TThe Role of Money in the Business Cycle
Zhao Jianglin Sanyuan Institute for Financial Studies, Beijing, 100097, China
Abstract
The aim of this paper is to reemphasize the money theory of exchange which is centered on the function of exchange medium of money, and make a contribution towards linearization of the quantity equation of exchange. A dynamical quantity equation is presented and an important balanced path of economic evolution is derived. To understand the business cycle we propose a hypothesis of natural cycle and driving cycle concerning the evolution of the balanced path and plentiful conclusions can be made.
Key Words : money exchange theory; dynamical quantity equation; business cycle; inflation; monetary policy; golden growth; stagflation ; buffer rule; sensitivity rule.
JEL Classification : E3;E4 Email address: [email protected] 2
Introduction
The people’s understanding of money begins with its basic function as medium of exchange and the well-known quantity equation of exchange well describes the feature of the exchange between money and products. However, since the quantity equation of exchange was found to be able to be endowed with the significance of interpreting the demand for money, much attention has also been paid to research on another function of money, namely store of value (Fisher 1911, Keynes 1936, Friedman 1956). As a matter of fact, the function of value store described by the demand theory of money and the function of exchange medium expressed by quantity theory of exchange are two sides of a coin. The money demand theory believes that the higher nominal income a person takes, the more money he or she will hold, because money has a function of reserving value. If money can reserve the value, then what value is reserved by it? As people know, a product (including financial product) itself cannot embody its own value and its value must be realized through exchange between the product and money. Therefore, if money can store the value, then it must store the exchange value reflected by nominal income in the process of exchange, and thus the purpose which money exists is both to exchange and to store value. If the function of money is exchange medium, then the demand of money can be viewed to dependent on actual exchange process rather than liquidity preference of economic individuals. In other words, as an exchange medium, the demand of money is only determined by the number of transactions and its price as well as velocity of money and has nothing to do with other variables. On the other hand, both the behavior that people cost money as consumptions and the one that they invest money as assets are to make an exchange, thus the money for consumption constitutes the supply of money for physical product exchange while the money for investment provides a monetary supply for special commodity exchange such as credit exchange or property right exchange. In brief, any form of monetary movement is a manifestation of its function of exchange medium, and the quantity theory of money is above all a theory of exchange. Since money always plays a role of supplying exchange medium in the process of product exchange, the quantity theory is always a theory emphasizing the supply of money. The aim of this paper is to reemphasize the money theory of exchange and make a contribution towards linearization of the quantity equation of exchange. Firstly, a dynamical quantity equation is presented and secondly an important balanced path of economic evolution is derived. In the third section of the article we propose a hypothesis of natural cycle and driving cycle concerning the evolution of the balanced path to understand the business cycle, followed by an interpretation of China's economic cycle utilizing it in the fourth section. Finally we discuss the issue of inflation and monetary policy. A dynamical quantity equation of exchange
The most basic difference between the demand theory of money and exchange theory of money lies in the understanding of quantity equation
YPvM . (1) Here M is money supply, P is price and Y is real output; in addition, v is constant velocity of money. The demand theory understands that Eq (1) reflects the needs of the economic individual for money, not only the meaning of exchange. Under the assumption of liquidity preference, the demand theory introduces nominal interest rate into demand function of money, thus exhibits more economic pictures than traditional quantity theory does. However, in this section, we will show another picture of economic movement through linearization of exchange theory emphasizing exchange medium function of money. Let us assume that the central bank provides a very small supply M of money, which implies that the value PY of products manufactured by the producer will be unable to be realized only through one transaction. The producer has to suspend the transaction until the purchasers possess money at hand again, which will elevate the transaction costs and even result in the bankruptcy of the producer. Then, will the producer do nothing and wait for the bankruptcy? In reality, producers would rather adjust sales value through raising or lowering the price or amount of product to attempt the realization of a maximal sales value M than reserve the stock of products to subject the sale to the limit of velocity of money. In other words, producer would adjust price or real output to control the velocity of money, since the velocity of money can influence the realization of the product value. Every time money changes hands, a transaction is completed; thus numerous turnovers of money for an individual during a given period of time constitute a macroeconomic exchange iii Yp ; if the prices i p can be replaced by an average price P , then we can rewrite the value of exchange as YPYp iii . In a real economy, the producer will manage to make YP close the money supply M as much as possible through adjusting the real output or its price. For example, when a retailer comes to a strange community to sale his (or her) commodities, he or she always prefers to make a price through trial and error. If he finds that higher price can still promote the sales amount, then he will choose to continue raising the price until the sales amount