The dynamic relationship of interest rate , price level , money supply and real gross domestic product : case study of Iran ”

The main purpose of the present study is to investigate the relationship between macroeconomic variables such as interest rate, price level, money supply and real gross domestic product for Iran by considering the effect of economic sanctions during a time period 1980-2014. To analyze the collected data, the VARX method was used and the data were analyzed by Eviews 9 software. Also, for data analysis, the variable of economic sanction was considered as exogenous variable and other variables were considered as endogenous variables. The empirical findings of the study show that there is a significant and bilateral relationship between most endogenous variables of the model. Also, it was observed that the variable of economic sanction has a significant effect on the intended macro variables.


Introduction
The relationship between macroeconomic variables has been always considered by researchers, because most theoretical questions raised in macroeconomic framework can be discovered. But there are also different approaches to study these relationships. Some researchers only evaluate the macroeconomic attitudes, for example, how the economic attitudes of Keynesian are supported in society. While some other researchers study the nature and concepts of these variables. For example how can inflation be a monetary phenomenon or how it can be related to economic development or the total economy? (Herwartz and Reimers, 2006) this regard, there are other questions that need to study the relationship between macroeconomic variables related to them in order to find the answers.
Although the relationship between the variables like interest rate, price level, money supply and real gross domestic product has been studied for developed countries (Urbanovsky, 2016), the results of previous works cannot be referred to, since in developing countries like Iran, interest rate was stabilized by the banking system. Most theoretical foundations discussed on the relationships between these variables are true for developed countries and the hypotheses of these theories are in accordance with the economic structure of these countries. Thus, the study results and testing the relationship between the discussed variables by using the data related to developing countries like Iran have more validity and the results and findings related to developed countries cannot be generalized to the country.
However, the issue that has been highly considered in the economy of the country after the victory of the Islamic revolution of Iran is the economic sanctions raised against Iran that can affect the macroeconomic variables. The macro effects of sanction on the economy of a country can be studied from two aspects: first, an economy needs to obtain production factors from different sources for growth and development and these production factors in an economic process can have an appropriate estimate for the economic development. In other words, economy needs capital resources, modern technology, initial or primary materials, appropriate management and organization and skilled human resource in order to be mixed and create an economic activity in different parts like industry, agriculture and services in form of production factors. However, the important point is that today not only country relies on its internal resources as production factors, but also relies on international resources in order to increase its productivity and attempts to use the external or foreign resources more than its internal or domestic resources. In other words, the production factors out of borders do not enter the internal economy of a country. Thus, the economy cannot be increasingly developed with a pure reliance on internal or domestic resources.
On the other hand, it should be said that healthy and productive economy does not mean without the presence of international markets and increase of competitiveness. If the economy of a country does not have a share and contribution in global markets, it will gradually face recession and lose its efficiency by moving away from the competitive atmosphere. Also taking a share from international markets needs the presence of normal conditions in the political atmosphere of a country. Thus, if the country is under sanction conditions, it cannot have an appropriate share of international markets and will lose its competitiveness. Thus, it should be generally said that, on the one hand, sanction will decrease the supply resources of production factors in the country of Iran and, on the other hand, it will increase our distance from other neighboring countries by reducing the economic share of Iran from international markets. The manifestation and expression of these two effects in the reduction of Iran's economic development is certainly revealed. In other words, the reduction of economic development is the main effect of macro sanction.
In this regard, the variable of economic sanction must be considered to answer this question: how is the potential relationship between interest rate, price level, money supply and real gross domestic product in Iran? Then, the theoretical foundations between macroeconomic variables in the study are presented. The next sections study the empirical background of the study and after that the research method and the estimation of the relationship between variables will be presented. Finally, data analysis and the obtained results will be presented.

