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 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 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 k= Yo b.

q(9 )

(9.40)

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 q(0) r s (9.42)

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 WS1

(b)

V wso ZPi ZP0 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)

'a)

w 231 Chapter 9: Search in the Labour Market

-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:

the use of labour.

) reflect the payment the firm

(9.43)

(9.44)

wage equation (9.44) can be

(9.45)

and (9.45).

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 advanced economies is the persistence of the unemployment rate. How can thp--

persistence be explained in the search-theoretic framework? In a recent cOntrifution, 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 9.42)

-00\-P 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