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Religious Polarization and Under-Supply of Public Goods

Pulkit Bajpai

3. Empirical Strategy

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3.1 Ordinary Least Squares

1I follow the empirical strategy used extensively in the literature on ethnic heterogeneity and public goods. The reduced form equation can be written as follows:

2Here Yijt is the availability of public good i in sub-district j in year t. RQijt is the religious polarization index, Sijt is a vector of religion-specific population shares, Xijt is a vector of sub-district level explanatory variables (nighttime luminosity, area size and average literacy level), Gijt is a vector of sub-district level geographical controls (temperature and rainfall), λt is the year fixed effect, δt is the sub-district fixed effect to account for unobserved heterogeneity and ϵjt is the sub-district level error term.

3Religious groups enter the framework through the RQ index and religion-specific population shares. This is carried out to measure the influence of the four largest religious groups (Hindus, Muslims, Christians and Sikhs) while capturing potential social antagonisms. Contrary to the existing literature, most notably similar being Besley et al. (2004), I find the relationship between various public goods and religion-specific population shares to be non-linear. Therefore, I estimate the relationship with an additional quadratic term for religion-specific population shares. This can be written as follows:

4In accordance with the literature, I estimate the above equation using OLS for 1991, 2001 and 2011 cross-sectional data. As a result of the unavailability of the 1991 Census of India data at the sub-district level, I restrict my analysis to the district level for 1991 while extending it to the sub-district level for the years 2001 and 2011.

3.2 Two-way Fixed Effects Model

5I use a two-way fixed effects (“within”) model suitable for my panel data from 2001 to 2011. This is a novel addition to the literature on ethnic heterogeneity, which focuses on cross-sectional empirical strategies. The error components model allows me to plausibly resolve time-invariant unobserved heterogeneity concerns.

6I use the standard notation from Wooldridge (2010) to set up my two-way fixed effects model for my unbalanced panel data. This can be written as follows:

7Here i is the public good, j is the sub-district, t is the time and ϵjt is the composite error term. The composite error term can be decomposed as follows:

8Here ϵjt is the composite error, λt is the time effect, δj is the sub-district effect and vit is the idiosyncratic error term. My choice of using the fixed effects model is appropriate under the assumption that a correlation exists between the time-invariant unobservables, the sub-district specific unobservables and the explanatory variables in my model. I test for the aforementioned assumption by testing for the joint significance of the two unobservable variables in the following manner:

9I obtain the Restricted Residual Sum of Squares from the Pooled OLS followed by the Unrestricted Residual Sum of Squares from the Within Estimation. I use the RRSS and the URSS to compute a joint F-test. I am able to reject (p-value = 0.056) the null hypothesis which suggests that time-invariant unobservables and sub-district observables are correlated with my regressors, thereby validating the choice of the fixed effects estimator.

3.3 Dynamic Spatial Autoregressive Model

10Despite using the fixed effects estimation to address unobservable heterogeneity, the strategy may still face potential problems such as path dependence of the dependent variables and spatial characteristics that may affect my estimates. These issues may not be adequately addressed by using time-invariant unobservables and sub-district specific unobservables. Therefore, I complement my previous estimation strategy using a dynamic spatial autoregressive model as proposed by Baltagi et al. (2011).

11I hypothesize the RQ index to be driven by spatial factors. I expect spatial factors such as coastline, mountain ranges and major river systems to determine religious settlement patterns, thereby affecting the RQ index. I restrict my focus to three regions in India – the Western Coast, the North Indian Plains and the Pakistan/Bangladesh Border regions. In the south of India, western coastal areas and port cities were settlement points for the French, Portuguese and British colonial empires. These coastal areas controlled by European empires became fertile ground for religious conversion by missionaries followed by the establishment of smaller Muslim kingdoms; consequently, these regions witnessed a rise in the number of non-Hindu populations. The North Indian Plains were the center of the Islamic empire as a result of their spatial accessibility from western Asia. Lastly, the large river systems in India’s west and east serve as approximate boundaries between India, Bangladesh and Pakistan, resulting in religiously heterogeneous populations in these border regions. I confirm my hypothesis by mapping out the RQ index spatially in Figure 3.1. I observe that the Western Coast, the North Indian Plains and the Pakistan/Bangladesh Border regions on average have higher religious heterogeneity than other areas in India, such as north Indian gangetic plains, southern Indian states. Further, following Gallup et al. (1999), I also theorize the supply of public goods to be driven by the aforementioned spatial factors. The Western Coast of India became an economics hub due and the North Indian Plains have been the largest contributor to the agricultural economy due to their geographic location.

12The distinct advantage of spatial panel models arises from their ability to control for spatial invariant effects. Spatial units of observation are likely to differ in their background variables, which are usually space-specific, affecting the dependent variable, but they are challenging to measure. My panel data provide disaggregated census data at the sub-district level.

13I match these sub-districts with their geocodes through Google API to construct a rich spatial panel data set. Unfortunately, my algorithm drops 1,500 sub-districts from each census cycle due to the lack of geospatial data. I carry out a balance test, comparing the omitted districts with 1,500 randomly

14selected sub-districts which were matched using Google API. I assign treatment status to the omitted districts and control status to iterative samples of 1,500 districts with Google API data. I carry out a balance test for all public goods considered, RQ index, EF index, religious population shares and control variables. The difference in means between the treatment and control groups for all my variables is statistically insignificant, allowing me to reject bias in selecting sub-districts.

15I adopt the methodology used in Elhorst (1970), which can be written as follows:

16Here Yijt is the public good i, for sub-district j at time t, Yijt1 is the autoregressive lag component, Yikt is the dependent variable for the neighboring sub-districts, wkj is the row-normalized spatial weights matrix with zero diagonal elements, RQijt is the Religious Polarization index and Xijt is the vector for exogenous explanatory variables. In accordance with LeSage (2010) I parametrize the spatial lag coefficient ρ1 to be restricted to the interval [1/rmin, 1], where rmin is the most negative purely real characteristic root of the row-normalized wkj matrix (Baltagi et al., 2011).

17I estimate the model using a one-way fixed effects model restricting the study to only account for spatial invariant effects due to computational issues. I test for model misspecification using the Mundlak test because it is robust to both heteroskedasticity as well as within serial correlation (Mundlak, 1978). I obtain a p-value of 0.24 which does not allow me to reject the null hypothesis of no correlation between the regressors and the unobservable spatial invariant factors; therefore, it is appropriate to use a one-way fixed effects model, primarily due to the relationship between the RQ index and spatial factors in India.

Figure 3.1: Chloropeth with area-wise RQ index

Figure 3.1: Chloropeth with area-wise RQ index


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