## 1. INTRODUCTION

There are two sources of increasing the government revenues: Seigniorage income and taxe. Tax is economically recognized as the most reliable source of income but in developing countries, due to the expansion of the state and the various programs it manages, usually, this source of income does not cover the cost of the government and the government will suffer a budget deficit (Komijani and Ismaeilnia, 2017). Seigniorage is called the printing of new money and it is considered as the true value of resources that government earn from its exclusive right to printing money (Dornbusch and Fischer, 1987). The entry of this added volume of liquidity to the economy from the government spending channel, will lead to higher prices and, consequently, inflation. Inflation caused by an increasein the amount of money, cause depreciation of money and this is like a tax imposed on the owners of money in the community. In the economic term, this tax is called an inflationary taxe. This inflation caused by the release of money, causes loss of social welfare and costs such as reducing consumer purchasing power, changing the menu costs, changes in relative prices, etc. (Mankiw, 1987). In moderate inflation which is commonly seen in industrialized and developed countries, these costs aren’t high. But for developing countries, these costs can have serious and significant social outcomes.

There are two different views to explain the relationship between Seigniorage, nominal interest rates and inflation: The first view belongs to the monetaryists. In monetary theory, an increase in monetary base, will increase the inflation rate. The increase in inflation also reduces the real money balance by increasing nominal interest rates. These factors affect the resetting of money between economic agents and will increase the price and reduce the consumption of the private sector. According to the second view, described by Phelps (1973), Seigniorage income is equal to the multiplication of nominal interest rates and money balance. So Phelps expresses that income earned by government depends on the nominal interest rate lost by the private sector.

Many economists, including Bailey (1956), Cagan (1956), Friedman (1971), Phelps (1972, 1973), and Marty (1967) pay attention to seigniorage income and analyzed it as an income source for the government. Among the cases in these studies, Inflationary taxe has a special relationship with seigniorage income. Inflation duo to seigniorage income, causing financial losses, therefore, there should be positive relationship between printing money, seigniorage income and inflationary taxe. In other words, by increasing the printing of money and inflation caused by that, financial losses also increases. According to the theory of optimal seigniorage, nominal interest rates and inflation will lead to the government’s need to finance its budget deficits. According to this theory, if the marginal cost of taxs increases with revenue, there will be a positive relationship between inflation and interest rates and taxes (Aslan, 2013). This theory shows that inflation and nominal interest rates have a random walk process, but both of them move along with tax rates. Mankiw (1987) tested this theory for the United States in the period 1952- 1985.

Certainly, in carrying out any study, it is necessary to use the experience of other studies to benefit from them and enrich the study. Therefore, in this section, a summary of the researches that are directly and indirectly related to the subject of this study is presented.

Mankiw (1987) is among the researchers who examined the optimal rate of seigniorage in the Turkish economy. He uses a method that Mankiw was implemented for America, and finds that in the long run there is a correlation between the nominal interest rate, inflation and the tax rate, Which will not increase the gap between these three variables in the long run.

Lu *et al*. (2011) conducted a study entitled Dynamic welfare cost of seigniorage tax and consumption tax in a neoclassical growth model. In this study, the time period to examine the effects is divided into two categories of short-term and long-term and then the change in household welfare is measured in the form of these two periods. They eventually concluded that in the short run, the seigniorage tax policy would reduce economic welfare to a lesser extent, but in the long run, the consumption tax policy is less costly.

Correia and Teles (1996) provide the law for optimal inflationary taxes using an optimal general equilibrium model. They have compared the optimal inflationary tax in different economic environments and eventually came to the conclusion that Friedman’s proposed policy of zero nominal interest rates is the best option possible. Their overall conclusion is that optimal tax on monetary patterns provide more reasoned results relative to the results of public tax patterns provided in other economic conditions. So Friedman’s law states that the zero-inflationary tax is a general result of the monetary economy structures which is based on a rational basis.

Palivos and Yip (1995) reviewed government spending in a growth model. Their analysis shows that seigniorage method is always preferred method to direct taxation, though the income tax has a lower inflation rate. Their analysis also showed that from the welfare dimension, optimal policy depends on that part of the investment that is bound to liquidity.

