Inequality and migration in Kenya: Investigating the subnational associations using census data

Data

Migration data was extracted from the 2009 Kenya Population and Housing Census micro data of the Kenya National Bureau of Statistics (KNBS) following a formal data request. The 2009 Population and Housing Census was conducted in August 2009, with the reference night being August 24/25. Data was collected for a period of one week, on all persons residing in Kenya on the census reference night (see Republic of Kenya, 2012). The unit of enumeration was the household unit and information were collected on type of household, access to social amenities, and demographic information on the household members including education, age, sex and occupation. Migration information was captured using the following variables: place of birth (P18), place of previous residence (P19), duration of residence (P20) and place of enumeration (P21) (Republic of Kenya, 2012:4). As information was collected on the persons who migrated at two points in time, at birth and at time of enumeration, there may be undercounts of migration transitions, as repeat movements and mortality of migrants are not captured.

For our study, we use two of the migration variables, namely place of birth (P18) and place of enumeration (P21) to generate information on lifetime migrants. Lifetime migrants were identified as persons whose place of birth was different from the place of enumeration at the time of the census. We derived the lifetime migration data from cross tabulating the place of birth by place of enumeration. The end result was a set of contingency flow for all the 47 counties showing in-migration and out-migration flows.

The next step in our analysis was generation of the migration intensity measure. Our dependent variable was migration intensity, a measure that captures both migration rates and impacts (Van Imhoff and Keilman, 1991; Rees et al., 2000; Bell et al., 2002; Liu, et al., 2011; Shi et al., 2020).

For each county, we generated net migration rates using the following formula

The Revised weighted migration rates, RNMi was calculated using the formula

RNMi considers the proportion of migrants in the total population of a given area, therefore considering the undercounts or overcounts that would occur due to huge differences in total population. When in-migrants are larger than out-migrants, the RNMi gives a positive result while negative results imply that more migrants are leaving the area. Thus, the RNMi gives a useful indicator of the intensity of migration and the impact that has had on population redistribution in a given county. Thus, the Revised Weighted Net Migration Rate, gives us the proportional distribution of migrants in a given county as a weighted count of all in-migrants in the country.

Inequality was captured using four key indicators, namely the County Human Development Index (HDI), the County Gini, the proportional access to water and proportional access to electricity within the counties. The four indicators were readily available in different reports based on the 2009 Kenya Population and Housing Census data. The County Gini variable was extracted from the Kenya Inequality Study⁴ jointly conducted by the Kenya National Bureau of Statistics and Society for International Development using a hybrid dataset that combines household data from the 2009 Kenya Population and Housing Census with livelihood data from the 2005 Kenya Integrated Household Budget Survey data to estimate monetary and non-monetary measures of inequality in Kenya (KNBS and Society for International Development, 2013).

The County Gini was derived using the small area estimation technique that followed three key steps. First, data for 1999 Kenya Population and Housing Census was matched to the 2009 Kenya Population and Housing census through a process of matching the clusters of the enumeration areas in these censuses. The use of 1999 census data was necessitated so as to trace the Kenya Integrated Household Budget Survey household clusters, as these were based on the sampling frame used in the earlier census of 1999. The variables that are similar in the 2005/6 KIHBS and 2009 census were identified. Second, a regression model was applied to identify household characteristics and the comparable consumption patterns from the KIHBS survey data. The resultant regression equation was then used to estimate the daily consumption and expenditure patterns using the 2009 variables including household size and other characteristics (KNBS and SID, 2013:3). Finally, through a simulation process, household expenditures for the 2009 census households were inputted using the socio-economic variables estimated using the survey data. Thereafter, the Gini coefficient was computed using consumption expenditure values obtained from the small area techniques. The value of Gini ranges from 0 to 1, with 0 implying there is perfect equality in incomes while 1, implies there is perfect inequality in incomes. A summary table capturing the county level Gini Coefficients can be found in the report (see KNBS and SID, 2013:43).

