American Economic Association

Keynesian Models of Recession and Depression Author(s): James Tobin Source: The American Economic Review, Vol. 65, No. 2, Papers and Proceedings of the Eighty-seventh Annual Meeting of the American Economic Association (May, 1975), pp. 195-202 Published by: American Economic Association Stable URL: https://www.jstor.org/stable/1818852 Accessed: 23-06-2019 17:41 UTC

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This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms Keynesian Models of Recession and Depression

By JAmES TOBIN*

Keynes's General Theory attempted to days and I shall not dwell on this point prove the existence of equilibrium with in- here. (See, however, A. S. Blinder and voluntary unemployment, and this pre- R. M. Solow and J. Tobin and W. Buiter.) tension touched off a long theoretical The second important point, the one on controversy. A. C. Pigou, in particular, which Pigou insisted, is that excess supply argued effectively that there could not be a of labor must cause money wages to de- long-run equilibrium with excess supply of cline. Even if this did not succeed in elimi- labor. The predominant verdict of history nating unemployment, one might not call is that, as a matter of pure theory, Keynes a situation in which money wages and failed to prove his case. prices are persistently falling an equi- Very likely Keynes chose the wrong librium. But of course Pigou went further battleground. Equilibrium analysis and in contesting Keynes's claim that a "trap" comparative statics were the tools to might exist from which the economy could which he naturally turned to express his not be rescued, however low the wage and ideas, but they were probably not the best . tools for his purpose. For one thing, he ex- Keynes tried to make a double argument plicitly confined the General Theory to a about wage reduction and employment. time period in which are given "the exist- One was that wage rates were very slow to ing skill and quantity of available labor, decline in the face of excess supply. The quality and quantity of available equip- other was that, even if they declined faster, ment, the existing technique" and other employment would not-in depression cir- factors. As he said (p. 245), "in this place cumstances-increase. As to the second and context, we are not considering or point, he was well aware of the dynamic taking into account the effects and conse- argument that declining money wage rates quences of changes in them." But his are unfavorable to .' model produces a solution in which, in But perhaps he did not insist upon it general, the stock of capital, and other strongly enough, for the subsequent theo- stocks, are not constant. Changes in these retical argument focused on the statics of stocks will in turn alter , saving, alternative stable wage levels. and other behavior. For this reason alone, The real issue is not the existence of a the solution of Keynes's model cannot be 1 s... . it would be much better that wages should be stationary, even in its own endogenous rigidly fixed and deemed incapable of material changes, variables; and on this ground alone, it fails than that depression should be accompanied by a gradual downward tendency of money-wages, a further to qualify as an equilibrium. The evolution moderate wage reduction being expected to signalise of Keynesian equilibrium as stocks change each increase of, say, 1 percent in the amount of un- is receiving a great deal of attention these employment. For example, the effect of an expectation that wages are going to sag by, say, 2 percent in the * Sterling Professor of Economics, Yale University. coming year will be roughly equivalent to the effect of a The research described in this paper was undertaken byrise of 2 percent in the amount of interest payable for grants from the National Science Foundation and the the same period. The same observations apply mittatis Ford Foundation. muitandis to the case of a boom." (See Keynes, p. 265.)

195

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms 196 AMERICAN ECONOMIC ASSOCIATION MAY 1975 long-run static equilibrium with unemploy- that Keynes was a "Marshallian in meth- ment, but the possibility of protracted un- od" and translated the supply-demand employment which the natural adjust- framework of Alfred Marshall from indi- ments of a market economy remedy very vidual markets to the whole economy. slowly if at all. So what if, within the "Where he deviated from Marshall, and it recherche rules of the contest, Keynes was a momentous deviation, was in re- failed to establish an "underemployment versing the roles assigned to price and equilibrium"? The phenomena he de- quantity. He assumed that, at least for scribed are better regarded as disequilib- changes in aggregate demand, quantity rium dynamics. Keynes's comparative was the variable that adjusted rapidly, statics were an awkward analytical lan- while price was the variable that adjusted guage unequal to the shrewd observations slowly, at least in a downward direction." and intuitions he was trying to embodly. Friedman is correct that this was a mo- If the purity of neoclassical equilibrium is mentous deviation, and one way to appre- preserved, this verdict is no real blow to ciate the point is to look explicitly at the Keynes or solace for Pigou. The Great dynamic stability implications of XVal- Depression is the Great Depression, the rasian vs. Marshallian assumptions about notorious "Treasury View" is still ridicu- quantity adjustment. lous, whether mass unemployment is a fea- Marshallian adjustment in a particular ture of an equilibrium or of a prolonged market is that quantity adjusts to the dif- disequilibrium. ference between demand price and supply The issue is by no means dead. Today price for existing quantity. Walrasian ad- "full employment" has become the "natu- justment is that quantity adjusts to the ral rate," and "equilibrium" often allows difference between demand and supply at for any steady rate of deflation or inflation, existing price. not just zero. But the proposition which Let us now apply these two adjustment Keynes was questioning is once again assumptions to a simple macroeconomic strongly argued in the profession and in model. Let Y be aggregate real output, public debate. Once again it is alleged that and Y* its value at full employment, i.e., the private market economy can and will, at the "natural rate" level of unemploy- without aid from government policy, steer ment. Let E be aggregate real effective itself to full employment equilibrium. This demand, which can differ in short-run dis- is the basis for advocacy of fixed rules of equilibrium both from Y and from Y*. monetary growth and fiscal policy, as Given the nominal stock of outside money against active discretionary policy re- M and other exogenous or policy-set vari- sponding to information fed back from the ables, effective demand E is a function private economy. At this very moment it E(p, x, Y) of three variables: p the price is the basis for a policy of letting the re- level, x its expected rate of change, and Y cession run its course, in confidence that in the level of output and real income. a relatively short run-two or three In finer detail, E is the sum of consump- years equilibrium will be restored at full tion C, private investment I, and govern- employment with reduced or even zero ment purchases G: inflation.

I. Keynesian and Marshallian (1) E-=C (Y, Y1*, -T, -R) GW Price Dynamics

Milton Friedman (p. 18) has pointed out + I(Yj Y*, -KY -R) + G

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms VOL. 65 NO. 2 KEYNESIAN MODEL 197

Here the C and I functions have positive run are private debts in the unit of ac- derivatives in all their arguments. T repre- count. These are a heavier burden to sents taxes, a function of Y and Y*. W is debtors the lower the price level, and there private wealth, equal to are good reasons why transfer of real in- come and wealth to creditors spells a net M -+ qK, deficit of aggregate demand. Debtors are p debtors because they have high propensi- where the coefficient q is the ratio of ties to spend. Many of them are liquidity- market valuation of capital equity to re- constrained, and as their debt/equity placement cost. An increase in the real ratios increase their credit lines dwindle or, R relative to the marginal in case of bankruptcies, disappear. Al- efficiency of capital makes q fall, and though these are "only" distributional makes investment fall. The marginal effi- effects, they may be more important than ciency of capital depends positively on Y the real value of outside money and debt. and Y*, negatively on K. The real interest The long-run comparative-static Pigou rate R depends inversely on both M/p and effect, in contrast, assumes that each alter- x, and rises with Y and W. native price level has prevailed for a suf- The price level effect E, on demand ficiently is long time so that inside debts are negative, for the following familiar combi- scaled to that price level although nation of reasons. First is the Keynes strangely enough exogenous outside money effect. A given nominal quantity of money is not. In this counterhistorical "as if " will be a larger real quantity at a lower mental experiment, debtors are no more price level. Consequently the interest rate burdened at one price level than at an- may be lower, and investment demand other. higher. The Keynes effect is expected to be As for the price change effect E,, there are weaker the larger the real supply of money several effects. A decrease in the expected relative to output Y, and to vanish alto- inflation rate raises the real rate of interest. gether in the "." This will This increase discourages investment, and tend to make Ep smaller in absolute value it also deters consumption both directly at low levels of Yp M. and by lowering the market value of Second is the Pigou effect, the wealth equity capital, one component of wealth. effect on consumption. T he lower the price On the other hand, expected capital gains level, the higher the real value of those on money holdings xMA'p are favorable to components of net private wealth fixed in consumption. This is a "flow Pigou effect," nominal value. The relevant components to be distinguished from the stock effect. are outside money (and some part of any The question here involves the size of the nonmonetary public debt in existence). marginal propensity to spend from ex- Consumption demand is expected, ceteris pected real capital gains. Econometric evi- paributs, to respond positively to increases dence has been that this marginal propen- of wealth. sity is small, although capital gains even- T he short-run Pigou effect is very likely tually affect consumption via the wealth weaker than the long-run effect and may effect. I have assumed that the other ef- not even have the same negative sign. And fects of expected inflation dominate the it is the short-run effect which is relevant flow Pigou effect. for Keynesian theory and for the dynamics The marginal propensity to spend E, is of this paper. The difference arises as fol- taken to lie between 0 and 1 on usual lows: among the stocks fixed in the short Keynesian grounds. As is well-known, a

