Time-Intensity and the Composition of Consumption: Theory

and Evidence

Yoo-Mi Chin�

Michigan State University

March 2007

Abstract

Although almost all consumption behaviors incur time expenditures in addition to monetary

expenditures, time inputs have often been ignored in analysis of consumer behavior. Becker�s

theory of home production was the �rst to systematically incorporate time in economic models,

and the theory generated much empirical research in a wide variety of areas. However, there are

two problems in the existing literature. The theoretic problem is that the model�s predictions

�substitution from time-intensive towards goods-intensive commodities arising from compen-

sated wage increases � are no longer clearly evident when more than two commodities exist.

The empirical problem is that the direct applications of Becker�s home production theory in

empirical research are scarce because of the innate immeasurability of commodities. In this

paper, I address these issues directly. First, I determine the conditions on the utility function

under which the Becker�s substitution e¤ects for the classic two commodities case exist for the

case of multiple commodities. Second, under certain assumptions about production technolo-

gies, I recover unobservable commodities from the cost functions. Then, using the Philippine

Bukidnon panel study of rural households, I test for the negative substitution e¤ects between

a time-intensive and a goods-intensive commodity arising from wage increases in the multiple

commodities setting. The estimates of the structural-form as well as the reduced-form relative

demand between childcare, which represents a time-intensive commodity, and meal consumption,

which represents a goods-intensive commodity, support the major predictions of the model.

�Yoo-Mi Chin, Michigan State University, East Lansing, MI 48824. E-mail: chinym@msu.edu. I am indebted toAndrew Foster for his guidance and insight. I am grateful to Mark Pitt and Nancy Qian for their helpful commentsand encouragement. I also thank Oded Galor, Vernon Henderson, Daniel Hamermesh, and Erik Thorbecke for theirbene�cial advice. Special thanks to Mee jin Cho, Delia Furtado, Chisoo Kim, Natsuko Kiso, Irina Paley, Doug Park,Almudena Sevilla-Sanz All remaining errors are mine.

1

1 Introduction

Almost all consumption behaviors require time expenditures apart from monetary expenditures.

Buying foods, for example, does not complete consumption of eating unless time is spent for cooking

and eating, while buying a ticket does not translate into the consumption of movies unless time

is spent in the theater watching movies. Given that time is such an important component of

consumption, a natural question that arises is how changes in the opportunity cost of time a¤ect

consumption patterns, the composition of consumption.

In his groundbreaking work, Becker (1965) proposes that �the household combines time and

market goods to produce more basic commodities1 that directly enter their utility functions,�such

as a home cooked meal or a pleasant evening. Because commodities di¤er in their time-intensities,

their relative prices change as the opportunity cost of time changes. As a result, Becker�s theory

predicts that there is a substitution from time-intensive towards goods-intensive commodities with

compensated wage increases. The theory of home production has been embraced by economists

across �elds and generated much empirical research.2

However, there are two issues that are not addressed in the existing literature. First, the pre-

dictions of Becker�s theory �substitution from time-intensive towards goods-intensive commodities

with compensated wage increases �are not applicable to the case of multiple commodities. These

substitution results only work in unambiguous direction when there are two commodities, and be-

come intractable when more than two commodities are present. Given that Becker�s original model

was developed in the multiple commodities setting, this lack of applicability to multiple commodi-

ties lessens the robustness of the theory. Moreover, it restricts the empirical applications of the

model, because empirical analysis usually deals with cases of more than two commodities.

1The innovation in this theory of home production is that the household is rede�ned as a production unit, inaddition to a consumption unit through the systematic incorporation of non-market time in the model.

2The theory has enabled a better understanding of household behaviors both in the market and non-market sectors(Apps and Rees 1996, Brown and Meghir 1991, Foster 2002, Grossman 1972, Michael 1973). It has also contributedto improving the performance of standard macroeconomic models (Baxter and Jerman 1999, Aguiar and Hurst 2004,Hurd and Rhowedder 2003, Benhabib, Rogerson, and Wright 1991).

2

Second, despite the growing number of empirical research that is based on Becker�s theory of

home production, the direct applications of the theory are scarce due to the unobservability of

commodities. As is noted by critics of Becker�s theory of home production (Pollak and Wachter

1975), in the absence of direct measurement of commodities, the major contribution of the theory

remains conceptual rather than empirically veri�able. Given that all the implications of the home

production theory regarding time and market goods can be translated into implications of the

derived utility functions3 (Michael and Becker 1973), the theory of home production could not

avoid the criticism that it is only a reformulation of well-known statements with slightly di¤erent

terminologies. The distinction between consumption and production, which Michael and Becker

(1973) call �the separation of objects of choice from the means used to produce them,�might be

useful in an analytical sense, but can hardly be a guideline for empirical investigations (Gronau

1986). Therefore, empirical studies hitherto have focused on inputs �market goods and time�

instead of dealing with commodities themselves.

In this paper, I address these issues directly. First, I enhance the generality and the applicability

of the theory of home production by deriving testable implications of the model in the multiple

commodities setting. I determine the conditions on the utility function under which Becker�s

substitution e¤ects for the classic two commodities case exist for the case of multiple commodities.

Moreover, I empirically separate consumption from production and apply the model�s predic-

tions directly on commodities. Under certain assumptions about production technologies, I recover

commodities from cost functions. Then, I test for the substitution e¤ects between child care, repre-

sentative of a time-intensive commodity, and meal consumption, representative of a goods-intensive

commodity, using the Philippine Bukidnon panel study of rural households. The estimates of the

structural form as well as the reduced form relative demand between the two commodities sug-

gest that there is a substitution from child care towards meal consumption when women�s wages

increase.

Furthermore, by empirically separating consumption from production, I disentangle the two

substitution e¤ects associated with wage increases. Increases in wage induce two substitution

3The derived utility function is obtained by directly substituting production functions into the utility function,and is more in line with the traditional theory.

3

e¤ects, one between commodities on the consumption side depending on their time-intensities, the

other between time and market goods on the production side. Using the recovered commodities and

the estimated parameters of production technologies, I separate the two substitution e¤ects and

�nd out how these e¤ects are translated into the eventual allocations of time and market goods. In

a thought experiment where meal consumption is �xed, the overall e¤ect of wage increase on time

for child care is negative, because both the consumption side substitution e¤ects and the production

side substitution e¤ects decrease the time for child care. On the other hand, the overall e¤ect of

wage increase on market expenditures for child care is positive, because the positive substitution

e¤ects on the production side dominate the negative substitution e¤ects on the consumption side.

The rest of the paper proceeds as follows. In Section 2, I provide a home production model in

the multiple commodities setting, and derive testable implications of the model. Descriptions of

the data, commodity construction, and the examination of relative goods/time intensities among

commodities are given in Section 3. In Section 4, I conduct empirical tests of the model and present

the results. Section 5 provides discussion of the results, and Section 6 concludes.

