Friedman, an American economist, believes that the theory of money quantity is not about output, money income or price level, but about money demand, that is, what factors determine money demand. Therefore, Friedman's restatement of the theory of money quantity is based on the demand for money.

Friedman regarded money as a form of assets and analyzed people's demand for money with the theory of consumer demand and choice. According to the consumption choice theory, consumers must consider three factors when choosing consumer goods: income, which constitutes budget constraints; Commodity prices and prices of substitutes and supplements; Consumer preference.

1. Similarly, the first factor that affects people's money demand is the budget constraint, that is, the amount of money that an individual can hold is limited by his total wealth. And take permanent income as the representative of total wealth. Permanent income refers to the average of past, present and future income, that is, the average of long-term income. Friedman noted that there are human wealth and non-human wealth in the total wealth. Human wealth refers to the ability of individuals to earn income, while non-human wealth refers to material wealth. Friedman regards the proportion of non-human wealth to total wealth as an important variable that affects people's money demand.

2. The second factor that affects money demand is the expected rate of return of money and other assets, including the expected rate of return of money, the expected rate of return of bonds, the expected rate of return of stocks and the expected rate of price changes.

3. The third factor that affects money demand is the preference of wealth holders.

Taking money as one of various assets, this paper puts forward the functional formula of money demand through the analysis of seven factors affecting money demand. The monetary school emphasizes that there is a functional relationship among money demand, permanent income and expected returns of various non-monetary assets, and the money demand function has the characteristics of stability.

He thinks:

Y is the actual permanent income;

W the ratio of non-human wealth to personal wealth;

Expected yield of rm currency;

Rb interest rate of fixed income securities;

Re non-fixed income securities interest rate;

Expected price change rate;

U other variable functions.

He emphasized that the fluctuation of permanent income is much smaller than that of regular income, and the speed of money circulation is relatively stable, so the demand for money is relatively stable.

Friedman believes that the money demand function is stable because:

1. The factors that affect money supply and money demand are independent of each other.

2. Some of the function variables are relatively stable.

3. The velocity of money circulation is a stable function.

Therefore, the influence of money on the overall economy mainly comes from the supply of money.

[Editor] Friedman's function hypothesis of money demand theory [1]

1929- 1933 World economic crisis, World War II, post-war European Renaissance, and long-term world economic downturn. Therefore, from 1936 to the end of 1950s, it was the heyday of Keynesian school. However, after that, the phenomenon of large-scale economic depression is no longer the theme of the world economy, but inflation. In the 1970s, simple inflation became more complicated "stagflation". This change in the economic environment has led to the revival of the theory of money quantity. Friedman's hypothesis is different from Keynes's hypothesis in the following two aspects:

1. Long-term analysis shows that price plays a role, and it also plays a role in future price expectations.

With the recovery of European economy, the world economy has grown substantially, as shown in Figure 2- 10, and the output (Y 1) is close to or reaches the output of full employment Y *. If the fiscal policy and monetary policy under the guidance of Keynesian economics are still followed, the total demand will further increase (from AD 1 to AD3), and the result can only be "stagflation"-only price increases, but no economic growth (from P2 to P3 prices). In the long run, price variables are variable and have an impact on national income. Under the condition of inflation (the price range is from P 1 to P2), the price will affect the real national income more or less (from Y 1 to y *); ; Under the condition of stagflation, the price affects the nominal national income.

The sustained inflation since the 1960s has had an impact on people's price forecast for the next period. There must be three kinds of price expectations: bullish, bearish and unchanged. The first two will have an impact on people's expenditure and thus on the economy. As many economists have said, "what most people expect will happen."

2. The level of money quantity is that it includes money and quasi-money.

Different from Keynes, Friedman expanded the coverage of money and defined money at the level of broad money, which is what the insiders said. As we all know, there are many definitions of money. For example, the Federal Reserve has at least six definitions of money. Most economists discuss the definition of money from a purely theoretical point of view, that is, the function of money. The monetary school is different. Friedman believes that the definition of money should be determined by strict econometric methods. The criteria for determining the most appropriate definition of money are:

(1) The correlation coefficient between monetary aggregate and national income is the largest. For example, if the correlation coefficient between M2 and GDP is greater than that between M 1 and M3 and GDP respectively, M2 is more likely to be used as currency. At the same time, we must look at the second standard.

(2) The correlation coefficient between monetary aggregate and national income is greater than that between each component of monetary aggregate and national income. For example, the correlation coefficient between M2 and GDP is greater than that between M0 (cash), Dd (demand deposit) and Dt (time deposit) and GDP.

The above two criteria must be met simultaneously. According to these two standards, Friedman and Anna Jacobson Schwartz (1915-) defined M2 as the best currency.

