Risk Allocation & Productive Efficiency

The importance of risk allocation and productive efficiency for a society’s welfare should be obvious. Risk allocation has not only a direct effect on individuals’ welfare but also indirectly influences the investors’ willingness to supply capital for risky investments and thereby the growth of the economy. Simultaneously the workers’ working performance may depend on their risk, which partially depends on the employment risk. The latter, in turn, may strongly influence the income accruing to the economy. Hence, the wage system can be assumed to influence strongly a society’s welfare.

In an excellent critique of the fixed-wage system, Gunter Franke (1977 a), has worked out a theoretical model of risk allocation and productive efficiency. This section relies heavily on his work. He offers the following criticism of the Fixed-Wage System:

  1. Under a fixed-wage system (without employment guaranteed) the worker faces on average higher probability of being laid off than under an adjustable-wage system. As a higher probability of being laid off may well increase the worker’s income risk, his income risk may be higher under a fixed than under a adjustable-wage system;
  2. A fixed-wage cannot reflect a worker’s marginal productivity in different states of nature; (Franke, 1977 b) and (Dreze, 1977); and
  3. If wages serve as financial incentives for the workers to work more or less for the employer, then the economy will not be productively efficient under a fixed-wage system: there is no incentive for the worker to work more in those states with high marginal productivity as opposed to states with low marginal productivity.

His analysis does not examine those markets where the wage system does not matter; for such markets are so unrealistic that application- oriented conclusions cannot be drawn. The theoretical basis of his contribution is thus derived from “less perfect markets”. Four different types of wage systems are studied for their risk allocation and productive efficiency. These are: (a) the pure profit-sharing system;

the profit incentive system; (c) the market value change incentive system; and (d) the portfolio incentive system.

The Pure Profit-Sharing System (PPS)

In PPS the wage base of a worker is the fraction of his fixed wage to fixed wages paid by the firm in state's’, the reward being a part of the firm’s profit. Hence, all workers together receive anPns as stochastic wages. Under this system the conventions by which profits are measured play a crucial role. By varying depreciation figures, for example, there is great degree of freedom to manipulate profits. Existing practices usually prescribe that expected future losses have to be anticipated whereas expected future profits must not be anticipated. Hence profit figures usually appear distorted as compared to income figures which are derived from capitalizing expected earnings or expected net cash flows.

Efficient risk allocation requires that wages depend on the market value of all risky securities. If investors regard profit figures as distorted, there is little hope, if any, for a stable relation between the firm’s market value and its profit figures. Hence, if all firms followed PPS with an being the same for all firms, the sum of all wages would correlate with the sum of all profits, but perhaps show no stable relation with the market value of all risky securities.

PSS does not provide an efficient risk allocation either from the investor’s point of view or from the viewpoint of a worker. The risk of all investors, taken together, depends on the changes in the market value of all risky securities. These changes would be reduced effectively if the sum of all wages varied with the market value of all risky securities. Hence, the investors would prefer such a wage system to PPS. A worker’s risk depends on the profit of his firm only; hence there is no diversification from which he benefits. The system also does not allow for an adjustment of wages to the worker’s risk-aversion and expectations. Hence, a worker with relatively high risk aversion has to bear a risk which would be borne better by other persons.

As the wage depends on the profit of the firm, one might assume that PPS provides performance incentives for the worker. But if the worker raises his performance so that the profit increases by (d Pns), the worker receives only the very small fraction ( W. wj ) of e n d Pn$. As has been argued often there is practically no performance incentive under PPS.

Profit Incentive System (PIS)

PIS is defined by Equation (2) — as shown in the Appendix. In this system one could measure the marginal gross contribution of a worker by the associated change in the market value of his firm. Hence wages would depend on profits and market values. Such a wage system appears rather complicated and oversteps the framework of profit- sharing. Thus, in PIS, marginal productivity is measured by profit changes (3Pns/3qjz). The constants bjz and bjz must be chosen such that the ratio of bjz and b-z equals the ratio of worker i’s and worker j’s expected values of marginal profits.

Compared to PSS, the economy in PIS is productively less inefficient, as a worker’s wage base depends on his performance and the expected value of profits produced by a marginal performance increases. With respect to risk allocation PIS is as good as PPS. It does not, however, consider the following two important aspects:

  1. risk allocation, viewed from the investor’s point of view, would be less inefficient if wages depended on market values rather than on profits; and (ii) productive efficiency suffers from the conventions of profit measurement: possibly the work of a given period increases primarily the profits of later periods so that the benefits which accrue to a worker as a result of marginal performance increase are clearly lower than his marginal gross contribution. This strengthens productive efficiency.

