Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

q(9) must

w, 8, and U.

(9.2

(9.7-

(9.:

or capital, determining duction) of each firm with diminishes as more car :k (K*) to the (exogenou By plugging this functio-

1 (9.27). Equation (9.26) is

.ption of free exit/entry of out of the Nash bargainir. seeker. Finally, (9.28) is the s equation is also known as

d real rate of interest. First, n as a function of the interfor w and 9 as a function s the unemployment=rate, mber of jobs is given by

Figure 9.1. In panel (a) the - .1 sloping in (w, 0) space:

(9.29)

f an occupied job and thus t equilibrium the expected ' , O increase, i.e.

urve (9.27). This curve is

(9.30)

part of the search costs h a vacancy (see above).

Chapter 9: Search in the Labour Market

0*

0

U"

Figure 9.1. Search equilibrium in the labour market

By combining ZP and WS0 in panel (a), the equilibrium wage, w*, and vacancyunemployment ratio, e*, are determined—see point E0 in panel (a).

In panel (b) of Figure 9.1 the equilibrium vacancy-unemployment ratio (the indicator for labour market tightness) is represented by the line LMT0 from the origin and BC is the Beveridge curve (9.28) rewritten in (V, U) space. By using V OU in (9.28), the Beveridge curve can be loglinearized:

	(1 \	( s+fri	u	(9.31)
	- r )	(1 - 77) )

where U dUIU,I7 dVIV, and 3 ds/s, and where 77 and f are given, respectively, in (9.4) and (9.5). 6 The Beveridge curve is downward sloping (since 0 < ri < 1). Intuitively, for a given unemployment rate, a reduction in vacancy rate leads to a fall in the instantaneous probability of finding a job (f) , i.e. for points below the BC curve the unemployment rate is less than the rate required for flow equilibrium in the labour market (U < s I (s + f)). To restore flow equilibrium the unemployment rate must rise. Equation (9.31) also shows that an increase in the job destruction rate s shifts the Beveridge curve up and to the right, a result which will be used below.

6 This expression is obtained as follows. Starting with (9.28) and noting that f (0) 0q(0) we find:

[s + f (0)] dU + Udf (0) = 0 dU + Udf (0) = (1 — U)ds

sU + Uf (0) [1 — ii(e)] 6. = s(1 - U),"s"

[s — f (0)U(1 — 17(0))] U + Uf (0)(1 — q(0))17 = s(1 — U)3.

By using U = s / (s + f) in the final expression and rewriting we obtain (9.31).

225

The Foundation of Modern Macroeconomics

9.1.3 Comparative static effects

In order to demonstrate some of the key properties of the model we now perform some comparative static experiments. The first experiment has some policy relevance and concerns the effects of an increase in the unemployment benefit z. It is clear from (9.27) that an increase in z leads to upward pressure on the wage rate as the fall-back position of workers in the wage negotiations improves. In terms of Figure 9.1, the wage setting equation shifts up from WS° to WS 1 and the equilibrium shifts from E0 to E 1 in panel (a). The equilibrium wage rate increases and the vacancy—unemployment ratio decreases. Intuitively, the policy shock causes the value of an occupied job to fall. In panel (b) of Figure 9.1, the reduction in the vacancy—unemployment ratio is represented by a clockwise rotation of the LMT line, from LMT0 to LMT1 . Since nothing happens to the Beveridge curve, the equilibrium shifts from E0 to E 1 in panel (b), the vacancy rate falls, and the unemployment rate rises.