2 Model

2.1 Household Optimization Problem

The household is assumed to maximize utility over commodities that are produced at home com-

bining market goods and time. On the consumption side, it is assumed that the utility function

is homothetic, all the commodities are net substitutes of each other, and the compensated cross-

price elasticities are the same for all commodities.4 On the production side, it is assumed that the

wife is a sole provider of the time for home production activities in the household.5 Further, each

4The assumption that the compensated cross-price elasticities are the same for all commodities means:

�ji = �hi for i; j; h = 1:::; n; i 6= j; i 6= h

where �ji stands for the compensated cross-price elasticity of commodity Zj with respect to the price of Zi:

The three assumptions - homotheticity, net substitutability, and the same cross-price elasticity - are all satis�edwhen the utility function takes the CES form.

5The assumption that only women contribute to home production activities might be rather restrictive, giventhat we can easily imagine that husbands will provide appreciable amount of time for home production activitiessuch as repairing and gardening. However, the household time allocation data of another Phillippine rural province,

4

commodity is produced by a separate production function with constant returns to scale and no

jointness. Under the assumptions, the household�s optimization problem is summarized as follows:

Max U(Z1; Z2; :::; Zn�1; Zn)

s:t:nPi=1�iZi = wT +m

where Z =�Zini=1

is a vector of commodities, �i is the implicit price of each commodity, w is the

wife�s opportunity cost of time (hourly market wage), T is the total time endowment of the wife, m

is the household nonlabor income. Then, the commodity demand functions in the structural form

are derived as follows:

Zi = Zi(�; I) i = 1:::; n (1)

where � is a vector of n implicit prices and I = wT +m is the full income.

The implicit prices of commodities are determined within the household by the home production

technology. Under the assumption of a separate production function with constant returns to scale

and no jointness, each implicit price is equal to the unit cost of production and thus a function of

the input prices and technology only. As the two inputs to each production are market goods and

the wife�s time, the implicit prices are de�ned as follows:

�i = �i(w; pi) i = 1:::; n (2)

where pi is the price index of market goods used for production of Zi.

By substituting equation (2) for (1), the reduced-form demand functions derive as follows:

Zi = Zi(w; p;m) i = 1:::; n (3)

Laguna (Evenson 1978) show that as far as child care and food preparation are concerened, the assumption is not tooexcessive. In average, women spend 11 hours for child care and 20 hours for cooking per week, whereas men spendonly 3 hours for child care and 1.5 hour for food preparation.

5

where p is a vector of n price indices.

2.2 Substitution E¤ect of Wage on the Demand for Commodity

2.2.1 Two Commodity Case

As the simplest case, suppose we have only two commodities, Zi and Zj ; where Zi is time-intensive,

and Zj is goods-intensive. Relative time-intensity between commodities is de�ned as follows:

De�nition 1 Zi is time-intensive relative to Zj if

�i0

�i>�j0

�j(4)

where �n0= @�n

@w ; n = i; j:

�i0

�imeasures the percentage change in the implicit price of Zi due to change in wages. Therefore,

if the percentage change in the implicit price of Zi due to wage increases are greater than that of

Zj , Zi is more time-intensive than Zj :

Proposition 1 When there are only two commodities that are separately produced by production

functions that exhibit constant returns to scale and no joint productions, the compensated wage

e¤ects substitute away the time-intensive commodity for the goods-intensive commodity.

Proof. The comparative statics of Zi; the time-intensive commodity, with respect to wage derive

as follows:@Zi

@w= Sii�

i0 + Sij�j0 + (T � �i0Zi � �j0Zj)@Z

i

@m

where Snk is an entry in nth row and kth column in the Slutsky matrix. The �rst two terms capture

the compensated wage e¤ect, while the last term represents the income e¤ect.

Using:

Sii�i + Sij�

j = 0 (5)

6

the compensated wage e¤ect on Zi can be rewritten as follows:

@Zi

@w

C

= Sii�i

��i0

�i� �

j0

�j

�< 0

where superscript C denotes compensated e¤ects, and the inequality follows from the negative own

compensated price e¤ect (Sii < 0) and (4).

Using the similar procedure, the comparative statics on Zj derive as follows:

@Zj

@w

C

= Sjj�j

��j0

�j� �

i0

�i

�> 0

where the inequality follows from the negative own compensated price e¤ect (Sjj < 0) and (4).

Therefore, the compensated wage e¤ect is clearly negative on the time-intensive commodity,

and positive on the goods-intensive commodity. The prediction results from the fact that agents

�nd the time-intensive activity more expensive than the goods-intensive activity with an increase

in wage.6 The overall e¤ect of wage increase depends on the sign and the size of the income e¤ect.

2.2.2 Three Commodity Case

Suppose now we have three commodities, Zi; Zh; and Zj , whose relative time intensities make the

following inequality:�i0

�i>�h0

�h>�j0

�j(6)

When there are more than two commodities, the theory still produces unambiguous predictions

on the most time-intensive commodity and the most goods-intensive commodity.

Proposition 2 When there are more than two commodities that are produced separately by produc-

tions functions that exhibit constant returns to scale and no joint productions, the compensated wage

6This consumption side substitution e¤ect between two di¤erent activities are di¤erent from the production sidesubstitution e¤ects in which agents substitute market expenditures for time in producing one activitiy. The con-sumption side substitution e¤ect suggests that the compensated demand for time-intensive activities such as �takingcare of a child�will decrease relative to goods-intensivie activities such as �meal consumption�with wage increaes.The production side substitution e¤ect, on the other hand, suggests that as the market wage of the wife increases,monetary expenditures on babysitters will substitute mother�s home time in the production of child care.

7

e¤ect on the most time-intensive commodity is negative, while the e¤ect on the most goods-intensive

commodity is positive.

Proof. Using the similar procedure as in the two commodity case, the comparative statics on Zi;

which is the most time-intensive commodity with respect to wage, can be written as follows:

@Zi

@w

C

= Sii�i

�i

0

�i� �

h0

�h

!� Sij�j

�h

0

�h� �

j0

�j

!< 0

The �rst term is negative following the negative own compensated price e¤ect (Sii < 0) and

(6) : The second term is positive given the net substitutability between Zi and Zj (Sij > 0) and

following (6) : Therefore, the overall compensated wage e¤ect is negative.

The e¤ect on Zj follows similarly, except that the signs of the two terms are reversed, resulting

in the positive compensated wage e¤ect.

Therefore, the compensated wage e¤ects on Zi and Zj show the same signs as in the two

commodity case: wage increase will decrease the compensated demand for Zi; but increase the

compensated demand for Zj : On the other hand, we do not have a clear-cut prediction about the

compensated wage e¤ect on the middle commodity, Zh:

Proposition 3 When there are more than two commodities that are separately produced by pro-

duction functions that exhibit constant returns to scale and no joint productions, the compensated

wage e¤ect on the middle commodity is ambiguous.

Proof. The comparative statics on the middle commodity, Zh; derive as follows:

@Zh

@w

C

= Shi�i

��i0

�i� �

h0

�h

�� Shj�j

��h0

�h� �

j0

�j

�(7)

In equation (7), the two terms have positive signs following (6) and net substitutability between

commodities (Shi > 0; Shj > 0). Therefore, the sign of the compensated e¤ect depends on the size

of the two terms, which is of an empirical matter.

