MEASURING FINANCIAL INCLUSION: AN AXIOMATIC APPROACH

Satya R. Chakravarty

Indian Statistical Institute (ISI), Kolkata, India satya@isical.ac.in

Rupayan Pal

Indira Gandhi Institute of Development Research (IGIDR), Mumbai, India rupayan@igidr.ac.in

1

• Develop an axiomatic measure of financial inclusion. This measure

is readily implementable and useful to determine policy priorities

to promote financial inclusion.

• Examine the usefulness of supply side data on banking services to

measure financial inclusion.

• Analyze financial inclusion across sub-national regions of India

during 1972-2009, using panel data econometrics techniques.

2

Definition

• In a broad sense financial inclusion refers to delivery of formal

financial services to each and every member of an economy.

• Financial inclusion can be defined as a process that serves to

remove the barriers and overcome the inabilities of some societal

groups and individuals, including the poor and disadvantaged, to

access and use low-cost, fair and safe formal financial services,

such as credit, deposits, insurance and payments, whenever needed

(Leyshon and Thrift, 1995; Carbo et al. 2005; Conroy, 2005;

Mohan, 2006; Rangarajan Committee, 2008).

3

Why an Index?

• It is evident that financial inclusion is a multidimensional

phenomenon.

• It is well documented that performance of financial system

significantly varies across different dimensions, across

geographical regions as well as over time (Beck et al., 2007;

Honohan, 2008; Pal and Vaidya 2011).

• Given the diversified picture of performance of financial system

along different dimensions, it is necessary to design an appropriate

index of financial inclusion in order to assess (a) the overall

performance of financial system in an economy in terms of

financial inclusion, (b) its dynamics and (c) its variation across

geographical regions.

4

Formal Framework

• Assume that the financial system has 1k ≥ dimensional activities.

• Each dimension represents a functioning.

• Let ix be the attainment level or the value of functioning i .

• The lower and upper bounds of ix are denoted by im and iM

respectively.

• Assuming that the bounds im and iM are attainable, we have

[ ],i i ix m M∈ .

• For empirical applications sample minimum and maximum can be

chosen as values of im and iM respectively.

5

• An indicator for functioning i is a real valued function A that

associates a value ( ), ,i i iA x m M to each [ ],i i ix m M∈ .

• We assume that A is continuous in its arguments. Continuity

ensures that minor observational errors on ,i ix m and iM will

generate minor changes in the value of A .

• There are numerous ways in which we can specify A explicitly.

We will focus here on one which is intuitively reasonable and has a

relation with the UNDP indicator for an attribute. This form of A is

given by

( ), ,r i i iA x m M =r

i i

i i

x mM m

⎛ ⎞−⎜ ⎟−⎝ ⎠

, (1)

where 0 1r< < is a constant.

The parameter r can be interpreted as an inclusion sensitivity

parameter in the sense that given ,i ix m and iM , as the value of r

decreases ( ), ,r i i iA x m M increases.

6

Axiom 1: Normalization: ( )1 ,

, ,0 .

i ii i

i i

if and only if x MA x m M

if and only if x m=⎧

= ⎨ =⎩

Axiom 2: Monotonicity: Given im and iM , for any 0δ > such that [ ],i i ix m Mδ+ ∈ ,

( ), ,i i iA x m Mδ+ - ( ), , 0.i i iA x m M >

Axiom 3: Homogeneity: For any 0c > , ( ), ,i i iA x m M = ( ), ,i i iA cx cm cM .

Axiom 4: Lower difference in gain at higher levels of attainment difference: Let

[ ],i i ix m M∈ be any attainment level for functioning .i.Then for any 0δ >

such that [ ],i i ix m Mδ+ ∈ the magnitude of gain in the indicator of

functioning .i, ( ), ,i i iA x m Mδ+ - ( ), ,i i iA x m M is a decreasing function of ix .

7

• It is straightforward to verify that our index fulfills the four basic

axioms for all values of0 1r< < . However if 1,r = rA satisfies the first

three axioms but not the ‘Lower difference in gain at higher levels

of attainment difference’. This particular case of rA was suggested

as an indicator of functioning .i by Sarma (2008).

