RDP 7704: Money and Money–Income: An Essay on the “Transmission Mechanism” III. Money Income, Real Income, and Prices

The IS-LM model set out earlier holds the price level constant and determines the level of real income. A common practice (though not one adopted by the builders of big models) in adapting it to the analysis of the determination of money income has been to replace real variables with nominal variables, to postulate that the way in which, and the extent to which, variations in the quantity of money affect money income is independent of the breakdown of changes in money income between real income and the price level. Such a procedure does of course underlie Friedman and Meiselman type studies, and it was defended by Friedman (1971) on grounds of theoretical convenience; it has also been implemented in empirical work using small-scale IS-LM models by Tanner (1969) and Moroney and Mason (1971).^[14]

Now if we consider the vertical segment of the “reverse L” aggregate supply curve and set Y constant in equations (1) and (2) , we may derive the following expression:

A simple comparison of equations (3) and (4) makes it obvious that, in terms of this model, the quantitative nature of the relationship between money and money income will depend open whether real income or the price level is varying. Only if either ℓ approaches zero or a infinity, do equations (3) and (4) reduce to the same expression, namely:

Here the money multiplier's size is independent of the breakdown of money income between real income and prices, but only because of the simplifying assumption that the relationship between the demand for money and real income is linear. In the special case of the model underlying equation (5) this assumption implies that the real income elasticity of demand for money is unity, and hence equal to the price level elasticity of demand. If the demand for money is not unit elastic with respect to real income, then even if the potential effects of interest rate variations on velocity are assumed away by making the LM curve vertical or the IS curve horizontal, the size of the money multiplier will vary with the division of money income fluctuations between real income and prices.

The evidence cited in the previous section of this paper on the role of interest rates in determining various components of expenditure makes it hard to believe in a horizontal IS curve, and the evidence against a vertical LM curve is overwhelming. Moreover, whatever might have been its value in earlier periods, it is clear that the short-run real income elasticity of demand for money, particularly if money is defined narrowly, has been significantly below unity in the United States, and in virtually every other developed economy as well, since World War II. The theoretically predicted value of unity for the price level elasticity of demand for money, on the other hand, is supported by a good deal of evidence.^[15]

Thus, although the practice of treating the determination of variations in money income as a problem prior to, and separate from, that of breaking such variations down between real income and prices would, as Friedman (1971) argued, greatly simplify macroeconomics, and though it is easy enough to find premises in terms of which such a practice could theoretically be justified, those premises are factually wrong. How much money income will change in response to a given change in the quantity of money depends upon how much of that change comes in real income and how much in the price level. The mechanisms which determine the interaction of prices and real output must be treated as an integral part of the transmission mechanism that links the quantity of money to money income^[16]

In recent years, the “expectations augmented Phillips curve” has become the centrepiece of models that attempt to come to grips with price and output interaction. Two alternative accounts of the behavior underlying this relationship are to be found in the literature and though the distinction between them is apparently irrelevant for many of the questions upon which the relationship may be brought to bear, it is critical as far as the subject matter of this essay is concerned: the very concept of a “transmission mechanism” is hard to square with what may be termed the “Fisherian” interpretation of the curve.^[17]

Consider an economy made up of perfectly competitive firms, with the output of each depending upon the relative price ruling for that output. Thus, where Y_it is the output of the i^th firm in time t, P_it is the price of that output, and the general price level as perceived by that firm, we have,

Summing over all firms and using conventional symbols for aggregate output and the general price level, we get

Using lower case letters for logarithms and assuming a log linear form for F, equation (7) may be written

If we define the inflation rate as

the expected inflation rate as

and measure units of output so that y takes the value zero in equation (8) when p = p^e, we may rewrite equation (8) as an expectations augmented Phillips curve

According to the foregoing analysis, therefore, the expectations augmented Phillips curve (11) is simply another way of writing an aggregate supply curve (8), which can be used instead of the textbook “reverse L” relationship; and can be brought together with an aggregate demand curve derived from an IS-LM framework in order to determine simultaneously, for given expectations about prices, the level of real income and prices.

There is a difficulty here. We can think of a change in the quantity of money operating through the type of “transmission mechanism” discussed in the preceding section of this paper to change the quantity of goods and services demanded at any given price level, and hence to shift the aggregate demand curve. In order to maintain equilibrium, output expands along the aggregate supply curve in response to an increase in the price level. However, that increase in the price level simply happens, and is of just the right size to generate the output change that will clear the market. A Walrasian auctionoer or some such agent must be brought in to bridge this vital gap in the sequence of events that leads from a change in the quantity of money to a determinate change in money income.^[18]

In certain markets-of the type that Sir John Hicks (1974) has called “flex-price”-the activities of specialist traders make it possible to treat all who are engaged in consumption and production as “price takers” but it is clear that, in Hicks' “fix-price” markets, which lack such specialist dealers, price and output decisions are taken by the same agents. It is equally clear that, in advanced economies, the latter type of market predominates. Thus, although it is certainly an advantage of the Fisherian interpretation of the expectations augmented Phillips curve that it is clearly grounded in orthodox microeconomics, and although it cannot be claimed that the alternative “Phelpsian” interpretation has such well-established micro foundations, the latter does have the great merit of enabling us to do without the Walrasian auctioneer: it treats prices as being set by firms rather than being taken by them “from markets.”^[19]