Theoretical foundations of the study
To study the relationship between macroeconomic variables and theoretical foundations related to these relationships, the theories in macro economy can be used. According to the highlighted role of the state in Iran's economy, the Keynesian economic models were selected as the theoretical framework of the study, because the Keynesian-oriented economists consider the presence of states and their active role in economy in their theories and argue that the decisions of the private sector may sometimes lead to inefficient results in macro economy and, thus, support the active policy making of the state in public sector.
In the framework of Neo-Keynesian monetary model, the monetary authorities of the country stabilize interest rate in a specific level and, then, supply the money according to the market demand. Thus, in this case, no change in demand for money in the society was completely answered and it will have no effect on the variables like gross domestic product and inflation. Theoretical foundations related to a standard monetary model were studied through optimizing the factors by Woodford (2003). The studies conducted by Woodford show that money plays an insignificant role in these models and the balance path related to production and inflation can be determined by considering interest rate at the desired level regardless of money supply or the factors related to demand for money. This conclusion is in conflict with the current empirical evidences. Friedman and Kuttner (1996) and Sterlla and Mishkin (1997) presented some evidence that money can have a determining role in determination of production and general level of prices. Its reason is the irregular behavior of velocity of money. In this regard, Nelson (2000) used the data related to the USA and England and concluded that money is an important and determining factor in production and general level of prices even if interest rate is controlled.
Leeper and Zha (2000) used the VAR structure model and concluded that removing money from empirical models is not harmless.
Thus, it can be said that money has an important and determining role in determination of the relationship between gross domestic product and general price level and it cannot be easily eliminated from empirical models. Now, the relationship between the above mentioned variables is studied by considering a Keynesian framework.
In this framework, it is assumed that the general price level increases in the society. According to this approach, the first variable that can be affected by the increase of the general price level is the real money balance. In other words, the increase of the general price level reduces the real money supply. In the framework of Keynesian analyses, the excess demand for money causes some disturbances in the economy. According to the Walrasian balance, a balance is created in the economy when the creation of the excess demand for money in the money market leads to the creation of oversupply in the bond market. It will also lead to the decrease of the bond price and increase of interest rate in the market. Thus, it is theoretically expected that the increase of the general price level increases interest rate and, thus, there will be a positive causal relationship from inflation rate toward interest rate. On the other hand, the increase of interest rate increases the cost of using capital that leads to the increase of production costs.
The above mentioned issues showed that in Keynesian framework, there is a relationship between macroeconomic variables of interest rate, general price level, gross domestic product and money and the relationship between each of these variables cannot be studied without considering other variables. Now, after the stabilization of the relationship between the mentioned variables, before testing this variable empirically in Iran, a brief study is carried out on the literature and background of the subject inside and outside of the county.

Empirical background of the study
Some studies were performed on the relationship between macroeconomic variables including interest rate, money supply, price level and real gross domestic product out of the country. However, in some cases like research methodology, the economic conditions of the studied countries and even the obtained results are different and here are some of these studies. There is a causal relationship of price level to interest rates, GDP to interest rate and GDP to price level. VAR method Interest rates, price levels, money and GDP Urbanovský (2016) money supply affects the inflation in Selected Asian Countries Panel method Money supply and inflation Nguyen (2015) money supply affects the inflation in the United States of America ARDL method Money supply and inflation Thornton (2014) There is a close relationship between interest rates and money supply for eurozone countries Panel method Interest rates and money supply Cendejas et al. (2014) If the inflation rate is more than 10%, there will be a significant negative relationship between inflation and economic growth .
Time series data and panel data Inflation and economic growth R Jha and TN Dang (2012) There is a causal relationship between money and production VAR method Money and production Canova and Menz (2011) There is A significant negative correlation between inflation and production Non-linear panel regression model Inflation and economic growth Omay and Kan (2010) high inflation costs a lot on economic activities particularly in developing economies. Panel observation model Inflation and economic growth Bittencourt (2010) The level of threshold inflation is equal to 12 percent and above that inflation is harmful to economic growth.

Method of instrumental variables
Inflation, population growth, education, government cost share of production and growth Wanna and Chiava (2007) There is a relationship between money supply growth and inflation in the long term VAR method Money growth and inflation Lenza (2006) There is a Causal relationship between nominal interest rate and inflation in Turkey.
Johansen co-integration and Granger causality methods Interest rate and inflation Gul and Ekinic (2006) The incidence of shock to Broad money demand affects production and general price level VAR method Money, production and general price level Favara and Giordani (2006) There is a long term relationship between money growth and inflation. ARDL method Money growth and inflation Benati (2005) There is a nonlinear negative relationship between inflation and growth Non-balanced panel method Inflation and economic growth Drukker et al. (2005) There is a causal relationship between money and production over time. VAR method Money and production Ravn and Psaradakis and Sola (2005) There is a correlation between macroeconomic variables and interest rates in Brazil.

VAR method and Monte
Carlo simulation Interest rate and macroeconomic variables Garsia and Rigbon (2004) There is A close relationship between interest rate and inflation for the countries of Europe and America.
Johansen co-integration method Interest rate and inflation Booth and Ciner (2001) There is a Non-linear negative relationship between inflation and growth. Endogenous growth model Inflation and economic growth Gilman et al. (2001) Source: research findings.
As Tables 1-1 and 1-2 show, many studies have been carried out inside and outside the country on the relationship between macroeconomic variables and their effectiveness on economic development. But it is observed that no study inside the country has investigated the relationship between these variables. Abroad, only one study was performed by Urbanovsky (2016) in Czech Republic and due to the different economic nature of this country from Iran, the obtained results cannot be simply generalized to Iran and it needs an empirical test on these variables.
After the review of literature and theoretical -empirical foundations related to the research subject, then, the research method and data analysis related to the desired variables will be discussed.

