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Экономика

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Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

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and N2.

►ever, this is exactly offset bus there is no change in ernment uses its foreign

e seen from the identity:

(5.52)

ctor must equal the sum

new equilibrium lies to on leads to classical unemhat the depreciation of the deficit, increases the home of labour (whilst the real

gent erodes the real value r goods and causes a trade 1 ity, labour demand and rtland for labour increases

•s the trade balance.

ig literature we now disdeveloped by Neary and alvsis of Barro and Gross- - 2mporal considerations. e of constraint expecta-

'show that when agents

-there is unemployment the sense that pessimistic

In and Svensson, 1983). is have an inelastic supply

r lifetime consumption

future wages, prices, and ly the first two periods are -e is summarized by the representative household

— X. By using this identity plus

Chapter 5: The Macroeconomics of Quantity Rationing

has a simple Cobb-Douglas utility function:
UH = C71 C22 m2,	(5.53)

with al, a2, y > 0 and al +a2 + y = 1. In (5.53), Ci represents consumption of goods in period i and m2 =- M2/P2 denotes real money holdings at the end of the second period, where M2 is nominal money balances and Pi is the price level in period i. The intertemporal budget constraint facing the household is given by:

o	7	7	(5.54)
+ P2c2 + m2 = Y m	+ Pi1	1 + P21 2,

where Mo denotes the household's initial endowment of nominal money balances, Y denotes total income, and Yi is production in period i. The first equality in (5.54) says that total household income can either be spent on goods consumption in the two periods or can be carried over into the future. The second equality in (5.54) says that, in contrast to what we assumed in section 1, profits and wages are distributed instantaneously to the household sectors. The notional demand functions of the household are obtained by maximizing (5.53) subject to (5.54):

CD = al1	( 11:1)	(5.55)
	( 11:1)
CI? = a2	(P1-2)	(5.56)
M2 = Y (k)		(5.57)
		(5.57)

The objective function of the representative firm is the sum of current and future profits:

H 71 + 72

- W1N1 + P2F(N2) - W2N2,

(5.58)

where Wi and Ni are, respectively, the nominal wage and demand for labour in period i, and FO is the production function featuring positive but diminishing marginal productivity of labour (FN > 0 > FNN ). The notional demands for labour and output supplies are obtained by maximizing (5.58) with respect to N1

The resulting expressions are:

Nip = ND (wi), NwD =1/FNN < 0,

YS (wi)) = yS(wi ) , viS„

FN/= (ND FNN ,

where wi Wi/Pi is the real wage in period i. Note that, unlike Neary and Stiglitz (1983), we ignore the possibility of firm investment.

The final agent in the model is the government which can purchase goods in each period (denoted by G,) and can make transfer payments to households thereby increasing their initial endowment Mo . The government finances its policy actions by printing money.

125

The Foundation of Modern Macroeconomics

5.3.1 Walrasian expectations

We first consider the case where agents do not expect to be constrained either today or tomorrow. This leads to the following goods market equilibrium (GMEi) and labour market equilibrium (LMEi) loci:

yS(wi) = ai (Mo ±PiF(1) P2F(1))	Gi,	(GMEi)
Pi
1 =ND (wi ).		(LME;)

The equilibrium condition (GMEi ) equates notional goods supply in period i (the left-hand side) to total notional goods demand in period i (right-hand side) given that household income is consistent with full employment of labour in both periods (i.e. Yi = F(Ni ) = F(1) in the two periods). Similarly, the equilibrium condition (LMEi ) equates labour supply (left-hand side) to notional labour demand (righthand side) in the two periods. If prices and wages are perfectly flexible, then (LME ; ) determines the equilibrium real wage in both periods and (GME i) determines the nominal prices (and thus the nominal wage) in both periods. The Walrasian pricewage vector is denoted by (W;', PO.

To reduce the dimensionality of the model somewhat we assume that Pi and W, remain always at their Walrasian level, i.e. we assume that Pi = PI and W2 = WI and concentrate on variations in Wi and P2. The notional equilibria can be illustrated with the aid of Figure 5.8. In this figure, the LME i locus is horizontal at Wi = which implies that w i = wI also since Pi = PI. For points above (below) the LME 1 line the real wage is too high (low) and there is excess supply of (demand for) labour. The GME1 locus is downward sloping because an increase in today's real wage (w1)

GME1 (ESL' )

KU 1

CU 1

KU 1

LM E1

	KU1	RI 1
	KU1
	LM (ESG 1 )	RI1
	LM (ESG 1 )	GME1
	GME1 (EDL1 )	GME1
	GME1 (EDL1 )
	2	P2

Figure 5.8. Notional and effective equilibria with

Walrasian expectations

411

- NUM 4111111

126

.onstrained either today quilibrium (GMEi) and

(GMEi)

(LMEi)

kupply in period i (the (right-hand side) given I labour in both periods equilibrium condition labour demand (rightly flexible, then (LMEi) :GMEi ) determines the s. The Walrasian price-

issume that P1 and W2

=PI and W2 = WI and ria can be illustrated

Drizontal at W1 = ove (below) the LME 1 of (demand for) labour. today's real wage (w1)

LME1

Chapter 5: The Macroeconomics of Quantity Rationing

reduces aggregate supply and a reduction in tomorrow's price level reduces total income and therefore reduces aggregate demand. For points above (below) the GME 1 line today's real wage is too high (low), supply is too low (high) and there is excess demand for (supply of) goods.

Now consider the case where agents expect the Walrasian equilibrium to prevail tomorrow yet allow for the possibility of quantity constraints today. This leads to the same type of spillover effects that were discussed above. When there is unemployment today (ND (1471 /PI) < 1) then households' effective demand for goods will be less than their notional demand and therefore, to maintain goods market equilibrium, today's real wage rate has to rise. The effective goods market equilibrium locus is given by:

		P2	(GME1 (ESL1 ))
YS ( W1 ) = al ( M° ±F (ND (W1))(—)F(1)) + G1,			(GME1 (ESL1 ))
Pi Pi	Pi	Pl

where the first term on the right-hand side of (GME 1 (ESL1 )) represents the effective demand for goods in period 1 by households (Yr). It follows in a straightforward fashion that GME 1 (ESL1 ) is steeper than the GME 1 line.

When there is excess demand for labour today (ND (Wi /PI) > 1) firms are constrained in their hiring of labour and their effective supply of goods is less than their

notional supply ( ySE (1) = F (1 ) <		0) The GME1 (EDL1 ) is given by:
MO	P2	(GME1 (EDL1 ))
F(1) =(— + F(1) +(--)F(1)) +
p.	P*

Since W2 does not feature in (GME 1 (EDL1 )) it follows that GME 1 (EDL1 ) is vertical. If there is an excess supply of goods today, firms' demand for labour is constrained by the demand for goods and therefore the LME i (ESG 1 ) locus coincides with the GME1 (ED14) line. This obviously rules out the regime of underconsumption due to the fact that there are no inventories. For obvious reasons, the LME 1 (EDG1 ) locus coincides with the LME 1 locus because the supply of labour is exogenous by

assumption.

The resulting effective goods market and labour market equilibrium loci divide up the space into three regimes, i.e. Keynesian unemployment (KU), classical unemployment (CU), and repressed inflation (RI). This is indicated in Figure 5.8.

5.3.2 Bootstrap effects

We now consider intertemporal spillover effects, that is, the effects of expectations of future quantity constraints on the current behaviour of households and firms. One of the objectives of Neary and Stiglitz (1983) was to demonstrate the existence of "bootstrap" phenomena. By this we mean that when households expect to be unemployed today, and when firms expect they cannot sell all their goods tomorrow, it is also more likely that firms will be unable to sell all their goods today. Such

127

The Foundation of Modern Macroeconomics

GME1 (ESL1 , CU2)	GM E5 (KU2)	GME1 (ESL1 , KU2)
GMEi (ESL] ) N
•		CU1, KU2
•		or
KU 1 , KU2		or
KU 1 , KU2		CU1 , CU2
or
KU1 ,CU2		LM E1
EW		LM E1
EW
	N	GME1 (CU2)
		GME1 (ESL2)
		GME1

