Question

Consider the labour market for nurses. Distinguish between the extensive and intensive margins of labour supply. Briefly explain why an increase in the wage might result in a nurse reducing labour supplied, and indicate whether this reduction occurs at the extensive or intensive margin.

Answer 1

Forty years ago the French and British used to work more than the Americans. They
now work less. The aim of this paper is to provide a coherent picture of these changes. To do
so we split the overall level of work activity into the number of individuals in work and the
intensity of work supplied by those in work. This reflects the distinction between whether
to work and how much to work at the individual level and is referred to, respectively, as
the extensive and intensive margin of labour supply. At the aggregate level the former is
typically measured by the number of individuals in paid employment and the later by the
average number of working hours.
The difference between the extensive and intensive margins has been highlighted in
recent research attempting to resolve differences between micro and macro responses of
labour supply to tax reform. For example, Rogerson & Wallenius (2009), following the
work of Prescott (2004), argue that the responsiveness of the extensive margin of labour
supply to taxation plays a major role in explaining aggregate differences in total hours
worked across countries. They show that an economy with fixed technology costs for firms
and an inverted U-shape life-cycle productivity for workers can produce large aggregate
extensive labour supply responses driven by movements in employment at either end of
the working life. This, they argue, can reconcile the small micro-based elasticities of hours
worked with the large responses required if taxes and social security are to explain cross-
country differences in total hours of work.
The distinction between the extensive and intensive margins has long been recognised
in microeconometric studies of labour supply (Heckman 1993). For example, building
on the insights by Gronau (1974) and Heckman (1974, 1979), Cogan (1981) documented
the importance of fixed costs of work in separating the link between responses at the
employment and hours margin. His study found that earlier estimates of hours of work
elasticities at the intensive margin for married women were biased upwards due to the
omission of fixed costs. In subsequent empirical analyses the size of the wage elasticities
at these two margins has been found to differ significantly by gender, family composition
and age (Blundell & Macurdy 1999). Typically the elasticity at the extensive margin has
been found to be somewhat larger than the elasticity at the intensive margin. Over time,
as labour force participation of women increased, the labour supply elasticities of men and
women have, to some extent, converged (Blau & Kahn 2007).
It is not only women with children where the role of the extensive labour supply margin
has been found to play a major role in understanding individual and family labour supplybehaviour over the life-cycle. ‘Early retirement’ behaviour has been found to respond
systematically to participation tax rates implicit in social security systems, see for example
Gruber and Wise (1999) and papers therein.
The relative size of labour supply responses at the intensive and extensive margin
has also been a key parameter in the public economics literature on earnings tax design,
see Diamond (1980), Saez (2002) and Laroque (2005). A ‘large’ extensive elasticity at low
earnings can ‘turn around’ the impact of declining social weights implying a higher transfer
to low earning workers than those out of work, in turn providing an argument for lower
tax rates at low earnings and a role for earned income tax credits. Participation tax rates
(PTR) and effective marginal tax rates (EMTR) at low earnings remain very high in many
current tax systems. This is carefully documented in the evidence to the Mirrlees Review,
see Brewer et al. (2010) and references therein. In the UK effective marginal tax rates are
well over 80% for some low income working families because of phasing-out of means-tested
benefits and tax credits.
A related discussion in labour supply elasticities is the time horizon of behavioural
responses. Many micro-based studies have focused on weekly hours of work while macro-
based analysis look at aggregate measures of annual hours of work. The measure and
properties of the extensive (no work at all vs. some positive work during the period) and
intensive (average hours supplied by the workers) margins are sensitive to the length of
the reference period. Furthermore, the labour elasticities are different when assessed at
the steady state or when they incorporate intertemporal substitution effects (Blundell &
Macurdy 1999, Chetty et al. 2011).
But what do we know about the importance of these margins for different types of
workers? How well does the extensive margin explain changes in total hours over time
and across countries? In this paper we provide a detailed decomposition of the evolution
of total hours of work into changes at the extensive and intensive margin. We examine
three key countries - the US, the UK and France. These three countries stand at the top,
middle and bottom, respectively, of Prescott’s 2004 table of labour supply flexibility. They
are also countries where we can access nationally representative detailed microdata over a
long period of time so as to examine the relationship between the extensive and intensive
margin across different individual types. We study the forty year period up to 2008. The
UK provides an interesting comparison with the polar cases of France and the US. Over
this period the UK has adopted many of the same (or similar) tax policies as in the US
(Blundell & Hoynes 2004) while, at the same time, it has moved from a dominant positionin the supply of total hours to one lying between the US and France.
This analysis, which complements the results presented in Blundell, Bozio & Laroque
(2011b), finds that neither margin dominates in explaining changes in total hours worked
for these countries, rather the relative importance of the extensive and intensive margin is
shown to differ systematically by age, gender and family composition.
Section 2 provides an overview of the changes in aggregate hours worked over the
last forty years. Section 3 presents a theoretical framework to decompose the aggregate
labour supply elasticity into extensive and intensive sub-elasticities. It applies a statistical
framework providing bounds on the empirical measures of the intensive and extensive