Research method
The main purpose of this study is to evaluate the dynamisms of the relationship between four macroe-conomic variables of interest rate, money supply, price level and real gross domestic product in Iran. But one of the subjects that have been raised in Iran since the early years of the Islamic revolution is the issue of economic sanctions that have affected the macroeconomic status of Iran. In this regard, the virtual variable of economic sanction was also considered to measure the relationship between the intended macroeconomic variables.
In this regard, the structural autoregressive model with weak endogenous variables (VARX) is used to study the relationship between the above mentioned variables. VAR models used Cholesky decomposition to obtain the impulse response functions. Cholesky decomposition implies a causal order and may be acceptable when the researcher wants to study the effects of more than one shock (Elbourne, 2008).
Bernanke (1989) developed the SVAR mode by considering the theoretical limitations of simultane-ous effects of shocks. Then, he identified the impulse response functions by theoretical limitations on the long-term effects of shocks. The main advantage of SVAR models than primary VAR models is that unlike non-binding VAR models in which the identification of structural shocks is done implicitly, the structural autoregressive models have explicitly an economic logic based on economic theories to apply limitations; these limitations can be short term or long term. After applying the limitations, the structural shocks are identified. These shocks can be used for creating impulse response functions, analysis and variance in order to evaluate dynamic effects on different variables. VAR models that used the Cholesky decomposition usually focused on partial identification and the focus on partial identification means that only one shock can be studied in each model.
Since the internal conditions of developing countries do not have much effect on economic variables at the international level, thus in VAR models, there are a series of endogenous variables for these countries. In fact, these variables cannot have a bilateral relationship in the system of equations. Thus, cointegration autoregressive models are used with exogenous variables (VARX).  [1991][1992][1993][1994][1995] and presented VARX method to solve the recognition problem and test the hypotheses in vector error correction models with weak endogenous variables that are used in the present study, unlike Johansson method in which cointegration analysis in VAR models is performed in VAR models by using statistical linear constraints (recognition problem is only solved by normalization and statistical techniques). In structural long term modeling method (VARX), the economic theory is used in order to solve the recognition problem. In other words, the long term limitations derived from DSGE model can be imposed on VARX model. Specifically, the techniques like Johansson method are unable in modeling the national economy in global atmosphere, because the endogenous variables of the first order cannot be considered in co-integration VAR model while in VARX method, there are two groups of endogenous variables of the first order and exogenous variables in the model.
According to the topics discussed in the theoretical part of the study, the present study evaluates the dynamism of the relationship between interest rate, price level, money supply and real gross domestic product from 1980 to 2014. Also, since economic sanctions can affect macroeconomic variables whether inside or outside of the country, this variable was used in the specification of the research model. However, because using a bilateral relationship between the variables of interest rate, price level, money supply and real gross domestic product and economic sanctions is not reasonable, this variable was used as endogenous in the model.

The research model.
According to the study performed by Urbanovsky (2016), the variables used in this study are the logarithm of interest rate, price level, money supply and real gross domestic product and virtual variable of economic sanction, the variables of the logarithm of interest rate, price level, money supply and real gross domestic product were considered as endogenous variables and the virtual variable of economic sanction was considered as exogenous variable. According to previous contents, the selected model in this study is as follows: , In this mode, X is the vector variable of endogenous variable and Z is the vector of exogenous variable. And U is the vector of disturbance terms in the model.
in which: GDP indicates the real gross domestic product index for Iran.
Mo indicates the money supply (M2) for Iran.
Pr indicates the annual interest rate on bank deposits for Iran.
In indicates the general price level that was calculated by GDP inflator index.
SANC indicates the virtual index for economic sanctions, so that a value equal to 1 will be considered for the years that there has been economic sanctions against Iran, otherwise, a value equal to zero will be considered. Also, β L and γ L are interruption operators from the first order. Also, C is the vector of independent terms.
Also, the databases of the central bank of the Islamic Republic of Iran, statistical center of Iran, World Bank website and WDI were used during the years 1980-2014 for data collection. Finally, the collected data were analyzed by using Eviews 9 software.

Descriptive statistics of the research variables.
The results obtained from descriptive statistics of these variables were given in Table 2.  In this study, the augmented Dickey-Fuller test was used for the stationary test of time series data. The results of unit root test were reported in Table 3. The results obtained from the augmented Dickey-Fuller test show that the logarithm of interest rate, volume of money, and real gross domestic product with one differencing order and the variables of economic sanction and general price level are at a stationary level.