Two non-income measures of inequality were used in the analysis, namely access to safe water sources, and use of electricity for lighting. Data on access to water and access to electricity was accessed from the Socio-Economic Atlas of Kenya report, which is based on deeper analysis of data from the 2009 Kenya Population and Housing Census data, and provides subnational analysis of county and sub-location level data (Wiesmann et al., 2014). Access to safe water sources was obtained from the 2009 census questionnaire, in which all households named their source of domestic water. The indicator of access to water captures the number of households with access to one or more water sources which may include piped, borehole, protected wells, protected springs or rainwater. The information is summarized by county giving the number and percentage of households with access to safe water (Wiesmann et al., 2014:64). In measuring the access to electricity, the study used data on the proportion of households using electricity as source of lighting. The data was extracted from the Socio-Economic Atlas of Kenya report (Wiesmann et al., 2014:78). We used this variable as a measure of the living standards of the household, as electricity distribution in the country is unequal. The variable captures the proportions of households in a given county who indicated that they use electricity as their main source of lighting.

The fourth variable, the County Human Development Index, County HDI was obtained directly from the 2009 Kenya National Human Development Report (UNDP Kenya, 2010). The report assesses the overall changes in the longer term, based on a composite measure of education and literacy rates, healthy living and access to social amenities, the gross domestic product and estimates of earned income by gender. From this report, we obtained estimates of the county HDI which were indicated by Province and district (see Annex 1.1, UNDP Kenya, 2010:77). To generate the values for the present-day counties, a matching process of district to county was employed and average measures used in situations where several districts made up one county, for example, in Nyanza Province, Bondo district and Siaya district are now part of one county, named Siaya County.

Analytical methods

To determine the interrelationship between migration and inequality, the two key analytical techniques were employed, namely correlation and regression analysis using spatial analysis techniques using ArcGIS. While the normal correlation analysis could help to determine if a relationship exists between migration and inequality, and the strength of the relationship, spatial analysis helps to unveil the patterns of flows and their divergence and connectedness. Spatial analysis derives from Tobler’s First Law ‘Everything is related to everything else, but near things are more related than distant things’ (Tobler 1970: 234). It is a measure of relationship between contiguous spatial units and measures spatial dependence or spatial heterogeneity (Anselin, 1990).

The bivariate correlation analysis was conducted using SPSS 22 software. The outcome of the bivariate correlation analysis is the Pearson product-moment correlation, Pearson r (Pearson, 1909). Bivariate correlation assumes that variables are normally distributed but has been found to perform well when normalcy is violated or when one of the variables is discrete. The values of Pearson r range from −1 to 1, where −1 indicates there is perfect negative correlation between variables, 0 indicates there is no correlation between variables, while +1 indicates there is a perfect positive correlation between the variables, such that a rise in one variable leads to a rise in the other. The output of correlation analysis includes the Pearson r value and the significance of the correlation (2 tailed). An asterisk denotes that the correlation is significant at the 0.05 level, while double asterisk shows correlation is significant at 0.01 level.

