Sunday, 3 May 2015

Risk aversion and the firm

A bit over a week ago in the comments to a post James asked,
Can I make a request for a topic? Since you're the resident expert on the theory of the firm, can you write something about any work that's been done on risk averse firms? (I.e. in contrast to the standard assumption about risk neutral firms). Does the risk neutrality assumption have any major implications for standard economic theory?
I've been away but now I'm back at home I can attempt a rough answer. Better late than never, I hope.

Back in 1974 when discussing the topic of 'risk, uncertainty, and the firm' Michael Crew wrote,
Like growth theory of the firm, the theory of the firm under uncertainty is not highly developed. Much of it is speculative.
And not much has changed since then, the theory still isn't that well developed. Knightian uncertainty rather than risk has become more important to the modern theories of the firm.

While little has been written on the topic of risk and uncertainty to do with the firm, the amount is not zero. Back in 1970, for example, Lintner wrote a paper in which pricing decisions of the firm are made on a fully rational profit maximising basis subject to risk aversion with respect to the uncertain profits involved. Assume the uncertainty is due to uncertainty to do with demand. It is uncertainty about the quantity that will be sold. Under the assumptions Lintner makes he can show, not surprisingly, that for a given price change the higher the degree of risk aversion the greater is the increase in expected profits profits requires by a firm (decision maker) in order to induce it to accept greater profits uncertainty. Also the effects of risk aversion on price and output are such that prices are lower when (1) the greater the uncertainty and (2) the greater the risk aversion the closer the price gets to marginal cost and thus the further a firms gets from the monopoly outcome. In addition Lintner can show that the greater the uncertainty about sales and volumes and the greater the risk aversion of the decision maker the greater will be the expected quantity sold.

Different forms of uncertainty can deliver different results. If uncertainty is about realised prices, rather than quantities, then Day, Aigner and Smith show that price is set higher than the monopoly outcome, the greater the degree of risk aversion.

Marcus Asplund has a 2002 paper on 'risk-averse firms in oligopoly'. Does risk aversion lead to softer or fiercer competition? This paper provides a framework that accommodates a wide range of alternative assumptions regarding the nature of competition and types of uncertainty. It shows how risk aversion influences firms' best-response strategies. Only in the case of marginal cost uncertainty does higher risk aversion make competition unambiguously softer. The risk-averse best response strategies depend on the level of fixed costs. This fact is used to analyse strategic investments in capacity and the importance of accumulated profits. The paper concludes with a discussion of ways of empirically testing for risk-averse behaviour in oligopoly.

In more modern approaches to the firm the work of Frank Knight on risk and the firm has been developed. The standard view of Knight’s rationale for the existence of the firm doesn't depend on profit, but on risk, or more accurately, risk distribution. The entrepreneur forms a firm as a way of specialising in risk-taking. Employees receive a stipulated income and the entrepreneur takes the residual income of the firm and thereby bears most of the risk associated with uncertainty about the future. The advantage of the firm, according to the standard view, is that there are gains to be made from this distribution of risk between the entrepreneur and the firm’s employees. The profit and loss consequences of fluctuations in the business outcomes can be better absorbed by the entrepreneur than the employees. The entrepreneur contracts to pay a fixed wage to workers, thereby protecting them from the fluctuations in business outcomes. Knight sees this as efficient since the entrepreneur is less averse to bearing risk. Presumably, risk is not handled as well without firms.

Other views of Knight have been put forward in papers by Barzel and McManus. Each puts forward a moral hazard explanation for the Knightian firm. The firm arises here because, for certain kinds of risks, the functions of risk taking and management are inseparable due to the prohibitively high costs of enforcing constraints that would induce one individual, the manager, to maximise the wealth of another, the risk-taker. As noted in the distribution of risk story above, firms are one way of specialising in risk-taking. Knight was aware of contractual and insurance arrangements as alternatives to the firm as ways of specialising in risk-taking but thought, because of the moral hazard problems, they were particularly costly to enforce in the case of risks of enterprise and hence the need for the creation of a firm. Presumably monitoring the manager is easier for the risk-taker in a firm that it is on the market.

In 1991 Holmström and Milgrom made two observations to do with the firm and its (risk-averse) employees. First, they note that there are a number of ways that an employee can spend their time, many of which can be of value to an employer. But if these multiple activities compete for the worker’s attention then the incentives offered for each of the activities must be comparable. Otherwise, the employee will put most effort into those things that are most well compensated and put less effort into the others activities. The second observation relates to the provision of strong incentives to a risk-averse employee. Providing strong financial incentives is costly because it loads extra risk into the worker’s pay. In addition, the cost is greater the more difficult it is to measure performance. This means that, other things being equal, tasks where performance is hard to measure should not be given as intense incentives as ones that are more accurately observed. But having low-powered incentives means that the employer needs to be able to exercise authority over the use of the employee’s time, since the employee will not have the proper incentives to be productive.

The above are all partial equilibrium models but a general equilibrium approach is taken in a 1979 paper by Kihlstrom and Laffont. They construct a theory of competitive equilibrium under uncertainty using an entrepreneurial model with historical roots, again, in the work of Knight in the 1920s. Individuals possess labour which they can supply as workers to a competitive labour market or use as entrepreneurs in running a firm. All entrepreneurs have access to the same risky technology and receive all profits from their firms. In the equilibrium, more risk averse individuals become workers while the less risk averse become entrepreneurs. Less risk averse entrepreneurs run larger firms and economy-wide increases in risk aversion reduce the equilibrium wage. A dynamic process of firm entry and exit is stable. The equilibrium is efficient only if all entrepreneurs are risk neutral. Inefficiencies in the number of firms and in the allocation of labour to firms are traced to inefficiencies in the risk allocation caused by institutional constraints on risk trading. In a second best sense which accounts for these constraints, the equilibrium is efficient.

No comments: