The University of Nottingham

School of Economics

L13500 Dissertation 2014

The Rise of the Stay-At-Home Father: A Cross-Country

Comparison of the Macroeconomic Factors Contributing to a

Changing Family Structure

Thomas Lansdowne

Student ID: 4165729

Supervisor: Dr. Giammario Impullitti

Word count: 7,500

This Dissertation is presented in part fulfilment of the requirement for the completion of an undergraduate degree in

the School of Economics, University of Nottingham. The work is the sole responsibility of the candidate.

I do give permission for my dissertation proposal to be made available to students in future years if selected as an

example of good practice.

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Table of Contents

Abstract

1. Introduction

2. Literature Review

2.1. Technological Change

2.2. Macroeconomic Drivers

2.3. Conclusion and Limitations of the Literature

3. Cross-Country Comparison and Context

4. Empirical Analysis

4.1. Data Limitations

4.2. Preliminary Analysis

4.3. Theoretical Predictions

4.4. Empirical Method

4.4.1. U.S. Regression Analysis

4.4.2. Canadian Regression Analysis

4.5. Granger Causality Testing

5. Evaluation

6. Conclusion

7. References

Abstract

This paper primarily seeks to determine whether a relationship exists between

technological change and the rise in Stay-At-Home Father Households witnessed in

many Western economies. A further purpose of this study is to analyse the key

macroeconomic variables that may have given rise to this widespread change, to

offer a theoretical basis for subsequent macroeconomic analysis. Key findings of the

paper are that technology has a positive effect on the proportion of Stay-At-Home

Fathers in an economy, when Total Factor Productivity is used as a proxy for

technological change, and that the fertility rate, unemployment rate, and level of

welfare spending of an economy each offer a significant amount of explanatory

power on the proportion of Stay-At-Home Fathers.

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1. Introduction

Over recent decades there has been an undisputed rise in Stay-At-Home Father (SAHF)

Families among Western economies, reaching 2.2 million in the U.S. in 2012, according to a

nonpartisan fact tank (Pew Research Center, 2014). Whilst SAHF Households remain the least

studied and least frequent type of family structure (Kramer & McCulloch, 2010), they have

recently gathered both growing academic and media attention (The Economist; Forbes; The

Spectator, etc.).

The majority of the literature regarding SAHFs attempts to assess the factors contributing

to this growth at a micro-level, exploring a change in the decision-making of families to elect a

SAHF family structure. This largely focuses on the decreased value of time allocation to domestic

work. However, the macroeconomic determinants of the increasing prevalence seem neglected,

in part due to data limitations and contrasting definitions (Kramer & McCulloch, 2010).

This paper offers a unique approach in the analysis of this phenomenon, providing a basis

for further study of the contributing macroeconomic factors. This is achieved through the use of

a proxy variable for SAHF Households previously unexplored, which enables novel results from

time-series econometric analysis. The focus of the paper is on the effect that technological

progress has on SAHF Households, providing a comparison between the Canadian, and U.S.

economies.

The empirical investigation outlined is based on previous micro-level and macro-level

findings, as well as economic theory. Whilst technological progress has been argued to have led

to a reduction in time-allocation towards domestic work, its effect is yet to be analysed in the

framework of SAHF Households. Due to the novelty of econometric analysis on this topic, the

paper does not intend to provide a comprehensive study of all factors contributing to the rise, but

instead aims to strengthen or weaken previous claims outlined in micro-level analyses, as well as

provide a basis for further macroeconomic study.

2. Literature Review

Whilst formerly the rise in SAHF Families had been largely attributed to changing social

attitudes and gendered expectations (e.g., Ellingsæter 1998; Chelsey 2011), Kramer & Kramer

(2013) expands on previous literature to suggest that a range of social and economic factors have

been driving this development. Pew Research Center (2014) calculated that there were 2.2

million SAHF Families in the U.S. in 2012; nearly double that of 1989. Whilst in Great Britain

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research carried out for The Spectator (Brown, 2012) by The ONS noted an increase greater than

300% since 1996. Nonetheless, research into this phenomenon is limited, which Latshaw (2009)

argues to be due to the lack of correlation between rising female employment and the greater

responsibility of domestic work amongst men, coined as the ‘stalled revolution’ (Hochschild,

1989).

This review will first analyse the literature supporting the significant effect of

technological advancement on time-allocation to market work, and thus the rise in SAHFs,

through a two-pronged approach. Initially, it will examine the rising female participation rate in

the U.S. driven by the polarisation of wages, before reviewing technological progress in household

production. Secondly, it will outline the economic factors contributing to the decision of fathers

to adopt a caregiver role in nuclear family households, before referencing certain prevailing

limitations of the literature.

2.1. Technological Change

The amount of time married families allocate to market work has risen significantly since

the 1950s (Greenwood & Guner, 2004). In the U.S. in 1990 married households contributed on

average of 33.5 hours per person per week to market work, compared to 25.5 hours in 1950. This

data is deemed reliable as it was extracted from U.S. Census data. In part, the authors attribute

this change to the rise in the labour force participation rate of married women, noted as a 47%

increase over the same period, driven largely by technology.

Whilst shifts in the aggregate production function have long been attributed to technical

change (Solow, 1957), Tinbergen (1974; 1975) proposed a link between the relative demand for

skilled labour and changing technology. This is in part strengthened by Katz and Murphy (1992),

amongst others, who produced a case study of the effect of technology on wage structure in the

U.S. using data from 25 consecutive Current Population Surveys (CPS) from 1964, a significant

sample size of approximately 1.4 million people. The paper evidences a changing pattern of

employment in part from dramatic increases in both the relative wages of women as well as the

volume of women in the workplace between 1963 and 1987, driven by changing relative demand

for labour in occupations favouring women.

Extensive literature evidences a skill-biased technical change amongst OECDs. Autor et al.

(2003) aim to streamline this consensus by formalising and testing previous theories focusing on

computerisation, attributing it to the changing pattern of employment in the U.S. in favour of

service sectors. By combining information on occupational requirements from the Dictionary of

Occupational Titles (DOT) with CPS and Census data, the authors are able to comment on

changing task inputs individually across occupations and industries, as well as within differing

levels of education. Computer technology is evidenced to impose a substitution effect for

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unskilled workers performing routine tasks, whilst complementing industries in which problem-

solving and creativity is necessitated (high-skilled labour). While the latter is pronounced

amongst both genders, it is however larger for women, suggesting that the changing relative

demand for labour is indeed in favour of female-rich occupations, contributing to the increase in

the average wage rate of women.

