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← 23. Asymmetric information: silence, signaling and suffering education

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Showing Revision 1 created 07/06/2012 by Amara Bot.

  1. Professor Ben Polak:
    So today we're going to
  2. study asymmetric information.
    It's our last week,
  3. and we're going to focus on
    signaling today.
  4. I'll spell it with one "L" here
    as a concession to the
  5. Americans.
    So we're going to divide this
  6. class into two parts.
    And for the first part we're
  7. going to focus on the case where
    there is some verifiable
  8. information in the problem.
    So we'll see what this means in
  9. a while, but let me just set up
    an example and we'll see where
  10. that takes us.
    So I want to return to a game
  11. we know well by this stage,
    which is the Cournot game.
  12. So there's two firms,
    and they're competing in
  13. Cournot--so they're competing in
    quantities--and we'll call the
  14. firms A and B.
    Suppose that Firm B has
  15. costs--so to be more formal,
    these are constant marginal
  16. costs--equal to cM,
    where M means middle or medium
  17. or something.
    Firm A also has costs but those
  18. costs could come in one of three
    types.
  19. It could be that Firm A has
    high costs, and high costs are
  20. equal to middle costs,
    plus a little bit.
  21. It could be that Firm A also
    has medium costs.
  22. And it could be that Firm A has
    low costs, and the low costs are
  23. just the medium costs minus a
    little bit.
  24. Now, before this competition's
    going to take place,
  25. before they're actually going
    to play the Cournot game,
  26. Firm A has an opportunity.
    Firm A's opportunity is to
  27. reveal its costs to Firm B.
    So to make this more explicit,
  28. initially, Firm B obviously
    knows his own costs and,
  29. since there is only one type,
    Firm A obviously knows those
  30. costs as well.
    So Firm A and Firm B know what
  31. Firm B's costs are.
    But initially,
  32. although Firm A knows her own
    costs, Firm B does not know Firm
  33. A's costs.
    So let's write that up.
  34. So Firm B knows only its costs,
    and Firm A knows both costs.
  35. But the key decision we're
    going to focus on is that Firm A
  36. has an opportunity to reveal its
    true costs to Firm B.
  37. Now, it can do so in a
    verifiable way.
  38. For example,
    it could hire an accountant.
  39. That accountant from a
    reputable outside firm could
  40. come in and do the accounts for
    Firm A and then publish them in
  41. The Wall Street Journal or
    something.
  42. So Firm A can do that,
    and let's assume it's costless
  43. for it to do that.
    So Firm A can costlessly and
  44. verifiably reveal its costs to
    B.
  45. The question is:
    this is going to happen before
  46. they play Cournot.
    The question is:
  47. should Firm A reveal those
    costs or not?
  48. Should Firm A publicize or give
    away its informational
  49. advantage, if you like,
    to Firm B by telling Firm B
  50. what its costs look like.
    So what do people think?
  51. Let me grab the mike and ask
    people a little bit.
  52. Imagine you're the manager of
    Firm A.
  53. Are you going to tell Firm B
    what you're costs are or not?
  54. Wave a hand in the air,
    or should I just cold call
  55. here?
    Let me cold call,
  56. so what's your name sir?
    Student: Hugh.
  57. Professor Ben Polak:
    Hugh, and so suppose you're
  58. the manager of Firm A,
    would you reveal the
  59. information or not?
    Student: I would tell
  60. them only if my costs were
    lower.
  61. Professor Ben Polak:
    All right,
  62. so Hugh says I would reveal the
    information only if my costs
  63. were lower.
    Now why do you want to reveal
  64. the costs if you have lower
    costs?
  65. Student: Because then my
    firm will produce at a lower
  66. cost so Firm B will produce less
    because they know that we'll get
  67. most of the market.
    Professor Ben Polak:
  68. Good.
    It's Hugh, is that right?
  69. Student: Yeah.
    Professor Ben Polak:
  70. So the point that Hugh is
    making is there may be some
  71. advantage in having the other
    side know my costs if my costs
  72. are low,
    since that may induce the other
  73. side to produce less.
    Let's just fill out that
  74. argument by putting in the
    Cournot diagram.
  75. So here's the Cournot diagram.
    Here's the quantity for Firm A.
  76. Here's the quantity for Firm B.
    And here is the best response
  77. or reaction curve for Firm B.
    And in this picture there's
  78. going to be three different
    possible reaction curves for
  79. Firm A, each one corresponding
    to different costs.
  80. So, for example,
    this could be the reaction
  81. curve or the best response for
    Firm A in the case in which it's
  82. medium.
    But if it had lower costs what
  83. would happen to that reaction
    curve?
  84. Would it shift in,
    would it tilt,
  85. what would happen to it?
    Someone shout it out.
  86. It would shift out.
    If it had lower costs then it
  87. would shift out so this would be
    the best response for Firm A in
  88. the low case,
    and conversely,
  89. this would be the best response
    for Firm A in the high case.
  90. So the point that Hugh is
    making--or he should correct me
  91. if this is unfairly paraphrasing
    him--is if I have low costs then
  92. I want the other side to know I
    have low costs because that puts
  93. us into the equilibrium in which
    this is my best response curve
  94. and this is the other side's
    best response curve,
  95. and Firm B ends up producing
    less and ends up lowering its
  96. production.
    Is that right?
  97. So the key idea here is that
    this is a game--an idea we've
  98. had often--this is a game of
    strategic substitutes.
  99. So if I have low costs,
    I want the other side to know
  100. that I have low costs because it
    will cut back its production
  101. which helps me.
    On the other hand,
  102. if I have high costs,
    then I kind of like to remain
  103. hidden.
    I really don't want the other
  104. side to know that I have high
    costs, because if I have high
  105. costs,
    the other firm's actually going
  106. to increase their production and
    that's going to hurt me.
  107. But notice I've twisted the
    question a little bit.
  108. The question I actually asked
    you was: would you reveal the
  109. information about your costs.
    And I flipped that around to a
  110. slightly easier question which
    is: what would I like the other
  111. side to know?
    Now what would I like the other
  112. side to know?
    I'd like the other side to know
  113. if I have low costs.
    I'd like the other side not to
  114. know if I have high costs,
    but that's not quite the
  115. question we asked.
    The question we asked was would
  116. you, given whatever your costs
    are, reveal that information to
  117. the other side?
    I think what Hugh has told us
  118. is--so to say exactly what he
    said--Hugh said if I had low
  119. costs I'm going to reveal it to
    the other side.
  120. Is that right?
    So, so far what do we know?
  121. So far we know that if I have
    low costs then I will reveal it.
  122. So far we know that.
    But what if I don't have low
  123. costs?
    What if I have middling costs
  124. or high costs?
    Well let's take these in turn,
  125. what about middling costs?
    What should I do if I have
  126. middle level costs?
    So somebody's got their hand
  127. up, let me go and take advantage
    of that.
  128. What's your name?
    Student: Alec.
  129. Professor Ben Polak:
    Shout it out so people can
  130. hear.
    Student: I think you
  131. should still reveal because they
    know if you had low costs you
  132. would reveal,
    and so if you had middle costs
  133. and you didn't reveal then they
    could think you either had
  134. middle costs or high costs and
    it's better for you to just
  135. reveal that you had middle
    costs.
  136. Professor Ben Polak:
    Good, did people hear that?
  137. Let me just repeat that.
    So you might think that if I
  138. have middle costs,
    you might think that I could
  139. reveal or not reveal,
    depending on what the other
  140. side thought.
