This study purposes to estimate Pakistan's informal economy by monetary methods. Ordinary least square is used for estimation. From the monetary approach, we conclude that the informal economy is increasing. In our study, particular implications of the informal economy are identified and conferred to accomplish and achieve the goal of continuous growth and progression of a country. The informal economy plays a main role in income inequality and reducing poverty. It limits the implementation of the operative public policy. The government should make such policies to control the informal economy and increase tax evasion.

An informal economy constitutes a varied group of activities, businesses, employment, and workforces that are not regulated or sheltered by the law. Such self-employment in unregistered ventures is usually related to the informal economy. Initially, Keith Hart introduced the term informal economy in 1970. He described the informal economy as an occupation outside of government and categorized it into legitimate and illegitimate activities. Feige (1990) classified the underground economy as, an unrecorded economy, an unreported economy, an informal economy, and an illegal economy. Moreover, the precise estimation of the informal economy shows that it is significant for the growth of the economy of Pakistan. Like the informal economy, tax evasion has also been a major problem in Pakistan resulting from continually low tax flexibility and low tax reforms. Economists, political leaders, policy-makers, and nongovernment administrations around the world are concerned about the expanding informal sector and increasing number of tax-evaded individuals in their countries. The monetary approaches are used to measure the extent of the informal economy. The monetary approach was founded by Cagan in 1958. During World War II, he estimated unreported income. Then it followed by Gutmann (1985), Feige (1979) and Tanzi (1983). The monetary approach is divided into three methods viz. the simple currency ratio method, the transaction method, and the currency demand method. Gutmann (1985) measured the USA's subterranean economy in 1976 and found approximately 10 percent of recorded GNP. Ogunc and Y?lmaz (2000) estimate the underground economy as 16 percent in Turkey According to Davidescu (2013), the simple currency ratio method has been the most popular method to estimate the shadow economy. The simple currency method argues by Feige (1979) that the irregular economy is more desegregated than the formal economy so it is probable that income velocity is high. Feige (1979) built the transaction method which was based on Fisher's equation of exchange. He distillates on the volume of payments instead of changes in demand for currency. According to Schneider (2000), this method links total nominal GDP to total transactions, and then the official GDP is subtracted from total nominal GDP to estimate the informal economy. Ahumada et al. (2009) examined the size of the informal economy as a discrepancy between estimated total nominal income and observed nominal income. Feige's method is critiqued by Tanzi (1983 & 1999). He claims that the estimates of Feige are sensitive to the selection of the initial period. Further, claims that the velocity of income depends on the opportunity cost of holding cash too along with other variables that encourage economic agents to make informal transactions. The currency demand approach is based on the assumption that transaction is mostly done in cash form Cagan (1958). It is the most emerging and developing method to measure the informal economy. It is based on the assumption that income in the informal economy is generated by avoiding tax Schneider and Enste (2000). The average value of the underground economy is 15 percent. Kemal (2003) measures the underground economy by the currency demand method but he uses currency in circulation (CC) with foreign currency accounts (FCA) to M2. Also, create dummy variables to analyze the impact of hundi after the liberalization of FCA. According to Yasmin and Rauf (2004), the rise in the shadow economy is due to taxation. Their result shows that the shadow economy grew from Rs. 12 billion in 1974 to Rs. 1085 billion in 2002. Ahmed and Hussain (2008) used the currency demand equation to measure the shadow economy and reported taxation as a major reason for the increase in the shadow economy. The main criticism is given by Feige (1996), who argues that the reason behind the increase in the informal economy was a decrease in demand deposits rather than an increase in currency demand deposits. With the growth in the informal economy, the socio-economic problems are rising especially, the increase in the fiscal deficit. It resulted in a loss in tax revenues. Government expenditures rise with the official economy as well as the informal economy whereas public revenues rise with the official economy. However, this study estimates the informal economy through different monetary approaches and analyzes the trends of the informal economy and tax evasion.