Autor and Dorn (2009) expand on this concept by outlining a displacement of less

educated workers towards low-skill service occupations, which are difficult to automate, creating

an increase in service sector wages. Adding weight to this conclusion, the authors also test for

various alternative hypotheses such as demographic and economic shifts, and off-shoring, none

of which provide statistically robust evidence to counter the null hypothesis. In tandem with an

increase in high-skilled labour, this phenomenon contributes to the polarisation of the U.S. labour

force. Thus, when taking into account the overrepresentation of males in middle-skill

occupations, this may act as further evidence for the strong performance of females in the labour

market relative to males (Acemoglu & Autor, 2011), reducing the value of their labour in

household production. Atesagaoglu et al. (2014) substantiates this claim with a life-cycle model

attributing 93% of the reduction in the gender unemployment gap to falling demand and wages

in male-heavy occupations, due to technological change. This increase in the wage ratio of female

to male earnings may partially explain the consistent rise in SAHFs, since this makes production

of domestic work by women more costly to the family (Mincer, 1962).

An additional component of technological progress that alters time-allocation of domestic

work is the gains in efficiency that reduce the hours needed to complete equivalent tasks over

time (Greenwood and Guner, 2004). Greenwood (2012) develops this hypothesis in referencing

the contributions that domestic inputs such as dishwashers, washing machines, and the internet,

have had on reducing the need for domestic labour. The paper highlights various channels of

technological progress that provide economies of scale in household maintenance. However,

since this paper focuses on divorce, it offers little by way of explanation for the rise in SAHFs.

It is clear that many academics have developed over time the economic theory explaining

the effects of technological advancement on time-allocation of market work and the gender wage

gap. However, very little quantitative analysis has attempted to determine the subsequent impact

on SAHFs, particularly across OECD countries, thus providing an interesting topic for exploratory

study.

2.2. Macroeconomic Drivers

The significant rise in SAHFs has been documented across a large amount of OECD

countries in recent decades, with the largest proportion of this change arising from fathers that

are choosing to be primary caregivers (Pew Research Center, 2014; Kramer & McCulloch, 2010).

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The latter study finds that this characteristic is prevalent in the U.S. amongst SAHF Families in

which the wife earns 100%, 90% and 75% of household income within each decade between

1968 and 2009. However, whilst a reliable and well-suited source of data is referenced (U.S. CPS),

a significant limitation of findings is that it is impossible to infer whether a greater percentage of

domestic work is in fact completed by the working mother and not the SAHF.

The division of labour amongst households is motivated by the substitutability of market

and domestic work between individuals (Becker, 1981). Whilst biological differences remain

prevalent in driving women to act as primary caregivers for the family, changes in experience and

investment into human capital may contribute to growing substitutability between male and

female labour.

Kramer & Kramer (2013) attempt to quantify the effect on stay-at-home fatherhood of

greater human capital of mothers relative to their male counterparts. Using logistic regression

analysis, the author finds strong evidence to support the claim that greater educational

attainment of the wife in a household over that of the husband, largely increases the likelihood of

a SAHF Family. However, one limitation of this conclusion is that although educational attainment

is viewed as a strong correlate of human capital, recognising the specific discipline of higher

education and amount of market work experience may enable a closer estimate of human capital

and thus develop the author’s findings.

Greenwood (2012) also references a dramatic increase in the rate of women in higher

education, stimulated in part by a rising college premium, raising the contribution made by

married women to household income. The increase in female education alone augments their

earning potential which may motivate some families to adopt a SAHF household income structure

(Kramer & McCulloch, 2010).

Additionally, how macroeconomic fluctuations effect the number of SAHF Households is

unclear. Whilst high male unemployment as a result of an economic downturn may stimulate

female participation through the ‘added worker’ effect, as households compensate for falling

household income, increasing female unemployment can discourage married women from

joining the labour force (Jaumotte, 2003). Kramer & Kramer (2013) provide deeper analysis of

the effect of macroeconomic fluctuations by separating caregiving SAHFs with those unable to

work. The authors provides evidence that the unemployment rate does not affect the amount of

caregiving SAHFs, which increases over time linearly, but does increase the likelihood of unable-

to-work SAHF Families by 8.1% for every 1% increase in unemployment. However, when using a

dummy variable to reflect periods of recession, as a means of isolating these economic

fluctuations, to avoid attributing the changing volume of SAHFs to changes in unemployment

alone, the results obtained were contrary to the previous. They indicate that recessions may in

fact reduce the amount of caregiving SAHF Families, and provide no significant correlation with

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those that are unable to work. It appears as though this area of study requires further

consideration.

The individual design and focus of economic policy across countries, with particular

reference to taxation and benefits, may also have a consequential impact on time-allocation to

market and domestic work of individual family members (Anxo, 2007). Time-use surveys are

analysed across four OECD countries which differ in terms of welfare policy. In Sweden, where a

low gender gap in time-allocation is present, public policy is characterised by individualised

taxation and extensive welfare support for childcare and parental leave. Contrastingly, Italy offers

restricted public support to families, with strong protection for those in permanent employment,

contributing to female unemployment as women are often seen as labour-market entrants.

Furthermore, the paper describes a contrast in the extent to which welfare support affects time

allocation across countries through empirical analysis. A limitation of the paper’s preference for

time-use surveys, however, is that they were undertaken by separate statistical authorities

during different time-periods, arguably skewing the results obtained when comparing

internationally. Jaumotte (2003) also found evidence to suggest that the specific tax treatment of

second earners, and the use of taxation to incentivise couples to divide market work, have an

effect on the likelihood of mothers to engage in market work.