Shodja *et al*., (2010) using a dynamic model with money in the utility function, has expanded analyse of optimal inflationary tax when there are distortive taxes. The overall result is that optimal inflationary tax is almost where the elasticity of money demand is equal to the extra pressure of other taxes. He shows that when additional pressure of other taxes tend to infinity, the government maximizes income that related to the creation of money.

Phelps (1973) has reviewed inflationary taxes using Optimal Taxation Framework. Phelps deals with money as a durable consumption good; Money provides useful liquidity services. So the real balance of money is brought in the utility function. Government revenue comes from imposing distortive taxes and the taxes will be set aside based on assumption.

Phelps using a static model showed that the taxes on labor and liquidity will both be optimal unless the compensated supply curve of the workforce is completely non-elastic. In the absence of cross-substitution effects, Taxation requires the imposition of taxes in a way that all items are reduced by a same ratio (Ramsey law). The more inelastic the demand for liquidity, the optimal inflationary tax will be higher for each given level of total required government revenue.

Samimi *et al*. (2012) examine the difference between the effects of inflation and inflationary tax.

In this study, countries are divided into two groups: high inflation and low inflation and found that in countries with high inflation, inflation has a negative impact on inflationary taxes and in countries with low inflation, this effect is positive.

Mojtahed and Ahmadian (2007) using the Mandel Flemming Model and macro-econometrics model, for three tax systems (tax on salaries, import taxes, and consumption taxes), studied the choice of the best tax system for Iran. The benchmark used for this selection is stability in target variables including price index, wage index, family welfare and imports. The results of this study show that the consumption tax is the best tax for Iran.

Komijani and Ismaeilnia (2017), measure seigniorage money in the economy of Iran using estimation of the demand for money according to Billy’s model. In this study seasonally statistical information for the period 1973-1994 have used and systematic method and the 3SLS least squares method has been used for estimation of the study. Results show that income elasticity of demand for money is about 0.2 in the short run, and 0.7 in the long run and the inflation rate in the money demand function is negative; That is, in inflationary conditions, people will try to reduce the demand for money and may preserve their wealth in other forms.

Most studies that have been done each has somehow followed one aspect of the discussion that follows this study, so what distinguishes this study from previous studies, is the review of Mankiw’s theory for the Iranian economy which has not been studied be the internal studied. In this study, the relationship between real seigniorage income and inflationary taxes in Iran will be reviewed seasonally in the period 1992-2014. Therefore, in the next section, theoretical and empirical foundations in the field of research are described. The second part is devoted to a review of previous studies. In the third section, the research methodology and the statistical basis are explained. In the fourth section, using the semi-parametric models, the research model was investigated and finally, a summing up and conclusion is presented.

## 2. THEORETICAL FOUNDATIONS

### 2.1. Iranian economy, Inflationary Taxes and Seigniorage Income

Iran’s economy after the eight-year imposed war with Iraq, suffered from chronic inflation in different periods, which peaked at 45% in 1994-1995. These years may be called “critical years” which oil revenues fell, failed to repay foreign debts and with abort of policy package of economic adjustment and the policy of unifying the exchange rate, rising inflation expectations and so on, inflation reached its highest point. In 2002, Central Bank in order to controling liquidity, has issued 18,000 billion Rials of equity bonds, but due to increasing monetary base and money multiplier, liquidity faces with growth of about 30% and the inflation rate reached 15.8. During the years 2003 and 2004, increasing trend of inflation was limited to 15.6% and 15.2%, respectively. In 2005, the inflation rate dropped by 3.1 and reached to 12.1%. In 2006, Iran was faced with tension in the region and intensified international sanctions, which coincided with the implementation of the fourth development plan. Oil revenues increased but the monetary expansion resulting from the use of the reserve currency account has led to an increase in monetary base and ultimately liquidity and inflation, so that the inflation rate went higher than the target rate. Iran’s economy entered the recession from the winter of 2011 and then in the year 2012 with the imposition of financial sanctions on international exchanges especiallyon the sale of oil and the transfer of foreign exchange into the country, foreign exchange income decreased drastically. Exchange volatility intensified in the years 2012 and 2013 and accordingly inflation in that years reached 30.5% and 34.7%, respectively. Table 1 shows inflation indicators, M1 to GNP, and liquidity (M2) to GNP in Iran. In this table it is clear that M1 and inflation are moving along together.

Table 2 also mentions inflation and the growth rates of money for some developing countries.

