The methodology of the paper provides a thorough discussion on factors influencing migration decision model to be estimated, followed by estimation technique, and finally, the data sources applied are discussed with some variable description.
The framework adopted is divided into three levels; see Fig. 3, i.e., how the economic, noneconomic, and demographic factors influence the flow of female migrant workers. Economic factors include macroeconomic and labor market indicators. The first macroeconomic factors is
$$ {\mathrm{emg}}_{ijt}= f\left({\mathrm{mac}}_{ijt}\right) $$
(1)
where emg_{
ijt
} shows the flow female workers from i origin (Bangladesh) to j destination countries in time t, while mac_{
ijt
} represents the macroeconomic conditions of origin and destination countries in time t. The macroeconomic conditions are reflected by real GDP per capita (PPP adjusted) and foreign direct investment. These factors are analyzed in the context of push (origin country characteristics) and the pull (destination country characteristics) factor theories of migration. Hence, if the effect of pull is negative, the effect of push could be positive.
For example, a decline in the GDP per capita of origin country indicates the deteriorating economic conditions leading to uncertainty in employment opportunities, hence pushes people to migrate while any improvement in the GDP per capita of destination will pull the workforce from origin country.
$$ {\mathrm{emg}}_{\mathrm{ijt}}=\mathrm{f}\left({\mathrm{mac}}_{\mathrm{ijt}},\ {\mathrm{lab}}_{\mathrm{ijt}}\right) $$
(2)
where lab_{
ijt
} represents the labor market conditions of origin i and destination j in time t. The indictors used here to explore the effect of labor market condition include employment to population ratio (used as proxy of unemployment), size of agriculture, manufacturing, and service sector. Though the effect of unemployment will be interesting to look at, but as most of the data on unemployment is missing across country or time, a proxy indicator, employment to population ratio is used to explore the effect of unemployment on migration decision. Negative impact of this proxy for origin means the higher the ratio the higher will be the employment opportunities available leading to lower migration rate. In contrast, for destination country, the higher ratio means that it may discourage or instead attract female migrant workers as employment opportunities increase in the destination country. Encouragement or discouragement will be based on the sector where employment is expanding skilled or unskilled. Further, industrialization creates demand for skilled workers, while females are mostly unskilled; hence, in both origin and destination countries, industrialization will result in decline in demand for unskilled females. These females then seek employment in the informal sector as unskilled workers. Females usually migrate as domestic helpers. Overall industrialization in origin pushes females to migrate while in destination country, industrialization discourages the demand for unskilled female migrants. However, in destination country, industrialization may increase the demand of skilled native female workers. These skilled female workers (native) of destination country then seek domestic workers for child care, generating demand for unskilled migrant workers, specifically females.
$$ {\mathrm{emg}}_{\mathrm{ij}\mathrm{t}}=\mathrm{f}\left({\mathrm{mac}}_{\mathrm{ij}\mathrm{t}},\ {\mathrm{lab}}_{\mathrm{ij}\mathrm{t}},\ {\mathrm{nmac}}_{\mathrm{ij}}\right) $$
(3)
where nmac_{
ijt
} represents the noneconomic factors influencing migration decision. These include distance between origin and the destination countries, measuring transportation cost, and religion. In Bangladesh, situation of female migrant workers is slightly different due to the Government policies and the social and cultural norms. Bangladeshi females usually seek work to Gulf and Middle East countries, such as Lebanon, Saudi Arabia, and UAE. The high demand of female Bangladeshi workers in these countries is due to common religious norms. Religion plays a major role for female workers in the scene that religion provides source of unity within the destination with respect to social norms. Further, the higher the distance the lower will be the migration rate as it increases the traveling cost which reduces the frequency of female visits to family.
$$ {\mathrm{emg}}_{\mathrm{ij}\mathrm{t}}=\mathrm{f}\left({\mathrm{mac}}_{\mathrm{ij}\mathrm{t}},\ {\mathrm{lab}}_{\mathrm{ij}\mathrm{t}},\ {\mathrm{nmac}}_{\mathrm{ij}},\ {\mathrm{dem}}_{\mathrm{ij}\mathrm{t}}\right) $$
(4)
where dem_{
ijt
} represents the demographic factors influencing migration decision. Demographic variable included in the study is fertility rate.
It is hypothesized that increase in population will create unemployment and burden the limited resources, hence foster migration from origin. While in the destination country, high fertility rate means that labor market may fail to absorb the flow of migrant workforce; hence, higher fertility rate will influence migration negatively. In sum, the impact of increase in population on migration decision will be positive for origin while negative for destination.