2.3. Conclusion and Limitations of the Literature

To summarise, the literature states that technological advancement has led to an increase

in the amount of time families contribute to market work over domestic work, whilst reducing

the comparative advantage that women have previously assumed for domestic work. This is

driven by dramatic increases in the relative wages of women and the volume of women in the

workplace, thus increasing the relative cost to families of women allocating time to domestic

duties. Developments in both skill-biased change in favour of women, as well as economies of

scale in household maintenance, act as partial drivers of this change, potentially leading to an

overall increase in SAHFs. Empirical evidence suggests that the largest percentage of the rise in

SAHF Families is accounted for by those choosing to be primary caregivers. The literature

proposes that factors driving this change include greater substitutability of market and domestic

work between genders, rising human capital of mothers relative to fathers and the extent to

which economies offer welfare support. The effect of macroeconomic fluctuations on SAHFs

remains ambiguous.

Finally, whilst empirical evidence seems in support of these determinants causing an

increase in SAHF Households, certain limitations to these explanations must be acknowledged.

Definitions and characteristics of SAHFs differ both over time and between countries, causing

difficulty in assuring accurate time-series and cross-country analyses. Additionally, when

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completing surveys, participants may be implicitly incentivised to be dishonest when referencing

their motivations for staying at home, by claiming to be unable to work, due to the pressure of

gender expectations and stigma of SAHFs (Zimmerman, 2000). This may deflate the figure of how

many fathers choose to act as primary caregivers.

3. Cross-Country Comparison and Context

In order to provide an informative comparative study of SAHF Households in Canada and

the U.S., the historical context of their prevalence in each country will be analysed, aiming to offer

potential explanations for key deviations in trends.

The below graph depicts the proxy used for total SAHF Households, as a percentage of

Husband-Wife families, for both the U.S. and Canada between 1978 and 2007.

Figure 2. SAHF Households: Canada and the U.S.

A steady upward trend is presented for both countries throughout the 29-year period,

with a 2.5 percentage point increase in the U.S., and a 3.8 percentage point increase in Canada.

Thus, whilst the direction of this change is common between countries, the magnitude varies

significantly.

One possible explanation for this difference is the contrasting income tax procedures.

Whilst Canadian couples must file their income tax returns separately, the U.S. Internal Revenue

Service (IRS) allows for joint filings. Those couples that decide to file jointly benefit from

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Stay-At-Home Father Families

SAHF USA SAHF CAN

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significant tax exemptions, as well as qualifying for multiple tax credits such as Child and

Dependent Care Tax Credit, and Earned Income Tax Credit (IRS.gov). This incentivises dual-

earner families, posing an additional opportunity cost for the husbands in SAHF Households in

the U.S. to stay out of the labour force, and act as the sole caregiver of children. This may partially

explain why the rise in SAHF Households in Canada is greater than that of the U.S.

A further potential explanation may be the contrasting fertility rates of the two countries,

and the subsequent effect on female labour force participation. Both countries faced a very similar

fertility rate in the late 1970s, however from 1980 onwards, Canada experienced a rate that

fluctuated between 1.5 and 1.7 (World Bank), whilst that of the U.S. was above 2 for

approximately 50% of the 29-year period, reaching 2.12 in 2007 (Statistics Canada), as shown in

the figure below.

Figure 3. Fertility Rate: Canada and the U.S.

In their cross-country empirical investigation into the effects of fertility on female labour

force participation, Bloom et al. (2007) discovered a strong negative effect resulting from a

combination of factors. They argue that a decline in the fertility rate leads to a reduction in

population growth and increase in the capital-labour ratio. Simultaneously, an increase in the

ratio of the working-age population is noted, which combined with the previous effects,

contributes to a rise in female labour force participation. Thus, it can be argued that a lower

fertility rate in Canada makes it less likely for married women to adopt the role of primary

caregiver in Husband-Wife families, leading to a greater increase in SAHF Households in Canada

relative to the U.S.

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4. Empirical Analysis

Based on both economic theory and past literature, various data have been collected to

analyse the direction and magnitude of several key variables through time-series econometric

modelling. This section will outline the advantages and limitations of using a proxy dependent

variable, as well as introduce the reader to the other variables used in the empirical analysis,

before outlining the econometric method adopted.

4.1. Data Limitations

The scarcity of academic study on SAHF Households, and its focus on micro-level analysis,

is partially explained by two reasons. Firstly, very few national and international databases

collect data relating to SAHF Households. Secondly, several definitions of varying restrictiveness

have been used when analysing SAHFs, leading to contrasting results (Kramer & McCulloch,

2010). By using a proxy variable for SAHFs for which there is attainable data, a common definition

can be used that enables a comparative study between the two countries, thus providing the

potential for original results.

Data for ‘Husband-Wife Families in which the Wife is the sole earner, as a percentage of total

Husband-Wife Families’ is used to represent the proportion of SAHF Households. The sources used

are the Bureau of Labor Statistics, and Statistics Canada, both of which ensure reliable results.

However, one main drawback of using a proxy variable with such a broad definition is that

couples without children may be included, albeit a very similar trend is expected as shown below.

This restricts the practical interpretation of any results specific to SAHFs.

The below graph depicts the data of the proxy variable as a line graph mapped against

SAHF data collected from the Integrated Public Use Microdata Series of the Current Population

Survey, of three different definitions of varying restrictiveness. The data used is taken from

Kramer & McCulloch’s (2010) paper. The three contrasting definitions are SAHF Households in

which the wife earns 100%, >90%, and >75% of total income, allowing for part of total household

income to be earned by the father. A further restriction is that each family also has one child of 18

years of age or below.

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Figure 1. SAHF Households: Alternative Definitions

The graph shows that the proxy selected fits rather closely with the three definitions,

suggesting that the potential inclusion of couples without children does not hugely inflate the results.

All variables used in the empirical analysis are presented and described in the table below,

referencing their original sources. Due to data constraints, the empirical analysis will use all data

between 1981 and 2007, totalling 27 years. Whilst performing an econometric regression with 27

entries is not optimal, it does allow for significant results, yet this will be considered in the evaluation

of the paper’s findings.