Figure 5.9. Effective equilibria with expectations of future Keynesian or classical unemployment

phenomena lead to the possibility of multiple equilibria for a given level of current and expected future wages and prices. For ease of exposition, we concentrate on the effects of expected Keynesian unemployment or classical unemployment. 5

Since the supply of labour is inelastic, the effective LME 1 locus coincides with the notional LME 1 locus as long as firms face no quantity constraints in the current period. When households expect to be constrained in their sale of labour tomorrow, their human wealth declines and therefore current consumption falls. The GMEi (ESL2 ) locus is defined as follows:

Ys W1 ) = al [ M° + F(1) + ( P2	F (ND p147,-))1+ Gi.	(GMEi (ESL2 ))
P* P* P*	P2

The comparison of (GMEi) (for period 1) and (GMEi (ESL2)) reveals that GMEi (ESL2) lies to the right of the GMEi locus. In Figure 5.9, GMEi, GMEAESLi), and LME1 have all been reproduced from Figure 5.8 for convenience. The GME i (ESL2 ) line has also been drawn and cuts the LME i line at point E". When firms expect to be unable to sell all their goods tomorrow, this does not affect the current effective supply of goods as we abstract from the intertemporal spillover effects arising from (reduced) inventories. This means that the GMEi (KU2) coincides with the GME i (ESL2) locus, where the notation KU2 stands for Keynesian unemployment in the second period, i.e. the combination of ESL2 and ESG2. This has also been illustrated in Figure 5.9.

If households expect that tomorrow there will be classical unemployment (CU2, consisting of excess demand for goods (EDG2) and excess supply of labour (ESL2)),

5 We have simplified the Neary-Stiglitz model by ruling out inventory holdings of firms. As a result, the behaviour of firms is entirely static and intertemporal spillovers only occur via household behaviour.

-,.. 10 ■-• •

aw hal

3 It

128

'ESL,, KU2)

CUi , KU2

O r

CU,, CU2

P2 P2

re Keynesian or

a given level of current we concentrate on the lemployment.S

locus coincides with t raints in the current sale of labour tomor- -, sumption falls. The

(GMEi (ESL2 ))

teals that GMEi (ESL2 ) Ei(ESLi), and LME 1 GME i (ESL2 ) line has - s expect to be unable !nt effective supply of -i sing from (reduced)

GMEi(ESL2 ) locus, in the second period, trated in Figure 5.9.

.lemployment (CU2, ly of labour (ESL2)),

"dings of firms. As a result,

.a household behaviour.

Chapter 5: The Macroeconomics of Quantity Rationing

then they will have less incentive to save as they cannot buy all the goods they want tomorrow anyway. Therefore current consumption increases. Indeed, the effective demand for goods in period 1 given that the household faces a constraint in the goods market (C2 < C2) in period 2 is obtained by maximizing (5.53) subject to (5.54) and the constraint. If the second-period constraint is binding (so that C2 = C2), we obtain:

CifE =	al ) [—Y – (PI) 2] •		(5.59)
	al + YPl	Pi

The GMEi (CU2) locus is then defined as:

al ) [ I±°- +F(1) +A) (F (ND (9) – C2		Gi.
( al + y CP1*	P2

(GMEi (CU2))

Of course, the GMEi (CU2) locus is only relevant for those values of P2 for which the household actually faces a constraint in the goods market tomorrow. This implies the following constraint:

[C1) --A a2	Mo	P*	F(1) + F (ND (	W*	))1 > C2.	(5.60)
	[— + (---1			2
	P2	P2		r2

The right-hand side of this inequality is the notional demand for period-2 consumption. Let P2W2) denote that value for P2 for which the constraint in (5.60) holds with equality. Then it follows that the GME i (CU2) locus coincides with the GMEi(ESL2) line for P2 in excess of 111 (2). Since future consumption is constrained, P/-W2 ) lies to the right of the Walrasian level P;—see Figure 5.9.