less changes; on the other hand, if he confirms that lower price can create the more sales amount, then he will decrease the price of the commodity. His strategy of pricing depends on price elasticity of demand for the commodity. However, the maximal value of the sales amount is determined by how much money the community can supply, thus the pricing of the retailer will make his or her sales close this maximal sale value, namely money for consumption of the community. This explains why the same commodity can always be sold at a higher price in the rich area. This section wishes to point out that quantity equation (1) is not an identical equation but an equilibrium state of exchange process in an economic system. Evidently, the difference YPM between the supply of money and present sales value provides a vacancy for elevating sales value, in other words, the supply of money acts as the role of a carrying capacity for sales value. We assume that the vacancy is in direct proportion to velocity of increase of the sales value, and then derive a dynamical quantity equation dt tYtPdktYtPtM )]()([)()()( . (2) Here k is a positive constant and expresses a characteristic time with which the vacancy is filled. This is a speculated basic dynamical quantity equation of exchange by money. In reality, the money supply )( tM can usually be given; hence Eq. (2) is actually an evolution equation of sales value )()( tYtP , which can uniquely determine an evolving path of the price. The role of money in the Eq. (2) can be seen that money is only a medium of commodity exchange, just like the chopsticks for eating and the soap for washing. All needs for money are or will be order to carry out the commodity exchange. The behavior of holding money of the economic individuals implies a potential exchange in the future, whether for speculation or for the preservation of wealth, but it cannot directly determine the present price because every realistic price always comes from the commodity exchange, and no exchange and no price. In other words, what we concern is not reason of money generation but form of money generation, namely we are concerned about money generation as a function of time rather than it as a function of income or interest rate. The potential needs for money which you can use various reasons to explain cannot contribute to price as long as the money does not participate in the exchange, thus the money supply not used to exchange will not occur in Eq.(2). On the other hand, the change in money supply would result in a temporary vacancy of sales value, although sales value will also be achieved through exchanging with the new money supply at the next moment, since the price or sales volume may change. For example, a group of residents spend M(t) to buy houses of P(t)Y(t) through the loan at time t, evidently M(t)= P(t)Y(t). At time t+1, another group of residents spend M(t+1) to buy houses of P(t+1)Y(t+1) through the loan, and M(t+1)= P(t+1)Y(t+1). Thus, we can consider M(t+1)- M(t) as increase in money supply, and this increase can cause a temporary vacancy of sales value M(t+1)- P(t)Y(t). It is this vacancy that encourages sellers to try to maximize sales through adjusting the price by trial and error and also real estate developers to increase or decrease their housing production. Ultimately, new prices and production are produced and the exchange is completed at the level of M(t+1)= P(t+1)Y(t+1). In reality, the gap between M(t+1) and M(t) is often much smaller than the vacancy M(t+1)- P(t)Y(t), therefore we can approximately consider M(t+1) as M(t) if the money supply function M(t) is continuous and smooth. However, it is necessary to emphasize that Eq. (2) is not a generation equation of demand function )( YP , which means Eq (2) is a unique equation of determination of price (path), since, from the perspective of monetary exchange theory, the evolution of price depends only on money supply and production and arises from commodity exchange rather than relationship between supply and demand of products in the traditional economics where the meaning of the exchange is not obvious. In addition, velocity of money is not contained in this dynamical quantity equation, but its significance PY/M will be endogenously exhibited by the system. Examples
Normally, the growth of the real output follows the Solow equilibrium, which brings the pressure of goods sale to the exchange market. Hence pricing of market is often passive, in other words, the price )( tP shows a result of changes in the money supply )( tM and the real output )( tY in Eq. (2). We will solve the dynamical equation (2) for the cases of a few typical supply functions of money to observe the evolutions of the price )( tP . 1) )( tM Constant or )()( PYtM ( ) This case shows that Eq. (2) conforms to the Inada condition, and thus there must be an equilibrium sales amount )( PY as well as the equilibrium money supply M in the economic evolution. For example, when )( MtM =Constant, dynamical equation (2) becomes )()( MtWdt tdWk . (3) Here )()()( tYtPtW . Its solution is kt eMWMtW )()( , (4) where W denotes the initial sales value. Eq. (4) indicates that the fixed supply of money will constitute gross income of the society in the long run. Hence, velocity of money MW for large times. If the real output follows the Solow equilibrium, namely gYY =Constant, then the evolution of price can be obtained tkggt eY MWeYMtP )1(0 0000 )( , (5) where Y is the initial output. It shows that price will decrease to 0 as the real output is increasing for the long term, provided g , while the price can also increase if the real output is reducing, namely g . This result points out that the impact of the output is also a source of fluctuations of prices. It can be seen from Eq. (5) that the inflation rate PPc can be expressed as kt ekMWMk WMgc
