Alessie, R.J.M.

Melenberg, B.

Weber, G.

English

Research Papers in Economics

~h~ J~G ~05
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o~~~ooo~~~~~~~ Q ~ ~~ IIIIIIIIIIIIIIIIIIIIIllliIIIIIIIIIIIIIIIIIII~IICONSUI~TION, LEISURE AND EARNINGS-
RELATED LIQUIDITY CONSTRAINTS: A NOTE
Rob Alessie
Bertrand Melenberg
Guglielmo Weber
~W 295 3ào. ~ ~ ~Consumption, Leisure and Earnings-Related Liquidity Constraints:
A Note.
Rob Alessie and Bertrand Melenberg
Tilburg University.
Guglielmo Weber
University College London
November 198~
The r.esult~ in this note were independentl.~~ deri-,ed by G. Web~r and ~~y
R.Alessie and B. Melenberg. R. Alessie and B. Melenberg wish to thank A.
Kapteyn and Th. Nijman for valuable comments and R. Alessie gratefully
acknowledges the Netherlands Organization for the Advancement of Pure
Research and the NMB Bank in the Netherlands for financisl support. G.
Weber is grateful for helpful discussions with M. Browning and F.
Schiantarelli.-2-
Abstract
The life-cycle model with liquidity constraints produces an Euler
equation with unobservable Kuhn-Tticker multipliers. If borrowing
restrictions depend on earnings, preferences are non-separable between
goods and leisure, and individuals are employed, we derive an Euler
equation involving only observable variables.-3-
1. Introduction
Recent studies of intertemporal behaviour in a risky environment have
adopted the Euler equation approach introduced by Hall (1978). Assuming
perfect capital markets, strongly separable preferences between goods and
leisure and rational expectations, Hall showed that the marginal utillty
oF consumption is a random walk.
However, several empirical papers have rejected the restrictions
implied by Hall's version of the Life-cycle Model (Flavin, 1981, Hall and
Mischkin, 1982. Hayashi, 1985 and Weber, 198~). Liquidity constraints and
preference interactions between goods and leisure have alternatively been
put forward as likely explanations of this failure.
As Muellbauer (1983), Zeldes (1985) and others point out, the Euler
equation for consumption with borrowing restrictions contains an
additional (unobservable) explanatory variable, the Kuhn-Tucker multiplier
associated with the net wealth condition. In this note, we argue that a
simple analytical framework for incorporating both earnings-dependent
liquidity constraints and non-separable preferences is readily available,
and we show that under weak conditions it produces an Euler equation
involving only observable variables.
This note is organized as follows: in section 2 we establish our
notation, and derive the standard Euler equation. Section 3 presents our
proposed extension, and discusses its empirical implications. Section 4
draws some conclusions.-4-
2. The Life-cycle model with Liguidity Constraints
We assume that goods snd leisure are choice variables, and that
capital markets are imperfect. Consequently, consumers solve the
following optimization problem:
L
max Et E (1tP)t-TU~(cT~~j)
T-t
s.t.
where
(1)
Ai -(1'ri-1)Ai-1 ~ mT ~ W,~(T-,C,~) - pTCT T s t,...,L (2)
AT 2 M,~ (3)
~,~ ~ T T - t,...,L (4)
At-1 given, AL - 0,
ut(.,.) :- Intratemporal utility functionl),
p,rT-1 .- Time preference and interest rates, respectively,
cT,~Ct .- Goods and leisure in period t, respectively,
A,~ .- Non human wealth at the end of period T,
mT .- Non labour income in period i,
p,~,wT .- Goods price and wage rate in period i,
L,T .- Length of life and time endownment.
The first order conditions for period t are:-5-
~ut(ct.~t)
- ~ (5) ~ct tpt
~ut(ct.~t)
~t - ~twt } yt
~t - Kt - Et(l~rt)~(1tP)attl
Kt(At-Mt) - 0; vt(T-~t) - 0
ut 2 0; vt 2 0
(6)
(7)
(8)
(9)
The variables
~t, ~ttl
denote the Lagrange multipliers
associated to (2), whereas Kt and vt are the Kuhn-Tucker multipliers
corresponding to the borrowing and the time constraints, ( 3) and (4),
respectively.
By using ( 5) we can rewrite the Euler equation (~) as
(ltrt) 1 ~ut}1(ct~l,~t}1) 1 ~utíct.~t)
(1tP ) ~Pt,~l
. ~ct~l - Pt ~ct - l~t ~ Et.l
where the error has zero conditional mean.
(10)
For estimation purposes, equation (10) is unsatisfactory in that it
contains the unobservable, endogenous variable ut . Only in special cases
a closed form solution can be found; moreover, in general. no information
can be gleaned from equation (10) as to whether liquidity constraints are
operating, i.e. whether ut is positive or zero.
The only case where equation (10) can be used to assess the
impcrtance of liquidity constraints is where prior information is
available: if we know that for some observations ut is zero, then we can
estimate (10) on this subsample and thus compute predicted ut for the
remaining observations. We can then check whether xt has a positive mean
for the liquidity constrained as the model predicts (Zeldes, 1985). The
trouble with the method is its absolute reliance on usually unavailable
sample separation information.-6-
3. An alternative epproach: earnings-related liquidity constraints
Let us now assume en earnings-related liquidity constraint
(as in Muellbauer, 1983):
