Spatial assessment of association between total fertility and under - - PDF document

Spatial assessment of association between total fertility and under five mortality rate in high fertility states of India

Author Akansha Singh Universite Catholique de Louvain, Belgium Email: akansha.singh@uclouvain.be Abstract Global efforts to reduce child mortality and fertility now include the need to address spatial inequalities in fertility and child mortality at the local level. Significant spatial variations in fertility and child mortality at the district level are observed within high fertility nine states

• f India, which include 50 percent of the Indian population. A spatial perspective to

examine the relationship between child mortality and fertility levels at the district level is still lacking in previous studies. The main objective of this study is to establish to what extent child mortality explains changes in fertility levels at the district level. Information on fertility, mortality and other socio-economic indicators was extracted at the district level from the Annual Health Survey 2011-12. Measures of spatial autocorrelation indicate strong and significant autocorrelation for total fertility and child mortality levels with apparent hot spots of districts with high fertility and child mortality. Spatial regression models suggest that even after adjusting the spatial autocorrelation and other covariates, child mortality plays a significant role in determining the fertility at district level. However, fertility response to external forces may vary across districts as highlighted by the district level local beta estimates of child mortality.

Introduction Over the past few decades, several studies have looked into the trends, patterns and determinants of total fertility rate in India. All studies have highlighted significant regional variations in fertility behaviour in India. This has beenmainly attributed to the cultural, economic and geographical diversity in the country. Mapping fertility transition during the period 1951-1991 showed that fertility decline began in India’s periphery, along the coasts and in the extreme south. The fertility decline then spread progressively inward, gradually moving north, to encircle the region surrounding the Ganges Valley, the heart of Hindi- speaking traditional India, where fertility has hardly declined at all (Guilmoto and Rajan 2001). This region in the upper part of India is predominantly identified by high fertility and child mortality rates. Several studies have shown the north, south divide in fertility and mortality transition in India (Saikia et al., 2011; Guilmoto and Rajan 2001). Moreover, improvements in total fertility and child mortality have been uneven and the burden of high fertility and mortality is still disproportionately borne by the certain pockets of this

• region. These studies illustrate significant variations in fertility and child mortality at the

district level within high fertility states of India (Guilmoto and Rajan 2013). These states include nine major states of India with 50 percent of the Indian population and lagging in many socioeconomic and demographic indicators. The population stabilization of India is contingent on the future fertility scenario in these states (Das and Mohanty 2012). Hence, there is huge significance of analysing fertility levels in these nine major states comprises Assam, Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Rajasthan, Uttar Pradesh and Uttarakhand (See Figure 1). Very few studies allow the assessment of fertility levels at the district level of India. These studies have tried to examine the factors associated with fertility at district level (Guilmoto and Rajan 2001; Guilmoto and Rajan 2013; Das and Mohanty 2012). A comprehensive spatial evaluation of the fertility at the district level in high fertility states of India is missing from all such studies. Child mortality has been identified as one of the most important factor explaining the variation in fertility at the district levels (Guilmoto and Rajan 2001; Das and Mohanty 2012). However, the basic question that comes is does this relationship hold even after adjusting for spatial dependency and controlling the socio economic condition of the districts. Further, the key lies in establishing to what extent child mortality explains the change in fertility levels in the global and the local levels in high fertility surroundings of India.

The objective of this study is twofold: (1) to understand the spatial differentials in total fertility rates and the child mortality rate in India and (2) to investigate the relationship between fertility level and the child mortality at the global and local levels adjusting for

• ther socio economic variables.

Data source This study is focused on nine high focus states in India - Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Orissa, Rajasthan, Uttarakhand, Uttar Pradesh and Assam, consisting of 284 districts. These nine states account for about 50% of the total population in the country, are the high focus states in view of their relatively high fertility and mortality indicators. The district level data of total fertility rate and under- five mortality rate for all nine states were obtained from the recently concluded Annual Health Survey (AHS) – 2011-12 (Registrar General and Census Commissioner 2015). Other socio-economic variables include the female literacy rate, female mean age at marriage, female work force participation, male work participation rate, proportion of urban population, female contraceptive prevalence rate and under five mortality rate. Table 1 provides the description of the variables used in this study.

