Andhra Bank (Union Bank) Loan Approval Analysis

Solution

This paradoxical result, where the overall loan approval rate for Andhra Bank decreases while the approval rates for individual loan products remain stable or increase, can most likely be explained by Simpson's Paradox or an effect related to changes in the composition (mix) of loan applications.

Explanation of Simpson's Paradox in this Context:

Simpson's Paradox occurs when a trend appears in several different groups of data but disappears or reverses when these groups are combined. In this case, the "groups" are the different loan products (Agriculture, Small Business, Home, Vehicle).

The paradoxical outcome could arise if there has been a shift in the proportion of applications towards loan types that inherently have lower approval rates, even if the approval rate for that specific loan type itself has slightly improved or remained stable.

• Changing Loan Application Patterns:
  • Suppose last week, Andhra Bank received a large proportion of applications for loan types with historically higher approval rates (e.g., Vehicle loans at 88%, Agriculture loans at 84%).
  • This week, there might have been a significant increase in the number of applications for loan types that typically have lower approval rates (e.g., Small business loans at 77%, or perhaps a new, riskier sub-category not explicitly listed but included in the overall calculation).
  • For example, if there was a surge in applications for Small Business Loans (popular in Hyderabad) which have a 77% approval rate, and a relative decrease in applications for Vehicle Loans (88% approval rate), the overall weighted average approval rate could decline, even if the approval rate for Small Business Loans themselves remained at 77% (or even slightly increased).
• Impact of Weights (Proportions):
  • The overall approval rate is a weighted average of the approval rates of individual loan products, where the weights are the proportion of total applications each product represents.
  • If the "weight" (proportion of applications) shifts towards products with lower approval rates (like those potentially sought by farmers in Guntur if their numbers increased but for a slightly riskier agriculture sub-loan, or more business loans in Hyderabad), the overall average will be pulled down.
• Illustrative Example:

  Let's say:

  Period 1 (Last Week): Total Applications = 200

  • Agriculture (84% rate): 100 apps -> 84 approved
  • Small Business (77% rate): 100 apps -> 77 approved
  • Total Approved: 161. Overall Rate: 161/200 = 80.5%

  Period 2 (This Week): Total Applications = 200

  • Agriculture (85% rate, increased): 50 apps -> 42.5 (let's say 43) approved
  • Small Business (77% rate, stable): 150 apps -> 115.5 (let's say 116) approved
  • Total Approved: 159. Overall Rate: 159/200 = 79.5%

  In this example, the Agriculture loan approval rate increased, and Small Business stayed the same. However, because the proportion of applications shifted towards the Small Business loans (which have a lower approval rate), the overall approval rate dropped from 80.5% to 79.5%, demonstrating the paradox.

Thus, the decrease in the overall approval rate from 85% to 82% for Andhra Bank is likely due to a compositional shift in the loan applications received across the Telugu states, with a higher proportion of applications now falling into loan categories that, despite stable or slightly improved individual approval rates, are inherently harder to approve than the mix of loans applied for previously.

Solution

To investigate if the paradoxical effect on Andhra Bank's loan approval rates is due to varying approval rates or changing application patterns between urban branches (e.g., Cyberabad) and rural branches (e.g., in Rayalaseema regions), I would perform a stratified analysis based on branch type or location.

Steps for Investigation:

1. 1. Segment Branches:
   • Categorize all branches into "Urban" (e.g., those in Hyderabad, Cyberabad, Visakhapatnam, major IT corridors) and "Rural/Semi-Urban" (e.g., those in Rayalaseema, smaller towns, agricultural centers like Guntur). This requires a clear definition based on location data.
2. 2. Calculate Aggregated Metrics for Each Segment:
   • For the "Urban Branches" segment:
     • Calculate the overall approval rate for the current week and the previous week.
     • Calculate the approval rate for each loan product (Agriculture, Small Business, Home, Vehicle) for the current and previous week.
     • Determine the proportion of total applications each loan product represents within the urban segment for both weeks.
   • For the "Rural/Semi-Urban Branches" segment:
     • Repeat the same calculations as above.
3. 3. Comparative Analysis:
   • Compare Overall Approval Rate Changes: Did the overall approval rate drop in both urban and rural segments, or was the drop concentrated in one segment?
   • Compare Product-Specific Approval Rate Changes within Segments: For example, did the approval rate for Agriculture loans (popular among Guntur farmers) increase similarly in both rural and urban branches (if applicable), or did it show different trends?
   • Analyze Changes in Application Mix within Segments: This is crucial.
     • Within urban branches, did the proportion of applications shift towards loan types with inherently lower approval rates (e.g., more Small Business loans popular in Hyderabad, fewer Home loans)?
     • Within rural branches, was there a similar or different shift in the application mix (e.g., more Agri loans which have high approval, or a surprising increase in applications for riskier loan types)?
4. 4. Look for Simpson's Paradox within Segments:
   • It's possible that the paradox is occurring primarily in one segment. For instance, urban branches might see a drop in overall approval rate despite stable product-specific rates if there was a large influx of applications for a traditionally lower-approval-rate product within that urban segment. The same could happen in rural branches if, for example, there's a sudden increase in applications for less-established small business loans over more standard agri loans.
5. 5. Visualization:
   • Use grouped bar charts or stacked bar charts to compare:
     • Overall approval rates (this week vs. last week) for Urban vs. Rural.
     • Product-specific approval rates (this week vs. last week) for Urban vs. Rural.
     • The composition of loan applications (by product type) for Urban vs. Rural segments for both weeks.

