Edwin Dickens, Keynes's Theory of Monetary Policy: An Essay In Historical Reconstruction, Contributions to Political Economy, Volume 30, Issue 1, June 2011, Pages 1–11, https://doi.org/10.1093/cpe/bzr001
Navbar Search Filter Mobile Enter search term Search Navbar Search Filter Enter search term SearchKeynes's theory of monetary policy is composed of three concepts—namely, the investment multiplier, the marginal efficiency of capital and the interest rate. By analyzing how these three concepts interact in the short period, Keynes explains why he is opposed to countercyclical monetary policies. And by analyzing how they interact in the long period, he explains why the economy tends to fluctuate around a long-period equilibrium position that is characterized by unemployment. Keynes concludes that the sole objective of the monetary authority should be to use its influence over the interest rate to dislodge the economy from its long-period equilibrium position that is characterized by unemployment and propel it toward a long-period equilibrium position that is characterized by full employment.
Perhaps a complex offer by the central bank to buy and sell at stated prices gilt-edged bonds of all maturities, in place of the single bank rate for short-term bills, is the most important practical improvement which can be made in the technique of monetary management ( Keynes, 1936, p.206).
The purpose of this paper is to reconstruct Keynes's theory of monetary policy, as stated in The General Theory of Employment, Interest and Money (1936). To accomplish this purpose, I build upon the work of Eatwell & Milgate (1983a, b; also see Eatwell, 1983 and Milgate, 1982). In particular, I use the classical long-period method to model the relationships between the investment multiplier, the marginal efficiency of capital and the interest rate—which constitute Keynes's theory—and I do so in such a way that the short-period fluctuations of the economy are around a long-period equilibrium position characterized by unemployment. I conclude that buying and selling ‘at stated prices gilt-edged bonds of all maturities … is the most important practical improvement which can be made in the technique of monetary management’, as noted above, because it would help propel the economy from a long-period equilibrium position characterized by unemployment closer to one characterized by full-employment. 1
The paper is organized as follows. In Section II, I use Keynes's concepts of the investment multiplier and the marginal efficiency of capital to specify the long-period equilibrium position of the economy which is characterized by unemployment.
In Section III, in order to explain why the economy fluctuates around a long-period equilibrium position characterized by unemployment, I specify the difference, as well as the relationship, between Keynes's concepts of probability and risk and the orthodox ones.
In Section IV, I use Keynes's concept of the interest rate to explain the effects of monetary policy, both in the short-period and in the long-period.
Lastly, in Section V, I provide a summary and conclusion.
Let N s be the supply of labor and N d the demand for labor, or the actual volume of employment (n). We can then define full-employment (no) as N d /N s = 1; unemployment (nk) as N d /N s < 1; and the unemployment rate as 1 − nk.
For Keynes (1936, pp. 25–29ff.), n is determined by the aggregate level of output (Y) and the productivity of labor (P). That is to say, by definition P = Y/N d . Re-arranging terms, N d = Y/P. Substituting into our definition of n, we thus get n = Y/P N s .
For Keynes (1936, p.96ff.), Y is determined, via the investment multiplier (defined as the reciprocal of the marginal propensity to save (s)), by the aggregate rate of investment (I). Consequently, we can derive the determinants of the unemployment rate (1 − nk) by building upon the following counter-posing of the effects of an aggregate rate of investment that is insufficient to generate full-employment (Ik) with the effects of an aggregate rate of investment that is sufficient to generate full-employment (Io) (see Shaikh, 2004 for a similar formalization):
where, ceteris paribus, 1 − nk is determined by Ik< Io.For Keynes (1936, pp. 135–137), I is determined by the net present value of prospective investment projects (NPV): 2
where Sp is the supply price of prospective investment projects; E is the profit expected from operating them for t periods; and rs is the ‘safe’ interest rate (see Section IV for an explanation of it). If NPV > 0, I increases. If NPV < 0, I decreases. If NPV = 0, I is in equilibrium.