    However, what Alec's arguing
  141. correctly, is if I don't reveal
    that I have middle costs,
  142. the other side,
    Firm B, knows that my costs are
  143. not low.
    So the only way they could
  144. mistake me is they could think
    I'm a high cost firm.
  145. They know I'm not a low cost
    firm.
  146. How do they know I'm not a low
    cost firm?
  147. Because the low cost firm would
    have revealed,
  148. that was Hugh's argument.
    So since low costs are firms
  149. are revealing,
    if I'm the middle cost firm,
  150. if I don't reveal no one's in
    any doubt I'm not a low cost
  151. firm.
    So all I could be is a middle
  152. cost firm or a high cost firm.
    All I could have is this
  153. reaction curve,
    which is the one I actually
  154. have, or this reaction curve.
    So if I don't reveal then the
  155. other side might think that I
    have high costs in which case
  156. they're actually going to
    increase their production and
  157. hurt me.
    So since the low cost firm is
  158. going to reveal,
    the medium cost wants to reveal
  159. to ensure that no one thinks
    it's high costs.
  160. So low cost reveals and
    therefore cM reveals as well to
  161. prevent being mistaken for a
    high cost firm.
  162. Now there was a question,
    let me come down and collect
  163. the question.
    Yeah?
  164. Student: I was just
    going to ask what if you have,
  165. A reveals to both to the low
    and middle class,
  166. then they're obviously going to
    know that he's a high cost,
  167. which means that the concealing
    doesn't do any good.
  168. Professor Ben Polak:
    Exactly,
  169. and your name is?
    Student: Bethany.
  170. Professor Ben Polak:
    So Bethany's pointing out
  171. that once we know the low cost
    type's going to reveal,
  172. we know that the middle cost
    type is also going to reveal so
  173. as not to get mistaken for being
    high cost,
  174. which means,
    if you're running a high cost
  175. firm, it really doesn't matter
    whether you reveal or not,
  176. because you're going to be
    revealed by the fact that you
  177. didn't reveal.
    Is that right?
  178. Had you been low cost you would
    have revealed.
  179. Had you been middle cost you
    would have revealed.
  180. And therefore,
    whether you choose to reveal or
  181. not, everyone knows that you're
    high cost.
  182. So therefore, cH is revealed.
    Everyone see that?
  183. Okay, now notice that in this
    argument we've just constructed
  184. there were three types of firms
    - high, middle,
  185. low.
    But I could have constructed
  186. exactly the same argument,
    albeit somewhat more tediously,
  187. with a 100 types of firms.
    Firms that had absolutely the
  188. lowest costs,
    firms that had the 99th highest
  189. costs, 98th highest costs,
    97th highest costs and so on.
  190. And this argument would have
    been exactly the same.
  191. At each stage the firm that's
    left in the analysis who has the
  192. lowest cost, will want to reveal
    to distinguish itself from those
  193. who haven't revealed "yet,"
    and therefore we'll get
  194. unraveling.
    We'll get information to be
  195. revealed, and notice
    interestingly,
  196. we'll get information to be
    revealed beyond the medium.
  197. So the 51st highest cost firm
    will reveal, therefore the 50th
  198. highest cost firm will reveal,
    therefore the 49th and so on.
  199. In fact, the only firm who
    won't explicitly,
  200. actively reveal themselves is
    the firm who has absolutely the
  201. highest cost.
    And as Bethany points out,
  202. they're going to be revealed
    anyway.
  203. So this is an idea--this idea
    is called "informational
  204. unraveling."
    And again, in keeping for my
  205. American audience,
    I'm going to put one "l" in
  206. unraveling.
    Is that right,
  207. there's one "l" in America
    right?
  208. Someone should just check that
    on Google or something,
  209. I think that's correct.
    What's the lesson here?
  210. So one lesson is that this
    happens.
  211. We'll come back to that,
    but another lesson,
  212. perhaps a more important lesson
    is: often the lack of
  213. information,
    the lack of somebody signaling
  214. to you, the lack of somebody
    trying to tell you something,
  215. conveys information.
    This was the point that Bethany
  216. was making.
    The fact that the high cost
  217. firm doesn't in fact go out and
    reveal information to you,
  218. reveals something about what it
    knows.
  219. So Hugh's initial comment was
    correct.
  220. If I was the high cost firm I'd
    like to remain hidden but I
  221. can't remain hidden.
    From your point of the view as
  222. the receiver of the information,
    there is information in the
  223. lack of the attempt to convey
    information.
  224. So lesson: the lack of a
    signal, the lack of an attempt
  225. of a firm to signal you some
    information, the lack of a
  226. signal can be informative.
  227. So this is an often forgotten
    lesson.
  228. It's a very simple idea,
    but there's a natural tendency
  229. when you're dealing with
    information to focus on the
  230. evidence that is there,
    rather than the evidence that's
  231. not there.
    There's an expression that goes
  232. with this.
    The expression is "silence
  233. speaks volumes."
    You've all heard that
  234. expression, silence speaks
    volumes.
  235. Let me give you one other
    example.
  236. So there's a Sherlock Holmes
    story--by the way,
  237. do you all know who Sherlock
    Holmes is?
  238. Good, so there's a Sherlock
    Holmes story in which Sherlock
  239. Holmes solves the murder.
    He figures out who did the
  240. murder.
    And Dr.
  241. Watson who's his sidekick is
    trying to figure out how Holmes
  242. could possibly have solved the
    murder.
  243. He says how did you solve the
    murder?
  244. Holmes says,
    it's because of the barking
  245. dog.
    And Watson says,
  246. what do you mean it's because
    of the barking dog?
  247. The dog didn't bark.
    Holmes says,
  248. that's exactly the point,
    the fact that the dog didn't
  249. bark, didn't make any sound
    tells us who must have committed
  250. the murder.
    It's very easy to fall into the
  251. trap of being Watson and to
    ignore the thing that didn't
  252. happen and focus on the things
    that did happen.
  253. Here, it's easy to forget that
    actually the high cost firm is
  254. revealed by doing nothing.
    So this is the idea that
  255. silence can speak volumes.
  256. Every year I go back and try
    and figure out what that
  257. quotation is from and I can
    never find it,
  258. so anybody who finds it I will
    give them a prize of some sort.
  259. Originally I thought it must be
    Shakespeare but it doesn't
  260. appear to be.
    So this is a little example
  261. involving Cournot,
    but I want to try and convince
  262. you that this example is more
    general.
  263. Let's pick up the question;
    sorry go ahead.
  264. Student: Isn't it
    possible that there's an
  265. equilibrium where the costs of
    remaining hidden as a middle
  266. cost firm outweighs the benefit.
    Professor Ben Polak:
  267. Not if we take the model
    literally.
  268. Not if we take the model in
    Cournot literally because,
  269. suppose Firm B doesn't know
    whether you're high or middle,
  270. then he's going to think your
    costs are somewhere in between
  271. and relative to your costs being
    middle he's going to produce
  272. more,
    that's the point here.
  273. Now it's true that in a richer
    model there may be some other
  274. advantage in having information
    hidden,
  275. but that would have already
    applied to the low cost firm.
  276. Let me give you some other
    examples and we'll see this in
  277. other contexts,
    and see that it might actually
  278. ring true.
    So one other example involves
  279. resumes.
    So this example requires some
  280. explanation for the
    non-Americans.
  281. How many of you are
    non-Americans here?
  282. So one thing you need to know
    as non-Americans is the way in
  283. which people write resumes in
    America.