In Lima, Hernando De Soto a president of the Institute for Liberty and Democracy (ILD) guided the Institute for Liberty and Demo (ILD) regarding the term informal sector. Hernando De Soto suggests that the informal sector is the sector, which works beyond the laws and regulations of government. He collected data on the housing, transportation, and trade sectors of the informal economy. Further, they calculated the income generated by these three sectors of the informal economy and found a huge size of informal activity. He claims that the government should remove regulations on housing, transportation, and trade sectors of the informal economy and should be allowed in the way of free market activity and capitalism. The government introduces programs planned to control the overpopulation problem, as it is the main cause of the housing. As informal housing, informal trade is considered another alternative for Peru's people to protect their private property rights. He divides informal trade into two parts i.e. informal markets and street vendors. De Soto expanded informal housing and informal trade through informal transportation. Similarly, to other informal sectors, informal transportation is divided into collective transport and minibus. In the second part of the book "The Other Path", De Soto compares the cost of the formal and informal sectors. And also estimate the role of the law in both sectors. He says "law is good", if it assures that they raise economic efficiency and "law is bad", if it delays or slows economic efficiency. Further, He concluded his study by saying that the economic indicators of Peru show a bleak image. According to him, the informal sector is only a path to attain the goals. Marquez (1990).

There are two approaches to measure informal economy i.e. direct approach and indirect approach. The direct approach is through conducting the samples and surveys but this approach is not reliable. Therefore, in our study, we use indirect approaches and through those approaches, we estimate the informal economy. The indirect approach is beneficial as compared to the direct approach because, in the direct approach, respondent does not want to recognize their informal activities. There are four types of indirect approach i.e. discrepancy approach, monetary approach, physical input approach, and model approach (Misra, Kumari, & Sajid, 2024; Kishwar, Bashir, Hussain & Alam, 2023).

The monetary approach is mostly commonly utilized to assess the extent of the informal economy. The monetary approach implies that the informal economy can be determined in the form of the demand for holding currency through which the extent of the informal economy and tax evasion is estimated. This approach comprises the simple currency method, the transaction method, and the currency demand method. All these methods are based on Cagan (1958).

The simple currency ratio method is the proportion between currency and demand deposits. This method indicates a rise in currency stocks and transaction payments that are unregistered by the government. Cagan's method was followed by Gutmann (1985) in finding the subterranean economy of the USA in 1976. Gutmann supposed that the increase in using the credit cards and checks is due to a comparative decrease in the currency demand over time. To this extent and growth of the informal economy can estimated. Guttmann indicates that the ratio increases because people are forced to withdraw their money by holding more currency and from demand deposits. But this is not necessarily in every case due to the transformation of money to time deposits from demand deposits. The mathematical equation of simple currency ratio can be given as

Yu = Yr (C ? KrD)/(Kr + 1)D…………………………………. (1)

According to this equation (1), if the formal economy improves, it will raise the growth of the informal economy rather than decrease it or it may remain unchanged if any improvement occurs. The simple currency ratio method is based on various assumptions. Firstly, all the informal transactions are done through using currency. Secondly, the currency to demand deposit remains unchanged excluding changes by the growing rate of unreported income. Thirdly the income velocity of money is the same for both the official and informal sectors. Fourthly there is a base year where there exists no informal economy.

Feige (1979) developed the transaction method. Transaction method is the relation among the volume of transactions and the GNP throughout the constant time. To assess the informal economy size, he uses the quantity theory of money which is eminent by the Fisherman equation of exchange. The equation is given as follows.

MV = PT …………………………………………………. (1)

According to this equation (1), Where M is known as the money supply, V is the velocity of money, P is the price of transactions and T is the volume of transactions. However, according to Feige, M is the currency in circulation plus total deposit. V is the velocity of money and PT is the nominal gross national product (GNP) minus real gross national product (GNP). The transaction method has various assumptions like the relation among the total transactions value and estimated GNP was normal as the informal economy was zero. If any increase occurs in the ratio of transactions it is because of the increase in the magnitude of the informal economy. There is the base year where the informal economy does not exist which further creates problems.