Table 1. Summary Table of Variables

Variable Measure Definition Units of Measure

Years Available

Source

SAHFt Stay-At-Home Fathers

Proportion of Husband-Wife families in which the Wife is the sole earner

Percentage of total Husband-Wife familes

USA: 1967-2007 CAN: 1976-2011

USA: Bureau of Labor Statistics (CPS) CAN: Statistics Canada

GERDt Gross Expenditure on Research and Development

Gross Government Expenditure on Research and Development as a proportion of GDP

Total Expenditure as a % of GDP

USA: 1981-2012 CAN: 1981-2013

OECD

TFPt Total Factor Productivity

Business sector Multifactor Productivity

Measured as a % change year-on-year

USA: 1948-2014 CAN: 1961-2011

USA: FRBSF Working Paper 2012-19 (March 2014) CAN: Statistics Canada

Patentst Total Patents Number of Utility Patent Grants in all industries

Total number per calendar year

1963-2012 US Patent Office

0

1

2

3

4

5

6

1968-1979 1980-1989 1990-1999 2000-2009

% o

f SA

HF

SAHF USA: Alternative Definitions

SAHF USA (100%) SAHF USA (>90%)

SAHF USA (>75%) SAHF USA (proxy)

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The majority of the data used have been collected from reliable national or international

statistics databases, such as the OECD, the World Bank, the U.S. Bureau of Labor Statistics,

Statistics Canada, and the U.S. Patent Office. Where possible, data for both countries have been

selected from a common source. This is the case for four of the eight variables, to ensure a reliable

comparative study that is not skewed by differences in data collection and definitions. There are

three proxy variables for technological progress; Gross Expenditure on Research and

Development (GERD) as a percentage of GDP; Total Factor Productivity (TFP); and Total Patents.

These will be used individually in seperate models to strengthen the reliability of any

interpretation of the effect of technological progress on SAHF Households.

There are several prevailing limitations of the reliability of certain variables which must

be addressed. Patent data has been collected from the U.S. Patent Office for both Canadian and

U.S. patents, which represents all Utility Patent Grants approved in the U.S. Therefore, Canadian

patents granted solely in Canada would not be included in these figures. However, this does not

greatly hinder the reliability of the results, as it can be assumed that the vast majority of Canadian

patents are also granted in the U.S.

A further limitation is that the data for Relative Secondary Education is only obtainable at

five-yearly intervals, thus, for them to be used in the statistical model, any missing data points

Fertilityt Fertility Rate Average expected number of children born to a woman assuming they reach the end of childbearing years

Average number of births per woman

USA: 1960-2012 CAN: 1960-2011

USA: World Bank CAN: Recent Social Trends in Canada, L. Roberts (1960-2002) Statistics Canada (2003-2011)

Unempt Unemployment Rate

Population aged 16+ actively seeking employment as a proportion of total labour force

Percentage of total labour force

USA: 1968-2009 CAN: 1976-2011

USA: Bureau of Labor Statistics (CPS) CAN: Statistics Canada

RelEd_St Relative Secondary Education

Relative female secondary education as Population of 15-64 year olds

Ratio of women to men

1970-2015 World Bank

Welfaret Welfare Spending

Total government welfare spending as a proportion of GDP

Total Expenditure % of GDP

1980-2011 OECD

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have been interpolated. This should not hinder the reliability of the model since the variable does

not appear to fluctuate significantly.

4.2. Preliminary Analysis

The below table provides an analysis of the key features of all variables, before the formal

econometric model is introduced.

Table 2. Key Statistical Features of the Variables

Firstly, across all three technology measures, Canada has a significantly lower mean and

median value, suggesting that each proxy consistently estimates a greater level of technological

advancement of the U.S. economy. Secondly, the mean and median value of welfare spending as a

proportion of GDP are greater for Canada, and the maximum is over four percentage points

higher. Thus, the two economies appear to prioritise welfare spending to varying degrees.

Furthermore, by examining the maximum and minimum values of each variable, it appears as

though there are no outliers in the data. Finally, the table shows that there is no unique number

of observations, which means that the model will have to use the range of data points of the

variable with the lowest amount of observations. As previously mentioned, this implies 27 data

points.

SAHFt GERDt TFPt Patentst Fertilityt Unempt RelEd_St Welfaret

Mean USA 4.19 2.52 0.88 54496 1.96 5.49 1.06 14.23

CAN 4.30 1.64 0.08 2060 1.63 7.92 1.03 16.76

Median USA 4.25 2.54 1.16 52742 2.00 5.83 1.06 14.30

CAN 4.25 1.62 0.15 1986 1.66 8.25 1.02 16.30

Maximum USA 5.60 2.65 3.37 89823 2.12 9.71 1.12 15.80

CAN 6.00 2.04 3.42 3606 1.76 12.00 1.07 20.50

Minimum USA 3.10 2.27 -2.77 30074 1.76 3.97 1.01 12.80

CAN 2.20 1.20 -2.70 867 1.49 6.00 0.99 13.20

Std. Dev. USA 0.71 0.10 1.44 20299 0.11 1.38 0.03 1.09

CAN 1.19 0.26 1.47 926 0.08 1.70 0.03 1.67

Skewness USA 0.42 -0.88 -0.64 0.36 -0.44 0.95 0.02 -0.04

CAN -0.43 0.13 0.21 0.28 -0.15 0.43 0.33 0.61

Observations USA 30 27 30 30 30 30 30 28

CAN 30 27 30 30 30 30 30 28

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4.3. Theoretical Predictions

Before outlining the empirical method, it is useful to discuss the theoretical predictions of

the regressors:

Technology;

As discussed in depth in the literature review, a positive correlation is expected between

technology and SAHF Households. As theorised by Katz and Murphy (1992), technological

progress has led to the polarisation of wages in the U.S., thus leading to a rise in female labour

force participation due to the overrepresentation of males in middle-skilled jobs. Also,

Greenwood (2012) argues that technology has contributed to changes in household production,

reducing the necessity of time allocation to domestic work.

Fertility Rate;

Consistent with the findings of Bloom et al. (2007), a fall in fertility rate is expected to

have a positive effect on SAHF Households, due to it increasing the volume of women in work,

with fewer of the constraints of having children.

Unemployment;

The effect of unemployment is ambiguous. As expressed in the literature review,

unemployment as a consequence of economic downturn may lead to the ‘added worker’ effect,

stimulating female participation, though it may equally discourage married women from joining

the labour force as they perceive there to be a high level of unemployment (Jaumotte, 2003).

Relative Education;

Kramer & Kramer (2013) evidence greater educational attainment increasing the

likelihood of SAHF Households, thus a similar effect is anticipated from an increase in the ratio of

relative secondary education of women to men.