• Since the difference ( )1 rA− represents the shortfall of the actual

value of the index from its maximum attainable value, it can be

regarded as a deprivation function for functioning .i If 1,r = the

deprivation function coincides with the one suggested by UNDP.

8

• By averaging the individual indicators in (1) across functionings

we get our desired financial inclusion index:

( ) ( )( )1 1 1, , ,....., , ,r r r k k kI A x m M A x m M1

1rk

i i

i i i

x mk M m=

⎛ ⎞−= ⎜ ⎟−⎝ ⎠∑ . (2)

• Like the individual indicator, the global index is a decreasing

function of r for a given ,i ix m and iM .

• For any 0 1r< < , the marginal rate of substitution between

functionings i and j along an iso-financial contour is given by

( ) ( )( ) ( ) ( )( ) 1r r

j j i i i i j jM m M m x m x m−

− − − − , which is independent of the

level of attainment of a third functioning. Clearly, it is non-

constant.

9

• As we go down along the contour more and more units of the

quantity of the functioning plotted on the horizontal axis are

required for substitution of each additional unit of the other to keep

the level of inclusion unchanged and the substitution becomes

increasingly difficult. As the value of r reduces the contours

become more convex to the origin.

• If we consider 1r = , any two functionings are perfect substitutes

because of constancy of the marginal rate of substitution between

them.

10

We now consider the following basic axioms for an arbitrary financial

inclusion index, I which is defined as a real valued function of the

individual indicators ( ), ,i iA x m M 1, where1 i k≤ ≤ .

(1) Boundedness : ( ) ( )( )1 1 10 , , ,....., , , 1k k kI A x m M A x m M≤ ≤ , where the lower

bound zero and the upper bound one are achieved if and only if for

all { }1,2,..,i k∈ , i ix m= and i ix M= respectively.

(2) Global monotonicity: If ( )1,...., kx x and ( )1,...., ky y are two functioning

attainment vectors where i ix y≥ with > for at least one i and [ ], ,i i i ix y m M∈ ,

1 i k≤ ≤ , then ( ) ( )( )1 1 1, , ,....., , ,k k kI A x m M A x m M > ( ) ( )( )1 1 1, , ,....., , ,k k kI A y m M A y m M .

1Dependence of the financial inclusion index on the individual indicators only may be interpreted as ‘independence of irrelevant information.’ An assumption of this type is frequently made in the literature, for instance, social welfare is regarded as a function of individual welfare levels.

11

(3) Global homogeneity: ( ) ( )( )1 1 1, , ,....., , ,k k kI A x m M A x m M =

( ) ( )( )1 1 1 1 1 1, , ,....., , ,k k k k k kI A c x c m c M A c x c m c M , where 0ic > , { }1,2,..,i k∈ ,is a scalar.

(4) Global lower difference in gain at higher levels of attainment

difference: For any [ ],i i ix m M∈ and for any 0≥iδ , with > for at least

one i , such that [ ],i i i ix m Mδ+ ∈ , { }1,2,..,i k∈ , the magnitude of the gain

( ) ( )( )1 1 1 1, , ,....., , ,k k k kI A x m M A x m Mδ δ+ + ( ) ( )( )1 1 1, , ,....., , ,k k kI A x m M A x m M− is a

decreasing function of sxi ' for which si 'δ are positive.

(5) Symmetry:

( ) ( )( )( ) ( ) ( )( )kkkkkk MmxAMmxAIPMmxAMmxAI ,,,,,,,,,,,, 111111 LL = ,

where P is a k k× permutation matrix2.

2 A non-negative square matrix of order k with entries 0 and 1 is called a k k× permutation matrix if each of rows and columns sums to unity.

12

• It is easy to verify that for all values of 0 1r< < the global index

satisfies all the five axioms we have introduced above.

• Since rI is the arithmetic mean of dimension-wise indicators, we

can use it to make quantitative assessment of individual

functionings.