000 00 )( . (6) Eq. (6) will not encounter the divergence because the denominator will never equal to 0 for positive , WM and t . Then the inflation rate and growth rate g for the real output should have the following relationship for the long term: gc . (7) It indicates a balanced path of price evolution, that is, the inflation rate will be the opposite number of the growth rate of the real output, when the monetary supply is fixed or output value-dependent. The equilibrium solution Eq(7) shows that price will hardly reaches equilibrium since it is mostly influenced by production, but the change rate of price, namely the inflation rate, will continue to move on the balanced path. There is a great difference between price equilibrium and price rate equilibrium. For example, the increase in production does not certainly lead to a decline in prices in the case of the fixed or the output value-dependent money supply, since it can only cause decline in the inflation rate and real price might still be rising. The traditional economics presents a concept of sticky price to bridge the difference between theory and reality, but it is unnecessary in the money exchange theory. 2) tVtM )( When the money supply equably increases as tVtM )( , where V is constant and defined as the supply rate of money, the dynamical equation becomes tVtWdt tdWk )()( . (8) Its solution with the initial condition )0( WW can be easily obtained kt eWkVtkVtW )()()( , (9) which shows a transient process of sales value decreasing since the term kt eWkV /00 )( will drop more rapidly for small times, while sales value and money supply will change in the same proportion in the long run. In other words, there will not be an equilibrium state of sales value in evolution of the system. In addition, velocity of money MW / will increase with time and be asymptotical to 1 for large times. Under the condition of the Solow production, the evolution of the price will be given by tkggt eY WkVetkYVtP )1(0 0000 )()( . (10) It is seen that the price will increase if the output is reduced, namely g . In addition, when g , the price could encounter a non-monotonic transient process in the early evolution, yet it will be asymptotical to 0 in the long run. The inflation rate can be expressed as )()( )()1(]1)([
000 000
WkVktkkVe WkVgktkgkVePP ktkt . (11) Evidently, the denominator will not equal to 0 for positive , WV and t , and when t , we have gc . In other words, there is the same balanced path of inflation rate here as that in the case of the fixed or the output value-dependent money supply. This path shows that a double drop of price and real production or a double rise of the two ones will not take place when money is supplied in term of constant, constant rate, or output value-dependent form, while deflation or inflation will occur only if economic growth is positive or negative in such an economy. Basically, a seesaw effect that inflation rate and economic growth remain always reverse is the only form of economic evolution for a non-exponential growth of money supply. 3) tq eMtM )( Money is normally plunged into the economy through bank loans to enterprises, essentially for the purpose of commodity exchanges. Hence, the supply of money is usually based on the exponential form tq eMtM )( . Here M is constant and q is constant growth rate of the money supply. Then the dynamical quantity equation of exchange can be is given by tq eMtWdt tdWk )()( . (12) Its solution can easily be obtained MkqWWeeMkqtW kttq . (13) It can be seen that sales value will exponentially grows as the money supply does for the long term, and the money supply serves as a driving force so that the sales value cannot attain an equilibrium state, but the system can still arrive at an equilibrium evolution path. In addition, Eq. (13) can become
MkqPY the constant coefficient kq And it shows that larger growth rate of the money supply will lead to a lower velocity of money in the long term, and when the growth of the money supply is zero, velocity of money becomes 1. In addition, in this model, velocity of money will not be greater than 1 for large times when growth rate of money supply q>0. In a similar way, we can derive the price expression )1( 1)(
MkqWWeeMYkqtP tkgtgq . (14) Evidently, the price will increase with time in a form of the exponential, so long as gq . Thus the inflation rate PPc may be given by )1( )()1( kqWWMek kqWWMkqqgc tkq . (15) We see that the inflation rate will be asymptotical to kg when kq , while it will be asymptotical to qg when kq . According to traditional quantity theory of money, the relation gqc can be derived when the assumption of constant velocity of money is made (Barro 1997, Mankiw 2003). However, the relation among the inflation rate and growth rate for the money supply as well as the rate for the real output is only a stable solution of our dynamical model when the money supply is provided in terms of the exponential form, and is not an identity relation. When the money supply is reduced at a higher rate kq , the inflation rate kgc will is not related to growth rate for the money supply in the long run, which implies that it could be the reason of hyperinflation or vicious deflation where the effect of money on the economy is failing. These results show that the well-known relation gqc holds only under certain conditions, while the equation kgc is a relation which has the same status as it, only the relation kgc is not a popular relationship since this situation seldom takes place. Since it is possible that g and q , the inflation rate will exhibit a complex behaviors which is showed as follows: c c kg kgq qkg kqg kqand kg kqand kg qgc kgc qgc kgc qgc Table 1. The long-run inflation behaviors for different relationships between the system parameters
