Abstract
Investigating the impact of the ambiguity factor in identifying the dynamics of bubbles that periodically form and collapse is one of the important challenges in empirical and applied studies. The present study uses the endogenous Markov regime change model to identify inflation rate bubbles as one of the macroeconomic variables that has always been volatile during the years 1397-1403. The research findings indicate that incorporating the ambiguity variable into the model leads to a structural change in bubble behavior. Specifically, the intensity of the explosive trend of the bubble decreases in the presence of ambiguity. This phenomenon can be interpreted scientifically as follows: informational ambiguity disrupts the predictive efficiency of economic agents, resulting in delayed market responses. This delay in response has two important consequences:
1. Reduction in Volatility (Uncertainty causes investors and consumers to act more cautiously in their emotional decision-making, which manifests as a slowdown in the rapid growth of bubbles).

Delayed Collapse) As the growth of the bubble slows down, the process of its sudden collapse is also delayed).

Therefore, although ambiguity can act as a deterrent against sudden shocks and rapid collapses, it simultaneously reflects market inefficiency in processing information and accurately predicting macroeconomic variables. These findings underscore the necessity of information transparency in economic policymaking to mitigate costs associated with inflationary fluctuations.
Purpose/Aims:
Investigating the impact of the uncertainty factor in identifying the dynamics of bubbles that form and burst periodically is one of the important challenges in empirical and applied studies. In fact, ignoring the impact of this factor in the process of forming fluctuations in macroeconomic variables, and in economies such as Iran that have the potential for this phenomenon to form, not only reduces the power of detection and forecast accuracy, but also, with the expansion of the dimensions of economic instability, causes the prediction of the future trend of these variables to often be accompanied by realities that are different from those expected. Research shows that rational bubbles, and in particular bubbles that form and burst periodically, can be affected by the presence of uncertainty-forming factors in economic markets. .In fact, receiving ambiguous information and subsequently expanding the dimensions of ambiguity in the market evokes conditions in which, on the one hand, the decision-making space governing the market can be a space distinct from risk, and on the other hand, it confirms that the trend of changes in macroeconomic variables does not always follow the predictions of the efficient markets hypothesis and households and firms cannot include all relevant information in the final price of goods and services in their buying and selling decisions. Therefore, as this hypothesis is questioned and the degree of market efficiency decreases, the probability of bubble phenomena increases. Accordingly, the purpose of this research is to extract the ambiguity index and introduce the effect of this exogenous variable in the model to answer the question of whether the ambiguity calculated by the probability of hidden factor changes has a significant role in the dynamics of bubbles?
Methodology & Findings:
In this study, the model specification without considering the ambiguity variable, the calculation of the ambiguity index, and the model specification with considering the ambiguity index are presented, in which the method of calculating the ambiguity index, which is based on the Kullback-Leibler divergence criterion, will also be discussed. After performing the hypothesis tests required to calculate the ambiguity index and then introducing this variable into the model, in response to the research question, the estimates of the bubble parameters ( and ( ) with values ​​of 0.519 and 2.621, respectively, confirm the nature of non-explosive and explosive behavior. On the other hand, the ambiguity variable with a value of -2.9901 has a significant and negative effect on the model at a confidence level of 95%, and by introducing the ambiguity variable into the model, the value of the logarithm of the maximum likelihood function has increased from -98.47 to -92.13, and the estimated value of the parameter has decreased from 4.076 to 2.621.
Discussion & Conclusion
The formation of inflation rate bubbles due to the imposition of increasing economic and social costs on society, the misallocation of resources, and the expansion of economic instability dimensions is always of concern to policy-making institutions and economic decision-makers, and the spread of the consequences of this phenomenon in the atmosphere of uncertainty prevailing in society is inevitable.Accordingly, the present study is trying to overcome some of the limitations raised in previous studies in this field by presenting a new approach to identifying bubbles, after extracting the ambiguity index and introducing the effect of this exogenous variable in the model, to answer the question: does the ambiguity calculated by the Transition probabilities of changes in the hidden factor play a significant role in the dynamics of bubbles? In order to answer the above question, in the first stage, within the framework of a forward-looking approach, the dynamic interactions between the inflation rate and its underlying latent factor were introduced in the model to identify bubble regimes. The estimation results showed that in the period 1397:01-1403:12, the estimated bubble conditional parameters, ) ( and) ( , are equal to 0.306 and 4.076, respectively, and confirm the nature of non-explosive and explosive behavior in the inflation rate variable during the period. In the next step, after entering ambiguity into the factors forming the transition probability matrix and estimating the Markov model in the ambiguity space, the null hypothesis of ambiguity with respect to the factors forming the transition probability matrix was tested against the alternative hypothesis of no ambiguity with respect to the factors forming the transition probability matrix based on the likelihood ratio statistic. The results show that the null hypothesis is not rejected at the 95% confidence level and the presence of ambiguity as an influential variable in the model is confirmed. Then, using the Kulbeck-Leibler divergence criterion, the ambiguity index was extracted based on the transition probabilities obtained from the estimation of the model without ambiguity and the transition probabilities obtained from the estimation of the model with ambiguity.Then by testing the hypothesis and based on the results in Table 6, the research hypothesis is confirmed and the ambiguity index can play a significant role in the dynamics of the inflation rate variable.
Given the importance of examining the effect of the uncertainty factor in the process of inflation rate bubbles formation, it is suggested that in order to accurately identify inflation rate bubble periods, in terms of methodology and within the framework of different economic markets, this extracted factor and its effect on the fluctuations of macroeconomic variables can be analyzed and examined. Certainly, considering this process can not only facilitate the process of predicting fluctuations of macroeconomic variables by increasing the power of detection and forecast accuracy, but also, at the macro level of society, by reducing the decision-making costs of economic and social planners and policymakers, reduce the dimensions of economic instability, and as a result, more realistic predictions of the future trends of these variables in the Iranian economy can be made.