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Linkages between poverty and income inequality of urban–rural sector: a time series analysis of India’s urban-based aspirations from 1951 to 1994 Shahriar Kibriyaa, David Besslerb and Edwin Pricea

aCenter on Conflict and Development, Texas A&M University, College Station, TX, USA; bDepartment of Agricultural Economics, Texas A&M University, College Station, TX, USA

ABSTRACT This study examines the impact of urban and rural development on poverty and inequality in India before economic reform. The methodology comprises two dimensions. Modern time series methods are used to uncover the dynamic patterns of urban–rural poverty and income inequal- ity. A machine-learning algorithm is used to determine the causal structure among the develop- ment indicators. Our results show that reductions in rural poverty appear to be a more effective in reducing both urban and rural poverty, although the costs of achieving these reductions have not been considered.

KEYWORDS Urban poverty; rural poverty; income inequality; India

JEL CLASSIFICATION I32; C22

I. Introduction

After gaining independence in 1947, India experi- enced pervasive poverty and inequality resulting in famine (Srinivasan and Sen 1983). Most of the popu- lation were rural dwellers and depend on agriculture for livelihood. However, an agricultural economy and dependency on imports of manufacturing goods was deemed rather ominous by the Indian policy makers. Even in the good harvesting years, India’s poverty measures consistently rose over 62%. To improve the situation, the policymakers decided to foster an industrialized and urban-based economy by initiating an import substitution growth which induced private and public investment to the urban sector, created easier access to cities, elevated higher education facil- ities inmetropolitanareas,enhancedcity-basedpublic distribution systems and provided better healthcare systems in the cities. A substantial amount of invest- ment in urban industries was managed at the expense of the agricultural sector (Teitelbaum 2004). For example, from 1951 to 1956, only 31% of India’s total budget was invested on more than 80% of its people – the rural peasants (Chandra, Mukherjee, and Mukherjee 2000). It is apparent that the policymakers conjectured that reducing urban poverty and inequal- ity will trickle down and decrease poverty and inequality in the rural sector.

While the 1992 policy reform of India ended import substitution and changed some of these policies, the dynamic relationship between urban and rural poverty-inequality remains an interest- ing question – especially for developing rural economies. In this article, we examine urban–rural poverty and Gini indices from India to discover the interactions between poverty and inequality in urban and rural sectors. We employ a time series techniques and machine-learning algorithm to understand the possible short- and long-run dynamics of poverty and inequality between urban–rural settings. The remainder of the article is organized as follows. Section II describes the method of analysis while Section III describes the underlying data and estimation results with Section IV offering a short discussion.

II. Methodology

We use modern time series methods, as categor- ized under the heading of vector autoregression (VAR). These methods represent the current value of a vector of poverty and Gini indices as a func- tion of time lags of the same vector and a current period innovation (error). Let Xt denote a vector which includes p indices (p = 4 in this study).

CONTACT Shahriar Kibriya [email protected] Center on Conflict and Development, Texas A&M University, 600 John Kimbrough Blvd, College Station, TX 77843, USA

APPLIED ECONOMICS LETTERS 2019, VOL. 26, NO. 6, 446–453 https://doi.org/10.1080/13504851.2018.1486973

© 2018 Informa UK Limited, trading as Taylor & Francis Group

Xt ¼ Xk

i¼1 ΦiXt�i þ et t ¼ 1; 2; :::; T ; (1)

where E(etet′) = Ω is a positive definite covariance matrix, Xt is a (4 × 1) vector of development observables, Φi is a (4 × 4) coefficient matrix, and et is a (4 × 1) vector of white noise innova- tions. T represents the number of observations on X used to estimate Φi and Ω.

The dynamic poverty and income inequality relationships can be best summarized through the moving average representation (Sims 1980). Given the estimated form of Equation 1, we can solve for its moving average representation, where the vector Xt is written as a function of the infinite sum of past innovations:

Xt ¼ X1

i¼0 Giet�i (2)

Here, Gi is a 4 × 4 matrix of moving average parameters, which map historical innovations at lag i into the current position of the vector X. The matrix G0 is generally not the identity matrix, as the elements of the vector e are usually not ortho- gonal. There may be nonzero correlation between contemporaneous innovations.

Following, we use a ‘Bernanke ordering’ (Bernake 1986) which requires writing the innova- tion vector (et) from the estimated VAR model as et = A

−1vt, where, in our case, A is a 4 × 4 matrix and vt is a 4 × 1 vector of orthogonal shocks.