Welfare Spending;

Since this variable does not provide specific information as regards to the specific target

of welfare spending, its effect on SAHF Households in this model is ambiguous. Anxo (2007),

argues that governments can increase female labour force participation by targeting welfare

spending at specific family policies and employment regimes.

4.4. Empirical Method

The formal econometric model attempts to provide empirical evidence supporting the

predictions stated. The analysis will focus on the U.S. example, before outlining any differences or

similarities for the Canadian data. As is typical of regression analysis, a general regression for

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preliminary analysis is first selected, before specifying a final model based on econometric

testing.

One crucial assumption of time-series regression analysis is that all variables are

stationary. It is common, however, for time-series data to have time-dependant movements.

Failing to correct for this may lead to a spurious relationship (Granger & Newbold, 1974).

As is clear from the graphs below, eyeballing the trends of the variables can indicate

whether non-stationarity is expected from the formal tests conducted.

Figure 2. Line Graphs of Variables

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At first glance, the majority of the variables seem to be non-stationary, with the exceptions

of TFP, and GERD. The Augmented Dickey-Fuller (ADF) test is a useful way of determining non-

stationarity, as it does not rely on the assumption that each variable has a random walk, instead

it allows for trends, and considers this when selecting the critical values to be tested against. The

below table displays the results from the individual ADF tests.

Table 3. ADF Tests: Results

Variables Country

Test

Statistic

1% Critical

Value

5% Critical

Value

10% Critical

Value

SAHF USA -2.139 -4.343 -3.484 -3.23

CAN -1.965 -4.343 -3.484 -3.23

GERD USA -3.018 -2.492* -1.711 -1.318

CAN -1.904 -4.371 -3.596 -3.238

TFP USA -4.992 -3.723* -2.989 -2.625

CAN -3.385 -2.473* -1.703 -1.314

Patents USA -3.064 -4.343 -3.584 -3.23

CAN -2.982 -4.343 -3.584 -3.23

Fertility USA -1.73 -4.343 -3.584 -3.23

CAN -0.677 -4.343 -3.584 -3.23

Unemp USA -2.344 -4.343 -3.584 -3.23

CAN -1.831 -4.343 -3.584 -3.23

RelEd_S USA -2.97 -4.343 -3.584 -3.23

CAN -1.557 -4.343 -3.584 -3.23

Welfare USA -3.303 -4.343 -3.584 -3.23

CAN -1.969 -4.362 -3.592 -3.235

For the majority of cases, the ADF test-statistics are greater than the 10% critical values.

Thus, for these variables we are unable to reject the null hypothesis that a unit root is present,

suggesting that they suffer from non-stationarity. Conversely, TFP, for the U.S. and Canada is

statistically significant at the 1% level, so too is GERD for the U.S. alone.

In order to correct for this, the first difference of the logarithm for non-stationary

variables will be used in the econometric model. After having conducted further ADF tests on each

of the variables generated by first differencing, it can be confirmed that they no longer suffer from

non-stationarity (see appendix).

16

To begin the formal econometric analysis, a model including two lags of both the

dependent and explanatory variables is selected, with the view to remove any insignificant lags if

signified by the initial results. The first technology proxy to be modelled is TFP, with U.S. data.

4.4.1. U.S. Regression Analysis

Equation 1.

𝑫_𝑺𝑨𝑯𝑭 = 𝑪(𝟏) + 𝑪(𝟐)𝑫_𝑺𝑨𝑯𝑭(−𝟏) + 𝑪(𝟑)𝑫_𝑺𝑨𝑯𝑭(−𝟐) + 𝑪(𝟒)𝑻𝑭𝑷 + 𝑪(𝟓)𝑻𝑭𝑷(−𝟏)

+ 𝑪(𝟔)𝑻𝑭𝑷(−𝟐) + 𝑪(𝟕)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚 + 𝑪(𝟖)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚(−𝟏) + 𝑪(𝟗)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚(−𝟐)

+ 𝑪(𝟏𝟎)𝑫_𝑼𝒏𝒆𝒎𝒑 + 𝑪(𝟏𝟏)𝑫_𝑼𝒏𝒆𝒎𝒑(−𝟏) + 𝑪(𝟏𝟐)𝑫_𝑼𝒏𝒆𝒎𝒑(−𝟐)

+ 𝑪(𝟏𝟑)𝑫_𝑹𝒆𝒍𝑬𝒅_𝑺 + 𝑪(𝟏𝟒)𝑫_𝑹𝒆𝒍𝑬𝒅_𝑺(−𝟏) + 𝑪(𝟏𝟓)𝑫_𝑹𝒆𝒍𝑬𝒅_𝑺(−𝟐)

+ 𝑪(𝟏𝟔)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷 + 𝑪(𝟏𝟕)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷(−𝟏) + 𝑪(𝟏𝟖)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷(−𝟐)

Figure 3. Baseline Model: TFP (U.S.)

17

When modelling time-series data, serial correlation is often found. This is when the residuals

of the variables used in the model are correlated with the residuals of the variables’ lagged

counterparts. Failing to account for serial correlation can exaggerate the goodness-of-fit, often shown

by an inflated R2, and can also lead to estimates with biased coefficients. The Breusch-Godfrey LM test

is used to determine the presence of first and second order serial correlation.

Figure 4. Test for First Order Serial Correlation (TFP, U.S.):

Figure 5. Test for Second Order Serial Correlation (TFP, U.S.):

18

The null hypothesis of the Breusch-Godfrey LM test is that serial correlation is not present

in the estimation. Thus, at the 5% and 10% critical values of the tests for first and second order

serial correlation, there is insufficient evidence to reject the null hypothesis, since 0.8754 and

0.4417 are larger than 0.1, implying that the estimation does not suffer from serial correlation.

Therefore, the inclusion of additional lags is not necessary.

Heteroskedasticity is also tested for, which occurs when the variance of the error term is

not constant, and varies depending on the value of the explanatory variables. This can lead to

incorrect standard error terms which alters the confidence intervals, potentially allowing

variables to be accepted or refused incorrectly at a given significance level. The Breusch-Pagan-

Godfrey test is used to test for linear heteroskedasticity, as a lack of observations in the model

prevents the White test, a popular test of heteroskedasticity, from being estimated.

