Hours Constraints and Unobserved Heterogeneity in Structural Discrete Choice Models of Labour Supply Alan Duncan CPE, University of Nottingham and IFS http://www.nottingham.ac.uk/~lezad http://www.nottingham.ac.uk/~lezad Mark Harris University of Monash and CEU
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Hours Constraints and Unobserved Heterogeneity in Structural Discrete Choice Models of Labour Supply Alan Duncan lezad CPE,
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Hours Constraints and Unobserved Heterogeneity in Structural Discrete Choice
Much of the recent literature on modelling household labour supply applies discrete choice econometric modelling methods
Why? Because discrete choice methods … allow for a series of improvements on traditional continuous
methods of estimation (Hausman,1985)
offer the potential to model household decisions cope relatively well with non-linear taxes in estimation translate easily to ex ante evaluation of policy reform
IntroductionIntroduction
What is the typical model of household labour supply?
Economic foundations direct estimation of well-defined preference function preferences expressed over discrete hours choices can model preferences at the level of the household
(Van Soest, JHR 1995) can accommodate fixed & search costs of work
(Blundell, Duncan, McRae & Meghir, FS 2000) can model welfare programme participation
(Moffitt & Keane, IER 1999)
IntroductionIntroduction
What is the typical model of household labour supply?
Econometric specification issues stochastic errors added to each discrete hours choice errors are typically extreme value, leading to a classic
conditional logit specification potential problem: IIA some models additionally allow for random preference
heterogeneity random heterogeneity is usually MVN, leading to a
mixed logit specification (Duncan and Harris, ER 2002)
Motivation for paperMotivation for paper
PROBLEMS:
1) the typical model remains relatively unchallenged in terms of its underlying stochastic structure
choice-specific errors are not strictly necessary extreme value assumption is potentially significant distributions for random heterogeneity terms are
not always obvious or intuitive
Motivation for paperMotivation for paper
PROBLEMS:
2) observed hours choices are generally equated to preferred hours choices – not always so.
people cannot always locate to their preferred hours choice (institutional constraints).
the range of hours alternatives from which people choose may depend on specific job characteristics
for some job types, the unconstrained choice of hours may simply not be available, or at least may be relatively unlikely
Motivation for paperMotivation for paper
IMPLICATIONS:
1) estimated models of household labour supply are not typically able to replicate the distribution of observed hours choices
one often sees peaks or clusters in observed hours distributions (0, 20, 38-40)
most household labour supply models are smooth functions, with a continuous stochastic structure.
they are therefore unable to replicate accurately such bunching in hours choices.
Motivation for paperMotivation for paper
IMPLICATIONS:
2) preference parameters may therefore be biased when institutional constraints are ignored
with optimising errors, one cannot assume that someone who is observed to work, say, 20 hours, would prefer 20 hours to any other choice;
they may have ideally liked to work, say, 27 hours, but labour market institutions prevent this
if ignored, estimated preference parameters in fact become a convolution of unconstrained tastes & labour market characteristics
Motivation for paperMotivation for paper
BACKGROUND:
institutional constraints have been addressed in continuous studies of labour supply
Arrufat and Zabalza (E’trica 1986) observed an absence of bunching of hours at kink points in the tax system, despite theory requiring that such bunching should be observed in observed choices
Motivation for paperMotivation for paper
BACKGROUND:
institutional constraints have been addressed in continuous studies of labour supply
Their explanation: institutional constraints in the labour market prevented workers from adjusting their hours choices to suit important parameters of the tax system
Motivation for paperMotivation for paper
BACKGROUND:
institutional constraints have been addressed in continuous studies of labour supply
Their solution: include optimising errors alongside random preference heterogeneity in a labour supply model, to ‘smooth’ observed outcomes around tax kinks.