So far, we have looked at the notional first-period loci when there are expectations of future quantity constraints. Now consider the effective loci when there are expectations of either Keynesian or classical unemployment. The effective GMEi (ESLi ,KU2 ) line is given by:

ys ( W1 ) [M°F (ND ( W1 )) + ( P2 ) F (ND ( 1471 ))]+ Gl,
P	P*	\PI	P2

(GMEi (ESLi ,KU2))

whilst the effective GME i (ESLi ,CU2) line is given by:

YSWl =ai	±F (ND
	M0	Pl
+ Y L Pl
+ (P14) (F (ND ( wp2		)) — C2	(GMEi (ESLi,CU2))

These two loci are only relevant above the LME 1 locus, that is, when there is unemployment today. Obviously, they pivot to the right because the existence of current

129

The Foundation of Modern Macroeconomics

unemployment means that today's demand for goods will be less and therefore the supply of goods needs to be choked off with a higher real wage in order to maintain goods market equilibrium in the first period. Clearly, the GME i (ESLi ,KU2 ) line lies completely to the right of the GME i (ESI4,CU2) line. It is now possible to divide the (Wi, P2) space bordered by the loci LMEi, GMEi (ESLi ,CU2), and GMEi (ES14,KU2) into combinations of current and expected regimes-see Figure 5.9. The regime that lies above the LMEi line and between GMEi (ESLi,CU2), and GMEi (ESLi,KU2) is the most interesting one and it consists of either Keynesian unemployment in both periods (KU1,KU2) or classical unemployment in both periods (CU1,CU2)-

The first thing to note is that the vector of current and future wages and prices consistent with Walrasian equilibrium is not unique since it depends on the nature of expectations about future quantity constraints. If W i and P2 are flexible, all points between E"' and E" on LME i are possible Walrasian equilibria, each associated with a different configuration of constraint expectations. The second point to notice is the non-uniqueness of effective equilibria for particular constellations of current and future wages and prices. The region above the LME i line and between GMEi (ESL]. ,CU2), and GMEi ,KU2) in Figure 5.9 is compatible with either KUi or CUi, depending on what agents expect tomorrow. The final point to notice is the "bootstrap" effect, that is, Keynesian (classical) unemployment is more likely to occur today when it is expected to prevail tomorrow. In terms of Figure 5.9, the region for which there is KUi is larger if KU2 is expected than if CU2 is expected. Conversely, the region for which there is CU i is larger if CU2 is expected than if KU2 is expected.

5.3.3 Rational constraint expectations

The previous subsection employed arbitrary expectations about future quantity constraints, which is undoubtedly the main reason for the non-uniqueness of the Walrasian and effective equilibria. In order to avoid this problem, one might borrow the assumption of rational expectations from the new classical school of macroeconomics (see Chapter 3). Although the assumption of rational expectations may be within the spirit of market clearing and other assumptions of the new classical school, it is a rather far-fetched assumption within a macroeconomic model with rationing. The assumption of rational constraint expectations presumes that agents have an enormous amount of information in order to be able to calculate the aggregate future quantity constraints in a rational fashion. However, it does not require knowledge of individual demands and supplies. This is just as well, since if this were the case firms and households could engage in bilateral bargaining which contradicts the fundamental assumption of fixed wages and prices. Due to the difficulties in the coordination of the behaviour of individual households and firms when information (at a disaggregated level) is imperfect, the assumption of rational constraint expectations may be a first step in removing the arbitrariness of expectations.

io understand rational - e is unemployment important at this stag there is real wage r:

locus that pertains L.. anininal wage rigidity (1 4,

income, Y2 =

-ice, since a higher prio , loyment,_ and in, rations, say the

the main implication 4

, ns consistent

;.44ici when Keynesian u - pected to prevail t( Lh.iihood of Keyn,,..,

sal holds when constra it expectations

t.41y and Stiglitz

nix lint expectations, I

...4ment and outp,„.