Friedman's theoretical function of money demand [1]

1956, Friedman published a famous paper "Restatement of the Theory of Quantity of Money". In this paper, Friedman expressed the theoretical function of money demand as follows:

( 1)

The symbolic meaning in equation (1) and the correlation between function and independent variable are as follows:

1 and Md are nominal money demand, which are dependent variables and determined by independent variables.

2.p is the price index. In order to realize normal consumption or operation, the higher the price of goods and services, the more money should be needed, which is positively related.

3. The expected nominal yield of bonds; Where rb is the bond interest rate. The confusing score is the expected rate of change in bond interest rates. Why is it written in this form? Let's make a simple explanation for this. Experience shows that the bond interest rate changes with time, that is, rb = f(t). If the rate of change of a function at any point is required, the logarithmic derivative (lnrb)t of the function is required. According to the derivative rule of composite function, there are

(2)

After understanding the meaning of mathematical expressions, let's discuss the correlation between variables and functions. The current bond interest rate MINUS the expected change rate of bond interest rate is the expected yield of bonds. The increase in the expected yield of bonds means that the opportunity cost of holding money increases, and rational economic individuals must reduce the demand for money as much as possible and replace it with bonds with higher expected returns. On the contrary, the opposite is true. Obviously, the expected yield of bonds is negatively correlated with the demand for money.

4. It is the expected nominal rate of return of the stock; Among them, re is the stock return rate; The expected rate of capital gains and losses, that is, the rate of change of stock prices, has the same mathematical significance as before; Is the expected rate of change in stock returns.

The mechanism of expected nominal return of stocks is the same as that of bonds, and the variables are negatively correlated with the function MD.

5. Like the previous reason, it is the expected price change rate. If the price is expected to rise, it means that the purchasing power of the next currency will decrease. In this way, people will inevitably reduce the amount of money they hold and use other assets that can be preserved to preserve their value. On the contrary, the opposite is true. Needless to say, the two are negatively correlated.

6.w is the ratio of human wealth to total wealth. According to Friedman's idea, it can be expressed by the following formula:

w=

Human wealth *

Human wealth+material wealth

income

destiny

What is the relationship between sum in Friedman's monetary demand theory function? I don't know why, but Friedman didn't explain. Moreover, in the monetary theory circle, there is no universally recognized research conclusion.

7.y is "permanent income". Permanent income is different from the concept of "statistical income" that we often use. It is the algebraic sum of statistical income and "temporary income". In other words, the statistics of permanent income is the geometric weighted average of statistical income. Why did Friedman replace general national income with permanent income? Our understanding is this: in the long run, assuming that a person's average income level is 6000 yuan per month, he basically forms a relatively stable consumption and expenditure habit, thus determining the demand for money. He will not change his consumption and expenditure habits because of the accidental increase or decrease of his income in a certain month, which will lead to the demand for money. For example, increase 1000 yuan, which he may use to buy government bonds; By reducing his holdings by 1 000 yuan, he may sell some bonds in his hand to ensure that his consumption and payment habits remain unchanged. If he is convinced that the average income has increased (decreased) to a new level, he will adjust his consumption and expenditure habits, thus determining the new money demand. The "average income" mentioned here roughly means "permanent income".

The correlation between permanent income and MD is positive, just like Keynes's income and MD.

8.u is other random factors that affect the utility of holding money, such as preference, institutional changes related to money, and so on. Obviously, due to the randomness of U, its relationship with Md is uncertain.

It should be noted that in many economic monographs, the relationship between variables and functions is expressed by first-order partial derivatives. As we know, the derivative is the rate of change of the function at a certain point on the curve and the slope of the tangent at that point. When this slope is greater than 0, the independent variable rises and falls with the function, and the positive number is related; On the other hand, if the slope is less than 0, the independent variable changes inversely with the function, and the negative number is related.

Later, in the book Currency Trends in the United States and Britain, Friedman simplified the theoretical function of money demand of a single wealth holder as:

(3)

The symbols in formula (3) have the following meanings:

1. is the actual money demand;

2.Yr is the actual permanent income, that is;

3.w and U have the same meaning (1);

3.Rm is the expected nominal rate of return of money, which can be understood as the expected rate of return of time deposits under other conditions unchanged. This is a new variable, because it measures the income from holding money, so it should be positively related to the demand for money.

4.Rb is equivalent to formula (1);

5.re is equivalent to formula (1);

6.gP is equivalent to formula (1).

In addition to replacing some difficult mathematical expressions in the formula (1) with simple symbols and adding variables of money yield, the significant difference between the formula (3) and the formula (1) is that the function replaces the nominal money demand Md with the actual money demand. How is this converted? In other words, how can the price variable be on the left side of the equation?