The spatial analysis was done using ArcGIS 10.5 software to derive two measures of autocorrelation, the Global Moran I, and the local Moran also known as the local indicator of spatial autocorrelation (LISA) which conducts cluster and hot spot analysis (Anselin, 1995). The Global Moran I determine whether there may be unique patterns, such as incidences of clustering. The Global Moran’s I, tests for spatial randomness, thus testing the null hypothesis that the spatial autocorrelation of a variable is zero. If the null hypothesis is rejected, the variable is said to be spatially autocorrelated (Ord and Getis, 1995). The output of the analysis returns five values: the Moran’s Index, Expected Index, Variance, z-score, and p value. The value of Moran’s I range from -1 to 1, with -1, where the value 1 means there is perfect clustering of similar values, while 0 means there is no autocorrelation, hence any clusters arising are of dissimilar values. Thus, a positive value of Moran’s I indicates that the values being analyzed tend to cluster spatially, either as high values clustering together, or low values clustering together. A negative index implies that high values repel each other and tend to be near low values. The results also include spatially generated maps that show clustering of migration patterns, as well as areas with divergent characteristics, thus visually clarifies the effect of migration on inequality. A criticism of Moran’s I is that the measure is limited only to the strongest associated locations (Wartenberg, 1985). The local tests for spatial association (LISA) helps in spatial cluster identification and spatial filtering (Tiefelsdorf and Boots, 1995, 1997; Hepple, 1998). The formula for calculating LISA (I_i) is expressed in the works of (Anselin, 2017). The output of LISA is evidence of clusters, where regions with high or low values are identified based on their degree of statistical significance, based on the Getis-Ord statistic, Gi*(d) (Getis and Ord, 1992). The interpretation of z-scores for the Gi* statistic is quite different from the interpretation of z-scores in the Global Moran’s I. The interpretation of the Gi* Statistic is that a positive association denotes a clustering of high values, while negative association denotes a clustering of negative values. Comparatively, for the Moran’s I, positive value of I_i indicates spatial clustering of similar values while a negative value of I_i indicates a clustering of dissimilar values.

Regression analysis was employed to determine the spatial relationship between the migration and inequality variables using two measures, the Ordinary Least Square regression (OLS) and Geographically Weighted Regression (GWR) tools in ArcGIS. The OLS regression analysis was employed to test if our model is effective in explaining the relationship between the variables. We conducted the Geographical Weighted Regression (GWR), which considers both geographical differences and spatial relationships in the data being analyzed. Geographically Weighted Regression fits a regression equation for all features in the data set using the dependent and explanatory variables, within similar neighborhoods. GWR builds on the OLS by allowing the relationship between the independent and dependent variables to vary by locality. The key assumption of GWR is that the strength and direction of the relationship between the dependent and independent variables is influenced and can be modified by contextual factors (Fotheringham et al., 2003). Several variables were included in the GWR regression equation. The dependent variable Y is migration intensity is measured by the Revised Weighted Net Migration Rate, that captures the temporal effect of migration on population distribution. The independent variables were the county-based measures of inequality including County Gini, County HDI, proportion of persons with access to power and proportion of population with access to water. The resultant equation was as follows:

Where, Y is the dependent variable and measures migration intensity, PWY is the autocorrelation factor, while the independent variables include the county inequality measures namely, County Gini, County HDI, proportion of persons with access to electricity in a given county, and proportion of population with access to water in a given county and B1, B2, … Bn are the coefficients to be estimated.

The OLS regression analysis yields an output that contains the following information: the OLS residuals, statistical results and diagnostics, a table of explanatory variables and their coefficients (called the OLS Summary Report) and a table of the regression diagnostics⁵. To interpret the results, we focus on the R-squared measures which shows how much change in the model is caused by the dependent variable, in our case, the migration intensity.

While the OLS regression is useful in providing an indication of the model efficacy, it has limitations. First, it does not cater for the spatial effects. Second, when there two or more variables that can affect the dependent variable and also affect each other, OLS regression will not be able to counter this multicollinearity effect, thus, the analysis will show that variables which may otherwise be significant in the analysis, rendered statistically insignificant (Young, 2018; Shrestha, 2020).

As a result, we applied as second regression model, the Geographically Weighted Regression (GWR) to the data, to cater for multicollinearity. The output of the Geographical Weighted Regression Analysis comprises of five features. These include; fields for observed and predicted response values, condition number (cond), Local R², explanatory variable coefficients, and standard errors generated by ArcGIS.⁶ The value called the condition number checks the level of local multicollinearity in the data. In case of strong evidence of multicollinearity, the results of the regression model will be unreliable, hence the variables being analyzed should not be larger than 30. The R Squared values indicate how well the model fits, and the values range from 0 to 1, indicating how well the model fits to the y values, thus a test of the fit of the model. Values closer to 0 has a poor fit. The output of the GWR analysis on ArcGIS produces a map of the Local R² values, to show where predictions were good and where they were not.