According to the above table, M1 and inflation in India and Egypt have not been moving along and in the countries of Qatar and Turkey have been moving along which is evidence that the reason for inflation in the countries of Qatar and Turkey is almost due to the printing of money while for Egypt and India should be looking for other causes. In the Figures 1, 2 and 3, Inflation (INFX), Inflationary Tax (INFTX), and seigniorage income (SEIG) of the Iranian economy are presented seasonally in the years 1992 to 2014 respectively, in which inflationary taxes were obtained according to Bailey’s (1956) work, by multiplication of seasonal changes in consumer price index and the monetary base. Also the seigniorage income is calculated according to Bailey’s (1956) which is equal to the changes in the monetary base. In the graphs below, both inflationary taxes and seigniorage income are divided into GNP.

As the graphs above show, the largest fluctuation in seigniorage income and inflationary taxes has begun since the middle of 2005 and are roughly the same trend. The highest inflation rate occurred in 2005, because of the infusion of money into development projects and booming of business. However, because of the injection of money between people in 2012 inflation has been rising. The difference between the years 2005 and 2012 is in the recession of the economy since 2011.

### 2.2. Mankiw’s Model of Optimal Seigniorage

Inflationary financing of the budget deficit, inflation tax and seigniorage has been in the special attention of governments and policymakers (Aslan, 2013; Bailey, 1956). In developing countries, compared to developed and industrialized countries, there are fewer options to finance the budget deficit and so the printing of money grows at a positive rate. Seigniorage is defined as a revenues earned by the government’s monopoly on printing money and is represented by the growth rate of money base divided by the consumer price index (ΔM / P). On the other hand, inflationary taxes arise as a result of inflation caused by the release of money in the community and it reduces the real capital holders’ money. Phelps (1973) obtained inflationary taxes from multiplication of the inflation rate and the real value of the amount of money, (Π.M / P). Marty (1967) using Tobin’s theory suggested another way to measure inflationary taxes. In this way, seigniorage income is equal to real balance of money multiplied by the sum of inflation and economic growth rate $\left(\text{\pi}+\text{g}\right)\hspace{0.17em}.\hspace{0.17em}\left(\frac{\text{M}}{\text{P}}\right)$.

Also, Phelps (1972) in his book Inflation Policy measures inflationary tax in the form of (*π* + r). (M / P) that r is the real interest rate. This definition states that revenues earned by the government after seigniorage, is equivalent to the loss of private sector interest rates.

Mankiw (1987) states that given government spending and budget constraints, when the government finances through monetary and financial policies, inflation rate and nominal interest rate move along with the tax rate more than ever. According to him, if fiscal policy dominates monetary policy (i.e monetary policies influenced by financial policies), government must target monetary and fiscal policies such that social costs associated with taxes and Seigniorage income reach their lowest value.

The Mankiw (1987) view can be summarized in the following framework. Temporary optimal monetary and fiscal policies should review by considering budget constraints, at present value. Government budget constraint is as follows:(1)

*G* (*t*): actual expenditures at time t

*T* (*t*): real income at time t

*B* (*t*): actual government debt at time t

*ρ*: Real discount rate

Expenditure in the exogenous form and future spending is a random variable. The government, taking into account the limitations, uses two ways to finance the budget deficit to minimize social costs: Taxes and seigniorage. If the level of production is indicated by Y (t) and the tax rate by *τ*(t), total revenue the government gains from taxes is equal to (*Y*(t) . *τ*(t)) and the social welfare that lost is equal to (*f*(τ) .*Y*) where *f*′ > 0 and *f*′′ > 0. If the exogenous money supply shown with M (t) and the price level at time *t* with *P*(t) and *k* is a constant, the demand for money will be as follows:(2)

If $\text{\pi}=\frac{\dot{P}}{P}$ and $g=\frac{\dot{Y}}{\text{Y}}$ respectively, show the inflation rate and the growth rate of real output, seigniorage income will be equal to:(3)

The proof of this relationship is as follows:

If receipts from direct taxes and seigniorage get together, the total government revenue is formulated as follows:(4)

Suppose that h (π) .Y refers to the social costs of inflation where *h*′ > 0 and *f* ′′ > 0. Examples of direct and indirect costs of inflation are menu costs and inefficient markets. To overcome this costs, government taking into account budget constraints, target minimizing expected present value of social costs. Therefore, the objective function according to the constraint stated in the previous section is equal to:(5)