Think of each firm in the economy as forming an expectation of what price it must charge in time t in order to maintain its real level of sales constant. Suppose that each firm sets its actual price above or below that level depending upon whether it wishes to contract or increase its level of sales. For the economy as a whole, there will exist some level of output and sales at which the number of firms (suitably weighted by their shares in output) which want to expand sales just equals the number that wish to contract. At that output level, the value for the general price index that results from their individual price setting behavior will be equal to an index of the prices which they expected would keep their sales level constant. If output and sales for the economy as a whole exceed this “natural” level, there will be a preponderance of firms wishing to contract, so that actual price level will be set above the “expected price level,” and vice versa.

Putting the end product of the above argument into algebraic terms, picking a log linear form, with units chosen so that the log of the output level at which the actual and expected price level are equal is zero, and using the same symbol as before for the “expected price level,” even though it is conceptually a somewhat different variable, enables us to write

which is obviously the inverse form of equation (8) from which we may derive

However, the choice of which way round to write this equation is, in the present context, neither arbitrary nor irrelevant. The “Phelpsian” account of its derivation reverses the direction of proximate causation between output and prices at the level of the firm's behavior, and in doing so enables us to discuss a transmission mechanism between money and money income without having recourse to an “auctioneer.” As before, think of an increase in the money supply leading to a higher level of demand for goods and services at any price level. As that higher level of demand, perhaps amplified by a multiplier process for which there seems to be no room in Fisherian analysis, materializes in the form of a higher level of real sales and real output, so will the number of firms wishing to contract their operations, or prevent them from expanding, increase. Thus the price level will rise relative to its expected level as these firm revise upwards the prices they set for their individual products. What happens then depends upon how expectations about prices, which we have held constant, respond to this sequence of events. These longer-run issues will be taken up below.

We can describe the above process in an alternative way which brings out more clearly the desirability of treating price and output interaction as an integral part of the transmission mechanism between money and money income. A higher than equilibrium quantity of money in the economy causes attempts to substitute other assets, and current consumption for money. Such behavior on the part of households must lead to an increase in firms' sales, and, if output does not respond immediately to meet this increase, to a rise in their holdings of money (and perhaps of such liquid assets as trade credit) and a diminution of their inventories. The act of increasing prices is an integral part of firms' response to the asset disequilibrium just described if the Phelpsian account of the Phillips curve is accepted. It would be wrong to claim that, in the present state of knowledge, the factors determining the extent to which such a disequilibrium would be met by price changes on the one hand, and output and inventory changes on the other, are understood.^[20] Barro's (1972) study of the pricing behavior of a monopolist who faces a stochastic demand function, and lump-sum costs of price adjustment, provides a potentially useful starting point for anyone dealing with this problem. Mussa (1976) has extended Barro's work to incorporate an explicit analysis of the behavior of goods inventories, though not of liquid asset holdings. He also explicitly analyzes the wage and employment decisions of his firm.

Of course, assumptions about the behavior of employment and money wages have been implicit throughout the preceding discussion. There exists a Fisherian interpretation of the interaction of money wages and unemployment exactly analogous to that of price and output interaction; an account in which the supply of labour and hence employment is made a positive function of the difference between the actual and expected level of money wages.^[21] The expected money wage level in turn depends on expectations about the price level and about labor productivity. This Fisherian approach then interprets all unemployment as being of the voluntary search variety. Phelps account of money wage-unemployment interaction (set out in (1968)) has firms forming expectations about the level of money wages that will maintain employment constant, and setting wages above, or below, that level depending upon whether they desire to expand or contract their labor force. There then emerges a “natural” level of search unemployment at which there is equality between the expected and actual wage on both sides of the market. When firms wish, on average, to reduce their labor forces, there emerges downward pressure on money wages relative to expectations and unemployment goes above its “natural” level, and vice versa.

Mussa's (1976) analysis explicitly incorporates lump-sum costs of adjusting the stock of employees and permits the manhours worked per employee to be a variable. The number of employees, and the intensity with which they work both become variables chosen by the firm along with wages, rather than being generated by supply side responses to wages set by the firm as they are in Phelps' model. Though the analysis has not yet been carried that far, it is an interesting conjecture that Mussa's model might prove capable of generating sufficient money wage and price rigidity as to permit a multiplier process to amplify output and employment fluctuations. Deviations of unemployment from its natural level could then be interpreted as involving “involuntary” unemployment of the type analyzed by Patinkin (1965) and Barro and Grossman (1975) , generated not by rigid wages, but simply by a failure of wages to fall fast enough to keep the labor market cleared.

