8 The Paradox of Thrift

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The idea that thrift is always virtuous is very deeply ingrained in our culture. It is a matter of philosophy, morals, and sometimes even religion. For example, in the Walt Disney movie Mary Poppins, Michael is being lectured by a banker that he should not be “feeding the birds” but instead invest his tuppence “wisely in the bank” to “be part of railways through Africa; Dams across the Nile, fleets of ocean Greyhounds; Majestic, self-amortizing canals; Plantations of ripening tea” (interestingly, these capital investments are all abroad; we shall come back to this later).

However, the model of lecture 7 implies that saving might be detrimental to the economy, at least when the economy has some slack. This phenomenon was explained by J.M. Keynes in the General Theory:

For although the amount of his own saving is unlikely to have any significant influence on his own income, the reactions of the amount of his consumption on the incomes of others makes it impossible for all individuals simultaneously to save any given sums. Every such attempt to save more by reducing consumption will so affect incomes that the attempt necessarily defeats itself. It is, of course, just as impossible for the community as a whole to save less than the amount of current investment, since the attempt to do so will necessarily raise incomes to a level at which the sums which individuals choose to save add up to a figure exactly equal to the amount of investment.

In this lecture, we use the Keynesian model outlined in the previous chapter, in order to understand that argument better.

8.1 The Paradox of Thrift before J.M. Keynes

At the outset, we should note that the paradox of thrift was known before J.M. Keynes, perhaps in the Book of Proverbs:

There is that scattereth, and yet increaseth; and there is that withholdeth more than is meet, but it tendeth to poverty. (Proverbs 11:24)

More certainly, it was present as early as in Bernard Mandeville’s The Fable of the Bees: or, Private Vices, Public Benefits (1714):

As this prudent economy, which some people call Saving, is in private families the most certain method to increase an estate, so some imagine that, whether a country be barren or fruitful, the same method if generally pursued (which they think practicable) will have the same effect upon a whole nation, and that, for example, the English might be much richer than they are, if they would be as frugal as some of their neighbours. This, I think, is an error.

This idea was also stated by Thomas Malthus:

Adam Smith has stated that capitals are increased by parsimony, that every frugal man is a public benefactor, and that the increase of wealth depends upon the balance of produce above consumption. That these propositions are true to a great extent is perfectly unquestionable… But it is quite obvious that they are not true to an indefinite extent, and that the principles of saving, pushed to excess, would destroy the motive to production. If every person were satisfied with the simplest food, the poorest clothing, and the meanest houses, it is certain that no other sort of food, clothing, and lodging would be in existence.

While it is quite certain that an adequate passion for consumption may fully keep up the proper proportion between supply and demand, whatever may be the powers of production, it appears to be quite as certain that a passion for accumulation must inevitably lead to a supply of commodities beyond what the structure and habits of such a society will permit to be consumed.

Thomas Malthus was inspired by events surrounding the post-Napoleonic wars period, during which time industrial depression in Britain was causing serious unemployment of labor and capital. Similarly, well before J.M. Keynes, Crocker and Macvane (1887) were writing about general overproduction24, which as we shall see, is very much linked to the issue of the paradox of thrift:

During the last twelve or fifteen years, business men have, almost without exception, complained that, so far at least as the particular business of each was concerned, there has been an actual overproduction; and, unless a majority of these men have been mistaken as to the proportion of demand to production in their own specialties, general overproduction must have been, in spite of the theories of the economists, an actual existing fact. In this conflict of theory with apparent fact, it becomes important carefully to test the theory, in order to see whether it is based on sound reasoning.

Thomas Malthus therefore really was a forerunner of J.M. Keynes. He set himself out to explain why unemployment could occur, as well as to suggest steps which might be taken to eliminate it. That this part of his thinking was not that original was in fact recognized by J.M. Keynes in Chapter 23 of the General Theory - Notes on Mercantilism, the usury laws, stamped money and theories of under-consumption, which I strongly encourage you to read. In fact, Adam Smith was very much writing against these theories of underconsumption. In the Wealth of Nations, he was writing:

What is prudence in the conduct of every private family can scarce be folly in that of a great Kingdom.

We will come back to it when we talk about open economy macroeconomics, starting in lecture 11.

Back to our Keynesian goods market model of lecture 7, we shall now study the paradox of thrift in more detail. We will consider three ways in which an economy might save more, which are all relevant in practice:

  1. an increase in the desire to save through a fall in autonomous consumption \(\Delta c_0<0\).

  2. an increase in public saving, also called deficit reduction, through a decrease in government spending \(\Delta G<0\).

  3. an increase in public saving, also called deficit reduction, through an increase in taxes or a decrease in transfers \(\Delta T>0\).

We will show that these acts of saving have very similar detrimental effect on output, and therefore saving.