As a second comparative static experiment we consider what happens when the exogenous rate of job destruction s rises. This shock is more complicated than the first one because it affects both the incentive for firms to create vacancies and the Beveridge curve itself. It is clear from (9.26) that, ceteris paribus the wage, the increase in the job destruction rate reduces the value of an occupied job as the rents accruing to the firm are discounted more heavily. Hence, in terms of panel (a) of Figure 9.2, the ZP curve shifts to the left from ZP0 to ZP1. Since nothing happens to the wage-setting curve, the equilibrium in panel (a) shifts from E0 to E1 and both the wage and the vacancy—unemployment ratio fall. In panel (b) of Figure 9.2, the LMT curve rotates in a clockwise fashion from LMT0 to LMT1 . As was noted above, the direct effect of an increase in the job destruction rate is to shift the Beveridge curve outward, say from BC° to BC1 in panel (b). We show in the appendix that

0

U

Figure 9.2. The effects of a higher job destruction rate

the outward shift in LMT curve (provides equilibrium E1 lies that both the unemi

9.2 Application

In this section we continue our study of the idea of treating happens if employer Finally, we briefly- explain the observed

9.2.1 The effects c

We assume that thei; must pay an ad val by tE . Second, the h by h.

The effects of the modified to:

rfo = F (K , 1) — (r -

so that the marginal fected, but the free el

FL[K(r+ 8),1) — M r + s

where we have also s capital stock (i.e. K* = The effects of the L benefit is untaxed angd real wage rate w(1 —

rY u = (r + s)z + • r +

rY E = sz + [r +

r +3 -

where the second expi to be willing to sear

226

he model we now perform ent has some policy relemployment benefit z. It is pressure on the wage rate ins improves. In terms of So to WS1 and the equilib- -lge rate increases and the le policy shock causes the

9.1, the reduction in the •vise rotation of the LMT kveridge curve, the equilibills, and the unemployment

ler what happens when the is more complicated than rms to create vacancies and teris paribus the wage, the an occupied job as the rents ice, in terms of panel (a) of 1 . Since nothing happens to Lifts from E0 to E 1 and both i panel (b) of Figure 9.2, the LNITi. As was noted above, to is to shift the Beveridge show in the appendix that

LMT0

BC0

Chapter 9: Search in the Labour Market

e outward shift in the Beveridge curve dominates the clockwise rotation in the LMT curve (provided a very mild sufficient condition is satisfied) so that the new uilibrium E1 lies in a north-easterly direction from the initial equilibrium E0 so

that both the unemployment and vacancy rates increase.

9.2 Applications of Search Models

In this section we use the search-theoretic approach to study three issues. First, we continue our study of the effects of taxation on the labour market. Second, we study the idea of treating workers like empty beer bottles. Specifically, we look at what happens if employers must pay (receive) a deposit if they lay off (hire) a worker. Finally, we briefly investigate how the search-theoretic approach can be used to explain the observed persistence in the unemployment rate.

9.2.1 The effects of taxation

We assume that there are two separate taxes levied on labour. First, the employer must pay an ad valorem tax on the use of labour (a payroll tax), which is denoted by tE. Second, the household faces a proportional tax on labour income, denoted by tL .

The effects of the employers' tax on labour are as follows. First, equation (9.11) is modified to:

rjo = F (K , 1) — (r + 8)K — w(1 + tE) — sIo

(9.32)

so that the marginal productivity condition for capital (equation (9.12)) is unaffected, but the free entry/exit condition (9.13) is modified to:

	FL [K(r + 8), 1] — w(1 + tE) _		Yo	(9.33)
	r + s	— (MY

where we have also substituted the implicit expression determining the optimal capital stock (i.e. K* = K(r + 8)).

The effects of the labour income tax are as follows. First, since the unemployment benefit is untaxed and exogenous, equation (9.14) is unchanged, but the after-tax real wage rate w(1 — tL) appears in (9.15), so that (9.16)-(9.17) are modified to:

rY u =	(r + s)z + q(0)w(1 — tL)				(9.34)
	r + s + 9 q(9)
rY E =	sz + [r +	8)] w(1 —	r [w(1 —	— z]	(9.35)
	9q(			+ rYu ,
	r + s + 9 q(0)		r + s + 90)

where the second expression in (9.35) shows that w(1—tL ) > z must hold for anybody to be willing to search, i.e. the labour income tax must not be too high.

