Distraction and Incentives
Distraction and Incentives
Abstract and Keywords
Efficiency wages have been proposed as a means to increase productivity by paying people higher than their outside option. In development economics, this means that paying workers higher wages will make them stronger and work harder. However, this theory has been criticized for being unrealistic, in part because it is not clear whether short-term spending on nutrition has a significant effect on work capacity. This chapter discusses the idea that poor people in developing countries are constantly dealing with problems not of their making (for example, flooding, no water or power, no money to buy medicines, and so on) and argues that this can decrease productivity. In the Banerjee-Mullainathan framework, attention can be purchased by acquiring so-called comfort goods (goods like health insurance or a house with a 24-hour power and water connection). This chapter explores how concerns about attention affect the design of incentives within a firm.
The idea of efficiency wages is that people should be paid higher than their outside option in order to increase their productivity. In development economics it is usually thought of in nutritional terms—if you pay workers higher wages, they will be stronger and work harder (see Dasgupta and Ray 1986 and Mazumdar 1959). This story is often criticized as being unrealistic, even though there is strong evidence of a link between nutrition and productivity. First, because as Srinivasan (1994) points out, even relatively low-paid workers in poor countries do not spend all their food expenditure on getting nutrients, as one might have expected of someone close to starvation. This suggests that they do not, rightly or wrongly, perceive themselves as starving and as a result, the relation between higher wages and nutrition is relatively weak. It is also questionable whether short-term nutritional spending has much of an effect on work capacity and while more sustained spending on food over a longer period probably does help, it is not clear that the current employer should take this into account in setting wages. (p.180) After all, how does she guarantee that the worker will not demand higher wages (or change employers) once her productivity goes up as a result of the extra investment by the employer in her nutrition?
In Banerjee and Mullainathan (2008) we proposed a very simple alternative model, which emphasizes workers' attention rather than their physical capacity and show that this can generate a pattern much like the nutrition-based efficiency wage model. In particular, the non-convexity in the work-capacity function with respect to nutritional inputs that underlies poverty traps in nutrition-based efficiency wage models (Dasgupta and Ray 1986) emerges naturally from our modelling of attention. The basic idea is that the poor in the developing world are constantly dealing with problems not of their making (no water, no power, flooding, sick children and no money to buy medicines) and that this substrate of persistent problems and worries about them can make people less attentive and, hence, less productive.1 In our framework, attention can be ‘purchased’ by acquiring what we call comfort goods, which are goods like a house with a 24 hour power and water connection, health insurance, a creche, etc. This gives employers a lever that they can use to affect worker productivity contemporaneously—essentially by paying employees more—without running into the kinds of commitment problems that arise in the case of investing in a worker's nutrition.
In this paper we return to the basic formulation of the previous paper with the goal of examining how concerns about attention affect the design of incentives within a firm. This is in contrast to the previous paper, which emphasized the difference between richer and poorer people and its connection to ideas about poverty traps, assuming away incentive problems. To analyse the effect of limited attention on incentives within a firm, we extend the model to a setting in which workers' choice of attention is potentially unobserved by the employer. The model in this paper is therefore slightly more general.
The first main insight we get from the analysis of incentives is that firms will pay efficiency wages. This is not surprising given (p.181) the fact that paying workers more increases productivity. Moreover, firms will discriminate against workers with certain attributes (women, new migrants, etc.), who they suspect of being more liable to suffer from attention problems. Further, in order to maximize the gains arising from efficiency wages, firms will try to induce their employees to take the extra wage mainly in comfort goods, which may explain institutions like company townships and company stores. Finally, the desire to monitor and control attention may explain why employers prefer factory production over putting-out production.
The next section presents the model. The basic analytics of the model are presented in the following section. The next section brings in the discussion of incentives. The last section provides a conclusion.
