Consumer lending efficiency: commercial banks versus a fintech lender

Financial Innovation

Table 7 2013 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 2010 to 2013_i	− 0.000067	0.802076
β₂	Contractual consumer loan rate_i	0.094798	0.003677
β₃	[Contractual consumer loan rate_i]²	− 0.185662	0.007190
β₄	[Contractual consumer loan rate_i] × [GDP Growth Rate_i]	− 0.006164	0.140330
β₅	[Contractual consumer loan rate_i] × [Herfindahl Index_i]	0.011745	0.778062
σ_μ = 1/θ		0.032451	0.000000
σ_ν		0.002119	0.044223

The data set includes LendingClub and 654 top-tier bank holding companies at the end of 2013 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 \(=4.3289 \left(>0\right)\Rightarrow\) positively skewed test statistic \(=20.6471\) 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 4
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 \(=753.2751\) 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)