Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

I

ss due to distortionary i2). The Lagrangean is:

I

(6.63)

(6.64)

(6.65)

ie requirement restric- " for the government's

greater than r) would '1 the future. In doing oposite holds for a very

the levels of the two

(6.67)

1

(6.68)

)licitly determined by exerts an influence on historical significance. now and in the future. e straight line through doping line is the rev-

.-.'1 fare loss curves (i.e. 0). The closer to the revenue is raised with revenue requirement

assuming that r = pG.

.ii in the two periods:

(6.69)

"tax smoothing".

Chapter 6: The Government Budget Deficit

t,

Figure 6.5. Optimal taxation

The left-hand side of (6.61) can also be expressed in terms of shares of current national income. After some manipulation we obtain:

Gc	(	1	G2 (r – rG G1		Bo
+		+ r	1 + r		± (1 ± r) yi
c (1+Y)			(r–rG)	+ (1 + r)bo,			(6.70)
=
+ r1 + r
where e			GII/Yi, and 190		Bo / Yi . Furthermore, using (6.57), the
ficit in period 1 can also be written in terms of national income in period 1:
, Di rBo + + G1 –				= rbo + + –		.	(6.71)
1,1
u1 — =

The spending point is defined as the point where Di = 0, and is drawn as point Eo in Figure 6.6. The optimal taxation point is given by point E.

With the aid of this simple model a number of "rules of thumb" can be derived for the government's finances. First, as was mentioned above, government investment projects earning a market rate of return can be financed by means of debt. Second, consumption spending and losses on public investment projects should be financed by means of taxation. Third, tax rates should be smoothed as much as possible to minimize the welfare loss due to taxation. Fourth, a temporary rise in government consumption may be financed by means of debt. Formally, a temporary increase does not raise the revenue requirement of the government is constant since

= –(1 + r)dq implies that d 7E1 = 0), so that the revenue requirement line stays put. In terms of Figure 6.6, the spending point moves from q, to Esi , the optimal taxes remain unchanged, and the temporary increase in government spending

155

The Foundation of Modern Macroeconomics

Figure 6.6. Optimal taxation and tax smoothing

is accommodated by an increase in the deficit (and hence debt) in the first period. This is a neoclassical policy prescription that looks a lot like old-fashioned Keynesian countercyclical policy. During (temporary) recessions there is no harm in letting the debt increase a little bit. Fifth, if it appears that the government's spending level has permanently increased (d6 > 0), tax rates should be increased immediately. For example, if we know that unemployment has permanently increased (and not due to a recession), taxes should be increased in order to finance the additional unemployment benefits. Sixth, if the government credibly announces that it is permanently lowering government spending, tax rates should be lowered immediately. This is a so-called "balanced decline" of the public sector. Seventh, if the government credibly announces that it will lower its consumption spending in the future (46 < 0), then the tax rates should be lowered immediately. In terms of Figure 6.6, the revenue requirement line shifts down and to the left, and the spending point moves from Ei5, to E2 directly below it. The deficit in the first period (and hence debt) increases as a result. Indeed, (6.69) and (6.70)-(6.71) predict that dcli I = (1+ y) (2 r + y) > 0.

In Chapter 10 we shall return to the issue of debt management and the nation's finances. We do this in the context of models in which the political process is made endogenous, the so-called "endogenous politicians" or New Political Economy approach to macroeconomics. In that context it is much more natural to discuss the otherwise "hard to swallow" debt and deficit norms agreed upon by members of the European Community in the Maastricht Treaty. For those who cannot wait, the article by Buiter, Corsetti, and Roubini (1993) makes excellent reading.

6.3 Punchlines

„s chapter two a introduced and

and the thc,ry starting with the fi of government spe

(bonds or taxi ilimancing method o:

.:, and weLAurt

Morig be stressed that 4:07 mption but ral..

.anment.

The intuition beh: -

. d ■.:lances the res.., jAit, since total reso -

terms, eventui-,..,

— :itsure that it will b ux cut by saving it. T •ouseholds and a

kithough the RET s) taken serio:.

