7/23/2019 Supervision 3 Essay NOTES

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Setting out “Diamond paradox” presented in Diamond (1971):• Consider McCall search model for rms: an! "age o#er a$o%e reser%ation

"age "ould decrease prots "ithout increasing the num$er of emplo!ed"or&ers'

• ence prot maximising to o#er " "r

• *ut if all rms o#er " " r+ then reser%ation "age e,uals unemplo!ment$enets

• -ntuiti%el!+ since rms can ma&e ta&e it or lea%e it "age o#ers+ rms ha%eall the $argaining po"er rms can extract the "hole rent from "or&ers+since la$our mar&et frictions pre%ent $et"een.rm competition(decentralised "age determination)'

• -f "ages pa! " $+ then there is no gain from searching for a job+ and

if there are an! search costs+ unemplo!ed "or&ers ha%e no incenti%e tosearch for a /o$'

•  0hus the la$our mar&et collapses'

• -n realit!+ "e o$ser%e that identical workers earn dierent wages (i'e'

2 3 4'5+ in "age e,uations "ith lots of control %aria$les)'

6etting out of the “Diamond paradox” 0his spar&ed a su$stantial de$ate to nd conditions consistent "ith e,uili$rium"age dispersion'

ne possi$ilit! is to ma&e dierent assumptions a$out the search process'

• 8or example in a “nois! search model”+ the num$er of o#ers a "or&er

recei%es in a period is treated as a random %aria$le+ meaning a rmo#ering a "age to a /o$ applicant cannot $e sure "or&ers dont ha%e a$etter o#er from another rm' 8or example+ *utters (1977)'

• on.se,uential search (*urdett and ;udd+ 19<=) can li&e"ise lead to "agedispersion'

• >llo"ing heterogeneit! across "or&ers other than producti%it!' 8orexample+ assuming some "or&ers ha%e ?ero monetar! search cost "hileothers ha%e a positi%e search cost (Salop and Stiglit?+ 1977)' -f smallproportion of people ha%e ?ero search costs+ the monopson! outcomeo$tains@ if large+ the competiti%e outcome o$tains@ for intermediate %alues+there is "age dispersion in e,uili$rium'

• *ut if the distri$ution of search costs has no mass point at ?ero+ then

Diamond paradox still holds'

Albrecht-Axell model>ssume there are t"o t!pes of "or&ers:

• 8raction A has high %alue of leisure and conse,uentl! high reser%ation

"age'

• 8raction (1 B A) has lo" %alue of leisure (and lo" reser%ation "age)'

• 8irms face trade.o# $et"een o#ering high and lo" "ages'o igh "ages attract more "or&ers than lo" "ages

o rots per "or&er a lo"er at high "age rms+ than at lo" "age

rmso -n e,uili$rium $oth rms can ma&e e,ual prots'

*ut pro$lem "ith the >l$recht.>xell model:

• igh "age rms ha%e no incenti%e to o#er a "age higher than thereser%ation "age of "or&ers "ith a high %alue of leisure'

7/23/2019 Supervision 3 Essay NOTES

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• >n search cost "ill pre%ent the "or&ers "ith the high %alue of leisure from

searching $ecause the expected pa!.o# from search is negati%e for them'

•  0hus+ onl! "or&ers "ith a lo" %alue of leisure "ill participate in the la$our

mar&et'

•  0hen+ "e are $ac& in the Diamond aradox'

Burdett-Mortensen model

•  0he &e! to this is assuming that there is on.the./o$ search+ "hich o#ers amore fundamental resolution of the Diamond paradox in the sense of generating e,uili$rium "age dispersion in a model "here "or&ers are ex 

ante identical'

• r  on emplo!ed /o$ see&ers is simpl! hisEher current "age+ so the

distri$ution of reser%ation "ages across /o$ see&ers is a mixture of thereser%ation "age of the unemplo!ed "ith the distri$ution of reser%ation"ages across emplo!ed searchers'

•  0he num$er of emplo!ed "or&ers "ill therefore increase "ith the "age

o#ered+ such that in e,uili$rium high "age rms "ith lo" prot per "or&er$ut large num$er of emplo!ees ma&e the same prot as lo" "age rmsthat earn a high prot per "or&er $ut ha%e onl! fe" "or&ers'

•  0his reser%ation "age heterogeneit! in turn supports e,uili$rium "age

distri$ution'

Fe! assumptions:

• *urdett and Mortensen assume that "or&ers randoml! search among

emplo!ers and assign each rm e,ual odds of $eing encountered+irrespecti%e of rm si?e' 0his regime is &no"n as random matching ("ithrms)

• Ginear production function

otential pro$lems:

• *urdett and Hish"anath (19<<) point out that random matching "ith rmshas the $i?arre implication that $! spitting itself in t"o+ a rm can increaseits recruitment rate'

  Gess a$stractl!+ Fuhn (2445) lets the reader /udge random matching "ith

rms $ased on the implication that “regardless of its si?e+ e%er! rm . fromthe local $a&er! to Microsoft . recei%es the same a$solute num$er of /o$applications per period'”

https://www.ocf.berkele.edu/!iromem/"e-interpreting#$%Burdett#$%and#$%Mortensen#$%-#$%Aug#$%&%'#$%$%&&.pdf