An alternative open-source software that can be used for the spatial autocorrelation analysis is R, although this has been developed recently⁷. Migration intensities, inequality data and County HDI can be exported from MS Excel to R using the.csv format. The county spatial maps are generated using the shapefiles, that can be read in QGIS or R package⁸. Linear regression analysis can be done using R package using the command Im. For the spatial autocorrelation analysis, which checks for clustering of migration intensities, the migration intensities and county shapefiles can be read in R. The ArcGIS analysis used the ‘distance bands’ to determine the nearest neighbor or contiguous county. In R package, one can use the ‘contiguity neighborhood’ as the measure of the connectedness of the counties, and calculate the mean values of the neighboring units. While ArcGIS runs the spatial autocorrelation using a weighted index, W, that captures the average weighted measure (spatial lag) of contiguous units, using R package, one can calculate the Moran’s I using the moran.test function which gives you the Moran’s I value and the p-values. Further information on spatial analysis using R can be obtained from several research works (see Baddeley et al., 2016; Roger, et. al, 2013).

Ordinary Least Square (OLS) regression results

We conducted spatial analysis of our model, with migration intensity as the dependent variable, and the four explanatory variables namely access to electricity, access to water, County Gini and County HDI. The purpose of this analysis was to provide evidence of spatial association between the variables, and the consistency of such association within the counties. The spatial analysis results from the ordinary least square regression (OLS) reveal several observations. First, the nature and direction of the relationship between the variables are captured using scatterplots and histograms as shown in Figure 1. The histograms show that the distribution of variables is not normal, with a left inclination, for the County Gini and access to power and a right inclination for the County HDI. The scatterplots show that the relationship between the variables and migration are non-linear. This corroborates literature findings implying that the relation between migration and inequality is curvilinear.

Figure 1. Scatterplot of variable distributions and relationships from OLS regression.

Table 2 presents diagnostic results of our OLS model. The Multiple R-squared value shows that our model explains up to 21 percent of the changes in migration intensity. Owing to the complexity of the relationship, we opt to use the Adjusted R-squared results, which show this efficacy level declines to 14 percent. The low explanatory level of our model implies that there may be other variables that could explain the variations in migration intensity, but these were excluded in our model. Despite this, our model is statistically significant, indicated by the Joint Wald statistic (p < 0.05). Now that we have our model and the efficacy confirmed, the OLS regression also tested if the observations of the relationship between the variables were consistent across the counties. The Koenker (BP) statistic checks for stationarity, and the results show a p value of 0.005, confirming that there is no heteroscedasticity in our model. Finally, the OLS results also confirm that the relationship between migration and inequality is non-linear, with the Jarque-Bera statistic value of 285 (p < 0.001) confirming this.

In Table 3, the OLS results show the explanatory powers of each of the variables in the regression. The results show that the County HDI and County Gini, have higher explanatory powers, although they influence migration intensity in opposite direction. The County HDI has a positive influence on migration intensity, while the County Gini has a negative influence on migration intensity. The remaining two variables, access to electricity and access to water, have lower explanatory powers in the equation. However, only the County Gini gives a statistically significant relationship when robust statistics is considered. A unit change in migration intensity results in a negative change of up to 567 units in County Gini, showing an inverse relationship between the two variables. This finding confirms earlier observations by Kuznets (1971) and other scholars of the inverse relationship between migration and income inequality.

Geographically Weighted Regression (GWR) results

The data was subjected to Geographically Weighted Regression (GWR) analysis and the attributes used in the analysis are shown in Table 4. With the GWR, the efficacy of our model improves and the model explains up to 20 percent of the relationship between migration and the inequality variables, as shown by the R² adjusted value. Just like the OLS model, the efficacy confirms that several other critical variables that could explain migration and inequality are missing in our model.

