How Insurance Works

18 2 Hidden Action and Hidden Information 953

Hi. In this set of lectures we are talking
about mechanism design. When you think about designing mechanisms in effect what
we are doing, we are designing incentive structures so that we get the sort of
outcomes we want. Now to get those outcomes often what we’re trying to do is
we’re trying to induce people into taking the right kinds of effort. So, for
example, if I’m an employer, what I’d like to do is I’d like to write a contract so
that people actually put forth a lot of effort in their work as opposed to
slacking off. Alternatively, if I’m auctioning something off, what I’d like
people to do is reveal their information. I like them to reveal how much they value
something. So, another feature that we want when we construct mechanisms is
revelation of information. So, when I think about mechanism design, two of the
core problems are dealing with these hidden actions and dealing with hidden
information. So, how do we write mechanisms or incentive structures that
overcome those two problems? That’s what we’re going to talk about in this lecture
in a really abstract way. So let’s start out by talking about [inaudible] matching.
And what do I mean? What I mean is this. Is, you’re an employer, and let’s suppose
you hire people who make pots. So they throw pots. These people can put forth
effort. They can put forth a lot of effort, or they can just slack off, and
not put forth much effort at all. What we’d like them to do is put forth a lot of
effort. But I can’t tell. The only way I can tell is if I sat there and monitored
them all the time, which would be really, really costly. So instead, what I’d like
to is I’d like to write some sort of contract, so that they always put forth
the right amount of effort. Now, sometimes these are called moral hazard problems.
And the reason is this, is that, because I’m not being watched if I’m the employee,
I sort of have some moral hazard. I could, I could cheat, I could slack off. And so
the question is, how do people write contracts to overcome these moral hazard
problems? So let’s write down a simple model and see sorta how it works. So let’s
suppose I get some workers, and these workers can take some effort, they can
take an effort level zero or an effort level one. And again, that’s not gonna be
observed. What is going to be observed is the outcome, I’m gonna see whether the pot
is good or whether the pot that they made is bad, or that it’s floppy. So I don’t
know whether it’s gonna be good or it’s gonna be a bad outcome. But I do know
this, I know that if they’re diligent and they put in an effort of one, the, the
probability that the output is good is, is one, it’s for sure gonna be good. But I
also have a slack off. There’s some probability P that it’s still gonna work.
That they’re gonna get a functional clay pot. What I’d like to do is I wanna induce
this effort level of one, but how do I do it? The reason it’s hard to do is because
it’s costly to put forward that effort. So worker is gonna pay this cost C. Of
working hard, and they’d rather not. They’d rather slack off. So what I wanna
do is I wanna write a contract so they put forth the right level of effort. Well, how
do I do it? Well, it turns out its not very complicated. What I wanna do is I
want a contract that says, I’ll pay you M, I’ll give you M dollars if it’s good, and
I’ll pay you nothing if it’s bad. Here’s the core idea. The idea’s I want what’s
known as incentive compatibility. Incentive compatibility means that it
makes sense for the worker to put in the effort. So I wanna [inaudible] money M, so
that everybody’s gonna put forward the effort. So how do I figure that out? Well,
it’s a very simple model. What’s their payout if they put forward the effort?
Well that’s M because they are gonna get the money M because the outcome is gonna
be good for sure. But then it’s gonna by minus C because they are gonna pay the
cost C. What’s their payout if they don’t put forth the effort? Well, it’s gonna be
P times M. Because, with probability P, they’re actually still gonna get a good
outcome. And so they’re gonna get P times M, which is the payout for getting a good
outcome. So the incentive compatibility constraint, which is that it makes more
sense for them to work hard, means that M-C has gotta be bigger than [inaudible].
And if I manipulate things around, I get the following Inequality that I’ve got to
pay them at least C over one minus P. So this is the solution. If I want to induce
people to work hard, the amount of money that I’ve got to pay them for a good clay
pot is gonna be the cost of effort divided by one minus the probability that if they
were lazy, they got a good outcome anyway, Me, very straightforward. Remember when we
do models, somebody’s going to get stuff for free? Well, here we’re going to get
something for free as well. These are sometimes called comparative statics. So,
[inaudible] you make in comparative statics is here’s my equilibrium level of
payment. This is what I should pay people to make a good clay pot. But what this
tells me is how that varies. As I change other variables. So, for example, what
happens if the cost of effort goes up? Well, if C goes up, then C over 1-P is
going to go up, which means that M has to go up. But that makes sense. If it’s
costlier to put forward high effort, then I’m going to have to pay people more money
In order for making a good pot, to induce them to work hard. What about P, well this
complicated; P is the probability that someone who slacks off still gets a good
