povertyandincomeinequa1.pdf

ARTICLE

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

http://www.tandfonline.com

http://crossmark.crossref.org/dialog/?doi=10.1080/13504851.2018.1486973&domain=pdf

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 ing’
(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.

http://www.phil.cmu.edu/projects/tetrad/

http://www.phil.cmu.edu/projects/tetrad/

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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450 S. KIBRIYA ET AL.

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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 ing 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.

452 S. KIBRIYA ET AL.

References

Bernanke, B.S. 1986. Alternative explanations of the
money-income correlation. Carnegie-Rochester confer-
ence series on public policy (Vol. 25, pp. 49-99).
North-Holland.

Census Data 2001: India at a Glance. Rural-Urban
Distribution. Office of the Registrar General and Census
Commissioner- India, 2002. Retrieved on 2015-11-26.

Chandra, B., M. Mukherjee, and A. Mukherjee. 2000. India
after Independence. New Delhi: Penguin Books.

Chickering, D. M. 2002. “Optimal Structure Identification
with Greedy Search.” Journal of Machine Learning
Research 3: 507–554.

Eastwood, R., and M. Lipton. 2004. Rural-Urban
Dimensions of Inequality Change. Inequality, Growth,
and Poverty in an Era of Liberalization and
Globalization. Oxford: Oxford University Press.

Lipton, M. 1977. Why Poor People Stay Poor: Urban Bias in
World Development. Cambridge: Harvard University
Press.

Pearl, J. 2000. Causality. Cambridge, UK: Cambridge University
Press.

Sims, C. 1980. “Macroeconomics and Reality.” Econometrica
48 (1): 1–48. doi:10.2307/1912017.

Spirtes, P., C. Glymour, and R. Scheines. 2000. Causation,
Prediction, and Search. Cambridge, MA: MIT Press.

Srinivasan, T. N., A. K. Sen. 1983. “Poverty and Famines: An
Essay on Entitlement and Deprivation.” American Journal
of Agricultural Economics 65 (1): 200–201. Oxford:
Clarendon Press, 1981, ix+ 257 pp. $17.95. doi:10.2307/
1240373.

Teitelbaum, E. J. 2004. “In the Grips of a Green Giant: How
the Rural Sector Defeated Organized Labor in India.”
Paper presented at the Political Economy Research
Colloquium at Cornell University, Ithaca, NY.

APPLIED ECONOMICS LETTERS 453

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Abstract
I. Introduction
II. Methodology
III. Data and results
IV. Discussion
Acknowledgements
Disclosure statement
Funding
References