Assume that t = 1 and Sp and rs are given. Then the expected profit (Eo) in equilibrium that induces investors to undertake the full-employment aggregate rate of investment (Io) and the expected profit (Ek) in equilibrium that induces them to undertake the less-than-full-employment aggregate rate of investment (Ik) can be distinguished as follows:
Equations (1–4) apply to both the long-period and the short-period, depending upon whether Ek and Eo denote long-term expectations or short-term expectations. Ceteris paribus, long-term expectations determine the volume of investment projects undertaken and short-term expectations determine the pace of their implementation.
Let A be the payoff required to induce entrepreneurs to undertake the full-employment rate of investment (Io). Then, following Dickens (2008, pp. 225–226 and 229), the difference between the long-term Eo and the long-term Ek can be analyzed in terms of the following formulation of the difference between Keynes's concepts of probability and risk and the orthodox ones:
where m is the number of occurrences of an outcome; z is the number of possible occasions for the outcome to occur; w is the weight of arguments; and q = 1 − po.
Equation (6) is derived from the law of large numbers and incorrectly assumes that the underlying causal structure that determines the outcome of investment projects is known in the same way that the underlying causal structure that determines the outcomes of coin tosses or turns of the roulette wheel is known. In fact, the underlying causal structure that determines the outcome of investment projects is either knowable but unknown or, as Keynes (1937a, b, c) argues, unknowable. Following Markowitz (1959, p. 39ff.), orthodox economists take this fact into account by interpreting equation (6) in terms of the principle of non-sufficient reason.
According to the principle of non-sufficient reason, if investors do not have a reason to assign different probabilities to a set of possible outcomes, they must assign them equal probabilities. Therefore, if qualms about factors that are knowable but unknown or unknowable undermine the confidence of investors in their calculations of the outcome of prospective investment projects, orthodox economists instruct them to assign equal probabilities to the outcomes they fear may result from these factors, with the sum of assigned probabilities being equal to one. Orthodox economists thus interpret the expected profit (Eo) in equation (5) as the mathematical mean of the sum of the products of all possible outcomes of investment projects and their probability. They then interpret the risk of investment projects as the variability (or standard deviation), of the sum of the products of all their possible outcomes and their probability, around the mathematical mean.
The orthodox concept of risk is obviously incorrect, since it includes the possibility that the actual profit of investment projects will exceed the expected profit. Risk (R) only results from the possibility that the actual profit will fall short of the expected profit, a fact that Keynes (1921, p. 348) formulates as follows:
As such, R represents the cost of insurance against catastrophic loss of the money waged on investment projects. The cost of re-insurance to the insurer (R1) would then be qR = q 2 Eo. If the re-insurance company buys re-insurance (R2), and that re-insurance company gets re-insurance, and so on, then the risk of loss is eliminated, but so is the expected profit (Eo). That is, . In short, Keynes formulates equation (8) in such a way that it is only by bearing some risk of loss that potential investors can expect to profit.
Less obviously, for Keynes (1936, p. 152; 1921, p. 77–80), the orthodox concept of expected profit (Eo) ‘leads to absurdities’ 3 because it ignores the weight of arguments (w). Following Dickens (2008, p. 227–228), w can be explained as follows: 4
where a is the proposition that A, as formulated in equation (5), will be the payoff from undertaking the full-employment aggregate rate of investment (Io); h is the set of propositions that constitute the premises of the argument for undertaking Io; po, as formulated in equation (6), is the proposition that dominates h; and w measures the extent of po's dominance.
Equation (9) can be read as ‘proposition a on the hypothesis h· po has a probability pk’. Alternatively, it can be read as ‘the conclusion a can be inferred from the evidence h· po with a probability of pk’.
In short, Keynes's concept of probability (pk), as formulated in equation (9), encompasses the orthodox concept of probability (po), as formulated in equation (6), and the relationship between the two is mediated by Keynes's concept of the weight of arguments (w).
