凯恩斯的宏观经济学：学术评价（1）

凯恩斯的宏观经济学：学术评价（1）

蒋闻铭

 

凯恩斯的投资乘数

一个人在一定时间段所赚取的钱是他的个人收入（Income）。所有个人收入加在一起是国民收入（National Income）。一方面由于凯恩斯理论的影响，另一方面由于保罗·萨缪尔森本科教材《经济学》的长期作用，收入分析已经成为了现代经济理论的重要组成部分。

从收入分析的视角来看马克思的理论，就可以发现他主要关注的是个人收入的来源和分配。他认为，在资本主义社会，赚钱的方式只有两种，而且仅有这两种：第一是出售自身的劳动，第二是拥有资本。由此，人口被划分为两个阶级：无产阶级（Proletarians），其收入完全来源于出卖劳动；以及资产阶级（Bourgeois），其收入完全来源于资本所有权。

他预言随着时间的推移，前者的人口将不断增加，但其在国民收入中的份额却会持续下降；而后者的人口将不断减少，但其在国民收入中的份额却会持续上升。这个理论其实从头到尾都是错误。事实就是当今资本主义社会中的大多数人口，既不是纯粹的无产阶级，也不是纯粹的资产阶级，而是中产阶级（Middle Class）：这一社会阶层虽然主要通过出卖劳动谋生，但同时也在一定程度上拥有资本（对每个个体而言只是边际性的资本占有，但总体合计却相当可观），并且在政治上具有主导性的影响力。

另一方面，凯恩斯的收入分析关注的是收入流向何处。他将国民收入划分为两部分：一部分用于消费，另一部分用于储蓄。随后他指出，在资本主义社会中，储蓄并不是以个人把现金藏在床垫下的形式存在，而是会完全重新流入经济体系，转化为新的资本。全体个人储蓄的总额，等同于整个国家新增资本投资的总额。因此他说：

T=C+I

其中，T表示国民收入，C表示消费支出的总额，I 表示储蓄的总额，而储蓄又等于新增投资的总额。进一步这就是：

T=(m+1)I

其中 m=C/I。他进一步说，m=m(T) 是 T的一个函数，并且随着 T 的增加而递减。也就是说，随着国民收入的增长，储蓄的增长速度会超过消费。在他那个时代，并没有经验证据表明这一判断是对是错，但即便这一点是错误的，也并不会对他的理论构成致命影响。

他接着提出了一些相当激进的主张：（i）总收入取决于总投资。要提高总收入，就必须增加总投资。（ii）由

T=(m+1)I

且 (m+1)>1，新增投资对总收入（从而对总就业）的影响会通过“投资乘数” m+1被放大。因此，任何形式的投资——甚至包括在地上挖坑再填回去这样毫无实际意义的行为——也会因为这一乘数效应而被认为是有益的。

凯恩斯并非投资乘数概念的最初提出者，但这一概念的广泛流行在很大程度上要归功于他。

数学公式本身当然不可能是错误的，但对公式的解释，却很容易出错。这个离奇的投资乘数，是对一个简单等式错误解读的典型例子。凯恩斯在这里所犯的数学性错误在于：他在解释过程中颠倒了因变量与自变量的角色。在推导

T=(m(T)+1)I

时，他（正确地）把 T视为自变量；但在解释时，却把 T当成了因变量。

我们可以用下面这个例子来说明，交换因变量与自变量的角色会导致多么严重的错误。假设有一个气压计（或仪表）用来反映室内温度。人们观察到，天气变暖时读数上升，天气变冷时读数下降。在这里，显然仪表读数是因变量，而天气才是自变量。现在，如果屋里的人在寒冷的天气里，决定把这两者的角色对调——也就是说，他们试图通过提高仪表读数（比如在仪表下面点一把火）来改变天气——听起来荒谬至极，但这正是凯恩斯在这一问题上所遵循的逻辑。

 

• 凯恩斯的宏观经济学：概述
• 凯恩斯的宏观经济学：背景

 

Critiques on Keynes's Investment Multiplier

The money an individual makes in a given period of time is his/her INCOME, and all individual income added together is the National Income. Partly due to Keynes theory and partly due to the long lasting influence of Paul Samuelson's undergraduate text book "Economics", Income Analysis has become an important part of the modern economics theory.

To view Karl Marx's theory from the standpoint of income analysis, we see that he was very much focused on how the individual income are generated and also on income distribution. He basically argued that there are two (and only two) ways of making money in a capitalist society. The first is to sell your own labor, and the second is to own capital. The population are duly classified into Proletarians, whose income is exclusively from the sales of their own labor,  and Bourgeois, whose income is exclusively from capital ownership. He predicted that, as time goes, the population of the former would constantly grow but their share in national income would constantly shrink, while the population of the latter would constantly shrink but their share of national income would constantly grow.

This theory has been proved wrong. As it turned out, that the majority of population in today's capitalist society is neither proletarian nor bourgeois. It is the middle class: a social class, though making their living primarily through the sales of their own labor, is also with capital ownership to certain degree (marginal capital ownership for each individual but substantial if added together), and with dominating political influence.

Keynes's income analysis, on the other hand, focused on the question of where the income goes. He divided the national income into two part: the part that is spent on consumption and the part that is saved. He then observed that, in a capitalist society, the saved part is not in the form of cash hoarded under the mattress for individuals. Savings are completely recirculated back into the economic system as new capital. The total of individual savings is the total of new investment of capital of the entire nation. Therefore, he wrote

T = C + I

where T is the National Income, C is the total spending in consumption and I is the total saving, which equals the total new investment. Keynes then proceeded to write

T = (m+1) I

where m = C/I. He then claimed that m=m(T) is a function of T, and as a function of T, m(T)$decreases as T increases. This is to say that, as total national income increases, the saving outpaces consumption. At his time there is no empirical evidence to indicate if this claim is right or wrong, but it would not be fatal to his theory even if it is wrong.

He then started to make wild claims: (i) total income depend on total investment. To increase total income, it is necessary to increase total investment. (ii) From T=(m+1)I and (m+1) > 1, the impact of new investment would be amplified in total income, therefore total employment, by the Investment Multiplier m+1. Investment in any form, including the useless practice of digging holes on ground then fill it in would be beneficiary because of this multiplier.

Keynes was not the original inventor of investment multiplier, but he was responsible largely for its popularity.

Mathematic formula, of course, cannot possibly be wrong, but their interpretation could easily go wrong. This bizarre investment multiplier is a perfect example of wrong interpretation of a straightforward equality. The mathematical error committed here by Keynes is that he switched the role of dependent and independent variable in a mathematical equality. In the way he derived

T=(m(T) +1)I

he argued (correctly) regarding T as the independent variable, but in his interpretation he regarded T as the dependent variable. 

Let us use the following example to illustrate to what degree one could be wrong in switching the role of dependent and independent variables. Let us say that there is a barometer that monitors the room temperature. One observes that when weather is warm, barometer goes up, and when weather is cold, the barometer goes down. Here obviously the number on the barometer is a dependent variable, but the weather is the independent variable. Now the people of the house, in a cold day, decided to switch the role of these two variables--this implies that they will try to get the number on the barometer higher (perhaps by burning a small fire under the barometer) to change the weather. As bad as it sounds, this is exactly the logic Keynes followed.

• 凯恩斯的宏观经济学：概述
• 凯恩斯的宏观经济学：背景