Friedman further assumed that the function is determined by real variables, that is, it is completely independent of the nominal unit for measuring monetary variables. If the unit for measuring price and nominal income changes, the money demand will also change in the same proportion. Described in mathematical language, the sum of the formula (1) is first-order homogeneous. Review the advanced mathematics we have learned;

If the independent variable of a function is multiplied by the constant λ, and the change of the function value is a multiple of λn, the function is called an n-order homogeneous function. Let the function f(x, y), if f(\λx, \λy)= \λf(x, y), then the function pair x, y is homogeneous.

In this way, the formula (1) can be written as:

(4)

Order, substituted in formula (4) are

(5)

According to the sign of formula (3), simplify and add the expected rate of return of money, that is

On the basis of the formula (1) (the symbol is simplified for convenience), Friedman further assumes that there is.

(6)

Move items, get

(7)

Order, write the nominal income as PYr, and substitute it into formula (7) to obtain

Md = kPYr or

After the money supply and money demand are equal, the subscript of the money demand symbol can be removed.

M = kPYr or (8)

Order, substituted in formula (8), there are

MV = PYr(9)

Formula (8) is simply the quantity equation of money of Cambridge School! Equation (9) is almost the same as the trading equation! However, the holding rate K or the velocity of money circulation V in Friedman's "New Money Quantity Theory" is no longer a constant, but a more complex function. We can see the correlation between k, v and various variables. Although Friedman's theory of money demand function reflects Keynes's influence in form, its content is more accurate than Keynes's liquidity preference theory. As far as the general forms of money demand functions (1) and (3) are concerned, they are basically accepted by the academic circles, and there is no dispute. Friedman transformed the money demand function into formula (8) or (9) by using homogeneous formula, which is undoubtedly the reconstruction of the classical theory of money quantity. At the same time, Friedman believes that although the quantitative theory of new money is different from the constant inference of Cambridge Equation and Fisher Transaction Equation, they are basically stable and measurable functions, even "more stable than consumption function or other major functions".

Friedman made an empirical research conclusion in the book "The History of American Currency from 1867 to 1960": during the period of 100, the speed of American currency circulation slowed down at an annual rate of 1%. The situation of dividing a long period of time is as follows: at 1880 ~ 19 14, the speed of money circulation decreased from 4.97 to1.91; From 19 14 to 1929, there is no obvious change in the speed of money circulation; From 1929 to 1946, the speed of money circulation decreased; After 1946, it began to rise, but it was still below the levels of 1920 and 19 14.

Friedman has been severely challenged by his peers for the problem that V decreases by 1% every year. Later, Friedman himself admitted that this conclusion was problematic. This scientific attitude of seeking truth from the masters of economics is worth learning from our younger generation.

[Edit] Simplification of theoretical function of money demand [1]

Friedman's monetary demand theory function includes many variables and complex forms, which can be simplified without damaging the main idea. Let's start with formula (3):

(3)

1, assuming that u is stable. Because money-related systems are usually relatively stable, preferences, habits and other factors will not change easily, so they can be regarded as constants and omitted from the function. So there are:

( 10)

2. Because the proportion of wealth is relatively stable in a certain period of time, its influence on money demand will not change significantly, so it can also be deleted from the function. So there are:

( 1 1)

3. According to the statistics of some countries, only when (or writing gP) changes greatly and lasts for a long time will it have a significant impact on money demand. Experience shows that this rarely happens. So it can also be omitted. So there are:

( 12)

4. Under normal circumstances, the narrow sense of money yield Rm only refers to the interest rate of time deposit Dt, which is usually not high. If the interest earned by time deposit Dt is divided by M2(M0+Dd+Dt), the calculated interest rate should be quite low. Moreover, the change of bank interest rate is generally quite slow. Therefore, the influence of this variable on money demand should be extremely insignificant and negligible. So there are:

( 13)

5. The yields Rb and Re of these two financial assets are highly positively correlated by roughly the same factor. Using one rate of return as a variable can completely replace and reflect the change of another rate of return. Therefore, the two can be combined and collectively referred to as "market interest rate". If the market interest rate is still expressed by, there are:

( 14)

Equation (14) is the final simplified equation of Friedman's monetary demand theory function.

[Editor] Demonstration of theoretical function of money demand [1]

The work of empirical research is to determine the function of each independent variable in the function. Specifically, what is the elasticity of money demand to interest rate? How sensitive is money demand to changes in income or wealth? How much does money demand depend on other variables included in the money demand function? Wait a minute. In addition, there is a basic concept, that is, what is money? What kind of money is more suitable?