8.2 Increase in individual saving \(\Delta c_{0}<0\)

In this section, we show that individual efforts by consumers to save more are self defeating in the aggregate, and that they lead to declining aggregate saving. We start from the extended goods market model with an accelerator effect on investment: \[ \begin{aligned} C &=c_{0}+c_{1}\left(Y-T\right)\\ I &=b_{0}+b_{1}Y. \end{aligned} \]

Direct proof. We write the investment = total saving identity: \[I=S+\left(T-G\right)\quad\Rightarrow\quad S=I-\left(T-G\right).\] We know that a fall in consumption of \(\Delta c_{0}<0\) leads to a decline in output \(\Delta Y<0\), and therefore through the equation giving investment as a function of output, to a decline in investment since \(\Delta I=b_{1}\Delta Y\): \[I=b_{0}+b_{1}Y\quad\Rightarrow\quad\Delta I=b_{1}\Delta Y.\] Because \(T\) and \(G\) are assumed to be fixed (so that public saving is fixed), the change in private saving is equal to the change in investment, and is therefore negative. Therefore, a fall in consumption, leads to a fall in private saving ! Again, that proof is probably not very intuitive. We now turn to the longer proof.

Intuitive proof. Again, we write that output equals demand, which allows to get an expression for output: \[Y=\frac{1}{1-c_{1}-b_{1}}\left(c_{0}+b_{0}-c_{1}T+G\right)\] We have the usual multiplier, compounding the consumption and investment effects (it is assumed here that \(c_{1}+b_{1}<1\)). Therefore, a given change in \(\Delta c_{0}<0\) leads to decline in output of: \[\Delta Y=\frac{\Delta c_{0}}{1-c_{1}-b_{1}}.\] Private saving is given by: \[ \begin{aligned} S&=(Y-T)-C\\ &=(Y-T)-c_0-c_1(Y-T)\\ S&=-c_{0}+\left(1-c_{1}\right)\left(Y-T\right). \end{aligned} \]

The change in private saving \(\Delta S\) is: \[\Delta S=\underbrace{\Delta(-c_{0})}_{\text{direct effect}}+\underbrace{\Delta\left[\left(1-c_{1}\right)\left(Y-T\right)\right]}_{\text{indirect effect}}\] The indirect effect is: \[ \begin{aligned} \Delta\left[\left(1-c_{1}\right)\left(Y-T\right)\right] &=(1-c_{1})\Delta Y\\ &=(1-c_{1})\frac{\Delta c_{0}}{1-c_{1}-b_{1}}\\ \Delta\left[\left(1-c_{1}\right)\left(Y-T\right)\right] &=\frac{1-c_{1}}{1-c_{1}-b_{1}}\Delta c_{0}. \end{aligned} \]

Therefore, the total effect on saving is negative: \[ \begin{aligned} \Delta S &=\Delta(-c_{0})+\Delta\left[\left(1-c_{1}\right)\left(Y-T\right)\right]\\ &=-\Delta c_{0}+\frac{1-c_{1}}{1-c_{1}-b_{1}}\Delta c_{0}\\ \Delta S &=\frac{b_{1}}{1-c_{1}-b_{1}}\Delta c_{0} <0 \end{aligned} \]

8.3 Fall in Government Purchases \(\Delta G<0\)

Direct proof. We know that a rise in public saving, arising from either a decrease in government spending, or a rise in taxes, or a decrease in transfers, leads to a decline in output \(\Delta Y<0\), and therefore through the above equation giving investment as a function of output, to a decline in investment since \(\Delta I=b_{1}\Delta Y\): \[I=b_{0}+b_{1}Y\quad\Rightarrow\quad\Delta I=b_{1}\Delta Y<0.\] Therefore, a deficit reduction is clearly bad for investment. However, once again, this calculation does not really help understand what the above reasoning was wrong.

Intuitive proof. The fall in government spending \(\Delta G<0\) leads to a rise in public saving: \[\Delta(T-G)=-\Delta G>0.\] However, this fall also leads to a fall in output, whose magnitude is given by the government spending multiplier. We write that output equals demand, to get an expression for output to get, once again, that: \[Y=\frac{1}{1-c_{1}-b_{1}}\left(c_{0}+b_{0}-c_{1}T+G\right)\] So the fall in output is: \[\Delta Y=\frac{\Delta G}{1-c_{1}-b_{1}}.\] Once again, private saving is given by disposable income \(Y-T\) minus consumption (what is earned, not paid in taxes, nor consumed, is saved), and therefore (see the previous sections): \[S=-c_{0}+\left(1-c_{1}\right)\left(Y-T\right).\] Therefore: \[\Delta S=(1-c_{1})\Delta Y=\frac{1-c_{1}}{1-c_{1}-b_{1}}\Delta G.\] Thus, we have a fall in private saving whose magnitude is larger than the rise in public saving. Overall, the effect on total saving, and therefore investment is negative: \[ \begin{aligned} \Delta I &=\Delta S+\Delta(T-G)\\ &=\frac{1-c_{1}}{1-c_{1}-b_{1}}\Delta G-\Delta G\\ &=\frac{1-c_{1}}{1-c_{1}-b_{1}}\Delta G-\frac{1-c_{1}-b_{1}}{1-c_{1}-b_{1}}\Delta G\\ &=\frac{1-c_{1}-(1-c_{1}-b_{1})}{1-c_{1}-b_{1}}\Delta G\\ \Delta I &=\frac{b_{1}}{1-c_{1}-b_{1}}\Delta G<0. \end{aligned} \]