margins to the case of France, the UK and the US. Section 4 presents detailed description
of the labour margins for some specific demographic groups, i.e. the young, the mothers
and the older workers. Section 5 concludes.
2 Working Hours in the US, the UK and France
2.1 Definitions and Data
Labour supply is a multi-faceted concept and can cover relatively broad definitions. Our
interest is in market work but we shall not equate non-market work with “leisure”, as it
could include household production and voluntary work. Even if we might like to measure
the amount of labour supply accounting for effort and productivity, we concentrate in this
paper on a narrower definition of labour, i.e. time spent in market work.
There are many different concepts of market work (or hours worked) that have been
used in the labour statistics literature: normal hours, hours paid, usual hours or actual
hours.1 Each varies depending whether one includes overtime hours, time traveling to
work, meal breaks, holidays, sick leave and many other periods which could be considered
paid work or not. In this paper, we use the concept of actual hours of work, excluding meal
breaks, travel to work, holidays and sick leave, but including short rests at the workplace.
To measure time spent in market work one needs to define a reference period. It is
generally the week or the year, but it could equally be a day or a lifetime. The choice
of the reference period is important, in particular to define the intensive and extensive
margins. In this paper, we use the civil year as the reference period so that we define Hit
as the total actual hours of market work of individual i in year t. The total actual hourscan be decomposed into an extensive and intensive component:
Hit = pit × hit (1)
We define the extensive margin of labour as the fraction pit of the reference period when
the individual is employed or self-employed. This definition is different from the more usual
one, i.e. whether in or out of the labour market, in two respects. First it relies on the notion
of employment, as opposed to positive hours worked, and thus captures the standard notion
of the extensive margin as a measure of “participation” to the labour market (Heckman
(1974) and Killingsworth (1983)).2 Second, defining the extensive margin as a fraction of
the reference period, as opposed to a dichotomous variable, makes the distinction between
extensive and intensive robust to the choice of the reference period.
From (1), it follows that the intensive margin of labour, hit, is defined as the total
number of hours of work worked in the reference period Hit divided by the fraction of the
reference period in employment, i.e. by the measure of the extensive margin, pit. This is a
measure of the intensity of work when employed. Note that with our definitions periods of
employment not worked, like holidays or sick leave, will appear as changes in the intensive
margin.
It may be useful to develop a few examples. Consider a worker A who is employed
during the entire reference year, working H hours in total during the year. Suppose that
she works at a constant rhythm, H/12 every month. Her intensive margin is H and her
extensive margin is 1. A part-time employee B, who works three quarters of H/12 each
month, has also 1 as extensive margin but her intensive margin is 3H/4. Consider now a
person C who works at the same rhythm as A between January and June and October-
December, while she is unemployed, out of work, not on paid leave, without a work contract
in July-September. She works three quarters of the year so her extensive margin is equal
to 3/4, while her intensive margin equal H. Thus her total annual hours worked is 3H/4,
equal to that of B, but her intensity of work when employed is similar to A.
The choice of the reference period is nonetheless important to capture movements in
the extensive and intensive margins. With the year as reference period, one misses seasonal
variations in the intensity of work, for instance in the number of weeks worked per year,
or daily variations in the intensity of work, for instance in the number of hours worked
per day or in the number of days worked per week. For a given number of hours workedper year, individuals might have very different timing for these hours. Although we do not
focus in this paper on these variations, we provide evidence in appendix B of significant
cross-country differences.3
The data used in this paper are Labour Force surveys, which are the main source of
information for measuring characteristics of labour force participation. More specifically,
we use the Enquˆete Emploi (EE) for France, the Labour Force Survey (LFS) and Family
Expenditure Survey (FES) for the UK and the Current Population Survey (CPS) for the
US for the period from 1968 to 2008.4 There are a number of measurement issues but the
main attraction of these data is to provide long series of micro-datasets, which provide
detailed information, every year, about employment patterns and hours of work, as well
as precise demographics like gender, age, education attainment, marital status, number
of children etc. No cross-country database is currently available to make these detailed
disaggregations.
Questions are comparable across countries as they follow ILO recommendations. We
make a very large use of continuous surveys, i.e. surveys which span the entire year and
therefore capture seasonal variations in hours worked. Each quarter, we observe individuals
from a representative sample in a particular week. We know whether employed and how
many hours worked in that week. We average over the year to get the employment and
hours of a broad category. For earlier years we have to rely on annual surveys and we make
adjustments between the two series.
Before digging deeper into these movements in hours and employment, we should note
that whereas the measure of the employment rates across time and countries is considered
fairly robust, the measure of annual hours of work is on much less firmer ground, in
particular in earlier years. This is largely due to the fact that only annual surveys are
available for earlier years which are inadequate to capture seasonal changes in hours worked.

Elasticities at the Intensive and Extensive Margins
Our aim here is to provide an illustrative theoretical framework to analyze the decom-
position of hours responses at the intensive and extensive margins. To do this we consider
an economy made of heterogeneous workers choosing between whether to work and how
many hours to supply in work. In the application we use more flexible specifications and
allow explicitly for observable as well as unobserved heterogeneity.