Spending time and money within the household

Martin BrowningUniversity of Oxford

Mette GørtzAKF, Copenhagen

IFS Family Workshop, September 2006

Goal of paper:

descriptive: what are the relative levels of the material welfare (derived from leisure and goods) of husband and wife within the household?

inference: what determines these relative levels?

Background on time use.

On average married women do less market work than married men but more housework.

On average, married women enjoy about the same leisure as married men.

These averages hide a great deal of heterogeneity with many married people enjoying much less leisure than their partner.

Suppose we observe a household in which the wife has much less leisure than the husband. At least three possible explanations:

1. Relative wages. In most Becker style models the person who has the highest wage works more in the market and less at home. The net effect on within household relative leisure is ambiguous (and depends on tastes and household production).

2. Heterogeneity. In a unitary framework, if there is heterogeneity in the taste for leisure then a wife who likes leisure more than her husband will take relatively more leisure.

3. Power. The wife has less ‘power’ in the household and is required to do more work (in the market and at home).

How to estimate the relative importance of the three effects?

With time use data alone we require excessively strong assumptions.

We need to observe ‘who gets what’ in the household.

Requires time use data and information on the intra-household allocation of goods for the same households. (Complementary data sets will not work without strong additional assumptions).

For a sample of households with the same relative wage we expect:

Heterogeneity: a negative correlation between the wife’s share of leisure and her share of consumption.

Power: a positive correlation between the wife’s share of leisure and her share of consumption.

Confounding factor: variation in relative wages. Relative wages are prices and hence affect the time spent in market work and housework in a unitary model and may also affect the distribution of power (relative wages may be a ‘distribution’ factor).

Data: Danish Time Use Survey, 2001.

Representative survey of Danish households.

For 1200 married couples, both partners keep a detailed time use diary for one weekday and one weekend day. Infrequency is a problem.

Also two survey questions on ‘normal’ time:

Normal hours per week in market work, including commuting.

Normal hours per week in housework (usual activities plus childcare, gardening and do-it-yourself).

Leisure ≡ 168 - market work - housework - 56.

We select both in fulltime market work (30+ hours per week) (and other information available): 617 couples.

WEEKLY HOURS OF LEISURE

0.0

1.0

2.0

3.0

4.0

5

0 20 40 60 80Hours of leisure per week

density: leisf density: leism

20

40

60

80

Hus

ban

d's

leis

ure

30 40 50 60 70 80Wife's leisure

leisf leismMedian spline Fitted values

05

10

15

20

Den

sity

.3 .4 .5 .6 .7Wife's share of total leisure

Data: Danish Time Use Survey, 2001 (contd).

Survey includes information on demographics.

Linked to register data which gives a measure of wages, household income and other information back to 1980.

Survey also collects information on expenditures for wife and husband.

Expenditures.

The survey collects information on expenditures for ‘clothing’, ‘leisure activities and hobbies’ and ‘other personal consumption’ by husband and by wife. Asked only of respondents (for them and partner).

“When you think of your own personal consumption, how large do you estimate it is normally on the following items during one month?” (Clothing, recreation, other personal).

Expenditures – validity.

Clothing and recreation values compare well to independent Danish family expenditure survey data on intra-household allocation.

Unclear what ‘other personal’ means to respondents. (No time to do focus groups or pilots).

We sum our three items for each partner to give ‘total expenditure’.

The mean of total expenditure is about 87% of assignable expenditures in family expenditure survey data.

In estimation we allow for this not being all assignable expenditures.

Mean expenditures

(Euro/year) Wife HusbandClothing 867 619

Recreation

Other

Total

Mean expenditures

(Euro/year) Wife HusbandClothing 867 619

Recreation 320 500

Other

Total

Mean expenditures

(Euro/year) Wife HusbandClothing 867 619

Recreation 320 500

Other 748 845

Total

Mean expenditures

(Euro/year) Wife HusbandClothing 867 619

Recreation 320 500

Other 748 845

Total 1,935 1,963

On average, husbands and wives have about the same ‘personal expenditures’. The values for each total are substantial - about 5% of disposable household income and about 14% of total expenditures on non-durables.

0.2

.4.6

4 5 6 7 8 9Log expenditures

density: lconsf density: lconsm

56

78

9H

usb

and'

s lo

g c

ons

um

ptio

n

5 6 7 8 9Wife's log consumption

lconsf lconsmMedian spline Fitted values

05

10

Den

sity

0 .2 .4 .6 .8Wife's share of total expenditure

.3.4

.5.6

.7W

ife's

sha

re o

f le

isu

re

0 .2 .4 .6 .8Wife's share of consumption

rel_leis Median splineFitted values

Relative leisures against relative expenditures

Structural model:

One private good, shared between partners A and B.