Therefore, when there are more than two commodities, the compensated wage e¤ects on the two

extreme commodities exhibit the same pattern as in the case of two commodities: the e¤ect is neg-

8

ative on the most time-intensive commodity and positive on the most goods-intensive commodity.

The e¤ects on the middle commodities, however, are ambiguous.

2.3 Substitution E¤ect of a Wage on the Relative Demand

As is shown in the previous section, if we have more than two commodities, the theory does not

generate a clear prediction about the e¤ects of a wage change on the middle commodities. Under

the assumptions about the utility function enumerated in Section 2.2, however, the theory predicts

a clear relationship between certain two commodities even in the multiple commodities setting.

Proposition 4 When commodities are net substitutes to each other, show the same cross-price

elasticities and are separately produced by production functions that exhibit constant returns to

scale and no joint productions AND when the utility function is homothetic, , with increases in

wages, there is a substitution from a more time-intensive commodity towards a more goods-intensive

commodity between any two commodities.

Proof. Suppose now we are interested in the wage e¤ect on the relative demand between Zi and

Zh, whose time-intensity follows (6). Taking log of the relative demand, the comparative statics

with respect to the wage derive in the following:

@

@wln

�Zi

Zh

�=�i0

�i

�Sii�

i

Zi� Shi�

i

Zh

�+�h0

�h

�Sih�

h

Zi� Shh�

h

Zh

�+�j0

�j

�Sij�

j

Zi� Shj�

j

Zh

�(8)

Note that given the homotheticity of the utility function, the two income e¤ects are cancelled

out, making the non-compensated wage e¤ect the same as the compensated e¤ect. Following the

assumption that the cross-price elasticities are the same for all commodities, and (5) for the case

of three commodities, (8) reduces to:

@

@wln

�Zi

Zh

�=

��i0

�i� �

h0

�h

��Sii�

i

Zi� Shi�

i

Zh

�< 0 (9)

where the inequality follows from (6) and the net substitutability of Zi and Zh (Shi > 0) :

9

Therefore, between any two commodities whose relative time-intensities can be de�ned, there

is a substitution from the time-intensive to the goods-intensive commodity when wages increase.

3 Data Description

3.1 Bukidnon Data

Prior to the empirical veri�cation of the model�s key prediction, the set of commodities and the rel-

ative goods/time intensities between them have to be outlined. Despite increasing consensus about

the importance of home production in consumer behavior, studies that elucidate the nature of the

home production process are scarce: little is known about what kind of commodities are produced,

how speci�c time and expenditures are combined to produce them, and how the commodities are

classi�ed by their input intensity (Gronau and Hamermesh 2003). The major reason for lack of

research in this direction might be that the appropriate data sets, which contain both expenditures

and the entire time allocation, are hard to �nd.

However, data sets collected in developing countries often provide time uses as well as expen-

ditures. This is the case given that home production is more relevant in the developing country

context. This study uses the data from a survey conducted by the International Food Policy

Research Institute and the Research Institute for Mindanao Culture in the southern Bukidnon

province on Mindanao in the Philippines. The southern Bukidnon project was undertaken to eval-

uate the e¤ects of agricultural commercialization on individual nutritional outcomes in the poor

agricultural households. The questionnaire was administered in 4 rounds between 1984 and 1985

at four month intervals to 488 households in the southern Bukidnon. Among the wide range of top-

ics addressed in the survey, this study speci�cally focuses on household expenditure data, and the

wife�s time allocation over numerous home production activities, the two main inputs in commodity

production.

The data set contains information on household expenditures over 16 categories. It also provides

the wife�s 24 hour recall on the time allocation over 28 di¤erent activities, amounting to 24 hours. It

is unfortunate that we do not have other family members�time uses, especially that of the husband.

10

However, this shortcoming can be mitigated to some extent by the fact that the wife is the main

provider of the home production activities in this rural context.

3.2 Commodity

3.2.1 Commodity Construction

Out of 16 expenditures and 28 time uses, 12 expenditure categories and 22 di¤erent time uses

are assigned to the construction of 7 di¤erent commodities: SLEEP, LODGING, APPEARANCE,

MEALS, CHILDCARE, LEISURE, and HEALTH. Time devoted to income generating activities

was excluded from home production, because it was transformed into money and put to use for

commodity production as market expenditures. The classi�cation of commodities follows the com-

modity set suggested by Gronau and Hamermesh (2003). Out of 9 commodities de�ned by them,

TRAVEL and MISCELLANEOUS are excluded due to lack of time use data on them. The detailed

time allocation and expenditures for each commodity are shown in Table (1).

3.2.2 Relative Goods Intensity of Commodities

Following Gronau and Hamermesh (2003), the relative goods-intensity was de�ned by the ratio

of goods to time inputs for a given commodity, to the ratio of total amount of goods and time

allocated to commodity production as a whole:

RGTIi =expenditurei=timeiP

i expenditurei=Pi time

i

Table (2) presents the mean household monetary expenditures (pesos per day) on goods, the mean

of the wives�time expenditures (minutes per day) for commodity production, and relative goods-

intensity for each commodity. The intensity was calculated based on the means.

In average, 92% of the household daily monetary expenditures and 87% of the wife�s daily time

endowment are used for commodity production. The remaining 8% of expenditures are mainly

spent for miscellaneous items or transportation, whereas 13% of time endowment is spent for

income generating activities.

11

Commodity Time Use Goods ExpenditureSLEEPING sleeping noneLODGING cleaning, gathering wood, fuel or light,

repairing, gardening, household servicesa

shopping for nonfood housingAPPEARANCE laundry, personal care personal care, non-durableb

clothing/textile for adultc

MEALS cooking, shopping for food, food, guest foodfetching water, eating

CHILDCARE feeding, bathing, playing, education,breastfeeding, clothing/textile for childrend

LEISURE visiting friends/relatives, recreation,attending meetings, church, cigarettes/alcohol�esta, resting

HEALTH care for illness healtheaExpenditures on household services include wages to servants, drivers, launderers, guardsand others.bNon-durable household goods include detergent, soap, and matches.c,dPredicted values based on the number of children (c), and the number of adults (d)eHealth expenses include medical care fees and drugs, traditional health fees (e.g., midwife,Seriyano, Mananambal, Hilot, Arbulario, Baylan) and drugs, and dental fees.

Table 1: Assignments of Inputs to Commodities

Commodity Goods Time RGTI(peso/day) (min/day)Mean S.D. Mean S.D.