The government has two choices to achieve this goal: The inflation rate π1 and another tax rate *τ*. Finally, Mankiw, considering the first-order conditions for Formula 5, reaches the optimal conditions as follows:(6)(7)(8)

Considering budget constraints, optimal monetary and financial policy, is represented by the three equations above. Intertemporal first order conditions of 6 and 7 Considered for the marginal social cost of taxes and inflation, in the present and future. Equation 8 also refers to the marginal social cost caused by government revenue through direct taxes and seigniorage. According to this equation, increasing government revenues requires an increase in both direct taxes and seigniorage. This function leads to a parallel move between taxation, inflation and nominal interest rates. Mankiw performed his optimal seigniorage theory for the period 1952 to 1985 in the United States and concluded that there is a direct relationship between nominal interest rate and direct tax rate and there is a long-term relationship between the inflation rate and the tax level.

## 3. METHODOLOGY

In this study, the theory of optimal seigniorage, has been tested for Iran’s economy using seasonal data between1997- 2014. The basic characteristic of the optimal seigniorage theory is that the inflation rate and nominal interest rate are determined by needs of government to revenue. In order to obtain an accurate estimate of the marginal social cost of inflation, the marginal social cost of taxes and interest elasticity of demand for money, in each time equation 8 can be used to derive the relationship between nominal interest rate, inflation, and taxes to time. In this research, due to lack of access to social costs, a semiparametric approximation of equation 8, (Similar to what Mankiw did with the American Time Series data), is estimated for the Iranian economy. In this regard, inflationary taxes, as described in the previous sections, is based on different aspects, which Phelps and Marty presented two aspects of its measurement methods. Therefore, the study of the relationship between inflation rate, nominal interest rate and inflationary tax can not be evaluated only with a parametric relationship, because it encompasses a vast space that does not have a particular functional form. Therefore given the concept of inflationary tax and inflation, and their relationship with nominal interest rates, the purpose of this study is to deal with this subject in a semiparametric form. Accordingly, application of nonparametric methods which do not require the specification of a parametric structure for functions and distributions in a model, can be appropriate.

### 3.1. Presenting Model

In conventional linear relations, a parametric approach is presented for analyzing the regression relationship. In the parametric form of analyzing the regression relationship, it is assumed that functional formis fully described by a limited set of parameters. A typical example of a parametric model is the polynomial regression equation whose parameters are the coefficients of the independent variables. A predetermined parametric model may be very restrictive and small in size to estimate the unexpected properties of the model, while the nonparametric uniforming approach, offers a flexible tool for analyzing unknown regression relationships. So the nonparametric term refers to methods without regard to distribution. Not the distribution of errors, nor the form of the function of the mean function is predetermined and clear.

In fact, a parametric approach, is based on the knowledge related to the past informations of the functional form of the relationship. If this knowledge is correct, the parametric method can correctly model most of the data. However, if the form of the selected relationship based on past information is false, results will have a large bias compared to competitive models (Fan and Yao). Parametric linear models as a kind of parametric regression, are often used to describe the relationship between explanatory variables and dependent variables. These models need to estimate a limited number of parameters. But why is a nonparametric regression important? Over the past decade, special attention has been paid to the nonparametric approach as a new method for estimating and predicting in various sciences, including economics. Nonparametric regression analysis putting aside the linearity assumption in regression analysis and gives more flexibility to the model. Also, these models do not need to specify functional forms for an item to be estimated. One of these methods, is the kernel method. Such methods are increasingly being considered for the analysis of practical data. Requesting non-parametric methods is derived from the fact that they lowered the parametric assumptions imposed on the data production process and let the data determine a suitable model. Rosenblatt in 1956, presented the first published paper includes kernel estimates, which his idea is suggested in a USAF Technical Report means separate analysis released from parametric specification. After that, this field has grown exponentially.

In nonparametric regression, the regression function of a variable y on an *x* variable is specified as follows:(9)

There are no assumptions about distribution, consistency of variance, serial correlation, or most importantly the form of a function. It may be that *μ* (*x*) is completely nonlinear. As this is a conditional average, the only real limitation is that the deviation from the conditional average function is not a function of *x*. So far, there are many possible techniques considered for the nonlinear average condition such as speline functions, polynomials, logarithms, imaginary variables, and so on. Here we are looking for ways which does not assume any form of functional function.

