Raiding and Signaling in the

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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 profs 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 profs productivity 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 ( ).
? 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
any productivity 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 gt 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 mimic an H. ? Let
S uniformly on -?, ? E(S) 0.
Satisfaction 0 _at_ U. ? Let m ? xH xL.
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? One who signals will quit if S xH gt wage
offer from U. ? For an L no counteroffer, so
quit if S gt -m (pL prob. quit). ? For an H
counteroffer WC, so quit if S gt WC xH (pH
prob. quit).
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? If WC gt xL, pH lt pL. ? Assume WC gt xL. ?
Now gt pH gt pL . for
ANY continuous dist. of S. ? Option value is
higher for an H than for an L.
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prob.
Fig. 1
S
-m
0
WC -xH
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Assumption One. ?/2 lt m lt ?. ? This ensures pL lt
1 WC gt 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 amended to allow for the possibility WC gt
xH.
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Signaling ? q of pubs. ? y profs effort
in publishing. ? for an H q by. ?
for an L q y. ? b gt 1.
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Effort cost for a prof y2. ? For an L,
producing q pubs requires effort q2. ? For an
H, producing q pubs. requires effort q2/b2. ?
A higher b lowers the MC of 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 lt pL, an H has a higher cutoff of S for
quitting than an L, option value is higher for
an H than for an L. ? IH gt IL for WC gt xL (m gt
?/2) even if b 1.
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Fig. 1
prob.
S
-m
0
WC -xH
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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 Hs is where IL
xL.
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? If ? gt m (pL lt 1), qR (m?)/2?1/2
?qR/?? gt 0. ? If ? lt 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 gt 2.31. ? If m ? ?/2 (qR?),
signaling is efficient if b gt 1.73.
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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 gt b. ? Signaling is
preempted if b lt b. ? We find b lt b (with
b lt 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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prob.
Fig. 1
S
-m
0
WC -xH
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Proposition Four. A policy of not matching
outside offers makes signaling less likely to be
efficient. ? Now signaling is efficient if b gt
b. However b gt 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 Hs option
value ?. ? The social gain from signaling is
lower signaling is less likely to be efficient.
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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) benefit from
signaling are reduced by the same . ? Net
social gain or loss from signaling is lower.
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Costly turnover ? If turnover is costly ? lt 0
is feasible (due to subsidies) WC xH
(T-?)/2, where T turnover cost per prof _at_
U. ? If T gt ?, WC gt 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 probability research would be efficient.