-,c-tations of Keynesian

..a expectations al

—cult is that an increase 'flistic about t:

.6 relaxes the con), Olt more labour and pro

constraint income and they th

--ich in turn increases

the sharp contray 1001 Their neutrality n

.11 expectations. Ra., policy in the ration

:Iolicy neutrality

_ rational expet -ids we discussed in de •

Stiglitz

- :•: - -s and of actual c , mmenemporal spillover etit,

130

I and therefore the 1 order to maintain rESLi ,KU2) line lies ssible to divide the

d GMEi (ESLi,KU2) ,9. The regime that

Ei (ESLi,KU2 ) is the -1 oyment in both

wages and prices ends on the nature P2 are flexible, all libria, each associle second point to r constellations of line and between le with either KU1 -oint to notice is ent is more likely of Figure 5.9, the I CU2 is expected.

expected than if

future quantity un iqueness of the )ne might borrow chool of macroexpectations may

he new classical omic model with mes that agents

.:ulate the aggre- does not require since if this were rig which contrato the difficulties

- ms when inforIt ional constraint nectations.

Chapter 5: The Macroeconomics of Quantity Rationing

To understand rational constraint expectations, let us focus on the case where

there is unemployment today and Keynesian unemployment is expected tomorrow. It is important at this stage to distinguish between real and nominal wage rigidity. If there is real wage rigidity (w2 constant), then the GMEi (ESLDKU2) locus is also the locus that pertains under rational constraint expectations. However, if there is nominal wage rigidity (W2 constant), one has to take account of the fact that second- period income, Y2 = F(ND (W2 /P2)), is an increasing function of the second-period price, since a higher price erodes the real wage and thus boosts labour demand, employment, and income. This means that the locus under rational constraint expectations, say the RCE locus, lies to the right of the GME i (ESLi ) locus. 6

The main implication of the above argument is that the set of (W1 , P2 ) combinations consistent with Keynesian rather than classical unemployment today is greater when Keynesian unemployment rather than when Walrasian equilibrium is expected to prevail tomorrow, so that rational constraint expectations increase the likelihood of Keynesian unemployment today. Hence, the "bootstrap" property still holds when constraint expectations are rational. The assumption of rational constraint expectations does reduce non-uniqueness of the set of equilibria.

Neary and Stiglitz (1983) also show that, under the assumption of rational constraint expectations, the effects of an increase in government spending on employment and output during a Keynesian regime is greater than under static expectations of Keynesian unemployment tomorrow and greater still than under Walrasian expectations about the future. The main reason for this interesting result is that an increase in government spending is more effective when firms are pessimistic about their future sales prospects. Also, the increase in government spending relaxes the constraint on current sales and therefore firms might plan to hire more labour and produce more output tomorrow. Under the assumption of rational constraint expectations, households realize that this increases their lifecycle income and they therefore increase consumption both today and tomorrow which in turn increases the effective demand for labour today.

Note the sharp contrast with the policy neutrality results of the new classical school. Their neutrality results depend on price flexibility (market clearing) and rational expectations. Rational expectations actually enhance the effectiveness of fiscal policy in the rationing approach. Hence, it follows that the essential ingredient of the policy neutrality propositions of the new classical school is market clearing rather than rational expectations. This, of course, was the message of Fischer (1977) which we discussed in detail in Chapter 3 above.

6 Neary and Stiglitz (1983, pp. 216-219) discuss an iterative procedure to obtain consistency of expectations and of actual outcomes, which demonstrates that this remains the case even when there are intertemporal spillover effects arising from inventories.

131

The Foundation of Modern Macroeconomics

5.4 Punchlines

We study the macroeconomic implications of two key insights in this chapter. First, if the price system does not work then quantity signals take over as a coordination device in the economy. Second, if there is quantity rationing in one market this may spill over into one or more other markets and affect conditions in these markets in a meaningful way. In the presence of quantity rationing so-called effective demands and supplies are relevant. These differ from the conventionally defined (or notional) demands and supplies in that they take the quantity restrictions into account. For example, for a household the notional demand for consumption goods is obtained by maximizing utility subject to the household budget constraint. In contrast, if the household is unable to sell all the labour it wants to sell, it faces a quantity restriction in the labour market. The effective demand for consumption goods is then obtained by maximizing utility subject to the budget restriction and the quantity constraint in the labour market.