227

to be refun

tE)), i.e.

The Foundation of Modern Macroeconomics

The second effect of the income tax operates via the wage bargaining process. By following the derivation in section 1.1, the rent-sharing rule (9.21) is modified to:

i —	-		1—	FA	-	Iv],	(9.36)
YE
		--13)1+4) L
so that the wage equation (9.22) becomes:
rYUFL(Ki, 1))							(9.37)
= (1 - (1			+,8	( 1+4
and (9.24) can be written as:
w = (1 — /3)				FL [K(r + 8), + OYo ,			(9.38)
			—ztL )q±			1 + tE
	(1

where we have once again substituted K* = K(r + 3).

The core part of the model consists of the Beveridge curve (9.28), the zero-profit curve (9.33), and the wage-setting curve (9.38). It is possible to explain the intuition behind the comparative static effects of the various tax rates by graphical means. (The formal derivations are found in the appendix.)

First we consider in Figure 9.3 the effects of an increase in the payroll tax, tE. It follows from (9.33) that the zero profit curve shifts to the left (from ZP 0 to ZP1 in panel (a)) as a result of the shock. Ceteris paribus the gross wage rate, the tax increase reduces the value of an occupied job so that the zero profit equilibrium is consistent with a lower vacancy—unemployment ratio. The payroll tax also features in the wage-setting equation. Indeed, it follows from (9.38) that the increase in the payroll tax puts downward pressure on the wage rate. Intuitively this is because the firm is interested in the net surplus of the match (equal to (FL + 6y0)/(1

it takes the payroll tax into account. Part of this surplus features in the wage which

Figure 9.3. The effects of a payroll tax

(a) w

I

Figure 9.4. The effe

thus falls on that accou:.. from WS0 to WS1 in pan wage rate and the vacan LMT curve rotates in a cl shifts from E0 to E1 . The I increases. 1

As a second comparativ in the labour income t,. The increase in the labou wage-setting equation s from (9.38) that the tax i wage bargaining process I ceteris paribus, to upw.. shifts from E0 to E1 , the g ratio falls. In panel (b) th

LMT1 , the equilibrium the unemployment rate increase in the unempIL

9.2.2 Deposits on wor

Some people return env from an environmental less interested in this nol environment, and only r the form of a deposit that should be tried in the lab( fires a worker,

228

1

e wage bargaining process. B. ng rule (9.21) is modified tr-

(9.3—

(9.3R'

r curve (9.28), the zero-profit ,ible to explain the intuition tax rates by graphical means.

icrease in the payroll tax, tE. : s to the left (from ZP0 to ZP, s the gross wage rate, the tax the zero profit equilibrium is ). The payroll tax also features (9.38) that the increase in the Intuitively this is because the

al to (FL + 8 Yo)/( 1 + tE)), i.e. lus features in the wage which

Chapter 9: Search in the Labour Market

(a) w

0

Figure 9.4. The effects of a labour income tax

thus falls on that account. In terms of Figure 9.3, the wage-setting curve shifts down from WS° to WS 1 in panel (a). The equilibrium shifts from Eo to E1, and both the wage rate and the vacancy—unemployment ratio fall (see Appendix). In panel (b) the LMT curve rotates in a clockwise fashion from LMT 0 to LMT1 and the equilibrium shifts from E0 to E1 . The equilibrium vacancy rate falls and the unemployment rate increases.

As a second comparative statics exercise we now consider the effects of an increase in the labour income tax, tL. The effects of this shock are illustrated in Figure 9.4. The increase in the labour income tax has no effect on the zero-profit curve but the wage-setting equation shifts up from WS0 to WS 1 in panel (a). Intuitively, it follows from (9.38) that the tax increase raises the outside option for the household in the wage bargaining process because the unemployment benefit is untaxed. This leads, ceteris paribus, to upward pressure on the wage rate. In panel (a) the equilibrium shifts from E0 to E1 , the gross wage rate increases, and the vacancy—unemployment ratio falls. In panel (b) the LMT curve rotates in a clockwise fashion from LMT 0 to LMT1 , the equilibrium shifts from Ea to E1 , and equilibrium vacancies fall whilst the unemployment rate rises. The tax shock works in exactly the same way as an increase in the unemployment benefit.