The estimate of the research model.
Here, the results obtained from the estimate of the research model are presented by VARX model. For each variable, the first row shows the coefficient, the second row shows probability and the third row shows t statistics.
The numbers in Table 4 show the estimated coefficients in VARX model. However, these numbers cannot be trusted and used for analysis because the estimated coefficients in the mode are summarized. In this model, most coefficients were significant and show a bilateral relationship between endogenous variables. Even if Granger causality test cannot confirm the bilateral relationship between endogenous variables, the results obtained from VARX model have more validity, because, contrary to Granger causality test, other criteria were also considered and the bilateral relationship was not only mentioned. In short, the results obtained from VARX model that were estimated in this model show that: In the first model of the study that real gross domestic product was considered as a dependent variable, the variables of volume of money with one interruption, interest rate with one interruption, real gross domestic product with one interruption and economic sanction with one interruption had a positive effect on dependent variable. While the variable of general price level had a negative effect and it is also observed that the effectiveness of all variables is statistically significant.
In the second model of the study that general price level was considered as a dependent variable, the variables of volume of money with one interruption, and real gross domestic product with one interruption had a negative effect on dependent variable, while other research variables had negative effectiveness. It is also observed that the effectiveness of all variables is statistically significant.
In the third model of the study that interest rate was considered as a dependent variable, the variables of volume of money with one interruption, interest rate with one interruption, general price level with one interruption and real gross domestic product with one interruption had a positive effect on dependent variable, while the variable of economic sanction had a negative effectiveness. It is also observed that the effectiveness of all variables except interest rate is statistically significant.
In the fourth of the study that volume of money was considered as a dependent variable, the variables of volume of money with one interruption, interest rate with one interruption, and general price level with one interruption had a positive effect on dependent variable, while real gross domestic product and economic sanction had negative effectiveness. It is also observed that the effectiveness of all variables is statistically significant.
Then, the results of the analysis of variance for real gross domestic product will be presented. The obtained results in Table 5 show that the shocks entered to gross domestic product occurred in the first ten periods. The first column from left shows the shocks resulted from changes in volume of money on real gross domestic product. The coefficients estimated for this column were significant from the first period, but this effectiveness in the first 3 periods is a small value and gradually increases. It can be said that in the short term, the increase of volume of money leads to the increase of a less value in real gross domestic product index, but in the next periods due to the money multiplier index, this increase is intensified and in the next periods, the effect of increase in volume of money on real gross domestic product will increase.
The second column shows the shocks resulted from changes in interest rate. The coefficients obtained for this column were significant from the first period and it shows that the shocks resulted from interest rate from the first period affect the real gross domestic product. The results obtained from this column show that the shocks from changes in interest rate in the short term have a little effect on real gross domestic product. Its reason is the indirect effectiveness of interest rate on real gross domestic product, because the increase of interest rate must lead to the change of investment and, then, this increase in investment demand leads to the increase of real gross domestic product, but from the fifth period onward, the trend of effectiveness of this variable increases and continuous to the 10 th period.
The third column involves the effect of the shocks resulted from the changes of general price level on real gross domestic product. The expectation of people for the temporary increase of prices in the short term leads to the fact that the effect of changes in the general price level is less in the first period, but in the next periods and after the adjustment of expectations, the effect of this variable from the second period takes an increasing trend. But the increase of general price level until 5 periods increases real gross domestic product but this effectiveness decreases in the long term and leads to the decrease of real gross domestic product.
The 4 th column also shows the effect of shocks resulted from changes in real gross domestic product in a period on the amount of this variable in the next periods. The coefficients estimated for the shocks are significant from the first period and shows that real gross domestic product is highly affected by the previous changes of this variable and is gradually decreased in the long term, so that as more periods are passed, the coefficient of shocks becomes smaller.
Finally, the effect of each shock entered to a variable and its effectiveness on other variables can be shown as follows: Response to Cholesky One S.D. Innovations ± 2 S.E.

Fig. 1. The results of impulse response functions test
Source: research findings.

Discussion and conclusion
The main purpose of the present study is to investigate the potential relationship between macroeconomic variables such as interest rate, price level, money supply and real gross domestic product for Iran by considering the effect of economic sanctions on them. For this purpose, the data related to Iran in 1980-2014 and econometric method of VARX were used. In general, the research findings showed that the virtual variable of economic sanction had significant effects on all the intended macroeconomic variables.
The effectiveness of this variable on real gross domestic product and general price level was positive and on other variables was negative. In other words, the consecutive years of sanctions against Iran made the economy of Iran find an economic independency and use the sanctions as an opportunity to increase its development and production after about 35 years of sanction. Although this economic independency had some costs like the increase of volume of money and interest rate and (especially in recent years) in case of macroeconomic variables, it was observed that there is a significant and bilateral relationship between almost all variables.