Household production of a public good using housework by both and money input.

Market work and housework perfect substitutes in utility function. Only leisure matters in the utility function.

Market work is completely flexible.

Person A has preferences over her own private consumption, the public good and her own leisure, represented by a felicity function:

, ,A A A Au u q Q l

No externalities. No complementarities in leisure.

Structural model (contd):

Caring: A’s level of felicity enters B’s social welfare function (and vice versa).

Collective model – outcomes are efficient. This implies that household choices can be rationalised by a household utility function:

U(household) = μ U(A) + U(B)

The Pareto weight, μ, reflects power and relative caring. ‘Power’ may depend on prices and wages (and other distribution factors).

Structural model (continued):

Fully parametric (all parameters have a strict interpretation).

Linear reduced forms with equations for log (ratio of expenditures) and log (ratio of leisures).

Cross-equation (proportionality) restrictions for distribution factors and wages.

Allow for unobserved heterogeneity in relative tastes for leisure and private consumption.

Allow for correlation between unobserved heterogeneity in tastes for leisure and relative wages. Exogeneity of latter is testable.

Allow for measurement error in relative expenditures

relative expenditures = her expenditure over his

relative leisures = her leisure over his

Pareto weight on wife's utility function

relative tastes for private consumption

relative tastes

x

l

for leisure

(common) curvature parameter for leisure

log relative wage (hers divided by his)

distribution factors

Decomposition of relatives:

ln ln ln ,

ln ln ln ,

x

l

z

z

z

Second equation gives a decomposition of the derivative of relative log leisures with respect to relative log wages into:

a unitary effect (negative)

plus

a collective effect (positive)

Observable heterogeneity

(after some preliminary analysis).

Preference factors (variables in utility functions):

Wife and husband’s education, young and older children dummies.

Distribution factors (variables in Pareto weight):

Log relative wage, relative age, log gross household income

Relative expenditures

Relative leisures

Relative age -0.016

[2.9]

0.001

[0.4]

Household income

0.146

[1.4]

0.003

[0.1]

Log relative wage

0.191

[2.8]

-0.051

[2.5]

Reduced form estimates for distribution factors

t-values in square brackets.

Correlation between residuals = 0.11 {χ2(1) = 7.0}.

Chi-sq (1) Probability

Relative ages

1.72 19%

Log house-hold income

0.14 71%

Relative wage

2.16 14%

Tests for cross-equation restrictions (for sigma = 0.1).

Test for ‘relative wage’ is test for exogeneity of relative wages in relative leisure equation..

Relative expenditures

Relative leisures

Relative age -0.015

[2.7]

-0.0015

[2.7]

Household income

0.138

[1.4]

0.0138

[1.4]

Log relative wage

0.189

[2.8]

-0.048

[2.5]

Parameter estimates with structural restrictions imposed (eis = 0.1)

Relative wage endogenous in relative leisure equation.

Relative expenditures

Relative leisures

Relative age -0.015

[2.7]

-0.0015

[2.7]

Household income

0.138

[1.4]

0.0138

[1.4]

Log relative wage

0.213

[3.2]

-0.080

[12.1]

Parameter estimates with structural restrictions imposed (eis = 0.1)

Relative wage exogenous.

Results for distribution factors:

The wife’s relative wage has a positive coefficient in the consumption share equation. Evidence of a power effect that depends on relative wages (and, maybe, other distribution factors).

The elasticity of the Pareto weight with respect to relative wage is positive and less than unity. For the leisure relative, the unitary comparative advantage effect outweighs the power effect. Increasing her relative wage leads to a fall in her relative leisure.

The error terms are positively correlated. Evidence in favour of the unobserved heterogeneity in power being stronger than the unobserved taste heterogeneity.

The future research agenda:

1. Richer structural model with weaker assumptions. A serious analysis of the identification of unitary and collective effects. Using diary information. Accounting for labour force participation and health.

2. Use of time use panel data information (first wave in 1988, but without consumption information).

3. Analysis with complementary data sets with extensive overlap in register data information:

(a) Danish intra-household expenditure survey. Much richer on the intra-household allocation of non-food expenditures, but no time use information (except for labour supply).

(b) Danish Consumer Panels to identify the allocation of food expenditures.