  284. Everyone know what a resume is?
    A CV, a resume, right?
  285. So when you look at a typical
    resume from an American
  286. student--if you're not American,
    for those of you who aren't
  287. American--how should I put this
    politely?
  288. It has a tendency to make you
    want to vomit.
  289. So that's basically the polite
    version of what I was going to
  290. say about that.
    So why does it have a tendency
  291. to make you want to vomit?
    Because Americans have a
  292. tendency to put down everything
    on their resume.
  293. So if they were captain of the
    chess team in third grade,
  294. and there they are now,
    they're forty and applying for
  295. a job, it still says I was
    captain of the chess team in
  296. third grade.
    And this is particularly true
  297. when it comes to public service,
    when it comes to sort of moral
  298. acts.
    So most people in Europe will
  299. be a bit embarrassed about
    writing their good deeds on
  300. their resumes,
    but Americans,
  301. there's a little spot on their
    resume which is about their good
  302. deeds or their public service
    and they put everything.
  303. When I was eight I helped a
    little old lady across the road
  304. with her shopping basket,
    and there it is on their
  305. resume.
    So why is it that Americans
  306. reveal so much information on
    their resume?
  307. Well think about informational
    unraveling, right?
  308. So resumes are verifiable
    information, it's hugely costly
  309. to be caught cheating about your
    resume.
  310. So basically you're not going
    to lie on your resume.
  311. And imagine if I'm admitting
    students, let's say to law
  312. school, to Yale Law School,
    and I'm reading the student's
  313. resume and in the spot where I'm
    expecting to see public service
  314. there's nothing written there.
    What do I assume about that
  315. student?
  316. I assume that the person did
    nothing.
  317. This person has been a self
    serving "evil git" their entire
  318. life, has never even helped a
    little old lady across the road.
  319. So people put down everything,
    even these minimal things,
  320. even these pretty shockingly
    tiny acts of charity to reveal
  321. themselves from those people who
    did absolutely nothing,
  322. that are basically the devil
    incarnate.
  323. So this is about resumes,
    let's just take this a bit
  324. further.
    How many of you are from Los
  325. Angeles?
    So in Los Angeles I'm led to
  326. believe, I'm told--you can
    confirm this or not--there are
  327. lots and lots of restaurants.
    This is true, right?
  328. Lots of restaurants and some of
    these restaurants are good and
  329. some of them are bad.
    And, more to the point for
  330. today's example,
    some of these restaurants are
  331. clean and some of them are not
    so clean.
  332. Is this true?
    So it turns out that until the
  333. late nineties,
    the Los Angeles Municipality
  334. rules,
    local law, said that every
  335. restaurant in Los Angeles
    County, I think it was,
  336. had to get visited by the
    health inspector.
  337. And the health inspector would
    come around, I think it was
  338. annually, and go to these
    restaurants and they would issue
  339. a certificate,
    and this was a health
  340. certificate and written on it
    large letters--I think they were
  341. red letters--was either A,
    or B, or C.
  342. There may even have been A- as
    well, but for the purpose of the
  343. story let's just call it A,
    B, and C.
  344. Now that was all the law said.
    The law did not say that you
  345. had to display your health
    certificate anywhere.
  346. So what does this model tell us
    to expect about Los Angeles in
  347. the mid-nineties?
    Well if you're running a little
  348. restaurant in Los Angeles and
    you get an A health certificate
  349. from the health inspector,
    what are going to do with that
  350. A certificate?
    You're going to display it
  351. prominently in the window,
    right?
  352. A health certificate.
    So if you're running a slightly
  353. less healthy restaurant,
    maybe this is Ale's pizza chain
  354. again,
    and you still get a B
  355. certificate from the Los Angeles
    Health Inspector,
  356. are you going to display it or
    not?
  357. You're going to display it
    right, because why not?
  358. We know the A's are going to
    display.
  359. These certificates are being
    given to everybody,
  360. so you're going to display even
    a B certificate.
  361. Now, I'm told,
    from people who lived in Los
  362. Angeles at the time,
    that you could go around to the
  363. greasiest spoon in Los Angeles
    and look through these grease
  364. smeared windows with the
    cockroaches running all up and
  365. down them,
    and if you looked carefully
  366. behind the cockroaches and the
    grease you'd see a certificate
  367. displayed that said C on it.
    Presumably there was a D grade
  368. as well: even the C's were
    displaying.
  369. So that's pretty dramatic
    information unraveling.
  370. Now, I'm exaggerating slightly
    to make a separate point.
  371. It turns out that in certain
    areas of Los Angeles you'd
  372. expect to see these health
    certificates displayed,
  373. even the C's,
    and in other areas you wouldn't
  374. expect to the see the C's
    displayed.
  375. Which areas would you expect
    not to see people bothering
  376. displaying their C or B-
    certificate?
  377. Any guesses?
    The tourist areas.
  378. Because for this story about
    information unraveling to work,
  379. the people who are the
    receivers of the information
  380. need to know that you got the
    certificates.
  381. So if you're a tourist in Los
    Angeles, you don't know this
  382. system is in place,
    and therefore if you're a C
  383. certificate right next to
    Disneyland or something,
  384. whatever it is,
    you can still make some
  385. tourists ill,
    without having to tell them
  386. you're about to do so.
    So that's a second example,
  387. let me give a third example,
    a little bit closer to home.
  388. At the last curriculum reform
    at Yale, there was a big debate
  389. about what to do with Credit
    D/Fail.
  390. And one of the proposals for
    Credit D/Fail was to allow
  391. students to take courses Credit
    D/Fail,
  392. but if they ended up getting an
    A or a B, they could display the
  393. A or the B on their resume.
    So they take a Credit D/Fail,
  394. but if they got a grade like an
    A or B, or an A- or whatever,
  395. then they could opt in and have
    it put on their resume.
  396. What's wrong with that?
    This is a serious proposal.
  397. I was on this committee.
    This was seriously made.
  398. I didn't make the proposal but
    this was made.
  399. What's wrong with this proposal?
    What's wrong with the proposal?
  400. What would displaying Credit on
    your transcript come to mean?
  401. It could come to mean C right,
    it would come to mean C,
  402. because all of the A's and the
    B's would unravel that
  403. information.
    So if information is verifiable
  404. and can be freely transmitted,
    it has a way of coming out.
  405. Let me give you one slightly
    more serious example.
  406. As you all know,
    if you're arrested in the
  407. U.S.--you should know this--you
    have the right to remain silent.
  408. I'm not saying you're all about
    to get arrested,
  409. but were you to be arrested,
    you have the right to remain
  410. silent.
    That right was true in Britain
  411. as well until recently,
    when the government,
  412. which isn't so big on civil
    liberties, changed the rule
  413. slightly.
    So now you have the right to
  414. remain silent in Britain,
    but the Court has the right to
  415. take into account as evidence if
    you remain silent.
  416. So what's that done to the
    right to remain silent.
  417. I'll leave it to you to figure
    out what that's done to the
  418. right to remain silent.
    So this idea that information
  419. unravels depended on certain key
    parts and the most important
  420. part was that the information
    was verifiable.
  421. It mattered that the
    information was verifiable.
  422. And to get full unraveling all
    the way down,
  423. in this case to the highest
    cost firm,
  424. you needed the people on the
    receiving side of the
  425. information to actually know
    that that information was there.
  426. So to get the full unraveling
    you really need something like
  427. common knowledge of the presence
    of the information.