Table 1: Main outcome and independent variables in the regression analysis Variables Description TFR Total fertility rate Fliterate Female literacy rate Fmarriage Female mean age at marriage FWPR Female work participation rate MWPR Male work participation rate Urban Proportion of urban population CPR Modern Contraceptive prevalence rate U5MR Under five mortality rate

Spatial analysis methods At the first state, spatial autocorrelation has been estimated to examine coincidence of value similarity with locational similarity (Anselin and Bera 1998). It can be computed at both national and local level. The former takes into account the spatial configuration of the whole area whereas the later measures spatial association of a variable at a location with that in its local neighbourhood. Computation of spatial autocorrelation requires constructing a matrix, known as spatial weights neighbourhood matrix (W), to quantify the spatial proximity for each observational unit (district). In this analysis, contiguity based weights (queen) with all first order neighbours were considered in generating the spatial

weights neighbourhood matrix. We used these weights to manifest the spatial clustering and outliers in the outcome variable (TFR) and main independent variable (U5MR) using Moran's I statistics and LISA (Local Indicators of Spatial Autocorrelation) (𝐽

𝑘 ∗).

Moran's I statistic (I) LISA statistic (𝐽

𝑘 ∗)

Here Yi is indicator of interest at ith district, 𝑍 ̅denotes its average over all regions/ districts, N is total number of regions/ districts and wij is an element of the matrix W defined above corresponding to the pair of locations i and j A correlation matrix was computed to assess the association between the outcome variable and predictors before applying the multivariate OLS and spatial models. We have tested the spatial dependency in classical statistical models using robust lagrange multiplier error and lag test. Further based on the finding from the classical analysis we moved further to compare three regression models to examine the relationship between the outcome variable and a set of predictors: ordinary least square (OLS), spatial lag model (SLM) and spatial error model. Spatial Lag Model: If dependent variable, Y, is correlated with weighted average of its value in the neighbourhood and other locations, this relationship can be expressed as:

Y = ρWY + βX + ɛ

Here, ρ is spatial lag parameter, W is spatial weights matrix, X is vector of explanatory variables and β is corresponding coefficient vector. It is assumed here that the error terms εs are identically and independently distributed (iids) although one can correct for heteroscedasticity (Anselin 2003). A significant spatial lag term may indicate strong spatial dependence. Spatial Error Model: If the spatial dependence enters the model through the error term, ε, we have the spatial error model:

Y = βX + ɛ ɛ = λWɛ + μ

Here, λ is spatial autoregressive parameter and the errors μs are iids. Thus, it is a special case of regression with non-spherical error term and OLS, although unbiased, is inefficient. A significant spatial error term indicates spatial autocorrelation in errors, which may be due to key explanatory variables that are not included in the model. In order to get the best model, Akaike’s Information Criterion (AIC) is estimated, which measure the fit of the model to the data but penalize models that are overly complex. Models having a smaller AIC is considered the better regression model. Further to examine the heterogeneity of relationship between under five mortality rate and total fertility rate we have used Geographically Weighted Regression (GWR) techniques (Muniz, 2009) i.e. local regressions which allows to estimate heterogeneous relationships between the dependent and independent variables. This technique is particularly useful when the magnitude of a relationship among variables differ from location to location (Fotheringham et al., 2002). In this study, GWR is a series of local regressions that consists

• f one local regression per district in the sample, with this local regression being centered
• n the geographic center of the district.

Basic Model: 𝑧𝑗 = 𝛾0(i) + 𝛾1(i)𝑦1𝑗 + …. + 𝛾𝑜(i)𝑦𝑜𝑗 + 𝜁𝑗 Parameter: 𝛾 ̂(𝑗) = (𝑌𝑈𝑋(𝑗)𝑌)−1𝑌𝑈𝑋(𝑗)𝑍 Where W(i): a n by n spatial weighting matrix GWR model is assuming that observed data near to point i have more of an influence in the estimation of the values located farther from i. The equation measures the relationships in the model around each point i.

Figure 1: Map of districts of India and AHS states

Results: Before doing statistical analysis, it was essential to create basic maps of total fertility and under five mortality rates in high fertility states of India. Figure 2 shows that there is significant variation in TFR and U5MR at the district levels in these nine states of India. High values are clustered in some selected districts of Uttar Pradesh, Bihar, Orissa and Madhya Pradesh with higher fertility as well as mortality levels as compared to the other region of the same state. Further, global measure of spatial autocorrelation shows that there is strong autocorrelation for fertility and child mortality levels in these states. The Moran’s I test statistics was more than 0.5 for both TFR and U5MR which indicates the higher intensity of this autocorrelation.

Figure 2: Spatial variation in total fertility rate and under five mortality rate in AHS states

Table 2: Moran I statistics for main outcome and independent variable Demographic indicators Moran I statistic P value Total fertility rate 0.63 < 2.2e-16 Under five mortality rate 0.50 1e-04

The local spatial autocorrelation helped us in identifying ‘geographic mortality and fertility traps’ in some areas of country. Therefore, it is quite possible that mortality and fertility risk tend to cluster in the specific areas. Some significant high-high spots were observed for total fertility rate and U5MR (Figure 3). We identify significant clusters of fertility and under five mortality in the districts of Bihar, Uttar Pradesh and Orissa. Presence of significant local and global spatial autocorrelation means both immediate and wider social environment influence total fertility and under five mortality.

