Consumer lending efficiency: commercial banks versus a fintech lender

Financial Innovation

Table 5 2016 Unsecured consumer loans–stochastic frontier estimation. Excluding the volume of unsecured consumer lending. Best-practice (minimum) ratio of nonperforming consumer loans

Parameter	Variable	Coefficient Estimate	Pr( >\|t\|)
β₁	Growth rate in consumer lending from 2013 to 2016_i	− 0.000513	0.006971
β₂	Contractual consumer loan rate_i	0.060001	0.000001
β₃	[Contractual consumer loan rate_i]²	0.070136	0.127654
β₄	[Contractual consumer loan rate_i] × [GDP Growth Rate_i]	− 0.005768	0.252876
β₅	[Contractual consumer loan rate_i] × [Herfindahl Index_i]	− 0.078812	0.000650
σ_μ = 1/θ		0.027062	0.000000
σ_ν		0.000438	0.009392

The data set includes LendingClub and 387 top-tier bank holding companies at the end of 2016 with plausible values of nonperforming unsecured consumer loans and total loans exceeding 10 percent of assets
Skewness and D’Agostino skewness test of OLS residuals \((\sim N\left(\mathrm{0,1}\right) \,\,\mathrm{asymptotically})\): skewness \(=4.7958 \left(>0\right)\Rightarrow\) positively skewed test statistic \(=16.7863\) with p-value < 2.2E−16 \(\Rightarrow\) positively skewed with statistical significance. Histogram and density of OLS residuals in the relative frequency scale appear in Appendix 3
Likelihood ratio test of \({H}_{0}: {\sigma }_{\mu }^{2}=0\) vs. \({H}_{1}: {\sigma }_{\mu }^{2}>0\) (asymptotically distributed as 50:50 mixture of \({\chi }_{(1)}^{2}\) and \({\chi }_{(0)}^{2}\)): test statistic \(=511.1877\) with p-value < 2.2E−16 \(\Rightarrow\) strongly reject linear regression model (i.e., absence of inefficiency) in favor of stochastic frontier model (i.e., presence of inefficiency)