Frijters, Haisken-DeNew, and Shields 655
Figure 1 Average Life Satisfaction for East and West Germans
relatively high level of life satisfaction reported by East Germans 6.56, reflecting the general “elation” felt by the population Bach and Trabold 2000. However,
this initial “elation” appears to have quickly dissipated, with average life satisfac- tion falling by around 0.60 by 1991. Thirdly, in the years between 1991 and 1999
East Germans experienced a steady increase in their life satisfaction. Fourthly, in comparison to East Germans, life satisfaction in West Germany remained fairly
constant between 1984 and 1999. If anything, there was a very gradual decline in life satisfaction in the West between 1984 and 1999; however, there was a slight
peak in 1991 off-setting this trend. Finally, nearly a decade after reunification size- able life satisfaction differentials still existed between East and West Germans
around 0.60.
IV. Econometric Framework and Decomposition Approach
A. Random Effects
Our indicator of perceived well-being: GS ∈ {0 . . . 10} is an ordinal indicator of
life satisfaction. This measure is available for a set of individuals indexed by i = 1 . . . n each observed over some contiguous subset S
i
of years indexed by t = 1 . . . T. For each year in which GS
it
is observed, we also observe a row vector x
it
containing
a set of covariates describing the characteristics and situation of individual i in year t.
We begin by fitting the following ordered probit model with individual random effects:
1 [
, GS
x GS
k GS
ν ε
λ λ
, ,
, ,
i t i t
t i
it i t
i t k
k 1
+ =
+ +
+ =
β δ
+
where
it
GS is latent general satisfaction; GS
it
is observed satisfaction; λ
k
is the cutoff point increasing in k for the satisfaction answers; x
it
are observable individual char- acteristics;
δ
t
denotes unobserved time-varying general circumstances; ν
i
is an indi- vidual normally distributed random characteristic that is orthogonal to x with
unknown variance; and ε
it
a time-varying normally distributed error-term that is orthogonal to all characteristics with a variance equal to 1.
Heterogeneity is handled by using Gauss-Hermite quadrature 20 points were cho- sen to integrate the effect out of the joint density. Frechette 2001 provides a deri-
vation of the likelihood function for this model, based on Butler and Moffitt 1982, and discusses estimation.
B. Fixed Effects
The recent psychology literature has found that fixed personality traits are important predictors of general satisfaction see, for example, Argyle 1999 and Diener and
Lucas 1999. This is particularly problematic for the random-effects estimates because these traits are related to many of the variables contained in x
it
, which means the random-effects results cannot generally serve as an indicator of causality.
Therefore, as our main model of causality, we fit the following fixed-effect ordered logit model developed in Ferrer and Frijters 2003:
2
it
GS x
f ε
, i t
t i
it
= +
+ +
β δ
it
[ ,
GS k
GS λ
λ
it k
k 1
+ =
+
where
it
GS is latent general satisfaction; GS
it
is observed satisfaction; λ
k
is the cutoff point increasing in k for the satisfaction answers; x
it
is observable time-varying characteristics;
δ
t
denotes unobserved time-varying general circumstances; f
t
is an individual fixed characteristic; and
ε
it
is a time-varying logit-distributed error-term that is orthogonal to all characteristics. Our conditional estimator for
δ
t
and β maxi-
mizes the following conditional likelihood: 3
,. . ,
冱
L I GS k
I GS k
I GS k
c
i i
iT i
t it
i 1
= R
T S
SS V
X W
WW
冱 冱
冱
e e
, GS
S ki c t
T I GSit
ki xit t
T I GSit
ki xit 1
1
=
= =
β β
The Journal of Human Resources 656
which is the likelihood of observing which of the T satisfactions of the same individual are above k
i
, given that there are c out of the T satisfactions that are above k
i
. Here, Sk
i
, c
denotes the set of all possible combinations of {GS
i 1
, . . , GS
iT
} such that ∑
t
I GS
it
k
i
= c. Also, GS
it
is used to denote the random variable and GS
it
the realization. As we see, the fixed effects have dropped out of this likelihood. It therefore yields
estimates only for δ
t
and β. This model is an extension of the fixed-effect logit model
by Chamberlain 1980. Unlike the Chamberlain methodology that recodes the data such that only crossing over a barrier that is the same for everyone say, k can be
used, our model uses crossings over person specific barriers say, k
i
. When some indi- viduals for instance only report values between 3 and 5, and others only between 6
and 8, then using the same barrier for everyone cannot record changes for both groups of individuals. Those individuals then have to be dropped from the estimation proce-
dure. With individual specific barriers all individuals whose satisfactions differ over time, can be included. The most important advantage is therefore that it allows us to
use more than 90 percent of the observations. In comparison, the loss of data in appli- cations with the Chamberlain method is usually over 50 percent see, for example,
Winkelman and Winkelman 1998; Hamermesh 2001; Clark, Georgellis, and Warr 2001; Clark 2003. Furthermore, the log-likelihood is greatly increased by choosing
k
i
optimally see Ferrer and Frijters 2003. The model is estimated by Maximum Likelihood in GAUSS.
One important methodological point concerns the use of this fixed-effect estimator. One cannot simultaneously include age, time, and fixed effects in the analyses. To see
this note that age
it
β
age
= age
i
β
age
+ t β
age
. Now, the effect of age
i
β
age
is time- invariant and will therefore be in the individual fixed effect, and t
β
age
will be the same for everyone at t and hence picked up by time dummies. We therefore drop lin-
ear age as a covariate and note that the time dummies will include age effects.
C. Specification Testing: Random or Fixed Effects