Figure 3: LISA maps for total fertility rate and under five mortality rate in AHS states

Figure 4 shows association of district level TFR and under five mortality rate. This scatter plot clearly suggest strong positive correlation between both. The districts with higher level TFR also had higher under five mortality rate. This clarify that the high level of child mortality is appendage with high levels of fertility in high fertility region of India.

Figure 4: Association of district level TFR and under five-mortality rate. Seven models have been used to examine the role of different independent variables in explaining the variation in total fertility rate in high fertility districts in India (Table 4). The seventh model gave a good fit to the data and in addition controlled the socio economic condition of the population. The results indicate that the female literacy, mean age at marriage, work participation rate and contraceptive prevalence rate are important in determining fertility levels at the district level in India. However, even after adjusting these significant factors, under five-mortality rate significantly effects total fertility rate. Further one unit increase in under five mortality increases the fertility rate by 0.01 units. This relationship is significant at p<0.001. Given our earlier observations on significant spatial correlations in total fertility rate and under five mortality rate, we carry out diagnostic testing of the residuals obtained from the OLS

• estimation. Significant Moran’s I indicate that the residuals of the OLS model are positively

spatially correlated. We then carry out robust LM (Lagrange Multiplier) test for both spatial lag and spatial error models. These test statistics were significant. Although these tests do not indicate whether to use spatial error or spatial lag model, they provide enough evidence to use either spatial lag or spatial error model. We therefore estimate both the spatial error and lag

• models. A crude look at the table indicates that OLS tend to overestimate the model parameter

in the presence of spatial effects.

1 2 3 4 5 6 7 20 40 60 80 100 120 140 160

TFR Under five mortality rate

Association of district level TFR and U5MR

Table 4: Ordinary linear regression with Total Fertility Rate as dependant variable. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Dependent Variable TFR TFR TFR TFR TFR TFR TFR Coef P val Coef p- val Coef p- val Coef p- val Coef p- val Coef p- val Coef p- val Intercept 6.07 *** 6.96 *** 7.43 *** 6.01 *** 5.98 *** 6.24 *** 6.23 *** Fliterate

• 0.05

***

• 0.04

***

• 0.04

***

• 0.04

***

• 0.04

***

• 0.04

***

• 0.02

*** Fmarriage

• 0.06
• 0.06
• 0.07

*

• 0.07

*

• 0.08

*

• 0.13

*** FWPR

• 0.01

***

• 0.02

***

• 0.02

***

• 0.02

***

• 0.01

*** MWPR 0.02 ** 0.02 ** 0.02 ** 0.01 Urban 0.00 0.00 0.00 CPR

• 0.01

*

• 0.01

* U5MR 0.01 *** Adj.r2 0.4

• 0.4
• 0.46
• 0.48
• 0.47
• 0.48
• 0.59
• AIC

468.58

• 468.54
• 439.62
• 432.25
• 434.22
• 429.83
• 366.

66

• NB

Weight Matrix First order queen contiguity Moran's I (Dep. Var.) 0.63 *** 0.63 *** 0.63 *** 0.63 *** 0.63 *** 0.63 *** 0.63 *** Moran's I (Model) 0.55 *** 0.55 *** 0.48 *** 0.47 *** 0.47 *** 0.47 *** 0.40 *** LMerr 204.20 *** 209.30 *** 160.04 *** 149.90 *** 150.38 *** 153.11 *** 106. 92 *** RLMerr 29.65 *** 33.98 *** 24.89 *** 18.71 *** 12.88 *** 16.04 *** 9.93 ** LMlag 179.39 *** 178.92 *** 141.21 *** 141.43 *** 150.03 *** 147.04 *** 115. 61 *** RLMlag 4.84 * 3.60 ' 6.06 * 10.24 ** 12.53 *** 9.96 ** 18.6 2 *** Multicolli nearity 13.45

• 55.94
• 62.18
• 72.91
• 78.36
• 85.76
• 92.5
• Jarque

Bera 0.45 0.53 1.55 1.15 1.16 0.52 2.26

Note: Significance ***p<0.001; **p<0.01; *p<0.05

Coefficients of the terms capturing spatial effects, viz., λ in spatial error model and ρ in spatial lag model, are statistically significant. High positive value of λ indicates that the unobserved variables that could not be controlled in the model (and are captured by the error term) are positively correlated across the neighbouring districts. On the other hand, high value of ρ indicates substantial spatial dependence in TFR across the neighbouring districts. Although, we discuss both the spatial error and lag models here, we prefer the spatial lag model because of lower AIC values. U5MR has been significant in each model. The female literacy, female mean age at marriage, contraceptive prevalence rate and female work participation rate are the other significant predictors of total fertility rate. Even after adjusting all these factors and spatial clustering, under five mortality still play an important and significant effect on fertility.