8.4 Increase in net taxes \(\Delta T>0\)

The direct proof is exactly similar at the one in the previous section. However, the intuitive proof is a bit difference.

Intuitive proof. If the government chooses to engage in deficit reduction through tax increases (or by reducing transfers), then denoting by \(\Delta T>0\) the increase in aggregate taxes, we have a rise in public saving given by: \[\Delta(T-G)=\Delta T>0.\] This leads to a fall in private saving through two channels:

  1. A direct channel which goes through the mechanic reduction in disposable income.

  2. An indirect channel which goes through the reduction in output, which lowers income.

The magnitude of the second channel can be computed using the above equation for output: \[\Delta Y=-\frac{c_{1}}{1-c_{1}-b_{1}}\Delta T.\] Again, given the above expression for private saving: \[S=-c_{0}+\left(1-c_{1}\right)\left(Y-T\right).\] we have: \[ \begin{aligned} \Delta S &=(1-c_{1})(\Delta Y-\Delta T)\\ &=(1-c_{1})\left(-\frac{c_{1}}{1-c_{1}-b_{1}}\Delta T\right)-(1-c_{1})\Delta T\\ \Delta S &=\underbrace{-\frac{c_{1}(1-c_{1})}{1-c_{1}-b_{1}}\Delta T}_{\text{Effect through output}}-\underbrace{(1-c_{1})\Delta T}_{\text{Reduction in disposable income}} \end{aligned} \] Therefore: \[\Delta S=-\frac{1-b_{1}-c_{1}+b_{1}c_{1}}{1-c_{1}-b_{1}}\Delta T.\] Overall, the effect on total saving, and therefore investment is decreasing: \[\Delta I =\Delta S+\Delta(T-G)=-\frac{b_{1}c_{1}}{1-c_{1}-b_{1}}\Delta T<0.\]

8.5 Literature after J.M. Keynes

Since J.M. Keynes, economists have come back and forth on the paradox of thrift.

Alvin Hansen is perhaps one of the most ardent defender of the view that desired saving can be higher than investment, even in the long run. This view is often referred to as the “secular stagnation” view. Hansen (1939) starts by noting that investment is probably not as sensitive to interest rates as neoclassical economics have it:

Less agreement can be claimed for the role played by the rate of interest on the volume of investment. Yet few there are who believe that in a period of investment stagnation an abundance of loanable funds at low rates of interest is alone adequate to produce a vigorous flow of real investment. I am increasingly impressed with the analysis made by Wicksell who stressed the prospective rate of profit on new investment as the active, dominant, and controlling factor, and who viewed the rate of interest as a passive factor, lagging behind the profit rate. This view is moreover in accord with competent business judgment." It is true that it is necessary to look beyond the mere cost of interest charges to the indirect effect of the interest rate structure upon business expectations. Yet all in all, I venture to assert that the role of the rate of interest as a determinant of investment has occupied a place larger than it deserves in our thinking. If this be granted, we are forced to regard the factors which underlie economic progress as the dominant determinants of investment and employment.

Noting that a big component of investment demand results from building residential structures, he notes that declining population growth will lead to a reduction of investment demand and therefore, that paradox of thrift problems will become more likely:

Now the rate of population growth must necessarily play an important role in determining the character of the output; in other words, the composition of the flow of final goods. Thus a rapidly growing population will demand a much larger per capita volume of new residential building construction than will a stationary population. A stationary population with its larger proportion of old people may perhaps demand more personal services; and the composition of consumer demand will have an important influence on the quantity of capital required. The demand for housing calls for large capital outlays, while the demand for personal services can be met without making large investment expenditures. It is therefore not unlikely that a shift from a rapidly growing population to a stationary or declining one may so alter the composition of the final flow of consumption goods that the ratio of capital to output as a whole will tend to decline.

We will talk more about Alvin Hansen and secular stagnation later in the class.

8.6 Empirical Macroeconomics and the Paradox of Thrift

  1. Crocker, Uriel H., and S. M. Macvane. 1887. “General Overproduction.” The Quarterly Journal of Economics 1 (3): 362–66. https://doi.org/10.2307/1882763.↩