It can be observed that the inflation will take place when growth rate for the money supply is greater than that for the real output, while the deflation will happen when the growth rate for the money supply is less than that for the real output. However, what kind of equilibrium path the economy is running along depends on a threshold value k of growth rate for money supply above which the economy will evolve in terms of the typical path gqc in the long run, and below which the economy would enter a disordered state where the inflation rate could depend only on rate for the real output, and have nothing to do with changes in money. The price function in terms of real output can thus be rewritten as kqYYkqWMWkqYYMYP kgkggqgq )|| 11(|| 10000||1||00 . (16) Since k , the long-run property of price function with respect to output depends on which of the two quantities, q and || g , is larger. Prices will be increasing with the real output in the long term if growth rate for the money supply is greater than absolute value of growth rate for the real output, which exhibits a rigid demand for the product of the market; while prices will drop as the real output is increasing if growth rate for the money supply is less than absolute value of growth rate for the real output, which shows an elastic demand for the product of the market. This is an intriguing conclusion because it shows that the price elasticity of the demand can change as growth rate for the money supply does. In other words, if the supply of money is fixed, then the demand for product will be elastic, which means that the price is a decreasing function of the real output; yet, when we exponentially increase the supply of money at a sufficiently large rate in the market, the demand for product will become rigid, which implies that the price is a increasing function of the real output. In other words, an iron needle can be turned into gold, provided the money is given fast enough . In reality, some governments have adopted policies to expand land supply in order to curb housing prices, but house prices have not been reduced. The dynamical quantity theory of money exchange by this paper can well explain this fact. However, although the increase in supply cannot reduce the price, it can reduce the price growth, which may be seen in balanced path gqc . It is necessarily noted that Eq. (16) reflects a relationship between price and output in the process of commodity exchange, thus Eq. (16) can be considered as both a demand function of product and a supply function of product. In this framework of money exchange theory, price is only derived from dynamical equation Eq. (2). We survey the existence of a balanced path gqc in the economy with data which World Bank provides. The Figure 1 plots average inflation against difference between average money growth and average real GDP growth for the period 1960-2015 for a sample of 161 countries. The figure provides powerful confirmation of the balanced path of the economy on inflation, money growth and real output growth. The linear regression in the logarithmic coordinates gives a slope of 1.054 with its standard error 0.058, and a correlation coefficient of 0.82, which shows that there exists a clear and strong linear relationship between the two variables. Figure. 1 The balanced path of inflation, money growth and real output growth.
The hypothesis of natural cycle and driving cycle
Since the equation gqc is equilibrium path of economic evolution, the economy will be evolving in terms of a straight line with a slope of -1 in the c-g space, and its intercept is money supply growth q. As you can see in the figure 2, each point on the line represents a state of economic evolution. If the other conditions do not change, the economy will always stay in a certain state. It is certainly impossible that the economy maintains such a fixed state, because real economy will be affected by a variety of shocks. Nevertheless, the state of the economic evolution should also move only on this straight line unless money growth q is changed. Therefore, we have reason to assume that the economy will always carry out periodic movement on this straight line, from a state of high inflation and low output growth to a state of low inflation and high output growth, and again from the state of low inflation and high output growth to the state of high inflation and low output growth, when q is fixed. Fig. 2 The hypothesis of natural cycle.
It is necessary to emphasize that this cyclical movement of the economy is a natural behavior when money growth is growing as a constant rate. Business cycle is the form of economic existence because the impact on the economy is always there. The economy will instinctively do the periodic movement on the balanced line for the constant growth of money when it is impacted by some factors. On the other hand, this reaction in accordance with natural cycle to economic shock implies that the economic crisis where inflation and economic growth will drop at the same time would never happen, unless money growth becomes smaller. The figure 2 also demonstrates two economic behaviors: the region A represents an economic type of high inflation and low output growth, which can be called stagflation , while the region B shows an economic type of low inflation and high output growth, which might be named as golden growth.
The economy will be coming from golden growth to stagflation and then come back, repeatedly, if money growth is steadily growing. Evidently, the hypothesis of natural cycle implies that high economic growth does not necessarily cause high inflation, which will be discussed in detail later. If money supply growth has been varying for some reason, which means that the straight line in the figure 2 will move up or down in parallel, then the equilibrium path of the economy will change. Normally, the economy is driven from the equilibrium state on the original line to the other one on the new line. This is another business c g Natural Cycle q A q B cycle that is different from natural cycle, it is caused and driven by changes in money growth, and it can produce two types of state migration: one is the “seesaw” effect between inflation rate and real output growth like natural cycle’s, and the other is “double” effect that inflation rate and real output growth change in the same direction. In short, we can call business cycle resulting from changes in money growth driving cycle . If the path of state migration goes along the dotted line which is within the rectangular fan AOB or COD in Figure 3, then inflation rate and real output growth will be dropping or rising at the same time. The economic situation where inflation rate and output growth are dropping at the same time, which can be called Double Drop (DD), is bad, and it reflects a basic characteristic of the economic crisis. On the other hand, the economic situation where inflation rate and output growth are rising at the same time, which can be called Double Rise (DR), is worrying, since it gives a false appearance that economic growth can bring inflation. Fig. 3 The hypothesis of driving cycle with the DD and DR.