9.2.2 Deposits on workers?

Some people return empty bottles to the store because they find it unacceptable from an environmental point of view to litter them. Most people, however, are less interested in this noble pursuit of a responsible attitude towards the natural environment, and only return the bottles because there is money to be made in the form of a deposit that will be refunded. One could argue that a similar system should be tried in the labour market. Why not have the firm pay a deposit when it fires a worker, to be refunded when it (re-) hires that (or another) worker? It turns

229

The Foundation of Modern Macroeconomics

out that this question can be analysed in the search-theoretic framework developed in this chapter.

Suppose that a firm that hires a worker receives a fixed once-off payment of b from the government, but that a firm that fires a worker must pay b to the government. Clearly, (9.9) would be modified to reflect this payment:

rlv = — Yo + q(9) [Io + b —

(9.39)

If a firm with a vacancy finds a worker, its capital gain will be Jo — Iv plus the payment from the government. Free exit/entry of firms will then imply the following expression for the value of an occupied job:

	Iv = 0	Yo	b.	(9.40)
		k= q(9)

Equation (9.40) shows that the deposit acts like a lump-sum subsidy to firms with a vacancy. The expected search costs yo/q(9) are reduced by the lump-sum payment received from the government.

For a firm with a filled job, the steady-state arbitrage equation reads as follows:

rIo = F (K, 1) — (r + 8)K — w — s [Jo + b] . (9.41)

If the job is destroyed, the firm not only loses the value of the occupied job, but must also pay back the deposit on its worker to the government. As a result, the expected capital loss is s(Jo + b). (Since the job destruction rate s is exogenous, the firm can do nothing to reduce the probability of an adverse job-destroying shock.) The marginal productivity condition for capital (9.12) still holds. By combining (9.12) with (9.40)—(9.41), the zero profit condition (given in (9.13)) is changed to:

(r + s)[(1Yo _b = F(K, 1) — FK(K, 1)K — w — sb

	Yo	(K, 1) — w rb	(9.42)
	q(0)	r s

The capital value of the deposit acts like a subsidy on the use of labour.

The rent-sharing rule (equation (9.21)) is modified to reflect the payment the firm receives if it employs the worker:

Yi — Yu =	1 — fi	)	+ b — Iv] ,	(9.43)
so that the wage equation (9.22) becomes:
wi = (1 — fi)rYu + [FL(Ki, + rb] .				(9.44)

Since the reservation wage is still given by (9.23), the wage equation (9.44) can be rewritten for the symmetric case (with wi = w) as:

w = (1 — 13)z + [FL(K, 1) + rb + 0 yo] .

(9.45)

The model consists of equations (9.25), (9.28), (9.42), and (9.45).

ra)

w

Figure 9.5. The effects o: .

In Figure 9.5 we illustr from (9.42) that the zero the interest payments the I pied job. These interest i wage-setting equation (9.-1. to WS1 in panel (a). It is sha unemployment ratio rise u) of the initial equilibrium wise fashion from LMT( , equilibrium vacancy rate

9.2.3 Search unemployi

As we saw in Chapter 7, advanced economies is the persistence be explained in tion, Pissarides (1992) shocks can persist for a lop lose some of their skills, t the firms. By sitting at hoi.. As a result, there are less va of unemployment increa , capital has decreased (due t market becomes "thin", iv There are less profitable n.. if the unemployed had n

230

eoretic framework develop(' a

Klonce-off payment of b frorrust pay b to the government nt:

(9.39)

n will be Jo — Jv plus the pay-

-' then imply the following

(9.40)

-sum subsidy to firms with a 4:1 by the lump-sum payment

e equation reads as follows:

(9.41)

klue of the occupied job, but wernment. As a result, the ction rate s is exogenous, the averse job-destroying shock.) 2) still holds. By combining ven in (9.13)) is changed to:

9.42)

the use of labour.