Given knowledge of A, the transformed VAR is given as Equation 3:

AXt ¼ Xk

i¼1 AΦiXt�i

þ Aet t ¼ 1; 2; :::; T ; (3) Then, we apply inductive the causation algorithms of Spirtes, Glymour and Scheines (2000) to place zeros on the A matrix. The idea is to use recent innovations in graph theory and search proce- dures to determine the causal pattern behind the correlation in contemporaneous innovations to construct orthogonal innovations (E{vt·vt′} = D). The reader is directed to Spirtes, Glymour and Scheines (2000) or Pearl (2000) for the theory behind algorithms of inductive causation.

III. Data and results

After 1994, India abandoned its import substitution growth and undertook a more comprehensive rural development approach; hence, this study examines data till 1994. We collected time series of poverty data from 35 National Sample Surveys spanning 1951–1994. The data were made available by World Bank’s research group of Ravallion and Chen.

Figure 1 shows, while the levels of sector pov- erty and Gini indices are different, the peaks and valleys, while not identical, are generally the same, apart from a few exceptions. Both rural and urban

Figure 1. Time series plots of rural and urban Gini indices and rural and urban poverty indices, 1951–1994 Indian data.

APPLIED ECONOMICS LETTERS 447

poverty have decreased over time; however, the Gini indices increased near the end of the study period. Table 1 gives the mean, SD, upper and lower confidence intervals, minimum and maxi- mum points from our data set. On an average, urban Gini (inequality) has been higher than the rural Gini. Poverty indices have also been higher in the urban sector. However, the SDs of the two sectors do not show much difference.

Table 2 presents Ljung–Box tests on autocorre- lation on innovations (residuals) from VARs fit with two lags and three lags. At three lags, we reject the null hypothesis of white noise for all the four variables and conclude that at three lags, the residuals are not auto correlated.

Innovations from the three-lag VAR are mod- elled in TETRAD (http://www.phil.cmu.edu/pro jects/tetrad/) using PC algorithm (at a 20% signif- icance level as recommended in Spirtes, Glymour, and Scheines 2000) and GES algorithm (Chickering 2002). Results are given in Figure 2. Note in panel A of the figure that PC and GES agree that innovations in urban poverty are a sink – receive information from rural Gini and rural Poverty but send out no information to the other variables. Note as well that both algorithms cannot

assign the direction of information flow between rural Gini and urban Gini – thus the undirected edge in panel A. Accordingly, we direct this edge two ways, in panel B as RG → UG and UG → RG

Table 1. Summary statistics.

Indicator Rural Gini

(%) Urban Gini

(%) Rural poverty

(%) Urban poverty

(%)

Mean 31.34 36.29 50.80 43.26 SD 2.18 2.18 8.46 6.40 95% LCI 30.46 35.41 47.40 40.68 95% UCI 32.22 37.17 54.21 45.84 CV 6.98 6.03 16.66 14.80 Min 27.72 30.79 34.3 32.76 Median 30.79 35.72 51.36 44.70 Max 35.54 40.98 64.3 52.91

The data are 1950–1994 time series data on rural Gini, urban Gini, rural poverty and urban poverty obtained from XXXXXX.

Table 2. Test for autocorrelation on innovations from VARs fit with two lags and three lags.

Two-lag VAR Three-lag VAR

Series Q-statistic (p-value) Q-statistic (p-value)

Rural Gini 3.31 (0.51) 2.02 (0.73) Urban Gini 3.88 (0.42) 3.28 (0.51) Rural poverty 7.38 (0.12) 1.18 (0.88) Urban poverty 16.49 (0.00) 2.57 (0.63)

The Q-statistic is the Ljung–Box test on autocorrelations in the estimated residuals for each equation of the two or three-lag VAR. The statistic is distributed Chi-squared with four degrees of freedom under the null hypothesis (on each series) that the innovations are white noise. The number given in parentheses is the p-value for rejecting the null hypoth- esis. We generally reject the null for p-values less than 0.05 or 0.10.

Panel A: Pattern found with PC (20%) and GES Algorithms

Panel B: Directed Acyclic Graph Panel C: Directed Acyclic Graph

Figure 2. Pattern (panel A) and directed acyclic graphs (panel B and panel C) on innovations from a three lag VAR fit to rural Gini (RG), urban Gini (UG), rural poverty (RP) and urban poverty (UP), India 1951–1994 data.

448 S. KIBRIYA ET AL.

in panel C. [Panel B and C are observationally equivalent, meaning that the data are not suffi- cient to distinguish between them.]

