Financial capital measure with item response theory: A didactic approximation

Abstract

Objective: The objective of the article is to present in a didactic and concise way the fundamental concepts of item response theory (IRT) and its possible application in the economic sciences and show the bias problem that occurred when estimating a latent variable such as financial capital in microentrepreneurs through IRT, assuming normal distribution in an unfounded a priori way. Research Design & Methods: We introduce a Bayesian hierarchical IRT model for graded responses where the latent traits have a skew normal distribution. Financial capital was measured by a survey applied to 384 microentrepreneurs from the metropolitan area of Bucaramanga (Colombia). The preliminary statistical analysis of data hints that the latent trait is not symmetric. Models that include a normal and a skew normal distribution were tested. Findings: We detected that assuming the distribution of the normal trait may overestimate the calculation of financial capital in microentrepreneurs, which would cause loans to be assigned without support. Implications & Recommendations: When applying IRT to economic matters such as in the measurement of financial capital, it is recommended to review the assumptions that this technique handles, especially the normal-ity of the latent trait, since if assumed without verification or theoretical support can cause bias in parameters. Contribution & Value Added: An improvement is presented to the graded response model with normal distribution in IRT for the measurement of financial capital, paying special interest in providing a pedagogical explanation for a public related to economics.