• The quantity ( ), , /i r i i iT A x m M k= may be regarded as the contribution

of functioning i to financial inclusion.

13

• The percentage contribution of functioning i then becomes

( ) ( ), , 100 /r i i i rA x m M kI .

• This kind of breakdown becomes helpful for identifying the

dimensions that are more /less sensitive to financial inclusion. The

less sensitive functionings require attention from a policy

perspective to reach higher level of financial inclusion.

14

• The index suggested by Sarma (2008) is given by

( ) ( )

k

mMxMS

k

iiiii∑

=

−−−= 11 . (3)

• This index first averages, in a particular way, the shortfalls of

individual attainments from their maximal attainable values,

namely ( )i iM x− ,as fractions of the ranges ( )i iM m− across different

functioning.

• Since the attainable upper bound of the average is one, its

difference from one gives us the financial inclusion index. It

satisfies all of our axioms for a financial inclusion index, except

axiom (4) in general. In fact, it attaches equal weight to attainment

difference at all levels of attainment.

• Because of its non-linear formulation it cannot be employed to

determine the percentage contributions made by different

functionings to the overall level of financial inclusion.

15

Measuring Financial Inclusion using Data on Outreach of Banking Services

• As argued before, financial inclusion refers to easy access and use of formal

financial services by each and every individual of a society.

• In other words, if an individual has easy access to formal financial services,

which can be reflected through the use of formal financial services by

him/her, that individual may be said to be financially included, otherwise

not. In a more strong sense, an individual can be said be fully (partially)

financially included, if his/her need for financial services is completely

(partially) served by the formal financial agencies such as banks.

• Clearly, to gauge the extent of financial inclusion directly, it is ideal to have

the necessary information at the individual level.

• It is more challenging is to measure financial inclusion using relatively

easily available data, such as data on outreach of banking services.

16

• We examine the validity of supply side information based estimate of rI

using data from 17 major states in India for the years 1982, 1992 and 2002,

for which comparable data on share of households using institutional

credits (SHIC) from household level survey is available.

• Given the availability of supply side information of banking services across

states in India, we consider the following six indicators of outreach of

banking services

17

(a) Geographic penetration, which is measured as the number of bank

branches per thousand square kilometer area.

(b) Demographic penetration, which is measured as the number of bank

branches per lakh people.

(c) Deposit account per thousand people, i.e., the number of deposit accounts

per thousand people.

(d) Credit account per thousand people, i.e., the number of loans per

thousand people.

(e) Deposit-Income ratio, i.e., the ratio of average size of deposits to per capita

net state domestic product.

(f) Credit-Income ratio, i.e., the ratio of average size of loans to per capita net

state domestic product.

18

• Simple correlation analysis reveals that there is significant positive

correlation between estimated rI and survey based measure of households’

access to formal credit services.

• Regression Results

)4()1991(

(0.064).03190)1981(

(0.185).02680)(

(0.000)39811.0

)0.461(0.0313-)( DummyYearDummyYearIIndexruralSHIC r +++=

R2 = 43.15%

)5()1991(

(0.175).02290)1981(

0.032) (.07050)(

(0.001)0.4405

)0.053( 0.095-)( DummyYearDummyYearIIndexurbanSHIC r +++=

R2 = 33.19%,

SHIC: share of households using institutional credits

19

• Results of these regressions suggest that supply side information based

estimates of rI are positively associated with the share of households using

institutional credits (SHIC) in both rural and urban areas.

• These results are in line with the findings of Beck et al (2007) based on

cross-country data.

20

Financial Inclusion across States in India and Role of Social Banking Program

• Each of the six indicators of outreach of banking services improved at a

rapid rate during the period of social banking (1977 – 1990) in India:

geographic penetration, demographic penetration, deposit account per

thousand people, credit account per thousand people, deposit-income ratio as

well as credit-income ratio grew by more than 11%, 6%, 17%, 21%, 3% and

5%, respectively, per annum.