At 2 ~0 . ~1wT(T-~T). T s 1....,L (3~)
where ~0 and ~1 are parameters. We expect the borrowing limit to
be inversely related to current earnings, i.e. ~1(0.
In this setting the first order condition (6) becomes
~utíct.~t)
~ - ~twt - ~1Ntwt . yt,
and we can use (5) and (6') to obtain an expression for
ut.
~u (c ~ ) ~u (c ~ ) 1 1 t t' t 1 t t' t 1 At -~1 Pt ~ct - wt ~. wt yt ,
Finally, we substitute equation (11) into (10) and get:, we get
(l~r ) ~u (c ~ ) ~u (c ,~ ) t 1 t~l t.l' t~l 1 1 L t t
(1~ P) Pttl ~ct~l - 1- ~11Pt ~ct
.
1 1~~ut(ct'~t) -v ~~ E , with E e - 0.
,~1 wt ~t - t t~l t t~l
(6')
(12)
We have thus obtained an Euler equation where ut does not appear.
In its place, we now have the Kuhn-Tucker multiplier on leisure, vt, which
is going to be positive when a corner solution obtains ín the labour
market. Once again, a closed form solution for this endogenous variable is
unlikely to exist; however, contrary to the case of capital markets, in
the case of the labour market sample separation information is readily
available.
If panel data on individual households are available, we can estimate
the parameters of equation (12) by the Ceneralized Method of Moments
(Hansen and Singleton, 1982) by restricting the sample to the employed in-7-
period t: no selection bias will arise, because the error term is
orthogonal to the selection rule (as vt belongs to the relevent
informatlon set ). We can then formally test for the absence of liquidity
constraints (i.e. by setting 1~Y'1-0 in equation (12)) by standard
statistical methods.
Some further remarks on equation (12) are in order:
1) equation (12) holds whether a consumer is liquidity
constrained or not and whether he is rationed in his labour
supply choice in period t;l or not;
2) equation (12) can only be derived if Y'1 differs from zero. The
limit case where `Y1 equels zero is discussed in section 2:
in this case standard rules for within period allocation of full
expenditure into goods and leisure are unaffected by the
presence of a binding constraint in the capital market (Blundell
and Walker, 1986);
3) consistent estimates of the parameters in equation (12) can be
obtained by truncating the sample to include only the workers.
Such estimates can then be used to compute vt for non
workers, which should be positive (this prediction provides a
simple specification check);
4) we can use equations (10) or (I1) and the parameter estimates
from (12) to compute y,t for each individual household.
The relationship between the formal test for (1~Y'1)-0 and the
informal computation of y.t is worth exploring. Inspection of equation (12)
and consideration of the underlying model suggest that rejection of the
null in the formal test does not imply that the estimated u's should be
zero: it is in fact possible for consumers not to be bound by the
liquidity constraint in period t even though the earnings-related
constraint exists in a non trivial form (i.e. Y'1 )-m).
4. Conclusions
In this paper we started from the well known result that the life-
cycle model with liquidity constraints produces an Euler equation with
unobservable Kuhn-~cker multipliers. We then showed that if borrowing
restrictions depend on earnings and leisure is a choice variable, the-8-
Euler equation involves only observable variables as long as we only
select those consumers who are employed in period t.-9-
Notes
1) We assume ct and .~t to be strictly positive.for example, by imposing
enough regularity conditions on uT(.,.).
References
Blundell, R.W., Walker, I., 1986, A Life-Cycle Consistent Empirical Model
of Family Labour Supply using cross-section data, Review of Economic
Studies , LIII, 539-558.
Flavin, M.A., 1981, The adjustment of eonsumption to changing expectations
about future income, Journal of Politcal Economy , 89, 974-1009.
Hall, R.E., 1978, Stochastic implications of the life cycle-permanent
income hypothesis: theory and evidence, Journal of Political Economy
, 86, 971-987.
Hall, R.E. and Mishkin, F.S., 1982, The sensitivity of consumption to
transitory income: estimation from panel data of households,
Econometrica , 50, 461-482.
Hansen, L.P. and Singleton, K.J., 1982, Generalized instrumental variables
estimation of nonlinear rational expectations models, Econometrica ,
50, 1269-1286.
Hayashi, F., 1985, The effects of liquidity constraints on consumption: a
cross-sectional analysis, Quarterly Journal of Economics, IC, 225-252
Muellbauer, J., 1983, Surprises in the consumption function, Economic
Journal, supplement, 34-49.
Weber, G., 1987, The Euler equation for aggregate consumption when capital
and labour markets are imperfect: time series evidence for the U.K.,
University College London DP 87-32.
Zeldes, S., 1985, Consumption and liquidity constraints: an empirical
investigation, Wharton Schooi WP 24-85, University of Pennsylvania.i
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Consumption, leisure and earnings-related liquidity constraints: A note

Consumption, leisure and earnings-related liquidity constraints: A note

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