SLEEPING 0 538.72 75.78 0LODGING 2.34 7.95 70.54 76.64 0.98APPEARANCE 2.45 3.47 74.1 80.49 0.97MEALS 32.22 22.15 237.39 108.02 4.00CHILDCARE 2.28 4.93 71.84 100.63 0.94LEISURE 3.11 5.9 255.25 168.46 0.36HEALTH 0.97 3.56 3.67 44.23 7.79

TOTAL 42.45 35.64 1251.49 192.23 1TOTAL AVAILABLE 45.91 34.11 1440

Table 2: Relative Goods/Time Intensity of Commodities

12

A fairly large amount of monetary expenditures is concentrated on MEALS production, which

re�ects that the samples are semisubsistence rural households.7 Out of the total expenditures used

for commodity production, 76% was concentrated on the production of meals, while only 2% was

spent for health production. The remaining portion is almost evenly distributed among the other

commodities. As expected, a large proportion of home production time is absorbed by LEISURE.

More than 20% of home production time, about half of the time spent for SLEEP, is used for

LEISURE production. MEALS is another commodity that takes a large share of times for home

production. Nineteen percent of home production time is employed for meal preparation and eating.

On the other hand, time inputs for health production are notably small. In average, only about

4 minutes are used for health production, and this comprises 0.3% of the daily home production

time. Given that the time for health production is de�ned by sick time, this little amount of time

for health production is not very surprising.

The last column in Table (2) presents the relative goods-intensity of each commodity de�ned

above. As stated earlier, although HEALTH is the commodity that takes up the smallest portion of

expenditures and the least amount of time, it is de�ned to be the most goods-intensive commodity,

because time used for health production is so little relative to market goods used for it. MEALS

is relatively goods-intensive despite its large time share. It uses 16% of the daily time endowment,

which is only 3% less than the percentage of time spent for LEISURE. As noted earlier, however,

a fairly large portion of money is spent for meal production. As a result, MEALS is classi�ed as a

relatively goods-intensive commodity.

Contrary to the usual expectations, LODGING is time-intensive relative to the average com-

modity and no more goods-intensive than APPEARANCE. This relative time-intensity can be

explained by the fact that more than 85% of the households8 reported that they have at least one

house and do not pay any rent or mortgage. Given that rent or mortgage payments would com-

prise relatively large shares of expenditures compared to time spending, high household ownership

percentages and a lack of mortgage payments explain why LODGING is classi�ed as a relatively

7The Bukidnon area su¤ered from chronic poverty for a long time. In 1997, for example, the poverty incidence inBukidnon was 42.5 %.

8Three hundred ninety eight out of 448 households in round 1 reported ownership of one or more houses, while385 households in round 4 did so.

13

time-intensive commodity to the average commodity. Therefore, it is very likely that LODGING

will be considered to be a relatively goods-intensive commodity, if we include the cash value of

accommodating services from a house. On the other hand, as is generally expected, LEISURE is

the second most time-intensive commodity, followed by CHILDCARE. SLEEP is the most time

intensive by construction.9

Unfortunately, these �gures do not exactly capture the relative time-intensities of commodities.

The calculation was based only on the wife�s time use without the time inputs of other family

members, especially that of the husband. As mentioned earlier, the fact that home production

activities basically fall in the woman�s sphere in this rural environments would alleviate to some

extent the lack of husband�s data, though it would not entirely resolve the problem. There are

still commodities that require input of personal time, such as LEISURE, APPEARANCE, and

HEALTH. However, the comparison with other countries for which both husband and wife�s time

uses were taken into account for commodity production shows that the current �gures still have

bearing on the ordering of the relative goods-intensities among commodities.

The �rst four columns of Table (3) present monetary and time expenditure patterns and the re-

sulting relative goods-intensities of commodities in the United States and Israel. Although in terms

of magnitude there are notable di¤erences in the relative goods-intensities between the two countries

and the Philippines, they share substantial similarities in terms of intensity ordering. Among the

7 commodities de�ned in all three countries, HEALTH was the most goods-intensive commodity,

followed by LODGING, EATING, APPEARANCE, CHILDCARE, LEISURE and SLEEP in the

United States and Israel. In the Philippines, all the other commodities follow the same ordering

except for LODGING, whose relative time-intensity was noted and explained earlier. Therefore,

we can infer that the relative goods/time intensities given in Table (3) are still informative, though

not rigorous.

9Following Gronau and Hamermesh (2003), it is assumed that no money expenditures are spent for sleepingproduction.

14

Com

modity

United

Statesa

Israelb

Philippines

Goods

Time

RGTI

Goods

Time

RGTI

Goods

Time

RGTI

($/mth)(hrs/mth)

(ILS/mth)(hrs/mth)

(peso/day)

(min/day)

SLEEPING

0485

00

469

00

538.72

0

LODGING

680

765.39

1925

556.88

2.34

70.54

0.98

APPEARANCE

153

651.42

385

451.69

2.45

74.1

0.97

MEALS

403

145

1.67

1175

127

1.82

32.22

237.39

4.00

CHILDCARE

4722

1.27

395

531.48

2.28

71.84

0.94

LEISURE

179

299

0.36

740

333

0.44

3.11

255.25

0.36

HEALTH

924

12.35

424

810.73

0.97

3.67

7.79

TRAVEL

364

603.63

723

712.02

MISCELLANEOUS

3719

1.16

270

321.68

TOTAL

1954

1176

16037

1192

142.45

1251.49

1

TOTALAVAILABLE

2141

1440

6139

1440

45.91

1440

a;bReproducedfrom

GronauandHamermesh(2003)

Table3:RelativeGoods/TimeIntensity,UnitedStates1985,Israel1992,Philippines1984-85

15

3.2.3 Commodity and Sample Selection

The prediction of equation (9) applies to any two commodities for which the relative goods/time

intensities can be de�ned. For n commodities, n(n�1)2 relative demands can be constructed and

tested. For the empirical analysis of this study, however, only two commodities were selected:

CHILDCARE and MEALS. The reason why these two commodities, in particular, are chosen is

because, given that the child care and the meal preparation mainly require the wife�s time, the

relative goods/time intensities between CHILDCARE and MEALS are not a¤ected by the fact

that the data set only provides the wife�s time use. As is apparent in Table (2), between these

two commodities, CHILDCARE is time-intensive relative to MEALS. Table (A.1) and (A.2) in the

Appendix provide relative goods-intensities of the commodities by wealth and women�s age quartile.

In every wealth and age quartile, CHILDCARE is less goods-intensive than MEALS, although the

goods-intensity of the CHILDCARE increases as the wealth and the women�s age increase along

the quartiles.

The data set provides the survey results of 448 households over 4 rounds, which comprise 1,792

total observations. The number of observations reduces to 1,687 due to missing values either in

time use and expenditures on MEALS and CHILDCARE or other demographic variables. Further,

in order to avoid a possible substitution by other females for the wife�s time for meal preparation

and child care, only those households that do not have women older than 15 other than the wife

herself were selected. This reduces the total observations to 1,196.

