In this study, monthly data of Consumer Price Index (CPI), Pharmaceutical Price Index (PPI), Health sector Price Index (HPI) (spanning from 2001 to 2017) were collected from the Central Bank of Iran to calculate the inflation in consumer prices index (P
c), inflation in pharmaceutical prices(P
d), and inflation in health sector prices (P
h). Aggregate Health Sector Price indexes are taken from component indexes used for specific health care goods and services. A CPI includes four specific categories of medical care expenditures from the perspective of the consumer’s out-of-pocket price: prescription and nonprescription medicine, medical equipment and supplies, professional services, and hospital and related services (
15). In this study, prescription and nonprescription medicines were used as representatives of the pharmaceutical price index.
Due to the balanced access to three variables, i.e., CPI, HPI, and PPI, monthly data spanning from 2001 to 2017 were used in this study. To calculate inflation, the growth rate of the variables was obtained by the first-order difference of their logarithms.
The use of traditional methods in econometrics for time-series studies is based on the assumption that variables are stationary. A variable is stationary if its mean, variance and covariance do not change over time; however, when a variable is non-stationary, false regression in time series modeling may be encountered. Therefore, in order to examine the stationary and non-stationary variables, Hylleberg-Engle-Granger-Yoo (HEGY) test was used. The test is an extension of a theory by Dickey-Fuller and is used to test seasonal unit roots. In this paper, this test was used for monthly data.
In the next step, the uncertainty in inflation was investigated to determine if the variance of inflation changed over time; consequently, the data generation of inflation was determined through Autoregressive–moving-average (ARMA) (p, q) process firstly. The number of sentences in Autoregressive AR (p) and the number of moving average sentences MA (q) were calculated by using the method proposed by Box-Jenkins (
16). Schwartz information criterion was used to select the best model. To examine the existence of heteroscedasticity, the autoregressive conditional heteroscedastic (ARCH) test was used. If the time-series variance fluctuates due to positive and negative shocks over time, it can be considered as an indicator of uncertainty. Thus, we can model the variance of time series error sentences and examine the uncertainties. In this study, the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model was used.
The EGARCH model is as follows:
(2)
The model provides the possibility of asymmetric effects of past error terms with the conditional error variance, called the GARCH exponential model. One of the problems of the standard GARCH models is that positive coefficients should be ensured; however, in this study, Exponential GARCH (EGARCH) was estimated to determine the possibility of negative coefficients too. Therefore, any fitted amount was considered as inflation uncertainty. After that, a model for the inflation uncertainty series was extracted.
In the next step, the Granger causality test was used to detect the direction of the causal relationship between inflation uncertainty, inflation, inflation in pharmaceutical prices, and inflation in health sector prices. Granger causality automatically considers two equations for estimating X and Y variables for both directions.
(3)
(4)
The tested null hypothesis in the Granger model was that in the first regression, X was not a Granger cause of Y, and in the second regression, Y was not a Granger cause of X, in other words:
(5)
Moreover, Wald statistic was used to test the above hypothesis:
(6)
where is the sum of the squares of the residuals from restricted H0, and is the sum of the squares of unrestricted H0. T is the number of observations, and q is the length of the interval in the causal variable; in other words, F compares the sum of the residuals with and without the restriction of H0 H1. Moreover, the Schwarz criterion was used to determine the interval between variables X and Y.