Table 5 Comparison of linear, spatial lag and spatial error model with TFR as independent variable Linear model Spatial Lag model Spatial Error Model

Estim ate Std. Error Z value Pr(>| z|) Estimat e Std. Error Z value Pr(> |z|) Estimat e Std. Erro r Z value Pr(> |z|) (Intercept)

6.23 0.71 8.80 *** 2.67 0.63 4.23 *** 5.20 0.88 5.94 ***

Fliterate

• 0.02

0.00

• 5.13 ***
• 0.01

0.00 -2.59 **

• 0.02

0.01

• 3.35 ***

Fmarr

• 0.13

0.03

• 3.98 ***
• 0.08

0.03 -3.23 ***

• 0.09

0.03

• 2.63 **

FWPR

• 0.01

0.00

• 5.75 ***
• 0.01

0.00 -3.23 ***

• 0.01

0.00

• 2.06 *

MWPR

0.01 0.01 1.50 0.01 0.01 2.20 * 0.01 0.01 1.34

Urban

0.00 0.00 0.90 0.00 0.00 -2.14 * 0.00 0.00

• 0.42

CPR

• 0.01

0.00

• 2.35 *

0.00 0.00 -1.61

• 0.01

0.00

• 2.75 **

U5MR

0.01 0.00 8.44 *** 0.01 0.00 6.55 *** 0.01 0.00 5.96 *** Adj R2 0.59 Wald statistics 143.03*** 175.3*** Rho (ρ) 0.57*** Lambda(λ) 0.68*** AIC 366.6 264.1 273.9 Moran I test for residuals Significant Not significant Not significant Significance codes: ***p<0.001; **p<0.01; *p<0.05; ‘p<0.1

Further, after examining the relationship of under five mortality with total fertility rate adjusting for the spatial autocorrelation, it was attempted to check the consistency of this relationship or in other words examined the heterogeneity of this relationship using geographically weighted

• regression. The other independent variables like female literacy and work participation rate and

urbanisation of the district were controlled in this regression analysis. Figure 5 shows the local beta estimates generated from the geographical weighted regression (GWR). The key insight here is that the association between under five mortality rate and fertility is not the same across different districts. The median beta coefficient is about 0.1. The plot of beta coefficients clearly show clusters of districts that differ in the obtained beta estimates of the association between fertility and child mortality.

Figure 5: Local Beta estimates of under five mortality from geographically weighted regression.

Conclusions This study has examined the relationship between total fertility rate and under five mortality in high fertility settings of India from the spatial point of view. Global and local measures of spatial autocorrelation indicate strong autocorrelation for total fertility rate and under five mortality in the high fertility region of India. LISA maps show that there are certain pockets of these states with significant clusters of districts with high fertility and mortality levels. Robust Lagrange multiplier error and lag test suggests spatial dependence in the linear model with total fertility rate as outcome and under five mortality along with other predictors as independent variables that needs to be controlled. Spatial-lag and error models advocate that the under five- mortality rate is an important predictor of the total fertility rate in this high fertility region of India even after controlling the spatial dependency and other important determinants of fertility. Local beta estimates of under five mortality from geographically weighted regression confirm

the importance of this relationship at the local levels in India. However, fertility response to under five mortality may vary across districts as highlighted by the district level local beta estimates of child mortality. Significant and strong effect of under five-mortality rate on total fertility rate indicates that reducing under five mortality in this high fertility region of India may not only help in achieving the sustainable development goals and in addition plays an important role in reducing fertility and reducing population growth. References Anselin, L. and A.K. Bera. 1998. Spatial dependence in linear regression models with an introduction to spatial econometrics in Handbook of Applied Economic Statistics. Aman Ullah and David E A Giles eds: Marcel Dekker, Inc., pp. 237-90. Das, M. and S.K. Mohanty. 2012. Spatial pattern of fertility transition in Uttar Pradesh and Bihar: a district level analysis. Genus LXVIII (No. 2): 81-106. Fotheringham, A.S., C. Brunsdon, and M.E. Charlton. 2002. Geographically weighted regression: the analysis of spatially varying relationships. West Sussex, England: John Wiley & Sons Ltd.,. Guilmoto, C.Z. and I. Rajan. 2001. Spatial pattern of fertility transition in Indian districts. Population and Development Review 27(4): 713-738. Muniz, J.O. 2009. Spatial dependence and heterogeneity in ten years of fertility decline in

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