• However, we observe mixed outcome in the post social banking era

(1991-2009). While credit-income ratio and deposit-income ratio increased

at a higher rate (7.37% and 5.29%, respectively per annum) in the post social

banking era, deposit account per thousand people and credit account per

thousand people grew at a considerably lower rate (1.85%, 2.34% and

2.13%, respectively, per annum) compared to that in the social banking

period.

• Further, demographic penetration of bank branches has declined from

7.29 in 1990 to 6.97 in 2009. Somewhat similar pattern is also observed in

case of most of the sates in India.

21

• In India, the level of financial inclusion increased by more than 100% from

0.152 in pre social banking period to 0.307 in the social banking period,

whereas it increased to only 0.419 in the post social banking period.

• Similar pattern is also observed in each of the sample states.

• Nonetheless, there are significant variations across states and over time in

terms of financial inclusion.

• The range of sub-period wise average financial inclusion increased from

0.231 in the pre social banking period to 0.327 in social banking period, and

further increased to 0.362 in the post social banking period.

• Though financial inclusion has increased over the years in most of the cases,

in six states (Bihar, Gujarat, Madhya Pradesh, Rajasthan, Tripura and West

Bengal) financial inclusion has actually declined in 2002 compared to that in

1992.

22

• Finally, in order to identify the policy priorities, we compute the percentage

contributions of the individual indicators of banking sector outreach to

overall financial inclusion across states in the year, 2009.

• It is evident that there are variations in terms of percentage contributions of

different attributes to overall achievement of the states in terms of financial

inclusion.

• In India, contribution of geographic penetration is the lowest (10.24%),

whereas the number of deposit accounts per thousand people contributes the

highest (20.84%), to overall achievement.

• Contribution of geographic penetration is the lowest also in case of ten states

(Andhra Pradesh, Assam, Gujarat, Himachal Pradesh, Karnataka, Madhya

Pradesh, Maharashtra, Orissa, and Rajasthan) in India.

• In the remaining seven states, it is either the number of credit accounts per

thousand people (in Punjab, Uttar Pradesh and West Bengal) or credit

income ratio (in Bihar, Kerala and Tripura) that contributes the least to

overall financial inclusion.

• It seems to imply that improvements in geographic penetration of bank

branches and credit availability should get the policy priority to enhance

financial inclusion in India.

23

• Results obtained from the econometric analysis indicate that the social

baking program in India during 1977-1990 has played crucial role to

improve the levels of financial inclusion across states.

• It seems that India could have achieved higher level of financial inclusion

during the last two decades, if the social banking program continued to be

effective, ceteris paribus.

• It also shows that overall economic development of a region is positively

associated, whereas dependence on agriculture and allied activities is

negatively associated, with the level of financial inclusion.

• The analysis of this paper reveals that acceleration of geographic

penetration of banking services and credit availability should get the policy

priority to enhance financial inclusion across states in India.

24

Table 5: Summary Statistics of Indicators of Outreach of Banking in India: 1972-2009 Variable Number of

Observations Mean SD Minimum Maximum

Demographic Penetration 646 6.494 2.681 0.846 14.282 Geographic Penetration 646 22.710 18.251 1.335 107.300 Deposit account per thousand people 646 334.871 202.270 11.249 962.948 Credit account per thousand people 646 54.231 39.668 0.651 255.016 Deposit-Income Ratio (%) 646 33.126 17.288 3.021 118.055 Credit-Income ratio (%) 646 18.907 13.401 0.705 110.848 Notes: Demographic (Geographic) Penetration is measured as the number of bank branches per 10 lakh people (per 1000sqkm). Deposit (Credit) A/C per-capita is measured as the number of deposit (credit) account per 1000 population. Deposit (Credit) Income Ratio (%) is the ratio of deposit (credit) size to income multiplied by 100.