) reflect the payment the firm

(9.43)

(9.44)

wage equation (9.44) can be

(9.45)

and (9.45).

Chapter 9: Search in the Labour Market

'a)	(b)
w	V
	WS1
	wso

ZPi

ZP0

0

Figure 9.5. The effects of a deposit on labour

In Figure 9.5 we illustrate the effects of an increase in the deposit, b. It follows from (9.42) that the zero profit curve shifts up (from ZP 0 to ZP1 in panel (a)) because the interest payments the firm earns on the deposit increase the value of an occupied job. These interest payments, however, also influence the wage rate via the wage-setting equation (9.45). Hence, the wage-setting equation shifts up from WS° to WS1 in panel (a). It is shown in the appendix that both the wage and the vacancy— unemployment ratio rise as a result of the shock, i.e. point E 1 lies to the north-east of the initial equilibrium Eo . In panel (b) the LMT curve rotates in a counterclockwise fashion from LMT0 to LMT1 and the equilibrium shifts from Eo to E 1 . The equilibrium vacancy rate rises and the unemployment rate falls.

	9.2.3 Search unemployment, loss of skills, and persistence—)
	As we saw in Chapter 7, one of the stylized facts about the labour markets of	-00\-P
	advanced economies is the persistence of the unemployment rate. How can thp--
	persistence be explained in the search-theoretic framework? In a recent cOntrifu-
	tion, Pissarides (1992) has shown that one of the mechanisms by which temporary
	shocks can persist for a long time has to do with loss of skills. If the unemployed
	lose some of their skills, they become less productive, and hence attractive
	the firms. By sitting at home without a job, they lose some of their human capital.
	As a result, there are less vacancies in the next period, and the expected duration.
	of unemployment increases.,Furthermore, because of the fact that average human
	capital has decreased (due to the loss of skills by the long-term unemployed), the
	market becomes "thin", in the sense that average labour productivity has decreased.
	There are less profitable matches in the economy than would have been the case
	if the unemployed had not lost some of their skills. There will, on average, be
	231

of the a

The Foundation of Modern Macroeconomics

more long-term unemployed, so that even if the original long-term unemployed have died (or found a job), the thinness of the labour market remains. A temporary shock is self-perpetuating.

9.3 Punchlines

In this chapter we discuss the flow approach to the labour market. This is by far the most technically demanding theory of the labour market discussed in this book because it abandons the notion of an aggregate labour market altogether and instead directly models the flows of labour that occur in the economy, namely the movements of workers from unemployment into jobs and vice versa.

Because the theory is inherently quite demanding, we only present the simplest possible search model. The central elements in the model are the following. First, there are frictions in the process by which job-seeking unemployed workers come into contact with firms that are looking for a worker to fill a vacancy. These frictions are costly and time consuming. Second, the crucial analytical device that makes the model tractable is the so-called matching function. (This function plays a similar role in the flow approach to the labour market that the neoclassical production function plays in the theory of factor productivity and growth.) The matching function relates the probabilities of workers meeting firms (and firms meeting workers) as a function of an aggregate labour market tightness variable. This tightness indicator is the ratio of vacancies and unemployed workers.

If the vacancy-unemployment ratio is high (low) then the probability that an unemployed job seeker finds a firm with a vacancy is high (low) and expected duration of the search for a job is low (high). The matching function also explains the conditions facing the other party on the market. Indeed, if the vacancyunemployment ratio is high (low), then there are many (few) firms trying to locate an unemployed worker so that the probability that an individual firm is successful is low (high) and the expected duration of the firm's search process is high (low).

