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 normality 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.

Keywords

IRT in economics, Skew model, Latent trait, Graded Model, Bayesian method, Financial Capital

Author Biography

Henry Sebastián Rangel Quiñonez

Economist and Philosopher. MSc in Statistics from Universidad Nacional de Colombia. Lecturer at Universidad Santo Tomas and Universidad Industrial de Santander. His research interests include item response theory, economic development, behavioral economics, and epistemology of science.

Alvaro Mauricio Montenegro Díaz

Mathematician. PhD in Statistics.  MSc in Statistics. Professor at Universidad Nacional de Colombia. His research interests include item response theory and Bayesian statistics.

Luisa Fernanda Arenas Estevez

MSc in Public Policy from Universidad Nacional de Colombia. Economist at Universidad Industrial de Santander. Lecturer at Universidad Pontificia Bolivariana. Her research interests include public policy, inequality, economic development, and data analysis.

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