  428. But often, the information that
    you have--you have information,
  429. you want to reveal that
    information--but unfortunately
  430. it's not so easily verifiable.
    So what we're going to focus on
  431. for the rest of today is
    information that is not
  432. verifiable.
  433. Let's start with an example
    that's pretty close to home.
  434. A lot of you have been doing
    job interviews recently.
  435. How many of you have been going
    out either doing interviews for
  436. internships or jobs?
    I know a lot of you are missing
  437. class so I'm assuming charitably
    that's what you were doing.
  438. So when you go to these job
    interviews you could imagine
  439. that you're turning up for some
    job interview,
  440. let's say it's at Boring Bank
    of Boston.
  441. And you turn up at this
    interview for Boring Bank of
  442. Boston, and one of the things
    that Boring Bank of Boston wants
  443. to know is are you interested in
    working for Boring Bank of
  444. Boston.
    That's a plus for them.
  445. What they tend to do is they
    ask you.
  446. More or less they say,
    are you interested in working
  447. for Boring Bank?
    Now by the way,
  448. if you are asked the question,
    and you're interviewing for
  449. Boring Bank,
    and you're asked the question
  450. by them are you interested in
    working for Boring Bank,
  451. what answer should you give?
    You should answer yes.
  452. How much information is there
    in the fact that you answer yes?
  453. None at all,
    right, because clearly you want
  454. the option of working for this
    bank, so you're going to answer
  455. yes anyway.
    Now you may think this is just
  456. a fictional example,
    it's not.
  457. I talked to some recruiters
    from a bank in Boston that we'll
  458. refer to as Boring Bank of
    Boston not so long ago,
  459. and I asked them about hiring
    Yale undergraduates and what
  460. Yale undergraduates should do to
    impress them.
  461. And the recruiter,
    who is a Yale graduate himself,
  462. said to me that frankly Yale
    undergraduates do less well in
  463. these interviews than Harvard
    undergraduates.
  464. I said, shattered and
    disappointed--I said why,
  465. and he said,
    well when we asked them if
  466. they're interested in working
    for Boring Bank of Boston the
  467. Yale guys say things like,
    well I don't know it sounds
  468. kind of boring.
    The Harvard guys,
  469. what do they do?
    They show up with The Wall
  470. Street Journal folded over
    conveniently on the page about
  471. Boring Bank of Boston,
    and sometimes they're wearing a
  472. silly hat with I'm boring on it.
    So I tried to persuade this guy
  473. that despite this fact,
    there's really no information
  474. in the fact that the Harvard
    guys are doing this,
  475. and in fact you should hire the
    Yale people because at least
  476. they were honest,
    and, hey, that might make the
  477. bank less boring in the future.
    This didn't work,
  478. so I need to persuade you guys
    to actually cough up and be
  479. dishonest here.
    There's a lesson here.
  480. So one lesson is,
    if you're asked by an
  481. interviewer for a summer
    internship or for a job later,
  482. if you want to work for them,
    the answer is yes.
  483. It's one of the few questions
    for which the answer is not
  484. backward induction:
    it's just yes.
  485. There's a secondary lesson
    here, which is,
  486. if an interviewer for a bank is
    asking you in the interview if
  487. you'd like to work for them,
    you probably will answer yes,
  488. but you probably want to work
    somewhere else.
  489. If they're dumb enough to ask
    you that question you probably
  490. want to work for someone else.
    But this is a real problem.
  491. The problem is here you are.
    You have some information you'd
  492. like to convey.
    Maybe you really are boring.
  493. Maybe you really do want to
    work for this bank.
  494. You want to convey this
    information, but it's hard for
  495. you to persuade the employer
    that this it is true because
  496. anybody can say they want to
    work for the bank.
  497. More generally in life,
    this isn't only about whether
  498. you want to work for a
    particular bank or whatever it
  499. happens to be,
    it's also about whether you are
  500. a good worker or not.
    So let's try and think about
  501. this in the context of not only
    workers being boring or not,
  502. but workers being good or not.
    So we're going to look at a
  503. costly signaling model.
    It's going to turn out,
  504. this model's going to be about
    costly signaling,
  505. and just for the purpose of the
    model we're going to assume that
  506. there are two kinds of workers
    in America.
  507. There are good workers,
    we'll call them G,
  508. and there are bad workers and
    we'll call them B.
  509. We'll assume that the
    productivity of a good worker,
  510. if you work for this firm,
    is going to be 50 and we can
  511. assume this is $50,000 or
    whatever but let's just forget
  512. units for now and just call it
    50.
  513. A bad worker,
    their productivity is only 30.
  514. So clearly, all other things
    being equal, the employer would
  515. rather employ a good worker than
    a bad worker.
  516. All other things being equal is
    important because then we have
  517. to pay the good worker more.
    Let's assume this is the U.S.
  518. economy, so roughly 10% of the
    economy are good workers and 90%
  519. are bad workers,
    something like that,
  520. and these are the proportions
    in the U.S.
  521. Let's also assume that firms
    are competitive.
  522. So firms are flooding into the
    Yale Careers Office,
  523. or the Yale Careers Fair,
    and they're just desperately
  524. trying to hire these workers.
    There's competitive hiring
  525. going on.
    So firms compete for workers.
  526. So they're going to pay 50 to a
    worker they identify as good.
  527. They pay 50 to a worker,
    they the firms identify as
  528. good.
    And they're going to pay 30 to
  529. workers they identify as bad.
    If you're bothered by this
  530. being exact, think of it as 50
    minus a penny,
  531. and 30 minus a penny.
    It's not going to make any
  532. difference to the analysis.
    So if they can't identify a
  533. worker, they think the worker's
    just the average worker,
  534. how much will the competitive
    wage be?
  535. What will be the competitive
    wage of the average worker in
  536. this economy?
    It's not a hard math question.
  537. Everyone's scratching their
    head down here.
  538. So this is 50 x 10% and 30 x
    90%, which averages out as?
  539. 32% all right.
    So they'll pay the average
  540. which is 32 to a worker they
    cannot identify.
  541. Now, clearly in this model,
    much like in the high cost
  542. firms we started with,
    the good workers would like to
  543. be identified because they get
    paid more.
  544. The bad workers do not want to
    be identified,
  545. they'd rather remain hidden.
    The problem here,
  546. however, is there typically
    isn't a verifiable piece of
  547. information.
    It's hard to verifiably
  548. communicate to the other side
    that you're a good worker.
  549. So you guys are all good
    workers right.
  550. You wouldn't be here otherwise,
    we hope.
  551. So you show up to this firm,
    this firm is looking for good
  552. workers, and you could tell the
    firm: "I'm a good worker."
  553. In fact I'm betting most of you
    have tried doing that in your
  554. job interviews:
    "I'm a good worker."
  555. You could even do this in a
    costly manner.
  556. You could humiliate yourself by
    jumping up on the table and
  557. dancing on one leg while singing
    some song about how you're a
  558. good worker,
    which would be humiliating but
  559. it wouldn't in fact communicate
    to the firm that you're a good
  560. worker.
    Why is it that you're dancing
  561. this beautiful jig on the table
    of the interview room,
  562. singing this beautiful song
    about how you're a good worker,
  563. why doesn't that convince the
    firm that you're a good worker?
  564. Who's been in job interviews
    recently?
  565. Has anyone tried this?
    Why is that not a successful
  566. strategy?
    Steven, is that right?
  567. Student: Yes.
    A bad worker could do that too.
  568. Professor Ben Polak:
    A bad worker could do that
  569. too.