Finally, it can be started that decision regarding migration is highly influenced by the positive support of the family friends and relatives which also motivate females to take decision of migration. Past migrants, on the basis of their experience, facilitate how migrants share their experience, search job opportunities for others, and provide temporary shelter to them. In contrast, the bad experience of one female migrant may discourage others to take decision for migration. The high trafficking of female workers, harassment, and severe working conditions faced by females at the destination country may demotivate other females to migrate. Therefore, decision of migration mainly depends on the past experience of migrant workers especially in the case of females. Hence, in the model, lagdependent variable of female flow of migrant workers is included. The hypothesis behind is that movement of new migrants depends on the past migrant decision. The final model therefore includes these migrant flows as well
$$ {\mathrm{emg}}_{ij t}=\mathrm{f}\left({\mathrm{mac}}_{ij t},\ {\mathrm{lab}}_{ij t},\ {\mathrm{nmac}}_{ij},\ {\mathrm{dem}}_{ij t},\ {\mathrm{emg}}_{t  \kern0.5em 1 ijt}\right) $$
(5)
4.1 Gravity model of migration
The above model of migration estimated on the basis of Newton’s Gravitational Law (1687). According to which, two different forces between the two bodies are directly proportional to the size but inversely proportional to the square of the distance between them
$$ {M}_{i j}= g\times \frac{P_i\times {P}_j}{D{2}_{i j}} $$
(6)
The modified law is referred as gravity model of migration. In the model, M
_{
ij
} represents the migration flow from country i to j, while g in the model is the gravitational constant. P
_{1} and P
_{2} are the population in the two country and d is the distance. Migration between origin i to destination j remains directly related to the size of origin’s and the destination’s population which is inversely related to the square of the distance between the two. For our model, we used gravity model approach to find the determinants of female migration. The problem we faced in fully adopting the gravity model is nonavailability of the bilateral data on female migrant workforce. Keeping the limitation, the study has estimated the model by including macroeconomic, labor market, demographic, and gravity variables for the origin and destination countries altogether by simply focusing on the out migration from Bangladesh to the rest of the world.
The gravity model is hence modified to form a model of outflow of migrant workers from Bangladesh to the destination country by time.
$$ {\mathrm{emg}}_{ij t} = {\mathrm{B}}_{\mathrm{O}}++\mathrm{B}{1}_{ij t}{\displaystyle \sum_{U=1}^4}{\mathrm{macr}}_{ij t}+\mathrm{B}{2}_{ij t}{\displaystyle \sum_{V=1}^3}{\mathrm{lab}}_{ij t}+\mathrm{B}{3}_{ij t}{\displaystyle \sum_{W=1}^2}{\mathrm{dem}}_{ij t}+\mathrm{B}4{\mathrm{dist}}_{ij}+\mathrm{B}5{\mathrm{relg}}_{ij}+{\upepsilon}_{ij t} $$
(7)
For estimation purpose, the study has applied the system GMM technique. The choice of GMM is because of the hypothesis that migration decision of this year is based on decision taken in the past. However, for the robustness check, we have also estimated the fixed effects model [see results presented in Appendix 2 for robustness check], as well. Further in the equation, u, v, and w represent the number of macroeconomic, labor market, and demographic indicators, respectively, included in the model.
4.2 Estimation technique
Many economic issues are dynamic in the nature. These dynamic relationships are characterized by the presence of a lagdependent variable among the regressors; because of the lagged variable, OLS is biased and inconsistent even if v
_{
it
} are not serially correlated. Since y
_{
it
} is a function of u
_{
i
}, so is y
_{
it − 1}. Anderson and Hsiao (1981) suggested the first differencing in the model to get rid of the u
_{
i
} and then using an IV method. However, this proposed method leads to consistent but not necessarily efficient estimates, because:

1.
It does not make use of all available moment conditions.

2.
It does not take into account the differenced structure on the residual disturbances ∆v
_{
it
}.
Arellano and Bond (1991) then proposed a more efficient estimation procedure. They argue that additional instruments can be obtained if one utilizes the orthogonality conditions which exist between the lagged values of y
_{
it
} and v
_{
it
}. It takes first difference to get rid of the individual effects and uses the past information of y
_{
it
} as instruments.
To illustrate, we have used the following model:
$$ {y}_{i t} = \delta {y}_{i, t1} + {u}_{i t} $$
where u
_{
it
} = μ
_{
it
} + v
_{
it
} with \( {\mu}_{it} \sim i i d\ \left(0\ {\sigma}_{\mu}^2\right) \) and \( {v}_{it} \sim i i d\ \left(0\ {\sigma}_v^2\right) \).
First, we took the difference to eliminate the individual effects:
$$ {y}_{i t}  {y}_{i, t1} = \delta \left({y}_{i, t1}{y}_{i, t2}\right) + {v}_{i t}{v}_{i, t1} $$
The first period where we can use an instrumental variable is t = 3, where we have
$$ {y}_{i3}  {y}_{i2} = \delta \left({y}_{i2}{y}_{i1}\right)+\left({v}_{i3}{v}_{i2}\right) $$
Here, y
_{
i1} is not correlated with the error and is therefore a valid instrument since it is correlated with (y
_{
i2} − y
_{
i1}) and not with (v
_{
i3} − v
_{
i2}). One period forward, we have
$$ {y}_{i4}  {y}_{i3} = \delta \left({y}_{i3}{y}_{i2}\right)+\left({v}_{i4}{v}_{i3}\right) $$
where y
_{
i1} and y
_{
i2} are valid instruments. Therefore, in period T, the set of valid instruments is (y
_{
i1} … (y
_{1T − 2})). But we still need to account for the differenced error term (v
_{
it
} − v
_{
i,t − 1}). See Appendix 1 for more details
4.3 Data collection procedure
For estimation purpose, the data of female migrant workforce is taken from Bangladesh Bureau of Manpower and Training (BMET). Demographic and other variables are collected from the secondary sources, such as the World Development Indicators (WDI), United Nation (UN), and CEPII (Research and Expertise on the World Economy). Time frame of the study consists of 13 years, from 2000 to 2012. The data is collected for 19 destination countries.