The hypothesis of driving cycle with the DD and DR tells us that it is monetary authority that has the primary responsibility for the economic crisis. If monetary authority was able to keep the money supply growing steadily, the economy will never fall into crisis and enter the normal business cycle through the way of self-regulation, because the Double Drop can take place only when money growth becomes smaller. c g Driving Cycle q DD q DR A B C D O However, the economy may also not enter the DD or DR process even though money growth changes. This could depend on the magnitude of the change in money growth. Empirically, when money growth changes evidently, the economy will go into DD or DR, while money growth is only slightly changing, the economy will still look like it is in the natural cycle where there is a “seesaw” effect between inflation rate and real output growth. Therefore, the driving cycle behaving as natural cycle can be called relative natural cycle (RNC), and the driving cycle accompanied by the DD or DR can be called strong driving cycle (SDC). In addition, natural cycle due to constant growth for money supply can also be named as absolute natural cycle (ANC). As you can see in Figure 4, when the paths of state migration pass through the rest of region except for the area of the right triangle in between two parallel lines, such as from the state A to C or the state A to B, the Double Rise of the economy will not happen. There is still a “seesaw” effect between inflation rate and real output growth in this process, like that in the natural cycle, but money growth has been increasing. This is the so-called relative natural cycle. But it is obviously different from absolute natural cycle, because absolute value of the elasticity ∂c/ ∂g of price to real output on the migration path AC always is greater than 1, while absolute value of the elasticity ∂c/ ∂g of price to real output on the migration path AB always is less than 1. These absolute values of the elasticity are not equal to one which is exactly absolute value of the elasticity ∂c/ ∂g of price to real output on the migration path DC or EB of absolute natural cycle. We can call the state migration represented by path AC greater inflation (GI), and the state migration by path AB greater output (GO). Similarly, when money growth becomes smaller economic crisis characterized by DD could also not take place. If the path of state migration bypasses the area of the right triangle in between two parallel lines in Figure 5 arriving from the state A to B or the state A to C, there is still a negative correlation between inflation rate and real output growth as it looks in the natural cycle, yet money growth has been decreasing. This is also the so-called relative natural cycle and the absolute value of the elasticity ∂c/ ∂g of price to real output on the migration path represented by the dotted line AC always is less than 1, while absolute value of the elasticity ∂c/ ∂g of price to real output on the migration path by the dotted line AB always is greater than 1. The elasticity ∂c/ ∂g in the RNC is totally different from that in the NC where the elasticity of price to real output is -1. We can call the state migration represented by path AC in Figure 5 less inflation (LI), and the state migration by path AB less output (LO). Fig. 4 The hypothesis of driving cycle with the GI and GO
Fig. 5 The hypothesis of driving cycle with the LI and LO g Driving Cycle q q A B C D E c LI LO DD g Driving Cycle q q A B C D E c GO GI DR In short, the hypothesis presented in this section divides economic cycle into two forms: natural cycle and driving cycle. Natural cycle is experienced by the economy under the condition of constant growth of money, while driving cycle is the form of economic evolution when money growth is changing. However, driving cycle includes two types of operation mode, one is called as relative natural cycle (RNC) which shows there is still an inverse relationship between inflation and real output growth for small changes in money growth, relating to the four behaviors, greater inflation (GI), greater output (GO), less inflation (LI), and less output (LO), respectively; and the other is called as strong driving cycle (SDC) which indicates a positive relationship between inflation and real output growth for large changes in money growth, expressed by the double drop behavior (DD) and the double rise behavior (DR). In addition, there are two behaviors, stagflation and golden growth , in the natural cycle. In other words, an economy can have eight kinds of behavior to show in front of people, which has been clearly exhibited in Table 2. natural cycle (NC) driving cycle (DC) relative natural cycle (RNC) strong driving cycle (SDC) stagflation golden growth greater inflation (GI) greater output (GO) less inflation (LI) less output (LO) double drop (DD) double rise (DR)
Table 2. The behaviors of business cycle
On the other hand, there is a triangular deterministic relationship among money growth q, the elasticity of price to real output ∂c/ ∂g and economic behaviors, which means if you know the information of any two factors, then you can determine the situation of the third factor. As the matter of fact, the elasticity of price to real output ∂c/ ∂g reflects if the economy is running in the natural cycle, because the economy will be either in the natural cycle or in the relative natural cycle when the elasticity ∂c/ ∂g <0, while the economy will experience the strong driving cycle characterized by the DD or the DR when the elasticity ∂c/ ∂g >0. In other words, the elasticity of price to real output ∂c/ ∂g also indicates the degree of change in monetary growth relative to that on the original equilibrium line. For example, it would show money growth has undergone great changes if ∂c/ ∂g >0 so that the economy can get rid of the effect of seesaw between inflation and production growth in the natural cycle or relative natural cycle. If = −1 , it would show the economy is still running on the original equilibrium path; while if −1 < < 0 or < −1 , it would show that money growth q less changes, compared with the case of ∂c/ ∂g >0, so that the economy can still exhibit a similar nature to that of the absolute natural cycle, such as the seesaw effect between inflation and production. Therefore, if we know the direction of change in money growth and the degree of it, we can deduce the behavior this economy should demonstrate; or if we know the behavior of the economy and the direction of change in money growth, we can estimate the degree of change in money growth, namely the elasticity of price to real output growth, and also if we know the behavior of the economy and the degree of change in money growth, we can determine the direction of change in money growth. This is the triangular deterministic relationship among the direction of change in money growth, the degree of it, and the behavior of the economy, which has been summarized in Table 3. q=constant q↑ q↓ | | =1 g↑,c↓(golden growth) g↓,c↑(stagflation) | | >1 g↓,c↑(GI) g↑,c↓(LO) | | <1 g↑,c↓(GO) g↓,c↑(LI) >0 g↑,c↑(DR) g↓,c↓(DD) Table 3. Triangular deterministic relationship among money growth, the elasticity of price to real output and economic behaviors. Finally, it can be concluded from the hypothesis of natural cycle and driving cycle that macroeconomic growth can naturally adjust to a suitable state when it is impacted by various economic factors if the money supply growth rate is stable, and the government's wrong monetary policy is the source of financial crisis. In other words, the economy will experience the cycle, but never encountered a crisis, unless the government implements a tight monetary policy.