    So it's true that it's costly
  570. and humiliating to dance up on
    the table on one leg and sing
  571. you're a good worker,
    but it's no more costly and
  572. humiliating for you than it is
    for a bad worker.
  573. So if that worked,
    a bad worker would do it too.
  574. So merely a song and dance
    isn't going to work.
  575. It's going to be hard to signal
    to the outside world that you're
  576. a good worker.
    That's going to be our starting
  577. point.
  578. So we need a way for good
    workers to distinguish
  579. themselves from bad workers.
    We need a way for them to
  580. signal, and what's key about
    that signal is it has to be a
  581. signal that they can make and a
    bad worker cannot make,
  582. or alternatively,
    a signal that they will want to
  583. make but a bad worker will not
    want to make.
  584. So dancing on the table doesn't
    do it, and the reason it doesn't
  585. do it is bad workers and good
    workers are symmetric with
  586. respect to the dishonor of
    dancing on the table.
  587. So we need a way for good
    workers, you guys,
  588. to distinguish yourself from
    bad workers, us guys.
  589. How in the American economy,
    what's the main way in the
  590. American economy in which good
    workers signal the fact that
  591. they're good,
    that they manage to distinguish
  592. themselves.
    What's the main signal used in
  593. the U.S.
    economy?
  594. Somebody?
    Yes, education.
  595. So the main signal in the U.S.,
    not the only one by any means,
  596. but the main signal is
    education.
  597. What's going to distinguish the
    good workers from the bad
  598. workers is the good workers are
    going to have degrees,
  599. more degrees,
    better degrees,
  600. more degrees,
    whatever.
  601. So what we're going to look at
    today is a model some of you
  602. have seen before but we'll do it
    in a bit more detail perhaps.
  603. It's a model due to a guy
    called Spence,
  604. Mike Spence,
    who actually won the Nobel
  605. Prize in large part for this
    model.
  606. The reason we know he won the
    Nobel Prize in large part for
  607. this model is he didn't write
    practically anything else,
  608. so it must have been for this
    model.
  609. So what we're going to do is
    we're going to imagine that the
  610. degree, the education that these
    people are going to get,
  611. that's going to distinguish
    themselves and show that they're
  612. good workers to the
    employers--let's assume that the
  613. employers once again are banks
    or whatever--we're going to
  614. assume that the extra piece of
    education they're going to get
  615. is an MBA.
    Some of you out there are
  616. getting an MBA.
    Where's my MBA? There he is.
  617. There's my MBA student up there.
    So the good workers are going
  618. to get an MBA,
    and the way this is going to
  619. work, it's going to work on the
    costs of getting an MBA.
  620. So to get to this to be a
    successful signal,
  621. to make this signal different
    from merely dancing on the
  622. table,
    it's either got to be the case
  623. that bad workers cannot get an
    MBA or it's got to be the case
  624. that it's so costly for bad
    workers to get an MBA that they
  625. won't bother.
    So we're going to make the
  626. difference in costs.
    So we're going to suppose that
  627. the cost per year of getting an
    MBA, of being in business
  628. school, MBA education,
    is 5 units if you're a good
  629. worker.
    We're going to assume that the
  630. cost per year of going to SOM
    and getting an MBA is a little
  631. bit over 10, so 10 and a penny
    if you're a bad worker.
  632. So notice I've assumed in this
    model that it's more costly per
  633. year to get an MBA at Yale say,
    if you're a bad worker than a
  634. good worker.
    Now, what are those costs?
  635. What are the costs of getting
    an MBA?
  636. What's causing that cost
    difference?
  637. Well let's be clear what it
    isn't.
  638. It can't be the fees.
    The fees are a large part of
  639. the costs.
    What are the fees of getting an
  640. MBA at Yale this year?
    Way too much right.
  641. So the costs per year in terms
    of fees are enormous,
  642. but the fees themselves are not
    going to do a good job of
  643. distinguishing between good and
    bad workers.
  644. Why?
    Because they're the same for
  645. both parties.
    We want something which is
  646. differently costly,
    so this is not the fees.
  647. It can't be the fees.
    They're the same for both
  648. parties.
    What other costs are there to
  649. getting an education?
  650. There's opportunity costs right.
    All of you are economists--or
  651. half of you are economics
    majors--so the first thing that
  652. should spring to mind is
    opportunity costs.
  653. But actually opportunity costs
    don't help me here much because
  654. if anything you'd think that the
    opportunity costs of going and
  655. getting an MBA at Yale are
    higher if you're a good worker
  656. than if you're a bad worker.
    After all, if you're a good
  657. worker you could stay home,
    not get an MBA,
  658. farm your parent's garden,
    and, since you're such a good
  659. worker, you'd have a high yield
    in carrots or whatever.
  660. Whereas, the bad workers will
    not produce anything,
  661. right?
    So this is not really about
  662. opportunity costs,
    in fact, we'll assume that
  663. they're zero.
  664. We'll assume there are no
    opportunity costs.
  665. So what is it that's driving
    this cost difference between the
  666. good worker at SOM and the bad
    worker at SOM?
  667. Was that a potential answer out
    there?
  668. Student: Is it the
    present value of future wages
  669. for a good worker?
    Professor Ben Polak:
  670. Okay, so there we're thinking
    about the future.
  671. No, let's just focus on the
    cost side.
  672. You're right there's going to
    be different things going on in
  673. the future, but let's focus on
    the cost side.
  674. I had you before so let's have
    this guy.
  675. Student: Mental effort.
    Professor Ben Polak:
  676. Mental effort,
    right.
  677. So where's my MBA student up
    there.
  678. Here he is--where is he,
    up there.
  679. It's pain and suffering,
    is that right?
  680. I can't see him yet.
    He's nodding, good.
  681. It's having--when you go to the
    MBA class--of thinking my God,
  682. thank goodness I escaped being
    an undergraduate,
  683. and you go back to the MBA
    class and I'm there
  684. again.
    I'm assigning the same horrible
  685. problem sets and you still can't
    read my handwriting and you've
  686. still got to deal with my
    accent, right?
  687. Good workers find it easier to
    read my handwriting and deal
  688. with my accent,
    right?
  689. So what it is?
    It's the mental effort.
  690. It's the pain and suffering.
    It's the pain of the work.
  691. The only thing that
    distinguishes the costs of good
  692. workers from bad workers in
    education is it's so painful to
  693. do the work.
    If we went to a party school,
  694. this wouldn't work.
    That's why we can't just have
  695. party schools.
    We actually have to put you
  696. through some pain in the
    classroom.
  697. I'm looking for some
    confirmation from up there.
  698. So the pain of the work is what
    distinguishes these things.
  699. Now I claim that we can have an
    equilibrium in this society in
  700. which there are good and bad
    workers;
  701. in which good workers cost per
    year is less than bad workers
  702. cost per year of getting,
    in this case,
  703. an MBA--we could do the same
    for undergraduate education but
  704. let's focus on the MBA for now.
    I claim there's an equilibrium
  705. in this society,
    there could be an equilibrium
  706. in which getting an MBA takes
    three years.
  707. So I claim there is an
    equilibrium here in which what
  708. happens?
    In which there are three year
  709. degrees, degrees take three
    years--a three year MBA sounds a
  710. bit frightening but never
    mind--in which the good workers
  711. all get MBA's and the bad
    workers do not.
  712. But to tell you this is an
    equilibrium I need to do a
  713. little bit more,
    so let me tell you one other
  714. thing.
