Modified Ramsey RESET and Double-Resampling Bootstrap for Semiparametric Path Modeling of Financial Literacy

Abstract

Financial literacy is a multidimensional construct that is becoming increasingly important in the digital age, yet modeling its determinants often poses challenges when some of the relationships among variables are nonlinear and the normality assumption is not met. This study compared the standard bootstrap and the double-resampling bootstrap within a semiparametric path analysis framework based on truncated splines, applied to the estimation of indirect (mediation) effects in financial literacy modeling. Primary data were collected from 100 college students in Malang City using purposive sampling, with technology access (X₁) as the exogenous variable, financial knowledge (Y₁) as the mediator, and financial literacy (Y₂) as the response variable. The Ramsey RESET linearity test indicated that the relationship between technology access and financial knowledge was nonlinear, and it was therefore modeled using a one-knot linear truncated spline (minimum GCV of 0.155), while the other paths were linear. A Monte Carlo study at four sample sizes (n = 50, 100, 200, and 1000) with R = 400 replications per cell evaluated both procedures on coverage probability, interval length, test size, and power in addition to bias, RMSE, and relative efficiency. Two formulations of the double-resampling standard error are distinguished. Under the √B₂-scaled formulation, the formulation that reproduces the empirical results reported here, the relative efficiency equals the number of second-stage repetitions B₂ exactly, at every coefficient and every sample size, which follows as an algebraic identity rather than as a property of the estimator. The resulting intervals were shorter by a factor of 1/√B₂ but attained an empirical coverage of 0.387 against a nominal 0.95, and the associated test rejected a true null hypothesis in 0.612 of replications against a nominal 0.05; neither quantity improved as n rose from 50 to 1000. Under the averaged-estimate formulation, that is, the definition as written, calibration was restored (coverage 0.950, test size 0.036) and the efficiency advantage was no longer present (relative efficiency 0.92). The standard bootstrap was well calibrated throughout (coverage 0.939, test size 0.046) and was therefore adopted as the basis for inference in this model. Technology access had a significant direct effect on financial literacy under both procedures; the indirect effect through financial knowledge was positive on both sides of the knot and was established at the 5% level under the standard bootstrap applied directly to the empirical estimates (t_calc = 4.523, p < 0.001 below the knot; t_calc = 3.215, p = 0.002 above it), even though the calibrated procedure attained a simulated power of only 0.520 below the knot and 0.355 above it for effects of the estimated size at n = 100.