Figure 6. Test for Heteroskedasticity (TFP, U.S.):

The null hypothesis of this test is that the variances of the error terms are equal, i.e. there

is no linear heteroskedasticity. Again, at the 5% and 10% levels, there is failure to reject the null

hypothesis, allowing the assumption that the model does not suffer from heteroskedasticity.

Furthermore, it is important to account for the possibility of over-specification. Therefore,

any insignificant lags of the variables that do not explain the variation in the dependent variable

are removed. This is based on the size of the probability value and t-statistics. As they can vary

once certain variables are removed, it is essential to eliminate any insignificant lags in stages.

Figure 7. Variables D_SAHF(-1), and D_RelEd_S(-2) are removed:

19

Equation 2.

𝑫_𝑺𝑨𝑯𝑭 = 𝑪(𝟏) + 𝑪(𝟐)𝑫_𝑺𝑨𝑯𝑭(−𝟐) + 𝑪(𝟑)𝑻𝑭𝑷 + 𝑪(𝟒)𝑻𝑭𝑷(−𝟏) + 𝑪(𝟓)𝑻𝑭𝑷(−𝟐)

+ 𝑪(𝟔)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚 + 𝑪(𝟕)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚(−𝟏) + 𝑪(𝟖)𝑫_𝑭𝒆𝒓𝒕𝒊𝒍𝒊𝒕𝒚(−𝟐) + 𝑪(𝟗)𝑫_𝑼𝒏𝒆𝒎𝒑

+ 𝑪(𝟏𝟎)𝑫_𝑼𝒏𝒆𝒎𝒑(−𝟏) + 𝑪(𝟏𝟏)𝑫_𝑼𝒏𝒆𝒎𝒑(−𝟐) + 𝑪(𝟏𝟐)𝑫_𝑹𝒆𝒍𝑬𝒅_𝑺

+ 𝑪(𝟏𝟑)𝑫_𝑹𝒆𝒍𝑬𝒅_𝑺(−𝟏) + 𝑪(𝟏𝟒)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷 + 𝑪(𝟏𝟓)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷(−𝟏)

+ 𝑪(𝟏𝟔)𝑫_𝑾𝒆𝒍𝒇𝒂𝒓𝒆𝑮𝑫𝑷(−𝟐)

Re-testing for first and second order serial correlation and the presence of

heteroskedasticity finds that the model does not suffer from any of those properties (see

appendix). Thus, having tested the robustness of the model, it can be concluded that it is a suitable

model with which to proceed to analysis. Due to there being lagged versions of the dependent and

explanatory variable, the model is defined as an autoregressive distributed lags model,

ARDL(1,2,2,2,1,2).

20

The adjusted R2 is used to assess the strength of the model as a useful predictor of

variation in the dependant variable. This measures the explanatory power of the independent

variables in predicting variation in the dependant variable, taking into consideration the number

of variables in the model. This shows that 59.92% (2.s.f) of the variation in SAHF Households is

explained by the model, which is relatively high. When comparing this to the Baseline Model in

Figure 3, it is clear that removing unnecessary lags has improved the explanatory power of the

model by approximately 10 percentage points, suggesting that the previous model was over

specified.

The coefficients of the three TFP lags individually represent the average marginal

percentage change in the dependant variable arising from a unitary percentage point change at

each lagged period, this is because TFP is measured as a growth rate. Thus, since the first

difference of the logarithm of all other variables has been taken, these coefficients have the same

interpretation. In this case, at the 5% significance level we can conclude that when all other

factors are held constant, on average a 1% increase in TFP leads to a 0.0872% (4.s.f) decrease in

the amount of SAHF Households in the economy, as a proportion of all Husband-Wife families.

An interesting insight arises when the long-run effect of a change in TFP is considered.

This is calculated by summing the coefficients of the TFP variable and its respective lags. In the

long-run it has a positive effect on SAHF Households suggesting that a 1% increase in TFP leads

to on average a (= -0.087235 + 0.137781 =) 0.0505% (4.s.f) increase in the proportion of SAHF

Households. Since the second lag of TFP is not significant at the 10% level it is not included in this

calculation. This result is consistent with the theoretical prediction that technological progress

has reduced the value of female time allocation towards domestic work, and has subsequently

increased the likelihood of the Wife being the sole-earner of a single-earner family. The initial

negative relationship between technology and SAHF Households, however, provides an

interesting insight. This suggests that after an increase in technological advancement, there is a

delay in this affecting the propensity of families to opt for a SAHF family structure. This is

unsurprising as decisions to enter or exit the labour market are often constrained by the time it

takes to find employment, as well as the legal obligation to forewarn employers in advance of

quitting a job.

Furthermore, at the 5% significance level, a 1% increase in the growth of unemployment

would lead to an average 0.6185% (4.s.f) increase in the proportion of SAHF Households in the

long-run, ceteris paribus. This appears to be an economically significant result. It may suggest that

the ‘added worker’ effect, which stimulates female labour force participation, outweighs the

discouragement experienced by married women from searching for employment arising from the

perception of high unemployment (Jaumotte, 2003).

21

Additionally, at the 5% significant level, a 1% increase in the percentage of welfare

spending as a proportion of GDP is shown to cause a 0.6412% (4.s.f) decrease on average in SAHF

Households at the second lag. This implies that U.S. welfare spending is not particularly targeted

at the specific family policies or employment regimes said to promote female labour force

participation outlined in Anxo’s 2007 paper.

Now, the same baseline regression is performed on the remaining two alternative proxy

variables of technology in turn. Consistent with the previous regression, two lags of the

dependant and explanatory variables are used in the initial estimation.

Tests for first and second order serial correlation, using the Breusch-Godfrey LM test,

were conducted on the resulting estimations.

Figure 8. Test for First Order Serial Correlation (GERD%GDP, U.S.):

Figure 9. Test for Second Order Serial Correlation (GERD%GDP, U.S.):

Both tests fail to reject the null hypothesis of no serial correlation at the 5% and 10%

levels, implying that the GERD model does not suffer from serial correlation.