The economic cycle of China
China's economy has made great growth since 1979. No doubt this achievement can be explained by technological progress, institutional change and good labor structure, but the implementation of a stable monetary policy by China's monetary authority also plays an important role. As a matter of fact, it is steady and rapid growth of the money supply that monetary authority has maintained, so that China can successfully weaken the impact of several global financial crises and thus keep a high economic growth in the long term. In this section, we would explain the cycle of Chinese economy according to the hypothesis of natural cycle and driving cycle. We cite annual data of growth for money, real GDP and consumer price index of China in the period 2002-2016 from OECD official website in order to certify our statement about business cycle. The data are exhibited in the table 4, where it may be observed that the whole period contains three types of cycle, respectively the DD cycle, the DR cycle and the relative natural cycle, and the contents of the thick box in the table 4 represent the type of relative natural cycle characterized by rising growth for real GDP and falling growth for CPI simultaneously, or falling growth for real GDP and rising growth for CPI simultaneously. In fact, the actual economy is difficult to appear in the absolute natural cycle because the value of monetary growth will change somewhat every year. On the other hand, the DD cycle is characterized by dropping growth for real GDP and growth for CPI simultaneously and the DR cycle is defined by rising growth for real GDP and growth for CPI simultaneously. Therefore the whole period can be divided into different regions represented respectively by the three cycle types, which has been demonstrated in the Table 5. year Growth for broad Money(M3) Growth for real GDP Growth for CPI 2002 16.8 9.1 -0.8 2003 19.9 10.0 1.2 2004 16.4 10.1 3.9 2005 16.0 11.4 1.8 2006 16.8 12.7 1.5 2007 17.5 14.2 4.8 2008 16.5 9.7 5.9 2009 26.2 9.4 -0.7 2010 20.9 10.6 3.3 2011 15.7 9.5 5.4 2012 17.3 7.9 2.6 2013 14.8 7.8 2.6 2014 12.8 7.3 2 2015 11.8 6.9 1.4 2016 12.1 6.7 2 Table 4. The growth for broad money, real GDP and CPI of China from 2002 to 2016. year 2002 2003 2004 2005 2006 2007 2008 2009 The type of cycle DR RNC DR RNC DD year 2010 2011 2012 2013 2014 2015 2016 The type of cycle DR RNC DD RNC
Table 5. The spectrum of the type of China's business cycle from 2002 to 2016. There are two laws of the evolution of business cycle that can be found in the above tables. Without these two laws, the interpretation of China's economic cycle is not so smooth in the context of the hypothesis of natural cycle and driving cycle. It can be observed that inflation rate will be very sensitive to money growth when money growth closes to real GDP growth. For example, money growth of China is 17.5% in 2007, only higher 23.2% than its real GDP growth 14.2%, and thus inflation rate becomes sensitive to money growth so that the growth for CPI may drop sharply from 5.9% in 2008 to -0.7% in 2009 when the growth for money falls less from 17.5 in 2007 to 16.5 in 2008. However, in 2000, money growth of China is higher 55.3% than its real GDP growth, which determines that inflation is not more sensitive to money growth. This sensitivity rule can be well explained by driving cycle hypothesis. Let us assume that line AB is specified as the initial equilibrium path of the economy in Figure 6, the point B represents an economic state where money growth q is closed to real output growth, and the point A represents an economic state where money growth q is far greater than real output growth. When the economy changes from the initial equilibrium line AB to another equilibrium line DC in parallel, the state B will move to the state C and the state A to D. If real output growth rates of both the state A and B have only a small change in the process of state migration so that changes in inflation of both states can be approximately considered as being equal, then the acceleration of inflation of state B will be much greater than that of state A, since inflation of the state B is less than that of the state A. Therefore, it can be inferred that an economy will be at risk of a crisis if its money growth is near to its real output growth . This is the first one of the two laws found in Table 4, which can be called sensitivity rule. The second law can be described as buffer rule that when money growth is evidently falling so that the economy can attain the DD, the economy will always experience a buffer period characterized by NC or RNC before both its inflation and growth for real output drop. For example, it can be observed in the Table 4 that the fact that the growth rate of money has been reduced from 2007 to 2008 would result in a DD, yet the DD does not happen immediately but occurs in 2009 after a RNC in the period 2007-2008. Similarly, the DD which takes place in 2012 is also the thing after experiencing the RNC in the period 2010-2011, but it should have happened immediately in 2011 due to the decline in money growth from 2009 to 2011. Fig. 6 The explanation for the sensitivity rule.