pot. Well if P goes up, that means that, so if P goes up that means one minus P.
Goes down, but it means one over 1-p goes up, so it means that m goes up. So what we
get here is that if the probability someone gets a good clay pot anyway.
Increases, I also have to pay people more. And the reason why is because there’s, if
you think about it, there’s more incentive to slack off. Because there’s a higher
probability I’m gonna get a good outcome anyway. So what we get, these comparative
statics are that M is increasing, both in the cost of effort, and in the probability
of getting a good outcome even if you’re not putting forward the effort. So we get
these nice, sort of, comparative statics results. Here’s maybe the most interesting
thing about his whole model. We now know what the action is. So even though I call
this a hidden action problem, if M is bigger than C over O minus P, I know what
the action is. I know the effort is one because it makes sense for people to put
forward high effort. So, I’ve taken a situation where I had hidden an action,
and now I know the action. However, it costs me. How much did it cost me? M, how
big is M, C over one minus P. Let’s now go to hidden information. What is hidden
information? Well, let’s suppose you?re an insurance provider and you don’t know
whether someone is a safe driver or a risky driver and what you like to do is
not get risky drivers and only get safe drivers or alternatively you would like
to, have risky drivers pay more for their insurances. Or let’s suppose you?re an
employer and there is two types of workers, theirs people that who really
have high ability theirs people who are low ability. What you like to do is, you
only like to hire the high ability workers. So, let’s, let’s work through
that scenario. Let’s suppose there’s two types of workers. There’s these high
ability workers, and there’s low ability workers. And you don’t know which is
which. We can look at their resumes, but it’s hard to tell. But suppose you know
the following is true. Suppose you know that the cost for these people to work.
For high ability workers, it’s fairly low cost to put forward an hour of effort. But
for low ability workers, it’s higher cost to put forth an hour of effort. So what
you can usually do is say, okay, you can come to work for me and I’ll pay you some
amount m. So suppose there is a fixed wage that you have to pay people, there is a
minimum wage. But you say this, But before you come work for me, what I want you do
is work a couple hours in the kitchen for me, and. You know work a couple hours on
this project for me just to see how well you do. Well let’s thi nk about the
incentives for these two types of workers. Let’s let k be the number of hours I want
to make these people work. If you’re a high ability worker, the cost of working K
hours is just K times little C. And you’re going to be willing to do that, you’re
going to be willing to put in these hours, as long as K times little C is less than
M, the amount of money you’re getting paid. But if you’re a low ability worker,
if you choose M so that it’s less than K times big C, you’re not gonna do it
Because your cost, K times big C, is going to be higher than the benefit, which is M.
So what you’d like to do, in a way, is say the number of hours is equal to M over
base C cuz it’s maybe you know plus maybe a little bit here. That way the low
ability workers won’t take the job but the high ability workers will. So what you’re
doing is you’re, even though the information is hidden, you don’t know
whether someone’s low ability or high ability, this will separate them out.
Let’s do comparative statics on this, how does the number of hours depend on M and
on C; well as M gets bigger K is gonna get bigger. But that makes sense. If the job
pays more, you’re gonna have to make people work more hours. What about with
respect to big C? Well if C goes up, K is gonna fall. This makes sense as well
because if the cost for these [inaudible] workers goes up then you are not gonna
have to make them work as many hours [inaudible] say look I’m not gonna do it,
it’s not worth it. Now, these are sometimes called costly signaling models.
And the reason why is this, is that the high ability workers had to signal, by
working K hours, that they’re really high ability. Let’s go back to this contract.
I’ve set K so that the high ability workers are willing to work K hours, but
the low ability workers are not. So, here’s what’s gonna happen. All the high
ability workers are gonna work, none of the low ability workers are gonna work.
So, I’ve separated them out. So, what I get is again, the information is no longer
hidden. I know whose high a bility, those who chose to take the job, and I know
whose low ability, Those who chose not to take the job. Alright, so the simple foray
and the [inaudible] information gives us sort of a starting point for thinking
about institutions and incentives. So how we can write down sources of actions,
payoffs from those actions to induce right levels of effort and also to separate out
who’s of one type, who?s of another type. What we’re going to do next is look at
auctions and see how we want to, how we can use different institutional structures
and those create different incentives, people to take different behaviors and how
those different institutional structures affect the outcome. In some cases they’ll
have big effects on the outcomes; in other cases they’ll have no effect. All right.
Thank you.

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