61 9.07 -8.74 10.20Wage MRF MRS

Males Aged 18-64

-7.74 Wage 8.03 -8.82 MRF 9.32 -56 M 6.19Females Aged 18-64

- 53 -

Fig. A2. Plot of Quantiles of Simulated Residuals AgainsLQuantiles of Normal Distribution

,0 /~~~~~~~~~~

-4.78 5.02 -8.82 9.32 -5.60 6.19W'Aage MRF MRS

Males 12-17

0 i

-9.45 9.46 -10.08 10.73 -5.32 5.97Wage MRF MRS

Females 12-17

- 54 -

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LSMS Working Papers (continued)

No. 54 The Willingness to Payfor Education in Developing Countries: Evidence from Rural Peru

No. 55 Rigidite des salaires: Donnees microeconomiques et macroeconomiques sur l'ajustement du marchedu travail dans le secteur moderne (in French only)

No. 56 The Poor in Latin America during Adjustment: A Case Study of Peru

No. 57 The Substitutability of Public and Private Health Care for the Treatment of Children in Pakistan

No. 58 Identifying the Poor: Is "Headship" a Useful Concept?

No. 59 Labor Market Performance as a Detenninant of Migration

No. 60 The Relative Effectiveness of Private and Public Schools: Evidence from Two Developing Countries

No. 61 Large Sample Distribution of Several Inequality Measures: With Application to Cote d'lvoire

No. 62 Testing for Significance of Poverty Differences: With Application to C8te d'Ivoire

No. 63 Poverty and Economic Growth: With Application to COte d'Ivoire

No. 64 Education and Earnings in Peru's Infonnal Nonfarm Family Enterprises

No. 65 Formal and Infornal Sector Wage Determination in Urban Low-Income Neighborhoods in Pakistan

No. 66 Testing for Labor Market Duality: The Private Wage Sector in Cote d'Ivoire

No. 67 Does Education Pay in the Labor Market? The Labor Force Participation, Occupation, and Earningsof Peruvian Women

No. 68 The Composition and Distribution of Income in C6te d'Ivoire

No. 69 Price Elasticities from Survey Data: Extensions and Indonesian Results

No. 70 Efficient Allocation of Transfers to the Poor: The Problem of Unobserved Household Income

No. 71 Investigating the Determinants of Household Welfare in Cote d'Ivoire

No. 72 The Selectivity of Fertility and the Determinants of Human Capital Investments: Parametricand Semiparametric Estimates

No. 73 Shadow Wages and Peasant Family Labor Supply: An Econometric Application to the Peruvian Sierra

No. 74 The Action of Human Resources and Poverty on One Another: What We Have Yet to Learn

No. 75 The Distribution of Welfare in Ghana, 1987-88

No. 76 Schooling, Skills, and the Returns to Government Investment in Education: An Exploration UsingData from Ghana

No. 77 Workers' Benefits from Bolivia's Emergency Social Fund

No. 78 Dual Selection Criteria with Multiple Alternatives: Migration, Work Status, and Wage;

No. 79 Gender Differences in Household Resource Allocations

No. 80 The Household Survey as a Tool for Policy Change: Less~ons from the Jamaican Survey of LivingConditions

No. 81 Patterns of Aging in Thailand and Cote d'Ivoire

No. 82 Does Undernutrition Respond to Incomes and Prices? Dominance Tests for Indonesia

No. 83 Growth and Redistribution Components of Changes in Poverty Measure: A Decomposition withApplications to Brazil and India in the 1980s

No. 84 Measuring Income from Family Enterprises with Household Surveys

No. 85 Demand Analysis and Tax Refonn in Pakistan

No. 86 Poverty and Inequality during Unorthodox Adjustment: The Case of Peru, 1985-90

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