1. 1 Raiding and Signaling in the Academic Labor Market Timothy Perri

2. 2 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.

3. 3  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.

4. 4 2) Suppose more able individuals are also more capable in research, so publications may signal a prof’s 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.

5. 5  For an individual of type “i”, option value = the prob. of a quit if raided (p i )  the conditional expected job satisfaction of a quitter ( ).  Option value is a social gain from signaling & raiding.

6. 6  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.

7. 7 Michael Spence, Nobel laureate in economics 2001.

8. 8 A MODEL.  U  university.  M  the mkt. (2+  universities that bid in Bertrand fashion for profs).  2 types of profs: (L & H).  productivity = x i, i = L, H; x H > x L.  M will bid x H for one believed to be an H.

9. 9 Wage for those who do not signal  Those who do not signal are paid x L. WHY?  Faculty slots are scarce & M will not bid for those not known to be Hs.  Also, S may be costly to provide.

10. 10 The quit decision  An L who mimics an H would be paid x H 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 @ U.}  Let m  x H – x L.

11. 11  One who signals will quit if S + x H > wage offer from U.  For an L: no counteroffer, so quit if S > -m (p L = prob. quit).  For an H: counteroffer = W C, so quit if S > W C – x H (p H = prob. quit).

12. 12  If W C > x L, p H < p L.  Assume W C > x L.  Now > & p H > p L. for ANY continuous dist. of S.  Option value is higher for an H than for an L.

13. 13 0 S prob. W C -x H -m Fig. 1

14. 14 Assumption One.  /2 < m < .  This ensures p L < 1 & W C > x..  Note. No fundamental results are changed if p L = 1.

15. 15 The optimal counteroffer  Assume U max. profit  .  = (x H -W C )(1-p H ).  W C = x H -  /2.  U does not match outside offer.  Later the model will be amended to allow for the possibility W C > x H.

16. 16 Signaling  q = # of pubs.  y = prof’s effort in publishing.  for an H: q = by.  for an L: q = y.  b > 1.

17. 17 Effort cost for a prof = y 2.  For an L, producing q pubs requires effort = q 2.  For an H, producing q pubs. requires effort = q 2 /b 2.  A higher “b” lowers the MC of signaling.

18. 18 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????

19. 19  I H = net return to signaling for an H.  I L = net return to signaling for an L.  As long as p H < p L, an H has a higher cutoff of S for quitting than an L, & option value is higher for an H than for an L.  I H > I L for W C > x L (m >  /2) even if b = 1.

20. 20 0 S prob. W C -x H -m Fig. 1

21. 21 Proposition Two. Signaling may be efficient, but is inefficient unless b is sufficiently larger than one.  Cost of signaling. Min level of q, q R, for which Ls will not mimic Hs is where I L = x L.

22. 22  If  > m (p L < 1), q R = (m+  )/2  1/2 &  q R /  > 0.  If  < m (p L = 1), q R = m 1/2.

23. 23 Each H spends (q R ) 2 /b 2, but has option value = p H. = 3  /16.  If m   (q R  ), signaling is efficient if b > 2.31.  If m   /2 (q R  ), signaling is efficient if b > 1.73.

24. 24 CAN SIGNALING BE PREEMPTED?  Let U offer W P = x L +  to those who do not signal.  Since U can anticipate what H will do, U only offers W P if it believes W P will deter signaling.

25. 25 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).

26. 26 EXTENSIONS. Commitment not to match outside offers  Suppose U can commit to only pay x L to those raided.  Now an H who signals & is raided is more likely to quit, & option value .

27. 27 0 S prob. W C -x H -m Fig. 1

28. 28 Proposition Four. A policy of not matching outside offers makes signaling less likely to be efficient.  Now signaling is efficient if b > b***. However b*** > b*.  For b  (b*, b***], signaling is not efficient with commitment not to match, but would otherwise be efficient.

29. 29  All that occurs with a policy of not matching counteroffers is p H , so  & an H’s option value .  The social gain from signaling is lower & signaling is less likely to be efficient.

30. 30 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.

31. 31 Costly turnover  If turnover is costly &  < 0 is feasible (due to subsidies): W C = x H + (T-  )/2, where T = turnover cost per prof @ U.  If T > , W C > x H.

32. 32 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.

33. 33  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.