    So I claim there's an
  715. equilibrium in which the degrees
    take three years,
  716. all the good workers get MBA's,
    all the bad workers do not get
  717. MBA's, and what?
    The employers identify MBA's as
  718. good workers.
    To make this work it has to
  719. convince the employers.
    So to make it work I need:
  720. and the employers identify MBA
    equals good, and not-MBA equals
  721. bad.
    So that's what I claim is an
  722. equilibrium here and what I want
    to do is I want us to show that
  723. this actually is an equilibrium.
  724. Now then, this is a slightly
    different kind of equilibrium to
  725. anything we've seen in the class
    so far,
  726. so I'm going to be a little
    slow and nerdy about what we
  727. need to check to check that this
    indeed is an equilibrium.
  728. So I'm going to leave some
    space on the board and you
  729. should leave some space too.
    So my claim is this is an
  730. equilibrium.
    And we're doing guess and check.
  731. I did the guess for you and
    we'll do the check together.
  732. To check, I claim,
    I need to check two things.
  733. One, I need to check that no
    type will deviate.
  734. So what do I mean by a type?
    I mean types of worker.
  735. Neither the good types of
    workers would want to deviate
  736. nor the bad types of worker
    would want to deviate.
  737. So this isn't new.
    When we've checked equilibrium
  738. we've always checked that people
    don't want to deviate.
  739. The only slight difference here
    is instead of checking that
  740. people won't want to
    deviate I'm checking that
  741. types of people won't
    want to deviate,
  742. but basically the idea is the
    same.
  743. Is that right?
    The idea's the same,
  744. so this is not really new.
    The new thing is I also need to
  745. check--actually I'll give myself
    a bit more room here--I also
  746. need to check that the
    employer's beliefs are
  747. consistent with the equilibrium
    behavior.
  748. So let's just stop and pause at
    that a second.
  749. We've never written down a
    condition like this for
  750. equilibrium, but here I have to.
    Here there was asymmetric
  751. information in the model.
    And, in this equilibrium,
  752. one important party to the
    equilibrium, namely the guys who
  753. are going to employ you,
    that's pretty important right?
  754. All they really have to do in
    this model, of any importance,
  755. is form an inference based on
    your actions.
  756. They observe whether you get an
    education or not and they
  757. conclude whether or not you're a
    good or bad worker.
  758. So we're going to write down as
    a condition of this being an
  759. equilibrium that those
    inferences "make sense."
  760. By make sense I mean that
    they're consistent with what
  761. actually is happening in
    equilibrium.
  762. So before we get too nerdy
    about that let's just think why
  763. that's a sensible thing to
    require.
  764. Suppose, in fact,
    suppose the world was like
  765. this.
    All good workers got MBA's,
  766. all bad workers did not get
    MBA's, and employers thought
  767. that the people who got MBA's
    were half good and half bad.
  768. That just doesn't sound right,
    right?
  769. If in fact it's the case,
    that it's the good workers who
  770. are getting MBA's and the bad
    workers who are not,
  771. then the only belief that the
    employers can have that's
  772. consistent is the MBA's are in
    fact the good workers and the
  773. non-MBA's are the bad workers,
    is that right?
  774. So I'm not making any deep
    point here, I'm just pointing
  775. out that we need to make sure
    that the beliefs that people
  776. hold in this equilibrium are
    consistent with what's actually
  777. going on in the equilibrium.
    But having said that,
  778. there's no mystery here,
    everything's fine.
  779. In this particular claim of an
    equilibrium, good workers are
  780. the ones who got the MBA's;
    bad workers are the ones who
  781. didn't get the MBA's;
    and the employers,
  782. when they see an MBA,
    indeed think they're good;
  783. and, when they see a non-MBA,
    they indeed think they're bad.
  784. So these beliefs are in fact
    consistent with behavior,
  785. so we're okay.
    Okay, so I've had to check that
  786. but it wasn't a big deal.
    Everyone okay about why I'm
  787. checking it?
    I don't want people to hold
  788. silly beliefs at equilibrium,
    that's basically what I'm
  789. saying.
    All right, now let's go back
  790. and check the sort of bread and
    butter thing.
  791. The bread and butter thing is
    we need to check that no type of
  792. worker is going to want to
    deviate in this equilibrium.
  793. So there's two types of worker.
    There's good workers--and good
  794. workers, what are they doing in
    equilibrium?
  795. What are the good workers doing
    in equilibrium?
  796. They're getting an MBA.
    So the good workers,
  797. they become MBA's,
    and what are the good workers
  798. identified as?
    Once they got an MBA what does
  799. the employer identify them as?
    Good workers, right?
  800. They're identified as good.
    They get MBA's.
  801. They're identified as good,
    and their payoff is what?
  802. What's the payoff of the good
    workers here?
  803. So they get paid 50 which is
    their productivity,
  804. but it costs them three years
    of putting up with my homeworks.
  805. So it costs them 3 x 5,
    five for each year.
  806. So 50 - 3 x 5 is what?
    35, good.
  807. So they get a total payoff of
    35, and let me just pause a
  808. second.
    I made an assumption here
  809. without telling you it,
    so I'm going to say it.
  810. Just to make the math simple
    we'll assume that once you get
  811. employed you work for a year and
    then you drop dead.
  812. That's a slightly morbid and
    unpleasant assumption,
  813. but otherwise we have to do
    kind of present discounted value
  814. of your whole future income and
    then it turns into an accounting
  815. class.
    So we'll just assume that
  816. everybody lives for one year.
    If you want to do a more
  817. complicated model then that's
    fine, the idea will be the same.
  818. So they get paid 50,
    it's cost them 3 x 5,
  819. and they get a total payoff of
    35.
  820. How about if they deviate?
    If they deviate that means they
  821. don't get MBA's.
    So they're not MBA's.
  822. They're identified as what?
    If they don't get an MBA,
  823. what are they identified as?
    What does the employer think
  824. the non-MBA's are?
    Bad.
  825. So if they deviate then the
    employers think they're bad.
  826. Even if they dance on the table
    and say they're good,
  827. they're in fact bad--they're
    identified as bad.
  828. And so their payoff is what?
    What are they going to get paid?
  829. They're going to get paid 30.
    And sure enough 35 is bigger
  830. than 30, so they're not going to
    want to deviate.
  831. So that's good news.
    What about the bad workers?
  832. Let's check them.
    So the bad workers,
  833. in equilibrium,
    they're not MBA's.
  834. They don't get an MBA.
    They're identified as bad.
  835. And they're paid what?
    What are they paid these bad
  836. workers?
    Somebody?
  837. They're paid 30.
    They're paid their productivity.
  838. So their payoff is just 30.
    They didn't get an education so
  839. it was free.
    They get 30 for free,
  840. so their payoff is just 30.
    If they deviate,
  841. if the bad workers deviate,
    then they get an MBA.
  842. So here come the bad workers.
    They find their way into my
  843. class in SOM.
    They have a miserable time.
  844. (I have a miserable time
    because they're having a
  845. miserable time.) But at the end
    of the day they're identified as
  846. good workers and hence they're
    paid 50.
  847. And their payoff is 50 - 3 x
    10.01 which is approximately 20.
  848. Is that right?
    So they don't want to deviate
  849. either and now I'm done,
    I've shown it's an equilibrium.
  850. So just to recap.
    To show that this was an
  851. equilibrium, I had to show that
    the good workers happily self
  852. select into education and don't
    want to deviate and skip
  853. business school.
