Estimating the effect of money illusion on the utility function of Iranian households: with Euler equations and GMM approach

Purpose: Extensive evidence shows that consumption-based asset pricing models (CCAPM) proposed by Lucas (1978) and Breeden (1979) have failed to explain average stock returns in cross-sectional data. In this context, we can refer to the studies of Breeden, Gibbons and Litzenberg (1989), Letas and Ludwigson (2001), and Jacobs and Wong (2004). In response to this failure, several studies used other variables than consumption growth in a single-factor model to improve the performance of the mentioned structure (such as Parker and Julliard (2005), Jaganthan and Wong (2007), Savo (2011) and Kroenke (2017)). In none of the domestic studies, inflation has been used as a risk factor. Therefore, this study aims to fill this gap by focusing on the impact of monetary illusion on the desirability of Iranian households in the period under review. In fact, this research is of novelty compared to the previous studies conducted inside the country. Firstly, with the inclusion of the inflation variable in the household preferences function, the CCAPM model has been developed in such a way that the inflation variable can be included in the household preferences function. Secondly, reversible preferences and non-reversible power utility have been used to estimate the monetary illusion parameter. Thirdly, in this research, the system of equations includes the return of various assets such as bank interest rate, stock return, housing return and labor wage return, and the parameters of the equations have been estimated by using different appropriate tools. 
Methodology: In order to include inflation as a risk factor and define a parameter that shows the degree of monetary illusion of brokers, Mayo (2018) specified a three-factor macro model for asset pricing including inflation rate, consumption growth and asset yield in the CCAPM structure. The underlying framework of the model includes a recursive inter-period utility presented by Epstein-Zine and Weil (1989). This framework made use of an intra-period utility function that corresponds to both real consumption growth and nominal consumption growth (with the specification a Cobb-Douglas function). Intra-period utility is appropriate for a case where the investor faces a partial monetary illusion, which is because he cannot fully distinguish real consumption from nominal consumption in his consumption/asset allocation decision. The degree of monetary illusion is represented by the monetary illusion parameter (ϵ), which varies from zero to one. Therefore, the assumption of monetary illusion allows the researcher to create a model in which the inflation variable is used as an endogenous risk factor in the pricing kernel. In this regard, there are three preferences parameters in the created model, including relative risk aversion coefficient, monetary illusion parameter, and inter-period substitution elasticity.
In this study, inflation is included in the function of households' preferences in the form of consumption capital asset pricing model (CCAPM) so as to estimate the impact of money illusion on the utility of Iranian households in the period of 1978-2021 To this end, the recursive preferences function provided by Epstein-Zin and a non-recursive power utility function with constant relative risk aversion are used in such a way that the inflation growth variable appears as a risk factor in the stochastic discount factor of the derived Euler equations. In fact, inflation arises endogenously in the pricing kernel by assuming an intra-temporal utility that depends on both real and nominal consumption. This suits an investor with partial money illusion. Then, the generalized moments method (GMM), MAE and MSE criteria are used to estimate the systems of equations and select the most appropriate model.
Findings and discussion: After the mentioned models are estimated, the mean absolute magnitude of errors (MAE) and mean squared errors (MSE) criteria are used to select the best model among the fitted ones. The results show that the model with recursive preferences has the lowest values ​​for the two mentioned statistics. Therefore, this model is chosen as the best one, based on which the effect of monetary illusion on the utility function of Iranian households has been 18% during the period under review. The criteria prove the superiority of recursive preferences. The results of the research also indicate that the money illusion parameter is statistically significant, and Hansen's J statistics confirm the appropriateness of the instruments. In the superior model, the effect of money illusion on the desirability of households is 0.18. The significance of the coefficients and the fit statistics of the models show that the inclusion of the data related to inflation growth in capital asset pricing models as a risk factor alongside the risk factor of consumption growth and asset return portfolio is significant.
Conclusions and policy implications: The findings show that, in the first model where return preferences are used, the effect of monetary illusion on consumers' desirability is 0.18. Also, in the second model, which is bounded by the first model and involves non-reversibility and ability utility, the effect of monetary illusion on the utility of Iranian households is 0.03. In both estimates, all the coefficients are statistically significant, and the diagnostic tests for the remaining phrases confirm the correctness of the estimates. After the models are estimated, the mean absolute magnitude of errors (MAE) and the mean squared errors (MSE) criteria are used to select the best model among the fitted ones. The results show that the model with recursive preferences has the lowest values in the two types of statistics. Therefore, this model is chosen as the best one. Based on it, the effect of monetary illusion on the utility function of Iranian households is found to have been 18% during the period under review. Considering the relative impact of monetary illusion on the utility of households, it is necessary for policy makers and planners to reduce and control prices in order to better adapt the utility of households to economic realities.