4 Empirical Speci�cation

4.1 Empirical Construction of Zs

The major obstacle to the research is that Zs are unobservable. That is, the two inputs, mar-

ket goods and time are observable, whereas the outputs are not. However, assuming that each

commodity production technology exhibits constant returns to scale with no jointness, Zi can be

16

obtained by dividing the total cost with its unit cost of production:

Zi =TCi

Unit Costi(10)

where superscript i stands for each commodity i:

The empirical speci�cation proceeds with the assumption that the total cost function of each

commodity Zi is a translog. Imposing constant returns to scale, the total cost function of a

commodity Zi is de�ned by:

lnTCi = �i0 + lnZi +Pl

�il�di�ln � il +

1

2

Pl

Pk

�ilk ln �il ln �

ik (11)

where l and k denote inputs such as market goods and wife�s time, �i0; �il; and �

ilk;are parameters,

di is a vector of demographic variables that a¤ect cost of Zi, and � il is a price of input l for Zi:

Symmetry implies �ilk = �ikl; and linear homogeneity in prices implies

Pl �

il = 1 and

Pk �

ilk = 0:

The implicit price of the commodity Zi is then de�ned as the exponent of the unit cost function:

�i = exp

��i0 +

Pl

�il�di�ln � il +

1

2

Pl

Pk

�ilk ln �il ln �

ik

�(12)

Then, the commodity Zi is derived by dividing the total cost of production, which is the sum

of market expenditure and time costs (women�s hourly wage10 multiplied by the time spent for

production) by (12).

By di¤erentiating (11) with respect to the input prices and applying the Shepherd�s lemma, we

extract the following input share equation:

@ lnTCi

@ ln � il= Sil = �

il

�di�+Pk

�ilk ln �ik

10Women�s hourly wages are calculated by dividing their daily wages by the number of hours of outside work. Forthose women who do not have hourly wages either because they do not work, or they do not report, hourly wages areimputed. In doing so, �rst, wages of those women who work but do not report the data are predicted based on theirdemographic variables and the local labor market situations, such as age, weight by survey round, average height,body mass index, energy expenditure for work, population density in the municipality, and survey round dummies.Then, by pooling both types of women - those who work and those who do not work - the hourly wages of women areestimated irrespective of whether they were actually employed in the labor market after correcting self-selection withHeckman selection procedure. The selection equation includes a woman�s age, and the age of her youngest child.

17

where Sil is a share of input l in the cost of Zi.

Given the unobservability of the total output Zi; only share equations can be estimated. Using

the parameter estimates of the share equations, we can construct the predicted marginal cost up

to a constant term �i0 :

~�i = exp(Pl

�il�di�ln � il +

1

2

Pl

Pk

�ilk ln �il ln �

ik) (13)

where �il and �ilk are the parameter estimates.

Then, the ~Z is derived from equation (10) using (13).

4.2 Estimation

4.2.1 Share Equations for MEALS Cost

Two inputs for MEALS production are the monetary expenditure for foods and the wife�s food

preparation and eating time. With linear homogeneity in prices and symmetry, the share equations

for MEALS cost are written as follows:

Smljt = �ml

�dmjt�+ �mll

�ln�ml�mk

�jt

+ !mljt (14)

where superscript m stands for MEALS, j is household, t is survey round, l and k are food

expenditure and wife�s time for meal production and l 6= k; !mljt is errors associated with cost-

minimizing behavior.

The disturbance term !mjt is de�ned by

!mljt = umlj + "

mljt , j = 1:::; N; t = 1:::; T (15)

where E�"mjt jxmj ; umj

�� N

�0; �2"

�; E

�umj jxmj

�� N(0; �2u); xj =

nxmjt

oTt=1; xit is a vector of

explanatory variables in equation (14):

18

.

RandomExpenditure Share

Constant 0.3227(6.25)**

Mother�s Age 0.0003(2.36)*

Mean Household Age 0.0002(1.77)

Number of Children 0.0205(6.04)**

Number of Adults 0.0221(3.51)**

Mother�s Nutritional Knowledge 0.0055(3.40)**

ln�Pm

w

�0.1680(9.07)**

Observation 1196No. Household 324

Table 4: Parameter Estimates of MEALS Cost Function

The demographic variables and the round dummies enter in the share equations as follows:

�ml�dmjt�= �ml0 + �

ml1MAGEjt + �

ml2MNAGEjt + �

ml3CHILDjt (16)

+�ml4ADULTjt + �ml5MNUTjt + �

m0l ROUNDS

where MAGE is the mother�s monthly age, MNAGE is the average household monthly age, CHILD

is the number of children, ADULT is the number of adults, MNUT is the mother�s nutritional

knowledge score, of which the highest is 17 and the lowest is 1, and ROUNDS are the dummy

variables for the survey round. The summary statistics of the explanatory variables are reported

in Table (A.1) in the Appendix.

The cost shares of the two equations always sum up to unity, making the sum of the disturbances

across the two equations zero at each observation. After arbitrarily dropping the time input share

equation in order to prevent singularity problem, the parameters are estimated with the random

e¤ect model. The results are reported in the second column of Table (4).

19

The random e¤ect estimates in Table (4) show that except for the average household age, all

the other demographic variables are signi�cant at the conventional level. The own and cross price

coe¢ cients are also statistically signi�cant. The signs of the coe¢ cients indicate that the share

of market goods in the total cost of MEALS production increases with mother�s age, number of

children, number of adults, and the mother�s nutritional knowledge. The positive e¤ect of mother�s

nutritional knowledge on the market expenditure share re�ects that most of the households in the

data are semisubsistence households. Therefore, a better knowledge of nutrition leads to more

monetary spending on food to provide essential nutrients, rather than to improvement of taste and

quality through increased food preparation time.

Using the parameter estimate of the relative price and the information on the cost shares, Allen

elasticities of substitution were calculated. The own elasticity of substitution is de�ned by:

�ill =�ilk + S

2l � Sl

S2l(17)

where �ilk is the coe¢ cient of the relative price.

The cross elasticity of substitution is de�ned by:

�ilk =��ilk + SlSk

SlSk(18)

Evaluated at the sample mean shares, the own elasticity of substitution for market goods is

-0.16 and the own elasticity of substitution for time is -0.48. The cross elasticity of substitution

between the two inputs is 0.28, suggesting that the two inputs are substitutes for each other.

4.2.2 Share Equations for CHILDCARE Cost

The share equations of the two inputs for CHILDCARE production, monetary expenditure for

children, and the wife�s time with children have the same structure as in equation (14) except that

they have di¤erent demographic variables.

20

Random Random TobitExpenditure Share Expenditure Share

Constant -0.1712 -0.4025(0.81) (-1.27)

Age of Youngest Child 0.0083 0.0127(12.44)** (12.26)**

Mother�s Age 0.0003 0.0004(0.66) (0.69)

Mean Household Age 0.0005 0.0007(1.67) (1.56)

Number of Children 0.0475 0.0631(5.49)** (4.85)**

ln(Pc

w ) 0.0148 0.046(0.25) (0.51)

Observation 1196 1196No. Household 324 324

Table 5: Parameter Estimates of CHILDCARE Cost Function

The demographic variables and the round dummies enter in the share equation as follows:

�cl�dcjt�= �cl0 + �

cl1AGEYNGjt + �

cl2MAGEjt + �

cl3MNAGEjt (19)

+�cl4CHILDjt + �c0l ROUNDS

where superscript c denotes CHILDCARE, AGEYNG is the age of the youngest child, and other

demographic variables are as de�ned in the previous section. The summary statistics of the ex-

planatory variables are reported in Table (A.1) in the Appendix.