    I have to show that the bad
  854. workers self select into not
    getting an education and don't
  855. want to deviate and become
    MBA's.
  856. And I have to show that the
    employers infer from this what
  857. they should infer from this,
    which was fine.
  858. So I'm done.
    This is indeed an equilibrium.
  859. So notice, in this equilibrium,
    the good workers do manage to
  860. distinguish themselves from the
    bad workers,
  861. and they do end up getting paid
    more (albeit at the cost that
  862. they're going to die a year
    later).
  863. So this is called a separating
    equilibrium--which I can never
  864. spell.
    I'm probably spelling this
  865. wrong.
    It's a separating equilibrium.
  866. Why is it called a separating
    equilibrium?
  867. It's called a separating
    equilibrium because the types
  868. manage to separate and get
    identified.
  869. That's slightly misleading.
    The good types manage to
  870. separate and get identified,
    and the bad types,
  871. they don't want to get
    separated, but they do get
  872. separated.
    Now, how many of you have seen
  873. some version of the Spence model
    before?
  874. Some of you,
    let's go into this in a little
  875. bit more detail to see if we've
    really understood it.
  876. So in particular could we get
    away with a shorter degree?
  877. Here we had people going to get
    MBA's and it took them three
  878. years each.
    That seems an awful long time
  879. to get an MBA.
    So how about a one year MBA.
  880. Some of you might think this is
    a somewhat abstract example but
  881. actually this is the kind of
    thing you hear about all the
  882. time.
    If you listen to ads in the
  883. education press you keep on
    hearing schools,
  884. perhaps schools who lack
    Economics professors,
  885. putting up the proposals for
    one year MBA degrees.
  886. I won't mention any schools by
    name because I'll probably get
  887. in trouble.
    So how about a one year MBA?
  888. Let's see if that will work.
    And we'll allow good workers to
  889. separate themselves from bad
    workers.
  890. Let's assume that the costs per
    year are the same as they were
  891. before.
    And let's suppose that this
  892. candidate equilibrium,
    this putative equilibrium,
  893. involves the good workers
    getting the MBA's;
  894. the bad workers not getting an
    MBA;
  895. and the employers,
    just as before,
  896. identifying MBA's as good and
    non-MBA's as bad.
  897. Question: is that an
    equilibrium?
  898. So who thinks yes?
    Who thinks no?
  899. So you can all tell my why then.
    So the answer is no.
  900. So why is that not an
    equilibrium?
  901. Somebody, anybody?
    Someone who hasn't answered yet.
  902. Your name is?
    Student: Asman.
  903. Professor Ben Polak:
    Asman, so shout out.
  904. Student: The bad workers
    would also benefit from doing
  905. the MBA because their payoff is
    still greater.
  906. Professor Ben Polak:
    Good, so what's wrong in this
  907. equilibrium, it's not the
    employer's beliefs.
  908. If in fact people did follow
    this behavior then employers
  909. would be right to identify MBA's
    with good.
  910. It's also not the good workers
    problem.
  911. If in fact, employers are going
    to pay more to MBA's,
  912. then the good workers are even
    more so going to want to go
  913. ahead and get MBA's.
    The problem here--this is not
  914. an equilibrium--and the problem
    is the bad workers.
  915. The bad workers' incentives are
    wrong here.
  916. Why?
    Because if the bad workers do
  917. what they're supposed to do in
    this equilibrium--actually it
  918. isn't an equilibrium,
    but in this supposed
  919. equilibrium--what they're
    supposed to do is not get an MBA
  920. and get a payoff of 30.
    But if they went and got an
  921. MBA, if they deviate and no one
    else deviates,
  922. just them deviating,
    if they deviate they get an
  923. MBA.
    According to the equilibrium,
  924. they're now identified as good
    workers.
  925. They're identified as good so
    their payoff would be 50 minus
  926. one year at approximately 10 for
    a total payoff of 40.
  927. But 40 is higher than 30 so
    that's violated our equilibrium
  928. condition.
    Everyone see that?
  929. So here the bad workers,
    if it only took one year of
  930. pain and suffering to get an
    MBA, the bad workers would go
  931. and get an MBA as well.
    And that would be trouble
  932. because now everyone gets an MBA
    and its just like dancing on the
  933. table again.
    So how long must an MBA be?
  934. In this model,
    with this cost structure,
  935. how many years must it take to
    get an MBA?
  936. Two years, right?
    One year didn't work but you
  937. can try at home and check that a
    two year MBA will work.
  938. Two years will be just enough
    to put off the bad workers.
  939. Leaving aside the numbers
    though, what's the idea here?
  940. The idea is that to work as a
    successful signal,
  941. the signal has to separate the
    good workers from the bad
  942. workers.
    The workers have to choose to
  943. be separated.
    They have to self select into
  944. being MBA's or not being MBA's,
    and we need just enough pain
  945. and suffering--and let's be
    careful--just enough
  946. difference in pain and
    suffering for the workers to
  947. select correctly.
    So what we need,
  948. we need enough difference in
    cost for good workers to get the
  949. degree and for bad workers not
    to want to do so.
  950. So one thing we could do is
    have a two year degree.
  951. If you absolutely insisted on
    having a one year degree,
  952. how could you create a
    difference in cost that would
  953. work?
    Suppose you were employed to
  954. advise some university out in
    the west somewhere,
  955. who wanted to have a one year
    degree program.
  956. What should you do in that one
    year degree program to make it
  957. work, to make it allow people to
    separate?
  958. Raising tuition isn't going to
    work because that's the same for
  959. good and bad workers.
    You need a way to separate the
  960. good and bad workers.
    How are you going to do it?
  961. You're going to make it really
    hard.
  962. If you want to have one year
    degree program,
  963. it's got to be really hard.
    You've got to really jack up
  964. the difference between the good
    and the bad workers,
  965. so you need to hire professors
    who have really bad handwriting.
  966. Let's try and take a step back
    from this model and see what
  967. we've learned here.
    Let's just try and draw some
  968. lessons off this.
  969. I want to draw two kinds of
    lessons.
  970. I want to draw lessons in
    general about what makes a
  971. successful signal in society,
    and then I want to draw lessons
  972. about education.
    So I want to start with some
  973. nerdy lessons about Game Theory
    if you like, and then I want to
  974. want to talk about some more
    specific lessons about the
  975. education system.
  976. So the key lesson here is the
    lesson we just learned.
  977. The key lesson is:
    to be a successful signal,
  978. to be able to separate types of
    people, you need there to be
  979. large differences in costs.
    So the first lesson is a good
  980. signal--it isn't that it has to
    be costly--it has to be
  981. differentially costly
    across types.
  982. The reason is you want the
    types to self select,
  983. so there better be differences
    in costs.
  984. Be a little bit careful here:
    you could have differences in
  985. benefits but we'll leave it as
    cost for now.
  986. That's one lesson.
  987. Now what's that telling us in
    this model?
  988. That's telling us that if you
    make it very,
  989. very easy to obtain
    qualifications in the U.S.
  990. society, for example,
    if you lower the standards that
  991. you need to get a high school
    degree and perhaps you lower the
  992. standards to get a college
    degree--I'm not saying that is
  993. happening,
    I don't want to take a
  994. political position on this.
    In England that's happening.
  995. I can do that.
    In England that seems to be
  996. happening.
    So you lower the standards it
  997. takes to get a high school
    certificate in England,
  998. and then you perhaps lower the
    standards to get a college
  999. degree, what are you going to
    see happen?
  1000. You're going to see
    qualification inflation.