In the early to mid-1970s a number of Keynes-inspired economists built general (dis-) equilibrium models of the macroeconomy, in which the price level and real wage are fixed and quantity rationing exists in the markets for good and labour. The aim of these economists was to weaken the challenge of the new classicals by providing Keynesian economics with firm microeconomic foundations.

In the standard models there are three macroeconomic regimes depending on the configuration of the real wage and the price level. In the Keynesian unemployment (KU) regime, there is excess supply of goods and labour, in the classical unemployment regime (CU) there is excess supply of labour and excess demand for goods, and in the Repressed Inflation regime there is simultaneous excess demand for goods and labour.

A rather interesting prediction of the standard model is that the effects of fiscal and monetary policy depend critically on the regime that the economy happens to be in. An increase in government consumption, for example, has a positive effect on output and employment in the KU regime, has no effect in the CU regime, and decreases output and employment in the RI regime. Whilst the first two cases are familiar from our discussion of Keynesians and classicals in Chapter 1, the third case is novel and somewhat surprising. The intuition behind the so-called supply multiplier is that the increase in government consumption worsens the quantity restriction experienced by households in the goods market. As a result, these households supply even less labour and thus aggregate employment and output fall.

In a similar vein, the effects of policy measures directly impacting on the real wage or the price level also depend critically on the regime the economy is in. To alleviate unemployment and boost output the real wage should fall in the classical regime (as expected from our earlier discussion). In sharp contrast, the real wage should rise if the economy is in the KU or the RI regime. The reasons for this result are different for the two regimes. In the KU regime an increase in the real wage boosts aggregate demand for goods because the household experiences a higher (labour)

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132

his chapter. First, is a coordination market this may hese markets in a - '- ective demands led (or notional) n to account. For oods is obtained n contrast, if the in tity restriction is then obtained intity constraint

sts built general :e level and real )od and labour. ew classicals by ions.

vending on the unemployment i cal unemploy-

. nd for goods, rnand for goods

its of fiscal and ippens to be in. e effect on out-

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the real wage n. To alleviate s i cal regime wage should v, is result are

I wage boosts eh er (labour)

Chapter 5: The Macroeconomics of Quantity Rationing

income. This in turn reduces the severity of the constraint experienced by firms and prompts them to hire more workers and thus to boost output. In contrast, in the RI regime the increase in the real wage boosts employment and output because the

supply of labour expands.

The standard model has been extended in a number of directions, the most interesting of which are the setting of a small open economy and the intertemporal setting. In the intertemporal disequilibrium model there is the possibility of intertemporal spillovers. It is possible, for example, to show that there may be an intertemporal bootstrap effect in the sense that pessimistic expectations about constraints in the future may increase the likelihood of such constraints in the present.

What is the lasting contribution of the rationing approach? Perhaps the single most important contribution of this approach to macroeconomics has been to clarify the nature of disequilibrium situations in an explicit general equilibrium framework. Due to disequilibria, notional plans lose their relevance and must be replaced by effective plans. The additional insights that flow from the approach are plentiful. Real wages may have nothing to do with unemployment in some cases, whereas they are of vital importance in others.

The quantity rationing approach suffers from one major defect, however, in the sense that the rigidity of prices and wages is simply postulated and not derived from maximizing principles. Indeed, it is straightforward to show that the rationing equilibria are in fact Pareto-inefficient. This begs the question why prices and wages are not changed by the economic agents. In that sense, the rationing approach resembles "Hamlet without the Prince" or "A pub without beer". The main character of neoclassical economics (i.e. the price mechanism) has been omitted from the play without any justification.

On the other hand, however, the slow adjustment of prices and wages seems to be a fact of life. See, for example, Blinder (1994) for empirical evidence on price adjustment by firms. In that sense, the rationing models may present a relevant description of the world as it actually is.

One strand of literature has instead chosen to remedy the lack of a "theory of pricing" by adopting explicit priceand wage-setting agents in the form of monopolistically competitive firms and labour unions. This literature will be discussed in detail in Chapter 13 which deals with new Keynesian economics.