Estimating the Underground Economy Using Fuzzy Indexation and the MIMIC Model within a SEM Framework

Abstract

The present study aimed to estimate the size and trend of the underground economy in Iran using fuzzy indexation and the Multiple Indicators Multiple Causes (MIMIC) model within a Structural Equation Modeling (SEM) framework and to examine the effects of selected macroeconomic determinants on underground economic activity. This applied, descriptive-survey study employed a hybrid methodological framework combining fuzzy logic and structural equation modeling. In the first stage, a fuzzy inference system based on Mamdani logic was developed to estimate the underground economy using seven macroeconomic indicators categorized into monetary, financial, and real-sector dimensions. The monetary dimension included liquidity growth and the relative price of non-tradable to tradable goods; the financial dimension included the ratio of oil revenues to GDP and the ratio of oil revenues to government budget revenues; and the real-sector dimension included the non-oil trade balance, the ratio of agricultural value added to non-oil GDP, and the ratio of construction value added to non-oil GDP. Triangular membership functions with five linguistic levels were defined using six-year moving averages and standard deviations. After fuzzification, rule construction, inference, and defuzzification, annual underground economy indices were estimated for the period 1996–2025. In the second stage, the estimated underground economy was modeled as a latent construct using Partial Least Squares Structural Equation Modeling (PLS-SEM) in SmartPLS. Gross Domestic Product, Money Supply, Activity Rate, Direct Tax Burden, and Gross Fixed Capital Formation were incorporated as explanatory variables. Reliability and validity were assessed through Composite Reliability and Average Variance Extracted, while hypothesis testing was conducted using standardized path coefficients and bootstrapping procedures. The results confirmed the adequacy of the measurement model, with Composite Reliability values ranging from 0.821 to 0.894 and AVE values ranging from 0.631 to 0.702. Kolmogorov–Smirnov tests indicated non-normality of all variables, supporting the use of PLS-SEM. Path analysis revealed that Gross Domestic Product had a significant negative effect on the underground economy (β = -0.360, t = 15.369, p < 0.01). Money Supply exerted a significant positive effect (β = 0.776, t = 28.960, p < 0.01). Direct Tax Burden showed a significant negative relationship with underground economic activity (β = -0.109, t = 2.195, p < 0.05). Activity Rate also had a significant negative effect (β = -0.048, t = 11.457, p < 0.01). Furthermore, Gross Fixed Capital Formation demonstrated a strong negative effect on the underground economy (β = -0.607, t = 9.527, p < 0.01). The fuzzy estimation indicated that the underground economy followed an upward trend after 2011 and averaged approximately 37% of GDP during the study period.