The GWR results provide a cold-to-hot rendered map of the standard residuals of the regression analysis. This map, shown in Figure 2, shows evidence of clustering of migration intensities in the country. For example, low migration intensities are found in Makueni, Machakos, Embu and Meru counties, respectively. Nairobi County has remarkably high migration intensity and is surrounded by regions with similarly high migration intensities, leading to a clustering of high-high migration. This may be because of the spillover effects of migration to Nairobi, hence migrants move to the next contiguous counties, as demonstrated by high intensities in Kajiado, Kiambu and Nakuru counties. In the western part of the country, there is a cluster of high migration in Vihiga County and similarly high migration in Migori County at the Kenya-Tanzania border. Comparatively, the coastal region shows evidence of low migration clustering in Mombasa and Kilifi counties, respectively.

Figure 2. Geographically Weighted Regression analysis.

Following the observed clustering of migration intensities in the country, a spatial autocorrelation of the residuals was applied to the data to confirm if the results are random, or clustered. The results of the Global Moran’s I are presented in Figure 3. Our Global Moran Index gives a value 0.105452, z-score is 3.0785, while p value is 0.002, implying that the data is spatially clustered and not randomly distributed. The positive value of Moran’s I indicates that while the values are spatially clustered, positive values are clustered together and negative values are clustered together. This leads to the conclusion that migration intensity is spatially clustered, with neighboring regions recording similar values.

Figure 3. Spatial autocorrelation using Global Moran’s I.

The results of the tests for identifying whether county migration is spatially clustered or not is presented in Figure 4 which provides evidence of hotspots. The spatial clusters of migration intensities of similar nature confirm the existence of two key migration hotspots in the country. There is a high migration hotspot in the lake basin region (comprising of Kisumu, Vihiga and Nandi counties) and a low migration hotspot in the coastal region (comprising of Mombasa, Kilifi and Kwale counties). The Getis-Ord Statistic GI* show a positive value indicating that migration intensities are clustered in these regions, with positive values together and negative values together.

Figure 4. Migration hotspots Kenya.

These finding confirms the importance of spatial factors in explaining demographic phenomena. In this case, the clustering of high migration intensities in the lake basin region confirms the previous observations of the region as a reservoir of migrants, having higher outflow of migrants largely due to scarcity of opportunities in the region. In a review of inequalities in Kenya, data showed the marginalization of the western part of the country owing to political reasons (Ajulu, 2002) resulting in lower human development outcomes (Society for International Development, 2004, 2006). For the coastal region, migration intensities are low with most movements towards Mombasa, the second largest capital city, and the counties that reported highest intensities are largely poorly resourced regions with high levels of poverty (KNBS and SID, 2013).

Underlying data

The internal migration dataset from the 2009 Kenya Population and Housing Census data is available from the Kenya National Bureau of Statistics (KNBS) and permission to obtain micro data can be obtained from their website. Access to the data requires registration and is granted for those who wish to use the data for legitimate research purpose. Alternatively, the micro data is available from Integrated Public Use Microdata Series (IPUMS) following user request from their registration page.

Inequality data was obtained from the Exploring Kenya Inequality National Report, published by the Kenya National Bureau of Standards (KNBS) and Society for International Development (2013). The report is available through this link: Exploring Kenya Inequality National Report - Kenya National Bureau of Statistics (knbs.or.ke).

County Human Development Index data was obtained from the 2009 Kenya National Human Development Report that can be accessed here.

Access to electricity and access to water data was obtained from the Socio-Economic Atlas of Kenya (Wiesmann et al., 2014) which contains analysis of the 2009 Kenya Population and Housing Census data. This can be accessed here.

A guide for using R program for spatial autocorrelation can be found here.