However, there is not the buffer phenomenon when the economy is going to the DR because of rising money growth. The economy can often enter the DR process soon after money growth evidently increases. The buffer rule only for the DD process implies an instinctive resistance of economy to the impact of falling, which also reflects that the response of economy is not symmetrical to the upward and downward impact. In addition, the fact that money growth has an evident increase when money growth is far away from real GDP growth can be empirically identified if money growth is increased by 3 percentage points or more; and the economic DR will take place once money growth increases evidently. On the other hand, the fact that money growth has an evident decrease when money growth is far away from real GDP growth can be empirically identified if money growth is reduced by 4 percentage points or more, which means that the terrible DD will arise once money growth falls by 4 percentage points or more. Finally, if money growth is close to real GDP growth, empirically money growth is less than 35% higher than real GDP growth, then the change of money growth only less than 1 percentage point can cause the DR or DD. Yet, these principles of experience are only limited to China's economy. g Driving Cycle A q q B D C c Let us explain the cyclical nature of China's economy in the period 2002-2016 in order to prove the hypothesis of the natural cycle and driving cycle is correct. We observe in Table 4 that an evident increase in money growth of China from 2002 to 2003 can account for economic DR happening in the period 2002-2004; yet the decline in money growth from 2003 to 2005 is not evident enough to cause the DD in the future, and continuous decline in money growth in the period 2003-2005 can account for the LO emerging from 2004 to 2005 if the slope of line connecting the state (10.1, 3.9) and (11.4, 1.8) is less than -1, in fact this slope of the state migration line between 2004 and 2005 is about -1.6 in line with our expectation. In addition, the fact that small increase in money growth from 2005 to 2006 can also account for the GO occurring in the same period because this slope of the state migration line between 2005 and 2006 is about -0.23 within our expectation. However, when money growth is only 32% higher than real GDP growth rate in 2006, the economy has become very sensitive so that slight increase in money growth can lead to the DR in 2007. Similarly, slight decrease in money growth can lead to the terrible DD in the context of the sensitive period of the economy, but the DD will experience a buffer period to happen. Thus the period 2007-2008 in the RNC may be understood as a buffer period after which the DD takes place in 2009. It must be admitted that we still have no way to confirm the type of economic behavior in the buffer period. It can be noticed that there is an evident increase in money growth from 2008 to 2009 and money growth is far away from real GDP growth in the same period, which can thus lead immediately to the DR in 2010. But money growth has an evident decline in 2011, which indicates a coming DD after a buffer period 2010-2011characterized by RNC. That is the reason that China’s economy has experienced a four-year period of inflation and production growth dropping simultaneously since 2011. In addition, small increase in money growth in 2012 can account for the GI in 2016 after the four-year period of DD because the slope of state migration line from 2015 to 2016 is about -3 conforming to the expectation of this theory; and not significant annual reduction in money growth since 2012 might also indicate that China’s economy will experience a RNC characterized by the LI or LO behavior in the future. Inflation and monetary policy
The traditional economics believes that there exists an output-inflation tradeoff in the short term, which means that it is impossible that both higher economic growth and low inflation can be attained at the same time. Policymakers may either increase the money supply to promote output but it will also push up inflation, or be reluctant to choose a recession to reduce inflation if they are faced with inflation problem. However, traditional economists also consider that output-inflation tradeoff does not exist in the long term since average inflation has no effect on average output. In order to bridge the contradiction between the two output-inflation relations, the dynamic-inconsistency theory has been proposed and developed (Kydland and Prescott, 1977 ; Barro and Gordon, 1983; Backus and Driffill, 1985; Rogoff,1985). It describes that the public’s knowledge of policymakers’ discretion will make policymakers deviate from their policy so that a low-inflation monetary policy may cause inflation without any increase in output, and thus the output-inflation tradeoff will vanish in the long run. Unfortunately, the dynamic-inconsistency theory can hardly predict actual inflation and account for the time-series variation in inflation (David Romer, 2003) so that the invalidity of it may be attributed to a belief on the part of policymakers that there might be a long-run output-inflation tradeoff (Samuelson and Solow 1960; De Long, 1997; Mayer,1999). The problem of how output-inflation tradeoff can lead to inflation has so far been confusing and controversial. In the framework of this dynamic quantity theory of exchange, there is no concept of the output-inflation tradeoff whether in the short run or in the long run. The economic situation of low inflation and at the same time high output growth is an ordinary economic operation form as stagflation where high inflation and low output growth occur simultaneously does. A low-inflation policy can lead to higher inflation