The Relationship between Inflation and Inflation Uncertainty with an Emphasis on Rational Expectation in Iran

Inflation rate in different countries can be considered as a positive or negative phenomenon¡ depending on the circumstances of each society; however¡ if inflationary shocks lead to inflation uncertainty¡ this will impair the optimum allocation of resources and price system function¡ and will in turn impose macro-economic costs on the enterprises. Due to the impact of these costs and rational behavior of economic agents on determining the expected inflation¡ the inflation rate may also be increased. Therefore¡ this study has reviewed the relationship between inflation and inflation uncertainty in Iran with an emphasis on rational expectations during the period of 1990 Q1-2015 Q4. Using EGARCH model¡ inflation uncertainty modeling showed that positive and negative inflationary shocks play an asymmetric role in the formation of inflation uncertainty. Also¡ Granger causality test and impulse response functions showed that an unanticipated inflation increase can lead to inflation uncertainty. The variance analyses also indicated that about more than 76 % of changes in inflation uncertainty can be explained in the long run¡ using unanticipated inflation¡ and also more than 16% of changes in expected inflation explained using inflation uncertainly.
In this study¡ the ARCH family models were used for modeling the fluctuation¡ the Granger causality to examine the causality between inflation uncertainty and inflation (unanticipated and anticipated) ¡ and the Vector Auto Regression (VAR) to analyze the revealed causes.
EGARCH model has some advantages over other asymmetric models such as threshold Arch (TGARGH) including 1) logarithmic transformations requires the positive conditional variance; 2) evaluation is not sensitive to outlier observations; 3) this model is not limited to parameters and is sufficient for stability of EGARCH process. In the present study¡ standard Granger causality test (1986) is used to determine if there is any relationship between inflation and inflation uncertainty. This test assumes that important data to predict each variable lies in the time series data related to it. In fact¡ Granger (1969) stated if the current value is predicted using past value ¡ in this case¡ is called the cause of. Granger causality test to investigate the hypothesis¡ «is not the Granger cause of» ¡ or vice versa¡ uses a vector autoregressive model (VAR).
After Granger causality test¡ through the impulse response functions and variance analysis in vector auto regression (VAR) ¡ better evidence of influence in the Granger causality has been obtained. In fact¡ based on the estimation of the VAR¡ also used byGranger causality test¡ the coefficients and the percentage of Explanatory model parameters is not as important as single-equation methods; therefore¡ the impulse response function (impulse response) and the variance analysis have been used in the analyses. Since the impulse response function measures the time path of impulse effect on the future status of a dynamic system¡ the effects of impulse can be seen in VAR patterns. The impulse response on variables assumes that the system is balanced¡ and the balance is in the coordinate system¡ so that all variables are equal to zero in equilibrium. The effect of the impulses once called a temporary variable¡ will return to its previous equilibrium value after several time periods; if this variable does not return to zero and is not settled in different balance amounts¡ it will be called a permanent impact. Variance analysis can measure the relative strength of Granger causality chain or exogenous degree of variables¡ regardless of the measured period¡ so the analysis of variance can be called causality test out of the sample period. This method can determine the role of imported shocks to different variables in explaining the anticipated error variance in short term and long term.
Results of Granger causality test showed Granger causality is not inflation uncertainty¡ and inflation uncertainty is neither unanticipated inflation Granger causality. On the other hand¡ unanticipated inflation is inflation uncertainty Granger causality¡ and inflation uncertainty is anticipated inflation Granger causality.
The results of this study showed that an unpredicted shock to the size of one standard deviation in inflation will increase inflation uncertainty as much as 0. 27158% in the first chapter¡ this increase reaches its peak in the second season (2. 85 511%) ¡ then the positive effects begin to decline¡ then turn to almost zero in Season XVI. The procedure of the effects of inflationary unanticipated shocks can be used to explain the changes of inflation uncertainty in Iran as much as 2. 82% in the first season¡ and more than 76 % in the long run. Also¡ an unforeseen shock to the size of one standard deviation in inflation will increase the expected inflation volatility from the second season¡ and this additive process will be positive for 20 years. The climax of this impact is in season 4 (0. 48354%). The effects of inflation uncertainty can display the changes of anticipated inflation as 3% in the second season¡ and more than 16 percent in the long term. Therefore¡ the results suggest that if inflation can (not) be predictable¡ then there will (not) be the rational expectations approach based on inflation uncertainty. Due to the rational behavior¡ inflation uncertainty lead to higher inflation rate.
Conclusions and recommendations: The results of this study show that isodiametric positive and negative inflation shocks are contributed to form the inflation uncertainty asymmetrically¡ and positive shocks spread more uncertainty. The results of Granger also show that Friedman hypothesis about inflation uncertainty caused by increasing inflation is not true for nonanticipated inflation in Iran¡ and the expected inflation has rejected this hypothesis. Also¡ Cukierman and Meltzer hypothesis about the causality result of inflation uncertainty has been confirmed in anticipated inflation and rejected in nonanticipated inflation.