-Jov. ever, been raised periment involx 4

1110i Like a comptc.i.c sources available to t •11 of taxes and no: Second, if the hous4

Abour income can: is that the hou

- constraints) is aft, :, if housetk-

- hole) is infinitely it ler the overt::

with ea,i, -:')uut each other's we

..:nce of intc: 0 _ -4itaied (in present it

wealthier and that the RLI

dr_ - ,:aively, a tax cut to :tab inht

156

p

t,

ng

ce debt) in the first period. l ike old-fashioned Keynesian sere is no harm in letting the vernment's spending level I be increased immediately. nently increased (and not a to finance the additional edibly announces that it is s should be lowered imme- ublic sector. Seventh, if the consumption spending in ered immediately. In terms c- n and to the left, and the deficit in the first period Ld (6.70)—(6.71) predict that

nagement and the nation's ;th the political process is s" or New Political Econis much more natural to t norms agreed upon by cht Treaty. For those who i (1993) makes excellent

Chapter 6: The Government Budget Deficit

6.3 Punchlines

In this chapter two concepts, both relating to the government budget constraint, are introduced and analysed, namely the so-called Ricardian equivalence theorem RET) and the theory of tax smoothing.

Starting with the first of these, the RET can be defined as follows. For a given path of government spending, the particular financing method used by the government (bonds or taxes) does not matter. More precisely, when the RET is valid, the financing method of the government does not affect real consumption, investment, output, and welfare and government debt is seen as a form of delayed taxation. It must be stressed that the RET is not a statement about the effects of government consumption but rather deals with the way these expenditures are paid for by the government.

The intuition behind the RET is quite simple. If the government cuts taxes today and finances the resulting deficit by means of debt, then households will realize that, since total resources claimed by the government have not changed in present value terms, eventually the tax will have to be raised again sometime in the future. To ensure that it will be able to meet its future tax bills, the household reacts to the tax cut by saving it. The tax cut does not affect the lifetime resources available to the households and thus does not affect their consumption plans either.

Although the RET was not taken seriously by David Ricardo himself, it was (and still is) taken seriously by most new classical economists. A lot of objections have, however, been raised against the strict validity of the RET. First, if the Ricardian experiment involves changing one or more taxes which distort economic decisions (like a comprehensive income tax) then RET will fail. Intuitively, the lifetime resources available to the households will in that case depend on the particular time path of taxes and not just on the present value of taxes.

Second, if the household is unable to borrow freely, for example because future labour income cannot be used as collateral, then RET fails. Again, the reason for this failure is that the household choice set (and the severity of the household's borrowing constraints) is affected by the time path of taxes chosen by the government.

Third, if households have finite lives whilst the government (and the economy as a whole) is infinitely lived, RET may or may not be valid. It turns out that it matters whether the overlapping generations which populate the economy are altruistically linked with each other or not. Generations are altruistically linked if they care about each other's welfare (like children caring for their parents or vice versa). In the absence of intergenerational altruism, the RET fails. Intuitively, a tax cut now matched (in present value terms) by a tax hike later on will make present generations wealthier and future generations poorer. With intergenerational altruism it is possible that the RET holds because transfers between generations will take place. Intuitively, a tax cut today will be passed on to future generations in the form of an (additional) inheritance.

157

The Foundation of Modern Macroeconomics

Other objections to the RET relate to net population growth, informational problems (irrationality, myopia, and lack of information), and the so-called "bird in the hand" fallacy. The upshot of the discussion is that there are ample theoretical reasons to suspect that the RET is not strictly valid. Unfortunately, as is often the case, the empirical evidence regarding the approximate validity of the RET is inconclusive.

Even if one is willing to assume that the RET is valid, this does not mean that public debt has no role to play in the economy. Indeed, according to the theory of tax smoothing the government can use public debt to smooth its tax rates over time. To the extent that these tax rates are distorting the behaviour of private agents, tax smoothing is socially beneficial because it minimizes the distortions of the tax system as a whole. A number of intuitive "rules of thumb" follow from the theory. First, government investment projects earning the market rate of return do not represent a net claim by the government on private sector resources and thus can be financed with government debt. Second, government consumptive spending (including losses on public investment programmes) should be financed by means of taxes. Third, tax rates should be smoothed and not display large fluctuations over time. Fourth, temporary spending shocks can be financed with debt but permanent shocks should be financed with taxes.

Further Reading

The theory of tax smoothing is due to Barro (1979a). Readers interested in the various issues surrounding the government budget constraint and the deficit are referred to Buiter (1985, 1990). The intertemporal consumption model used in this chapter is due to Fisher (1930). See Deaton (1992) and Attanasio (1999) for recent surveys of intertemporal consumption theory.