The disturbance term also has the same structure as in equation (15). Again, after dropping

arbitrarily the time input share equation, the random e¤ect model was applied in estimating the

market expenditure share equation for CHILDCARE production. The results are reported in the

second column of Table (5).

The estimates in the second column indicate that the age of the youngest child, mean household

age, and number of children have statistically signi�cant e¤ects on the market expenditure share.

As the relative price of market goods increases, the cost share of market goods also increases,

although the own and cross price have statistically insigni�cant e¤ects on the market goods share.

21

There is a positive relationship between the age of the youngest child and the market goods

share, which re�ects that the time required for child rearing decreases and �nancial spending

increases as children grow older. The market goods share also increases with mean age of the

household and number of children.

Some observations have zero monetary expenditure for child rearing, which leads to market

expenditure share of 1. In order to deal with this censoring problem, the random e¤ect Tobit

model was estimated and the results are reported in the third column of Table (5). The coe¢ cient

estimates have the same sign as those of random e¤ect estimation, and the two estimates do not

show notable di¤erences in terms of signi�cance.

Again, using the parameter estimate of the relative price and the information on the cost shares,

Allen elasticities of substitution were calculated as de�ned by equation (17) and (18). Evaluated at

the sample mean shares, the own elasticity of substitution for market goods is -1.52, for time it is

-0.93, and the cross elasticity of substitution is 1.19, suggesting that the two inputs are substitutes.

4.2.3 Reduced Form Relative Demand Estimation

The implicit prices of MEALS and CHILDCARE are constructed as in the equation (13) using the

random e¤ect estimates reported in Table (4) and the random e¤ect Tobit estimates reported in

Table (5), respectively. After MEALS (Zm) and CHILDCARE�Zc�are obtained by dividing the

total costs with each implicit price, the log relative demand between CHILDCARE and MEALS�ln Zc

Zm

�is constructed. The relative demand in the reduced form is then estimated as follows:

ln�Zc=Zm

�it

= �0 + �01P

mit + �2WAGEit + �10ln(WEALTH)it (20)

+�011ROUNDS+ �it

where �0 = �ce0 � �me0 + ~�0; �it = (�c � �m)it + �it; �i is the disturbance term in the total cost for

commodity Zi, �it = �i + �it; E (�itjxi; �i) � N�0; �2�

�; E (�ijxi) � N(0; �2�); xi = fxitgTt=1 ; xit

is a vector of explanatory variables in equation (20)11, WAGE is the wife�s hourly market wage,

11The constant terms in the total cost functions for each commodity (�c0; �m0 ) are subsumed in the constant term

in the relative demand equation. The disturbance terms from the cost minimizing behaviors �c��m are also included

22

Random E¤ect Fixed E¤ect(1) (2) (1)

Constant -2.223 -3.0643 -2.1808(6.37)** (7.28)** (4.41)**

Pm 0.3058 0.3137 0.2341(2.63)** (2.70)** (1.55)

Wage -0.0984 -0.0843 -0.0656(3.75)** (3.16)** (1.3)

ln(Wealth) � 0.0878 �(4.15)**

Time dummy Yes Yes YesHausman Test 0.1(1)Observation 1,196 1,196 1,196No. Household 324 324 324Robust standard errors are in parenthesis.Heteroschedasticities are corrected by Jacknife sampling.

Table 6: Parameter Estimates of the Reduced Form Relative Demand between CHILDCARE andMEALS

ln(WEALTH) is the log mean wealth of the household for four rounds. The summary statistics of

the explanatory variables are reported in Table (A.1) in the Appendix.

The error term structure in the relative demand equation requires random e¤ect estimation.

The estimation results are reported in Table (6).

As is predicted by the theory, increases in wage have negative e¤ects on the relative demand

between CHILDCARE and MEALS. As a woman�s opportunity cost of time increases, households

decrease the consumption of CHILDCARE, a time-intensive commodity, relative to MEALS, a

goods-intensive commodity.

The interpretation of the negative substitution e¤ects of increases in wage is a little di¢ cult

because all the e¤ects are in relative terms. In order to make the interpretation simpler, suppose

that we �x the consumption of MEALS by compensating the income when wages increase. Then,

evaluated at the sample mean, a 10% increase in wages decreases the demand for CHILDCARE by

3.2%, which is decomposed into 3.1% decrease in time and 3.4% decrease in expenditures. On the

other hand, a 10% increase in wages substitutes market expenditures for time on the production

in �it:

23

side, as time becomes a more expensive input. The substitution e¤ects on the production side will

decrease time by 2.9% and increase market expenditures by 4.8%. Therefore, the overall e¤ects of a

10% increase in wages are 6% decrease in time and 1.4% increase in expenditures for CHILDCARE.

For a robustness check, the �xed e¤ect model was estimated. As is shown in the fourth column

of Table (6), wages still have negative and signi�cant e¤ects on the relative demand. The Hausman

test on the wages, the regressor of interest, is also reported in Table (6). The test statistic is 0.1,

and the critical value from the chi-squared table with one degree of freedom is 3.84, which is far

larger than the test value. Therefore, the hypothesis that the individual e¤ects are uncorrelated

with the wage cannot be rejected.

The positive e¤ect of wealth on the relative demand suggests that agents�demand for CHILD-

CARE increases faster than the demand for MEALS as wealth increases, violating the homotheticity

assumption. However, the fact that the gross wage e¤ect including both substitution and income

e¤ects on the relative demand is negative implies a greater negative �compensated� substitution

e¤ect between CHILDCARE and MEALS, supporting the prediction of the model.

4.2.4 Structural Form Relative Demand Estimation

As is mentioned in Section 2.1, CES utility function satis�es all the assumptions imposed on

the utility function in the model. Therefore, this paper proceeds to assume that the household

maximizes a CES utility function over commodities�Zi�; de�ned by:

U�Z1; :::; Zn

�=�P

�i�Zi��� 1

�

wherePi�i = 1:

Then, the log linear relative demand between Zc and Zm derives as follows:

ln

�Zc

Zm

�= ln

��c

�c

��� ln

��m

�m

��(21)

where � = 11�� is the elasticity of substitution, and �

i; i = c;m is the implicit price of commodity,

de�ned by (12) :

24

Substituting (12) for CHILDCARE and MEALS and imposing symmetry and homogeneity in

prices, the log relative demand can be written:

ln

�Zc

Zm

�= �[ln

�c

�m� (�c0 � �m0 + �ce (dc)

�lnP c

w

�(22)