Market Value Change Incentive System (MIS)

The two problems mentioned at the end of the last section can possibly be resolved by replacing the reward “part of the firm’s profit” by “part of the change in the market value of the firm (before payments between the firm and the investors)” in the time between states s and z. If the change in the market value of the firm n can be ascertained, would define a Market Value Change Incentive System (MIS). Using this equation, in conjunction with other conditions, Franke (1977 a) has clearly demonstrated that under MIS the wage system is based on market values. Conventions of profit measurement are irrelevant and therefore the problem in question mentioned at the end of the previous section is solved by MIS.

The tractibility of MIS, of course, depends crucially on one’s ability to obtain reliable estimates of the performance indicators (bjz and qjz). In fact in a complex organization it is extremely difficult to measure the increase in the firm’s market value generated by marginal performance increase. Hence some simplifying measurement rules have to be adopted. In order to make the performance measures of different workers comparable, a worker’s actual performance should be divided by a standard or budgeted performance level which has been set before for the worker’s job. Such a measurement seems possible because Wj is known from labour contracts and the measure of qjz resembles closely the output measures of accounting systems.

Risk allocation from the investors’ viewpoint fares better under MIS than under PIS, as wages depend on market values and thereby reduce the variations in market value. Risk allocation from the workers’ point of view is about as good under MIS as under PIS since the problems (i) and (ii) raised in Section IV.2 still remain unresolved, with profits being replaced by market value changes. Employment risk is about the same as under PIS. Since neither MIS nor PIS solves the problems in question a Portfolio Incentive System is suggested.

A Portfolio Incentive System (FIS)

Since workers have different risk aversions and different expectations, a wage system that takes this into account should allow for some individual wage specification. Instead of forcing the worker to take the firm’s market value, Vnz as his “portfolio”, let him freely choose a portfolio in state z (when he is hired) which at that time has the same market value Vjz as “his” firm. Then his reward is the change in the market value of this portfolio in the time between state s and z (seSz) multiplied by an. Having defined the change in the market value of the portfolio chosen by worker i in states s and z Equation (3) has to be replaced by Equation (4). This equation then describes the “Portfolio Incentive System” (FIS).

There are two main advantages of FIS with respect to risk allocation: (i) the worker avoids paying the transaction cost to the bank and there is no diversification problem created by the indivisibility of share; (ii) a risk-averse worker can choose a risk-free portfolio; a less risk-averse worker a risky portfolio. Moreover, every worker can choose according to his expectations. If a worker faces a high probability of being laid off, and expects a decrease in the market value of “his” firm, he may choose shares in other firms or a negative number of shares of “his” firm. Then his wage is higher, the more the market value of “his” firm decreases. By buying a negative number of shares the worker can avoid, or at least reduce, the financial risk produced by PPS, PIS, and MIS.

A possible advantage of FIS with respect to risk allocation is that a firm may have to pay high wages though its own profit and liquidity may be poor. Hence, the firm incurs additional risks which have to be borne primarily by its shareholders. The firm can, however, hedge against his risk. If it knew in state z the end-of-period wage base of every worker, then it would aggregate all portfolios chosen by its workers, weighted by the wage bases, and immediately buy this portfolio on the stock exchange. This would give a perfect hedge. In fact the firm does not know state z whereas the wage base depends on the sign of (Vjs —Vjz). Hence, it does not know in state z exactly the fraction of (Vjs — Vjz) which the worker will receive. The hedge, therefore, remains imperfect.

FIS implies a similar hiring and firing policy as MIS insofar as it relates to employment risk. With respect to productive efficiency we have demonstrated above that FIS, theoretically requires that b.Jb. equals the ratio of the marginal gross contribution of worker i and j. Assume that the worker’s portfolio contains negative shares of “his” firm whereby his Vjs is higher as the market value of the firm in state s is lower. Does this create a “negative” performance incentive from the viewpoint of the firm or even a “sabotage behaviour” and hence productive inefficiency.

The answer would depend on the efficiency of the capital market. If it is efficient such that Vnz reflects correctly all monetary performance effects, then a worker receives about “his” marginal gross contribution for a marginal performance increase. The worker cannot benefit from a sabotage behaviour as the market would anticipate that. The converse would obtain, however, if the capital market functions in an inefficient manner (Franke, 1977 a).


Source: Fiscal Policy and Resource Allocation in Islam, Ziauddin Ahmed, Munawar Iqbal and M. Fahim Khan. Republished with permission. 

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