through three ways. The economy may arrive in high inflation with small or large change in real output through the direct RNC process if money growth slowly increases or declines, namely through GI or LI behavior of economy (See Figure 4 or 5). The economy can also experience a DR process when money growth is evidently increases and then do a NC due to production atrophy to attain the high inflation region. The economy is certainly likely to reach high inflation only along the balanced path where money growth rate is constant. We can observe that a low-inflation policy may eventually result in inflation because of changes in money growth or production atrophy, and thus it does not need to use the output-inflation tradeoff theory and dynamic-inconsistency theory to explain. According to the dynamic quantity theory, it is not necessary that the policymakers make a choice between low inflation and high economic growth. The policymakers only need to maintain the stability of monetary growth so that the economy can run in the natural cycle where economic crisis characterized by the Double Drop may be avoided. The policymakers may of course take an accelerated monetary policy for the economy to go into the Double Rise channel, but once the economy is not able to have greater growth, the economy will inevitably be slipping to stagflation. Moreover, the inflation is caused only by the accelerated monetary growth or the decelerated output growth in this framework and accelerated output growth resulting from financial incentive policy never induces inflation. This could be a long-term misunderstanding of economic growth and inflation. Conclusion
The aim of this paper is to reemphasize the money theory of exchange and linearize the quantity equation of exchange. We present a dynamical quantity equation and then an important balanced path of economic evolution is derived. To understand the business cycle we propose a hypothesis of natural cycle and driving cycle concerning the evolution of the balanced path and plentiful conclusions can be made. First conclusion is that there is no price balance in the free economy but a balance of price growth, which can well understand why more housing supply cannot stop the long rise in housing prices in many countries since variation in output growth changes the balanced price growth rather than the balanced price. Secondly, it is believed that the economy will intrinsically never encounter the crisis where inflation and output growth are simultaneously dropping if money growth is stable, unless money growth is evidently reduced. Thus policymakers should ensure the borrowing of private enterprises and also should promote borrowing of public projects when the private sector's demand for money is insufficient in order to maintain the stability of the money supply. The business cycle can be divided into two types, natural cycle and driving cycle; and driving cycle includes relative natural cycle and strong driving cycle; while all economic performance can be attributed to one of the eight behaviors. Moreover, there is a triangular deterministic relationship among money growth q, the elasticity of price to real output ∂c/ ∂g and eight economic behaviors, which means that you can judge the situation of any one factor when the other two factors are known. This paper also discusses the problem of inflation and monetary policy and point out that there is not the output-inflation tradeoff, and accelerated output growth will never raise inflation rate. The inflation is caused only by the accelerated monetary growth or the decelerated output growth in this framework. Moreover, both golden growth and stagflation do not need to be explained in particular, since the two economic situations are only normal state of economic evolution. In addition, we also find technically effects of money growth, output growth, and inflation, for example, buffer effect that the economy will always experience a buffer period before it is doing the DD migration between states, and sensitivity effect that inflation rate will become very sensitive to changes in money growth when money growth closes to real GDP growth. References
Fisher, Irving. , The Purchasing Power of Money , (New York: Macmillan, 1911).
Keynes, John M. , The General Theory of Employment, Interest and Money , (London: Macmillan, 1936).
Friedman, Milton. , “The Quantity Theory of Money—a Restatement”, in Milton Friedman, ed., Studies in the Quantity Theory of Money , (Chicago: University of Chicago Press, 1956).
Barro, Robert J. , Macroeconomics , 5th edition, (Massachusetts: MIT press, 1997)
Mankiw, N Gregory. , Principles of Macroeconomics , Kydland, Finn E, and Prescott, Edward C. , “Rules Rather than Discretion: The Inconsistency of Optimal Plans.”,
Journal of Political Economy , 85 (June), 1977, pp. 473-492.
Barro, Robert J, and Gordon, David B. , “A positive Theory of Monetary Policy in a Natural Rate Model.”,
Journal of Political Economy , 91 (August), 1983, pp. 589-610.
Backus, David, and Driffill, John. , “Inflation and Reputation”, American Economic Review , 75 (June), 1985, pp. 530-538.
Rogoff, Kenneth. , “The Optimal Degree of Commitment to an intermediate Monetary Target.”, Quarterly Journal of Economics,
100 (November), 1985, pp. 1169-1189.
David, Romer. , Advanced Macroeconomics , 2nd edition, (Shanghai University of Finance & Economics Press and McGraw-Hill, 2003)
Samuelson, Paul A, and Solow, Robert M. , “Analytical Aspects of Anti-Inflation Policy.”,
American Economic Review , 50 (May), 1960, pp. 177-194.
De Long, J. Bradford. , “America’s Peacetime Inflation: The 1970s.”, In Christina D. Romer and David H. Romer, eds.,
Reducing Inflation: Motivation and Strategy , pp. 247-276, (Chicago: University of Chicago Press, 1997).