25

Table 8: Predicting Use of Institutional Credit Services across States in India with Financial Inclusion Index

States

Year: 1982 Year: 1992 Year: 2002

Fina

ncia

l Inc

lusi

on In

dex

Share of households using institutional credit

Fina

ncia

l Inc

lusi

on In

dex

Share of households using institutional credit

Fina

ncia

l Inc

lusi

on In

dex

Share of households using institutional credit

Rural Area Urban Area Rural Area Urban Area Rural Area Urban Area A

ctua

l

Pred

icte

d

Act

ual

Pred

icte

d

Act

ual

Pred

icte

d

Act

ual

Pred

icte

d

Act

ual

Pred

icte

d

Act

ual

Pred

icte

d

Andhra Pradesh 0.275 0.111 0.112 0.076 0.104 0.396 0.165 0.159 0.143 0.102 0.411 0.149 0.137 0.108 0.091

Assam 0.125 0.011 0.054 0.013 0.037 0.261 0.030 0.106 0.052 0.042 0.274 0.016 0.084 0.022 0.030

Bihar 0.216 0.039 0.089 0.048 0.078 0.373 0.094 0.150 0.038 0.092 0.335 0.057 0.108 0.033 0.057

Gujarat 0.306 0.125 0.124 0.105 0.118 0.411 0.120 0.164 0.113 0.109 0.408 0.147 0.136 0.110 0.090

Haryana 0.279 0.058 0.114 0.041 0.106 0.406 0.216 0.162 0.070 0.107 0.410 0.156 0.137 0.074 0.091

Himachal Pradesh 0.281 0.089 0.114 0.050 0.107 0.471 0.130 0.187 0.134 0.136 0.474 0.102 0.162 0.089 0.120

Karnataka 0.363 0.143 0.146 0.413 0.144 0.491 0.220 0.195 0.152 0.145 0.493 0.161 0.169 0.106 0.128

Kerala 0.463 0.253 0.185 0.250 0.189 0.590 0.283 0.234 0.269 0.189 0.640 0.328 0.226 0.313 0.194

Madhya Pradesh 0.187 0.131 0.078 0.084 0.065 0.337 0.151 0.135 0.097 0.076 0.313 0.152 0.099 0.109 0.047

Maharashtra 0.343 0.173 0.138 0.137 0.135 0.459 0.195 0.183 0.147 0.130 0.483 0.228 0.165 0.119 0.124

Orissa 0.166 0.175 0.070 0.089 0.056 0.318 0.185 0.128 0.115 0.067 0.324 0.179 0.104 0.130 0.053

Punjab 0.408 0.102 0.164 0.067 0.164 0.555 0.181 0.220 0.072 0.174 0.592 0.116 0.208 0.053 0.172

Rajasthan 0.193 0.123 0.080 0.092 0.068 0.307 0.138 0.124 0.083 0.062 0.305 0.124 0.096 0.057 0.044

Tamil Nadu 0.349 0.117 0.141 0.112 0.138 0.492 0.167 0.196 0.150 0.145 0.508 0.139 0.175 0.111 0.135

Tripura 0.211 NA 0.087 NA 0.076 0.367 0.215 0.147 0.068 0.089 0.318 NA 0.101 NA 0.050

Uttar Pradesh 0.216 0.073 0.089 0.056 0.078 0.366 0.125 0.147 0.059 0.089 0.374 0.102 0.123 0.046 0.075

West Bengal 0.323 0.106 0.131 0.079 0.126 0.461 0.206 0.184 0.122 0.131 0.437 0.121 0.147 0.073 0.103

ALL-INDIA 0.272 0.108 0.111 0.092 0.103 0.398 0.156 0.159 0.118 0.103 0.401 0.134 0.133 0.093 0.087

Notes: Financial Inclusion Index corresponds to r = 0.75, and is measured using State-level data on banking services. Actual values of share of households using institutional credit services are collated from various reports on latest three rounds of All India Debt and Investment Survey, which provides household level data, conducted by the National Sample Survey Organization, Ministry of Statistics and Program Implementation, India, during 1981, 1991 and 2001.