Figure 10. Test for First Order Serial Correlation (PATENTS, U.S.):

22

Figure 11. Test for Second Order Serial Correlation (PATENTS, U.S.):

Again, at the 5% and 10% critical values we fail to reject the null hypothesis for the model

using Patents as a proxy for technology, suggesting serial correlation is not present in the model.

Next, both models are tested for linear heteroskedasticity using the Breusch-Pagan-

Godfrey test.

Figure 12. Test for Heteroskedasticity (GERD%GDP, U.S.):

Figure 13. Test for Heteroskedasticity (PATENTS, U.S.):

The results of both tests show failure to reject the null hypothesis of no heteroskedasticity

at the 5% and 10% levels, thus allowing the assumption that both models have homoscedastic

error terms.

After removing any insignificant lags of the independent variables, based on their

probability values, the resulting model with GERD as the technology proxy is as follows:

23

Figure 14. Variables GERD_GDP, D_FERTILITY, D_FERTILITY(-1), D_RELED_S, D_RELED_S(-2), and D_WELFAREGDP are removed:

The first thing to notice is that the adjusted R2 is negative, which severely weakens the

interpretation of any findings as it has very insignificant explanatory power. This can be

interpreted as having an adjusted R2 of zero. This may be caused by the lack of observations used

due to the insufficient data available. Alternatively, it may be as a result of too many variables

being included.

Figure 15 below shows the results of removing the insignificant lags of the independent

variables in the Patents model.

24

Figure 15. Variables D_SAHF(-1), D_SAHF(-2), D_PATENTS(-2), D_RELED_S, D_RELED_S(-2), and D_WELFAREGDP are removed:

Similarly to the previous example, the adjusted R2 is very low at 0.0328 (4.s.f) thus

rendering the findings of the model of little use in terms of their interpretation as predictors of

the proportion of SAHF Households in the economy.

It can be concluded from these three models that the technology proxy with the greatest

explanatory power on the proportion of SAHF Households is TFP, and so it will be used to provide

the analysis of the macroeconomic factors contributing to the rise in SAHF Households.

4.4.2. Canadian Regression Analysis

In the same manner as with the U.S. example, separate models for each technology proxy

with two lags of the dependent and independent variables are estimated. They are then tested for

serial correlation and heteroskedasticity, resulting in three final models once insignificant lags

are removed, which are re-tested for these characteristics. The complete stages of these processes

are presented in the appendix. The three resulting models are given below.

25

Figure 16. Final Model (TFP, Canada), Variables D_SAHF, D_FERTILITY, D_UNEMP(-1), D_RELED_S are removed:

Figure 17. Final Model (GERD%GDP, Canada), Variable D_WELFAREGDP(-2) are removed:

26

Figure 18. Final Model (GERD%GDP, Canada), Variables D_SAHF(-1), D_PATENTS, and D_PATENTS(-2) are removed:

After conducting the same tests as outlined previously, not one of the three models

showed an indication of first or second order serial correlation, nor of linear heteroskedasticity.

Interestingly, contrarily to the results of the three U.S. models, all three adjusted R2 statistics show

that the models are well specified and have strong explanatory power. The adjusted R2 shows

that 66.15%, 55.50%, and 56.06% (2.s.f) of the variation in the dependant variable SAHF

Households can be explained by the independent variables in the TFP model, the GERD model,

and the Patents model respectively. Since the model with the greatest explanatory power is the

one that uses TFP as a proxy for technology, the findings of this model will be explored in more

depth.

The first noteworthy piece of information arises in the analysis of TFP. At the 1%

significance level, a 1% increase in the growth of TFP would lead to, on average, a 0.1741% (4.s.f)

increase in SAHF Households as a proportion of all Husband-Wife families. However, the effect of

the lags of TFP are not statistically significant even at the 10% level. Whilst this is slightly

dissimilar from the results obtained in the U.S. example, TFP is still shown to have a positive effect

on SAHF households, thus remains consistent with the theoretical prediction.

Furthermore, a novel insight from this model is that the lagged explanatory variable

D_SAHF(-2) is statistically significant at the 5% level, suggesting that a 1% increase in SAHF

Households would lead to a 0.4507% (4.s.f) decrease in SAHF Households after two lagged

27

periods on average, other factors held constant. Interestingly, this is contrary to economic theory

regarding changing gendered expectations, which argues that as couples increasingly perceive

SAHF Households around them, their reluctance to adopt a SAHF family structure reduces, due to

a deterioration in gender role stereotypes (Kramer & Kramer, 2013; Chesley, 2011). A possible

explanation for the negative relationship shown by the model is that in the relatively short term

couples may be deterred from choosing a SAHF Household the more they come into contact with

an existing one. This may be as a result of an increased awareness of the negative stereotype of

stay-at-home fatherhood before the positive effect on changing gendered expectations is realised.

This model also has some predictive power in the long-run. At the 10% significance level,

a 1% increase in the fertility rate causes a 9.6275% (4.s.f) increase in the proportion of SAHF

households on average, ceteris paribus. This result has particular economic significance due to its

magnitude, however, the implications of this are more restricted due it not being significant at

the 5% level. Furthermore, this is inconsistent with the theoretical prediction evidenced by

Bloom et al. (2007), that a higher fertility rate increases the constraints imposed on women of

having children, thus decreasing the proportion of SAHF Households. A possible explanation of

this result is that an increase in the average number of children per family may in fact increase

the likelihood of a couple opting for a sole-earner family structure. This would most likely

increase the volume of SAHF Households as well as Stay-At-Home Mother Households, the

increased proportion of SAHFs may therefore be a result of there being a greater propensity of

the father choosing to stay at home than the mother.

Finally, welfare spending as a % of GDP is also significant at the 10% level, suggesting that

on average a 1% increase in welfare spending leads to a 0.3566% (4.s.f) increase in SAHF

Households in the long-run. This is consistent with the theoretical predictions, yet inconsistent

with the U.S. example. It suggests that in comparison with the U.S., Canada targets a greater

proportion of welfare spending at family and employment policies that aim to incentivise female

labour force participation.

4.5. Granger Causality Testing

To further test the significance of the models’ findings, Granger Causality tests, which

have been used extensively in econometric analysis since its conception in 1969, were conducted

to determine whether any causal relationships exist between variables. Granger Causality is

deemed to be in effect if the historic values of a given variable provide statistically significant

information on future values of another variable. This predictive power is based solely upon

lagged values of a variable (Granger, 1969). The below figures display the results of conducting

Granger causality tests for both countries. Each includes 2 lags of the variables keeping consistent

with the previous models.