Production, Problems and Attention
Production requires human capital and attention. Each worker who has human capital h produces output h. However, with probability pf, there is a problem in production which has the potential to destroy the worker's output. Attention is needed to detect the problem: with probability 1 − θ, which depends on how much attention the worker pays to her work, the problem is detected and no output is lost. Hence, the firm's expected output is h[1 − Pfθ].
As we said, θ depends on how much attention the worker pays to the potential problem. The worker has a fixed supply of attention equal to 1, which she divides between work (1 − θ) and home (θ). Home gets attention because there are also problems at home, with probability ph. If the worker detects a problem at home, she can solve it with probability κθ and it has no utility cost. The utility cost of an unsolved problem is discussed next.
Preferences: Food Versus Comfort
Workers can buy two types of goods in this economy: call them food f and comfort c. The utility that these two goods generate (p.182) directly is fα c 1 −a. As discussed earlier, comfort goods have the additional feature that they make it easier to deal with problems. If the worker has no comfort goods, an unsolved problem costs her ϕb. If she has c comfort goods, it costs her only ϕ(b−μc). Putting these two elements together, her utility function can be written as fαc 1−α − ϕph(1 − κθ) (b − μc)
Assume that over the relevant range of c, b − μc is always positive. Assume further that one unit of production output can be transformed costlessly into either one unit of food or one unit of comfort.
The price of all three goods is therefore set to 1.
The worker first chooses θ, then she buys c. Her income is not yet determined (there may be a problem at work), but it is assumed that she can get credit to buy the desired level of c and that interest rate on this credit is zero. However, she cannot condition her demand for c on the realization of her income. She simply spends less on f if her income is lower.
After she buys c the problems at home and at work are realized. We assume that the realizations of the two sets of problems are independent. Then her income is realized and she pays back what she borrowed to buy c, before spending the rest of her income on f. This timing, while somewhat artificial, allows us to analyse this problem in a static framework.
Consequences of Utility Maximization
Suppose that the worker gets an income β 1 y when the firm does not have problems (probability 1 − pfθ) and an income of β 2 y when it does (probability pfθ), where β 1 〉 β 2. We do not explicitly model the choice of the worker's incentive scheme in this section, though it is easy to see that it could come out of the firm's profit maximization. Instead we take as given the incentive scheme and examine its implications for the worker's consumption (p.183) and attention allocation choices. For a given θ, the worker will choose c to maximize:
Let U (β 1, β 2, y, θ) represent the maximized value of this expression and c(β 1, β 2, y, θ) its maximizer, which satisfies the first order condition:
Several observations follow from this expression. First, the unique solution of the problem has the form c = m(β 1, β 2, θ)y. Second, as is easily checked, m is increasing in β 1 and β 2. Third, the expression is an increasing function of β, which implies that the left hand side of equation (11.2) is decreasing in θ, so c must go down when θ increases. In other words, comfort goods and attention towards home are substitutes. Finally, because c is proportional to y, U (β 1, β 2, y, θ) is linear in y, i.e.,:
for some function n(β 1 , β 2, θ). This means that the income effects that are central to our model do not come from a change in risk tolerance: rich people and poor people are both risk-neutral. However, this does not mean that risk does not matter: The expression is a concave function of β for fixed values of c and y. Hence, a mean-preserving squeeze in β (that is, if β 1 goes down and β 2 goes up keeping mean income constant) raises the left hand side of the expression in (11.2): The optimal value of c must therefore go up. Reducing income risk increases the consumption of the comfort good, because the worker has to commit to the consumption of c before she knows her income.
Hence, at any potential interior optimal value of θ, either:
which implies that it is optimal to increase θ further, or:
in which case θ = 0 is at least as good. This implies that the maximization problem has a ‘bang-bang’ solution unless U (β 1 , β 2, y, θ) = U (β 1 , β 2, y, θ)—either the individual pays full attention at home (θ = 1) or full attention at work (θ = 0). We can get very ‘non-convex’ behaviour as a result of the behavioural reactions induced by a model of consumer choices where there are no ‘technological’ non-convexities.2
What determines the choice between these two alternatives? A worker strictly prefers θ = 0 if U (β 1 , β 2, y, 0) 〉 U (β 1, β 2, y, 1), which is the case if:
This observation immediately gives us our first result:
(p.185) Proposition 11.1. There is a cutoff value yc, such that people with y 〉 yc will strictly prefer θ = 0 while those with y 〈 yc will strictly prefer choose θ = 1. At y = yc they are indifferent.
