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Raiding and Signaling in the Academic Labor Market

Timothy Perri

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INTRODUCTION.

An inefficiently large level of research may occur even if research has direct social value.

A professor who publishes is more visible & more likely to receive an outside offer (Siow 1995, 1998). A prof’s private gain (a higher wage) may exceed the social gain from research.

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However, a prof may not spend too much time in research.

1) the more visible a prof, the higher the wage the university must pay.

Waldman (1984) found firms promote an inefficiently small # of individuals.

Schools may not reward research enough.

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2) Suppose more able individuals are also more capable in research, so publications may signal a prof’sproductivity & lead to raids.

If a prof. with an outside offer learns job satisfaction, S, at a raider, there is an option value to the prof: if S is high---quit, otherwise stay.

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For an individual of type “i”,option value = the prob. of a quit if raided (pi) the conditional

expected job satisfaction of a quitter ( ).iS

Option value is a social gain from signaling & raiding.

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Ignore any direct social value from research. Thus I understate the social gain from research.

This is similar to ignoring anyproductivity effect of education in the basic signaling model (Spence, 1974), except one social gain remains:option value.

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Michael Spence, Nobel laureate in economics 2001.

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A MODEL.

U university.

M the mkt. (2+ universities that bid in Bertrand fashion for profs).

2 types of profs: (L & H).

productivity = xi, i = L, H; xH > xL.

M will bid xH for one believed to be an H.

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Wage for those who do not signal

Those who do not signal are paid xL.WHY?

Faculty slots are scarce & M will not bid for those not known to be Hs.

Also, S may be costly to provide.

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The quit decision

An L who mimics an H would be paid xH by M.

For signaling to work, we must make sure an L would not mimican H.

Let S ~ uniformly on [-, ]; E(S) = 0. {Satisfaction = 0 @ U.}

Let m xH – xL.

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One who signals will quit if

S + xH > wage offer from U.

For an L: no counteroffer,so quit if S > -m (pL = prob. quit).

For an H: counteroffer = WC,so quit if S > WC – xH (pH = prob. quit).

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If WC > xL, pH < pL.

Assume WC > xL.

Now > &pH > pL .

for ANY continuous dist. of S.

Option value is higher for an H than for an L.

LSHS

HS LS

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0S

prob.

WC -xH-m

Fig. 1

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Assumption One./2 < m < .

This ensures pL < 1 &WC > x..

Note. No fundamental results are changed if pL = 1.

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The optimal counteroffer

Assume U max. profit .

= (xH-WC)(1-pH).

WC = xH - /2.

U does not match outside offer.

Later the model will be amendedto allow for the possibility WC > xH.

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Signaling

q = # of pubs.

y = prof’s effort in publishing.

for an H: q = by.

for an L: q = y.

b > 1.

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Effort cost for a prof = y2.

For an L, producing q pubs requireseffort = q2.

For an H, producing q pubs. requireseffort = q2/b2.

A higher “b” lowers the MCof signaling.

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Proposition One. Ignoring for now the possibility of a higher wage preempting signaling, signaling will always occur, even if b = 1.

Why can signaling occur even if an L can produce pubs. at the same cost as an H????

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IH = net return to signaling for an H.

IL = net return to signaling for an L.

As long as pH < pL, an H has a higher cutoff of S for quitting thanan L, & option value is higher for an H than for an L.

IH > IL for WC > xL (m > /2) even if b = 1.

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0S

prob.

WC -xH-m

Fig. 1

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Proposition Two. Signaling may be efficient, but is inefficient unless b is sufficiently larger than one.

Cost of signaling. Min level of q, qR, for which Ls will not mimic Hsis where IL = xL.

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If > m (pL < 1),

qR = (m+)/21/2 &

qR/ > 0.

If < m (pL = 1),

qR = m1/2.

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Each H spends (qR)2/b2,but has option value =pH . = 3/16.

If m (qR), signaling is efficient if b > 2.31.

If m /2 (qR), signaling is efficient if b > 1.73.

HS

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CAN SIGNALING BE PREEMPTED?

Let U offer WP = xL + to those who do not signal.

Since U can anticipate what H will do, U only offers WP if it believes WP will deter signaling.

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Proposition Three. There are some cases when signaling may (profitably) be preempted, but only when signaling is inefficient.

Efficient signaling occurs if b > b*.

Signaling is preempted if b < b**.

We find b** < b* (with b** < b*if there are any Ls in the population).

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EXTENSIONS.

Commitment not to match outside offers

Suppose U can commit to only pay xL to those raided.

Now an H who signals &is raided is more likely to quit,& option value.

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0S

prob.

WC -xH-m

Fig. 1

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Proposition Four. A policy of not matching outside offers makes signaling less likely to be efficient.

Now signaling is efficient ifb > b***. However b*** > b*.

For b(b*, b***], signaling is not efficient with commitment not to match, but would otherwise be efficient.

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All that occurs with a policy of not matching counteroffers is pH , so & an H’s option value .

The social gain from signaling is lower & signaling is less likely to be efficient.

HS

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Not all who signal are raided

Proposition Five. The condition for signaling to be efficient is independent of the fraction of those who signal who are raided.

Cost & (expected) benefitfrom signaling are reducedby the same %.

Net social gain or lossfrom signaling is lower.

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Costly turnover

If turnover is costly & < 0 is feasible (due to subsidies):

WC = xH + (T-)/2,

where T = turnover cost perprof @ U.

If T > , WC > xH.

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CONCLUSION.

A prof who signals productivity via publishing may receive an outside offer, & learns job satisfaction (S) at a raiding university.

S is a social benefit of signaling, so signaling may be efficient.

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When it is not efficient, signaling may be preempted by a higher wage.

Commitment to not match outside offers reduces the expected gain in job satisfaction from those who quit when raided.

A direct value for research an even larger probabilityresearch would be efficient.