A Closer Loa

Labour Mall

I- pose of this chapter

•nat are some of the m advanced capitalist ecorw

now can we explain some \et used so far? Hoy'.

3 hOw can we explain re dement between

•••hat do we mean by e

...3iployment?

.1 Some Stylized Fa

stylized facts about the 1 d into the two L

ne main indicator of ce the Great Depr, _ic research. The folk

Aimed for most countries in t:

I

1: 1 he unemploymL lit :nemployment rate for a from Figure 7.1, u:..

-*data are taken from vario ,amdlindized unemployment dam

158

p

on growth, informational probDn), and the so-called "bird in that there are ample theoretialid. Unfortunately, as is often roximate validity of the RET is

valid, this does not mean that ideed, according to the theory :bt to smooth its tax rates over '`- e behaviour of private agents, nizes the distortions of the tax Numb" follow from the theory. market rate of return do not sector resources and thus can

ment consumptive spending ) should be financed by means t display large fluctuations over inced with debt but permanent

ers interested in the various issues /' licit are referred to Buiter (1985, is chapter is due to Fisher (1930). ys of intertemporal consumption

A Closer Look at the

Labour Market

-t-ie purpose of this chapter is to discuss the following issues:

1.What are some of the most important stylized facts about the labour market in advanced capitalist economies?

2.How can we explain some of these stylized facts in the standard model of the labour market used so far? How do these theories fall short of providing a full explanation?

3.How can we explain real wage rigidity as the outcome of an implicit contractual arrangement between risk-neutral firms and risk-averse workers?

4.What do we mean by efficiency wages and how do they lead to equilibrium unemployment?

7.1 Some Stylized Facts

The stylized facts about the labour market in advanced capitalist countries can be subdivided into the two categories of time series evidence and cross-section information. The main indicator of labour market performance is the unemployment rate. Ever since the Great Depression of the 1930s this has been at the forefront of macroeconomic research. The following stylized facts about unemployment can be established for most countries in the Western world (see, e.g. Layard et al., 1991, ch. 1).

Fact 1: The unemployment rates fluctuates over time In Figures 7.1-7.3, we plot the unemployment rate for a number of regions and countries since 1967. 1 As is evident from Figure 7.1, unemployment was relatively low and stable in the EC

The data are taken from various issues of the OECD Economic Outlook. Where possible we make use of standardized unemployment data.

The Foundation of Modern Macroeconomics

European Community

1967

1973

1979

1985

1991

1997

Figure 7.1. Unemployment in the European Community and the United States

10—

Sweden

8 —

E

O

6

C

4 —

Japan

0	I I I I I I I I I	I I I I I I	I 1-	I I I I I	I I I I I I I I I
I
1967	1973	1979	1985	1991	1997

Figure 7.2. Unemployment in Japan and Sweden

up until the time of the first oil shock in 1973. After that, for about a decade, the employment rate followed a steady trend upward, peaking in 1985-1986 and again in 1995. Unemployment in 1997 is estimated to be 10.6% in the EC (this amounts to 17.8 million people out of work!). Unemployment in the US seems to be hovering around 6% during that same period, and in 1997 it stands at 4.9%.

Figure 7.3. Unerr.

Netherlands

I

The unemployment exi Japan and Sweden. 2 As countries have had a stable yment experience in U. ,.reemployment has dropper

F _ re 7.3.

tact 2: Unemployment tia business cycles In Figur ,

and the United King,.. .

truly deserves its name, e1/4 - longed period of time ‘: unemployment were pui, mulch more regular pattern __,.4ment slightly differ,...

persistence, much more that :ssing unemployment 43

We focus on the figures for 5 , •

—ea CFA). Other member cou:

have precluded us from c^ The data for the period urn.

111--r the United Kingdom and fr, - Sir period 1994-2000 have been t

160

European Community

"♦

`, United States

1991 1997

ommunity and the

1

1

1

1

1

1

1

1

1

1

:491 1997

len

that, for about a decade, the ng in 1985-1986 and again ).6% in the EC (this amounts n the US seems to be hovering

ands at 4.9%.