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms 198 AMERICAN ECONOMIC ASSOCIATION MAY 1975 high response of investment demand to the demand which must always equal Y to contemporaneous income could easily preserve the national income identities. make Ey exceed one. But Keynes typically Let D be a function of f as well as of x, p, regarded investment as determinied more and Y. Then D(f , x, p, Y) = Y, E(x, p, Y) by long-run sales and profit expectations =D(O, x, p, Y). Equation (2.1.1) follows than by current business activity. The from a negative value of OD/8 , which likelihood that, in prolonged departures means that demand is lower, at given Y, from full employment, investment will when Y is increasing. Lags in consumption come to be governed more by contempo- spending lead to this sign and so does un- raneous than by full employment sales and intended inventory decumulation. The in- profits is a source of possible instability vestment accelerator works in the other and of prolonged disequilibrium to which direction, but for the reason already given I shall return later in the paper. it is not a Keynesian idea. In equilibrium, the following three con- Equation (2.2.1) is a natural-rate ver- ditions hold: sion of the Phillips curve. The short-run Phillips curve is the obvious Keynesian (2.1) E(p, x, Y) - Y = 0 version of price dynamics. Throughout (2.2) y- Y* = this paper I am condensing product and labor markets into one sector and assuming (2.3) x =p/p - 0. with Keynes that prices are determined by (I shall also denote p/p marginal as variabler.) costs, i.e., by labor costs. I shall call the first dynamic version of Excess labor supply and Y- Y*, the this model the WKP model (Walras- "Okun gap," are linked, when one is zero Keynes-Phillips). All the adjustment func- so is the other. So it is the gap which causes tions which follow will conform to the wage rates to fall. But to "fall" does not notation AYz, where y is the variable acl- mean to decline absolutely; it means to de- justing, z the variable on which the adjust- cline relative to x, the accustomed and ex- ment depenids, and Ay a positive constant. pected rate of inflation of both labor costs The WKP model is as follows: and prices. This is the more modern wrinkle. By here assuming (2.2.1) 1 do not The WKP Model mean necessarily to associate myself- (2.1.1) V= Ay(E - Y) much less Keynes!-with the natural-rate hypothesis in all its power and glory. (2.2.1) 7r = AP(Y- Y*) + x The third equation (2.3.1) is the well- (2.3.1) Z = A(7r -x) known model of adaptive expectations. There is nothing particularly Keynesian Equation (2.1.1) says that production Y about this equation, and the same formu- moves in response to discrepancies of E lation will carry over to the non-Keynesian and Y. This implements the Keynesian dynamic model. Keynes himself would view that in the very short run money scorn it and stress instead the stochastic wages and prices are set and output re- and historical sources of expectations. But sponds to variations of demand. like so many of his observations, these do How can E and Y diverge even for an not lend themselves to simple formal instant? Many words have been spilled, analysis. both by Keynes himself and by others, on As two extremes of interest I shall wish this question, usually posed in terms of the to consider: possibility of inequality of Saving and In- vestment. In our present context, let D be (2.3.2) x= 7r

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms VOL. 65 NO. 2 KEYNESIAN MODEL 199