26

Table 10: Period-wise Average Levels of Financial Inclusion across States in India: 1972-2009 State/Region

Mean of Financial Inclusion Index (I) Tests of Differences Pre social-

banking period: 1972-1976

Social-banking period:

1977-1990

Post social banking period:

1991-2009

H0: Ipre-sb=Isb H1: Ipre-sb<Isb

p-value

H0: Isb=Ipost_sb H1: Isb<Ipost-sb

p-value

Ipre-sb Rank Isb Rank Ipost-sb Rank Andhra Pradesh 0.129 9 0.310 10 0.433 8 0.0000 0.0000 Assam 0.040 16 0.168 17 0.286 17 0.0001 0.0000 Bihar 0.090 12 0.252 12 0.360 12 0.0001 0.0000 Gujarat 0.221 5 0.334 8 0.403 10 0.0000 0.0000 Haryana 0.142 8 0.315 9 0.428 9 0.0000 0.0000 Himachal Pradesh 0.122 10 0.336 7 0.485 6 0.0000 0.0000 Karnataka 0.228 4 0.406 3 0.520 5 0.0000 0.0000 Kerala 0.244 1 0.495 1 0.648 1 0.0000 0.0000 Madhya Pradesh 0.076 14 0.231 14 0.328 15 0.0001 0.0000 Maharashtra 0.238 2 0.376 5 0.525 4 0.0000 0.0000 Orissa 0.031 17 0.210 16 0.341 14 0.0000 0.0000 Punjab 0.236 3 0.451 2 0.589 2 0.0000 0.0000 Rajasthan 0.088 13 0.226 15 0.316 16 0.0001 0.0000 Tamil Nadu 0.217 6 0.386 4 0.536 3 0.0000 0.0000 Tripura 0.042 15 0.238 13 0.351 13 0.0000 0.0000 Uttar Pradesh 0.102 11 0.261 11 0.381 11 0.0001 0.0000 West Bengal 0.201 7 0.356 6 0.453 7 0.0000 0.0000 Range 0.213 0.327 0.362 ALL-INDIA 0.152 0.307 0.419 0.0000 0.0000 Notes: Financial inclusion index is measured by considering r = 0.75.

27

Table 11: Financial Inclusion Index and Percentage Contributions of Attributes across States in India: 2009

Stat

e/R

egio

n

Per-

capi

ta In

com

e (N

SDP)

Fina

ncia

l Inc

lusi

on

Inde

x

Ran

k - F

inan

cial

In

clus

ion

Percentage contribution of

Geo

grap

hic

Pene

trat

ion

Dem

ogra

phic

Pe

netr

atio

n

Cre

dit a

ccou

nt

per

thou

sand

pe

ople

D

epos

it ac

coun

t pe

r th

ousa

nd

peop

le

Cre

dit-

inco

me

ratio

Dep

osit-

Inco

me

ratio

Kerala 48111.13 0.7713 1 21.608 19.554 16.096 19.929 9.534 13.278 Maharashtra 58095.10 0.7628 2 7.152 12.325 21.850 15.777 21.215 21.680 Punjab 45909.06 0.6971 3 16.507 21.204 9.733 23.705 12.548 16.303 Karnataka 36882.59 0.6773 4 9.476 18.460 15.871 19.928 16.847 19.418 Tamil Nadu 44584.38 0.6695 5 13.185 16.581 19.346 20.280 16.239 14.368 Andhra Pradesh 36639.96 0.5815 6 9.051 17.859 18.719 22.918 16.026 15.427 Himachal Pradesh 42914.36 0.5756 7 6.966 28.958 12.435 25.289 8.939 17.413 Haryana 55974.41 0.5387 8 17.149 21.162 11.251 24.225 11.139 15.074 West Bengal 30237.19 0.5085 9 20.589 15.534 8.712 20.413 14.632 20.120 Gujarat 48583.96 0.4699 10 10.644 21.150 11.175 25.696 13.525 17.810 Uttar Pradesh 16428.11 0.4504 11 17.661 15.628 10.264 21.809 12.300 22.338 Orissa 23793.21 0.4313 12 9.456 20.670 15.392 20.356 13.280 20.846 Tripura 33318.74 0.3985 13 11.732 20.670 18.230 24.172 7.608 17.589 Rajasthan 23709.39 0.3948 14 7.429 20.854 12.803 22.024 17.614 19.277 Madhya Pradesh 19858.11 0.3918 15 8.206 20.058 12.437 20.321 16.037 22.941 Bihar 11117.44 0.3712 16 21.675 14.848 10.671 16.829 10.034 25.945 Assam 20125.21 0.3563 17 11.742 18.317 12.188 22.757 11.898 23.098 ALL-INDIA 38280.39 0.5266 10.244 17.554 14.893 20.884 16.550 19.874 Notes: Financial inclusion index is measured by considering r = 0.75. Per-capita NSDP is in Rupees, 2004-2005 prices.