For Keynes (1921, p. 77–80), w measures the vague but pervasive sense of inadequacy that investors feel when they compare what they know with what they think they ought to know in order to make informed investment decisions. If w = 1, then the interpretation of equation 6 in terms of the principle of non-sufficient reason has quelled investors’ sense of inadequacy, po is completely dominate and equation (9), and pk = po. If 0 < w < 1, then investors do not suppress the fact that setting w equal to one leads to absurdities (see Dickens (2008, p. 224–225) for an explanation of why), and the factors making the underlying causal structure determining the outcome of investment projects knowable but unknown or unknowable take the form of propositions in h which weigh against po's dominance, so that pk < po.
Even if w = 1, pk is still less than po once we add Keynes's concept of risk, as formulated in equation (8), to w as a mediating factor between pk and po, and thereby obtain equation (7). Keynes (1921, p. 348) formulates equation (7) in such a way that two conditions are met: If po = 1 and w = 1, then pk = 1; and if po = 0 and w = 0, then pk = 0. It follows that, if 0 < w < 1 and/or 0 < po < 1 (so that q = 1 − po has a value between zero and one), then pk < po. Of course, po = m/z = 1 only if there is apodictic certainty about the underlying causal structure that determines the outcome of investment projects, in the way that there is apodictic certainty about the outcome of tossing a two-headed coin—hardly a relevant case to evaluating prospective investment projects.
If pk < po, then we know from equations (5), (4), (1), and (2), respectively, that Ek < Eo → Ik < Io → Yk < Yo → 1 − nk > 0. In short, if Keynes's concepts of probability and risk are correct, the long-period equilibrium position of the economy is characterized by unemployment.
The monetary authority directly controls the short-term interest rate. 5 With ‘a modest measure of persistence and consistency of purpose,’ Keynes (1936, p. 204) asserts that the monetary authority can also influence the long-term interest rate. 6 Orthodox economists (see, for example, Ingersoll, 1989, pp. 173–178) have accepted Keynes's assertion, taking it to mean that the long-term interest rate is the mathematical mean of the sum of the products of all possible outcomes of the short-term interest rate and their probability. For example, the yield on the 10-year bond allegedly equals the mathematical mean of the expected yields on 3-month securities for the next 10 years, plus an illiquidity premium which reflects the orthodox concept of risk. Unfortunately, orthodox economists ignore the difference between Keynes's concepts of probability and risk and the orthodox ones, and reject the classical long-period method, which Keynes uses to distinguish between the long-period equilibrium values of variables and their short-period values. To reconstruct Keynes's theory of monetary policy, these oversights must be rectified.
For Keynes (1936, pp. 144–145, 222–229 and 240), the long-term interest rate is ‘a duplication of a proportion of entrepreneur's risk,’ modified to take into account the weight of arguments (w). Consequently, the long-period equilibrium value of the long-term interest rate—what Keynes's calls the safe long-term interest rate (rs)—and its relationship to the actual long-term interest rate (ra), as determined in the bond market, can be represented as follows: 7
where 0 < g < 1 (i.e. g measures the proportion of the entrepreneur's risk that is duplicated); the bracketed expression in equation (10) takes into account both entrepreneur's risk and w, as they are formulated in equation (7); and Ea is the actual expected profit from investment projects, as determined in the stock market. 8
Equation (11) reformulates equation (4) to specify the relationship between rs and ra. In the same way, equations (1) and (2) can be reformulated as follows to specify the relationship between the long-period equilibrium aggregate rate of investment (Ik) and the actual aggregate rate of investment (Ia), and thus the relationships between the long-period equilibrium aggregate level of output (Yk) and the actual aggregate level of output (Ya), and between long-period equilibrium employment (nk) and actual employment (na), respectively are as follows:
In equation (11), rs is the center of gravitation of the short-period fluctuations of ra; in the same way that, in equations (12) and (13), Ik, Yk, and nk are the centers of gravitation of the short-period fluctuations of Ia, Ya, and na, respectively.