28

Figure 19. Granger Causality Test (U.S.):

Figure 20. Granger Causality Test (Canada):

29

Looking at the Canadian results, it is interesting to note is that by analysing the probability

values, we can see that the fertility rate, unemployment rate, and proportion of welfare spending

as a percentage of GDP all appear to have a causal influence on SAHF Households, since the null

hypothesis of the variables not G-Causing SAHF Households can be rejected. Whilst

unemployment and welfare spending are both significant at the 10% level, the fertility rate is

significant at the 5% level, strengthening the previous evidence of a correlation with SAHF

Households. Importantly, a conclusion of causality can not necessarily be drawn, since the

relationship between the two variables may occur as a result of an unspecified process having

predictive power over both variables in question.

The results of the U.S. example, however, suggest no significant causal relationships,

which arguably limit the implications of the Canadian findings. One possible reason for an

underestimation of causality is the small number of lags used, as increasing the lags augments the

likelihood of any dynamic relationships being accounted for.

Finally, an additional dynamic relationship seemingly captured in the Canadian example

is that of the proportion of SAHF Households having a causal effect on the growth of TFP at the

5% significance level. Whilst this relationship requires further testing and analysis for it to be

considered as significant, it does offer an interesting insight into the potential implications of an

increasing proportion of SAHF Households. As previously stated, the ARDL model noted a

statistically significant positive relationship between TFP and SAHF Households. A positive causal

effect of the proportion of SAHF Households on TFP may be explained by the existence of gender

stereotypes and expectations dis-incentivising females from joining the labour force in place of

males in Husband-Wife families. Due to this, females would need to be able to significantly

outperform their male counterparts in work for the couple to elect a SAHF family structure.

Therefore, when SAHF Families do arise, this may contribute to a higher level of economic growth

and efficiency, evidenced by a rise in TFP. This finding appears to support ‘exchange theory’

(Kramer & McCulloch, 2010), suggesting that there is a greater likelihood of families to have a

SAHF Household when the wife’s earnings potential is significantly greater than that of wives in

other family structures. However, whilst the implications of a causal effect may offer an

interesting interpretation, it must be realised that the Granger Causality test implies that the

values of SAHF Households reflect useful predictive information with regards to the direction of

TFP growth, above true causality (Hamilton, 1994).

30

5. Evaluation

The results of econometric modelling are ambiguous in the conclusion of the paper’s

primary research question: the effect of technological change on SAHF Households. Of the six

estimations specified, two provide statistically and economically significant evidence of a positive

correlation. At the 1% significance level TFP is shown to have a positive impact on SAHF

Households, a result that is consistent across both countries, albeit at contrasting lags. In neither

country is there a significant relationship evidenced between SAHF Households and GERD or

Total Patents, as proxies for technology. Noteworthy is the success of TFP as a predictor of

technical change (Easterly & Levine, 2001), which has been well documented due to its

interpretation as a measure of total output not caused by factor inputs, often referred to as the

‘Solow residual’.

The paper’s secondary objective is to assess the explanatory power of certain

macroeconomic variables on SAHF trends. The paper has evidenced a strong positive relationship

between the fertility rate and SAHF Households, prevalent across all Canadian estimations,

restricting the negative relationship documented by Bloom et al. (2007) to female labour force

participation. The paper also evidences a net positive effect of unemployment on SAHF

Households in the U.S., suggesting the ‘added worker effect’ outweighs any discouragement to

join the labour force resulting from the perception of high unemployment. However, contrasting

results across Canadian estimations significantly limit the strength of this conjecture.

Furthermore, the explanatory power of welfare spending on SAHF Households is inconclusive

due to the lack of in-depth analysis into the specific target of welfare spending regimes in each

country. The presence of contrasting results across the two countries provides a motivation for

further academic study due to the significance that this difference may have for public policy,

potentially highlighting certain benefits of targeting welfare spending. Equally, the possibility of

an increased volume of SAHF Households having a negative effect on the likelihood of other

couples adopting a SAHF family structure in the short-term, provides a novel in the literature,

offering a topic for further exploratory study.

The paper’s success in achieving these objectives, however, is hindered by certain data

limitations which must be evaluated, especially considering the novelty of the use of econometric

analysis in the literature. The broad definition of the proxy variable for SAHF Households

allowing for the inclusion of couples without children, limits the interpretation and implication

of any findings. The data that is needed for a successful cross-country analysis that accounts for

this limitation is currently unavailable, thus would necessitate a change in the collection of data

regarding family structure by international databanks. Equally, a lack of sufficient data for several

key variables has led to estimations with very few observations, limiting the strength of the

31

conclusions that can be drawn. Having insufficient observations increases the likelihood of the

model not accounting for true relationships, or overestimating others.

6. Conclusion

The effect of technology on SAHF Households has previously been unexplored. This paper

uses extensive time-series econometric modelling to analyse the potential relationship that exists

as a result of a combination of the role technology has played in increasing female labour force

participation, and reducing the necessity of time allocation to domestic work. In considering the

issues faced by economists when empirically analysing the effects of technological change, three

separate technology proxies are selected in a bit to strengthen the paper’s conclusion. The

strength of the argument that technology has had a positive effect on SAHF Households relies on

the suitability of TFP as a proxy. Whilst further exploratory study is needed to substantiate this

conjecture, the paper nonetheless contributes to the literature by being the first to evidence a

positive relationship between technology and SAHF Households, as well as by providing

empirical support for several other macro-level determinants which must be accounted for in

future studies.

The paper offers two novel insights which, if supported by further academic study, may

have significant implications for public policy. Firstly, the paper evidences contrasting effects on

SAHF Households of the two countries’ welfare spending regimes. Future studies should focus on

the consequences for SAHF Families of varying welfare states, as this may offer key insights into

the significance that certain benefit structures may have for micro-level decision-making

regarding family structure. Secondly, the paper argues that an increase in SAHF Households may

have a positive effect on TFP itself, which could enable governments to restructure welfare

spending in a way that might benefit long-term economic growth.

32

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