This says that people whose earnings are higher to start with for some exogenous reasons (say greater human capital) will be able to buy more comfort goods and pay more attention at work, which further boosts their income—so that there is a critical level of human capital at which productivity jumps up discretely. If we set productivity equal to income we have recreated the basic elements of a poverty trap, even though we have a linear production function and perfect credit markets.3 This ‘poverty trap’ was at the heart of the previous paper. In this paper we develop the implications of this framework for incentives within a firm.
Moreover, applying the envelope theorem to the two sides of (11.3) gives us:
Proposition 11.2. For y not too large (to ensure that ) there is a cutoff value of ϕ, ϕc, such that such that people with ϕ ≤ ϕc will choose θ = 0 while people with ϕ 〉 ϕc will choose θ = 1. Similarly, there is a cutoff value of ph, pc h, such that people with ph ≤ pc h will choose θ = 0 and the rest will choose θ = 1.
Finally the assumption that over the relevant range of y and (hence c), , guarantees that is increasing in κ. It is also evident that is increasing in b. So we have the following result:
Proposition 11.3. There is a cutoff value of κ, κc, such that those with κ ≤ κ c will choose θ = 0 and the rest will choose θ = 1. Likewise there is a cutoff value of b, bc such that those with b ≤ bc will choose θ = 0 and the rest will choose θ = 1.
Not surprisingly, people who have a higher cost of ignoring problems at home, either because they care more about them (p.186) (higher ϕ) or because the problems are inherently more serious, are more likely to choose θ = 1. People who have more problems at home (higher ph) or who are better at solving these problems (higher κ), will also choose θ = 1.
Implications for the Employment Contract
Let us now introduce the idea that the technology of production is owned by a firm that hires workers to work in the firm. If the θ chosen by workers is observed by the firm, it will simply offer each worker her outside option and require her to deliver the right θ. This might require paying workers more than what they would get paid in a different industry which is less demanding of attention, but in utility terms they should be indifferent. Moreover, there would be no cause to discriminate. Any worker who agrees to the terms of the job will be as likely to be hired as any other.
Now assume that the firm does not observe the θ chosen by the worker. This gives a rationale for the firm to provide incentives for workers to pay attention at work. Assume that the only incentive scheme available is to offer a worker with human capital h a fixed wage λh for some λ, and to impose on her a non-pecuniary utility cost of l if there is an unsolved problem. The worker's maximand is now4
Clearly, the introduction of the non-pecuniary cost term does not affect the choice of c as a function of θ. Hence, c is given by m (1, 1, θ)λh. The choice of θ now depends on the sign of ϕphκ(b − μc) − pfl, and the worker will choose θ = 0 if:
and θ = 1 otherwise.
This immediately tells us that at the same wage, workers with values of ϕ, ph and κ below a certain threshold will be more productive. Hence, the firm wants to discriminate against those who are too attached to their home life, those who have too many problems at home and even those who are just good at fixing problems at home. In other words, at the same wage the firm has a strict preference for one type of worker over the other. This explains why, for example, some employers may discriminate against women, particularly against married women (note that it is enough that employers believe that women have these preferences, whether or not this is actually the case) and why urban employers might give preference to workers who have left their families behind in the villages (and hence who are in no position to solve problems at home).
Since the firm has a lot to gain by getting the worker to choose θ = 0, it will be willing to raise λ slightly, if that ensures that ϕph (b − μm (1, 1, θ)λh) ≤ pfl. In other words, even if the worker is willing to work for λh, the firm may pay her λ′h 〉λh in order to improve her attention at work and, hence, increase her output.