  1001. If you make it easy for
    everybody to get the first
  1002. degree, the good workers are
    going to go on and have to get a
  1003. second degree.
    If you make it easy to get the
  1004. second degree,
    they're going to go on and get
  1005. the third degree.
    So what this model predicts is
  1006. if you get rid of this cost
    difference then workers will
  1007. find a new way to raise the cost
    difference again.
  1008. The way that takes place,
    at least in some economies,
  1009. is you start seeing
    qualification inflation.
  1010. By qualification inflation I
    mean that, pretty soon,
  1011. even to drive a dump truck you
    need to have a university
  1012. degree.
    Okay, now what are the lessons
  1013. here for education more
    generally?
  1014. This is a pretty sparse model
    of education but all of you,
  1015. and more immediately me,
    are involved in the education
  1016. system.
    So we should care about it a
  1017. bit.
    It's probably the most famous
  1018. model of education.
    As I say, it won somebody the
  1019. Nobel Prize.
    What is it telling us about
  1020. education?
    So the first thing I claim,
  1021. I claim that this is a rather
    pessimistic model of education.
  1022. Why is this a pessimistic model
    of education?
  1023. What's pessimistic about this
    model?
  1024. Let's talk about that a bit.
    Anybody, some hands up?
  1025. Some different hands?
    Why is this a pessimistic model
  1026. of education?
    Way over there,
  1027. a hand in another part of the
    room, that will give the camera
  1028. a work out anyway.
    Student: You won't learn
  1029. anything as a rule,
    as that school has absolutely
  1030. no value for education.
    Professor Ben Polak:
  1031. Good, so shout it into the
    microphone, but that was right.
  1032. Student: You don't learn
    anything at school in this
  1033. model.
    Professor Ben Polak:
  1034. Right, this is a model with no
    learning.
  1035. There's no learning in this
    model.
  1036. In fact, people in this model
    go in with their productivities
  1037. at 50 and 30 and they come out
    with their productivities at 50
  1038. and 30.
    Nothing you do at school
  1039. enriches you or makes you more
    productive.
  1040. That's a pretty pessimistic
    lesson.
  1041. Here we are in Lecture #23 or
    something.
  1042. And the message of this model
    is, you guys haven't learned
  1043. anything: you've just had a lot
    of pain and suffering.
  1044. So there's no learning in this
    model.
  1045. Now I hope that's not true as a
    model of education.
  1046. I hope it's not true that we
    only have pain,
  1047. but nevertheless,
    let's pretend it's true at
  1048. least for now and see where it
    takes us.
  1049. So a second observation of this
    model, if we believe this model
  1050. of education in which you don't
    learn anything,
  1051. education is just being used by
    those people who are good anyway
  1052. to separate from those people
    who were bad anyway,
  1053. then education in this model is
    socially wasteful.
  1054. Why is education socially
    wasteful in this model?
  1055. In what sense is it socially
    wasteful?
  1056. Think of it from the point of
    view of an economist?
  1057. In this model,
    the productivity of the workers
  1058. doesn't change because of
    education,
  1059. but some resources were used by
    the good workers to get an
  1060. education.
    At the end of the day,
  1061. the good workers are better
    off.
  1062. The bad workers are worse off
    and employers are the same as
  1063. they would have been otherwise,
    but that's just redistribution.
  1064. There's no product from
    education but resources were
  1065. wasted in education.
    Does that make sense?
  1066. So in particular,
    in our two year equilibrium,
  1067. or in our three equilibrium,
    it was the good workers who
  1068. went to college,
    or in this case went to
  1069. business school and they wasted
    three years at five a piece.
  1070. So there's a waste of 15--a
    waste of 10 in the two year
  1071. model.
    According to this model,
  1072. education is socially wasteful.
    How do we actually visualize
  1073. that waste in society?
    So let's take the model
  1074. seriously, where is that waste
    manifested in society?
  1075. Where is that waste manifested?
    So you guys aren't working,
  1076. and where else is it
    manifested?
  1077. You guys sitting here is part
    of the waste.
  1078. You should be out doing
    something else,
  1079. and where else is the waste?
    Me.
  1080. You should take all your Yale
    professors, stop using them as
  1081. Yale professors and wasting
    those resources,
  1082. and have us go out and till the
    fields or drive taxis or
  1083. something.
    So there's a social waste here
  1084. and what we should do is,
    according to this model,
  1085. is we should send the
    professors to drive taxis or
  1086. dump trucks I guess.
    I'm not claiming we'd be good
  1087. at driving dump trucks.
    Our comparative advantage is
  1088. certainly in teaching classes
    rather than driving dump trucks.
  1089. But it turns out that,
    in this model,
  1090. teaching classes is completely
    a waste of time,
  1091. and therefore you're better off
    using those resources to drive
  1092. dump trucks.
    Third, notice that in this
  1093. model the result of education is
    what?
  1094. It's good for the good workers,
    you guys managed to separate
  1095. yourselves and get paid high
    wages.
  1096. That's nice for the Yale
    graduates here,
  1097. but who were the losers in this
    model?
  1098. Who were the losers?
    The bad workers,
  1099. the 90% of workers in this
    economy who aren't naturally
  1100. gifted, who aren't going to find
    education easy.
  1101. They, in this model,
    end up being paid 30.,
  1102. Without the education system
    how much would they have been
  1103. paid?
    32.
  1104. So in this model education
    increases inequality,
  1105. and it doesn't increase
    inequality in a benign way just
  1106. by making the rich richer.
    It increases inequality by
  1107. making the poor poorer.
    Education, in this model
  1108. increases inequality.
    In this model it actually hurts
  1109. the poor.
    Now, that strikes me as a
  1110. pretty important lesson
    actually.
  1111. Again, I don't think we should
    take this model too literally.
  1112. In the real world,
    I at least hope that some of
  1113. you are learning something at
    Yale.
  1114. You're looking extremely
    doubtful that you could possibly
  1115. learn anything at Yale,
    so maybe you're not,
  1116. I don't know.
    But, in the real world,
  1117. I'd like to believe people are
    learning here at Yale.
  1118. But one of the things that's
    going on in education in
  1119. addition to learning,
    one of the things is that you
  1120. guys are separating yourselves
    and signaling to employers that
  1121. you're going to be good workers
    for them.
  1122. As a consequence,
    that's great for you but
  1123. someone else is being paid less.
    This strikes me as an important
  1124. lesson to hear in an election
    year.
  1125. In every election year in
    America--I've been in a few
  1126. election years in America
    now--there are two things that
  1127. all politicians agree on,
    whether they're far right or
  1128. far left.
    All politicians agree on two
  1129. things.
    They agree that two things are
  1130. good.
    One: kissing babies.
  1131. Two: they all want to be "the
    education President," is that
  1132. right?
    All of them, is that right?
  1133. Now, as a parent of some
    babies, I'm not sure I want to
  1134. have politicians' kissing babies
    but that's for another day.
  1135. The point here is what we're
    learning--don't go yet
  1136. guys--what we're learning here
    is that if education hurts the
  1137. poor maybe we shouldn't be so
    keen to decide that we should
  1138. subsidize the education sector
    itself.
  1139. Although, as an educator,
    I hope you don't tell that to
  1140. anybody.
    What's the take away message of
  1141. this model then?
    The take away message is for
  1142. education to work as a signaling
    device, for education to
  1143. generate a separating
    equilibrium,
  1144. some children have to be left
    behind.
  1145. We'll talk about that more on
    Wednesday.