The third key ingredient of the search model concerns the wage formation process. Once a firm with a vacancy meets an unemployed worker a pure economic rent is created consisting of the sum of foregone expected search costs by the firm and the worker. This surplus must be divided somehow between the firm and the worker. The typical assumption in this literature is that the two parties bargain over the wage.

The fourth ingredient of the model is the so-called Beveridge curve which relates the equilibrium unemployment rate to the (exogenous) job destruction rate (regulating the flow into unemployment) and the workers' job finding rate (regulating the flow out of unemployment). The job destruction rate is strictly positive because previously profitable firm-worker matches are destroyed due to idiosyncratic shocks.

The model yields a general equilibrium solution for, inter alia, the unemployment rate and the vacancy rate as a function of the exogenous variables. We perform

a

various comparative stati. tion rate leads to an increa a decrease in the vacancv--1 We complete this chap settings. First, we show ha Second, we show that a N, unemployment rate. (Lind( ment when it hires a w( again.) Finally, we briei.) a of the stylized facts of the in the unemployment ra their skills while unemplo)

thus face a longer search i

I

Further Reading

Key references to the mod 1982b, 1986, 1989), Diamor__ (1994), and Blanchard and E present good (but advanced theoretic properties of the s, /creation process is present,. very extensive survey

Appendix

section 1.3 we graphically benefit, z, and the job destr..

.11y. First we loglinearize equ ,„ FL, and K). After some mar

[	11(w — FL) —1	1
	PYo9 1	"..

where I/ is defined in (9.4), H solutions for 6 and dw:

6 _V —U_ — (FL — w

dw = (FL — w)[—r36A)k,i

232

nal long-term unemployed market remains. A temporary

labour market. This is by far our market discussed in this abour market altogether and in the economy, namely the and vice versa.

we only present the simplest del are the following. First, g unemployed workers come fill a vacancy. These frictions tical device that makes the Phis function plays a similar :oclassical production funcvt h.) The matching function 1 firms meeting workers) as a ible. This tightness indicator

en the probability that an igh (low) and expected durahi ng function also explains n. Indeed, if the vacancy- y (few) firms trying to locate individual firm is successful !arch process is high (low). the wage formation process. rker a pure economic rent is rch costs by the firm and the 'le firm and the worker. The ties bargain over the wage. veridge curve which relates I) job destruction rate (regu-

,ob finding rate (regulating is strictly positive because

I due to idiosyncratic shocks. r, inter alia, the unemployenous variables. We perform

Chapter 9: Search in the Labour Market

various comparative static experiments. For example, an increase in the job destruction rate leads to an increase in both the unemployment and vacancy rates and to a decrease in the vacancy-unemployment ratio.

We complete this chapter by applying the search model in a number of different settings. First, we show how the search equilibrium is affected by the tax system. Second, we show that a worker-deposit scheme can be used to affect the equilibrium unemployment rate. (Under the scheme the firm receives a grant from the government when it hires a worker but must repay the grant when the job is destroyed again.) Finally, we briefly argue that a modified search model can account for one of the stylized facts of the labour market, namely that there is strong persistence in the unemployment rate. The key notion here is that the unemployed may lose their skills while unemployed and become less attractive employees to firms (and thus face a longer search process) as a result.

Further Reading

Key references to the modern search-theoretic literature are Mortensen (1978, 1982a, 1982b, 1986, 1989), Diamond (1984a, 1984b), Mortensen and Pissarides (1994), Pissarides (1994), and Blanchard and Diamond (1994). Mortensen and Pissarides (1999a, 1999b) present good (but advanced) surveys of the literature. Hosios (1990) studies the welfaretheoretic properties of the search model. Microeconomic evidence on the job destruction /creation process is presented by Davis, Haltiwanger, and Schuh (1996). For a recent and very extensive survey of the matching function, see Petrongolo and Pissarides (2001).