In addition to building a scientific model and using correct measurement methods, the premise of empirical research is to obtain reliable statistical data. In fact, if there is no statistical data, empirical research can not be carried out at all. Therefore, the data of empirical research mostly come from the United States, Western Europe and Japan, where statistical work is relatively perfect.

According to the simplified formula of the theoretical function of money demand (14), the actual money demand is determined by two factors: actual income and market interest rate. However, the formula (14) is only a general functional form and needs to be expressed in the form of an equation. Friedman and his monetary school explored the following equations in a large number of empirical analysis:

( 15)

Equation (15) is the regression equation of power function curve, and A, B and C are the parameters determined by regression analysis. It is difficult to test the nonlinear equation by regression analysis, and the nonlinear equation can be transformed into a linear equation by logarithmic method:

( 16)

Equation (16) is a binary regression equation, which is regarded as "the basic formula obtained by money quantity theorists through a large number of empirical studies on money demand in recent years". The regression coefficient can be obtained by least square method. According to the statistical data of the United States 1892 ~ 1960, the monetary school calculated:

ln a = 3.003 b = 1.394 c =-0. 155 R2 = 0.99

Writing the above regression coefficient into the equation, including

( 17)

In the formula (17), m is the broad money M2, Yr is the actual permanent income, and I is the commercial paper interest rate of 4-6 months. Equation (17) shows that the change of Yr and I can be highly explained (goodness of fit R2 = 0.99) and the income elasticity of actual money demand is 1.394. Income elasticity shows that when the real income increases by 1%, the real money demand will increase by 1.394%. On the contrary, the opposite is true. At the same time, the formula (17) also shows that the interest rate elasticity of the actual money demand is -0. 155, that is, when the interest rate increases 1%, the actual money demand decreases by 0. 155%, which is almost inelastic.

However, Friedman himself made many amendments to the income elasticity conclusion of money demand.

1959, which he thinks is1.8;

At 1970, he thought it was 1.0 ~ 2.0, which was divided into 1.0 ~ 1.5 and 1.5 ~ 2.0.

Needless to say, many scholars have differences with Friedman and his monetary school in empirical aspects.

[Editor] Friedman's Contribution to Money Demand Theory [1]

1. Regard money as an asset, put the monetary theory into the framework of portfolio selection theory, and abandon the narrow concept that the classical school regards money as a pure trading tool.

2. In the modern portfolio theory of general equilibrium, the pivotal role of money quantity in the economy is particularly emphasized, which corrects the prejudice of Keynesian school that ignores money quantity.

3. In the function of money demand, firstly, the independent variable of expected price change rate is set to determine the position of expected factors in money theory.

4. Strictly distinguish between nominal quantity and actual quantity.

5. Emphasize the importance of empirical research, correct the defects of previous scholars in economic theory, especially monetary theory, and make monetary theory closer to operational monetary policy.

[Editor] The difference between Friedman's money demand theory and Keynes's money demand theory

1. In Keynes's money demand function, the interest rate is limited to the bond interest rate, and the income is the actual income level at the spot. In Friedman's money demand function, interest rate includes the rate of return of various wealth, and income is a highly stable and permanent income, which is the main factor determining money demand.

2. Keynes's money demand function is based on the liquidity preference of interest rate, and thinks that interest rate is an important factor to determine money demand. Friedman, on the other hand, believes that the interest rate elasticity of money demand is low, that is, it is insensitive to interest rates.

3. Keynes believed that the function of money circulation speed and money demand was unstable. Friedman, on the other hand, believes that the function of money circulation speed and money demand is highly stable.

4. Keynes believed that national income is determined by effective demand, and the influence of money supply on national income is an indirect process, that is, it acts on total social demand and national income through interest rate, investment and investment multiplier. Friedman believes that because the speed of money circulation is stable, the change of money circulation speed directly causes the change of nominal national income and price level, so money is the main factor to determine the total expenditure.

Post-Keynesian money demand theory

After World War II, many western scholars further developed Keynes's motivation of money demand and supplemented and revised Keynes's theory of money demand.

(A) the development of Keynes's trading demand theory-the square root law model and its revision

Economists after Keynes objected to Keynes's view that the demand for transactional money depends on income and has nothing to do with interest rates. For example, American economist A.H. Hansen proposed in 1949 that when the interest rate rises to a considerable height, the transaction balance of money also has interest rate elasticity. However, it was the American economist W. baumol who first analyzed the relationship between transactional money demand and interest rate. From 65438 to 0952, baumol published the article "Trading Demand of Cash: Analysis of Inventory Theory", which applied the optimal inventory theory to the study of money demand, and thought that the money demand of trading motivation was not only related to income, but also closely related to interest rate.