��me (dm)�lnPm

w

�+ �ceeF

c � �meeFm)]

where subscript e denotes market goods expenditures, �ce (dc) is de�ned by equation (19), �me

is de�ned by equation (16), F c = [12 (lnPc)2 � (lnP c) (lnw) + 1

2 (lnw)2];and Fm = [12 (lnP

m)2 �

(lnPm) (lnw) + 12 (lnw)

2]:

Then, comparative statics with respect to wage derives as follows:

@

@wln

�Zc

Zm

�= � �

w[�me (d

m)� �ce (dm)� �cee�lnP c

w

�+ �mee

�lnPm

w

�] (23)

Given the unobservability of commodities, equation (22) cannot be estimated. However, the

constant returns to scale technology implies:

Zi =TCi

�i(24)

Substituting (24) in (22) and rearranging terms, equation (22) can be rewritten as (i) of equa-

tions (25). Combining (i) with the two share equations of each cost function, the following system

of nonlinear equations is estimated with the seemingly unrelated regression method:

i) ln

�TCc

TCm

�= �

�ln�c

�m

�+ (1� �) [�c0 � �m0 + �ce

�lnP c

w

�(25)

��me�lnPm

w

�+ �ceeF

c � �meeFm] + "jc

25

ii) Sce = �ce0 + �ce1AGEYNGj + �

ce2MAGEj + �

ce3MNAGEj + �

ce4CHILDj

+�ce5

�lnP c

w

�j

+ �c0e ROUNDS+ "

cje

iii) Sme = �mm0 + �me1MAGEj + �

me2MNAGEj + �

me3CHILDj + �

me4ADULTj

+�me5MNUTj + �me6

�lnPm

w

�j

+ �m0

e ROUNDS+ "mje

where j is each observation and "j =n"jc; "

cje; "

mje

o� N(0;

P) is a vector of disturbance terms

either associated with unknown preferences or with cost minimizing behaviors.12

The estimation results are reported in Table (7). The estimates of production technologies

are similar with the results of separate estimations of each share equation, in terms of signs and

signi�cance.

Using the parameter estimates of the nonlinear seemingly unrelated regression, the e¤ects of

wage on the relative demand de�ned by (23) are calculated for all 1196 observations. Figure (1)

illustrates the distribution of these wage e¤ects. The mean of the wage e¤ects on the relative

demand is -0.1086 and the standard deviation is 0.0981. As is shown in Table (6), the wage e¤ect

in the reduced form relative demand is -0.0843 and this is within one standard deviation of the

mean e¤ects of wage in the structural demand.

5 Discussion

5.1 Contributions

In this study, I provide empirical evidence that there is a substitution from a time-intensive commod-

ity towards a goods-intensive commodity following a wage increase, which veri�es that households

systematically take into account the time component in consumption decisions. The traditional

labor-leisure dichotomy model explains how changes in wages induce agents to reallocate their time

at home and time in the market. In fact, home time itself is composed of numerous sub-time uses

12For the identi�cation purpose, �c0 � �m0 is normalized to zero.

26

Nonlinear Seemingly Unrelated Regression

(i) Relative Demand (ii) CHILDCARE (iii) MEALS

��ln �c

�m�

0.2491 � �(18.3)**

� 0.8359 � �(51.44)**

Constant � -0.2255 0.3012(1.46) (6.16)**

Age of Youngest Child � 0.0084 �(16.52)**

Mother�s Age � 0.0003 0.0004(1.03) (2.98)*

Mean Household Age � 0.0005 0.0002(2.19)** (2.42)**

Number of Children � 0.0498 0.020(7.42)** (8.25)**

Number of Adults � � 0.0292(5.52)**

Mother�s Nutritional Knowledge � � 0.0048(4.24)**�

ln Pc

w

�� -0.0327 �

(0.75)�ln P

m

w

�� � 0.1617

(8.37)**

Table 7: Parameter Estimates of the Nonlinear Seemingly Unrelated Regression

27

02

46

Den

sity

-1 -.5 0 .5 1Effect_Of_Wage

Figure 1: E¤ect of Wage on Relative Demand

28

such as time for child care, eating, shopping, and sleeping. The traditional model is, however, silent

about how these speci�c time allocations are a¤ected by the wage changes. The empirical results

in this study suggest that speci�c time uses as well as market expenditures associated with them

will be di¤erentially a¤ected depending on the nature of home production. For example, time for

child care, which is used for a relatively time-intensive activity and for which market goods are

highly substitutable, incurs a greater negative substitution e¤ect when the opportunity cost of time

increases.13

Further, I separate the "objects of choice" from "the means used to produce them" by disen-

tangling the consumption side substitution e¤ect and the production side substitution e¤ect. A

bulk of recent literature that deals with home time as a subject of analysis generally focuses on

its role on the production side. Time use, however, is also a¤ected by preferences in addition to

home production technology.14 Therefore, ignoring the consumption side substitution e¤ect might

lead us to draw a wrong conclusion about the overall e¤ects. For example, suppose that the price

of market goods for child care decreases due to subsidy for educational costs of children or price

decline in baby sitters. Then, time use for child care will surely decrease through the production

side substitution e¤ect because mother�s time is now a more expensive input. However, the overall

e¤ect on time for child care is ambiguous because the consumption side substitution e¤ects are

likely15 to be positive due to a lower implicit price of CHILDCARE (� (w; p)) :

Lastly, the �nding that there is a negative relationship between women�s opportunity cost of

time and demand for child care recon�rms that increasing women�s human capital and expanding

their labor market opportunities is an e¤ective way to control high fertility in developing countries.

13The thought experiment in Section 4.2.3 shows that out of 6% decrease in time for child care driven by a 10%increase in wage, 3.4% comes from the consumption side substitution e¤ect and the remaining 2.9% comes from theproduction side e¤ect.14This is di¤erent from the argument that agents attach a direct urility to time use. The utility is assigend only

to the �nal commodity, say, �CHILDCARE�, and time spent for child care itself is a neutral component. If an agentfeels that she enjoys her time with children, it is because her time contributes to the production of �CHILDCARE�from which she receives utility, not because she attaches a direct utility to the time itself.15As is noted in Section 2.2.2, the direction of this consumption side substitution e¤ect is an empirical matter when

we have more than two commodities.

29

5.2 Other Issues

The prediction on the substitution e¤ects between two di¤erent commodities in a multiple com-

modity setting is based on strong assumptions on the utility function: it is assumed that the utility

function is homothetic, all the commodities are net substitutes of each other, and the compen-

sated cross-price elasticities are the same for all commodities. These strong assumptions might not

always accord with reality. The comparison of the reduced-form results and the structural-form

results, however, suggest that the assumptions on the utility function are reasonably well met in

the Bukidnon data set: the wage e¤ects on the relative demand in both cases are fairly close to

each other (-0.0843 vs. -0.1086). 16

On the other hand, on the production side, it is assumed that the technology exhibits no joint-

ness. In reality, many home production activities are jointly provided and the secondary time use

is not negligible. For example, if a person cleans up the house while listening to music or watching

TV, LODGING and LEISURE are being jointly produced. Given that meal production and child

care provision are predominantly women�s duties, the two commodities can be easily jointly pro-

duced, making the interpretation of the empirical results di¢ cult. However, the prevalence of the

joint production is not likely to compound the implication of the results, given that the results are

based on the �recall�data. In other words, the time allocation data re�ect the perception of the

interviewed about time-intensities of various activities, which might be di¤erent from actual time

intensities including secondary time use, but will still be the basis of the agents�decisions. For

example, suppose again that a woman cleans up her house while listening to music or watching TV.