28

Table 12: Results of Arellano and Bond (1991) GMM estimation

Dependent Variable: Financial Inclusion ( rI ) Explanatory Variables

(1) (2) (3) (4) (5) Coefficients (p-values)

Coefficients (p-values)

Coefficients (p-values)

Coefficients (p-values)

Coefficients (p-values)

Financial Inclusion, Lag 1

0.9947*** (0.000)

0.8920*** (0.000)

0.8689*** (0.000)

0.8415*** (0.000)

0.8448*** (0.000)

Sbank 0.0044*** (0.000)

0.0097*** (0.000)

0.0139*** (0.000)

0.0136*** (0.000)

0.0129*** (0.000)

Post-sbank – 0.0041 (0.217)

– 0.0101** (0.012)

– 0.0021 (0.539)

0.0029 (0.721)

0.0018 (0.700)

Trend 0.0016***

(0.000) 0.0010***

(0.008)

Per-capita income 0.0010***

(0.001) 0.0013***

(0.000) 0.0006***

(0.007)

Share of agriculture -0.0012***

(0.000)

Constant 0.0131*** (0.000)

0.0167*** (0.000)

0.0144*** (0.000)

0.0369*** (0.000)

0.0929*** (0.000)

Number of observations 612 612 612 612 612

Test for overall significance of the model

Chi2(3)= 41200.9 Prob>Chi2(3) = 0.000

Chi2(4)=102226.8 Prob>Chi2(4) = 0.000

Chi2(5)= 60733.0 Prob>Chi2(5) = 0.000

Chi2(4)= 63881.8 Prob>Chi2(4) = 0.000

Chi2(5)= 56152.9 Prob>Chi2(5) = 0.000

Sargan test Chi2(104) = 14.67 Prob>Chi2(104) =0.999

Chi2(104) = 15.07 Prob>Chi2(104) =0.999

Chi2(104) = 15.03 Prob>Chi2(104) =0.999

Chi2(104) = 13.27 Prob>Chi2(104) =0.999

Chi2(104) = 13.16 Prob>Chi2(104) =0.999

Test for serial correlation (2)

z = 1.14 Prob>z = 0.255

z = 1.24 Prob>z = 0.215

z = 1.39 Prob>z = 0.165

z = 1.52 Prob>z = 0.129

z = 0.40 Prob>z = 0.687

R-squared 0.992 0.986 0.988 0.983 0.985 Notes: We report the p-values of the coefficients in parenthesis below the reported coefficients. Following the prescription of Arellano and Bond (1991), reported coefficients are obtained from GMM two-step estimation and reported p-values are obtained from GMM one-step estimation. Needless to mention here that in each of the five regressions state specific fixed effects have been controlled for. *** indicates significance at 1% level and ** indicates significance at 5% level. Results of the overall significance test suggest that the estimated model is overall significant in all the five cases. Sargan test is a Chi2 test of over identifying restrictions, where the null hypothesis is ‘H0: over identifying restrictions are valid’. Results of Sargan test suggest that the instruments used for estimation are valid in each of the five cases. Test for serial correlation (2) is the Arellano Bond N(0, 1) test for second order serial correlation of errors, results of this test suggest that there is no second order serial correlation. The variable ‘Per-capita income’ is measured in Rupees thousand, at 2004-05 prices. ‘Share of agriculture’ is the percentage share of agriculture and allied activities out of total net state domestic product. Reported R-squared is calculated based on linear predictions after two-step GMM estimation.