(extrapolation of current inspires adjustments rates of production of andprice chanige) employment. This is because they are asso- (2.3.3) x = 0 ciated with gaps of the same sign between (extrapolation of current price level) the demand price for labor (the value of its marginal product) and its supply price.3 'T'he alternative dlynamic version may be The idea is that when Y* exceeds Y the called the Al moclel (Marshall). Tl'he equa- real wage is less than marginal productiv- tions are: ity. Competitive employers therefore add to their work forces and their production. The M Model In Keynesian theory, on the other hand, (2.1.2) 7= BP,(E - F) + X production increases only when demand at existing prices expands. (2.2.2) I; = y (Y*- Y) II. Local Stability of the Two Models (2.3.2) = Ax(7r - x) (or 2.3.1 or 2.3.3) Let us now consider the local stability of As compared with the IJJ7KP model, the the IVKP and M models, around their adjustment roles of the first two equations equilibrium values Y= Y*, p= p*, x= O. are interchainged. 'I'he first equation now For this purpose it is convenient to sub- says that the immedliate impact of excess stitute in the third equation the value of demanid( for goods and services is to raise 7r-x drawn from the second or first equa- prices, or mlore strictly to raise them faster tion. Thus the third equations in the WKP thani they had been expected to rise. (It is and M models become respectively: not en-tirely accurate to regard (2.1.2) as non--Keyinesian. When- there is an infla- (3.1) x = AXAP(Y- Y*) tionary gap (E> Y*, Y =Y*), this looks (3.2) x= AxBp(E - Y) very much like the Keynesiain model of For the WKP model, the linearized inflation. But in Keynes's inflation theory, equations are: Y* is considerecl an absolute short-run constraint on pro(luction, as in wartime. _y_ -Ay(E,-1) AyEp AyEx- In normal conditions, Keyines would, I (3.3) A pp* O p* think, regard Y* as a medium-run labor market equilibrium with normal margins AxA . 0 of excess capacity and of frictional un- [Y-Y*] employment, a level of output which could .P-P* be at least temporarily exceeded.)2 In any event, equation (2.1.2) is one way to inject into the model the view that prices respond The critical necessary condition for sta- quite flexibly to changes in excess demand bility is: for goods, whether or not the economy is close to full employment. (3.4) p*Ep + AxEx < 0 The non-Keynesian partner of this price The first term of (3.4) is negative and the adjustment equation is (2.2.2), where the second term positive. As would be ex- gap between potential and actual output pected, a strong negative price-level effect

2 In the General Tlheory, Keynes discusses frictional on aggregate demand, a weak price- and involuntary unemployment on p. 6 and, in defining involuntary unemployment on p. 15, says, "Clearly we 3This is true even if the labor supply curve is down- do not mean by 'involuntary' unemployment the mere ward sloping, provided it is closer to vertical than the existence of an unexhausted capacity to work." schedule of marginal productivity of labor.

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms 200 AMERICAN ECONOMIC ASSOCIATION MAY 1975 expectation effect, and a slow response of 2= E(P, X, 12) price expectations to experience are con- ducive to stability. In one extreme case E 12 Lou y* I,(p, x, 1,) (2.3.3), where x=.X=O, the system is of E= Y loci / * E,(p, x1, course stable. In the other extreme case (2.3.2), where x=7r, the first term of (3.4) drops out and the system is necessarily unstable. or The M model is quite different. It is separable into output and price equations. Equation (2.2.2) is a stable differential x 0 equation in the single variable Y. The sta- bility of the price system depends on (3.4), in the same way as the stability of the WKP model. The formal system is: irx+Ap(Y - Y*)

(3.5) [ =

-By 0 0 Bp(Ey- l)p* Bpp*Ep Bpp*E+?p* _AxBp(Ey-1) AxBpEp AxBpEx i

Y- Y*- * _*

x FIGURE 1 As Friedman surmised, Keynes's choice of adjustment mechanisms is a crucial ele- along which the condition is met. The ment of his theory. In particular, the slope of such a locus, -ExIEp, is positive. Walras-Keynes-Phillips adjustment model Each locus is for a given value of Y; a re- allows the distinct possibility that lapses duction in Y shifts the locus to the left. from full employment will not be auto- In the Figure, the right-most locus is for matically remedied by market forces. full employment output Y*. The weaken- Keynes could also be interpreted to hold ing or vanishing of the "Keynes effect" at the view that price-level effects Ep are low values of Y and p tends to reduce Ep weak relative to speculative effects Ex. I in absolute value. This is reflected in the shall discuss this interpretation further in curvature of the loci. the next section. Consider an initial position T1 at levels of E and Y short of Y*. Prices begin to de- III. Irreversible Recessions and cline because Y1 is less than Y*. To a de- Deep Depressions gree that depends on the speed of adapta- Let us take a more global look at the tion, expectations of price change become equilibrium condition E = Y (2.1). In Fig- negative. The arrow indicates the direction ure 1 are shown in (p, x) space several loci of movement. As drawn, the movement is