The simplest form of analysis is that many observations on *y _{i}* will be made with any particular value

*x*. Then, the conditional mean function can be estimated using the mean of the sample group. Smooth techniques are designed for the structure of estimating the conditional mean function without making strong assumptions about the behavior of the function between points. These techniques maintain the usefulness of the concept of the closest neighbor and they use accurate and detailed maps to create well behaved and smooth functions. The general class may be defined by a conditional mean estimated function:(10)

_{i}

When the sum of the weights becomes one, linear least squares regression line is like a fitting. Predictor (calculator) is as follows:(11)

When a and b are constant and slope of least square respectively. For this function it can be shown that:(12)

The problem with this particular weighting function is that all *x _{i}* are in the vicinity

*x*

^{*}, but it does not decrease the weight of each xi when it is far away from

*x*

^{*}, exactly what we want to avoid.

In fact, the purpose of a regression analysis is to provide a reasonable rational analysis for an unknown reaction and response of the function m, when for n data (*x _{i}* and

*y*), the relationship can be modeled as follows:(13)

_{i}

Contrary to the parametric view in which the function m is completely described by a finite parameter set, the nonparametric model adapts a very flexible form of the regression curve.

According to the materials mentioned, in this study Mankiw model of optimal seigniorage in the form of a semi -parametric spesification is defined as below:(14)(15)(16)

So that *B*(*z*) is based on the parametric approach and *m*(*w*) consists of the nonparametric part of the pattern which includes the tax rate variable, in this way, a semiparametric approach is used to explain the relationship between tax rate, inflation rate and nominal interest rate.

If these three variables have a long-term relationship with each other, there must be an equilibrium point that these three variables converge at that point. Also, the data used in this study are seasonal and in the period of 1992- 2014 Which is derived from time series data of the Central Bank and Statistics Center.

### 3.2. Estimation Results

In the previous section it was shown that the relationship between tax, inflation and interest rates can be presented using the nonparametric approach, and as there are different interpretations of inflationary taxes, by considering it in the nonparametric section, analysis of this relationship can be reviewed in the form of a semiparametric model. For this purpose it is necessary to be tested whether there is any difference between the parametric and the nonparametric model and whether the use of non-parametric models is allowed or not. The results of the second grade and first grade tests of Hardel and Mummen in this case is came in below:

In the above tests, the null assumption is that there is no difference between the parametric and the nonparametric model. The results of the Tables 3 and 4 indicate that the null hypothesis is rejected and analysis of the studied pattern can be investigated in the form of nonparametric model.

To estimate the model using the kernel method in the framework of nonparametric models, there are several options and in this regard, different results can be achieved due to the choice of different kernels. Among the kernels different from of the Gaussian kernel, Epanechnikov and Parzan have been selected and to calculate the standard deviation of the coefficient of parameteric section, bootstrap simulation is used. The results of each one are presented in Tables 5 and 6:

In each of the Tables 5 and 6, Epanechnikov, Gaussian and Parzent kernels is used respectively. In the first part of each table, the parametric results and in the second part, the nonparametric results are shown along with the corresponding confidence interval. As indicated in each figure, higher nominal rate, is along with the higher tax rate, as well as higher inflation which confirms the results of the Mankiw.

## 4. CONCLUSION

The discussion of monetary policy and its impact on the economy is mong the most important issues in the field of monetary economics and is devoted a large part of the research ti itself. Policy makers, through policies that they adopt, by adjusting and controlling the volume of liquidity, can affect the behavior of economic agents. One of these policies is government borrowing policy and finance the budget deficit through the creation of powerful money. One of the effects of this policy, which greatly affects society, is inflationary taxes. Discussion of inflationary taxes and earning money by the government from printing money, comes from the legal and exclusive right of government to printing money to finances its budget deficit by raising money and increasing the monetary base. Inflation caused by an increase in the amount of money, reduces the value of money which is like a tax imposed on the owners of money in the community. In this research, the Mankiw’s (1987) theory of optimal seigniorage were examined for the Iranian economy using seasonal data for the period of 1992-2014. For this purpose, semi-parametric models were used and the resulting relationship indicated that the higher tax rate is associated with higher inflation and higher nominal rates. The results indicate that there is a positive relationship between tax rate, nominal interest rate and inflation rate which is consistent with the findings of Mankiw.