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Modeling the Investment Structure Through
Micro-ﬁnance in Greater Rangpur
Hasan Shahriar Miraj
Institute of Statistical Research and Training
University of Dhaka
June 23, 2015
Hasan Shahriar Miraj (I.S.R.T) Modeling the Investment Structure Through Micro-ﬁnance in Greater RangpurJune 23, 2015 1 / 27

Acknowledgement
Acknowledgement

Acknowledgement
Acknowledgement
1 Institute of Microﬁnance

Acknowledgement
Acknowledgement
2 Dr. Atunu Rabbani
Professor, Department of Economics
University of Dhaka.

Acknowledgement
Acknowledgement
2 Dr. Atunu Rabbani
Professor, Department of Economics
3 Paritosh Kumar Roy
Lecturer, I.S.R.T

Outline
Outline
Idea of the study
Background of the study
Objectives of the study
Methodology
Analysis
Conclusion

Introduction Idea
Idea of the study

Introduction Idea
Idea of the study
Prof. Dr. Mohammad Younus

Introduction Idea
Idea of the study
Grameen Bank

Introduction Idea
Idea of the study
Grameen Bank
Microcredit

Introduction Background
Background of the study
Palli Karma Sahayak Foundation (PKSF) initiated the project entitled
Programmed Initiative for Monga Eradication (PRIME) in the greatest
Rangpur region in 2006. Initially it was introduced in ﬁve upazillas
(sub-districts) of Lalmonirhat and later PKSF expanded the program
to cover all ﬁve districts of the current Rangpur Divisions (Gaibandha,
Kurigram, Nilphamari and Rangpur being the other four districts)
To facilitate the support for the ultra-poor in the Rangpur region
PKSF initiated PRIME which was later supported by Department for
International Development (DFID) under Promoting Financial Service
for Poverty Reduction (PROSPER) from July, 2007.

Introduction Background
The program design has changed somewhat over the years while
returning many of the core aspects of the initial intervention at place.
Micro-finance support through both micro-credit (typically associated
with some income generating activity or IGA) and Mobilizing savings
from the poor households has been the crux of the program all along.
There were also multiple types of micro-finance products covering
both flexible and emergency in nature, albeit emergency loans
constituting a small fraction of total loans disbursed. There were also
some ancillary non-credit financial services such as remittance services
offered to the PRIME beneficiaries.
As a result the economic status of the household of PRIME benefiters is
gradually changing.

Overview of data Data variable
Data variable
According to the objectives, we assume factors related to the investment
are converts under the subtitle-
1 Borrowing loan from micro-ﬁnance.
2 Borrowing loan from other sources like bank loan.
3 Household size.
4 Are they PRIME participant ?
5 Year of education of household.
6 Number of micro-ﬁnance loan taking by household.

Overview of data Graphical presentation
Histogram of Investment
Log(Investment)
Frequency
4 6 8 10 12 14
050100150200250300
Figure: Histogram of Investment

Histogram of Micro-ﬁnance loan
Log(Micro−loan)
Frequency
7 8 9 10 11 12
0100200300400
Figure: Histogram of Micro-ﬁnance loan

Other-source loan
Log(Other−Source Loan)
Frequency
4 6 8 10 12
050100150200250
Figure: Histogram of Other-source loan

Number of Loan
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468101214
Number of loan
log(Investment)
Figure: Box-plot of Number of Loan vs investment

Household size
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Household Size
log(Investment)
Figure: Box-plot of Household size vs investment

Education of Household Head
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0 1 2 3 4 5 6 7 8 9 12
468101214
Education of HH head
log(Investment)
Figure: Box-plot of Household head education year vs investment

Prime Participation
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Participants Control
468101214
Prime participations
log(Investment)
Figure: Box-plot of PRIME participation vs investment

Overview of data Data summarizing
Data summarizing
We divide the total number investor into four categories. They are-
1 Category-1:The HH who borrowed only micro-finance loan
2 Category-2:The HH who borrowed only other sources loan
3 Category-3:The HH who borrowed both types of loan
4 Category-4:The HH who hadn’t borrow any kinds of loan
Table: Borrower vs Investor for different category
case No loan Micro-finance loan Other-source loan Both loan total
Lone borrower 2489 1140 1394 952 5975
Investor 363 465 301 370 1499

Table: Percent of Investor vs diﬀerent amount of investment
Loan Type no invest <10000 10001-30000 >30000
No loan 86.90 7.12 3.70 2.24
Other source loan 79.51 12.71 5.71 1.90
Micro-ﬁnance loan 61.11 18.88 14.62 5.71
Both loan 62.50 20.36 13.20 3.81
Here arise some question-

No loan 86.90 7.12 3.70 2.24
Both loan 62.50 20.36 13.20 3.81
Is HH invest money taking micro-ﬁnance loan ?

No loan 86.90 7.12 3.70 2.24
Both loan 62.50 20.36 13.20 3.81
If they take micro-ﬁnance loan then what is the impact in investment?

No loan 86.90 7.12 3.70 2.24
Both loan 62.50 20.36 13.20 3.81
If they take micro-finance loan then what is the impact in investment?
What is the impact of Micro-finance for different categories
investment?

