Moral Hazard: Labour Market & Insurance

Moral Hazard” is a very fashionable concept that has been thrown around a lot since 2007/08 as a result of bad practices by bankers. It is also a common place in discussions of central Bank’s intervention, the Debt Monetisation risks of Quantitative Easing and their potential for creating hyper-inflation. Most relevantly to this website, it is also an issue within the discussion of the broader future of Europe and the implications of different modalities of fiscal federalism.

However, at its heart, Moral Hazard can be seen under two lights. It is a Principal-Agent problem, first explored in the context of the labour market, as well as an information asymmetry that undermines the sustainability of insurance contracts. This post offers a general review of the concept so that it may intelligently be used in the future. While issues of signalling are not inappropriate to consider, they are left for another occasion. The principal-agent focus is on monitoring, as per Shapiro and Stiglitz (1984), but with a more general use of “Asset Pricing Equations“. Their model goes into much more depth than this discussion does. All I intend to do here is to circumscribe the concept of Moral Hazard. Finally, some attention is also paid to the insurance aspect of moral hazard and the model that describes it.

MORAL HAZARD: The Principal-Agent Model and the Labour Market

In economics, Moral Hazard is a contractual issue which arises from information asymmetries when someone (the principal) delegates some task to someone else (the agent). It is the situation whereby an able agent changes his behaviour and attempts to circumvent his part of a contract once the contract is signed. Therefore it exploits the inability of a the other party, the principal, to perfectly observe his behaviour and confirm that the agent is complying with the terms of the contract. In this sense it presents the principal with a problem of hidden actions from the agent, rather than hidden characteristics (which would be a problem of adverse selection).

The Variables of the Model

Consider a situation where an individual may either be unemployed or employed, in which case it is faced with the choice between being professional and exerting some effort in his job or be lazy.

  • To the employed worker (agent) that makes an effort, the value of this choice (rVE) is  worth the wage he makes (w) discounted by the cost of his effort (e), any unemployment-conditional benefits or income (w’) and the expected value of loosing his job [b(VE-VU)].
  • To the employed worker (agent) who is lazy, or “shirks”, the value of shirking (rVS) is  worth the wage he makes (w) discounted by any unemployment-conditional benefits or income (w’) and the expected value of loosing his job [(b+q)(VS-VU)].
  • To the unemployed individual the value of being unemployed (rVU) is  worth the  unemployment-conditional benefits or income (w’) discounted by the expected value of finding a job [a(VS-VU)]

In summary, the model will include the following variables

Assumptions

As all models, this one is permeated by assumption, which are practical, but of which readers should be aware. The main assumption most economic models make is that all individuals concerned are the same. This is not a fatal flaw. For one, as with many other social phenomena, it is not impossible that behaviour in the labour market behaves is regulated by stable relationships and confined to well behaved probability distributions. From another point of view, even if the insights of this model are lost in the collective, it is still an interesting short cut to think of individuals.

The reader should also keep in mind that probabilities, “a”, “b” and “q” are considered as is often usual, to be independent and identically distributed (iid) and exogenously given. This is a very useful little trick for computational reasons, but in social relationships it is a very unrealistic approach, given that the systems are all very interdependent and endogenous.

Laying out the Model

The afore stated relationships can be modelled, following the asset price model path, in the following manner:

Notice that the difference between a lazy and a hard-working agent is the “effort” that the shirker does not have to make and the monitoring intensity which the other does not have to worry about. Of course, this is a binary system. The agent either makes an effort or he doesn’t. This model does not assume any continuum of effort, along which the principal might have different attitudes to.

No Shirking Condition

The above model therefore includes a situation under which individuals may be paid and refuse to work. Therefore it is necessary to understand under which conditions the individual makes an effort or not. This leads to the following “No-Shirking Condition”

Unsurprisingly, the result is quite self evident, despite its appealing internal consistency. The amount of effort will be a function of the monitoring intensity, rising with the value of being employed and falling with the value of being unemployed. The point is, monitoring matters and can be used to make people make more of an effort in whatever task their were delegated to pursue as agents of some principal.

MORAL HAZARD: The Insurance Problem

Moral Hazard – The Insurance Model

The following discussion is based on the contributions by Gravelle & Rees’ discussion. I am grateful to this post for drawing my attention to that discussion. It considers how moral hazard may arise not from a delegation problem between principals and agents but rather in the context of an insurance contract.

Consumers and their Loss Indifference Curves

An individual can who has signed on to a contract agreement has the choice between exerting an effort (“e”) to avoid the loss making event or not. If he makes an effort, the loss making event takes place with probability p = p(e). If he does not make an effort, the probability of the loss making event taking place is higher, at p = p(ne) , such that

p(ne) > p(e), 0 < p(i) < 1

Ignoring for the time being the different payouts under loss (ILi) and no loss (INLi), we can say that the total expected utility of an individual will depend on whether he makes an effort to avoid the loss making event or not.

This can be generally expressed as

This gives us the slope of the indifference curve at full insurance.

Insurance Firms and the Pricing of Insurance Premia

Perfectly competitive insurance firms will price at the level of costs and make no profit, so that

Insurance Firms and their Isoprofit Curves

Slopes of indifference and isoprofit curves

Now, it should be immediate to show that the slope of the indifference curve for the individual who exherts more effort is steeper (larger) than the slope of the individual who decides to be lazy. Here’s how it works:

A similar fact about the slopes of the isoprofit lines is observed, which results in the figure described above.

Assume for now that     E(U(e)) < E(U(ne)). We will revisit this assumption and the necessary conditions for it to hold after looking at the asymmetric information case.

 

Perfect Information Equilibrium

Therefore, at the equilibrium, where the consumer’s demand meets the insurance firm’s supply, at full insurance is given by

Under perfect equilibrium, individuals will chose to exercise effort or not, but ultimately, the insurance firm will be able to tell and so will allocate contract A or B, depending on whether an effort is made or not. Given that the intial wealth starting points are always the same, with the steeper curves of effort making indifference curves, A will always offer a higher utility than B, pushing the individuals to make some effort in the perfect equilibrium model.

Asymmetric Information

Interestingly, whereas in the adverse selection problem individuals cannot chose their indifference curves, the distinguishing feature of the Moral Hazard problem is that in this case, the same individual has two indifference curve functions, from which to choose from, depending on whether he prefers to make an effort or not. If the insurance firm is unable to observe whether an individual is making an effort or not and if it offers both contracts, then individuals will enter into the contract which presumes effort, but then decide to make no effort. However, the result is that at that point “C” the probability of incurring a loss is not the same as the one used to compute the premia.

Avoiding Moral Hazard: Monitoring and Incentivising Good Behaviour

To understand whether an individual prefers to be lazy or to make an effort, it is important to model the pay-outs. Assuming that the insurance consumer has initial wealth “W”, receives an insurance compensation “C” for loss “L”, that the insurance firm makes a monitoring effort “m” to monitor the effort of the individual (where “m” is normalised to be 0 < m < 1), and that the effort has an exertion cost e*, then the individual making an effort (e) will experience the following payouts, in case the loss making event takes place or not, respectively:

About these ads
This entry was posted in Economic Concepts, Uncategorized and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s