If she perceives this time use as �clean-up time�rather than �leisure�, she will report it accordingly

and more importantly, her decision will be based on such perceptions. Including the secondary time

use, her actual time used for leisure creation might be much longer than she feels. However, as long

as she does not de�ne this time use as �leisure�, she is likely to feel that she spends relatively little

time for leisure. Thus, whenever her income or time costs change, her reaction to these changes

16Although the positive wealth e¤ect on the relative demand (0.0878) in the reduced form estimation implies aviolation of the homotheticity assumption, this does not nullify the empirical evidence of a negative compensatedsubstitution e¤ect of the wage. The coe¢ cient of the wage now captures the gross wage e¤ect including the positiveincome e¤ect from MEALS to CHILDCARE. The fact that the gross wage e¤ect is still signi�cantly negative suggestsa greater negative compensated substitution e¤ect.

30

will be based on such perceptions. Therefore, although the empirical results in this study do not

incorporate the secondary time use, as long as agents�decisions are plausibly based on perceivable

time intensities of commodities rather than actual time intensities including secondary time use,

the results reasonably capture how agents incorporate time in their consumption decisions.

6 Conclusion

In this study I provide empirical evidence that veri�es the core of the Becker model, which so far

has had only an intuitive appeal. The estimates of the reduced-form relative demand between child

care, representative of a time-intensive commodity, and meals, representative of a goods-intensive

commodity, support the substitution e¤ects from the former towards the latter with compensated

wage increases. The estimates of the structural-form demand also support the predictions of the

model.

According to a thought experiment in which meal consumption is �xed, evaluated at the sample

mean, a 10% increase in wages will decrease demand for child care by 3.2%. This 3.2% decrease is

translated into 3.1% decrease in time and 3.4% decrease in market expenditures for child care. At

the same time, a 10% increase in wages induces substitution between time and market goods on

the production side. Evaluated at the sample mean, a 10% increase in wages leads to 2.9% decrease

in time and 4.8% increase in market expenditures for child care. Overall, a 10% increase in wages

decreases time for child care by 6% and increases expenditures for child care by 1.4%.

The empirical veri�cation that commodities exhibit di¤erential responses to changes in the

opportunity cost of time, according to their time use patterns, reemphasizes the importance of the

study of home production in understanding consumer behaviors and devising appropriate policies.

Questions such as how the retirement and the changes in time and market goods allocations will

a¤ect consumer welfare, and how the home production time and associated market expenditures

will respond to change in income taxes cannot be answered without understanding the nature of

home production. It is necessary to collect the appropriate data and to fully explore the potential

of the theory.

31

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34

Appendix

Variables Obs Meana Std.Dev.

ADULT 1196 2.32 0.69

AGEYNG 1196 24.27 22.71

CHILD 1196 4.03 2.11

FAGE 1196 425.86 93.25

FEDU 1196 5.69 2.78

ln(Pc/WAGE) 1196 0.005 0.58

ln(WAGE) 1196 1.23 0.56

ln(WEALTH) 1196 8.56 1.60

MAGE 1196 377.44 78.72

MEDU 1196 6.38 2.65

MNAGE 1196 183.46 54.29

MNUT 1196 7.68 3.18

WAGE 1196 3.98 2.21

a Means for all four rounds

Table A.1: Summary Statics of Demographic Variables, Wage, and Price

35

1st Quartile 2nd Quartile

Commodity Goods Time RGTI Goods Time RGTI

(peso/day) (min/day)

Mean Mean

SLEEPING 0 557.3 0 0 548.11 0

LODGING 0.96 75.57 0.63 1.80 72.34 0.93

APPEARANCE 1.63 81.57 0.98 2.04 75.77 1.01

MEALS 21.51 265.92 4.04 26.19 258 3.81

CHILDCARE 0.42 96.72 0.22 0.90 82.80 0.41

LEISURE 1.80 250.57 0.36 2.21 228.95 0.36

HEALTH 0.41 6.70 3.05 0.58 0.90 24.21

TOTAL 26.74 1334.34 1 33.72 1266.86 1

TOTAL AVAILABLE 27.96 1440 35 1440

3rd Quartile 4th Quartile

Commodity Goods Time RGTI Goods Time RGTI

(peso/day) (min/day)

Mean Mean

SLEEPING 0 546.38 0 0 524.56

LODGING 1.14 71.65 0.64 4.7 73.82 1.29

APPEARANCE 1.77 82.91 0.85 3.83 81.24 0.95

MEALS 25.36 253.90 3.99 42.13 242.27 3.52

CHILDCARE 1.08 80.36 0.54 4.58 71.16 1.30

LEISURE 1.93 229.42 0.37 5.05 254.87 0.40

HEALTH 0.42 1.58 10.62 1.68 5.43 6.26

TOTAL 31.70 1266.19 1 61.98 1253.36 1

TOTAL AVAILABLE 32.36 1440 67 1440

Table A.2: Relative Goods/Time Intensity of Commodities by Wealth

36

Age 15-23 Age 23-32

Commodity Goods Time RGTI Goods Time RGTI

(peso/day) (min/day)

Mean Mean

SLEEPING 0 558.64 0 0 547.63

LODGING 0.70 77.77 0.36 1.66 72.97 0.92

APPEARANCE 1.44 78.09 0.63 1.90 79.59 0.96

MEALS 19.27 280.1 2.36 24.72 257.62 3.88

CHILDCARE 0.19 94.48 0.07 0.81 86.35 0.38

LEISURE 1.68 270.32 0.21 2.07 235.09 0.36

HEALTH 0.29 0 n/a 0.59 3.69 6.46

TOTAL 23.57 1359.41 1 31.74 1282.94 1

TOTAL AVAILABLE 24.14 1440 33.02 1440

Age 32-40 Age 40-49

Commodity Goods Time RGTI Goods Time RGTI

(peso/day) (min/day)

Mean Mean

SLEEPING 0 534.50 0 0 526.03 0

LODGING 2.57 66.22 1.04 2.07 76.30 0.71

APPEARANCE 2.39 72.84 0.88 2.27 84.73 0.71

MEALS 33.96 221.90 4.09 34.48 243.41 3.72

CHILDCARE 3.03 80.22 1.01 3.84 64.11 1.57

LEISURE 3.44 254.30 0.36 3.22 244.75 0.35

HEALTH 0.78 3.98 5.24 1.61 6.16 6.85

TOTAL 46.18 1233.95 1 47.49 1245.48 1

TOTAL AVAILABLE 48.70 1440 49.69 1440

Table A.3: Relative Goods/Time Intensity of Commodities by Age

37