The currency demand method was originally presented by Cagan (1958) and then followed by Gutmann (1985) and Tanzi (1980). The currency demand method supposes that informal transactions are mostly done in the cash payments form so due to this demand for money is increasing. The increase in currency signifies the informal growth of the economy. Their result shows that tax evasion is the cause of the informal economy. This method involves the estimation of a currency demand equation. It was developed by Tanzi (1980). The major assumption of the currency demand method is that the informal sector grows by evading tax. Moreover, cash is used as a means of exchange for all informal economic activities and there exists a base year where there is no informal economy. Further, assume that the velocity of money is the same in formal economies as well as in informal economies. This method can be done in two steps, at first in the current state it is estimated through a currency demand equation, and secondly the tax rate zero. The discrepancy among these estimates indicates the currency in circulation used in the informal economy. And then by multiplying this discrepancy with the income velocity of money, the informal economy can be estimated. To estimate the informal economy, the econometric model used as follows

(CC/M2)t=??+?? (DT/Y)t_?+?? (TT/Y)t_?+ ??BSt+??IRRt+??YGt+??(CC/M2)t_?+? ……………………………….. (1)

Where, ??, ?1, ?2, ?3, ?4, ?5, and ?6 are the parameters and ? is an error term.

In Equation (1), the ratio of currency in circulation to the money supply (CC/M2) is used as the dependent variable. The other independent variables are lagged value of the ratio of domestic tax to GDP (DT/Y)t-1, lagged value of the ratio of international trade tax to GDP (TT/Y)t-1, banking services(BS), real interest rate(IRR), GDP per capita growth (YG) and lagged value of the ratio of currency in circulation to money supply (CC/M2)t-1. The theoretical justification for the several explanatory variables is given below. After estimating the currency demand equation, the informal economy and tax evasion are estimated. The predicted levels of currency ratio with taxes (CC/M2)t and without taxes (CC/M2)wt are estimated by utilizing an estimated regression equation. The discrepancy between (CC/M2)t and (CC/M2)wt indicates how much tax is induced by holding currency. Also shows that high amounts of direct and indirect taxes encourage people to hold high amounts of currency. The high level of currency demand indicates the size of tax evasion, which can be delineated as illegal money (IM). IM is illegal Money. It is the proportion of currency circulation to money supply with taxes minus the proportion of currency circulation to money supply without taxes multiplied by M2.

Mathematically it can be written as follows:

IM = (CC/M2)t - (CC/M2)wt * M2 ………....… (2)

The estimated illegal money yields legal money (LM). The illegal money is subtracted from narrow money (M1) we get legal money (LM). The legal money can be mathematically written as follows:

LM = M1 – IM………………………… . (3)

The gross national product (GNP) divided by legal money (LM) gives the income velocity of legal money (IV). It can be mathematically written as:

IV = GNP/LM ………………… ……... (4)

The illegal money (IM) is multiplied by the income velocity of money (IV), and the informal economy (IE) can be estimated. And can be mathematically written as follows:

IE = IM * IV …………………………...… (5)

The estimates of the informal economy are multiplied by the ratio of overall taxes (T) to GNP, and tax evasion (TE) can be estimated. The tax evasion can be mathematically written as follows:

TE = IE * (T/GNP) ……………………… (6)