Appendix

In section 1.3 we graphically derive some results regarding shocks to the unemployment benefit, z, and the job destruction rate, s. In this appendix we derive these results analytically. First we loglinearize equations (9.26)—(9.27) holding constant r and 8 (and thus also FK, FL, and K). After some manipulation we obtain:

[	ri(w - FL) -1 1[	8 [(FL - w) [yo + (s I (r + s))3] 1,				(A9.1)
	-13)/0 1 dw (1 — 13)dz + Syo9Po
				ds/s. Solving (A9.1) yields the
where ri is defined in (9.4),		d1910, Po	dyo/yo, and
solutions for 9 and dw:
			--	— (1 —	mdz
	1.7 = - F(L - w + OA)) Po - (FL — w)(s I (r + s))s					(A9.2)
		11 (FL, —	+ POYo
dw = (FL w) [ 130)/0[(1 — n)Po + (s/ (r + s)A + 77(1 — i3)dz						(A9.3)
		71 (FL —	+ 139yo
						233

11

II

The Foundation of Modern Macroeconomics

It follows that an increase in the unemployment benefit (dz > 0) raises the wage (dw > 0) and reduces the vacancy—unemployment ratio (6 > 0) as is illustrated in Figure 9.1. An increase in the job separation rate (3 > 0) leads to a reduction in both the wage and the vacancy—unemployment ratio (dw < 0 and ö < 0) as is illustrated in Figure 9.2. Finally, an increase in the search costs (yo > 0) reduces both the wage and the vacancy—unemployment ratio (dw < 0 and ö < 0). Students are invited to draw the corresponding graph and to provide the economic intuition.

It remains to show that an increase in the job destruction rate raises both the unemployment and vacancy rates, as is asserted in the discussion surrounding Figure 9.2. By using

(9.31) and (A9.2) (and setting yo = dz = 0) we obtain a system in V and U:
L	1	fs(1±±7,77)	. v1				(A9.4)
		-1	s	(1 — n)(FL —		1 —
			r +s 71(FL		+ P)439
Solving (A9.4) yields the following expressions:
				—
		(s+	( s±f") r s+ ?AFL — + 00] 3 > 0,				(A9.5)
U"		fs) —		— 1_			(A9.6)
		+ f L-	+ s ) n(FL, — w) + f3y00		>0

Unemployment unambiguously rises but the effect on the vacancy rate is ambiguous in general. It is not difficult to show, however, that the term in square brackets on the righthand side of (A9.5) is positive if a rather weak sufficient condition is satisfied. First we note that (9.26) gives rise to the following result:

	FL —w	r s	(A9.7)
	?AFL — + PYoe rAr + s)+ Pf .

By using (A9.7) the term in square brackets on the right-hand side of (A9.5) can be simplified to:

[.] =—s±f11( (		r +s
f Rr+s) q(r+s)+ /3f
f [rri + fin —s2
f [77(r + + fir]
frrl f2 [/3 (Sin	2 ]
f [17(r+s)+ fif]	•

The denominator in (A9.8) is positive and, since numerator to be positive also is /6 > (s I f)2 or:

>U \2

1 - U)

(A9.8)

frii > 0, a sufficient condition for the

(A9.9)

where we have used the fact that U = s/(s + f). Provided the relative bargaining power of the worker (13) is not very small, the inequality in (A9.9) is satisfied and the term in square brackets on the right-hand side of (A9.5) is positive. In fact, the sufficient condition is quite

weak. Even for the relatil satisfied if /3 > 1/9. See, a condition.

In section 2.1 we mod labour market. An inat unemployment benefit other than the payroll to

w(1 + tE) —

1 + tE

13Yo0

1 + tE where tE = dtE (1 + tM)- 5

w(

=

[FL -

/30yo [(1 —

dw =

rl [FL — Ktil

I

where it follows from (9...

In section 2.2 we stud all exogenous variables c and (9.45):

[n (w — — rb) —11

— PO 1111

Solving for 6 and dw yleli

	=	1 —
		77 (FL + rb — w

(13 pyo + r7 (i_4.1 dw = ri (FL + rb

234