Note that this is not a conventional incentive payment: the worker is not being paid extra to make the loss of the job more painful. In our model the punishment for an unsolved problem is fixed and changing the wage does not affect it. The reason to give her some rents is similar to why workers get rents in nutrition-based efficiency wage models (see Dasgupta and Ray 1986), in which workers are paid extra so that they can be stronger; here it is to make them less distracted. The advantage of our theory over the nutrition-based theory is that it may be possible to reduce distraction very quickly once the person has the right comfort goods, while building up strength may take more time. Moreover, it applies not only to people at the margin of starvation, but also to somewhat richer people. In this sense, our paper is in the spirit of Dasgupta's (1997) claim that the ‘nutrition—productivity (p.188) construct provides a metaphor’ for a broader class of economic environments.
Given that the firm is paying extra to enable its workers to get comfort goods, it may make sense for it to give the extra directly in terms of comfort goods, so as to limit the household's choice. This may be one rationale why company townships army cantonment townships and government housing complexes exist, and exist particularly in countries where the overall infrastructure is weak. By providing a large fraction of a person's salary in terms of provided facilities—housing with electricity, water, etc., a nearby school of some quality, a health centre at hand and so on—the employer makes sure that the worker spends the requisite fraction of her income on comfort goods, above and beyond what she would voluntarily choose, and therefore is in a position to be attentive at her job.
This also suggests that while the much reviled institution of a company store may indeed be a way to sell things to people at much inflated prices (though it is not quite clear why that would be better than just paying less), it might sometimes also serve the purpose of changing the relative prices of company employees' purchases in the direction of what the company wants them to buy, which is nutrition and comfort goods.
Finally, there is a line of argument in economics going back to Adam Smith that the decline of the putting-out system of production in western Europe and its replacement by the factory system was a result of the need to realize gains from division of labour. More recently, Marglin (1974) argued that these gains could not have been large enough, and that factories were important as a way for the capitalists to control workers better (that is, to provide better incentives). Our framework suggests a third view: in the putting-out system, workers worked at home, which meant that the problems at home had an immediate claim on their attention, both because they were confronted with them all the time and because they were in a position to solve them. The role of the factory, in this third view, was to put some distance between the workers and their homes and, hence, to get them to pay more attention at work.
The very simple idea of comfort goods as a way to limit distraction can help us understand a number of phenomena, ranging from poverty traps to company townships. However, it also raises a number of important research questions: First, we emphasized the problem of too little attention at work. How about the opposite problem of too little attention at home, especially to problems (like children's education) that may have social spillovers? Does this say something about the importance of what are sometimes called good jobs, i.e., jobs that allow a good balance between work life and home life? Second, is it empirically reasonable to assume that comfort goods reduce the need for attention and therefore make people more productive? There is evidence that married men are paid more, and this could be because marriage allows them to transfer some of their more domestic concerns to their wives. On the other hand, a marriage also creates its own sources of problems (children, for example) so this is by no means obvious and moreover, it is not clear that the effect is causal (Chiodo and Dwyang 2002 provide a useful summary of the evidence). Being married to a woman who does not work outside the home is also positively correlated with a man's earnings after controlling for observables, as our model would predict, but once again establishing causality is not easy (Jacobsen and Rayack 1996 summarize the evidence, stressing the difficulties in interpreting it). Finding more direct evidence on the role of comfort goods would obviously strengthen the argument we are making substantially.
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(*) We are immensely grateful to Maitreesh Ghatak and Chris Udry for thoughtful comments and to Frank Schilbach for research assistance well beyond the call of duty.
(2) However the shape of the utility function does matter. If the function was much more concave as a function of θ for example, we might not get the same kind of extreme behaviours.
(3) Note however, that in this view, it is income, not utility, that bifurcates. So those right above and below the threshold earn very different amounts but have similar utility.
(4) In terms of the framework above, this corresponds to the case of β 1 = β 2 = 1and y = λh, with the additional feature of the non-pecuniary utility cost.