Page 26 - IJPS-7-2

International Journal of
Population Studies Gender gap in life expectancy in South and East Europe

(http://data.worldbank.org/indicator). Furthermore, data Where, fX is the function of k-vector of
it,,
about the Gini index have been obtained from the Our regressors and its coefficients for cross-section i, at period
World in Data platform whose data are based on the World t; and Y is the dependent variable for cross-section i at
it
Bank Poverty and Inequality Platform. Finally, data about period t. The fundamentals of GMM estimation include a
the health expenditure as percentage of GDP have been clear identification of the instruments Z and a selection of
retrieved from World Health Organisation databases and the weighting matrix H and determining an estimator for
additionally from other WHO data link. coefficient covariance Ʌ (Baltagi, 2005; Wooldridge, 2002).
Conceptually, these nine indicators should be The linear dynamic panel data specification can be
differentiated into at least three groups. In reality, they considered as given by Eq. (3):
were classified into four groups: GDP per capita and p
it
the percentage of the urban population are preferably Y jitj X i t  it (3)
’

Y

it
categorized under economic development and as j1
indicators related to social development are included
secondary education (% females) and health expenditure Where, Y is the dependent variable for cross-section
it
as percentage share of GDP). Two of our explanatory i at time t; Y is the dependent variable at lag j for cross-
ij−j
variables – difference in employment rate in total section i and time t; p is the total number of instruments;
population 15+ and the difference in unemployment rate ρ is the average of the j-th order auto-covariance; X is
j
it
by sex as percentage of total labor force – are related to the k-vector of regressors for cross-section i at time t; β
the issue of employment. These two employment variables represents the coefficients that vary across cross-sections
have been defined as a simple difference between sexes and periods; δ and γ represent cross-section and period-
t
i
of employment rate in total population 15+ and as a specific effects (fixed or random), respectively, and ∈ is
it
difference between sexes in unemployment rate, separately the error term for cross-section i at panel period t. First,
for each of the countries and for each year. In addition, as differencing of the specification in Eq. (3) removes the
economic-related indicators within this study are included individual effect and generates an expression of the form
GDP growth rate and Gini index as a proxy measure of shown in Eq. (4), where denotes the difference operator:
income inequality. Mortality gender gap as the dependent p ’
it
Y
variable was calculated by the author as a difference Y jitj X  , (4)
it

it
of the LEAB between females and males (i.e., females’ j1
LEAB – males’ LEAB) from the UN database, from 1991 to which can be estimated using GMM techniques
2020, separately for each of the countries and for each year. (Wooldridge, 2002). An efficient GMM estimation of this
type of equation should commonly use a different number
2.2. Methods of instruments for each period, with the period-specific
This research uses the GMM/DPD, an estimation technique instruments corresponding to the different number of
commonly used in econometrics (Arellano & Bond, 1991; lagged dependent and pre-specified variables accessible
Baltagi, 2005; Wooldridge, 2001a), to analyze related in a given period. Therefore, despite all strictly exogenous
factors associated with the gender gap in LEAB. GMM variables, one should use period-specific instrument sets
panel estimators are based on moments of the general form that correspond to the lagged values of the dependent
in Eqs. 1 and 2: and other predetermined variables. Given estimates of
the residuals from the one-step Arellano-Bond estimator,
M M
g g () Z () (1) where it is assumed that ∈ are not autocorrelated, the
’
it
ii
i
d
i1 i1 optimal GMM H weighting matrix for the differenced
specification may be given as in Eq. (5):
Where, Z is a T × p matrix of instruments (i.e.,
i
i
exogenous explanatory variables) for cross-section country M 1
d
’
i (i=1, 2,….,M); g is T × k derivative matrix of β coefficients H M 1 ZZ i (5)
i
i
i
estimator; T refers to the total number of time periods; k i1
M
refers to the number of regressors; represents total Where, is the matrix and Z contains a mix of strictly
i
i1 exogenous and predetermined instruments (Wooldridge,
sample moments; and ∈ (β) represents a vector of errors of 2002). It is noteworthy to observe that this weighting
i
coefficients for cross-section i, and matrix is the one employed in the one-step Arellano-Bond
f X
 ( Y i t ), (2) estimator. The weighting matrix is a major component for
it
,,
i
an efficient GMM analysis. The weighting matrix can be
Volume 7 Issue 2 (2021) 20 https://doi.org/10.36922/ijps.v7i2.389