To summarize the contemporaneous and dynamic the interactions among urban and rural poverty and Gini indices, we present the forecast error variance decompositions in Tables 3 and 4. These tables are associated with the three-lag VAR with contemporaneous structure from Figure 2 panel B in Table 3 and from Figure 2 panel C in Table 4. [Similar results hold for the two-lag VAR and can be obtained from the authors.]

Column 1 depicts the horizons (years) associated with the four variables. The first panel of Table 3, labelled ‘Rural Gini’ gives contribution of innovations in each series (rural Gini, urban Gini, rural poverty and urban poverty) to the forecast uncertainty in rural Gini at each of the reported horizons: 0, 1, 2, 10 and 20 years ahead. This uncertainty in rural inequality (as expressed by the SE at each horizon) is almost totally attributable to the rural sector (>85% to rural poverty

and rural Gini together at all horizons presented (0, 1, 2, 10 and 24 years ahead). In Table 4 (where UG → RG), we see that the relative importance of the rural sector in accounting for variation in the rural Gini remains large but drops to greater than 60% at all horizons, as here urban Gini explains up to 34% of the forecast error variance in contemporaneous time in Table 4.

Forecast error variance decompositions on the urban Gini (focus on the second panel labelled ‘Urban Gini’) show that the urban sector explains from about 45% of the variation in urban Gini in Table 3 and over 60% in Table 4. The rural sector (the rural Gini components of the decomposition added to the rural poverty components) explains never more than 60% of the variation in urban Gini in Table 3 and never more than 35% for the urban Gini variation in Table 4.

Uncertainty in rural poverty is primarily explained by variation in rural sector in both Tables 3 and 4 at all horizons. Here, we see the greatest influence of the

Table 3. Forecast error variance decomposition from three lag VAR fit to 1951–1994 India data, with contemporaneous caus- ality following Figure 2 panel B: RG → UG. Horizon (years ahead) SE

Rural Gini

Urban Gini

Rural poverty

Urban poverty

Rural Gini 0 0.76 100.00 0.00 0.00 0.00 1 0.83 87.23 2.65 9.58 0.53 2 1.22 55.97 1.24 37.06 5.73 10 1.61 52.93 4.77 35.56 6.75 24 1.66 51.84 4.88 35.20 8.08

Urban Gini 0 1.26 34.30 65.70 0.00 0.00 1 1.34 33.59 58.98 6.78 0.65 2 1.41 37.12 53.22 9.08 0.58 10 1.74 41.30 36.99 15.25 6.45 24 1.81 39.90 34.92 17.94 7.24

Rural poverty 0 3.28 0.00 0.00 100.00 0.00 1 5.05 1.58 .56 94.07 3.79 2 5.78 5.68 3.32 86.02 4.98 10 7.39 6.21 19.62 66.13 8.04 24 8.92 16.86 16.96 60.19 5.99

Urban poverty 0 2.26 28.72 0.00 42.33 28.96 1 3.24 18.65 0.02 60.21 21.12 2 3.67 21.43 7.70 48.81 22.06 10 5.14 16.58 16.11 47.79 19.52 24 66.78 27.11 13.56 47.41 11.91

Error variance decompositions are partitions based on observed innova- tions from the estimated vector autoregression model. The entries sum to 100% (within rounding error) for any particular row. The interpretation of each row is as follows (for the sub-panel headed by the label in italics Urban Poverty): looking ahead at the horizon given in the first column on the left (0, 1, 2, 10 or 24 years), the uncertainty (SE) in urban poverty at 10 years into the future is attributable to variation in each series labelled as the column heading: 16.58% due to variation in rural Gini, 16.11% due to variation in urban Gini, 47.79% due to variation in rural poverty and 19.52% due to variation in urban poverty.

Table 4. Forecast error variance decomposition from three lag VAR fit to 1951–1994 India data, with contemporaneous caus- ality following Figure 2 panel C: UG → RG. Horizon (years ahead) SE

Rural Gini

Urban Gini

Rural poverty

Urban poverty

Rural Gini 0 0.76 65.70 34.30 0.00 0.00 1 0.83 61.07 28.82 9.58 0.53 2 1.22 38.28 18.93 37.06 5.73 10 1.61 29.62 28.08 35.56 6.75 24 1.66 28.90 27.82 35.20 8.08 Urban Gini 0 1.26 0.00 100.00 0.00 0.00 1 1.34 1.48 91.09 6.78 0.65 2 1.41 5.37 84.97 9.08 0.58 10 1.74 15.93 62.36 15.25 6.45 24 1.81 15.29 59.52 17.94 7.24 Rural poverty 0 3.28 0.00 0.00 100.00 0.00 1 5.05 2.12 .02 94.07 3.79 2 5.78 8.97 0.03 86.02 4.98 10 7.39 12.48 13.34 66.13 8.04 24 8.92 11.91 21.91 60.19 5.99 Urban poverty 0 2.26 18.86 9.85 42.33 28.96 1 3.24 11.96 6.71 60.21 21.12 2 3.67 23.38 5.75 48.81 22.06 10 5.14 15.96 16.73 47.79 19.52 24 66.78 14.07 26.60 47.41 11.91