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Table 13: Estimation Results by using different methods Dependent Variable: Financial Inclusion ( rI )

Explanatory Variables

FE (1)

FE (2)

FE (3)

FE (4)

FE (5)

Tobit (6)

FGLS (7)

PW (8)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Coeff. (p-values)

Financial Inclusion, Lag 1

0.9910*** 0.9146*** 0.9175*** 0.9393*** 0.9234*** 0.9234*** 0.9187*** 0.9193***

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Sbank 0.0073** 0.0079*** 0.0123*** 0.0133*** 0.0129*** 0.0129*** 0.0122*** 0.0131***

(0.015) (0.008) (0.000) (0.000) (0.000) (0.000) (0.000) (0.003)

Post-sbank – 0 .0015 – 0.0126*** – 0.0052 – 0.0001 – 0.0022 – 0.0022 0.0003 -0.0016

(0.689) (0.005) (0.104) (0.968) (0.469) (0.419) (0.930) (0.791)

Trend 0.0013*** 0.0006**

(0.000) (0.020)

Per-capita income 0.0009*** 0.0011*** 0.0010*** 0.0010*** 0.0005*** 0.0009***

(0.003) (0.000) (0.001) (0.000) (0.000) (0.000)

Share of agriculture -0.0004** -0.0004*** -0.0005***

-0.0004***

(0.046) (0.000) (0.000) (0.000)

Constant 0.0120*** 0.0179*** 0.0112*** 0.0077*** 0.0314** 0.0319*** 0.0419*** 0.0350***

(0.000) (0.000) (0.003) (0.003) (0.018) (0.000) (0.000) (0.000)

Number of observations

629 629 629 629 629 629 629 629

Hausman test Chi2(3)= 6.85 Prob>Chi2 = 0.077

Chi2(4)= 69.21 Prob>Chi2 =0.000

Chi2(5)= 76.46 Prob>Chi2 =0.000

Chi2(4)= 71.05 Prob>Chi2 = 0.000

Chi2(5)= 88.96 Prob>Chi2 =0.000

-- -- --

Test for overall significance of the model

F(3,16)= 30356 Prob>F= 0.000

F(4,16)= 23933 Prob>F= 0.000

F(5,16)= 24326 Prob>F= 0.000

F(4,16)= 19522 Prob>F= 0.000

F(5,16)= 25332 Prob>F= 0.000

LR Chi2(21)= 2967.49 Prob>Chi2=0.000

Wald Chi2(21) =134626 Prob>Chi2

= 0.000

Wald Chi2(21) = 94697 Prob>Chi2

=0.000

R-squared (overall) 0.9923 0.9907 0.9925 0.9927 0.9926 -- -- 0.9934

Notes: FE, Tobit, FGLS and PW indicate ‘fixed effects (within group) estimates’, ‘estimates from random effects Tobit regression with censored dependent variable’, ‘ cross-sectional time series feasible generalized least square estimates considering heteroskedastic panels with cross-sectional correlation and common AR(1) coefficient for all panels’ and ‘estimates from Prais-Winsten regression considering correlated panels corrected standard errors (PCSEs)’, respectively. In FE regressions, state specific fixed effects are controlled for. In Tobit, FGLS and PW regressions, 16 state dummy variables have been used as regressors to control for state-specific unobserved effects, coefficients of the state dummies are not reported in the table. In FGLS and PW estimations common AR(1) coefficients for all panels is found to be 0.0524 and 0.0592, respectively. *** indicates significant at 1% level. ** indicates significant at 5% level. We report the p-values of the coefficients in parenthesis below the reported coefficients. The variable ‘Per-capita income’ is measured in Rupees thousand, at 2004-05 prices. ‘Share of agriculture’ is the percentage share of agriculture and allied activities out of total net state domestic product. Null hypothesis for Hausman test is ‘Ho:Difference in coefficients not systematic’. Results indicate that we cannot accept the null hypothesis at 10% level of significance for specification (1), and at 1% level of significance for specifications (2), (3), (4) and (5). So, we choose fixed effects estimators over random effects estimators. Tests of overall significance of model indicate that in each case the model is overall significant.

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Figure 1: Financial inclusion in India and her states (1972-2009)