From the above literature, the informal economy can estimated through direct or indirect approaches. These methods use the following variables. Total deposits are used as all types of deposits by overall banks. The gross national product is the aggregate of all final newly, produced goods and services within a country and net factor income from abroad. It was taken with base year 2005-2006. The income velocity of money is the quarterly average of monetary assets (M2) or as a GDP at current factor cost. Money supply comprises M1 and further types of deposits like savings deposits. A domestic direct tax is directly imposed upon the taxpayer. Domestic Indirect Tax is a tax which indirectly imposed on consumers by paying higher prices International trade taxes tax contains exchange profits, exchange taxes, import duties, export duties, import monopolies, or profits of export. Gross domestic product is the total aggregate market value of all final newly produced goods and services within a country in a given time period. It was used with the base year 2005-2006. Banking services that are an aggregate of total deposits to overall bank accounts. The real interest rate is different between the discount rate and expected inflation for a year. GDP per capita growth which obtained by dividing gross domestic product by midyear population. The narrow money includes all coins, currency used by the public, other deposits with the State Bank of Pakistan excludes IMF and SAF accounts, deposits with international government, organizations, and central banks plus scheduled time deposits exclude other deposits with interbank, international constituents, central and provisional government and plus resident foreign currency deposits. Data for all variables was taken in terms of Rupee units excluding real interest rate which was taken in percentage units. The analysis of this research is the major macro indicator of the economy in Pakistan. Secondary data was used. Data is collected through the State Bank of Pakistan, Labour Force Statistic, UN data, and World Bank. In simple currency method and transaction method, data was used from 1981 to 2017. For the currency demand method use data for the 1977 to 2017 time period.

The monetary approach is divided into three methods i.e. simple currency ratio method, transaction method, and currency demand method.

This method indicates a rise in currency stocks and transaction payments that are unregistered by the government. For the simple currency ratio method, the 1981 to 2017 time period is used to measure the informal economy. First, we find currency in circulation and total deposits of the informal economy. The currency in circulation of the informal economy is estimated by multiplying the forecasted value of the proportion of currency in circulation to total deposit by total deposit. For a total deposit of the informal economy multiply the forecasted value of the proportion of currency in circulation by total deposit by currency in circulation. After that, we can estimate the informal economy. For 2012 we assume that there is no informal economy or less that can be snubbed. It can choose where the proportion of currency in circulation to deposits (C/D) is minimal, so we chose 2012 as the base year. The estimated result shows that the informal economy is increasing in the overall time period in 2016 it decreased by 8736356? million. The informal economy as a percent of GNP also increased except from 2000 to 2006 and after 2016, the informal economy decreased as shown in Table A.1. The informal economy estimated by the simple currency method can also be shown in the graph in Figure 1. The graph illustrates the increasing trend of the informal economy but in 2016 it fell but overall informal economy shows an upward trend. The informal economy as a percent of GNP shows an upward trend but from 2000 to 2006 it falls and becomes downward in Figure 2. After 2006 it rose again and moved upward in 2016 and then again fell in 2017.

The size of the informal economy can be indicated by the discrepancy between MV and PT. For this method, we use data from 1981 to 2017. The estimated result shows 272056.49 million in 1981 and then increased to 963820.92 million in 1999. From 2000, it further increased by 3231274.1 million to 10684178 million in 2017 which is reported in Table A.2. The informal economy shows stagnant growth from 1981 to 1999 but after 2000 it shows an upward trend with the increasing rate in Figure 3. The monetary sector is influenced by informal income that varies the economy's liquidity position. Such as income from the informal economy is often used as an alternate source of finance, and the credit rationing policies of the monitory authority are established as incompetent.