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms VOL. 65 NO. 2 KEYNESIAN MODEL 201 stabilizing, taking the economy to higher and gross investment is zero; production is E and Y, toward Y* and the equilibri- solely to meet minimal private and social umrS. consumption requirements, which are in- TI he lower panel of Figure 1 concerns the dependent of income and wealth. The de- direction of the arrow, the relationship of pression phase lasts a long time, while r and x. The horizontal axis matches in depreciation slowly whittles the capital origin and scale that of the upper panel. stock down to the amount needed for floor The lines are parallel 45 degree lines, for level production. Y*, Y1, and Y2, the same output levels as It is not part of this paper to provide a in the upper diagram. T1he points S, T1, T2 modlel of such a floor. The relevant ques- corresl)ond to the similarly labeled points tion is whether deflation will by itself lift above. At S, r= O. At T1, r is negative. So the economy from the floor. Will deflation is x, by an amount l)roportional to the dif- so augment private wealth that consump- ference between 7r and x, shown horizon- tion rises above its floor level? Clearly this tally as x/Ax. will not happen unless condition (3.4) is Consider instead an initial position T2 in met at the depression income level. the two panels. At I'9 both the slope of the But at the floor, E. is higher than in the E-=Y locus and that of the arrow are normal regime. An increase in the deflationi steeper. JThe reason that the arrow is rate - x lowers the value of the capital steeper canl be seen in the lower panel: stock. The physical capital stock declines x/Ax has double(l, but r has more than slowly. But its value-its real value-can doubled. The net outcome could go either decline rapidly; when no gross investment way. The possibility illustrated is that at is taking place, the existing stock will be 72 the locus E = Y is so steep that the valued well below replacement cost. At the movement is destabilizing. The system liquidity trap, the real interest rate is the might be stable for small deviations from irreducible nominal rate r plus the ex- its equilibrium but unstable for large pected rate of deflation - x. The value of shocks.4 The failure of automatic market a unit of capital is (p-a (r-x)) where processes to restore full employment would p - a is the marginal productivity of capital be reinforced if large and prolonged reces- net of depreciation. Although the attrition sion caused investors to gear their esti- of the stock slowly raises p, deflation mates of the marginal efficiency of capital rapidly raises r-x. more to current than to equilibrium de- IV. Concluding Remarks mand and profitability. Under these adverse circumstances, and God may have made the world so that in the absence of countercyclical policy, full employment equilibrium exists and is the economy could slip into a deep de- stable. Perhaps the divine design guaran- pression. tees that capitalist market economies will In nonlinear nonmonetary business cycle never be trapped in depressions with in- models like those of M. Kalecki, R. Good- voluntary unemployment and will never win, and Sir John Hicks, a long depression need to depart from fixed no-feedback phase occurs with the economy at a floor. rules of fiscal and monetary policy. But At this floor the capital stock is excessive Keynes had good empirical and theoretical reason to suspect otherwise. He did not 4Robert Solow has pointed out to me that the possi- establish an underemployment equilib- bility illustrated by T2 is only suggestive of a global rium. But he did not really need to. Even instability. The global properties of the system require further investigation. with stable monetary and fiscal policy,

This content downloaded from 189.6.25.92 on Sun, 23 Jun 2019 17:41:06 UTC All use subject to https://about.jstor.org/terms 202 AMERICAN ECONOMIC ASSOCIATION MAY 1975

combined with price and wage flexibility, M. Friedman, A Theoretical Framework for the adjustment mechanisms of the econ- Monietary Anialysis, Nat. Bur. of Econ. Res. omy may be too weak to eliminate per- occas. pap. 112, New York 1971. J. M. Keynes, The General Theory of Employ- sistent unemployment. ment, Interest, and Money, 1st ed., London REFERENCES 1936, 245. A. S. Blinder and R. M. Solow, "Does Fiscal J. Tobin and W. Buiter, "Long-Run Effects Policy Matter?," in J. of Pub. Econ., 1973, of Fiscal and Monetary Policy on Aggregate 2, 319--37, and Econ. of Pub. Fin., Brook- Demand," Cowles Foundation disc. pap. ings Institution, 1974, 452-58. no. 384, Dec. 1974.

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