By segmenting the data by branch type (urban Cyberabad vs. rural Rayalaseema) and then analyzing both the approval rates for each loan product and the mix of loan applications within these segments, we can determine if the overall drop is due to:

• A genuine decrease in approval stringency in one type of branch.
• A shift in the types of loans being applied for, specifically within one type of branch (e.g., urban areas seeing more applications for lower-approval-rate loans).
• Or a combination, where the overall bank-wide application mix shifted, and this shift was more pronounced or had different characteristics in urban versus rural areas.

This detailed investigation will help pinpoint whether the paradox is a bank-wide phenomenon driven by overall shifts in application types or if it's more localized to specific branch categories within the Telugu states, reflecting different economic activities or customer needs (e.g., agri loans in Guntur vs. home loans in IT corridors).

 

Solution

To better understand the paradoxical loan approval rates at Andhra Bank and to disentangle the effects of changing application patterns, product-specific rates, and potential branch-level variations (e.g., urban Cyberabad vs. rural Rayalaseema), I would need to collect additional data and employ more sophisticated statistical methods.

Additional Data Needed:

• 1. Applicant-Level Data:
  • Detailed Demographics: Age, income bracket, occupation (e.g., farmer, salaried, self-employed business owner), credit score/history, existing relationship with Andhra Bank.
  • Loan Application Specifics: Exact loan amount requested, loan purpose (if more granular than product type), loan-to-value ratio (for secured loans like home loans).
  • Geographic Information: Specific branch where the application was submitted, applicant's district/pin code to accurately classify as urban/rural or by specific region (coastal Andhra, Rayalaseema, Telangana districts like Guntur or those in IT corridors).
• 2. Branch-Level Data:
  • Classification of each branch (urban, semi-urban, rural).
  • Historical approval rates and application volumes per product for each branch.
  • Any specific targets or policy changes implemented at the branch level.
• 3. Temporal Data:
  • Precise application dates and approval/rejection dates for all loans over a longer period (more than just two weeks) to establish more stable baselines and observe trends.
• 4. Number of Applications per Category:
  • Crucially, the number of applications received for each loan product, for each branch type (urban/rural), for both time periods (this week and last week). This is essential to confirm if a compositional shift in applications is the driver of Simpson's Paradox.

Statistical Methods for Deeper Analysis:

• 1. Detailed Stratification and Cross-Tabulation:
  • Beyond just urban/rural, stratify by loan product AND branch type simultaneously. Calculate approval rates for "Agriculture loans in Rural Branches," "Small Business loans in Urban Branches," etc., for both weeks. This will show exactly where product-specific rates are stable/increasing and how application volumes within these strata have changed.
• 2. Standardization of Rates:
  • Use statistical standardization (e.g., direct or indirect standardization) to calculate what the overall approval rate would have been this week if the distribution of loan applications by type (and/or by branch type) had remained the same as last week. If this adjusted rate is still lower, it suggests factors beyond just compositional changes are at play.
• 3. Logistic Regression Modeling:
  • Develop a logistic regression model where the dependent variable is loan approval (1=approved, 0=rejected).
  • Independent variables would include: loan product type, applicant characteristics (income, credit score, occupation), loan characteristics (amount), branch type (urban/rural), and a time period indicator (this week vs. last week).
  • This multivariate approach can help isolate the effect of each variable while controlling for others. We can see if, after controlling for changes in applicant risk profiles or loan types, there's still a significant effect of the "current week," and if this effect interacts with branch type or loan type.
• 4. Analysis of Change in Applicant Pool Quality:
  • Using the detailed applicant data, compare the average risk profile (e.g., average credit score, average income to loan amount ratio) of applicants for each loan type and in each branch segment between the two weeks. A shift towards a riskier applicant pool for certain high-volume loan types could explain stable/improving individual approval rates but a lower overall rate if underwriting standards remained constant.
• 5. Contribution Analysis:
  • Quantify how much of the change in the overall approval rate is attributable to (a) changes in product-specific approval rates and (b) changes in the compositional mix of loan applications.

By collecting more granular data and applying these more advanced statistical methods, we can provide Andhra Bank with a comprehensive understanding of the factors driving the observed paradoxical trend in loan approval rates across their operations in the Telugu states, allowing for more targeted interventions if needed.