Error variance decompositions are partitions based on observed innova- tions from the estimated vector autoregression model. The entries sum to 100% (within rounding error) for any particular row. The interpretation of each row is as follows (for the sub-panel headed by the label in italics Urban Poverty): looking ahead at the horizon given in the first column on the left (0, 1, 2, 10 or 24 years), the uncertainty (SE) in urban poverty at 10 years into the future is attributable to variation in each series labelled as the column heading: 15.96% due to variation in rural Gini, 16.73% due to variation in urban Gini, 47.79% due to variation in rural poverty and 19.52% due to variation in urban poverty

APPLIED ECONOMICS LETTERS 449

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APPLIED ECONOMICS LETTERS 451

urban sector at 24 months in Table 4, where the urban sector accounts for at most 28% (21.9% plus 5.99%) of the uncertainty in rural poverty. Finally, over 50% of the uncertainty in urban poverty is explained by variation in rural sector, with poverty explaining over 40% of the uncertainty in urban poverty at all horizons in both Tables 3 and 4.

Rural poverty and inequality depend most on rural factors rather than urban sector factors. Urban sector poverty is substantially (predomi- nately) explained by rural sector factors. This asymmetry of effects of information flows in the two sectors is a major finding of this study. This result is restated below in terms of the associated impulse response functions, which summarize how each series responds to a one time only shock in each series of the VAR.1

Figures 3 and 4 presents the normalized impulse responses of rural–urban Gini and rural–urban poverty to a one time shock (innova- tion) in each index over horizons of 0–24 years, with the contemporaneous casual flow modelled as in Table 2, panel B in Figure 3 and Table 2, panel C in Figure 4. Normalization has been done with respect to one historical SD on each series. The responses in the Figures 3 and 4 are quite similar, in fact the third and fourth columns of Figures 3 and 4 are identical. Differences arising from the ordering RG → UG (Figure 3) and RG ← UG (Figure 4) are found in the first two columns of Figures 3 and 4. And these are not great. The main focus of this article is how rural poverty affects urban poverty and vice versa. This focus directs us to the third and fourth columns of Figure 3 or 4. Here, we see that innovations in rural poverty have a greater effect on urban pov- erty than do innovations in urban poverty have on rural poverty. Notice the last two sub-graphs of the last row of Figure 3 (or 4). Innovations in rural poverty have a relatively greater effect on urban poverty, than do innovations in urban poverty have on urban poverty. Of course these responses are measured at the level of development expen- ditures actually made over our period of observa- tion (1951–1994). Our results may be telling us that the marginal contribution of programmes to

reduce rural poverty is greater, as fewer funds are expended there (reflecting the law of diminishing marginal returns). And, as we do not have actual expenditures made in both sectors, we have to remain silent as to the cause of this difference (leave it to others to debate).

IV. Discussion

Our findings suggest that reductions in urban poverty and inequality had modest effects on rural poverty and inequality, much smaller than the effects of reductions in rural poverty and rural inequality on urban poverty and inequality in pre- reform India. More importantly, we discover that the dominate development flows are generated from the rural sectors and infiltrated to the urban sectors. Additionally, we show that policies that reduce urban inequality and poverty were not particularly effective in the rural areas. This reve- lation reaffirms the need for rural-based growth in developing agricultural economies (Lipton 1977; Eastwood and Lipton 2004). For such economies, urban-based public policies can have weak or even negative consequences in poverty and inequality reduction. Strategies designed to assist the urban poor might well be offered in conjunction with policies for the rural sector.

Acknowledgements

We acknowledge the Howard G Buffett Foundation and United States Agency for International Development for providing the resources to conduct this study. The views expressed in this article are solely of the authors and any limitations of the research are solely and equally shared by the authors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the Howard G Buffett Foundation (http://www.thehowardgbuffettfoundation.org/) and United States Agency for International Development.

1The impulses reported here are to a one SE shock in each of the associated series. The shock is positive. In reading the associated Figures 3 and 4, one should keep in mind that India’s pre-reform policy was to reduce poverty; thus, the shock should be multiplied by −1 to give a reduction in poverty. We leave the shocks in the outputted form and trust the reader to make this mental adjustment.

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