Objective
Objective of the study
As mentioned earlier this study aimed at ﬁnding a relationship with the
investment amount and the micro-ﬁnance. Along with this the other
objectives of the study are-

Objective
To see the changing economic status of household in greater Rangpur.

Objective
To ﬁt logistic regression model to see the direct relationship between
investment and micro-ﬁnance.

Objective
To ﬁt ordinal logistic model to see the impact of diﬀerent variable on
categorized investment.

Objective
To fit ordinal logistic model to see the impact of different variable on
categorized investment.
To fit censored Tobit model for the continuous variable investment.

Methodology
Methodology
Logistic regression model
1 Maximum likelihood estimation
2 Newton-Raphson Method
Ordinal logistic regression model
Proportional odds ratio
Tobit regression model
Maximum likelihood estimation

Analysis Logistic model
Logistic analysis
The outcome of the logistic regression analysis is-
Table: Results of Logistic regression analysis
Coeﬃcients Estimate Std error P-value
Intercept -1.722 .129 2×10−16
Micro-ﬁnance 7.38×10−05 5.75×10−06 2×10−16
Other-sources .00514 .002607 .000286
HH size .00053 .0015 .0489
HH head education year -.1227 .00816 .0154
Null deviance: 3763.6 on 3455 degrees of freedom
Residual deviance: 3526.2 on 3450 degrees of freedom
AIC: 3538.2

Analysis Logistic model
We are mainly interested in the relative goodness of fit of the model, but
nevertheless, the high residual deviance shows that the model cannot be
accepted to have been likely to generate the data (pchisq
(3526.2; 3450) ≈ 1). However, it certainly fits the data better than the
null model (which means that a fixed mean probability of deletion is used
for all cells): Chisq (3763.6 − 3526.2; 3455 − 3450) ≈ 1.

Analysis Ordered logistic model
Ordered logistic analysis
Table: Number of investor vs diﬀerent categories loan
Loan Type No invest <10000 10001-30000 >30000
Other Loan 654 105 47 16
Micro-credit Loan 383 119 92 36
Both Loan 341 111 72 21
No Loan 1268 104 54 31
The following proportional odds model was ﬁtted to these data:
log π1
π2+π3+π4
= β01 + β1x1 + β2x2 + β3x3
log π1+π2
π3+π4
= β02 + β1x1 + β2x2 + β3x3
log π1+π2+π3
π4
= β03 + β1x1 + β2x2 + β3x3

The analysis result is:-
Residual deviance: 11.16418 on 6 degrees of freedom
Log likelihood: -40.09469 on 6 degrees of freedom
Table: Ordered Logistic Regression Analysis
Coeﬃcients Estimate Std.error z-values
β01 0.53823 0.086928 6.19166
β02 1.52964 0.093316 16.39204
β03 2.90874 0.124379 23.38613
β1:Micro-ﬁnance -1.11315 0.116824 -0.96856
β2:No loan 1.35563 0.116253 11.66098
β3:Other loan 0.83432 0.122166 6.82941

For this model the log likelihood l(b) =-40.09469. For the minimal model,
with only β01, β02 and β03 the maximum value is l(bmin) = −51.26, so
likelihood Chi square statistic C = 2 × (−40.09469 + 51.26) = 22.32, and
pseudo R2 = (−51.26 + 40.09469)/(−51.26) = .217 For micro-ﬁnance the
estimated probabilities are ˆπ1 = 0.62548, ˆπ2 = 0.1936, ˆπ3 = 0.12916,
ˆπ4 = 0.05175. The probabilities for other covariates patterns are-
Table: Expected probablity for investment
Loan Type No invest <10000 10001-30000 >30000
Other-source loan 0.797 0.116 0.062 0.023
Both 0.631 0.190 0.126 0.051
No loan 0.869 0.077 0.039 0.013

Analysis Tobit model
Tobit model
According to the data set provided by PRIME borrowing data the
structural equation will be-
yi =
y∗
i if yi > 0
0 if yi = 0
Observations:
Total Left censored Uncensored Right censored
3456 2646 810 0

Analysis Tobit model
Table: Results of Tobit regression analysis
Coefficients Estimate Std error P value
Intercept -73850 4689 2×10−16
Borrowing money from micro-finance 2.501 .1120 2×10−16
Borrowing money from 1.629 .1014 2×10−16
HH size 1325 880.7 0.132
HH head education year 815.1 506.9 0.108
Prime participants 1789.1 2862.2 0.522
Log sigma 10.99 .0262 2×10−16
Here the result shows that micro-finance and other source of loan both
have a significant effect on investment. With one unit change in
micro-finance investment changes almost 2.5 unit. On the other hand one
unit change in other source loan increase the investment 1.6 unit.
Household size also have an impact on investment.

Conclusion
Conclusion
The overall summary of the study are-
The independent variable ‘Household size’ have impact on investment.
With increase of household size probability of investment is increasing.
The independent variable ‘PRIME participation’ have no impact on
investment.
The independent variable ‘Household head education year’ have no
impact on investment.
The independent variable ‘Other sources loan’ have impact on
investment less than borrowing loan from micro-ﬁnance.
The independent variable ‘Borrowing loan from micro-ﬁnance’ have
great impact on who have invested in Rangpur.

Conclusion
Thank You

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