Through the estimation of a currency demand equation, the informal economy can be estimated. The currency demand equation estimated by regression and unit root test and lag selection criteria is also done. The stationarity can be tested through the Augmented Dickey-Fuller (ADF) test, Ng-Perron test, and Phillips-Perron (PP) test. The most frequently used test among all tests is the ADF test. The ADF test shows all variables stationary at 1st difference except real interest rate and per capita economic growth which are stationary at level. There are various criteria for the lag length selection, the Akaike Information Criterion (AIC) and Schwarz Information criterion (SC) are the most important criteria among them. The optimal lag is selected on the basis of the minimum value of lags. According to the lag selection criteria, lag 3 is selected as it gives a minimum value. The regression model is run through the ordinary least squares (OLS) technique to estimate the currency demand equation. The results are acceptable as the coefficient signs are according to our expectations. As hypothesized coefficient signs of lagged domestic taxes (DT/Y)t-I and international trade taxes (TT/Y)t-1 are supposed to be positive signs and both (DT/Y)t-I and (TT/Y)t-1 are statistically significant positive which indicates that if the levels of domestic taxes and international trade taxes increase, individuals participate in tax evading activities. The coefficients of banking services (BS) and annual growth in real per capita GDP (Yg) are negative as assumed. It indicates that improvement in banking services and an increasing level of economic development may decrease the demand for holding currency. The coefficient of real interest rate (IRR) also results in a negative sign as expected, indicating that a high real interest rate may increase the opportunity cost of holding currency, and due to this demand for holding currency decreases. The coefficient of lagged currency-money ratio (CC/M2)t-1 is a positive sign as assumed showing the strong significance of current demand for holding currency with its lagged demand for holding currency. The R square is high i.e. 0.91 which is 91%, so our model is a good fit. The Durbin-Watson statistic is 1.54 indicating autocorrelation. The F-statistic probability is 0.00 which shows the overall model is significant. The explanatory variables' parameter estimates will be jointly statistically significant. The result is reported in Table A.3 in the appendix.

The size of the informal economy and tax evasion is estimated for the time period of 1977-2017. The estimated result shows that the informal economy grew rapidly to 13541414.31 million in 2017. On the other side, tax evasion grew rapidly from 2005 to 76184.06 million and increased to 4623503.14 million. The result shows the remarkable size of Pakistan's informal economy and tax evasion in Table A.4. The result is also portrayed in the figures. Between 1980-1986, it shows a downward trend in the informal economy. But from 1987-1998, it shows an upward trend and from 1999-2006, it increases at a decreasing rate. Then from 2007-2017, it shows an upward trend with an increasing rate as also shown in Figure 4. The informal economy was increasing in the period of 1990s because of the majority of tenuous and feeble political regimes. While the formal economy rose with a moderate growth rate, the informal economy can decrease the attributable involvement by the tax reforms for political stability, documentation, and developed governance. The rising public sector deficit is relatively due to the high growth of the informal economy considered an important factor because government expenses are rising with the formal and informal economy while government revenues rise with the formal economy at a slower rate. Figure 5 indicates tax evasion which shows stagnant growth from 1977-2004 but after 2004 it shows an upward trend with an increasing trend. The estimation of tax evasion is based on a pungent assumption that the informal incomes will be taxed at the same rate as the formal incomes.

The purpose of this paper is to estimate the informal economy by different monetary approaches, thus different methods yield different results but all of them show an increasing trend of the informal economy in Pakistan. All these methods give an accurate and reliable result but the currency demand method gives a more appropriate result. The estimated result explains the significant size of the informal economy. The monetary approach highlights the high influence of the informal economy with the increasing trend. There are several reasons behind the informal economy but according to estimated results, tax evasion was found the main factor affecting the informal economy. The estimated result of our study is different from previous studies done in Pakistan due to using different variables and different methods of monetary approach. The study provides an essential result for policymakers. Good governance may help to decrease the informal economy and tax evasion. The easy and simple taxation registration process can reduce tax evasion and the informal economy. Economic reforms should create political stability and a struggle against corruption and tax evasion. The government should make such policies to control the informal economy and increase tax evasion and corruption. If the government formalizes the informal economy by registering them at a low cost, making the registration process easier, and lowering the amount of taxes imposed on them, the country's growth will be doubled as compared to eliminating the informal economy. As we already know the current situation of Pakistan is suffering from socio-economic problems like unemployment, poverty, inflation illiteracy, etc.

Table 1