Chapter 7: A Closer Look at the Labour Market

12	—
10 —
as
E
8	—						United
C.
							Kingdom
6	—
4	—
2							Netherlands
0	I I	I I I I I	I 1 I I I	I I I I I I	I I 1 I	I I I I	I I I I I I I
	1967	1972	1977	1982	1987	1992	1997

Figure 7.3. Unemployment in the United Kingdom and the

Netherlands

The unemployment experience in the US and the EC differs markedly from that in Japan and Sweden. 2 As is shown in Figure 7.2, until the early 1990s, the latter countries have had a stable and low unemployment rate of around 2%. The unemployment experience in the UK looks very much like the EU pattern whereas Dutch unemployment has dropped off rather dramatically during the last few years—see Figure 7.3.

Fact 2: Unemployment fluctuates more between business cycles than within business cycles In Figures 7.4 and 7.5, we plot the unemployment rate for the US and the United Kingdom for extended periods of time. 3 The Great Depression truly deserves its name, especially in the US. Unemployment was very high for a prolonged period of time and peaked at close to 25%! Another thing to note is that, if unemployment were purely a business-cycle phenomenon, one would expect a much more regular pattern than the one observed in these figures. To put the same argument slightly differently, the time series of unemployment displays a lot of persistence, much more than is consistent with the business cycle. For example, by regressing unemployment on its own lagged variable, Layard, Nickell, and Jackman

2 We focus on the figures for Sweden because it is a representative member of the European Free Trade Area (EFTA). Other member countries are Norway, Sweden, Finland, Austria, and Switzerland. Lack of

data have precluded us from constructing a consistent unemployment index for the EFTA countries. 3 The data for the period until 1993 have been taken from Mitchell (1998a, pp. 163, 165, 168-169)

for the United Kingdom and from Mitchell (1998b, pp. 112, 114) for the United States. The data for the period 1994-2000 have been taken from OECD (2001, Table 21).

161

The Foundation of Modern Macroeconomics

	16—
-	14 —
c
72.	12 —
F	10-
	8—				p
	6—
	4—
	2—
	0	f )	)	V	)	))	fl
	1855	1865 I	1885 I 1905	1915	1925 I	1945 I 1965 I		1985
		1875	1895		1935	1955	1975	1995

Figure 7.4. Unemployment in the United Kingdom, 1855-2000

25.0

Es
L 20.0
0
TD_
15.0
10.0
5.0
0.0	1920	1	1940	1	1960	1980	1	2000
1900
1890	1910	1930		1950		1970	1990

Figure 7.5. Unemployment in the United States, 1890-2000

(1991, p. 77) obtain the following fit for the UK during the period 1900-1989:

IJt = 0.0041 + 0.934 Ut_1,	(7.1)
(0.039)
and for the US:
(it = 0.0080 + 0.877Ut _1,	(7.2)
(0.051)

where Ut is the act - edicted by the rt ):.4ndard error (ji 4ed unemplc - . - •of persistent, .

:Awes a long time 1

..,t 3: The rise increase in long-t unemployed

. 4, p. 575), ‘s, ilk developed w,

.;:nt,„8e

= Tressed as a per(

k ,)WS" me,:

4%. a job express, The striking p,: -

. i vitireen 1979 and

much by probabilay

1 same pat! and

Milemployment

TJble 7.1.

1 S• es

won

hon-EC hoop

I

•cs

▪pt

JAC Oki '

Some: Bean I

162

1965 I	1985
1975	1995

n, 1855-2000

1980	I	2000
-0	1990

10-2000

OP period 1900-1989:

(7.1)

(7.2)

Chapter 7: A Closer Look at the Labour Market

where Ut is the actual unemployment rate at time t and Chis the unemployment rate predicted by the regression equation. The numbers in parentheses are the estimated standard error of the coefficient estimates. In both countries the coefficient for lagged unemployment is high (and close to unity) and significant. This suggests a lot of persistence in the unemployment time series. High persistence implies that it takes a long time before the effects of a particular shock die out (see below).

Fact 3: The rise in European unemployment coincides with an enormous increase in long-term unemployment Almost half of Europe's unemployed have been unemployed for more than one year. In Table 7.1, which is taken from Bean (1994, p. 575), we show the unemployment composition for a number of regions of the developed world for 1979 and 1988. The column "Annual Inflows" measures the percentage inflow into unemployment, i.e. the number of people who lose their job expressed as a percentage of the number of employed people. The column "Annual Outflows" measures the flow out of unemployment, i.e. the number of people that find a job expressed as a percentage of the number of unemployed people.