optimising errors were separately identified by exploiting the non-linearities in the tax system
Motivation for paperMotivation for paper
BACKGROUND:
some unusual suggestions in discrete studies of labour supply
Van Soest, Das and Gong, 1999: define a discrete (Heckman-Singer) distribution for preference heterogeneity
The number of support points assessed empirically leads to them categorising a finite set of ‘taste types’
conditional on observed characteristics bunching is therefore caused by types of people rather than
labour market institutions
Motivation for paperMotivation for paper
OUR APPROACH:
confront the presence of institutional constraints in discrete labour supply models directly
(1) model directly the degree of captivity to each observed hours alternative (DOGIT)
(2) attempt to control for optimising error in the conditional logit model by integrating the error over its (finite) empirical distribution (cf.Arrufat&Zabalza)
CLOE (Conditional Logit with Optimising Error)
an economic model of labour supply an economic model of labour supply
the basic model: preferences over hours h (or ‘leisure’ T-h) and net
income yh: U=U(h, yh | X)
budget constraint:
yh=w.h+I-T(wh,I; Zt)+B(w,h,I; Zb)
missing wages:
log(w)=Xwbw+ uw , uw has density f(uw)
discrete labour supply estimation discrete labour supply estimation a structural discrete model of labour supply: Assume that hours h(.) chosen from a set of J discrete alternatives:
h(.) = h1 if h <= h1
B
h(.) = h2 if h1
B <= h < h2B
……….
h(.) = hJ-1 if hJ-1
B <= h < hJB
h(.) = hJ if h > hJ
B
Household net incomes are calculated for each h(.) ={h1, h2,…, hK } as yh =w.h(.)+I-T(wh(.),I; Zt) + B(w,h(.),I; Zb)
a discrete choice seta discrete choice set
yh
h
yh
h
a discrete choice seta discrete choice set
yh
h
h(.)*=maxh(.) U= U( h(.) , yh | X )
a discrete choice seta discrete choice set
discrete labour supply estimationdiscrete labour supply estimation
a structural discrete model of labour supply: Define preferences over h(.)={h1, h2,…, hJ }:
Choice of h(.) {h1, h2,…, hJ } solves
maxh(.) U= U( h(.) , yh | X )
s.t. yh =w.h(.)+I-T(wh(.) ,I) + B(w,h(.) ,I)
Avoids the complexities of nonlinear functions T(.) & B(.) Problem? Introduces rounding errors through h =h(.). Needs testing…
functional form choice for U(.): We follow a number of authors in choosing a quadratic
direct utility:
Blundell, Duncan, McCrae and Meghir (2000)Duncan and Harris (2002)Keane and Moffitt (1998)
2 2( , )h yy h hh yh h y h hU h y y h y h y h
specifying preferencesspecifying preferences
unobserved preference heterogeneity Observed and unobserved heterogeneity enters through
preference terms. eg,
Unobserved heterogeneity in preferences is typically assumed multivariate normal.
small increase in marginal utility of income under CLOE
differences not significant
Predicted hours distribution under DOGIT and CLOE match observed frequencies very closely
unsurprising
Issues is there a formal
equivalence between CLOE and DOGIT under certain restrictions?
not clear yet, but if so, this offers the first grounding of DOGIT in economic theory
SummarySummary
Concerned with ‘received wisdom’ in modelling household labour supply using discrete methods Stochastic structure often unchallenged Failure to recognise some pertinent labour
market issues in estimation Possibility that preference estimates and
simulated policy responses are inaccurate
SummarySummary
Paper attempts to confront directly the effect of institutional constraints on household decisions DOGIT model deals with constraints by setting
up a parametric form of labour market ‘inertia’ CLOE attempts to integrate out the (discrete)
optimising error, using tax/welfare variation Both models suggest preference estimates do
adjust, with stronger ‘unconditional’ wage & income responses.
SummarySummary
Work is still early… How do DOGIT and CLOE methods relate one
to another? How do both methods respond to admitting
correlation between adjacent state-specific errors (OGEV, DOGEV)
And to other discrete choice methods (eg. using so-called Alternative-Specific Constants, ASCs, as in nested logit)