An investigation into the effect of liquidity and exchange rate on inflation in time-frequency domain

Extended Abstract
Purpose: Despite the fact that there is consensus regarding the effects of inflation and the need to deal with it, the determinants of inflation, the evolution of the relationship between them, and the comparison of the intensity and weakness of each one is areas of controversy. Meanwhile, the frequency of exchange rate and liquidity in the corresponding studies stand out more than other variables. It is recommended to follow the exchange rate transition theory to control inflation through this channel. It is also necessary to control monetary aggregates according to what the monetarists have depicted about the origin of inflation across space and over time.
Regardless of the intensity and weakness of the influences of the two variables in the context of time and in different horizons, inspired by the revealed facts and the support of the literature, what makes the problem more complex is the likelihood of the flow of causality to change between the variables. Therefore, although the effects of liquidity and exchange rate on inflation have been investigated in several studies, the reported results are not consistent. This situation can have different reasons, the discovery of which improves the cognitive processing power and provides immediate requirements for adopting efficient policies.
In this direction, attention is paid to the intertwining of the above three variables, knowing the net effect of liquidity (exchange rate) on inflation by removing the effect of exchange rate (liquidity), and investigating the possibility of its change over time and in short-term and long-term horizons. In terms of intensity and flow of causation, it can be useful and become the subject of policy making.
Methodology: The Granger causality test is a regular method of econometrics in which the causal relationship between time series is examined without referring to economic theories. According to its nature, this method provides a momentary measure of causality but is unable to analyze the dynamics and reliability of causality. In addition, in the Granger causality method, intermittent values of variables are used, and, as a result, there will be a possibility of eliminating instantaneous effects. To solve this problem, spectral analysis is used. Fourier transform is one of the widely used topics in spectrum analysis, which serves to reveal the existing relationships between time series at different frequencies. Due to the fluctuating nature of the correlation among some economic time series, it is investigated in the analysis. The dynamics of causality can also be used. In the Fourier transform, in addition to the local time information being left out, the stability of the hypothetical time series is essential. However, many time series are unstable and most of their characteristics change over time. Due to this limitation, the wavelet transform is considered as a useful alternative to the Fourier transform in discovering causal relationships. The present research investigated the relationship of liquidity growth and exchange rate with inflation. For this purpose, seasonal data from 1990 to 2022 and continuous wavelet transformation were used. The distinguishing feature of the research was the use of multiple coherence tools, partial coherence, partial phase difference and partial wavelet gain.
Findings and Discussion: The results of the multiple correlation showed that, in the context of time and in the horizons of less than eight years, the growth of liquidity and the exchange rate are simultaneously a suitable explanation for the changes in inflation (similar to the coefficient of determination in the regression). Coherence, phase difference and partial wave interest showed that the growth of the exchange rate on all scales (up to 8 years) and over time creates inflationary pressure, the corresponding coefficient of which is less than 0.5. Liquidity growth and inflation have experienced an unstable relationship in terms of intensity, direction and flow of causality. So, within 1.5-4 years in the late 2010s, the growth of liquidity had a strong effect on inflation. In the horizon of 4-8 years in the 1997-2001, 2006-2011, and 2019-2020 periods, this pattern was repeated. This is important due to the inflationary conditions and the government budget. Liquidity following inflation has also happened on different scales, which can be attributed to the internalization of money in Iran's economy.
Conclusion and Policy Implications: The results have two important policy implications as follows:

As long as the growth of the exchange rate and liquidity-induced inflationary pressure are concerned, the effect of the exchange rate is always little and stable. Therefore, it is suggested that exchange rate changes be included in the dynamics of inflation considered by the policy maker. This important point will not occur, unlike the current procedure which mainly occurs with the pattern of repression and mutation due to the inability to suppress. Therefore, instead of nominally anchoring the exchange rate, it is necessary for the policy maker to commit to maintain stability in the growth of the exchange rate so that the effects of inflation will be less.
Although the growth of liquidity has not created inflationary pressure in all the years ever since this relationship was established, the effects will be severe and destructive for the general level of prices. Therefore, it is necessary to prevent the transfer of discontent in the economy and monetize them, regardless of setting a horizon on inflation and expecting immediate effects. To this end, it is necessary to reduce the budget deficit and the imbalance in the banking system as two sources of liquidity expansion. In addition, it is not enough to look at the past history of liquidity following inflation and target liquidity growth; it should base a tool to guide monetary policy. Therefore, in addition to using the common monetary policy tool (interest rate), it is necessary to consider the control of monetary totals so that the monetary policy can achieve its original goals.