If, as output and employment fluctuate about their “natural” levels, money wages as well as prices did not in fact fluctuate relative to their expected levels, as the expectations augmented Phillips curve predicts, then we would be left with an exogenously given money wage rate as the principal determinant of prices, with only the mark-up between wages and prices potentially susceptible to variation in response to market forces.^[22] The evidence on the interaction of prices, wages, output and employment has been surveyed recently (see Laidler and Parkin (1975) Section 3) and shows that the price level does vary (relative to expectations) with the level of real output, while the level of money wages varies (again relative to expectations) with unemployment. Also, although the point is not a vital one, the mark-up of prices over money wages does seem to vary with market pressures (pace Godley and Nordhaus (1972)). All this is true, not only of the United States, but of Britain, Canada, and many other countries. Moreover, unemployment and output changes seem to precede the price and wage changes associated with them. To the extent that one may make inferences about the direction of causation from data on timing, the evidence supports the Phelpsian rather than the Fisherian interpretation of the expectations augmented Phillips curve.^[23] Hence it is compatible with a chain of causation such as I described earlier, that does not need to rely on an “auctioneer” Moreover, a pattern of wage-price-employment-output interactions such as I have just described is a feature of both the EMP model and of RDX2. To a degree at least theory and econometric modelling have complemented one another in developing this aspect of the analysis of the transmission mechanism, and have done so with considerable success.

Though there is a good deal of empirical evidence that the economy works “ is if” the processes I have been describing are in operation, there still exist improcesse gaps in our knowledge of this stage is to transmission mechanism. I have suggested that the multiplier process and the Patinkin-Barro-Grossman treatment of involuntary unemployment might have a part to play in the transmission mechanism, but this is yet to be demonstrated. Moreover, the labor market analysis I have described takes no account of the presence of powerful bargaining units on the supply side of the market, so that many find it hard to swallow as an account of the processes whereby unemployment affects wage bargaining in labor markets as they exist despite the amount of support that it gets from the empirical evidence. It is to be hoped that work now in progress on what Gordon (1976) has called the “new-new microeconomics,” dealing as it does with the question of the optimal length of wage and employment contracts, and the reasons for wage rigidity within the contract period, will soon begin to help us fill these gaps in our knowledge.

Footnotes

Tanner and Moroney and Mason both use dynamic versions of the IS-LM model as originally developed by Tucker (1966). The theoretical model in question was explicitly of the fixed price level kind. [14]

For evidence on these matters see Laidler (1977), Ch. 7. [15]

Acceptance of the foregoing arguments make the evidence generated by reduced form studies of the Friedman-Meiselman type hard to interpret, as I argued in Laidler (1971) . Note that there is an even more fundamental reason, that arises from analysis that involves the rational expectations hypothesis, why we must regard price and output interaction as part of the transmission mechanism. This is taken up below. (See, pp. 29–31.) [16]

The mechanism in question is sketched out in Fisher (1926) and cited with approval by Friedman (1975) . In the modern literature the Fisherian approach to the transmission mechanism underpins the work of Lucas (1972) (1975), and Sargent and Wallace (1975). [17]

Of course the absence of a Walrasian auctioneer makes a fundamental difference to our whole view of how the macroeconomy works. This is precisely the theme of the work of Clower (1965) and Leijonhufvud (1968). The Fiaherian approach to the expectations augmented Phillips curve, particularly when it is combined with a rational expectations hypothesis, essentially leads to a macroeconomics based on Walrasian general equilibrium analysis, and which thus seems quite incompatible with the Clower-Leijonhufvud extension of Keynesian economics. On this matter, see Coddington (1973). [18]

The paper in the Phelps (1970) volume which explicitly analyzes the price setting behavior of firms is of course that of Phelps and Winter. [19]

Jonson et al. (1976) , have explicitly utilized such a view of the transmission process in a small scale econometric model of the Australian economy with some success. As the reader will recognize, and as Jonson et al. acknowledge, the underlying mechanics of this process are very similar to those first set out by Archibald and Lipsey (1959) in their commentary on Patinkin (1956). Note that Howitt (1974) embeds this mechanism in a model in which price setting is endogenous, and shows that it still leads to stable equilibrium in a monetary economy. Hicks (1974) makes much of the role of inventories in permitting output dynamics to get underway and persist over time, but his analysis differs crucially from that outlined here in not permitting wages and prices to vary systematically (relative to expectations) with the level of real activity. [20]

Lucas and Rapping (1969) , Alchian (1970) and Mortersen (1970) are among those who have analyzed a labour market Phillips curve as a supply curve. [21]

Thus, Hicks (1974), Ch. 3, argues that the behavior of money wages is dominated by institutional factors and hence is not susceptible to influence, to a policy relevant extent, by variations in the level of aggregate demand in the economy. This view was, until recently, widely held among British Keynesian economists, far more widely held than Ball and Burns (1976), who themselves did not hold this view, seem to think. [22]

Friedman when discussing actual inflationary processes (e.g. (1974), pp. 87-9) has it that monetary policy affects output first, and prices sub-sequently, the whole chain of causation taking about two years to work out. I find it hard to reconcile Friedman's perception of the facts—with which I agree-with his espousal of the Fisherian approach to the analysis of the interaction of prices and output. It is worth noting that, in (1968) his 1967 AEA Presidential Address he seemed to adopt a Phelpsian interpretation of these matters, and only subsequently (1971) adopted the Fisherian view. [23]