The striking pattern that can be observed in Table 7.1 is that the inflow rates are relatively similar in the two years, but that the outflow rate in the EC has halved between 1979 and 1988! In words, the high unemployment level in the EC is caused not so much by an increased probability of losing one's job, but rather by a reduction in the probability of finding a job when one is unemployed (Bean, 1994, p. 576).

The same pattern is observed in Table 7.2 which has been taken from Layard, Nickell, and Jackman (1991, ch. 1). Between 1979 and 1990, the total level of unemployment has risen in most countries, but in the ten EC countries the

Table 7.1. The nature of unemployment

		Annual	Annual	Long-term
		Inflows'	Outflows°	Unemployment"
European Community	1979	0.27	9.8	29.3
	1988	0.33	5.0	54.8
United States	1979	2.07	43.5	4.2
	1988	1.98	45.7	7.4
Japan	1979	0.31	19.1	16.5
	1988	0.37	17.2	20.6
Non-EC Europe'	1979	0.70	38.1	5.3
	1988	0.80	30.4	7.3

Notes:

a Percentage of source population

b Percentage of total unemployment c Nordic countries only

Source: Bean (1994)

163

The Foundation of Modern Macroeconomics

Table 7.2. Unemployment duration by country

	1990			1979
	All	Under	Over	All	Under	Over
		1 year	1 year		1 year	1 year
Belgium	8.7	1.9	6.8	8.2	3.4	4.8
Denmark	9.6	6.8	2.8	6.2	-	-
France	8.9	5.4	3.5	5.9	4.1	1.8
Germany	5.0	2.6	2.4	3.2	2.6	0.6
Ireland	14.0	4.8	9.2	7.1	4.8	2.3
Italy	7.9	2.4	5.5	5.2	3.3	1.9
Netherlands	7.6	3.8	3.8	5.4	3.9	1.5
Portugal	5.1	2.5	2.6	4.8	-	-
Spain	1	6.7	9.5	8.5	6.1	2.4
United Kingdom	6.5	3.6	2.9	5.0	3.8	1.3
Australia	6.8	5.2	1.6	6.2	5.1	1.1
New Zealand	7.6			1.9	-	-
Canada	8.1	7.6	0.5	7.4	7.1	0.3
United States	5.5	5.2	0.3	5.8	5.6	0.2
Japan	2.1	1.7	0.4	2.1	1.7	0.4
Austria	3.3	2.9	0.4	1.7	1.5	0.2
Finland	3.4	2.8	0.6	5.9	4.8	1.1
Norway	5.3	4.7	0.6	2.0	1.9	0.1
Sweden	1.6	1.5	0.1	1.7	1.6	0.1
Switzerland	1.8			0.9	-

Source: Layard, Nickell, and Jackman (1991, p. 6)

rise in long-term unemployment has been much larger than that in short-term unemployment. We shall return to this issue below.

Fact 4: In the very long run unemployment shows no trend This fact has been graphically illustrated in Figures 7.4 and 7.5. Although there are sharp peaks and deep troughs, there does not seem to be any noticeable trend in the unemployment rate for the US and the UK. This is all the more remarkable in view of the enormous productivity gains that have been made in the last century and a half. Apparently, the nineteenth century luddite fear of physical capital permanently pushing workers into unemployment has proved unfounded.

More formally, and in terms of equations (7.1)-(7.2), the coefficient of the lagged unemployment rate is high but less than unity. Ultimately, there are mechanisms at work whereby unemployment returns to some average level. The

convergence to this avera..: : ilows. From equations hi.,

unemployment rate U:

I

Ut = ao + ai Ut-

would equal 6.21% 1 - he adjustment speed by sol ;:employment rate at time can be solved by repeated su

•= ao + ai Uo,

U2 = ao + al Ui =- ao + ai

Ut = ao [1 + ai + a; +

expression can be re% ai

Ut - f7/ = [ U0 - a 41

fquation (7.5) can be used een U0 and U to be el Uo and the long-run 111

e, for example, before hL: as z.e indicator for the au,

[ UtH -U] = [Uo - UJ a A a - 1

tit log ai = - log 2

the UK this amounts to - than a decade before e

.....6 -run unemployment ra

ignore the fact that we ar nce intervals for U.

trick is to write the term .-

1 -0- a I + ai	=	1 -
		1 -

zing this result plus the de:'

164