For Keynes (1936, pp. 202, 206 and 313–320), the short-period fluctuations of ra around rs are strictly limited to ‘the difference between the[ir] squares’. 9 In contrast, since the stock market determines the actual expected profit (Ea) in the short-period, the short-period fluctuations of Ia and Ya around Ik and Yk are unlimited. 10 Therefore, efforts by the monetary authority to stabilize the short-period fluctuations of the economy are futile for two reasons. First, any drastic changes that the monetary authority makes in the short-term interest rate simply cause a more steeply sloped yield curve as ra reaches the limits of its variability around rs. Second, such drastic changes in the short-term interest rate threaten to shatter the confidence of investors in their calculations of Ea. If drastic enough, such changes may thus cause a severe recession as investors contemplate trillions of dollars of losses on their bets in the stock market.
More importantly, Keynes (1936, pp. 119, 206, 301–304 and 321–322) argues that the monetary authority, rather than attempting to stabilize the short-period fluctuations of the economy around a long-period equilibrium position characterized by unemployment, should attempt to reduce the amount of unemployment that characterizes the long-period equilibrium position, which can be done by making a credible commitment ‘to buy and sell at stated prices gilt-edged bonds of all maturities’. To see why, equations (9), (5), and (10) can be reformulated as follows:
where, in equation (14), h1 includes the proposition that ‘the monetary authority has made a credible commitment to buy and sell at stated prices gilt-edged bonds of all maturities’ and h2 includes instead the proposition that ‘the monetary policy is committed to changing the short-term interest rate in an effort to stabilize short-period fluctuations of the economy’.
If the monetary authority has the discretion to change the short-term interest rate, investors must take into account the possibility that future investment projects, with lower financing costs, will compete against investment projects undertaken today at higher financing costs. As a result, h2 weighs more heavily than does h1 against the dominate proposition for undertaking investments projects (po). That is to say, w1 > w2. It follows from equation (15) that pk1 > pk2 → Ek1 > Ek2; and from equation (16) that rs1 < rs2.
We are now in a position to complete Keynes's theory of monetary policy by building as follows upon equations (11), (1), and (2):
In equation (17), NPV1 > NPV2 because Ek1 > Ek2 and rs1 < rs2. Therefore, in equations (18) and (19), respectively, Yk1 > Yk2 and nk1 > nk2. In short, the change from a discretionary monetary policy to one committed to buying and selling at stated prices gilt-edged bonds of all maturities reduces the unemployment rate that characterizes the long-period equilibrium position of the economy from 1 − nk2 to 1 − nk1.
Looking backward, we observe long-run trends shaping economic events. The confidence to undertake investment projects depends upon our ability to project these trends into the future. The problem is that we know these trends are not governed by natural laws but are instead the result of the series of investment projects undertaken by forward-looking investors in the past. In every short-period situation in which such investment projects were undertaken, the long-run trends of the economy would have taken off in a different direction, if those investment projects had not been undertaken.
For this reason, investors take a two-step approach to the evaluation of prospective investment projects. First, they project long-run trends into the future by assigning probabilities to the likelihood of their continuance, and thereby calculate the expected profit (Eo). 11 Second, they contemplate the degree to which the principle of non-sufficient reason captures their uncertainty about the degree to which knowable but unknown or unknowable factors may cause the future trends of the economy to differ from past ones, and thereby calculate the expected profit (Ek).
Monetary policy is a factor that has shaped the long-run trends of the economy. It is thus necessary for investors to assign a probability to the likelihood that the monetary authority will continue to act in the same way that it has in the past, and incorporate it into the calculation of Eo. If the monetary authority has the discretion to act differently in the future than it has in the past, investors are compelled to contemplate monetary policy itself as a knowable but unknown or unknowable factor that may cause future trends of the economy to differ from past ones, and thus take it into account as a factor that makes Ek < Eo. If the monetary authority would make a credible commitment to buying and selling at stated prices gilt-edged bonds of all maturities, this element of uncertainty would be alleviated, thereby reducing the difference between Ek and Eo. The purpose of this paper has been to show that, as a result, the long-period equilibrium position of the economy would be characterized by less unemployment.